MATHEMATICAL MODELLING OF CALCIUM

DEPENDENT ACTIVE CONTRACTION IN A

GASTROINTESTINAL SMOOTH MUSCLE CELL

VIVEKA GAJENDIRAN

NATIONAL UNIVERSITY OF SINGAPORE

2011

MATHEMATICAL MODELLING OF CALCIUM

DEPENDENT ACTIVE CONTRACTION IN A

GASTROINTESTINAL SMOOTH MUSCLE CELL

VIVEKA GAJENDIRAN

(B.Tech, Anna University, India)

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DIVISION OF BIOENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2011

ACKNOWLEDGEMENTS

First and foremost, I would like to express my deepest gratitude to my supervisor, Dr.

Martin Buist for his excellent guidance and remarkable patience throughout the project.

I thank him for being very approachable. He has immensely contributed to my writing and presentation skills. I sincerely thank him for making my PhD study a fruitful and pleasant journey. If not for his encouragement, the Young Investigator Award during

World Congress on Biomechanics (2010) would not have been possible. In addition to acquiring technical skills, I have also learnt from his strive for perfection and remarkable professionalism.

I am grateful to National University of Singapore for providing me the research scholarship and a favourable environment for carrying out my PhD study.

I sincerely thank my labmates: William, Yong Cheng, Dr. Alberto, Aishwariya,

Nicholas, May Ee, Dr. David Nickerson, Ashray, Viknish and Vinayak for their valuable feedbacks and also for their help and friendship. Thanks to all of them, the

Computational Bioengineering lab has always been an excellent and peaceful working place.

I am grateful to three of my friends: Niranjani, Narayanan and Meiyammai for making my stay in Singapore a memorable one. They have been like my extended family providing me great support. I take this opportunity to thank Kalpesh, Balaji, Shalin,

Sounderya, Anju, Jagadish, my flatmates and my other beloved friends for their friendship and timely help. I sincerely thank all the Bioengineering Graduate Student’s Club members for their team spirit in conducting the NUS-Tohoku symposium (2009) when I was the Vice-president of the club. Lectures of Dr. Lakshminarayanan

Samavedham (fondly called Prof. Laksh) have helped me greatly and his contagious enthusiasm and passion for teaching will always be remembered by me.

Lastly and most importantly, I would like to thank my parents (Mr. Gajendiran and

Mrs. Elayaselvi), sister Deepika and my husband Jayandan for their unconditional love and unwavering support. My family is my greatest strength. I dedicate this thesis to them.

Abstract

Motility in the gastrointestinal (GI) tract is brought about by the coordinated contraction and relaxation of the smooth muscle (SM) layers in the walls of the GI tract which are in turn controlled by the underlying electrical activity of the pacemaker cells and smooth muscle cells (SMC).

A mathematical model to study the relationship between the free intracellular calcium

2+ concentration ([Ca ]i) and active contraction in gastric SMCs has been developed.

Calcium is the interface between electrical activity and the active mechanical response

2+ in a SMC. An increase in [Ca ]i causes contraction and a decrease causes relaxation.

Electrical models of GI SM have studied their electrophysiological behavior and have simulated the membrane potential regulation, the ionic current across the cell and the intracellular Ca2+ concentration. The work presented in this thesis takes the next step of

2+ linking the [Ca ]i to active force production. A mechanistic model that succinctly packages the cellular events and biochemical regulation involved in cross-bridge formation has been developed.

First, contraction triggered by calcium dependent activation of Myosin Light Chain

Kinase (MLCK) has been described in terms of two interacting modules. The first module describes the activation of MLCK through its interactions with calmodulin

(CaM) and Ca2+, and the second module consists of a four-state scheme describing myosin phosphorylation and cross-bridge formation between actin and myosin.

Comparison between model predictions with and without the cooperative binding between Ca2+, CaM and MLCK, have shown that cooperativity between binding sites of CaM affect the dynamics of MLCK activation. The model, when simulated with 2+ [Ca ]i input signal recorded from canine antral SM, show the characteristic phasic contractile behavior observed in gastric SMCs. The model simulations match the experimental force behaviour during the contraction phase well, while the relaxation was more rapid in the experimental results.

Next, a hypothesis of activation of Myosin light chain phosphatase (MLCP) for rapid relaxation has been tested and modelled. Motivated by literature evidence that MLCP is regulated and activation of MLCP by a cellular protein called telokin can be attributed to the rapid relaxation in phasic SMCs, a formulation for Ca2+ and time dependent variation of [MLCP] has been implemented. The results show an improvement in the t1/2 for relaxation with [MLCP] regulation.

Finally, calcium desensitization has been investigated by describing two secondary regulatory pathways – (i) down regulation of MLCK activation through its phosphorylation and (ii) enhanced activation of MLCP. The secondary regulatory pathways act as a negative feedback control to the primary pathway described in the first two sections of the model. With calcium data measured from spontaneously active

SMCs and experimentally induced abnormal calcium transients, both the amplitude and the temporal dynamics of force was affected by the two secondary regulatory mechanisms.

The model can thus explain the triggering of active contraction by the Ca2+ dependent

MLCK activation and shows the effects of secondary regulatory pathways on contractile behavior. By describing the downstream cellular events triggered by

2+ increase in [Ca ]i, a framework for studying electro-mechanical coupling in gastric

SMCs has been laid. CONTENTS

Abstract ...... iv List of Figures ...... ix List of Tables ...... xvi Abbreviations ...... xviii

1. Introduction ...... 1 1.1. Gastrointestinal System ...... 3 1.2. Smooth Muscle ...... 6 1.3. Motivation ...... 12 1.4. Objective and Specific Aims ...... 15 1.5. Thesis Overview ...... 16

2. Literature Review ...... 18 2.1. Electrical basis for gastric Motility ...... 18 2.1.1. Electrophysiology of GI Smooth Muscle ...... 18 2.1.2. Excitation-Contraction Coupling ...... 23 2.2. Signaling for Contraction and Relaxation in Gastric Smooth Muscle ...... 27 2.3. Calcium, Myosin Phosphorylation and Force ...... 30 2.4. Smooth Muscle Contraction Modelling Review ...... 34 2.4.1. Hill’s Model (1938) ...... 34 2.4.2. Huxley’s Sliding Filament Model (1957) ...... 36 2.4.3. Gestrelius and Borgstrom’s Model for SM Contraction (1986) ...... 37 2.4.4. Hai and Murphy’s Four-state Model (1988) ...... 42 2.4.5. Bursztyn et al.’s Uterine SM Model (2007) ...... 45 2.4.6. Lukas’ Model (2004) ...... 47 2.4.7. Mbikou et al. ’s Model (2005) ...... 49 2.5. Summary ...... 52

vi

3. Modelling Active Force Production in Gastric SMCs through Ca2+ dependent MLCK Activation...... 53 3.1. Introduction ...... 53 3.2. MODULE I: MLCK activation by Ca2+ signaling pathway ...... 55 3.2.1. MLCK activation: preliminary model ...... 55 3.2.2. MLCK activation: extended model ...... 59 3.2.2. Module I: Parameter Estimation ...... 61 3.2.3. Calmodulin is a limiting factor in the cell...... 73 3.2.4. Cooperativity between binding sites of calmodulin ...... 75 3.2.5. Transient MLCK activation ...... 85 3.3. MODULE II: Active force generation ...... 87 3.3.1. Module II: Parameter Estimation ...... 92 3.4. Calcium, myosin phosphorylation and cross-bridge formation ...... 96 3.4.1. Input Calcium Signal ...... 97 3.4.2. Simulation of Myosin Phosphorylation ...... 100 3.4.3. Simulation of Phasic Contraction ...... 102 3.4.4. Effect of MLCP Concentration ...... 104 3.5. Function based description for Module I ...... 107 3.5.1. Results and Discussion ...... 109 3.6. Summary ...... 116

4. SMC relaxation mediated through MLCP regulation ...... 119 4.1. Introduction ...... 119 4.2. MLCP regulation hypothesis ...... 126 4.3. MLCP regulation model ...... 129 4.4. Effect of MLCP regulation on phasic contraction ...... 134 4.5. Summary ...... 137

5. Ca2+ induced Ca2+ desensitization...... 140 5.1. Regulation of Ca2+ Sensitivity ...... 140 5.2. Hypothesis 1 – Calcium desensitization through MLCK phosphorylation . 143 5.2.1. MLCK phosphorylation pathway ...... 145 5.2.2. Results and Discussion ...... 149

vii

5.3. Hypothesis 2 – Calcium desensitization through MLCP activation ...... 154 5.3.1. Enhanced MLCP activation model ...... 155 5.3.2. Results and Discussion ...... 156 5.4. Summary ...... 162

6. Conclusion ...... 164 6.1. Limitations and Future work ...... 165

Appendix I ...... 168 Appendix II ...... 173 Publications ...... 177 Bibliography ...... 180

viii

List of Figures

Figure Page

1.1 Human gastrointestinal tract...... 3

1.2 Structure of the human stomach and organization of the stomach wall tissue. . . 4

1.3 Peristalsis in the GI tract...... 5

1.4 Structure of smooth muscle cell. (Watras, 2004) ...... 7

1.5 Regulation of SM myosin interactions with actin by Ca2+ stimulated

phosphorylation. (Watras, 2004) ...... 10

1.6 Phasic contraction and Tonic contraction. (Watras, 2004) ...... 12

1.7 Chart showing the interdependence of the changes induced in the electrical and

contractile activity and the causes for the clinical expression of a GI motility

disorder (adapted from Malykhina and Akbarali, 2004)...... 15

2.1 ICC-SMC network in stomach (Hirst and Edwards, 2006) ...... 19

2.2 Experimental recording of slow wave (Ward and Dixon et al., 2004) ...... 20

2.3 Intracellular recordings of the SM electrical activity from stomach (Kutchai,

2004) ...... 21

2.4 Principal mechanisms determining the cytoplasmic [Ca2+] in smooth muscle

cell (Watras, 2004) ...... 25

2.5 Relationship between membrane potential and contraction of SM...... 26

2.6 Pathways involved in excitation-contraction coupling in GI smooth muscle

(Sanders, 2008)...... 30

2.7 Recordings from canine antrum SM strip showing spontaneous slow-wave

2+ activity, [Ca ]i , and muscle tension from Ozaki and Gerthoffer et al., 1991. . . 32

ix

2+ 2.8 Concentration dependent effect of Acetylcholine on slow waves, [Ca ]i , and

tension from Ozaki and Gerthoffer et al., 1991...... 33

2.9 Hill’s Model (Hill, 1938)...... 35

2.10 Huxley’s sliding filament model (Huxley, 1957)...... 36

2.11 Gestrelius and Borgstrom’s Vascular SM contraction model (Gestrelius and

Borgstrom, 1986)...... 38

2.12 Force-velocity and active force- time relationships predicted by Gestrelius and

Borgstrom model (Gestrelius and Borgstrom, 1986)...... 41

2.13 Relationship between the number of active cross-bridges and active isometric

force predicted by Gestrelius and Borgstrom model (Gestrelius and Borgstrom,

1986)...... 41

2.14 Hai and Murphy’s four-state cross-bridge model (Hai and Murphy,

1988)...... 42

2.15 Myosin phosphorylation and stress curves from the Hai and Murphy model

(Hai and Murphy, 1988)...... 43

2.16 Time course of force, myosin phosphorylation and maximum shortening

velocity in tracheal smooth muscle strips (Kamm and Stull, 1985)...... 44

2.17 Bursztyn et al.’s model: Simulation of myosin light chain (MLC)

phosphorylation (A) and force production (B) in human nonpregnant

myometrium...... 47

2.18 Lukas’ pathway model for myosin light chain phosphorylation and

dephosphorylation (Lukas, 2004)...... 48

2.19 Fajmut et al. ‘s theoretical model for the interaction of Ca2+, CaM and MLCK

(Fajmut and Brumen et al., 2005)...... 50

x

3.1 Calcium-dependent mechanism of active contraction...... 54

3.2 Signal transduction pathway for MLCK activation by Ca2+ through

calmodulin...... 57

2+ 3.3 Free (Ca )4CaM concentrations in cells expressing two CaM binding proteins

of varying affinitites at different intracellular free Ca2+ concentrations.

(Persechini and Cronk, 1999)...... 63

2+ 3.4 Simulated free (Ca )4CaM concentration from the model fitted to experimental

2+ free (Ca )4CaM concentration measured in the presence of binding protein

(FIP-CBSM-38) shown in Figure 3.3...... 66

2+ 2+ 3.5 Changes in the free concentrations of Ca and (Ca )4CaM produced in

response to an agonist in cells expressing FIP-CBSM-38 (Kd = 45 nM).

(Persechini and Cronk, 1999)...... 67

2+ 3.6 Simulated free (Ca )4CaM concentrations produced in response to transient

change in intracellular free Ca2+...... 68

2+ 2+ 3.7 Relationship between free (Ca )4CaM and free Ca concentrations in the

2+ presence of MLCK. Simulated free (Ca )4CaM concentration from the model

2+ fitted to experimental free (Ca )4CaM concentration...... 70

3.8 Effect of CaM concentration on MLCK activation...... 75

2+ 2+ 3.9 Relationship between free (Ca )4CaM concentration and Ca from the

extended model and the preliminary model...... 76

3.10 Relationship between MLCK activation and Ca2+ with (extended model) and

without (preliminary model) the explicit description of Ca2+ binding at C-

terminal and N-terminal of CaM...... 77

3.11 Formation of CaM-MLCK complex...... 80

xi

3.12 Simulated time course of a Ca2+ transient and the time course of the occupancy

of the CaM N-terminal and C-terminal Ca2+ binding sites of CaM. (Johnson

and Snyder et al., 1996)...... 82

2+ 2+ 3.13 Formation of (Ca )2CaM and (Ca )2CaMC-MLCK complexes...... 83

2+ 3.14 Formation of (Ca )4CaM-MLCK complex in the extended model and the

preliminary model...... 85

2+ 3.15 Relationship between MLCK activation and [Ca ]i under transient condition. . 86

3.16 Extended Hai and Murphy model...... 88

3.17 Spontaneous contractions and Ca2+ transients measured in antral circular

smooth muscle by Ozaki and Gerthoffer et al.(1991)...... 92

3.18 Fitting of the normalized force from the model to the experimental normalized

force from Ozaki and Gerthoffer et al.(1991)...... 94

2+ 3.19 Relationship between myosin phosphorylation and intracellular free [Ca ]i

under steady state conditions...... 97

3.20 A) Ca2+ transients observed in guinea pig gastric myocytes under various

2+ experimentally evoked depolarizations (Kim and Ahn et al., 1997). B) [Ca ]i

transient produced by Equation 3.11...... 99

2+ 2+ 3.21 [Ca ]i transient produced by Equation 3.11 for two different [Ca ]max values. . 101

3.22 Myosin phosphorylation produced in response to the two Ca2+ transients shown

in Figure 3.21...... 101

3.23 Normalised force predicted by the model for the prescribed Ca2+ transient with

2+ a [Ca ]max of 0.6 µM...... 103

3.24 Effect of the MLCP concentration on the normalized force values...... 105

3.25 Effect of the MLCP concentration on the normalized force values...... 105

xii

2+ 3.26 Comparison of steady state relationship between [Ca ]i and MLCK activation

between pathway based model and function based model...... 109

2+ 2+ 3.27 Simulated normalized force for the prescribed [Ca ]i transient with a [Ca ]max

of 0.6 µM from function based model...... 110

3.28 Comparison between normalised force produced by the function based model

and the pathway model...... 111

3.29 Normalised force from the function based model for a given experimental Ca2+

transient with MLCP concentration of 7 µM...... 112

3.30 Normalised force from the function based model for a given experimental Ca2+

with an increased MLCP concentration of 10 µM...... 113

3.31 Effect of MLCP concentration on normalized force predicted by the function

based model...... 114

3.32 MLCKactive concentration produced by the function based model and the

pathway model for a give Ca2+ transient...... 115

4.1 Accelerated relaxation of Ca2+ induced force in telokin KO ileal SM upon

addition of 10 µM of recombinant telokin. (Khromov and Wang et al., 2006). . 124

4.2 Effect of MLCP inhibitor (calyculin-A) on [Ca2+], muscle tension and MLC

phosphorylation (Ozaki and Gerthoffer et al., 1991) ...... 127

4.3 Effect of reduced MLCP concentration on the contractile behavior...... 128

4.4 The change in [MLCP] as a function of Ca2+ described by Equation 4.1...... 131

4.5 MLCP dynamics shown in comparison to MLCK activation...... 131

4.6 Simulated normalized force with [MLCP] regulation...... 132

4.7 Simulated normalized force for a given experimental Ca2+ transient with

[MLCP] regulation and with constant [MLCP] ...... 133

xiii

4.8 Phasic contraction produced by the [MLCP] regulated model for a prescribed

2+ 2+ Ca transient with a [Ca ]max of 0.6 µM...... 134

4.9 Change in MLCP concentration for the prescribed Ca2+ transient with a

2+ [Ca ]max of 0.6 µM...... 135

4.10 Change in MLCP concentration with time in response to the Ca2+ transient

shown in Figure 4.9...... 135

4.11 Effect of [MLCP] regulation on myosin phosphorylation and force...... 136

4.12 Dephosphroylation of myosin in the model with [MLCP] regulation and

constant [MLCP]...... 137

5.1 Contractile behavior of canine antral smooth muscle during a sustained

maintenance of high calcium concentration as a result of elevated K+ in the

external solution (Ozaki and Gerthoffer et al., 1991)...... 141

5.2 Pathway scheme showing phosphorylation of MLCK catalysed by CaMKII and

2+ binding of phosphorylated MLCK to (Ca )4CaM...... 146

5.3 Reaction scheme showing phosphorylation of MLCK catalysed by the CaMKII

and dephosphorylation by unknown phosphatase...... 146

5.4 Reaction scheme showing binding of phosphorylated MLCK to (Ca2+)4CaM. . . 147

5.5 Effect of MLCK phosphorylation on the simulated force behavior for a given

2+ [Ca ]i signal...... 150

5.6 Effect of MLCK phosphorylation mechanism on the activation of MLCK. . . . . 151

5.7 Effect of myosin phosphorylation on MLCK activation at sustained high Ca2+

concentration...... 152

5.8 Concentration of MLCP for a given Ca2+ signal in the presence and absence

of the enhanced MLCP activation reaction (Equation 5.3)...... 157

xiv

5.9 Effect of enhanced MLCP activation on the normalized force behavior for a

given Ca2+ signal ...... 157

5.10 Simulated normalized force behavior for a prescribed Ca2+ transient in the

presence of desensitization mechanisms...... 158

5.11 Experimental results from canine antral smooth muscle showing changes in

Ca2+ and muscle tension in response to Ca2+ depletion and re-addition (Ozaki

and Gerthoffer et al., 1991) ...... 159

5.12 Simulated normalized force for a given experimental Ca2+ signal shown in

Figure 5.11 in the presence and absence of desensitizing mechanisms...... 161

5.13 Simulated normalized force for a given experimental Ca2+ signal shown in

Figure 5.11 in the presence and absence of desensitizing mechanisms...... 161

xv

List of Tables

Table Page

2.1 Merits and limitations of the previous modelling studies on SM contraction. 51

3.1 Reactions involved in the activation of MLCK (Module I) by the interaction

between CaM, Ca2+ and MLCK in the preliminary model...... 58

3.2 Reactions involved in the activation of MLCK (Module I) by the interaction

between CaM, Ca2+ and MLCK in the extended model...... 61

3.3 Reactions with the binding of a target protein with Kd = 45 nM (TP45) and the

respective forward and reverse reaction rates...... 65

3.4 Reactions with the binding of a target protein with Kd = 2 nM (MLCK) and the

respective forward and reverse reaction rates...... 71

3.5 Initial concentration of the species in Module I used for steady state simulations. . 72

3.6 Effect of free CaM concentration on MLCK activation...... 74

3.7 Difference in the binding properties of the two Ca2+ binding sites of CaM...... 77

3.8 Cooperativity between the two calcium binding sites of CaM...... 78

3.9 Cooperativity between calcium binding and target protein binding sites of CaM. . 80

3.10 CaM bound to Ca2+ ions binds to MLCK rapidly and with more affinity...... 81

3.11 Reactions involved in active force generation via cross bridge cycling (Module

II), as described by Equations 3.3 - 3.6...... 89

3.12 Parameters involved in Module II, as described by Equations 3.3 - 3.6, and their

respective values...... 95

xvi

3.13 Steady state values of the various species of the Module II at the resting Ca2+

concentration...... 95

3.14 Values for the parameters used in Equation 3.11 for the first cycle of Ca2+

transient...... 99

5.1 Parameters involved in the MLCK phosphorylation pathway described by

Equations 5.2 and 5.3...... 147

xvii

Abbreviations

A Actin

AM Latch bridge between actin-myosin

AMp Cross bridge between actin-myosin

ATP Adenosine triphosphate

BP Buffering Protein

Ca2+ Calcium ion

2+ [Ca ]i Intracellular calcium concentration

CaM Calmodulin

CaMKII Calcium-calmodulin dependent protein kinase II

GI Gastrointestinal

ICC Interstitial Cells of Cajal

IP3 Inositol trisphosphate

M Myosin

MLC Myosin Light Chain

MLCK Myosin Light Chain Kinase

MLCKp Phosphorylated Myosin Light Chain Kinase

MLCP Myosin Light Chain Phosphatase

Mp Phosphorylated myosin

NO Nitric Oxide

ODE Ordinary Differential Equation

SM Smooth Muscle

SMC Smooth Muscle Cell

xviii

1. Introduction

The digestive system consists of a muscular tube called the gastrointestinal (GI) tract and its accessory organs. Propulsion, mixing, secretion, digestion, absorption and excretion of the luminal contents, are the main functions of the GI system. These functions are facilitated by the various motility patterns of the GI tract which are carried out by the coordinated patterns of contraction and relaxation in the visceral smooth muscle tissue under the control of sensory and motor nerves, pacemaker cells and endocrine or paracrine factors.

Functional GI disorders such as gastroparesis, cyclic vomiting syndrome, delayed or rapid gastric emptying, dysphagia, irritable bowel syndrome and gastroesophageal reflux disease all involve disturbances to normal GI motility. National Institutes of

Health (NIH) reported 60-70 million Americans to be affected each year by digestive diseases at a cost that exceeds $100 billion in direct medical expenses (NIH, 2009).

Digestive diseases are associated with significant mortality, morbidity, and loss of quality of life. Numerous systems and processes may be impaired in GI motility disorders, including brain-gut interactions, the enteric nervous system, pacemaker activity, smooth muscle cells, pain and sensory mechanisms, the gut mucosa and musculature, the intestinal microflora, and immune and inflammatory responses. A multitude of signalling pathways and cellular proteins have been identified to regulate smooth muscle contractility at the cellular level. Disturbances in the pathways regulating the contraction, leading to abnormal contractility in smooth muscle cells, have been implicated in disease states (Malykhina and Akbarali, 2004; Kim et al.,

2008).

1

As with other muscle types, the primary means of generating an active contractile response in a SMC is through an elevation of the intracellular free Ca2+ concentration, and the primary means of elevating intracellular free Ca2+ is through an electrical depolarization of the cell membrane. This process is commonly termed electro- mechanical coupling. Over the years, numerous studies have investigated the electrical behavior of the smooth muscle cells and have studied the dynamics of the intracellular

Ca2+ concentration (Vogalis et al., 1991; Kim et al., 1997). To quantitatively describe how the electrical activity is transduced into a mechanical output in a smooth muscle cell, it is necessary to properly describe the subcellular processes that link Ca2+ to contraction.

Experimental studies have been carried out to quantify the mechanical response of gastric smooth muscle under various experimental conditions both at the single cell and tissue levels. The roles of various cellular proteins and pathways in the regulation of contractility have been identified and studied in many isolated experiments. By integrating the knowledge and data from such experimental studies, a dynamic pathway model of the signal network underlying contraction and relaxation has been developed. It is envisaged that this mathematical model, in addition to increasing our understanding of the underlying mechanisms, will be able to simulate known experimental observations and also be a predictive tool that can aid in the design of future experiments.

2

1.1. Gastrointestinal System

Structure of the GI tract: The major structures of the GI tract are the mouth, pharynx, oesophagus, stomach, small intestine (duodenum, jejunum and ileum), colon, rectum and anus (Figure 1.1). Gastric motility refers to the organized motor patterns uniquely suited to each organ in the GI tract that accomplish the physiological functions of mixing, breakdown, propulsion and expulsion of the ingested food. The mechanical activity of the gastric musculature plays an important role in gastric motility.

Figure 1.1. Human gastrointestinal tract (adapted from Martini, 2006).

The structure of the gastrointestinal tract varies from region to region, but common features exist in the overall organization of the tissue. Figure 1.2 depicts the layered structure of the stomach wall. The mucosa is the innermost layer of the GI tract and consists of an epithelium, the lamina propria, and the muscularis mucosae. The epithelium is a single layer of specialized cells that lines the lumen of the GI tract. In the stomach, the columnar epithelium contains secretory cells which secrete hormones

3 that aid in digestion. The lamina propria consists largely of loose connective tissue containing collagen and elastin fibrils. It is rich in several types of glands and contains lymph nodes and capillaries. The muscularis mucosae is the thin, innermost layer of smooth muscle and contractions in these layers move the epithelial folds and ridges. The submucosa, which is the next layer, consists largely of dense irregular connective tissue. Large blood vessels and lymphatic vessels lie in the submucosa.

The muscularis externa in general consists of two substantial layers of smooth muscle cells, an inner circular layer and an outer longitudinal layer. In stomach, muscularis externa has an extra inner oblique layer of smooth muscle cells. Contractions of the muscularis externa mix and circulate the contents of the lumen and propel them along the gastrointestinal tract. The serosa is the outermost layer of the GI tract and consists mainly of connective tissue and covers the entire stomach (Kutchai, 2004; Martini,

2006).

Figure 1.2. Structure of the human stomach and organization of the stomach wall tissue. The muscularis externa consists of two substantial layers of smooth muscle cells – an inner circular layer and an outer longitudinal layer and in stomach, it has an extra inner oblique SM layer. Contractions of the muscularis externa mix and circulate the contents of the lumen and propel them along the gastrointestinal tract (Enclyopaedia Britannica, 2003).

4

The wall of the GI tract contains many interconnected neurons. The submucosa contains a dense network of nerve cells called the submucosal plexus (Meissner’s plexus). The prominent myenteric plexus (Auerbach’s plexus) is located between the circular and longitudinal SM layers in the muscularis externa. These intramural plexuses, together with other neurons of the GI tract, constitute the enteric nervous system. The enteric nervous system helps to regulate the motor and secretory activities of the GI system. The GI tract also receives both sympathetic and parasympathetic innervations. The autonomic nervous system influences the motor and secretory activities of the GI tract by modulating the enteric nervous system (Kutchai, 2004).

Figure 1.3. Peristalsis in the GI tract. Contraction of the circular SM layer leads to partial or total occlusion of the lumen and movement of the contents as seen in (A) and (C) and contraction of the longitudinal SM layer (B) stretches the stomach wall and creates cavity to accommodate the propelled contents. (adapted from Marieb, 2004).

Peristalsis: Peristalsis is the synchronized contraction and relaxation pattern of the longitudinal and circular muscle layers which enables the propulsion of the luminal contents in the anal direction and also provides the mixing function. During peristalsis,

5 evoked by enteric nervous system in response to a bolus, contraction is evoked oral to the bolus and relaxation is observed anal to the bolus as shown in Figure 1.3. While the contraction of the circular SM layer leads to partial or total occlusion of the lumen and movement of the contents, contraction of the longitudinal SM layer stretches the stomach wall and the relaxation of the muscle layers on the anal side forms a cavity for the contents propelled by the oral contraction (Smith and Robertson, 1998;

Huizinga and Lammers, 2009).

Regulation of contraction in GI SMCs: Contraction of the gastric smooth muscle is controlled by its intrinsic electrical activity which is in turn regulated by the pacemaker cells, interstitial cells of Cajal (ICC) present in the gastric musculature.

ICC cells cause rhythmic changes of smooth muscle cell membrane potential in the form of slow waves. When the slow waves depolarize the smooth muscle cell above a threshold, contraction is triggered. In addition to the slow waves, contraction is regulated and coordinated by hormones, paracrine agonists and neurotransmitters

(Sanders and Publicover, 1993; Kutchai, 2004; Sanders et al., 2006). The regulation of contraction by slow waves is described in detail in Chapter 2.

1.2. Smooth Muscle

Smooth muscle cells are a major component of the cardiovascular, respiratory, digestive, and reproductive systems. Although there are differences among smooth muscles in different organs anatomically, functionally, mechanically and in their response to drugs, there are common features. Smooth muscle cells have dimensions of around 100-200 µm in length and 2 – 10 µm in diameter, and are spindle-shaped

6

(Guilford and Warshaw, 1998). The nucleus is centrally located. The contractile unit of smooth muscle cell contains thin filaments composed of α- and γ-actin and thick filaments composed of myosin of class II isoform (Figure 1.4). Unlike striated muscles, the contractile filaments are not arranged in uniform transverse alignment, and therefore no striations are seen in smooth muscle.

A B

Figure 1.4. A) Organization of cell to cell contacts, cytoskeleton, and myofilaments in smooth muscle cells (Watras, 2004). Linkages consisting of specialized junctions functionally couple the contractile apparatus of adjacent cells. B) Pictorial representation of contraction and relaxation in a single smooth muscle cell (Martini, 2006). A single smooth muscle in relaxed state is spindle shaped.

Smooth muscle contains intermediate filaments which form a structural backbone.

Desmin and vimentin are two protein components of this cytoskeleton. Gap Junctions allow direct electrical communications between adjacent smooth muscle cells and with the pacemaker cells. Mechanical junctions also attach adjacent smooth muscle

7 cells (Horowitz et al., 1996; Watras, 2004). Smooth muscle contains no T-tubules and no terminal cistern system. The functions of the sarcoplasmic reticulum include Ca2+ storage, Ca2+ homeostasis, generating local and global Ca2+ signals, and contributing to cellular microdomains and signaling in other organelles (Wray et al., 2010).

Contractile elements composed of actin and myosin functionally equivalent to a sarcomere underlie the similarities in mechanics between smooth and striated muscles.

Smooth muscle myosin II is a hexamer, composed of two heavy chains (≈200 kDa each), each having a pair of light chains, a regulatory light chain of 20 kDa (LC20) and an essential light chain of 17 kDa (LC17). Each of the heavy chains has a globular head domain at its N-terminus followed by the tail region which consists of an extended rod like formation of the two α helices of the heavy chains. A lever like swinging arm of 8.5 nm- long α helix, stabilized by the two light chains, lies between the globular heads and the tail region (Finer et al., 1994; Guilford and Warshaw,

1998). Each globular head of myosin, in the form of a projection from the myosin filament, extends towards the actin filament (Guilford and Warshaw, 1998; Alberts,

2002). These projections are the molecular motors that convert the chemical energy from the hydrolysis of ATP into mechanical work during their cyclic interaction with actin as shown in Figure 1.5.

Contraction of SM cell: In smooth muscle, Ca2+ is the main trigger for contraction

(Sanders, 2008). When the concentration of intracellular Ca2+ increases, a series of events take place. The ubiquitous cytoplasmic protein calmodulin binds to Ca2+ ions in a ratio of 4:1 (Horowitz et al., 1996; Guilford and Warshaw, 1998; Watras, 2004).

The Ca2+-calmodulin complex binds to a specific site on the myosin light chain kinase

8

(MLCK) converting it from the inactive form to the active form. This allows the

MLCK to phosphorylate the regulatory light chain.

When the regulatory light chain of myosin is phosphorylated at a specific site, Ser19, myosin undergoes a conformation change. The conformational change enables the interaction of myosin head with actin and activates the Mg-ATPase of myosin. When myosin head attaches to the actin filament, ADP and inorganic phosphate (Pi) are released from the myosin head allowing an ATP molecule to bind. ATP decreases the affinity of myosin for actin resulting in the release of myosin from actin. Mg-ATPase of myosin hydrolyses the newly bound ATP and the energy from the hydrolysis of

ATP produces a conformational change in the myosin head and enables its attachment to actin. This is called the cross-bridge cycle and this continues as long as the myosin remains phosphorylated (Horowitz et al., 1996; Guilford and Warshaw, 1998; Alberts,

2002). Force generated by the myosin-actin interaction is transmitted to the adjacent cells through actin filaments anchored to electron-dense bodies within the cytoplasm and electron-dense plaques in the cell membrane (Figure 1.4). Dense bodies contain the protein actinin and are functionally analogous to Z-lines in striated muscle

(Guilford and Warshaw, 1998). With decrease in [Ca2+], MLCK becomes inactive and the cross-bridges are dephosphorylated by myosin phosphatase. Dephosphorylation of myosin inhibits its interaction with actin (Horowitz et al., 1996).

9

Figure 1.5. Regulation of smooth muscle myosin interactions with actin by Ca2+ stimulated phosphorylation (Watras, 2004). In the relaxed state, cross-bridges are present as myosin-ADP-Pi complex. Phosphorylation of myosin light chain (LC20) by Ca2+-calmodulin dependent myosin light chain kinase (MLCK) leads to change in conformation of the cross-bridge and enables its interaction with actin. Phosphorylated cross-bridges (colour) cycle until they are dephosphorylated by myosin phosphatase. Myosin phosphorylation by MLCK and cyclic interaction with actin require ATP. CM- calmodulin.

10

Smooth muscle contraction can be broadly classified into two types: tonic contraction and phasic contraction (Gregersen and Kassab, 1996; Watras, 2004). During a tonic contraction, the force increases and is maintained at a particular level which contributes to maintaining the shape of the organ against an imposed load. During a phasic contraction, the force increases rapidly from the baseline, reaches a peak and then returns back to the base line in response to the Ca2+ transients produced in the activated SM cell. GI SM exhibits rhythmic contractions i.e., phasic behavior due to the slow waves generated in the cell (Figure 1.6A). In GI smooth muscle, the phasic contractions are essentially superimposed over the basic tone of the GI SM (Murthy,

2006). The phasic contractions lead to the observed motility pattern in GI tract. In some regions of the GI tract, tonic contractile behavior is exhibited (e.g., the fundus of the stomach) (Gregersen and Kassab, 1996).

A smooth muscle cell shows slow and prolonged contractions compared to skeletal muscle which contracts and relaxes rapidly. However the ATP requirement is lower in

SM. Hence SM has a slower action but a higher economy compared to skeletal muscle.

Skeletal muscle has a force-velocity curve in which shortening velocities are determined only by load and the myosin isoform. In contrast, when smooth muscle activation is altered, e.g., by changing a hormone or agonist concentration, a different set of force-velocity curves can be obtained. This difference is due to the regulation of both the number of active cross bridges (determining force) and their average cycling rates (determining the velocity). The number of active cross bridges is primarily regulated by myosin phosphorylation which is in turn regulated by the intracellular

Ca2+ concentration. Though many other additional regulatory mechanisms have been attributed to the activation of contraction, the central mechanism in GI-SM is

11 excitation-contraction coupling in the SM (Sanders and Publicover, 1993; Somlyo and

Somlyo, 1994; Sanders, 2008).

Figure 1.6. Time-course of events in cross-bridge activation and contraction in two kinds of contractile behavior shown by smooth muscle (Watras, 2004). A) A brief period of stimulation leads to a Ca2+ transient which causes cross-bridge activation and a phasic contraction. B) In a sustained tonic contraction produced by prolonged stimulation, the Ca2+ and phosphorylation levels fall after reaching a peak. However force is maintained during the tonic contraction at reduced Ca2+ concentration and low level of myosin light chain phosphorylation.

1.3. Motivation

Motility at the organ level is caused by the contractile function of smooth muscle cells.

Hence, a cellular level model for contraction would play a significant role in the development of tissue level and organ scale models to study gastric motility.

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GI motility disorders

GI motility disorders are defined by the presence of observable disturbances in the functioning of the smooth muscle layers or in the neuromuscular functioning of the enteric nervous system. Gastroesophageal reflux disease (GERD), functional dyspepsia, irritable bowel syndrome (IBS) and constipation represent some of the more common motility disorders that have a prevalence of 5-20% in the US population (Everhart and Ruhl, 2009). Gastroparesis, chronic intestinal pseudo- obstruction, Hirschsprung’s disease and faecal incontinence have a lower prevalence but can be deleterious and can seriously affect the quality of life. The socio- economic burden of GI disorders has been estimated to be as significant as some of the life threatening diseases (Talley, 2008).

The functional failure of smooth muscle cells leads to motility disorders of the gastrointestinal tract due to abnormal contractility. Pathways that regulate SM contractility can be broadly classified under three major types of mechanisms: 1) mechanisms that regulate changes in the phosphorylation of the myosin light chain, which is the focus of this work; 2) mechanisms that regulate the availability of actin to interact with myosin via the action of actin-binding proteins, and 3) mechanisms by which the cytoskeleton is remodelled to facilitate the transmission or maintenance of force developed by actomyosin interactions. An abnormal contraction can be due to dysfunction of one or more factors in the smooth muscle cells. For example, any disturbance in electrical activity, the pathways regulating the mechanical contraction, or pathogen induced disturbances could result in abnormal SMC function.

Advances in molecular studies and electrophysiology have enabled significant understanding of the mechanism associated with altered motility. For example, in

13 human and in animal models, intestinal inflammation results in the disturbance of motility and is associated with changes in SM function and/or the enteric nervous system (Ohama et al., 2007). Both increased and decreased SM contractility has been observed in intestinal inflammation. Studies show that three types of functional failure in SM appear to be involved in abnormal contractility: 1) changes in activity of muscarinic receptors, 2) changes in activity of ion channels, mainly L-type Ca2+ channels and KATP channel, and 3) changes in activity of the MLC phosphatase inhibitor CPI-17 (Ohama et al., 2007; Ohama et al., 2008). Other mechanisms, such as damage to the nervous system, disruption of the ICC network and hyperplasia and hypertrophy of SMCs, also lead to abnormal contractility in SMCs.

Damage to the ICC network and changes in the ion channel activity have been associated with the changes in the resting membrane potential, the duration and amplitude of slow waves. These changes in the electrical activity have been correlated with altered phasic contractile responses and tone generation during inflammation

(Farrugia, 2008). A network of signalling pathways tightly couple the ion channel activity to the downstream force generating mechanisms. Hence, it is important to study electro-mechanical coupling in SMCs to understand the regulation of contraction by the underlying electrical activity.

The following table, adapted from Malykhina and Akbarali (2004), shows the impact of electro-mechanical coupling in causing abnormal motility during inflammation induced channelopathies in gastric SMCs. Malykhina and Akbarali (2004) have proposed that some of the clinical symptoms of altered smooth muscle contraction in pathogenesis of gut disorders, such as inflammatory bowel disease, may be regulated at the level of the ion channel (Malykhina and Akbarali, 2004).

14

Figure 1.7: The chart adapted from Malykhina et al. shows the interdependence of the changes induced in the electrical and contractile activity and the causes for the clinical expression of a GI motility disorder (Malykhina and Akbarali, 2004). The highlighted region shows the scope of this work. (RMP-Resting Membrane Potential)

Hence understanding the signalling cascade beginning with ICC pacemaker activity to the mechanical response of SMC is of great importance. The highlighted region in

Figure 1.7 shows the role of the model developed here within the big picture of understanding GI motility.

1.4. Objective and Specific Aims

The objective of the study is to develop a mathematical model to simulate the phasic contractile behaviour of a gastric smooth muscle cell for a given intracellular Ca2+ concentration profile.

15

To achieve this objective, the study is divided into three specific aims. The first aim is to describe Ca2+ dependent MLCK activation, which is the central mechanism in the initiation of contraction. The Ca2+ dependent MLCK activation is linked to myosin phosphorylation and the cross-bridge formation pathways to study the relationship between calcium and force.

The second aim of the study is to develop a mathematical formulation for the Ca2+ and time dependent variation of MLCP. This is of particular importance to the relaxation phase where MLCP regulation plays an important role in the dephosphorylation of myosin leading to relaxation.

The third part of the study aims to investigate the phenomenon of calcium desensitization using the models developed in Specific Aims 1 and 2. Two secondary regulatory pathways – a) MLCK phosphorylation and b) enhanced activation of

MLCP are modelled and their effects on the calcium-force relationship are also studied.

1.5. Thesis Overview

The underlying theme of the thesis is that intracellular Ca2+ is the interface between electrical activity and active contraction in smooth muscle cells, and by mathematically describing the cellular events involved in the Ca2+ dependent contraction, a framework to study electro-mechanical coupling can be developed. The thesis focuses on the development of a quantitative description of the contraction and relaxation of a GI smooth muscle cell in response to a given intracellular Ca2+ concentration.

16

The objective and the specific aims of the study are listed in the following section

(Section 1.4) and the motivation for the study is explained in Section 1.5. A literature review on the electrical and mechanical properties of the smooth muscle, experimental studies on the contraction of gastric smooth muscle and various modelling work related to the study is reported in Chapter 2. Intracellular calcium is the main link between the electrical activity and contraction in smooth muscle. In Chapter 3, a model for the calcium dependent signalling of active contraction in gastric smooth muscle is presented. In Chapter 4, modelling of the regulation of relaxation is described. Chapter 3 and Chapter 4 together present the model to describe the phasic contractile behavior in a gastric smooth muscle cell. The model has been validated against experimental data and predicts the relationship between intracellular calcium concentration and active force in the gastric smooth muscle. In Chapter 5, a model for experimentally observed phenomenon called calcium desensitization in phasic smooth muscle is reported. While Chapter 3 and Chapter 4 focus on the primary mechanism of contraction, in Chapter 5 the model shows the role of two secondary regulatory pathways in determining the contractile behavior of the smooth muscle.

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2. Literature Review

2.1. Electrical Basis for Gastric Motility

2.1.1. Electrophysiology of GI Smooth Muscle

Interstitial Cells of Cajal (ICC)

As described in Chapter 1, the wall of the gastrointestinal tract contains two muscle layers: a thin outer longitudinal layer and an inner thicker circular muscle layer. The intrinsic electrical activity of the gastric SMC layers is attributed to the presence of pacemaker cells called ICC. Slow waves generated by ICC are spread through the ICC network and from ICC to SMCs via gap junctions. Two types of ICC have been identified based on their location. In between the circular and longitudinal SMC layers,

ICC are found in the myenteric plexus (ICCMY). The second set of ICC, ICCIM are found amongst the SMCs of the circular layer. ICCMY are responsible for the active generation and propagation of slow waves throughout the gastric musculature. ICCIM mediate the pathway between enteric nerve terminals and smooth muscle cells and also play a role in the propagation of slow waves (Szurszewski, 1987; Hirst and

Edwards, 2006; Sanders et al., 2006). While mutant mice lacking ICCMY failed to generate slow waves, mutant mice containing ICCMY but lacking ICCIM generate incomplete slow waves and fail to respond to excitatory or inhibitory nerve stimulation unlike the wild type mice (Szurszewski, 1987; Hirst and Edwards, 2006).

The ICC-SMC network and the generation of slow waves are shown in Figure 2.1.

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Figure 2.1. ICC-SMC network in stomach. ICCIM can be seen interspersed within the SMCs of the circular layer. Slow wave from the corpus depolarizes the ICCMY network in the antrum and triggers a pacemaker potential as shown. Each driving/pacemaker potential propagates anally through the ICCMY network. The circular SM bundles get depolarized and antral ICCIM are activated and the regenerative component of the slow wave is generated. The regenerative potential rapidly conducts circumferentially and depolarizes nearby smooth muscle cells triggering a ring of contraction. Figure modified from Hirst et al. cf. (Hirst et al. Figure 4) (Hirst and Edwards, 2006).

Slow waves

The stomach generates a characteristic pattern of coordinated electrical activity which forms the basis for its motility. The successive descending rings of contraction in the stomach are triggered by waves of electrical activity known as slow waves (Figure 2.2) which originate in the corpus and migrate slowly down the stomach to the duodenum

(Kutchai, 2004; Martini, 2006). Intracellular recordings from different regions of the stomach, as shown in Figure 2.3, indicate that all regions, except the fundus generate slow waves (Kutchai, 2004).

19

Figure 2.2. Experimental recording of slow wave obtained from a canine gastric SM strip (Ward et al., 2004).

In the fundus and sphincters, electrical activity is characterized by slow tonic changes in membrane potential. Most other regions of the GI tract have phasic electrical activity in the form of slow waves. The frequency of slow waves depends on the section of the GIT and is usually reported as cycles per minute (cpm). In the normal human stomach it is 3 cpm and the frequency is highest at 11-13 cpm in the duodenum but declines along the length of the small intestine to 8 cpm in the terminal part of the ileum. The amplitude and, to a lesser extent, the frequency of the slow waves are modulated by the activity of the intrinsic and extrinsic nerves and by hormones and paracrine substances (Szurszewski, 1987; Kutchai, 2004).

Slow waves are found to be triphasic in the antrum. As can be seen in Figure 2.2 and

Figure 2.3, the slow wave has an initial depolarization phase and after reaching a peak and quick repolarization, plateau phase is maintained. Later the membrane potential falls to the resting membrane potential and forms the repolarization phase. Neural and hormonal control in organs like small intestine and colon trigger action potentials.

They are superimposed on the basal slow wave. When the membrane potential of a

GI SM cell nears the peak of a slow wave, a train of action potentials may be fired.

The extent of depolarization of the cells and the frequency of action potentials are

20 influenced and enhanced by neurotransmitters (e.g., acetylcholine) and agonists (e.g., gastrin). Inhibitory hormones and neuroeffector substances (e.g., norepinephrine) hyperpolarize the SM cells and may diminish or abolish action potential spikes

(Szurszewski, 1987; Kutchai, 2004).

mV

mV

Figure 2.3: Intracellular recordings of the electrical activity in SM of isolated strips of various regions of a dog’s stomach (Kutchai, 2004). Slow waves are absent in the fundus and weak in the orad corpus, and gain in strength and definition toward the antrum. The action potentials on the plateaus of the slow waves elicit stronger contractions in the terminal antrum and pylorus.

21

SMCs have a negative resting membrane potential determined by the relative permeabilites of the plasma membrane to physiological ionic species. SMCs demonstrate dominant permeability to K+ ions. However there is contribution from non-selective cation conductances in the presence of agonists. The Na+-K+ pump also contributes to the resting potential. Resting membrane potentials of GI SMC in different regions of the gut vary widely from -85 mV to -40 mV (Sanders and

Publicover, 1993). Regulation of the resting membrane potential preconditions the responses of SMC to depolarizations from the pacemaker cells and agonists.

Depolarization leads to increase in open probability of voltage dependent Ca2+ channels (VDCC) and result in the influx of Ca2+ (Figure 2.4). The increase in intracellular Ca2+ is the main trigger for contraction in GI SMCs as explained further

2+ in detail in Section 2.1.2. Contraction is caused by the increase in [Ca ]i and these

2+ cells relax when there is a decline in [Ca ]i. Excitatory agonists increase the amplitude of depolarizations and cause increased Ca2+ entry. Inhibitory agonists reduce the depolarization amplitude reducing the magnitude of Ca2+ entry and hence reducing the force of contractions. The modulation of the amplitude of slow waves of the cell results in a range of contractile amplitudes.

Figure 2.3 shows the intracellular recordings of the electrical activity in SM cells of isolated strips of various regions of a stomach. When a wave of oesophageal peristalsis begins, a reflex causes the lower oesophageal sphincter (LES) to relax. This relaxation of the LES is followed by receptive relaxation of the fundus and body of the stomach. The stomach relaxes to accommodate the bolus of food. The nerve fibers mediate the reflex relaxation of the stomach by releasing transmitters such as vasoactive intestinal peptide (VIP) and/or nitric oxide (NO). The muscle layers in the

22 fundus and body are thin and, due to the absence of slow waves, only weak contractions are seen in these parts. As a result, the contents of the fundus and the body settle into layers based on their density. Gastric contents can remain unmixed for as long as one hour after eating. The contractions usually begin in the middle of the body of the stomach and travel toward the pylorus. They increase in force and velocity as they approach the gastro-duodenal junction. Thus, the major mixing activity occurs in the antrum of the stomach. The electrical activity in the antrum (shown in Figure

2.3) corresponds to forceful and rapid contractions. The more rapid contractions at the terminal antrum propel the chyme back into antrum when the pyloric sphincter is closed (retropulsion) and push the chyme into the duodenum when the pyloric sphincter is open. The electrical activity of the SM and the mechanical response

(contraction and relaxation) through electro-mechanical and pharmaco-mechanical coupling facilitate the motility functions of the GI system (Kutchai, 2004).

2.1.2. Excitation-Contraction Coupling

The signalling for the contraction and relaxation of gastric SM cells can be through two forms of excitation-contraction coupling: electromechanical coupling and the pharmaco mechanical coupling (Sanders and Publicover, 1993; Bolton et al., 1999;

Sanders, 2001; Sanders, 2008). An increase in the intracellular calcium concentration is the main trigger for excitation-contraction coupling in GI SMCs. Figure 2.4 shows the important cellular mechanisms that determine the intracellular calcium level.

In electromechanical coupling, changes in the smooth muscle membrane potential lead to contraction. Changes in the membrane potential, in the form of slow waves,

23 lead to an increase in the intracellular Ca2+ level by inflow from the extracellular space via voltage operated Ca2+ channels on the plasma membrane of the cell as

2+ 2+ shown in Figure 2.4 (Carl et al., 1996). The increase in [Ca ]i also leads to Ca induced Ca2+ release from sarcoplasmic reticulum. L-type (slow) Ca2+ channels and

T-type (fast) Ca2+ channels are the prominent voltage dependent calcium channels

(VDCC) in SMC. Several other channels, such as the inward rectifier K+-channel and delayed-rectifier K+ channels are also calcium sensitive. A few receptor operated channels such as the ligand-operated G-protein dependent K-channel and ligand- operated ATP-sensitive K-channel, can also change the membrane potential. The change in membrane potential secondarily opens or closes voltage-dependent Ca2+ channels to cause contraction or relaxation respectively (Guyton and Hall, 1996;

Watras, 2004).

Gastric SM contracts only when the depolarization during the slow wave exceeds the threshold for contraction. Below the threshold, slow wave does not elicit contraction.

The greater the extent of depolarization and the longer the muscle cell remains depolarized above the threshold, the greater is the force of contraction. The action potentials evoke much stronger contractions compared to slow waves that are not accompanied by action potentials. The individual action potentials in a train do not cause distinct twitches as in skeletal muscle; rather they sum temporally to produce a smooth increase in the muscle tension as can be seen in Figure 2.5. Ca2+ influx during action potentials initiates large amplitude contractions and propulsive contractions in the small and large intestines (Szurszewski, 1987; Kutchai, 2004).

24

Figure 2.4. Principal mechanisms determining the cytoplasmic [Ca2+] in smooth muscle cell (Watras, 2004). G – Guanine nucleotide binding proteins; ATP- Adenosine triphosphate; PLC- phospholipase C; PIP2- Phosphotidylinositol biphsophate; IP3 – Inositol 1,4,5-trisphosphate; CM- Calmodulin; MLCK- Myosin light chain kinase.

Between each slow wave, the intracellular Ca2+ levels and the tension developed by

GI SM fall but not to zero. This nonzero resting, or baseline, tension of smooth muscle is called tone (Figure 2.5). In GI SM, the phasic contractions are essentially superimposed over the basal tone (Gregersen and Kassab, 1996; Murthy, 2006).

25

Figure 2.5. Pictorial representation the relationship between membrane potential and contraction of SM. SM contracts when the depolarization during the slow wave exceeds the threshold for contraction. The action potentials evoke much stronger contractions compared to slow waves that are not accompanied by action potentials (Kutchai, 2004).

In pharmacomechanical coupling, chemicals or agonists such as neurotransmitters and hormones cause excitation-contraction coupling in SM through multiple cellular signalling mechanisms that can influence the level of force without a necessary change in membrane potential (Somlyo and Somlyo, 1994; Horowitz et al., 1996). In this situation, activated receptor operated channels directly affect the contractile machinery through G-proteins and second messengers. The second messengers can lead to a rise in [Ca2+] through receptor operated Ca2+ channels on the plasma membrane of the cell or from the sarcoplasmic reticulum via inositol triphosphate (IP3) receptor operated Ca2+channels, as shown in Figure 2.4, and activate contraction.

Contraction through calcium independent mechanisms and modulation of the sensitivity of force to Ca2+ are other major mechanisms of pharmaco-mechanical coupling (Sanders, 2008). Both the amplitude of phasic contractions and the tone are altered by neuroeffectors, hormones, paracrine substances and pharmacological agents

26

(Sanders and Publicover, 1993; Bolton et al., 1999; Kutchai, 2004; Murthy, 2006;

Sanders, 2008).

During electro-mechanical coupling, pharmaco-mechanical mechanisms can be activated through second messengers and during pharmaco-mechanical coupling, opening of ligand gated channels can result in hyperpolarization, depolarization or no change in membrane potential (Bolton et al., 1999). Thus excitation caused by a single agent may be the result of either electro-mechanical coupling or pharmaco-mechanical coupling, or a combination of both. Both calcium dependent and calcium independent mechanisms can operate simultaneously in a given SM cell to cause contraction

(Harnett and Biancani, 2002; Vladimir Ganitkevich, 2002).

2.2. Signalling for Contraction and Relaxation in Gastric Smooth

Muscle

An increase in the concentration of cytosolic free Ca2+ is the primary trigger for the contraction of smooth muscle. When the intracellular Ca2+ levels increases, it binds to the ubiquitous cytoplasmic protein calmodulin in the ratio 4:1. Binding of four Ca2+ ions to calmodulin induces allosteric changes in calmodulin. The conformational change in calmodulin enables it to bind to its target proteins. Myosin light chain kinase, a high affinity target protein of calmodulin, gets activated upon its binding to calmodulin. Activation of MLCK leads to phosphorylation of Ser19 on the 20 kDa regulatory light chain of myosin II (MLC20), activation of actin activated myosin

ATPase and the interaction of actin and myosin which initiates contraction (Sanders

27 and Publicover, 1993; Somlyo and Somlyo, 1994; Horowitz et al., 1996; Murthy,

2006).

Relaxation of smooth muscle is associated with low intracellular calcium concentrations. When the signals for elevation of the cytosolic [Ca2+] cease, Ca2+ is pumped out of the cytosol by calcium extrusion from the cell using the 3Na+/Ca2+ exchanger and sarcolemmal Ca2+ ATPase, and by reuptake by the sarcoplasmic reticulum using the sarcoplasmic reticulum’s membrane ATPase. The decreasing concentration causes the dissociation of the Ca2+/Calmodulin/MLCK complex and inactivation of the kinase. The phosphorylated myosin light chains are dephosphorylated by myosin light chain phosphatase (MLCP) and muscle relaxation takes place (Somlyo and Somlyo, 1994; Horowitz et al., 1996; Murthy, 2006).

In the presence of agonists, G-protein dependent cellular events augment contractile activity at fixed Ca2+ concentrations. Agonists activate Gq-coupled receptors and phospholipase C (PLC), and lead to generation of IP3 (Inositol triphosphate). The IP3- dependent Ca2+ release through IP3 receptor channels elevates intracellular Ca2+ and activates contraction through Ca2+-CaM dependent MLCK (Somlyo and Somlyo,

1994; Horowitz et al., 1996). In pharmaco-mechanical coupling, agonists also induce contraction through regulated inhibition of MLCP and other calcium independent mechanisms. Rho kinase and Protein Kinase C (PKC) are known to inhibit MLCP

(Murthy, 2006). The inhibition of MLCP leads to increased levels of myosin phosphorylation and a sustained contraction of the smooth muscle. After activation by diacylglycerol (a second messenger), PKC activates thin filament associated proteins, calponin or caldesmon via the Ras/Raf/MEK/MAPK phosphorylation cascade, and plays a role in smooth muscle contraction (Morgan and Gangopadhyay, 2001). cAMP-

28 dependent relaxation by β-adrenergic agonists, adenosine and PGI2 (Ozaki et al., 1992) and cGMP-dependent relaxation by NO are some of the other Ca2+ independent mechanisms of SM activation reported in the literature (Guyton and Hall, 1996;

Watras, 2004).

Thus, the signalling reactions involved in smooth muscle contraction can be broadly classified under electro-mechanical coupling pathways and pharmaco-mechanical coupling pathways, based on the type of signal that initiates the contraction. In this study, the focus is on the spontaneous contractions due to slow waves in the absence of any kind of external agonist stimulation. In this scenario, the reactions pertaining to the electro-mechanical coupling pathway are the primary reactions involved in SM contraction. Hence pharmaco-mechanical coupling pathways signalled by agonists and Ca2+ independent SM contraction are not the focus of this study.

The scope of the study is electro-mechanical coupling. The electrics part of the electro-mechanical coupling has been investigated and modelled already (Corrias and

Buist, 2007; Corrias and Buist, 2008). The electrical models predict the dynamics of intracellular Ca2+ concentration for a given change in the membrane potential. Hence the study here focuses on the mechanical part of electro-mechanical coupling by developing a model for the mechanical pathways triggered by Ca2+.

29

Figure 2.6. Schematic representation of major pathways involved in excitation- contraction coupling in GI smooth muscle by Sanders (Sanders, 2008). The diagram shows the mechanisms involved in both electro-mechanical coupling and pharmaco-mechanical coupling. Ca2+ entry through VDCC is the primary mechanism in electro-mechanical coupling.

2.3. Calcium, Myosin Phosphorylation and Force

Yagi et al. (1988) studied the relationship between force and the Ca2+ concentration in single smooth muscle cells isolated from the stomach of the toad Bufo marinus. Both

2+ [Ca ]i and force were measured after maximal electrical stimulation. The calcium threshold for the elevation of force was reported to be 125-150 nM. The maximum sensitivity of force to Ca2+ was observed in the Ca2+ range between 150 and 500 nM.

The study showed a delay of several hundred milliseconds between electrical

30 stimulation and the onset of force, and this delay was attributed to the steps involved in the activation of the contractile apparatus within the cell. A delay was also observed between stimulation and myosin phosphorylation. This led the authors to associate the delay to the steps linking Ca2+ and light chain phosphorylation. The rate of increase in force was dependent on the rate of Ca2+ elevation until a maximum Ca2+ concentration of 1 µM, beyond which there were only small changes in force.

Ozaki et al. (1991b) made simultaneous measurements of membrane potential, cytosolic Ca2+ and tension in intact canine antral smooth muscle strips to study the

2+ 2+ change in [Ca ]i during slow waves and see if the Ca levels reached during slow waves were capable of eliciting contractions. Figure 2.7 shows recordings of spontaneous slow wave activity from canine antrum smooth muscle, the associated

Ca2+ transients and muscle tension (Ozaki et al., 1991b).

The increase in force occurred approximately 0.3 s after initiation of the Ca2+ transient.

The muscle tension reached a maximum after the maximum increase in Ca2+ was achieved. However muscle tension decreased more rapidly than Ca2+ indicating the role of an inactivation process in the regulation of the contractile activity. The paper reported the antral contractions appear to be biphasic, the first phase occurring in response to the upstroke of the slow wave and the second phase being dependent on the amplitude and duration of the plateau potential.

31

(A)

(B)

Figure 2.7. (A) Recordings from canine antrum smooth muscle strip showing spontaneous slow-wave activity (MP), cytosolic [Ca2+] (shown as fluorescence F400/F500 ratio), and muscle tension. (B) Superposition of membrane potential, 2+ [Ca ] (F400/F500 ratio) and tension (Ozaki et al., 1991b).

Szurszweski (1987) hypothesized that the first contractile phase is generated each time a slow wave propagates through the muscle and is not affected by inhibitory or excitatory agonists. The second phase is not always present and its amplitude can be varied by different excitatory and inhibitory agonists. If a minimum plateau level, called the ‘mechanical threshold’ is not reached, the second phase of contraction was undetectable. The mechanical threshold for excitation-contraction coupling was detected at a membrane potential between -60 and -40 mV. The plateau phase of the slow wave caused a sustained influx of Ca2+ and when the Ca2+ current causes a Ca2+

32 concentration above the threshold for contraction, a second phase of contraction is initiated. Ozaki et al. (1991b) showed that the Ca2+ during the upstroke and the associated contraction was not significantly affected by acetylcholine and hence not regulated by cholinergic stimulation. Acetylcholine was shown to cause a concentration dependent increase in the magnitude of the second phase of the Ca2+ transient and muscle tension as shown in Figure 2.8.

Figure 2.8. Concentration dependent effect of Acetylcholine (ACh) on slow waves, [Ca2+], and tension from (Ozaki et al., 1991b). Control recordings are superimposed with responses to three concentrations of acetylcholine denoted by asterisk: 10-7 M (A), 3 x 10-7 M (B) and 10-6 M (C). Magnitude of the second phase of Ca2+ transient and tension increased with increase in ACh concentration.

33

2.4. Smooth Muscle Contraction Modelling Review

2+ To understand and quantify how [Ca ]i signal is transduced into a mechanical force output, and ultimately motility, it is necessary to understand the cellular processes that take place when such a signal is received. A number of theories and models have been proposed to explain smooth muscle contraction. A literature review on the models that are relevant to the current work is reported in this section.

2.4.1. Hill’s Model

Hill (1938) proposed a model to explain the mechanical behavior of the skeletal muscle. Hill’s model (Figure 2.9) represents an active muscle as composed of three elements. Two elements are arranged in series: a) a contractile element which has zero tension, but when activated is capable of shortening; b) an elastic element in series with the contractile element. The third component is an elastic element in parallel to the contractile element and series elastic element.

The active state of the contractile component was defined by Hill’s characteristic equation,

, (2.1) where T represents tension in the muscle, v represents the velocity of contraction, and a, b and T0 are constants.

34

(A) (B)

Figure 2.9: (A) Three Component Model. (B) The properties of the contractile component are determined from its force-velocity curve, and the properties of the series elastic component are determined from its force-extension curve (Hill, 1938; Fung, 1993).

The contractile component represents the contractile element of the muscle. In the later years the contractile element was identified to contain the actin and myosin molecules and the active contraction was described by the formation of cross-bridges between actin and myosin. The series elastic component is essentially a spring that represents the contribution of the intrinsic elasticity of the contractile elements and other tissue components in active tension generation. The passive elastic component in parallel represents the potential energy stored in relaxed state of the muscle when it is stretched beyond its natural resting length. This is due to passive elastic structures such as the connective tissue. The contractile component is considered to be ‘freely extensible’ and is activated at the onset of active contraction. Hence, the series elastic element carries no load at the resting (or relaxed) state. The properties of the resting muscle and its contribution to tension was described by the parallel elastic component.

The total tension generated in the muscle is thus a combination of the three

35 components. Although the model was proposed for striated muscle, it has been adapted to study smooth muscle too (Gestrelius and Borgstrom, 1986). Hill’s model provided a basis for explaining the contractile function of skeletal muscle under various conditions (e.g., isometric, isotonic contractions). In the later years, models adapted and modified Hill’s three component model to accommodate the experimental findings in the field of smooth muscle mechanics (Gestrelius and Borgstrom, 1986).

2.4.2. Huxley’s Sliding Filament Model

According to Huxley’s Sliding Filament Model (Huxley, 1957), muscle contraction is caused via myosin and actin filaments sliding past one another by the combination of sites projecting from the myosin backbone of the thick filament and active sites on the actin thin filament. The process was presumed to be cyclic with repetitive attachment and detachment of cross-bridges.

Figure 2.10. The figure shows the tension-generating mechanism in Huxley’s model. M- Cross bridge; O- equilibrium position; A-active site on the actin thin filament (Huxley, 1957).

36

Huxley’s theory was based on three basic premises – (i) Cross-bridges can exist only in two states: attached or detached; one ATP molecule is split when a cross-bridge passes in sequence through these states, (ii) cross-bridges exert force only when attached and the magnitude of that force depends on the displacement of the thick and thin filaments with respect to each other and the distance between active sites on the thin filament (to which the cross bridges can attach) is assumed to be large enough that only one site at a time is within range of the myosin head, and (iii) rate constants for the transition between the states are functions of the relative displacement of thick and thin filaments. The rate constants were chosen such that the cross bridges attach more readily at positive displacements than at negative displacements, with the converse holding true for detachment.

2.4.3. Gestrelius and Borgstrom’s Model for SM Contraction

Gestrelius and Borgstrom (1986) proposed a model based on Huxley’s sliding filament theory and Hill’s three component model, and developed a dynamic model for the contraction of vascular smooth muscle. The model was parameterized using experiments on vascular smooth muscle from the rat portal vein. The Gestrelius-

Borgstrom model (Figure 2.11A) has four elements: (i) an active contractile component, which comprises the actin and myosin filaments of the SM; (ii) an elastic component coupled in series with the contractile component; (iii) an external elastic component in series and (iv) an elastic component inserted in parallel.

37

(A) (B)

Figure 2.11. (A) Dynamic Model for Vascular SM contraction proposed by Gestrelius and Borgstrom (1986). cc- contractile component; x, hc, d, and l are lengths; Fcc, FS, FP, and FT denote forces and ks , kc and kp are stiffness of the components. (B) Schematic diagram of the friction clutch assumption used in the model.

The mathematical equations in the Gestrelius and Borgstrom model describe the different properties of the smooth muscle under the two major categories of active force production and passive properties of the SM. The active force production was described through friction-clutch mechanism (Figure 2.11B). It was assumed here that the transfer of energy and force from the active cross-bridges to the actin filaments can be described by a ‘friction clutch’ mechanism and was described by the following ordinary differential equation.

(2.2)

where Fcc is the active force of the contractile component, nc is a normalized factor reflecting the maximum number of cross-bridges available for interaction at a certain degree of activation, fc is a measure of force interaction between the cross-bridges and the actin filaments vc is the average velocity of the cross-bridge displacement and x

38 is the resulting contraction velocity of the muscle. The length-active force relationship was described by,

(2.3)

Here an and bn are constants; l is the actual length of the muscle and l0 is the optimum muscle length.

Assuming a linear cross-bridge elasticity, the total force sustained by the cross-bridges, which must equal the total active force Fcc, was described by the following relation.

(2.4)

Here nc is the normalized number of cross-bridges available for interaction, kc is the stiffness of a cross-bridge and hc is the average cross-bridge extension.

The important contribution of the model was the external series elasticity that accounts for the compliance of the muscle which cannot be solely attributed to the cross-bridges. This was not addressed by the classic Hill Model (Hill, 1938). The model has attempted to address extensively the various properties of smooth muscle under both active and passive conditions. The force-velocity relationship, length- passive force and length-active force relationships, and the relationship between number of active cross bridges and isometric force are the important predictions made by the model. The model predicts a non-hyperbolic force-velocity relationship under high force conditions and is able to maintain isometric force under conditions of a reduced maximum contraction velocity as shown in Figure 2.12. These are the features that differentiate smooth muscle mechanics from skeletal muscle mechanics

39 as explained by the classic Hill model. The active force production in the muscle was described by a frictional clutch mechanism (shown in Equation 2.7) which represents the transfer of energy and force from the active cross-bridges to the actin filament.

Due to the large number of active cross bridges in a muscle, their combined action was adequately described by an average cross-bridge function.

The model proposed by Gestrelius and Borgstrom describes both the active and passive components of smooth contraction and takes into account the mechanical properties of the SM. The model emphasizes active contraction in terms of myosin interactions with actin, the number of active cross-bridges, and the velocity of cross- bridge displacement. However the model gives only a basic description of the contractile component. The model’s parameters have been fitted using experimental studies on SM from the rat portal vein, which primarily shows tonic contraction and linear correlation between active force and the number of cross-bridges was prescribed by the model (Figure 2.13). The model does not include any biochemical aspects such as the activation and regulation of the number of the cross-bridges.

40

Figure 2.12. (a) Comparison between the force-velocity curve of the model (solid line) and a Hill equation (dashed line) based on average parameters of seven portal veins; (b) Comparison of active force-time relationships between model prediction (solid line) and AC stimulated hog carotid SM (dashed line), assuming the same force-velocity curve (dotted line) in the model simulation as in the in vivo experiment. (Figure. 3 and 7c in Gestrelius and Borgstrom (1986)).

Figure 2.13 Relationship between the number of active cross-bridges, nc/no and active isometric force, F/Fo in the model. (Figure.7a in Gestrelius and Borgstrom (1986)).

41

2.4.4. Hai and Murphy’s Four-state Model

Hai and Murphy (1988) developed one of the first models that explain active force production in SM cells through myosin phosphorylation and cross-bridge formation.

The model consists of four states of myosin leading to the attachment to and then detachment from actin. The model hypothesizes that there are two types of cross- bridge interactions: cycling phosphorylated cross-bridges (AMp) and non-cycling dephosphorylated cross-bridges, called latch-bridges (AM). These are regulated by the phosphorylation and dephosphorylation of myosin molecules, the cycling rates of the cross bridges and the formation of latch bridges. According to the model, both AMp and AM contribute to the development of stress in SM. A schematic representation of the four- state model is shown in Figure 2.14.

Figure 2.14. Four-state cycling cross bridge model proposed by Hai and Murphy (Hai and Murphy, 1988). A- Actin; M- Myosin; Mp – phosphorylated myosin; AMp – cross-bridge and AM – latch bridge. K1-7 are the rate constants.

From Figure 2.14, the mathematical formulation of the model was constructed as a set of four differential equations (Equation 2.10 - 2.13).

42

(2.5)

(2.6)

(2.7)

(2.8)

Solving Equations 2.10 - 2.13, total phosphorylated myosin was calculated as the sum of Mp and AMp. Stress was described as the sum of AMp and AM and was normalized to a maximum value which was assumed to be 80% of total myosin concentration.

Figure 2.15. The figure shows the fitting of the myosin phosphorylation and stress curves from the Hai and Murphy model to the experimental data shown in Figure 2.16 (Hai and Murphy, 1988).

43

Figure 2.16. Time course of force, myosin phosphorylation and maximum shortening velocity (Vo) in neutrally stimulated strips of tracheal smooth muscle (Kamm and Stull, 1985).

The model was based on the hypothesis that myosin phosphorylation is both necessary and sufficient for the development of stress. This hypothesis has been incorporated into the model by the activation of MLCK as the only regulated mechanism and the regulation was modelled by choosing different parameter values for K1, corresponding to the transient increase in Ca2+ as shown in Figure 2.15. The latch state hypothesis has been implemented by postulating the transformation of AMp to AM to explain the basic observation of stress maintenance with low myosin phosphorylation (Dillon and

Murphy, 1982). Thus, the model, by considering two different attached cross-bridge states, constant cross-bridge cycling rates and only one regulatory mechanism, has proposed a simple hypothesis to explain the development of stress and steady state stress maintenance in smooth muscle. The parameters were determined by fitting the model to experimental data shown in Figure 2.16. An alternative theory of variable cycling rates would have required more than one regulatory or control mechanism

44

(Warshaw et al., 1988; Paul, 1990; Hellstrand and Nordstrom, 1993). Since the model was able to predict the stress and phosphorylation patterns quantitatively and also the energetics data qualitatively, the simple formulation was considered sufficient. Model simulations predicted a hyperbolic dependence of steady state stress on myosin phosphorylation, which corresponded with the experimental observation of high values of stress with low levels of phosphorylation in intact tissues (Kamm and Stull,

1986). The authors also claimed that from the model simulations it is evident that the initial phosphorylation transient only accelerates stress development, with no effect on the final steady state levels of stress.

However, the Hai and Murphy model has its limitations. One of the main limitations is that although the transient activation of MLCK is reported to be due to the transient intracellular Ca2+ levels, no direct relationship between the Ca2+ concentration and

MLCK kinetics was included. The transient behavior was implemented as a step change in K1 value fitted to the experimental data. The model was developed based on the experimental studies from swine carotid media which exhibits mainly tonic activity and thus has limited applicability to a phasic smooth muscle.

2.4.5. Bursztyn et al.’s Uterine SM Model

Bursztyn et al. (2007) developed a model for excitation-contraction coupling in a uterine smooth muscle cell based on the four-state model of Hai and Murphy. The four-state model was coupled to the Ca2+ concentration through the rate constant for myosin phosphorylation. The rate constant of myosin phosphorylation, K1, was modelled as a function of calcium as shown in Equation 2.14.

45

(2.9)

Here Cahalf_max is the calcium concentration required for half maximal activation of

MLCK by Ca2+/CaM and n is the Hill coefficient of activation. The parameters

(Cahalf_max and n) of Equation 2.14 and other constants in the four state model, K2, K3 and K7, were estimated by fitting to experimental data from uterine smooth muscle

(Word et al., 1994). The model described a sigmoidal relationship between MLCK activity and Ca2+ concentration as observed experimentally (Geguchadze et al., 2004).

The sigmoidal relationship showed three characteristics of MLCK activation behavior in the smooth muscle cell: i) below the threshold Ca2+ concentration, there is minimal activation of MLCK; ii) a steep relationship between MLCK activation and Ca2+ concentration can be observed in the optimal Ca2+ range and iii) at higher Ca2+ concentration desensitization due to phosphorylation of MLCK reduces its activation.

The model shows a good correlation between the predicted force and the experimental force for conditions of increasing Ca2+ concentration (Figure 2.17). However, under phasic Ca2+ transient conditions, although the authors claim a good correlation with the experimental results, the rate of force development is slower in the model compared to the force behavior shown by experiments (Word et al., 1994). The rate of relaxation is also lower and the force does not fall to resting levels. Force reaches a steady state above the resting level and this can be attributed to the description of the dephosphorylation of myosin by constant rate parameters (K2 and K5).

46

Figure 2.17. Bursztyn et al.’s model: Simulation of myosin light chain (MLC) phosphorylation (A) and force production (B) in human nonpregnant myometrium in response to an increase in CCa,i (C), which was used as an input for the simulation. Experimental data of CCa,i, MLC phosphorylation, and stress are shown as open circles. (Bursztyn et al., 2007)

2.4.6. Lukas’ Model

Lukas (2004a and 2004b) developed a cell signalling model beginning at the activation of plasma membrane receptors by agonists and ending with myosin phosphorylation. Agonist induced receptor activation, Ca2+ mobilization, and activation of MLCK leading to myosin phosphorylation was modelled on the Virtual

Cell platform (Loew and Schaff, 2001). The model consists of an extensive pathway that includes calcium-calmodulin binding, activation of MLCK, regulation of MLCP by agonists, phosphorylation and dephosphorylation of myosin (Figure 2.18). The model also includes CaM buffering and MLCK phosphorylation reactions. The model predicts the amount intracellular calcium and myosin phosphorylation for a given agonist concentration. The model showed the amplitude of myosin phosphorylation

47 and the time taken to reach the maximum value to be dependent on the agonist concentration. The model also showed that agonist induced MLCP inhibition increases myosin phosphorylation levels. The model elucidates the cell signalling processes in a generic smooth muscle cell. Though the model includes primary and secondary pathways in the regulation of myosin phosphorylation, the model does not take into account the differences in the type of smooth muscle (phasic and tonic) and the results are not validated against experimental data. The model is more useful for studying, the downstream events in a signalling cascade due to receptor activation by agonists.

Figure 2.18. The pathway of myosin light chain phosphorylation and dephosphorylation through the dynamic regulation of MLCK and MLCP implemented by Lukas in the Virtual Cell platform (Lukas, 2004b).

48

Although the Lukas model describes the reactions regulating contraction that are common across SM types and provides a pathway framework for SM contraction that can be modified or extended, the model is not specific to a particular type of SM. The focus of Lukas model is the pharmaco-mechanical pathways stimulated in response to agonists.

2.4.7. Mbikou et al. Model

Fajmut et al. (2005a) and Mbikou et al. (2006) have derived a theoretical model describing the interaction between calcium, calmodulin and MLCK in a smooth muscle cell and studied the relationship between free calcium concentration and

MLCK activation. The theoretical model consists of eight different species with twelve reactions in the pathway leading to the formation of the active MLCK complex.

The theoretical model was coupled to the four state Hai and Murphy model to study the contraction of airway smooth muscle model as shown in Figure 2.19 (Fajmut et al.,

2005b; Fajmut et al., 2005c; Mbikou et al., 2006; Fajmut and Brumen, 2008). The model showed a reasonable correlation to experimental observation with respect to the steady state sigmoidal relationship between MLCK activation and Ca2+ concentration.

The authors showed that increasing MLCK concentration increased the magnitude of force and decreased the time taken to achieve its half-maximal value while increasing

MLCP concentration decreased the magnitude of force (Fajmut and Brumen, 2008). In addition to Ca2+ dependent activation of MLCK, a MLCP inactivation mechanism was included to explain the tonic force behavior of the airway smooth muscle. The progressive inactivation of MLCP in the model and slow deactivation of MLCK compared to its activation resulted in a Hill shaped force response for a given phasic calcium transient signal. MLCP inhibition has been predominantly attributed to

49 agonist induced cell stimulation (Richards et al., 2002; Murthy, 2006). The model is hence useful to study the tonic contractile behavior and force enhancement due to

MLCP inactivation, but has limited applicability to phasic contraction with relatively rapid contraction and relaxation cycles.

Figure 2.19. Theoretical model of Fajmut et al. (2005a) for the interaction of Ca2+, CaM and MLCK (a) coupled to Hai and Murphy’s four state model (b) to model the calcium-contraction coupling in airway smooth muscle (Mbikou et al., 2006).

The relationship between Ca2+ concentration, myosin phosphorylation and force varies significantly between tonic smooth muscle and phasic smooth muscle (Himpens et al.,

1988b; Gerthoffer et al., 1991; Zhao et al., 2008) due to differences in the expression level of contractile proteins and other cellular proteins (Szymanski et al., 1998;

Mahavadi et al., 2008), activation properties of MLCK (Gerthoffer et al., 1991; Word et al., 1994), regulation of MLCP (Gong et al., 1992a), cross-bridge kinetics (Marston,

1989; Hellstrand and Nordstrom, 1993; Murphy, 1994; Gregersen and Christensen,

50

2000; Murphy and Rembold, 2005) and secondary regulatory mechanisms (Krymsky et al., 2001; Lorenz et al., 2002; Choudhury et al., 2004). Hence, models developed for tonic contractile behavior cannot be used directly to study phasic smooth muscle contraction which is the focus of this work.

Table 2.1. Merits and limitations of the previous modelling studies on SM contraction.

Model Type of SM Merits Limitations

Does not take into Description of the Gestrelius and account the active and passive Borgstrom’s Vascular SM biochemical regulation components of SM model (1986) of cross-bridge contraction formation

Captures the No direct link between Hai and mechanism of cross- myosin Murphy’s General SM bridge formation phosphorylation and model (1988) between actin and Ca2+ concentration myosin a) The focus of the model is on agonist Detailed pathway induced SM Lukas Model General SM model for SM contraction. (2004) contraction b) The model is not addressed towards a specific SM type. Detailed description of MLCK activation and Model for airway SM Mbikou et al.’s extension of Hai and Airway SM which exhibits tonic model (2006) Murphy model with the contractile response Ca2+ dependence and MLCK kinetics

Extension of Hai and Ca2+ dependent MLCK Bursztyn et Murphy model with activity is described al.’s model Uterine SM Ca2+ dependence for a using a sigmoid (2007) phasic SM type function

51

2.5. Summary

In summary, experimental studies have provided an understanding of the regulation of smooth muscle contraction at various levels. Electrophysiological studies have shown the regulation of GI motility by the electrical behaviour of the SMCs and the excitation-contraction coupling through the regulation of intracellular Ca2+ concentration (Section 2.1). Protein interaction and signalling studies have elucidated the reaction network involved in SM contraction (Section 2.2). Force measurements at cellular and tissue level have generated data on the contractile response of SM for an intracellular Ca2+ transient generated in response to an electrical stimulus (Section

2.3). SM electrical models have been successful in describing the change in intracellular Ca2+ concentration as a function of change in SM membrane potential

(Corrias and Buist, 2007). In moving towards the target of a model for GI motility, the next step would be to develop a model to link electrical activity and mechanical activity of a SMC. Though generic models of SM contraction and models for other

SM types (e.g., airway, vascular which are primarily tonic SM) have been developed

(Section 2.4), a model specific for phasic gastric SM has not yet been developed. This study is hence aimed at developing a model for gastric smooth muscle and providing a framework for electro-mechanical coupling.

52

3. Modelling Active Force Production in Gastric SMCs

through Ca2+ dependent MLCK Activation.

3.1. Introduction

Calmodulin (CaM) is a 17 kDa Ca2+ binding protein involved in several intracellular

Ca2+ dependent signalling pathways. Protein-protein interaction studies have shown that CaM has target binding sites for Ca2+ at two locations, one near the C-terminal and one near the N-terminal, with each site binding two Ca2+ ions (Persechini and

Cronk, 1999). Thus, up to four Ca2+ ions could potentially bind to CaM in any order.

2+ 2+ CaM bound to four Ca ions ((Ca )4CaM) undergoes a conformational change which enables it to bind target proteins and regulate their activity. Numerous intracellular

2+ proteins bind to (Ca )4CaM with high (Kd ≤ 10 nM), intermediate

(10 nM < Kd < 100 nM), and low (Kd ≥ 100 nM) affinities (Persechini and Cronk,

1999). The myosin light chain kinase (MLCK) enzyme is a high affinity target protein of CaM with the dissociation constant of approximately 1 nM (Kasturi et al., 1993;

Johnson et al., 1996; Persechini and Stemmer, 2002; Geguchadze et al., 2004). The local intracellular availability of CaM is of biological significance because different

CaM binding proteins are regulated over a wide range of free CaM concentrations as well as by the amplitude and frequency modulation of intracellular calcium. Though high amounts of CaM are present in the cell, the involvement of CaM in numerous pathways results in limited levels of free cytosolic CaM (Persechini and Stemmer,

2002). The relatively low levels of free CaM consequently limit the maximum achievable MLCK activation even at high Ca2+ concentrations.

53

Studies with the inhibitory agent wortmannin and knockout studies have shown that

2+ MLCK activation by (Ca )4CaM is the primary and necessary mechanism for the initiation of contraction in SMCs (Burke et al., 1996; He et al., 2008). MLCK has a

2+ catalytic core and a substrate binding site. MLCK, when bound to (Ca )4CaM, forms the active kinase complex which can phosphorylate the regulatory light chain (RLC) of the thick myosin filament. Phosphorylation of the myosin RLC results in a conformational change of the myosin heads and stimulation of actin-activated

MgATPase resulting in cross-bridge cycling and active force production. Hence, when there is a transient increase in the intracellular Ca2+ concentration, Ca2+ ions bind to

2+ CaM to form the (Ca )4CaM pool, which then goes on to activate MLCK. The activation of MLCK results in contraction of the SMC through myosin phosphorylation and its subsequent interaction with actin (Murthy, 2006). The active force produced is a function of the number of cross-bridges formed between actin and myosin (Gestrelius and Borgstrom, 1986; Hai and Murphy, 1988). A schematic representation of the calcium dependent cross-bridge formation mechanism is given in

Figure 3.1.

2+ 2+ 2+ 4Ca + CaM  (Ca )4 CaM + MLCK  (Ca )4 CaM-MLCK

A+ M AM p

Figure 3.1. Calcium-dependent mechanism of active contraction. MLCK is activated when bound to calmodulin carrying four Ca2+ ions. The activated MLCK enzyme triggers phosphorylation of 20 kDa light chain of the myosin filament which leads to formation of cross-bridges between myosin (M) and actin (A). The formation of cycling cross-bridges (AMp) results in shortening of the smooth muscle cell.

54

In this thesis, two approaches to describe MLCK activation have been explored. The first method, described in Section 3.2 was to develop a signal transduction pathway based description of MLCK activation following Figure 3.1. Inspired by experimental results depicting the activation of MLCK at various Ca2+ concentrations, the second approach described in Section 3.3 was to explain the Ca2+ dependence of MLCK activation through a direct mathematical function that would describe the experimentally observed relationship between MLCK activity and Ca2+.

2+ The mechanism of [Ca ]i dependent active force production is described here in terms of two modules, the first describing the activation of MLCK through its interactions with calmodulin and Ca2+ ions, and the second consisting of a four state scheme describing myosin phosphorylation and cross-bridge formation between actin and myosin.

3.2. MODULE I: MLCK activation by Ca2+ signalling pathway

3.2.1. MLCK activation: preliminary model

2+ The formation of the (Ca )4CaM-MLCK complex through the binding of CaM to

Ca2+ and MLCK leads us to several possible binding orders. A theoretical model has been developed by Fajmut et al. (described in Section 2.4.7) with eight possible complexes through twelve reactions (Fajmut et al., 2005a). However protein interaction studies and kinetic studies point toward six significant complexes in the pathway with other possible complexes being too transient to affect the pathway flux

(Kasturi et al., 1993; Johnson et al., 1996).

55

Although the Lukas model is not specific to a type of SM, the reactions regulating contraction that are common across SM types have been described elaborately and the model provides a pathway framework for SM contraction that can be modified, refined and extended. Hence, the generic model for smooth muscle contraction developed by Lukas (Lukas, 2004) was used as the starting point for describing the

MLCK activation. As mentioned in Section 3.1, up to four Ca2+ ions could potentially bind to CaM in any order. Insufficient experimental data is available to properly quantify the range of potential binding combinations and it was therefore assumed that

Ca2+ ions bind to CaM in pairs, such that both of the sites at one terminal are occupied simultaneously. In addition, it was assumed that the binding was order independent, meaning that it was sufficient to model CaM as having two binding sites and not explicitly tracking which of the binding sites was occupied. Based on these assumptions, a pathway model was developed that contained nine reactions to describe the interaction between calcium, calmodulin and MLCK (Gajendiran and

Buist, 2011). In the preliminary model, shown in Figure 3.2, zero, two or four Ca2+ ions are bound to CaM as shown by the horizontal transitions.

56

Figure 3.2. Signal transduction pathway for MLCK activation by intracellular Ca2+ ions through calmodulin. CaM = calmodulin; MLCK = myosin light chain kinase; Ca = Ca2+ ion; BP = buffering protein. Reactions are numbered and the corresponding details can be found in Table 3.1.

A CaM buffering system was included following Lukas (Lukas, 2004b). Myosin Ic has been implicated in CaM buffering process where CaM bound to actomyosin filaments are released when Ca2+ concentration increases i.e. actomyosin filament gets unbound to CaM upon CaM binding to Ca2+ ions (Lukas, 2004b). Here CaM forms a complex with a buffering protein (BP) that sequesters CaM in the absence of free Ca2+.

As the intracellular Ca2+ level increases, CaM is liberated from the BP as shown by the transitions marked as 8 and 9 in Figure 3.2. The scheme proposed by Lukas assumed that the binding of two Ca2+ ions dissociates CaM from a buffer complex and

2+ 2+ then (Ca )2CaM rapidly acquires two more Ca ions before binding to and activating

2+ MLCK. Experiments have shown that both CaM and (Ca )2CaM can bind to MLCK, albeit without activating the enzyme (Johnson et al., 1996). MLCK is only activated

2+ 2+ by the complex containing CaM and four Ca ions ((Ca )4CaM). The binding and

57 unbinding of MLCK to CaM and its Ca2+ bound complexes are depicted as vertical transitions in Figure 3.2. The reactions involved in the pathway scheme shown in

Figure 3.2 are given in Table 3.1.

Table 3.1. Reactions involved in the activation of MLCK (Module I) by the interaction between CaM, Ca2+ and MLCK in the preliminary model .

No. Reaction

2+ 2+ 1 CaM + 2Ca ↔ (Ca )2CaM

2+ 2+ 2+ 2 (Ca )2CaM + 2Ca ↔ (Ca )4CaM

3 CaM + MLCK ↔ CaM-MLCK

2+ 2+ 4 (Ca )2CaM+ MLCK ↔ (Ca )2CaM -MLCK

2+ 2+ 5 (Ca )4CaM + MLCK ↔ (Ca )4CaM -MLCK

2+ 2+ 6 CaM-MLCK + 2Ca ↔ (Ca )2CaM -MLCK

2+ 2+ 2+ 7 (Ca )2CaM-MLCK + 2Ca ↔ (Ca )4CaM –MLCK

8 CaM + BP ↔ CaM-BP

2+ 2+ 9 CaM-BP + 2Ca ↔ (Ca )2CaM + BP

In kinetic studies of biochemical reactions, the rate constants are commonly estimated by fitting to mass-action reaction kinetics and usually first order kinetics are assumed

(Hartshorne, 1987). Hence, each of the reaction pathways shown in Figure 3.2 was assumed to exhibit mass action kinetics and the signal transduction system was described in terms of first order differential equations (ODEs) representing the fluxes

58 into and out of each state. This is best explained through an example using reaction 1 from Table 3.1 and Figure 3.2 where two Ca2+ ions bind to one molecule of CaM.

(3.1)

Given a forward reaction rate constant, kf, and a reverse reaction rate constant, kr, the rates of change of the reactants and product are given by

(3.2)

Performing a similar analysis on each of these reactions yields a single ODE for each species. The ODEs were solved in MATLAB using the in-built ODE solver. To check convergence of the solution, the model was solved using two different ODE solvers, ode15s (a stiff solver) and ode45 (a non-stiff solver) and changing the tolerance values of the solvers. The solutions were invariant.

3.2.2. MLCK activation: extended model

After the initial studies, the binding of Ca2+ ions at the C-terminal and N-terminal binding sites of CaM was explicitly described. The difference in the binding properties between the N-terminal and C-terminal binding sites were subsequently included. The binding of calcium is slow and stronger (higher affinity) at the C- terminus and rapid at its N-terminal site with lower affinity. C-terminus of CaM has 2-

3 fold higher affinity for calcium than the N-terminus of CaM. The N-terminus of

59

CaM binds Ca2+ faster compared to the C-terminal and has faster dissociation rate compared to the C-terminus (Johnson et al., 1996). The explicit description of the binding of calcium ions at the C-terminal and N-terminal binding sites subsequently led to the inclusion of cooperativity between the binding of Ca2+ ions and MLCK to

CaM. Experiments studying Ca2+ exchange with calmodulin in the presence of target proteins have shown that MLCK binding to CaM reduced the rate of Ca2+ dissociation from the N-terminal sites (a 140-225 fold decrease) and the C-terminal sites (a 6-24 fold decrease) (Hartshorne, 1987, Kasturi et al., 1993). MLCK binding has also been shown to increase (by 9-fold) the C-terminal Ca2+ affinity. Thus CaM bound to

MLCK binds to Ca2+ rapidly at the C-terminus and more strongly at the C and N- terminal sites compared to unbound free CaM. The explicit description of Ca2+ binding at the C-terminal and N-terminal binding sites of CaM resulted in an extended pathway scheme with eleven reactions as shown in Table 3.2.

60

Table 3.2. Reactions involved in the activation of MLCK (Module I) by the interaction between CaM, Ca2+ and MLCK in the extended model with the explicit description of Ca2+ binding at the C-terminal (indicated with subscript C) and N-terminal binding sites (indicated with subscript N) of CaM.

No. Reaction

2+ 2+ 1 CaM + 2Ca ↔ (Ca )2CaMC

2+ 2+ 2 CaM + 2Ca ↔ (Ca )2CaMN

2+ 2+ 2+ 3 (Ca )2CaMN + 2Ca ↔ (Ca )4CaM

2+ 2+ 2+ 4 (Ca )2CaMC + 2Ca ↔ (Ca )4CaM

5 CaM + BP ↔ CaM-BP

2+ 2+ 6 CaM-BP + 2Ca ↔ (Ca )2CaMC + BP

2+ 2+ 7 (Ca )4CaM + MLCK ↔ (Ca )4CaM -MLCK

2+ 2+ 8 (Ca )2CaMC + MLCK ↔ (Ca )2CaMC -MLCK

9 CaM + MLCK ↔ CaM-MLCK

2+ 2+ 10 CaM-MLCK + 2Ca ↔ (Ca )2CaMC -MLCK

2+ 2+ 2+ 11 (Ca )2CaMC -MLCK + 2Ca ↔ (Ca )4CaM -MLCK

3.2.2. Module I: Parameter Estimation

Persechini and Cronk (1999) showed the relationship between free intracellular Ca2+

2+ and free (Ca )4CaM in intact cells in the presence of two CaM-binding proteins.

Stably transfected HEK-293 cells that express one of three CaM indicators with

61 varying affinities to CaM, FIP-CBSM-41 (Kd = 2 nM), FIP-CBSM-38(Kd = 45 nM) and

2+ FIP-CBSM-39 (Kd=400 nM) or only the Ca indicator, FIP-CA37 (Kd = 0.6 µM) were produced (Persechini and Cronk, 1999). The CaM-binding sequences in the indicators were altered versions of the avian smooth muscle myosin light chain kinase sequence.

FIP-CBSM-41 has a high affinity of Kd = 2 nm which is essentially the same as the affinity of MLCK to CaM with a Kd value of 1-2 nM (Persechini and Cronk, 1999;

2+ Persechini and Stemmer, 2002; Geguchadze et al., 2004). The free (Ca )4CaM concentrations produced in cells expressing each CaM indicator at different intracellular concentrations of free Ca2+ were calculated from the indicator emission

2+ 2+ ratios. The relationship between free (Ca )4CaM and free intracellular Ca was shown to follow a sigmoid behavior. The experimental results shown in Figure 3.3 were used to estimate the parameters of the Module I whose values were not available in the literature.

The model can be visualized as a combination of two interdependent pathways. One consists of the reactions involved in the binding of four Ca2+ ions to CaM (reactions 1-

6 in Table 3.2) and the second consists of the interaction of the various species of the first pathway leading to target protein activation (reactions 7-11 in Table 3.2). The parameters of module I were estimated in two steps using the two different experimental data sets from Persechini et al. shown in Figure 3.3 (Persechini and

Cronk, 1999).

62

2+ Figure 3.3. Free (Ca )4CaM concentrations in cells expressing FIP-CBSM-38() 2+ and FIP-CBSM-41() at different intracellular free Ca concentrations. The binding curves for the data are shown (Persechini and Cronk, 1999).

3.2.2.1. Estimation of parameters pertaining to reactions involved in the binding of four Ca2+ ions to CaM (Reactions 1-6 in Table 3.2).

2+ First, the parameters involved in the formation of (Ca )4CaM through the interaction

2+ of Ca and CaM were estimated by replacing the MLCK with a target protein (TP45) of affinity 45 nM. The reactions are shown in Table 3.3. The model was simulated to reach steady state at each Ca2+ concentration within a range of 0-100 µM and the steady state concentration of the species at each Ca2+ concentration was noted. The

2+ amount of free (Ca )4CaM simulated from the model was compared and fitted to the

63

2+ experimental free (Ca )4CaM data corresponding to FIP-CBSM-38. The result is shown in Figure 3.4 and the parameters are shown in Table 3.3.

Most of the values for parameters shown in Table 3.3 were taken or derived from the literature. The rate constants of the respective reactions are indicated by the reaction number in the form of superscript. For few parameters (indicated by asterisk * in

Table 3.3) the values were estimated by fitting to experimental data. Two methods were used for the parameter estimation. In the presence of a range for the parameter

4 11 values (kr and kr ), simulations were run with step increment of the parameter values from the lower bound to upper bound value of the range till the objective function met a specified tolerance value. The maximum of the absolute difference between the

2+ 2+ experimental free (Ca )4CaM concentration and the predicted free (Ca )4CaM concentration values from the model was used as the objective function and a

-3 7-9, 11 tolerance value of 10 was specified. The apparent dissociation constant (Kd in

Table 3.3) of TP45 binding to various species of CaM was estimated by this method within a range of 0.04-0.06 µM (Pepke et al., 2010). The experimental data used for fitting represents the binding of target protein with a Kd value of 0.045 µM.

64

Table 3.3. Reactions with the binding of a target protein with Kd = 45 nM (TP45) and the respective forward (kf) and reverse (kr) reaction rates determined by parameter estimation. *- parameters estimated through fitting. #- the parameter calculated from the other two values. The rate constants of the respective reactions are indicated by the reaction number in the form of superscript in the main text.

kf kr Kd No Reaction Ref (µM-1s-1) (s-1) (µM)

2+ 2+ (Johnson et 1 CaM + 2Ca ↔ (Ca )2CaMC 2.3 2.4 1.043 al., 1996)

2+ 2+ (Johnson et 2 CaM + 2Ca ↔ (Ca )2CaMN 160 500 3.125 al., 1996)

2+ 2+ 2+ (Johnson et 3 (Ca )2CaMN + 2Ca ↔ (Ca )4CaM 2.8 2.4 0.857 al., 1996)

(Johnson et al., 1996; 2+ 2+ 2+ * # 4 (Ca )2CaMC + 2Ca ↔ (Ca )4CaM 100 253 2.53 Fajmut et al., 2005; Pepke et al., 2010)

(Black et al., 5 CaM + BP ↔ CaM-BP 5 15 3 2004; Lukas, 2004) CaM-BP + 2Ca2+ ↔ 6 27.6* 55.2# 2 (Black et al., 2+ 2004) (Ca )2CaMC + BP

2+ (Ca )4CaM + TP45 ↔ 7 60 2.4 0.04 (Pepke et al., 2+ 2010) (Ca )4CaM-TP45

2+ (Ca )2CaMC + TP45 ↔ 8 0.92 0.049 0.054 (Pepke et al., 2+ 2010) (Ca )2CaMC-TP45

* # 9 CaM + TP45 ↔ CaM- TP45 110 5.61 0.051 fitted

2+ CaM- TP45 + 2Ca ↔ 10 44 0.49 0.011 (Pepke et al., 2+ 2010) (Ca )2CaMC-TP45

2+ 2+ (Ca )2CaMC-TP45 + 2Ca ↔ 11 76# 4.1* 0.054 (Pepke et al., 2+ 2010) (Ca )4CaM-TP45

65

The buffering scheme of CaM was adopted from the model developed by Lukas

(Lukas, 2004b). However the apparent dissociation constant of the binding of the

5 2+ buffer protein (Kd in Table 3.3) and the binding of Ca to the CaM-buffer protein

6 complex (Kd in Table 3.3) were derived from Black et al.’ studies of the relationship between the CaM concentration available for binding of proteins and intracellular Ca2+

6 concentration (Black et al., 2004). The forward reaction rate (kf ) was estimated using the MATLAB built-in function ‘fminsearch’ which is an unconstrained nonlinear optimization procedure. The maximum of the absolute difference between the experimental data and the predicted values from the model was used as the objective function for estimating the parameters.

Simulated free [(Ca2+) CaM] (microM) 4

Experimental free [(Ca2+) CaM] (microM) 0.02 4

(Persechini and Cronk, 1999)

CaM] (microM) CaM]

4

) +

2 0.01 Free [(Ca Free

0

0.01 0.1 1 10 100 [Calcium] (microM)

2+ 2+ Figure 3.4. Relationship between free intracellular Ca and free (Ca )4CaM 2+ concentration. Simulated free (Ca )4CaM concentration (—) from the model 2+ fitted to experimental free (Ca )4CaM concentration (●) measured in the presence of binding protein (FIP-CBSM-38) shown in Figure 3.3.

66

After the fitting, the model was validated with a transient Ca2+ signal produced by a cell in response to an agonist as shown in Figure 3.5. FIP-CBSM-38 expressing cells, when treated with thyrotropin releasing hormone, produced reproducible intracellular

2+ 2+ 2+ free Ca transients . The time course of free Ca concentration and free (Ca )4CaM concentration after the addition of the agonist were determined in the FIP-CBSM-38 expressing cells (Figure 3.5). The experimental Ca2+ curve was digitised using software called GetData. The transient Ca2+ concentration shown in Figure 3.5B was

2+ given as an input to the model and the time course of free (Ca )4CaM concentration

2+ obtained from the simulation were compared to the experimental free (Ca )4CaM concentration as shown in Figure 3.6.

2+ 2+ Figure 3.5. Changes in the free concentrations of Ca and (Ca )4CaM produced in response to an agonist in cells expressing FIP-CBSM-38 (Kd = 45 nM). A) The 2+ 2+ relationship between the free Ca and (Ca )4CaM concentrations. B) Time 2+ 2+ courses for the free Ca and (Ca )4CaM concentrations produced after the addition of agonist. Data from the traces in B were used to generate the relationship in panel A (Persechini and Cronk, 1999).

67

3 Free [Ca2+] - input signal i Simulated free [(Ca2+) CaM] 1 4 2.5 Experimental free [(Ca2+) CaM] 4

0.8 (Persechini and Cronk, 1999) 2

CaM] CaM]

4

) + 2 0.6 1.5

0.4 1

Free [(Ca Free

[Calcium] (microM) [Calcium] fraction of their maximum their of fraction 0.2 0.5

0 0 0 50 100 150 200 250 Time (second)

2+ Figure 3.6. Changes in the free (Ca )4CaM concentrations produced in response to transient change in intracellular free Ca2+. Both simulated and experimental 2+ free (Ca )4CaM have been normalized to their respective maximum values. A good correlation is observed between the simulation result and experimental data.

2+ 2+ A discrepancy in the relationship between free (Ca )4CaM and intracellular free Ca concentrations obtained from two different experimental setups (Figure 3.3 and Figure

2+ 3.5A) was reported. It was noted that the maximum free (Ca )4CaM concentration

(Figure 3.5A) obtained from the transient Ca2+ signal in response to agonist was noticeably less than the value determined in cells subjected to varying controlled free

Ca2+ concentrations (Figure 3.3). To make a meaningful comparison, it was therefore

2+ necessary to normalise the free (Ca )4CaM concentrations from the model and the experiment to their respective maximum value. From Figure 3.6, it can be seen that there is good correlation between the experimental data and the simulation result.

68

3.2.2.2. Estimation of the parameters pertaining to MLCK binding reactions

(Reactions 7-11 in Table 3.2).

After the estimation of parameters pertaining to reactions involved in the binding of four Ca2+ ions to CaM (Reactions 1-6 in Table 3.2), the next step was estimating the parameters pertaining to MLCK activation reactions (Reactions 7-11 in Table 3.2).

For this, the experimental result from Persechini et al. corresponding to FIP-CBSM-41 shown in Figure 3.3 was used. FIP-CBSM-41, with the peptide sequence of MLCK, has the same affinity as MLCK (Persechini and Cronk, 1999). This particular experimental data was chosen over other experimental results (Gallagher et al., 1991;

Geguchadze et al., 2004) used by similar modelling studies (Fajmut et al., 2005) for the reason that the experiments were performed in an intact cell and the relationship has been shown in terms of absolute concentrations rather than MLCK activities measured from in vitro enzyme assays.

The model with MLCK binding reactions was simulated for different Ca2+ concentrations in the range of 0-100 µM under steady state conditions and the amount

2+ of free (Ca )4CaM was compared and fitted to the experimental data of free

2+ (Ca )4CaM in the presence of high affinity target protein. The result is shown in

Figure 3.7 and the parameters are shown in Table 3.4. The initial amount of free CaM and the binding indicator proteins were not reported for the experimental data. Here

10 µM of total MLCK was used in the model and an initial free CaM concentration of

2 µM was used (Persechini and Stemmer, 2002; Lukas, 2004b; Hong et al., 2009). It has been reported that in a cell the CaM-binding proteins outnumber CaM by a factor of approximately 2 on a molar basis and availability of free CaM is a limiting factor in

69 the activation of target proteins (Persechini and Cronk, 1999; Persechini and Stemmer,

2002). The initial concentration of the species in Module I used for steady state

2+ 2+ simulations are shown in Table 3.5. The concentration of (Ca )2CaMN, (Ca )4CaM,

2+ 2+ 2+ (Ca )2CaM, (Ca )2CaMc-MLCK, (Ca )4CaM-MLCK were assumed to be zero. The concentration of CaM-MLCK was estimated by fitting. The steady state concentration of the species at the resting Ca2+ concentration (0.1 µM) was used as the initial condition for transient simulations and given in Appendix I.

-3

x 10 Simulated free [(Ca2+) CaM] (microM) 4

4 Experimental free [(Ca2+) CaM] (microM) 4 Binding curve fit to the experimental data (Persechini and Cronk, 1999)

3

CaM] (microM) CaM]

4

) +

2 2

1 Free [(Ca Free

0 0.01 0.1 1 10 100 [Calcium] (microM)

2+ 2+ Figure 3.7. Relationship between free (Ca )4CaM and free Ca concentrations in the presence of MLCK, a high affinity CaM-binding protein. Simulated free 2+ (Ca )4CaM concentration ( —) from the model fitted to experimental free 2+ (Ca )4CaM concentration (*).

70

Table 3.4. Reactions with the binding of a target protein with Kd = 2 nM (MLCK) and the respective forward (kf) and reverse (kr) reaction rates determined by parameter estimation in step two are shown in bold. The fitted parameters not shown in bold are the ones estimated in # step one involving TP45. *- parameters estimated through fitting. - the parameter calculated from the other two values.

K No Reaction kforward kreverse d Ref (µM-1s-1) (s-1) (µM)

2+ 2+ (Johnson 1 CaM + 2Ca ↔ (Ca )2CaMC 2.3 2.4 1.043 et al., 1996)

2+ 2+ (Johnson 2 CaM + 2Ca ↔ (Ca )2CaMN 160 500 3.125 et al., 1996)

2+ 2+ 2+ (Johnson 3 (Ca )2CaMN + 2Ca ↔ (Ca )4CaM 2.8 2.4 0.857 et al., 1996) (Johnson 2+ 2+ 2+ * # et al., 4 (Ca )2CaMC + 2Ca ↔ (Ca )4CaM 100 253 2.53 1996; Pepke et al., 2010) (Black et 5 CaM + BP ↔ CaM-BP 5 15 3 al., 2004; Lukas, 2004) 2+ 2+ 6 CaM-BP + 2Ca ↔ (Ca )2CaMC + 27.6* 55.2# 2 (Black et BP al., 2004)

2+ (Johnson 7 (Ca )4CaM + MLCK ↔ * # et al., 201.81 0.222 0.0011 1996; 2+ (Ca )4CaM-MLCK Torok et al., 1998) 2+ 8 (Ca )2CaMC + MLCK ↔ 840 45.36 0.054 (Fajmut et 2+ al., 2005) (Ca )2CaMC-MLCK

9 CaM + MLCK ↔ CaM-MLCK 12.8 64# 5* (Fajmut et al., 2005)

2+ 10 CaM-MLCK + 2Ca ↔ (Johnson 2.3 0.39 0.1696 et al., 2+ (Ca )2CaMC-MLCK 1996)

(Kasturi 2+ 2+ et al., 11 (Ca )2CaMC-MLCK + 2Ca ↔ 160 36.8# 0.23* 1993; 2+ Johnson (Ca )4CaM-MLCK et al., 1996)

71

The values of the parameters indicated by asterisk (*) in Table 3.4 were estimated as explained in Section 3.3.1. Török et al. estimated that the association rate constant of

2+ 7 8 -1 -1 MLCK to (Ca )4CaM (kf in Table 3.4) will be ~ 10 M s (Torok et al., 1998). The

2+ maximum of the absolute difference between the experimental free (Ca )4CaM concentration in the presence of target protein, FIP-CBSM-41 (Kd = 2 nM) and the

2+) predicted free (Ca 4CaM concentration values from the model in the presence of

MLCK binding was used as the objective function and a tolerance value of 10-3 was specified.

Table 3.5. Initial concentration of the species in Module I used for steady state simulations. The steady state concentration of the species at the resting Ca2+ concentration (0.1 µM) was used as the initial condition for transient simulations and given in Appendix I.

Initial concentration Species Ref (µM) (Persechini and Cronk, 1999; CaM 1.980 Persechini and Stemmer, 2002) 2+ (Ca )2CaMC 0.020 (Johnson et al., 1996)

CaM-BP 2.885 (Lukas, 2004)b

BP 15.0 (Lukas, 2004)b

MLCK 9.385 (Lukas, 2004)b

CaM-MLCK 0.615 fitted

The results (Figure 3.7) from the model show a biphasic behavior with an initial increase and then a decrease after reaching the maximum value (2.8 nM) under CaM limiting conditions (i.e. for a total [CaM] of 5.5 µM with initial free CaM concentration of 2 µM). With 10 µM of total CaM and 10 µM of total MLCK, the biphasic behavior was still observed. However, there was an almost 6 times increase

72

2+ in the maximum free (Ca )4CaM concentration (16.6 nM). With a total CaM concentration of 11 µM, greater than the 10 µM initial MLCK concentration, free

2+ 2+ (Ca )4CaM showed a sigmoid relationship with the Ca concentration. Under these conditions, CaM is in excess compared to the amount of its target protein and thus does not limit target protein activation.

Since the model includes only the activation of one CaM target protein, unlike an intact cell with numerous CaM binding proteins, a limited concentration of initial free

CaM (2 µM) that would be entirely available for MLCK binding and activation was used in the model (Persechini and Stemmer, 2002). Hence in the model, due to high

2+ affinity and cooperative binding, the free (Ca )4CaM produced from the limited total

2+ CaM is rapidly converted to (Ca )4CaM-MLCK and causes the decrease in the

2+ concentration of free (Ca )4CaM as seen in Figure 3.7.

3.2.3. Calmodulin is a limiting factor in the cell.

It has been shown that CaM plays more significant role in signal transduction and regulation of its numerous target proteins than just being a passive relay channel for intracellular Ca2+ (Persechini and Stemmer, 2002). In particular, the limited pool of

CaM within the cell impacts the signalling of the target proteins and also enables cross-talk between CaM dependent signalling pathways. The effect of the limited

CaM pool is demonstrated in Table 3.6 and Figure 3.8.

73

Table 3.6. Effect of concentration of free [CaM] on MLCK activation. The first row shows a CaM limiting condition where [CaM]total is less than the [MLCK]total. The second shows a [CaM] excess condition. The respective MLCK activation levels are tabulated and shown in Figure 3.8

Total [CaM] Percentage of total (µM) MLCK activated

5.5 60 %

11 100 %

With a limiting total CaM concentration of 5.5 µM, even at high Ca2+ concentrations, the level of MLCK activation is limited to 60% of its theoretical maximum. Increasing the concentration of total CaM (11 µM) in excess to total MLCK (10 µM) sees full activation of MLCK in a high Ca2+ environment. Thus, it is evident that MLCK activation is directly affected by the CaM concentration as well as the Ca2+ concentration.

74

Total [CaM] less than total [MLCK] 100 Total [CaM] greater than total [MLCK]

80

e

v

i t

c 60 a

MLCK 40

percentage of total MLCK total of percentage 20

0

0.01 0.1 1 10 100 [Calcium] (microM)

Figure 3.8 Effect of CaM concentration on MLCK activation. Percentage of MLCK activation has been shown for two concentrations of total CaM - total CaM of 5.5 µM with initial free CaM of 2 µM (solid line) and total CaM of 11 µM (dashed line).

3.2.4. Cooperativity between binding sites of calmodulin

As mentioned in Section 3.2.1, the interaction between Ca2+, CaM and MLCK was first modelled with a compact description with nine reactions (Table 3.1). The binding of calcium ions at the C-terminal and N-terminal binding sites were not described

2+ explicitly. With this description, free (Ca )4CaM behavior did not show good agreement with the experimental result as shown in Figure 3.9. The results from this description also showed minimal and slow activation of MLCK at Ca2+ concentrations between 0.1-0.4 µM as shown in Figure 3.10 and did not fit well to the trend shown by experimental results (Figure 3.3). Though MLCK activation reached the same steady state maximum in the preliminary nine reaction model and the extended eleven

75 reaction model, the rate of activation was higher in the eleven reaction model as seen in Figure 3.10.

The reactions and their parameter values shown in Table 3.4 have been extracted and shown in smaller tables (Table 3.7, Table 3.8, Table 3.9, and Table 3.10) to explain the cooperativity between binding sites of CaM. Table 3.7 and Table 3.8 show the cooperativity between Ca2+ binding sites of CaM and Table 3.9 and Table 3.10 show the cooperativity between Ca2+ binding and MLCK binding to CaM.

-3 x 10 8 Extended model 7 Preliminary model 6 Experimental data (Persechini and Cronk, 1999) 5

4

CaM] (microM) CaM]

4

) + 2 3

2

Free [(Ca Free 1

0 0.01 0.1 1 10 100 [Calcium] (microM)

2+ 2+ Figure 3.9. Relationship between free (Ca )4CaM concentration and Ca from the extended model (solid line) with the explicit description of Ca2+ binding at C- terminal and N-terminal of CaM and the preliminary model (dashed line) without the explicit description of Ca2+ binding at C-terminal and N-terminal of CaM. The extended model showed good agreement with the experimental result compared to the preliminary model. The cooperativity between the binding sites 2+ of CaM leads to higher levels of (Ca )4CaM formation. However the increase in 2+ 2+ (Ca )4CaM levels lead to increased (Ca )4CaM-MLCK formation causing a biphasic behavior. Cooperativity in binding to MLCK as explained in Table 3.9 2+ 2+ leads to greater conversion of (Ca )4CaM to (Ca )4CaM-MLCK, hence giving 2+ lower levels of (Ca )4CaM in the extended model.

76

With explicit description of 60 Ca2+ binding at C-terminal & N-terminal of CaM

50 Without explicit description of Ca2+ binding at C-terminal & N-terminal of CaM 40

concentration 30

e

v

i

t c

a 20 MLCK percentage of total MLCK total of percentage 10

0

0.01 0.1 1 10 100 [Calcium] (microM)

Figure 3.10. Relationship between MLCK activation and Ca2+ with (eleven reaction model - solid line) and without (nine reaction model - dashed line) the explicit description of Ca2+ binding at C-terminal and N-terminal of CaM. The cooperativity between the binding sites of CaM leads to faster activation of MLCK at the optimal Ca2+ range.

The difference in the binding properties of the two Ca2+ binding sites of CaM has been incorporated in the model as shown in Table 3.7.

Table 3.7. Difference in the binding properties of the two Ca2+ binding sites of CaM. In the model, the N-terminal of CaM binds Ca2+ 70 times faster and has 208 fold faster dissociation rate compared to the C-terminal. The 3 times higher Kd value for N-terminal binding shows its lower affinity compared to the C-terminal.

kforward kreverse Kd No Reaction (µM-1s-1) (s-1) (µM)

2+ 2+ 1 CaM + 2Ca ↔ (Ca )2CaMC 2.3 2.4 1.0435

2+ 2+ 2 CaM + 2Ca ↔ (Ca )2CaMN 160 500 3.125

77

In addition to the difference in the binding properties, cooperativity between the two calcium binding sites of CaM has been observed and shown in Table 3.8 (Johnson et al., 1996; Kasturi et al., 1993). CaM with Ca2+ bound at its N-terminal acquires two

Ca2+ ions at its C-terminal with more affinity and binding of Ca2+ at the C-terminal reduces the dissociation rate of Ca2+ from the N-terminal. In the model, CaM bound with Ca2+ at its N-terminal binds to Ca2+ at its C-terminal 1.2 times faster compared to

1 3 free CaM as reflected by kf values of reaction 1 and 3 (kf and kf ) in Table 3.8. CaM bound with Ca2+ at its C-terminal binds to Ca2+ at its N-terminal with 1.2 times more affinity compared to free CaM as reflected by Kd values of reaction 2 and 4 in Table

3.8. Thus cooperativity between the two calcium binding sites lead to elevated levels

2+ 2+ 2+ of free (Ca )4CaM at high Ca concentrations. Elevation of free (Ca )4CaM levels

2+ leads to its binding to the target protein MLCK forming the active (Ca )4CaM-MLCK complex.

Table 3.8. Cooperativity between the two calcium binding sites of CaM. In the model, CaM bound with Ca2+ at its N-terminal binds to Ca2+ at its C-terminal 1.2 times faster compared to 2+ free CaM as reflected by Kf values of reaction 1 and 3. CaM bound with Ca at its C-terminal binds to Ca2+ at its N-terminal with 1.2 times more affinity compared to free CaM as reflected by Kd values of reaction 2 and 4.

kforward kreverse Kd No Reaction (µM-1s-1) (s-1) (µM)

2+ 2+ 1 CaM + 2Ca ↔ (Ca )2CaMC 2.3 2.4 1.0435

2+ 2+ 2 CaM + 2Ca ↔ (Ca )2CaMN 160 500 3.125

2+ 2+ 2+ 3 (Ca )2CaMN + 2Ca ↔ (Ca )4CaM 2.8 2.4 0.8571

2+ 2+ 2+ 4 (Ca )2CaMC + 2Ca ↔ (Ca )4CaM 100 253 2.53

78

In addition to the cooperativity between Ca2+ binding sites of CaM, MLCK binding to

CaM has also been shown to affect the Ca2+ binding dynamics of calmodulin (Kasturi et al., 1993; Johnson et al., 1996). Calmodulin has been shown to be present both in free form and in complex with target proteins (Hong et al., 2009). Apart from the calcium dependent binding of CaM to MLCK, CaM-MLCK complexes associated with acto-myosin filament structures have been isolated (Hong et al., 2009). MLCK binding to CaM has been found to increase the Ca2+ affinity at the N-terminal of CaM.

The dissociation rates of Ca2+ from the C-terminal and N-terminal binding sites of

CaM have also been shown to reduce in the presence of MLCK (Kasturi et al., 1993;

Johnson et al., 1996). The effect of MLCK binding on the Ca2+ binding kinetics of

CaM is shown in Table 3.9. In the model, MLCK binding to CaM decreases the

2+ -1 -1 dissociation rate (kr) of Ca from the C-terminal binding site from 2.4 s to 0.39 s

(reactions 1 and 10 in Table 3.9) as reported by Johnson et al. (1996) and Kasturi et al.

(1993) and increases the the Ca2+ affinity at the N-terminal of CaM by 11 times as reflected by the Kd values in reactions 4 and 11. This results in the endogenous CaM-

MLCK complex of the acto-myosin structure and resting CaM-MLCK pool acquiring calcium rapidly when intracellular calcium level rises. At a resting Ca2+ concentration of 0.15µM, 19.5% of total CaM was bound to MLCK as shown in Figure 3.11.

79

Table 3.9. Effect of MLCK binding on the Ca2+ binding kinetics of CaM. In the model, MLCK 2+ binding to CaM decreases the dissociation rate (Kr) of Ca from the C-terminal binding site from 2.4 s-1 to 0.39 s-1 as seen in reactions 1 and 10 and increases the the Ca2+ affinity at the N-terminal of CaM by 11 times as reflected by the Kd values in reaction 4 and 11.

kforward kreverse Kd No Reaction (µM-1s-1) (s-1) (µM)

2+ 2+ 1 CaM + 2Ca ↔ (Ca )2CaMC 2.3 2.4 1.0435

2+ 2+ 10 CaM-MLCK + 2Ca ↔ (Ca )2CaMC-MLCK 2.3 0.39 0.1696

2+ 2+ 2+ 4 (Ca )2CaMC + 2Ca ↔ (Ca )4CaM 100 253 2.53

2+ 2+ 11 (Ca )2CaMC-MLCK + 2Ca ↔ 160 36.8 0.23 2+ (Ca )4CaM-MLCK

25

20

15

10 CaM-MLCK

percentage of total CaM total of percentage 5

0 0.01 0.1 1 10 100 [Calcium] (microM)

Figure 3.11. Concentration of CaM-MLCK complex. CaM-MLCK complexes associated with acto-myosin filament structures and calcium dependent binding of CaM to MLCK resulted in a CaM-MLCK concentration of 19.5% of total CaM at resting Ca2+ concentration (0.15µM).

80

CaM bound to Ca2+ at its C-terminal site also acquires MLCK with increased affinity compared to free CaM. CaM bound to four Ca2+ ions binds to MLCK with the highest affinity of 1 nM. This is shown in Table 3.10.

Table 3.10. CaM bound to Ca2+ ions binds to MLCK rapidly and with more affinity. In the model, CaM bound to Ca2+ at its C-terminal site acquires MLCK rapidly and with increased 2+ affinity compared to free CaM as could be seen in reactions 10 and 11. (Ca )4CaM binds to MLCK with the highest affinity of 0.0011 µM as seen in reaction 7.

kforward kreverse Kd No Reaction (µM-1s-1) (s-1) (µM)

10 CaM + MLCK ↔ CaM-MLCK 12.8 64 5

2+ 11 (Ca )2CaMC + MLCK ↔ 840 45.36 0.054 2+ (Ca )2CaMC-MLCK

2+ 2+ 7 (Ca )4CaM + MLCK ↔ (Ca )4CaM-MLCK 201.81 0.222 0.0011

During a rapid Ca2+ transient (half-width 0.6 ms) as shown in Figure 3.12 and in the absence of a target protein, it was observed that 70% of N-terminal and 20% of the C- terminal to be occupied with Ca2+ (Johnson et al., 1996). Binding of four Ca2+ ions at the calcium binding sites has been found to cause a change in the conformation of the

CaM molecule exposing the protein binding site thus enabling the binding of the target protein to the Ca2+-CaM complex. Thus, it can be understood that when there is rapid increase and decrease in intracellular calcium, the N-terminal binding site acts as a sensor by responding rapidly to the Ca2+ flux and causing opening or closing of the protein binding pocket of CaM.

81

Figure 3.12. Time course of a Ca2+ transient (∆) and the time course of the occupancy of the CaM N-terminal () and C-terminal () Ca2+ binding sites in response to the Ca2+ transient were simulated by Johnson et al.(Johnson et al., 1996). In the absence of a target protein, it was observed that 70% of N-terminal and 20% of the C-terminal to be occupied with Ca2+.

2+ 2+ The formation of (Ca )2CaM complexes and (Ca )2CaMC-MLCK complexes is shown in Figure 3.13. Due to cooperativity in binding shown in Table 3.7 and Table

2+ 2+ 2+ 3.10, CaM bound to Ca at its C-terminal site ((Ca )2CaMC) binds to two more Ca

2+ at its N-terminal site with more affinity to form (Ca )4CaM or binds to MLCK to

2+ 2+ form (Ca )2CaMC-MLCK. Hence the concentration of (Ca )2CaMC is lower

2+ compared to (Ca )2CaMN as seen in Figure 3.13. Owing to strong affinity and low dissociation rate of calcium at the C-terminal binding site, it has been suggested that at resting calcium levels in cells, 50-80% of CaM’s C-terminal may be bound to calcium

(Johnson et al., 1996). Our model showed 37.5% occupancy at the C-terminal at the

2+ resting Ca level ([Carest] = 0.15µM). The value suggested by Johnson et al. (1996) may be higher because, the C-terminal Ca2+ dissociation rate (0.07 s-1) of the peptide complex, RS-20, used to study Ca2+ occupancy of CaM was 6 times lower than the C- terminal Ca2+ dissociation rate of MLCK (0.39 s-1). As shown in Figure 3.13, 26% of

82

2+ total [CaM] are converted to (Ca )2CaMC-MLCK complexes by two reactions, (i)

2+ (Ca )2CaMC, binding to MLCK rapidly and with stronger affinity compared to free

CaM and (ii) CaM-MLCK acquiring two Ca2+ ions at its C-terminal site with

2+ increased affinity compared to free CaM. After reaching a peak, (Ca )2CaMC-MLCK

2+ concentration decreases due to its conversion to (Ca )4CaM-MLCK with an increasing Ca2+ concentration.

0.6 (Ca2+) CaM 30 2 C

(Ca2+) CaM 0.5 2 N 25 (Ca2+) CaM-MLCK 2

0.4 20

CaM 2

) 0.3 15

+

CaM-MLCK

2

2

)

+ 2

(Ca 0.2 10

(Ca percentage of total CaM total of percentage percentage of total CaM total of percentage 0.1 5

0 0

0.01 0.1 1 10 100 [Calcium] (microM)

2+ 2+ Figure 3.13. Formation of (Ca )2CaM and (Ca )2CaMC-MLCK complexes. Calcium binding to the C-terminal with strong affinity but at a slower rate is 2+ 2+ shown by the solid line. (Ca )2CaMC is rapidly converted to either (Ca )4CaM 2+ and (Ca )2CaMC-MLCK. Calcium binds to the N-terminal rapidly but with a 2+ lower affinity and is shown by dashed line. (Ca )2CaMC-MLCK complexes shown by dotted lines are formed by two reactions –(i) CaM bound to calcium at its C-terminal site, binds to MLCK rapidly and with stronger affinity compared 2+ to free CaM to form (Ca )2CaMC-MLCK complex and (ii) CaM bound to MLCK acquires two Ca2+ ions at its C-terminal site with increased affinity compared to free CaM by reducing the rate of dissociation and lead to formation 2+ of (Ca )2CaMC-MLCK complex.

Calmodulin bound to MLCK and calcium at the C-terminal binding site i.e.

2+ 2+ 2+ (Ca )2CaMC-MLCK at resting Ca levels would rapidly acquire two Ca ions at the

83

N-terminal site when there is an increase in intracellular Ca2+, thus leading to the rapid activation of MLCK and hence initiation of contraction. This is shown in Figure 3.14 where the inclusion of the cooperativity leads to rapid and increased activation of

MLCK compared to the preliminary model. CaM bound to MLCK reduces the rate of dissociation of Ca2+ from the binding sites on CaM and this allows a rapid Ca2+ transient to result in formation of a stable active enzyme pool to facilitate the contraction of smooth muscle.

Similarly when Ca2+ declines, Ca2+ dissociates from the N-terminal faster due to greater dissociation constant compared to C-terminal and leads to inactivation of

MLCK. Since four Ca2+ ions are required for the active enzyme complex, dissociation of Ca2+ from the N-terminal site is sufficient to cause inactivation. Since the dissociation of Ca2+ from the C-terminal binding site is too slow, the rate of dissociation of Ca2+ from the N-terminal binding site controls the rate of inactivation of MLCK.

84

100 Extended model

Preliminary model

80

e

v i

t 60

c a

MLCK 40

percentage of total CaM total of percentage 20

0

0.01 0.1 1 10 100 [Calcium] (microM)

2+ Figure 3.14. Formation of MLCKactive i.e., (Ca )4CaM-MLCK complex in the extended model (solid line) and the preliminary model (dashed line). It can be 2+ seen that the formation of (Ca )4CaM-MLCK is rapid in the extended model with the explicit description of Ca2+ binding at C-terminal and N-terminal of CaM.

3.2.5. Transient MLCK activation

Figure 3.14 shows MLCK activation for a wide Ca2+ range of 0.01-100 µM under steady state conditions. Under physiological conditions, a typical range of 0.1-1.0 µM

2+ of [Ca ]i has been observed (Kim et al., 1997; McCarron et al., 2006) and MLCK is

2+ 2+ activated transiently with respect to changes in [Ca ]i. A transient signal with Ca concentrations in the range of 0.2 – 1.2 µM showed corresponding activation of

MLCK with a steep relationship with Ca2+ in the range of 0.4 µM to 0.8 µM as seen in

Figure 3.15.

85

A B 1.2 50

1 40

0.8 e

v 30

i

t

c a

0.6

] (microM) ] +

2 20 MLCK

[Ca 0.4

percentage of total MLCK total of percentage 10 0.2

0 0 1 2 3 4 5 0 1 2 3 4 5 Time (second) Time (second)

C

Figure 3.15. A) Transient Ca2+ signal of concentrations 0.2 µM 0.4 µM, 0.6 µM, 0.8 µM, 1 µM and 1.2 µM. B) MLCK activation corresponding to the Ca2+ signal shown in (A). A 50% increase in the Ca2+ concentration from 0.4 µM to 0.6 µM resulted in an increase of 140% in MLCK activation. However a 50% increase in the Ca2+ concentration from 0.8 µM to 1.2 µM resulted in an increase of only 37% in MLCK activation. This reflects the steep relationship between MLCK activation and Ca2+ in the Ca2+ range of 0.4 µM to 0.8 µM as seen in Figure 3.14. C) Increase in Ca2+ concentration above 0.4 µM decreased the time taken for half-maximal (t1/2) activation of MLCK. t1/2 for 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 µM of Ca2+ are 2, 2.02, 1.99, 1.97, 1.96, and 1.96 s respectively.

A 50% increase in the Ca2+ concentration from 0.4 µM to 0.6 µM resulted in an increase of 140% in MLCK activation. However a 50% increase in the Ca2+ concentration from 0.8 µM to 1.2 µM resulted in an increase of only 37% in MLCK

86 activation. This reflects the steep relationship between MLCK activation and Ca2+ in the Ca2+ range of 0.4 µM to 0.8 µM as seen in both transient condition (Figure 3.15) and steady state condition (Figure 3.14). In addition to Ca2+ dependent change in amplitude of the MLCK activation, simulation under transient conditions (Figure 3.15) showed that increase in Ca2+ concentration increased the rate of activation of MLCK.

As shown in Figure 3.15, increase in Ca2+ concentration decreased the time taken for half-maximal activation of MLCK with a significant decrease in the Ca2+ range of 0.4

2+ µM to 0.8 µM. Hence, when the intracellular [Ca ]i increases above the threshold concentration, MLCK activation is triggered and contraction in initiated. The

2+ relationship between [Ca ]i and MLCK activation can be attributed to the active force behavior in SMCs. Experiments have shown that force development exhibited

2+ maximal sensitivity to [Ca ]i between 0.15 µM and 0.5 µM and also physiological stimuli increasing Ca2+ to a maximum of 0.6 µM - 0.8 µM produce full contraction

(Yagi et al., 1988).

3.3. MODULE II: Active force generation

The first component of the model, Module I predicted the Ca2+ dependent MLCK activation. The relationship between MLCK activation and cross-bridge formation between actin and myosin is explained in Module II. Module II, shown in Figure 3.16, describes the active force generation in SMCs and has been developed based on Hai and Murphy’s four state model described in Section 2.4.4 (Hai and Murphy, 1988).

2+ The activated form of MLCK (MLCKactive or (Ca )4CaM-MLCK) upregulates the availability of actin binding sites on the myosin light chains, allowing cross-bridge

87 formation and active force generation (Murthy, 2006). Here the concentration of

MLCKactive is calculated in Module I and is the key input to Module II. A second enzyme, myosin light chain phosphatase (MLCP), dephosphorylates the regulatory myosin light chain and the resulting conformational change inhibits cross-bridge formation. The level of cross-bridge formation thus depends on the balance between the activities of MLCKactive and MLCP.

Figure 3.16. Extended Hai and Murphy model. A = actin; M = myosin; Mp = phosphorylated myosin; MLCKactive = activated myosin light chain kinase; MLCP = myosin light chain phosphatase; ATP = adenosine-5'-triphosphate; K1-7 = reaction rate constants. The corresponding details can be found in Table 3.11.

The cross-bridge attachment rate (K3), detachment rate (K4) and latch bridge detachment rate (K7) influence the total number of cross-bridges and are shown as vertical transitions in Figure 3.16. The Ca2+ sensitive control mechanisms regulate the horizontal transitions in Figure 3.16, moving from a passive state (either decoupled or

88 in a latch bridge) to an active state in which cross-bridge cycling occurs upon an increase in intracellular Ca2+. The resulting four reactions are given in Table 3.11.

Table 3.11. Reactions involved in active force generation via cross bridge cycling, as described by Equations 3.3-3.6.

No. Reaction

1 A + M ↔ A + Mp

2 A + Mp ↔ AMp

3 AMp ↔AM

4 AM → A + M

Using the enzyme kinetics data of MLCK from Hong et al. (2009), phosphorylation of regulatory MLC by MLCKactive was modelled based on Henri-Michaelis-Menten enzyme kinetics whereby the flux is directly dependent on the enzyme concentration as shown in Equation 3.3 (Bowden, c2004). Thus, the rate of myosin phosphorylation is a function of the concentration of MLCKactive available at any given time. This control mechanism provides the link between the intracellular Ca2+ concentration and cross-bridge cycling and was used to extend the four state model of cross-bridge cycling (Hai and Murphy, 1988). The rate constants K1, K2, K5 and K6 controlling the phosphorylation and dephosphorylation of myosin in the original Hai and Murphy model have been replaced by Henri-Michaelis-Menten kinetics as shown in Equations

3.3 - 3.6. The evolution of the four species (M, Mp, AMp and AM) shown in Figure

3.16 with time is described by Equations 3.3 - 3.6. It was assumed that actin is present

89 in abundance and its concentration does not affect the cross-bridge dynamics. The concentration of MLCKactive in Equations 3.3 - 3.6 is received from Module I.

(3.3)

(3.4)

(3.5)

(3.6)

The sum of the concentration of the four species (M, Mp, AMp, and AM) at any point of time will be equal to the total myosin concentration ([M]total) and this was verified in the model solutions. In order to extract physically meaningful output from the model, the values of [Mp], [AMp] and [AM] were used to calculate the percentage of myosin phosphorylation and number of cross-bridges formed in a SMC as specified in

Equations 3.7 and 3.8.

90

(3.7)

where [M]total is the total myosin concentration. Upon myosin phosphorylation, active force is generated through the formation of cross-bridges (AMp) and latch-bridges

(AM).

(3.8)

The concentration of cross bridges (n) are normalized to their maximum value (nmax) as given in Equation 3.9. The maximum number of cross bridges was set to 80% of total myosin (Hai and Murphy, 1988).

(3.9)

Previous studies have suggested that active force, F can be considered to be proportional to the number of cross-bridges and latch-bridges (Gestrelius and

Borgstrom, 1986). Based on this premise, the fraction of attached cross- and latch- bridges, N, was used to estimate the resultant force,

(3.10)

91 where Fmax is the maximum achievable force. For N, a value of zero indicates the absence of any cross- or latch-bridges, and a value of one indicates the production of a maximal force where 80% of total myosin heads are bound to actin.

3.3.1. Module II: Parameter Estimation

To parameterize Module II, the model was simulated with transient calcium data obtained from gastric smooth muscle cells and the force values from the same experiment as shown in Figure 3.17. Ozaki et al. (1991a) measured the Ca2+ transients and spontaneous contractions in canine antral circular smooth muscle strip.

Figure 3.17. Spontaneous contractions and Ca2+ transients measured in antral circular smooth muscle by Ozaki et al. Data in the traces have been normalized to their respective maximum values (Ozaki et al., 1991a).

92

However, the experimental work reported calcium transients in terms of flourescence ratio (F340/F380) and did not give calibration details. Hence it was necessary to estimate the calcium concentrations corresponding to the ratio values reported. To overcome this, calcium concentration values corresponding to spontaneous slow waves with a plateau membrane potential of -40 mV were obtained from an electrophysiology model developed by Corrias and Buist (2007). The experimental curve for calcium was digitised with a resting Ca2+ concentration of 0.1 µM and a peak Ca2+ concentration of 0.326 µM (Kim et al., 1997; McCarron et al., 2006, Corrias and

Buist, 2007). The model was simulated with the digitised Ca2+ time course, as an input as shown in Figure 3.18. The values of K3, K7 and MLCP concentration were estimated by fitting to experimental data from canine antral smooth muscle (Ozaki et al., 1991a). As mentioned in Section 3.3, normalized force (N) was calculated as the total number of cross bridges normalized to their maximum value (80% of total myosin). The absolute difference between the experimental normalized force values and the predicted normalized force values from the model was used as the objective function for estimating the parameters (K3, K7 and MLCP). A mean square error of

1.957e-06 between the model normalized force and experimental normalized force was obtained.

A total myosin concentration of 45 µM was used in the model (Hong et al., 2009).

The steady state values of the various species of the module II at the resting Ca2+ concentration (0.1 µM) are listed in Table 3.13.

The experimental force values were also normalized to the maximum value of N, to facilitate the comparison between model results and experimental values and fitting of the model. The fitting of normalized force from the model to the experimental force

93 values is shown in Figure 3.18 and the parameters are shown in Table 3.12. The model showed a good fit to the experimental force behavior in the upstroke phase. However the relaxation phase produced by the model was slower than the experimental result.

3 Simulated normalized force

Experimental normalized force (Ozaki et al., 1991) 0.3 Calcium concentration (microM) 2

0.2

1

[Calcium] (microM) [Calcium] Normalized Force (%) Force Normalized

0 0.1

0 5 10 15 20 Time (second)

Figure 3.18. Fitting of the normalized force from the model to the experimental normalized force from Ozaki et al. (1991a). The corresponding input Ca2+ data is shown as dash dotted line. The parameter values are listed in Table 3.12.

94

Table 3.12. Parameters involved in active force generation via cross bridge cycling, as described by Equations (3.3) - (3.6), and their respective values. Vmax (= kcat. [E]) is the maximum reaction rate of enzyme E and Km is the substrate concentration at which a half-maximal reaction rate is achieved.

Parameters Values Ref.

(Persechini and Hartshorne, 1983; -1 kcat_MLCKactive 47 s Ikebe and Reardon, 1990; Lukas, 2004b; Hong et al., 2009)

(Persechini and Hartshorne, 1983; Km_MLCKactive 10 µM Ikebe and Reardon, 1990; Lukas, 2004b; Hong et al., 2009)

-1 K3 39.577 s fitted

K4 K3/4 (Hai and Murphy, 1988)

-1 (Ichikawa et al., 1996; Feng et al., kcat _MLCP 30 s 1999)

(Ichikawa et al., 1996; Feng et al., Km_MLCP 14.3 µM 1999)

-1 K7 29.333 s fitted

[MLCP] 7.703 µM fitted

Table 3.13. Steady state values of the various species of the module II at the resting Ca2+ concentration (0.1 µM).

Concentration Species (µM)

M 44.953

Mp 0.004

AMp 0.003 AM 0.006

95

3.4. Calcium, myosin phosphorylation and cross-bridge formation

The objective of the modelling work here is to study the relationship between the intracellular calcium concentration and active force production. Active force production in a smooth muscle cell is induced by phosphorylation of myosin by

MLCKactive and subsequent cross-bridge formation between actin and myosin. Myosin phosphorylation (Equation 3.7) was calculated at each Ca2+ concentration in the range

0.01-100 µM, under steady state conditions and is shown in Figure 3.19. A limiting free CaM concentration of 2 µM giving 60% of maximum MLCK activation resulted in a maximum of 61% of myosin phosphorylation with a constant MLCP concentration of 7.7µM. Ozaki et.al (1991a) showed a maximum of 0.3 mol Pi/mol light chain of myosin phosphorylation in smooth muscle exhibiting acetylcholine stimulated contractions which showed peak force five times higher than the peak of spontaneous contractions. Maximum contraction of SMCs have been observed at Ca2+ concentrations around 0.6 - 0.8 µM (Yagi et al., 1988). At 0.8 µM of Ca2+, 30% of myosin phosphorylation was predicted by the model. This is in close agreement with the myosin phosphorylation levels reported by Ozaki et.al (1991a) in agonist stimulated cells.

96

70

60

50

40

30

20

17.09

Myosin phosphorylation Myosin percentage of total myosin total of percentage 10 5.72 0 0.01 0.1 1 10 100 [Calcium] (microM)

Figure 3.19. Relationship between myosin phosphorylation and intracellular free 2+ [Ca ]i under steady state conditions. With a constant MLCP concentration, 2+ myosin phosphorylation also shows a sigmoid relationship with [Ca ]i. The two points (■) show the steady state myosin phosphorylation levels corresponding to 2+ the [Ca ]max values (0.4 µM and 0.6 µM) used for transient simulation in Figure 3.22.

3.4.1 Input Calcium Signal

After the steady state analysis, the model was simulated under transient conditions. A

2+ prescribed intracellular [Ca ]i transient, such as the one that accompanies membrane depolarization during a slow wave, was used as the input signal to the model to simulate the phasic contractions. Ca2+ transient function (Equation 3.11) was adapted

2+ from Mbikou et al. (2006) and the dynamics were modified to represent the [Ca ]i

2+ cycling typically observed in GI SMC by fitting t1,t2 ,t3 and Ca decay constant, k

(Kim et al., 1997; Corrias and Buist, 2007). The intracellular Ca2+ concentration rises

2+ 2+ from a resting value, [Ca ]r at time t1 to reach a maximum value, [Ca ]max at time, t2

2+ before returning to [Ca ]r at time t3.

97

(3.11)

2+ 2+ The values of [Ca ]r and [Ca ]max were derived from the intracellular calcium recordings from Kim et al. (1997) and McCarron et al. (2006). One such experimental

2+ [Ca ]i transient is shown in Figure 3.20 from Kim et al. (1997). Kim et al. (1997) reported Ca2+ peak values from 350 nM to 800 nM under various experimental conditions. Calcium recovery to its resting level (100 nM) was reported to be completed within 15-20 seconds. Vogalis et al. (1991) reported that on repolarization,

2+ intracellular [Ca ]i decreased slowly with a time constant of 2-3 seconds and the rate

2+ depended on the magnitude of intracellular [Ca ]i. Based on these experimental observations, for a calcium wave of three cycles per minute (Corrias and Buist, 2007), the estimated values of t1, t2 and t3 for the first cycle are 0 s, 2 s and 20 s, respectively.

A Ca2+ decay constant, k, equal to 0.4 s-1 was used. A typical calcium transient

2+ generated by Equation 3.11 is shown in Figure 3.20B for a [Ca ]max value of 600 nM.

98

Table 3.14. Values for the parameters used in Equation 3.11 for the first cycle of Ca2+ transient.

Parameter Value Ref

(Vogalis et al., 1991; Kim et al., 2+ [Ca ]r 0.1 µM 1997; McCarron et al., 2006; Corrias and Buist, 2007)

2+ (Vogalis et al., 1991; Kim et al., [Ca ]max 0.6 µM 1997; McCarron et al., 2006)

(Vogalis et al., 1991; Kim et al., t1 0 s 1997; McCarron et al., 2006; Corrias and Buist, 2007)

(Vogalis et al., 1991; Kim et al., t2 2 s 1997; McCarron et al., 2006; Corrias and Buist, 2007)

(Vogalis et al., 1991; Kim et al., t3 20 s 1997; McCarron et al., 2006; Corrias and Buist, 2007)

-1 (Vogalis et al., 1991; Kim et al., K 0.4 s 1997; McCarron et al., 2006)

A B

0.6

0.5

0.4

] (microM) ] 0.3

+ 2

[Ca 0.2

0.1

0 0 10 20 Time (second)

Figure 3.20. A) Ca2+ transients observed in guinea pig gastric myocytes under various experimentally evoked depolarizations (Kim et al., 1997). In cells held 2+ under voltage clamp at -80 mV, the resting [Ca ]i was 102 ± 6.3 nM. Upon 2+ repolarization to -80 mV, [Ca ]i slowly recovered to its resting level. Recovery 2+ was completed within 15-20 seconds. B) [Ca ]i transient produced by Equation 3.11 for the values listed in Table 3.14.

99

3.4.2 Simulation of Myosin Phosphorylation

Calcium transients with two different peak values, as shown in Figure 3.21, were used to study the relationship between Ca2+ and myosin phosphorylation. In the physiological situation, the intracellular Ca2+ concentration that is reached during a phasic activation is modulated by neurotransmitters and other agonists. Here, the

2+ 2+ [Ca ]max variable in the Ca input signal was used to represent different levels of cellular excitation (Kim et al., 1997; McCarron et al., 2006).

From Figure 3.21 and Figure 3.22, it can be seen that, as expected, an increase in the magnitude of the Ca2+ concentration results in increased myosin phosphorylation levels in the cell due to elevated levels of MLCKactive. Increasing Camax by 50% resulted in a 203.4% increase in the peak levels of myosin phosphorylation. This can be explained in part by considering Figure 3.14 and Figure 3.15 where it can be seen that the relationship between the Ca2+ concentration and MLCK activation is relatively steep at these Ca2+ levels. This result is also qualitatively consistent with experimental observations that have shown large changes in active force production for relatively small changes in Ca2+ levels (Ozaki et al., 1991a; Ozaki et al., 1991b).

2+ The basal tone was unaffected by the change in [Ca ]max.

100

0.7 [Ca2+] = 0.4 microM max [Ca2+] = 0.6 microM 0.6 max

0.5

0.4

] (microM) ] +

2 0.3 [Ca 0.2

0.1

0 0 10 20 30 40 50 60 Time (second)

2+ Figure 3.21. [Ca ]i transient produced by Equation 3.11 for two different 2+ [Ca ]max values.

16 [Ca2+] = 0.4 microM max 14 [Ca2+] = 0.6 microM max 12

10

8

6

4

Myosin phosphorylation Myosin percentage of total myosin total of percentage 2

0

0 10 20 30 40 50 60 Time (second)

Figure 3.22. Myosin phosphorylation produced in response to the two Ca2+ transients shown in Figure 3.21. Increasing Camax by 50% resulted in a 203.4% increase in the peak levels of myosin phosphorylation. This can be attributed to the steep relationship between the Ca2+ concentration and MLCK activation at these Ca2+ levels.

101

3.4.3 Simulation of Phasic Contraction

Upon myosin phosphorylation, active force is generated through the formation of cross-bridges (AMp) and latch-bridges (AM). As mentioned in Section 3.3, active force (F) can be considered to be proportional to the number of cross-bridges and latch-bridges [31] and based on this premise, the fraction of attached cross- and latch- bridges, N, was used as an estimate of the resultant force. For N, a value of zero indicates the absence of any cross- or latch-bridges, and a value of one indicates the production of a maximal force where all myosin heads are bound to actin. The simulated normalized force for the prescribed input calcium signal generated by

2+ Equation 3.11 with a [Ca ]max of 0.6 µM and compared to experimental force values from Ozaki et al. (1991a) is shown in Figure 3.23.

The simulated force exhibited some of the key characteristic features of the contraction patterns observed through experiments done at tissue and cellular level

(Himpens and Somlyo, 1988; Yagi et al., 1988; Ozaki et al., 1991a; Ozaki et al.,

1991b). Contraction was initiated after a short delay of 60 milliseconds following the rise in cytosolic Ca2+ and the maximum generated force also lagged behind the Ca2+ peak by 180 milliseconds. Yagi et al. (1988) showed several-hundred millisecond delay between stimulation and onset of force development. Yagi et al. (1988) attributed this delay to the step(s) linking Ca2+ and myosin light chain phosphorylation because a delay of several hundred milliseconds was seen between stimulation and the first significant increase in myosin light chain phosphorylation. The model results showed a 40 millisecond delay between rise in Ca2+ and increase in myosin phosphorylation and 160 millisecond delay between Ca2+ peak and myosin phosphorylation peak (Figure 3.22). Mechanical relaxation preceded the decline of

102 cytosolic Ca2+ and occurred at a faster rate. The resting force between the phasic

2+ 2+ contractions is non-zero and reflects the resting cytosolic Ca concentration ([Ca ]r).

This provides the basal tone onto which the phasic contractions are superimposed.

Simulated Experimental [Ca2+] (microM) 20 normalized Force normalized Force (Ozaki et al., 1991a) 0.6 15

0.4 10

0.2 Normalized Force (%) Force Normalized

5 (microM) [Calcium]

0 0

0 10 20 30 40 50 60 Time (second)

Figure 3.23. Normalized force predicted by the model for the prescribed Ca2+ 2+ transient with a [Ca ]max of 0.6 µM. The simulated normalized force values (solid line) are compared to experimental force data (dotted line) in the first cycle. The Ca2+ transient (dashed line) was generated by Equation 3.11. Contraction was initiated after a short delay following the rise in cytosolic Ca2+ and the maximum generated force also lagged behind the Ca2+ peak. Mechanical relaxation preceded the decline of cytosolic Ca2+ and occurred at a faster rate. Phasic contractions are superimposed on a non-zero resting tone. These are some of the characteristic features of the contraction pattern observed through experiments done at tissue and cellular level.

103

3.4.4 Effect of MLCP Concentration

As mentioned earlier in the Section 3.3, only the dynamic changes in MLCKactive are explicitly described and the MLCP concentration was assumed to be constant. With no direct data for the amount of MLCP in smooth muscle cells, the concentration of

MLCP had to be estimated through fitting as explained in Section 3.3. Th effect of changing the MLCP concentration on the force values is shown in Figure 3.24 for two contant values of MLCP concentration. Varying the constant concentration value of

MLCP altered the rate of relaxation and the amplitude of the force.

To study the effect of the MLCP concentration on the dynamics of cross-bridge formation, the normalized force values for each MLCP concentration were normalized to their respective maximum values and compared as shown in Figure 3.25. It was observed that changing MLCP concentration had an effect on both the onset of force development and the relaxation phase.

104

50 [MLCP] = 7 microM

[MLCP] = 2 microM 40

30

20 Normalized Force (%) Force Normalized 10

0 0 5 10 15 20 Time (second)

Figure 3.24. Effect of the MLCP concentration on the normalized force values. Changing the MLCP concentration has an effect on the amplitude of the force values and the relaxation phase.

1 [MLCP] = 7 microM

0.8 [MLCP] = 2 microM

0.6

0.4 Normalised Normalised Force

fraction of the their valuemaximum 0.2

0 0 5 10 15 20 Time (second)

Figure 3.25. Effect of the MLCP concentration on the normalized force values. The normalized force values for each MLCP concentration are shown relative to their respective maximum values to facilitate comparison. Changing the MLCP concentration has an effect on both the onset of force development and the relaxation phase.

105

In summary, the relationship between calcium and active force production depends on the level of myosin phosphorylation and cross-bridge formation. Myosin phosphorylation depends on the activities of MLCK and MLCP. Activation of MLCK is regulated by the intracellular calcium concentration and also depends on the concentration of CaM. The cooperativity between the three binding sites of CaM regulates the dynamic relationship between Ca2+ and MLCK activation. The availability of CaM influences the level of MLCK activation.

To validate the model, simulations were run using a second independent set of data.

Here, forces measured from spontaneously contracting canine antrum SM, as shown in Figure 3.23, were simulated (Ozaki et al., 1991a). The phasic contractile behavior predicted by the model shows a good qualitative agreement with the experimental observation as (Figure 3.23). The experimental force results available for gastric SMC

2+ have their corresponding [Ca ]i values reported in terms of the fluorescence ratio.

Lack of actual Ca2+ concentration data or the calibration details, has made it difficult

2+ to validate the model in terms of quantitative agreement. However the [Ca ]i values

2+ assumed are well within the working range of [Ca ]i observed widely in gastric

SMCs.

106

3.5. Function based description for Module I

2+ The steady state relationship between [Ca ]i and MLCK activity has been observed to follow a sigmoidal relationship (Gallagher et al., 1991; Persechini et al., 1994;

Gallagher et al., 1997; Persechini and Cronk, 1999; Geguchadze et al., 2004) and can be described by a mathematical function (Bursztyn et al., 2007). Similar to a detailed

2+ pathway description, a sigmoid function can describe the relationship between [Ca ]i and MLCK activation over a given Ca2+ range. Bursztyn et al. (2007) developed a uterine SM contraction model based on Hai and Murphy’s model using a function to describe MLCK activation (Bursztyn et al., 2007). Motivated by the simple implementation, a function based description for Module I was developed for gastric

SM contraction. While Bursztyn et al. (2007) described the parameter K1, which is the rate of phosphorylation of myosin light chain in the Hai and Murphy’s four state

2+ model, as a direct function of [Ca ]i, in this study the concentration of MLCKactive has

2+ been made a function of [Ca ]i.

Using fluorescent biosensor studies, the relationship between free Ca2+ and MLCK activation has been determined (Kasturi et al., 1993; Johnson et al., 1996; Persechini and Cronk, 1999; Geguchadze et al., 2004). MLCK activation increased with increase

2+ in intracellular [Ca ]i in a sigmoidal manner and started to reach steady state at

2+ approximately 5 µM free [Ca ]i (Persechini and Cronk, 1999). Based on the available data on Ca2+ concentration and MLCK activation, a direct function was adopted based on the Hill’s equation described for the co-operative binding between two molecules.

107

(3.12)

2+ Here, [Ca ]50 is the intracellular free calcium concentration producing half of the maximum activation of MLCK, and n is the Hill coefficient describing cooperativity between the binding molecules, here calcium and CaM bound MLCK. The Equation

3.12 can be considered to be a bundled description of the binding of four Ca2+ ions to

CaM bound with MLCK i.e. CaM-MLCK to form the active MLCK complex i.e.

2+ (Ca )4CaM-MLCK.

Since the availability of CaM is the limiting condition in the activation of MLCK

(Persechini and Stemmer, 2002), the concentration of CaM available for MLCK activation has been incorporated into Equation 3.12. The parameters of Equation 3.12 were determined from the experimental data from Persechini A et al. (Persechini and

2+ Cronk, 1999) (shown in Figure 3.3) and the values of [Ca ]50 and n are 1.149 µM and

2.376 respectively. The experimental results showed the relationship between

2+ 2+ intracellular free [Ca ]i and free (Ca )4CaM in the presence of two indicator proteins

(FIP-CBSM-38 and FIP-CBSM-41) with the peptide sequence of myosin light chain kinase and varying affinities. FIP-CBSM-38 has low affinity with Kd= 45 nM and FIP-

CBSM-41 has a high affinity of Kd= 2 nm. From the experimental results, the amount of

2+ (Ca )4CaM bound to MLCK can be estimated as the difference between the amount

2+ of free (Ca )4CaM concentration in the presence of low affinity protein FIP-CBSM-38

2+ and the amount free (Ca )4CaM concentration in the presence of high affinity protein

FIP-CBSM-41. By fitting the Hill equation (Equation 3.12) to the difference between these results, the parameters of the Equation 3.12 were estimated. The MLCKactive

108 concentration for a CaM concentration of 5.5 µM (the total CaM concentration used in pathway model) was estimated at various Ca2+ concentrations in a given range.

3.5.1 Results and Discussion

The steady state behavior of MLCKactive predicted by the function model differed from the behavior predicted by the pathway model as shown in Figure 3.26. The difference can be attributed to the difference in the method of fitting the parameters in function based model and the pathway model.

100 Function based MLCK activation

Pathway based MLCK activation 80

60

concentration

e

v i

t 40

c

a percentage of total CaM total of percentage

MLCK 20

0

0.01 0.1 1 10 100 [Calcium] (microM)

2+ Figure 3.26. Comparison of steady state relationship between [Ca ]i and MLCK activation between pathway based model and function based model. The function based model fitted to data from Persechini A and Cronk (1999) shows a slower rate of MLCK activation compared to the MLCK activation result from pathway model.

109

The MLCKactive concentration estimated by Equation 3.12 was used in Equations 3.3-

3.6 in Module II (Section 3.2.2) to predict the force generation in response to the given calcium. In the uterine contraction model, the rate of phosphorylation of myosin

2+ light chain by MLCK was defined as a Hill function of [Ca ]i (Bursztyn et al., 2007).

In the current model, MLCK active concentration is estimated through Hill function and then rate of phosphorylation is computed using Henri-Michaelis-Menten kinetics as explained in Section 3.3.

The function based model was then simulated with the prescribed calcium transient

2+ with [Ca ]max value of 0.6 µM and the phasic force response is shown in Figure 3.27.

0.6 6

0.4

4

] (microM) ]

+ 2 0.2

2 [Ca Normalized Force (%) Force Normalized

0 0

0 10 20 30 40 50 60 Time (second)

2+ Figure 3.27. Simulated normalized force for the prescribed [Ca ]i transient with 2+ a [Ca ]max of 0.6 µM. The total CaM concentration (5.5 µM) in pathway model was used as the concentration of CaM available for MLCK activation.

110

With 5.5 µM of calmodulin concentration ([CaM] in Equation 3.12), which is the total

CaM concentration used in the pathway model, the function based model produced a maximum normalized force (6.3%) which was less than the maximum normalized force produced by the pathway model (17.04%) (Figure 3.23 and Figure 3.27).

Increasing the [CaM] concentration to 12.395 µM produced normalized force with the peak equal to the one produced by the pathway model. A comparison between the normalized force results with the same peak value from the function model and pathway model show that, the onset of force development is faster in the function model inspite of a slower MLCK activation rate in the steady state condition and the resting force is greater than the resting force in the pathway model.

18 Simulated normalized force 16 from function based model 14 Simulated normalized force from pathway based model 12

10

8

6

Normalized Force (%) Force Normalized 4

2

0 0 10 20 Time (second)

Figure 3.28. Comparison between normalized force produced by the function based model (solid line) and the pathway model (dashed line). The onset of force development is faster in the function model and the resting value is greater than the resting value of the pathway model.

111

The function based model was next tested with an experimental Ca2+ transient from

Ozaki et al. (1991a) and compared with the experimental force values.

4 [Ca2+] (microM) Simulated normalized force 0.3 from function based model 3 Experimental normalized force (Ozaki et al., 1991) 0.25

2

0.2 [Calcium] (microM) [Calcium]

Normalized Force (%) Force Normalized 1 0.15

0 0.1

0 5 10 15 20 Time (second)

Figure 3.29. Normalized force from the function based model (solid line) for a given experimental Ca2+ transient (dashed line) from Ozaki et al. (1991a) is compared to the experimental normalized force values (dotted line). MLCP concentration of 7 µM used for the pathway model was used here in the function based model.

In Figure 3.29, it can be seen that the onset of force in the function based model precedes the experimental force. With the experimental force normalized to the peak force value from the model, the model shows a higher resting values compared to the experiment. The normalized force values during the relaxation phase were greater compared to the experimental force values. Increasing the MLCP concentration did not accelerate the relaxation phase as shown in Figure 3.30 for increased MLCP concentration of 10 µM.

112

3 Simulated normalized force from function based model Experimental normalized force 0.3 (Ozaki et al., 1991) [Ca2+] (microM) 2

0.2

1

[Calcium] (microM) [Calcium] Normalized Force (%) Force Normalized

0 0.1 0 5 10 15 20 Time (second)

Figure 3.30. Normalized force from the function based model (solid line) for a given experimental Ca2+ transient (dashed line) from Ozaki et al. (1991a) is compared to the experimental normalized force values (dotted line). An increased MLCP concentration of 10 µM affected only the amplitude of the force and did not have an effect on the relaxation phase.

The effect of MLCP concentration on normalized force predicted by the function based model was studied with three different MLCP concentrations as shown in

Figure 3.31. As the change in MLCP concentration affected the amplitude of the force values, the normalized force values were reported in relative to their maximum value to facilitate the comparison of the effect of MLCP on the relaxation phase. It was seen that MLCP concentrations greater than 7 µM had no significant effect on the relaxation phase. Hence, increasing the MLCP concentrations did not solve the problem of fitting the relaxation phase of the normalized force from the model to the experimental force values.

113

1 [MLCP] = 2 microM [MLCP] = 7 microM

0.8 [MLCP] = 12 microM

0.6

0.4 Normalised Normalised Force

fraction of the their valuemaximum 0.2

0 0 5 10 15 Time (second)

Figure 3.31. Effect of MLCP concentration on normalized force predicted by the function based model. The normalized force values are reported in relative to their maximum value to facilitate the comparison of the effect of MLCP on the relaxation phase. It is seen that MLCP concentration greater than 7 µM had no significant effect on the relaxation phase. Hence increasing the MLCP concentration did not solve the problem of fitting the relaxation phase of the normalized force from the model to the experimental force values.

This can be attributed to the MLCK activation dynamics in the function based model.

The MLCKactive concentration produced by the function based model and the pathway model for a given Ca2+ transient are compared in Figure 3.32. Under transient conditions, MLCK activation in function based model was rapid and greater compared to the pathway model. The MLCKactive concentration values have been normalized to their maximum value, since the values depend on the CaM concentration and the same total CaM value in function based model and pathway model produce different

MLCKactive concentrations. In Figure 3.32, the MLCKactive concentrations produced by

114 the pathway model and function based model were normalized to their respective maximum values and compared to study their temporal dynamics with respect to the

Ca2+ transient dynamics.

1 Function based model Pathway model 0.3

0.8 [Ca2+] (microM)

]

e v

i 0.6

t

c a

0.2

0.4

[MLCK [Calcium] (microM) [Calcium]

0.2 fraction of their maximum value maximum their of fraction

0 0.1 0 5 10 15 20 Time (second)

Figure 3.32. MLCKactive concentration (normalized to their maximum values) produced by the function based model (solid line) and the pathway model (dotted line) for a give Ca2+ transient (dashed line). It is seen that under transient conditions, MLCK activation in function based model is rapid and greater compared to the pathway model.

Though the function based model is able to predict the sigmoidal steady state relationship between MLCK activation and Ca2+ concentration, under transient conditions, the results differ from the pathway results. From Figure 3.32, it can be seen that under transient conditions, MLCK activation in function based model is rapid and greater in amplitude compared to the pathway model. Since MLCKactive concentration is estimated at each [Ca2+] (t) value, the function based model is not

115

2+ able to show the time delay between rise in [Ca ]i and the onset of rise in MLCKactive levels. Hence the onset of contraction is rapid in the simulations from the function based model compared to the onset of force development in the experimental data and the pathway based model. Though function based model is a comparatively simple description of MLCK activation and is capable of predicting the phasic contractile

2+ behavior for a given [Ca ]i transient, it has its limitations in predicting the temporal dynamics of the force behavior.

3.6. Summary

In this Chapter, the implementation of a pathway description for the Ca2+ dependent activation of MLCK is explained by describing the interactions between Ca2+, CaM

2+ and MLCK. MLCK, upon binding to (Ca )4CaM, gets activated and forms the active

2+ enzyme complex (MLCKactive). For a given Ca concentration, the model predicts the activation level of MLCK. A direct function based model for MLCK activation has also been implemented and tested. MLCKactive phosphorylates myosin light chain and enables cross-bridge formation between myosin and actin. According to sliding filament theory, cross-bridge formation leads to contraction of the SMC. MLCP on the other hand dephosphorylates myosin light chain and leads to detachment of the cross- bridges and hence relaxation of the SMC. MLCK activity and MLCP activity together with the cross-bridge cycling kinetics predict the fraction of total myosin forming cross-bridges with actin. From evidence in the literature, force was made proportional to the number of cross-bridges formed and the phasic force response elicited by

2+ transient [Ca ]i was simulated using the model. With descriptions for the electrical

116 activity of single gastric SM cells predicting the intracellular Ca2+ dynamics, the model provides a framework to study electro-mechanical coupling.

MLCK activation is the central mechanism in contraction of SMCs. One of the significant components of the model is the role of calmodulin and the properties of its three binding sites in regulating MLCK activation. CaM content has been reported to vary between different cell types. The effect of the CaM concentration on MLCK activation (Figure 3.8) shows the need for estimation of CaM content (bound and free) in specific cell types. The difference in the results from the preliminary and the extended pathway models, show how the binding dynamics between proteins influence the activities of the proteins. Module I has shown the active role of CaM in the MLCK activation pathway than just being a passive conduit for intracellular Ca2+.

Replacing the fixed rate constants for phosphorylation and dephosphorylation in Hai and Murphy’s model with Henri-Michaelis-Menten’ enzyme kinetics has enabled the study of regulation of myosin phosphorylation by MLCK and MLCP. Almost all the pathways mediating contraction through regulation of myosin phosphorylation, impose a positive or negative feedback on the activity of either MLCK or MLCP.

While MLCK has been studied extensively, there is lack of data on the cellular content of MLCP and activity of MLCP in SMCs. Hence, the concentration of MLCP had to be estimated and the effect of MLCP on the model behavior (Figure 3.24) shows it is a key player in Module II of the model.

The cross-bridge cycling kinetics has been retained the same way as in the Hai and

Murphy model. They are defined by the fixed parameters K3 and K4. Few studies have suggested time dependent variation in the cross-bridge cycling kinetics with a slower detachment rate during force maintenance in tonic SMCs (Arner and Hellstrand, 1983;

117

Hellstrand and Nordstrom, 1993; Vyas et al., 1994). Though this has not been addressed in the model at this stage due to lack of specific data for phasic SM, a more detailed description of the cross-bridge cycling kinetics would be a significant improvement to the existing four-state model.

In summary, the main objective of this chapter is to describe the link between Ca2+,

MLCK activation, myosin phosphorylation and cross-bridge formation. This has been achieved by bringing together two sets of experimental data: the relationship between

Ca2+ and MLCK activity and the relationship between Ca2+ and force. The link between Ca2+ and force observed at single cell level has been established by describing the Ca2+ activated biochemical reactions.

118

4. SMC relaxation mediated through MLCP regulation

4.1. Introduction

According to the MLCK activation model of active force production relaxation is brought about by a reduction in intracellular calcium and consequent decrease in

MLCK activity. However, studies have shown that the fall in tension is faster than would be predicted by calcium decline and MLCK inactivation alone (Yagi et al.,

1988; Ozaki et al., 1991a). Yagi et al. (1988) observed an uncoupling of force from the activating stimulus and a desensitization to calcium. The greater rate of muscle

2+ relaxation compared to the rate of decline in [Ca ]i can be attributed to this uncoupling. This suggested that, in addition to events following a decline in calcium, secondary mechanisms may play a regulatory role in the relaxation of SMC.

In Chapter 3 it was assumed that the MLCP concentration was constant. However, recent data have indicated pathways and molecules that inhibit or activate phosphatase activity under certain conditions (Yagi et al., 1988; Somlyo and Somlyo, 1994;

Hartshorne et al., 1998; Hartshorne et al., 2004). Studies have been carried out to characterize the type of phosphatase that is present in smooth muscle cells and is capable of binding to myosin and dephosphorylating the myosin light chains (Shirazi et al., 1994; Huang et al., 2004). Though the studies have yielded sometimes confounding results, pointing to more than one type of phosphatase, most of the results have pointed to type I phosphatase activity in SMCs. Biochemical and gene sequencing studies have shown that type I phosphatase consists of three main sub- units: (i) 38 kDa catalytic subunit called PP1cδ, (ii) 110 kDa – 133 kDa target binding

119 subunit called MYPT1, and (iii) a 20 kDa subunit with an unknown regulatory function (Ichikawa et al., 1996; Hartshorne et al., 1998; Khatri et al., 2001;

Hartshorne et al., 2004; Matsumura and Hartshorne, 2008). Modification of the PP1c subunit or the MYPT1 subunit alters the activity of the enzyme and/or binding of substrate to the enzyme.

Based on experimental evidence that MLCP is indeed regulated and dephosphorylation of myosin is caused by the phosphatase enzyme, the rapid relaxation due to a greater dephosphorylation rate compared to the decline of calcium in phasic SM cells can be attributed to activation of MLCP. The activation of MLCP can be considered to happen in two ways: i) direct activation of MLCP, and ii) down regulation of the pathways inhibiting MLCP activity.

MLCP activation by telokin: Phenotyping of the contractile properties of tonic and phasic SM has given insight into the presence of a 17-kDa acidic protein called telokin that is expressed exclusively in smooth muscle cells (Hong et al., 2009). Telokin is expressed at very high levels in intestinal, urinary, and reproductive tract smooth muscle, at lower levels in vascular smooth muscle, and at undetectable levels in skeletal or cardiac muscle and non-muscle tissues (Gallagher and Herring, 1991;

Herring et al., 2006; Khromov et al., 2006; Mahavadi et al., 2008). The tissue specific differential expression of telokin suggests that the protein may play a physiological role in the smooth muscle cell function. Wu et al (1998) showed that the major in situ

2+ effect of telokin was desensitization to [Ca ]i through a mechanism that does not affect phosphorylation but accelerates the dephosphorylation of the myosin light chains. The high abundance of telokin in phasic smooth muscles compared to tonic smooth muscles and the observed higher phosphatase activity of phasic smooth

120 muscle reflect a possible link between telokin and phosphatase activity (Gong et al.,

1992a). Studies have implicated telokin in the activation of MLCP in SMC (Wu et al.,

1998; Walker et al., 2001; Choudhury et al., 2004; Khromov et al., 2006). However the mechanism of activation has not yet been established.

The mylk1 gene encodes at least four protein products: two isoforms of the 220-kDa

MLCK, a 130-kDa MLCK, and telokin (Herring et al., 2006). Transcripts encoding these products are derived from four independent promoters within the mylk1 gene.

High levels of telokin transcription in phasic smooth muscle cells is mediated by a combination of cell- and tissue-restricted factors, acting together with more general transcription factors. Among different smooth muscle tissues, unique but overlapping sets of transcription factors have been found to direct high levels of telokin expression

(Herring et al., 2006).

Sobieszek et al., (2005) isolated actomyosin filament structures that contain endogenous CaM, MLCK and MLCP complexes. Purified myosin filaments have also been shown to contain endogenous CaM, MLCK and MLCP. Protein purification and sedimentation techniques have quantified the molar ratio of the molecules. The study has also shown the presence of telokin at a high molar ratio with myosin. When

2+ [Ca ]i & ATP were added to the actomyosin filament preparation, phosphorylation and dephosphorylation of the myosin light chains were observed similar to the contraction-relaxation cycle observed in intact smooth cells & tissue preparations.

During in vitro studies done on intact actomyosin structures and purified myosin filaments, telokin has been found to increase the dephosphorylation rate of the myosin light chains (Sobieszek et al., 2005). It has been suggested that telokin modulates the dephosphorylation of myosin by activating the endogenous MLCP associated with

121 actomyosin structure. This argument is plausible since MLCP is the key regulatory enzyme causing the dephosphorylation of myosin light chains. There are conflicting reports on the effect of telokin on MLCK activity. While Sobieszek et al (2005) claim that it inhibits the phosphorylation event mediated by MLCK, Khromov et al (2006) and Choudhury et al (2004) have shown that it does not affect the phosphorylation of myosin. Various mechanisms for telokin’s contribution have been tested. One of the possible modes of action being probed is the binding of telokin with the myosin filament structure and its contribution to the conformation state of the myosin filaments (Sobieszek et al., 2005; Hong et al., 2009). According to this argument, telokin acts on the substrate (myosin filaments) rather than on the enzymes (MLCK and MLCP) per se. There are reports on the ability of telokin to dimerize the MLCK complex causing activation of the phosphatase enzyme in the complex (Sobieszek et al., 2005).

It should be noted that most of the above mentioned observations made on telokin have been obtained from studies done in vitro (Wu et al., 1998; Walker et al., 2001;

Choudhury et al., 2004; Sobieszek et al., 2005). One of the significant works on telokin done in vivo by investigating telokin knockout mice has demonstrated the

2+ importance of telokin in regulating the relationship between [Ca ]i and force

(Khromov et al., 2006). The important finding of the experiments was that in telokin deficient mice, a marked decrease in myosin phosphatase activity was observed along

2+ with a significant leftward shift in the [Ca ]i-force relationship and an increase in myosin phosphorylation as compared to wild-type mice. These experiments were performed in the phasic phenotypic SM (ileal SM). However in tonic SM (aortic SM), there were no significant changes due to the telokin deficiency. Contrary to the results

122 from in vitro studies, there was no marked effect of telokin deficiency in the assembly and conformation of myosin filaments in the cell (Sobieszek et al., 2005).

The in vivo study showed a 0.3 pCa units leftward shift in the force calcium curve in

2+ telokin knockout (KO) ileal SM and a 2-fold greater force for a given [Ca ]i over the physiologically relevant steep portion of the force curve. The effect was nearly completely rescued by the addition of 15 µM S13D recombinant telokin. Hence the observed shift cannot be attributed due to any adaptive changes in expression of contractile proteins that occurred secondary to knockout of telokin. Telokin did not alter the calcium induced force development caused by activation of MLCK when

MLCP (MYPT1) was inhibited by microcystin. Hence it can be inferred that telokin’s action of accelerating the myosin dephosphorylation is not through inhibition of

MLCK activity.

Under the condition that neither MYPT1 (subunit of MLCP) or MLCK content differed in the telokin knockout mice and wild-type mice, the reduction in the rate of relaxation in SM of knockout mice and the rescue of the effect by addition of recombinant telokin, support the theory of activation of MLCP by telokin. Figure 4.1 shows the effect of addition of recombinant telokin to telokin KO ileal SM on the relaxation phase of Ca2+ induced contraction. However the temporal dynamics of

MLCP activation under physiological conditions has not yet been quantified.

123

Figure 4.1. Relaxation of Ca2+ induced force was significantly accelerated in telokin KO ileal SM upon addition of 10 µM of recombinant telokin. At the plateau phase of the Ca2+ induced force trace, MLCK activity was inhibited by the addition of MLCK inhibitor. The rate of relaxation was taken as an index of in vivo MLCP activity which is accelerated by the addition of recombinant telokin (Khromov et al., 2006).

The expression and role of telokin has thrown light on the differences in protein content between different SM types contributing to the phasic and tonic phenotype.

Quantification of telokin content has shown that it is expressed in abundance (27 ± 4.6

µM) in phasic type of SMCs while it is present in very low levels in tonic SMCs (6 ±

1.7 µM) (Khromov et al., 2006). An interesting observation is that the calcium-force relationship of the telokin knock-out mice was similar to the wild-type aortic SM calcium-force relationship. Hence, it can be said that telokin and its suggested activation of MLCP contribute for the observed difference in the [Ca2+] - force relationship and contractile behavior between phasic and tonic SMCs. This also points to a general mechanism of smooth muscles’ regulation in which the contractile properties of different smooth muscle are likely to be dictated by the expression levels of distinct subsets of signalling proteins.

124

Inhibition of MLCP: Most of the studies made on MLC phosphatase indicate two events that inhibit MLCP: i) phosphorylation of MYPT1, and ii) binding of a molecule called CPI-17 as a result of its phosphorylation to PP1c subunit (Gong et al., 1992a;

Shirazi et al., 1994; Somlyo and Somlyo, 1994; Hartshorne et al., 1998; Richards et al., 2002; Hartshorne et al., 2004; Murthy, 2006; Lincoln, 2007; Mahavadi et al., 2008;

Ohama et al., 2008). Inhibition of MLCP has been found to be mainly linked to agonist stimulation of SMC via numerous GPCRs and RhoA mediated pathways

(Gong et al., 1992b; Richards et al., 2002; Hirano et al., 2003; Murthy, 2006).

However, under conditions of electrical excitation and depolarization, there is no strong evidence for MLCP inhibition. Since the current model focuses on electro- mechanical coupling and not pharmaco-mechanical coupling (stimulation by agonists), inhibition of MLCP is beyond the scope of this work. Studies have indicated the activation of MLCP by inhibition/downregulation of the MLCP inhibitory pathways

(Ichikawa et al., 1996; Huang et al., 2004; Lincoln, 2007; Paul, 2009). PKA & cGK have been suggested to inactivate the inhibitory RhoA/ROK pathway and hence activate the MLCP. A possible role for telokin in activation of PKA & cGK has also been reported (Walker et al., 2001; Khromov et al., 2006).

From the available literature on MLCP regulation, a direct relationship between calcium and MLCP regulation cannot be established. However, from an analysis of the pathways leading to MLCP regulation and experimental results showing the temporal dynamics of calcium and force response, it can be argued that Ca2+ and/or

2+ the pathways leading to an increase in intracellular Ca , through secondary messengers are likely to mediate MLCP regulation.

125

4.2. MLCP regulation hypothesis

In antral smooth muscles, it has been demonstrated that the muscle force and MLC20

2+ phosphorylation decrease more rapidly than the decline in [Ca ]i after the peak phasic contraction (Ozaki et al., 1991a). This phenomenon may be due to a Ca2+ dependent

2+ and time dependent decrease in the [Ca ]I sensitivity of the contractile apparatus during phasic contractions. Such dissociation between [Ca2+] and force has been reported in phasic and mixed smooth muscles. Yagi et al. (1988) observed a shift in

2+ the coupling of the [Ca ]i signal and force production occurring in a time-dependent manner after the activation. Yagi et al. (1988) also found that Ca2+ sensitivity decreased with time in spontaneously contracting gastric smooth muscle cells.

Himpens et al. (1989) reported that Ca2+ sensitivity decreased during the contraction relaxation cycles in guinea pig ileum muscle.

There is compelling evidence in the literature that force is more closely related to phosphorylation than Ca2+. The fall in force has been observed to have good

2+ correlation with the rate of dephosphorylation rather than the rate of decline in [Ca ]i concentration (Ozaki et al., 1991a). Ozaki et al (1991a) suggested that the relationship between [Ca2+], myosin phosphorylation and contraction changes as a function of [Ca2+] in canine antral muscles and this may be due to a Ca2+ and time dependent phosphatase that regulates the level of myosin phosphorylation.

MLCK and MLCP are the two prominent players in regulating the contraction- relaxation cycle in SMC. The net phosphorylation and hence the force depends on the dynamic ratio between MLCK and MLCP activity (Gong et al., 1992a; Choudhury et al., 2004). Inhibition of smooth muscle phosphatase(s) using calyculin-A, a type-I

126 phosphatase inhibitor showed the abolition of one phase of relaxation in the smooth muscle as shown in Figure 4.2. The study clearly indicated the role of phosphates(s) in the relaxation phase of phasic contractions. The phosphatase inhibitor calyculin-A caused a significant increase in myosin phosphorylation without changing the Ca2+ transient. Hence the change in the contractile behavior in the presence of calyculin-A is effected through a change in myosin phosphorylation levels. Ozaki et al (1991) hypothesized presence of two types of phosphatases with the calyculin-A insensitive phosphatase(s) (type-2B phosphatase) regulating the initial phase of relaxation and a calyculin-A sensitive type-I phosphatase causing the second phase of relaxation as seen in Figure 4.2.

2+ Figure 4.2. Effect of MLCP inhibitor (calyculin-A) on [Ca ]i, muscle tension and MLC phosphorylation.Ca2+ transients and phasic contractions are displayed under control condition (0%) and during the presence of calyculin –A (at 68% of peak response) and at the maximal response to calyculin-A (100%). The initial phase of relaxation of the phasic contractions was not affected by calyculin-A, but the later phase was markedly reduced. The average level of MLC phosphorylation also increased in response to calyculin-A as shown by the bar graph. The change in the contractile behavior is correlated to the change in myosin phosphorylation due to MLCP inhibition (Ozaki et al., 1991a).

Figure 4.2 shows the effect of MLCP inhibition using calyculin-A in canine antral SM

(Ozaki et al., 1991a). A complete inhibition of MLCP in the model produced a steady state force. Hence 50 nM of MLCP was used to simulate the condition of MLCP

127 inhibition. Figure 4.3 shows the force behavior under 7 µM of MLCP and 50 nM

MLCP. Under very low MLCP conditions, decreased myosin dephosphorylation lead to increase in the amplitude of the force and slower relaxation to the resting state compared to the control condition. In the model with low [MLCP], the relaxation is

2+ predominantly caused by the MLCK inactivation in response to decrease in [Ca ]i and the cross-bridge cycling caused by the low levels of MLCP.

1 A B Normalized force Normalized force with 50 nanoM 0.03 with 7 microM of MLCP of MLCP 0.3 2+ 0.3 [Ca2+] [Ca ]

0.8 0.02

0.2 0.2

0.6 (microM) [Calcium]

Normalized force Normalized Normalized force Normalized

0.01 (microM) [Calcium]

0 0.1 0.4 0.1

0 5 10 15 20 0 5 10 15 20 Time (second) Time (second)

Figure 4.3. Effect of reduced MLCP concentration on the contractile behavior. A) Normalized force with a constant MLCP concentration of 7 µM showed rapid relaxation to the resting value. B) Normalized force with a constant MLCP concentration of 50 nM showed increase in the amplitude of force and greatly reduced relaxation.

From MLCP inhibitory studies, Ozaki et al (1991a) suggested that dephosphorylation of myosin may be accelerated in phasic smooth muscles causing rapid relaxation and the myosin dephosphorylation may be regulated by MLCP. However no studies have been done so far to estimate the amount of MLCP in SMCs during active contraction.

Based on the knowledge that MLCP is being regulated by intracellular proteins

(Section 4.1) and dephosphorylation of myosin in phasic SMCs is regulated by MLCP,

128 a hypothesis for MLCP regulation is proposed. According to our hypothesis, a Ca2+ and time dependent regulation of MLCP concentration leads to the regulation of dephosphorylation and hence relaxation in phasic SMCs.

Analyzing the [Ca2+]-force behavior reported in the experimental results (Yagi et al.,

1988; Ozaki et al., 1991a) and the predictions made from our model with only MLCK activation (Chapter 3), a mathematical formulation for MLCP regulation as function of Ca2+ and time is proposed as an embodiment of this hypothesis.

4.3. MLCP regulation model

Though telokin is associated with MLCP activation, there is no data in the literature as to the mechanism of activation. Also, no quantitative data on the dynamics of MLCP regulation is currently available. Hence, after analyzing the relationship between force and Ca2+, Ca2+ and time dependent variation in MLCP concentration is assumed to be causing rapid relaxation and a feedback equation regulating MLCP concentration is proposed.

(4.1)

The parameters control the concentration of MLCP with A controlling the amplitude of activation and ω (=1/τ) representing the time constant of MLCP activation. From

2+ Equation 4.1, the concentration of MLCP as a function of time and [Ca ]i can be predicted and linked to the Module II of the muscle model in Equations 3.3-3.6

(described in Section 3.2.2). The parameter, ω in Equation 4.1 was estimated using

129 the in-built MATLAB function “fminsearch” as described in the previous chapter

(Section 3.2.2). The force data from Ozaki et al (Ozaki et al., 1991a) shown in Figure

3.9 was used for fitting the parameter value. The value of the parameter, A, was derived from the telokin concentration in phasic SM cells. By linking MLCP activation to the telokin concentration in the SMCs through the parameter ‘A’, the amplitude of MLCP activation was made suggestive of the telokin level in the cell.

The values of A and ω were 27.4 and 2.5 s-1 respectively.

The MLCP dynamics predicted by Equation 4.1 for a given Ca2+ transient are shown in Figure 4.4. In the absence of experimental data, MLCP concentration was determined by Equation 4.1 using the parameter values estimated through fitting force values as shown in Figure 4.6. The concentration of MLCP increases from a basal resting value with increase in Ca2+ concentration and reaches a peak when Ca2+ concentration falls to 20% of its peak value.

The MLCP dynamics is shown in comparison to MLCK activation in Figure 4.5. It can be seen that peak of [MLCP] follows the peak of [MLCKactive]. The ratio between [MLCKactive] and [MLCP] is dynamically altered with time as a function of change in Ca2+ concentration. This ratio determines the phasic contractile behavior in the SMC. As seen in Figure 4.4 low levels of MLCP during the onset of Ca2+ increase, lead to rapid initiation of contraction. The steep increase in MLCKactive levels leads to rapid contraction with the peak myosin phosphorylation and contractile force corresponding to the peak in MLCKactive levels. The [MLCP] peak following the peak in [MLCKactive] with a time delay leads to rapid dephosphorylation of myosin and relaxation of the SMC as shown in Figure 4.6.

130

7 [Ca2+] 0.3 6 [MLCP]

5 0.25

4 0.2 [MLCP] (microM) [MLCP] 3 0.15 (microM) [Calcium]

2 0.1

0 5 10 15 20 Time (second)

Figure 4.4. The change in [MLCP] as a function of Ca2+ described by Equation 4.1. The concentration of MLCP increases from a basal resting value with 2+ 2+ increase in [Ca ]i and reaches a peak when Ca concentration falls to 20% of its peak value.

7 [MLCP] 0.5 [MLCK ] 6 active 0.4

5

0.3

] (microM) ]

e

v

i

t c

4 a

0.2

[MLCP] (microM) [MLCP] [MLCK 3 0.1

2 0

0 5 10 15 20 Time (second)

Figure 4.5. MLCP dynamics shown in comparison to MLCK activation. It can be seen that peak of [MLCP] follows the peak of [MLCKactive]. The ratio between [MLCKactive] and [MLCP] is dynamically altered with time as a function of 2+ change in [Ca ]i.

131

5 [Ca2+] (microM) 0.3 Simulated normalized force 4 Experimental normalized force (Ozaki et al., 1991)

3

0.2

2

[Calcium] (microM) [Calcium] Normalized Force (%) Force Normalized 1

0.1 0 0 5 10 15 20 Time (second)

Figure 4.6. Normalized force produced by the model with [MLCP] regulation. The corresponding Ca2+ transient (dash dotted line) and normalized experimental force (dotted line) are shown.

The model with MLCP regulation (Figure 4.6) gave a better fit with the experimental data compared to the model with [MLCP] held constant (Figure 3.18). The relaxation was faster in the [MLCP] regulated model. The t1/2 for relaxation was 1.28 seconds in the [MLCP] regulated model and 1.39 seconds in the constant [MLCP] model. Ozaki et al. (1991a) reported a t1/2 value of 1.1 seconds for relaxation as seen in the experimental data (Figure 4.6). It should be noted that the peak [MLCP] (6.42 µM) produced by the [MLCP] regulation model (Figure 4.4) was slightly less than the constant [MLCP] (7.70 µM) used in Chapter 3.

The peak force produced by the model with [MLCP] regulation was 1.78 times higher than the peak force produced by constant [MLCP] model. To enable comparison of

132 the temporal dynamics, the normalized force values from the [MLCP] regulation model and the constant [MLCP] model were normalized to their maximum values as shown in Figure 4.7.

1 With [MLCP] regulation

0.8 With constant [MLCP] Experimental data (Ozaki et al., 1991) 0.6

0.4 Normalized Force Normalized

fraction of maximum value maximum of fraction 0.2

0 0 5 10 15 20 Time (second)

Figure 4.7. Normalized force for a given experimental Ca2+ transient produced by the model with [MLCP] regulation (solid line) and with constant [MLCP] (dashed line). The force values from Figure 4.6 and Figure 3.18 are expressed as a fraction of their maximum value. The normalized experimental force values are shown as dotted line. The t1/2 for relaxation was 1.28 seconds in the [MLCP] regulated model and 1.39 seconds in the constant [MLCP] model. The experimental data shows a t1/2 value of 1.1 seconds as reported by Ozaki et al (1991a).

MLCP regulation, in addition to causing rapid relaxation, also affected the temporal dynamics of onset of force and the peak force. Contraction was initiated after a short delay of 210 milliseconds following the rise in cytosolic Ca2+ in the model with

MLCP regulation while in the model with constant [MLCP], contraction was initiated after a short delay of 240 milliseconds. The maximum generated force also lagged

133 behind the Ca2+ peak by 60 milliseconds in the [MLCP] regulated model and by 170 milliseconds in the constant [MLCP] model. The digitized experimental data from

Ozaki et al. (1991a) showed a delay of 374 milliseconds in the onset of increase in force and 110 milliseconds delay in the peak force in comparison to Ca2+ transient.

4.4. Effect of MLCP regulation on phasic contraction

2+ 2+ For a prescribed Ca transient (Equation 3.11) with a [Ca ]max of 0.6 µM, the [MLCP] regulation model produced the characteristic phasic contractile behavior (Figure 4.8) as explained in Section 3.4 similar to the constant [MLCP] model. However dephoshorylation and relaxation were faster in the [MLCP] regulated model as seen in

Figure 4.11. The transient change in MLCP concentration for the prescribed Ca2+ data is shown in Figure 4.9.

Simulated normalized force [Ca2+] (microM) 20 0.6

0.4

10 [Calcium] (microM) [Calcium]

Normalized Force (%) Force Normalized 0.2

0

0 10 20 30 40 50 60 Time (second)

Figure 4.8. Phasic contraction produced by the [MLCP] regulated model for a 2+ 2+ prescribed Ca transient (dashed line) with a [Ca ]max of 0.6 µM.

134

0.8 [MLCP] [Ca2+] 10

0.6 8

0.4

6 [MLCP] (microM) [MLCP]

0.2 (microM) [Calcium] 4

2 0 0 10 20 30 40 50 60 Time (second)

Figure 4.9. Change in [MLCP] (solid line) for the prescribed Ca2+ transient 2+ (dashed line) with a [Ca ]max of 0.6 µM. Maximum value of [MLCP] is reached when the Ca2+ falls to 40% of the peak value.

10 With [MLCP] regulation

With constant [MLCP] 8

6 [MLCP] (microM) [MLCP] 4

2 0 5 10 15 20 Time (second)

Figure 4.10. Change in MLCP concentration with time in response to the Ca2+ transient shown in Figure 4.9. The constant MLCP concentration used in the model without [MLCP] regulation is shown as dashed line. The effect of changing [MLCP] and constant [MLCP] on myosin phosphorylation and force is shown in Figure 4.11.

135

The effect of [MLCP] on myosin phosphorylation is shown in Figure 4.11A. The dephosphorylation with a t1/2 of 0.73 seconds in the [MLCP] regulated model was slightly faster compared to the dephosphorylation with a t1/2 of 0.97 seconds generated by the constant [MLCP] model. Regulation of [MLCP] affects the contractile behavior by regulating the phosphorylation of myosin in the model. The normalized force values from the model with [MLCP] regulation and constant [MLCP] for one cycle of the prescribed Ca2+ transient in Figure 4.11B.

A B 20 20

With [MLCP] regulation With [MLCP] regulation

With constant [MLCP] With constant [MLCP] 15 15

10 10

Phosphorylation 5

5 (%) force Normalized percentage of total myosin total of percentage

0 0

0 5 10 15 20 0 5 10 15 20 Time (second) Time (second)

Figure 4.11. Effect of [MLCP] regulation on myosin phosphorylation and force. A) [MLCP] regulation had an effect on the onset of myosin phosphorylation and rate of dephosphorylation. B) By regulating the myosin phosphorylation, the change in [MLCP] with time affected the contractile behavior as seen by the change in force values with (solid line) and without (dashed line) [MLCP] regulation.

MLCP regulation resulted in an 8% reduction in the t1/2 for relaxation as shown in

Figure 4.12 . Khromov et al., (2006) showed a 17% reduction in the t1/2 for relaxation when the telokin knockout ileal SM was treated with 10 µM of recombinant phosphorylated telokin (Figure 4.1).

136

20

With [MLCP] regulation

With constant [MLCP] 15

10 Phosphorylation

5 percentage of total myosin total of percentage

0

3 3.5 4 4.5 5 5.5 6 Time (second)

Figure 4.12. Dephosphorylation of myosin in the model with [MLCP] regulation (solid line) and constant [MLCP] (dashed line). The myosin phosphorylation 2+ 2+ curve for the prescribed Ca transient with [Ca ]max of 0.6 µM shown in Figure 4.11 is re-plotted to show only the dephosphorylation phase.

4.5. Summary

In summary, a feedback equation (Equation 4.1) for regulating MLCP concentration has been proposed. By fitting the parameters of the equation to experimental force data, the MLCP dynamics were predicted for the given input Ca2+. The model was simulated with a prescribed Ca2+ transient and the effects of MLCP regulation on the myosin light chain phosphorylation and contractile behavior are studied.

The main motivation to extend the model framework described in Chapter 3 was to simulate the rapid relaxation shown by experimental results. As discussed in Chapter

3, changing the constant value of [MLCP] did not induce rapid relaxation. From telokin knockout studies, a crucial link between telokin and contractile behavior has been established. Telokin’s role in accelerating the myosin dephosphorylation and hence the relaxation has been associated to activation of MLCP from MLCP activity assays. However the exact mechanism of MLCP activation by telokin and the mode of

137 interaction between telokin and MLCP are not yet known. Once the reaction scheme for MLCP activation is available, the Equation 4.1 can be modified to describe the reaction kinetics.

2+ Yagi et al. (1988) observed a shift in the coupling of the [Ca ]i signal and force production occurring in a time-dependent manner after the activation. From the results

2+ it can be observed that the desensitization to [Ca ]i in the form of MLCP activation is a slow process taking many seconds to develop and persist for few seconds after the

2+ decline in [Ca ]i and MLCK activation. In phasic SM types such as the gastric cells that contract rhythmically, the relaxation event after the contraction is important for the proper functioning of the tissue. Hence a desensitization process could be playing role in the relaxation process of phasic SMCs, similar to the sensitization processes

2+ helping in maintenance of tone at lower [Ca ]i levels in tonic SMCs (Himpens et al.,

1990; Somlyo and Somlyo, 2003). Though the results from Yagi et al. (1988) do not give any information about the mechanisms that might cause the desensitization, they strongly suggest the presence of such a regulatory mechanism causing a negative feedback on the force production. Here in this study MLCP regulation was hypothesized as the negative feedback mechanism.

The time dependent change in MLCP concentration in addition to regulating the relaxation phase also had accelerated the time taken to reach the peak force. Low levels of MLCP at the initiation of contraction, cause rapid initiation of contraction.

2+ Slow increase of MLCP with the peak following the [Ca ]i peak and MLCKactive peak, caused accelerated relaxation after the maximum force was reached. The model results predict the physiologically observed phenomenon of rapid activation of contraction and rapid relaxation following maximum force. However the MLCP

138 regulation had only a minimal effect on the relaxation dynamics with 8% reduction in the t1/2 for relaxation. The model could not fully predict the fall in force near the return to basal tone. It is likely that there are other Ca2+ desensitizing mechanisms and

2+ feedback mechanisms present in phasic SMCs that dissociate force from the [Ca ]i.

139

5. Ca2+ induced Ca2+ desensitization.

5.1. Regulation of Ca2+ Sensitivity

2+ Slow waves induce a transient increase in the intracellular [Ca ]i concentration and a corresponding increase in muscle tension. Contraction is initiated after the increase in

2+ [Ca ]i with a short delay of few hundred milliseconds and the peak of the contraction

2+ occurs after the peak in [Ca ]i. In Chapter 3 and Chapter 4, the typical phasic calcium-force behavior observed in SMCs under normal slow wave depolarizations

2+ has been described. However, experimental conditions that induce abnormal [Ca ]i transients, e.g., a sustained high calcium concentration over time, have shown different force behavior which cannot be explained with the model described in

Chapter 3 and Chapter 4.

Ozaki et al. (1991a) showed that the relationship between Ca2+, MLC phosphorylation

2+ and force changes as a function of [Ca ]i in canine antral SMCs. In Figure 5.1, an external solution with 59.5 mM of KCl caused an increase in Ca2+ and tension. While

2+ the [Ca ]i reached a relatively stable phase with only a slow decline after reaching its maximum value, the muscle tension reached a maximum level and relaxed to the

2+ 2+ resting state before the decline in [Ca ]i. During the slow decline in [Ca ]i, muscle tension reached its maximum value and declined more rapidly. This suggests that the

2+ [Ca ]i sensitivity of the contractile apparatus decreased over time.

140

Figure 5.1. Experimental result from canine antral smooth muscle showing a sustained maintenance of high calcium concentration as a result of elevated K+ in the external solution (Ozaki et al., 1991a). The experimental result showed muscle tension declining rapidly after reaching a peak in comparison to a slowly 2+ 2+ declining Ca and relaxed to the resting state much before [Ca ]i reached its resting value.

Previous studies have shown that regulation of calcium sensitivity is predominantly achieved through agonists and is caused by the regulatory pathways mediated by the

2+ agonists. However, Yagi et al. demonstrated that [Ca ]i sensitivity decreased

2+ spontaneously with time (Yagi et al., 1988). Himpens et al. showed that [Ca ]i sensitivity also changed during stimulation with a high K+ solution (Himpens et al.,

1988; Himpens and Somlyo, 1988; Himpens et al., 1989). Ozaki et al. has also shown

2+ that modulation in [Ca ]i sensitivity occurred independently of agonist stimulation, during depolarization by elevated external K+ or other exogenous stimuli (Ozaki et al.,

1991a; Ozaki et al., 1992). Thus it appears that the sensitivity of the contractile

2+ response is dynamically altered depending on the [Ca ]i signal irrespective of the mode of stimulation.

141

2+ [Ca ]i sensitization was observed to be time dependent and depends on the rate of

2+ change of [Ca ]i (Ozaki et al., 1991a). During rapid changes in calcium, as observed

2+ during spontaneous activity, a steep relationship between [Ca ]i and force was observed (Ozaki et al., 1991a; Ozaki et al., 1993). However, during slow changes in

2+ [Ca ]i, calcium desensitization occurred and caused a decrease in force. These

2+ observations lead to the hypothesis that one or more [Ca ]i desensitizing

2+ mechanism(s) are activated when there is a slow change in [Ca ]i.

To understand if myosin phosphorylation is also involved in this feedback mechanism,

2+ MLC phosphorylation was measured with respect to [Ca ]i (Himpens et al., 1988;

Ozaki et al., 1991a; Ozaki et al., 1993). Changes in MLC phosphorylation were

2+ closely correlated with the change in muscle tension rather than the change in [Ca ]i.

The rate of relaxation and dephosphorylation were faster than the decay rate of calcium. This implies that the desensitization mechanism is related to or rather regulates myosin phosphorylation. During rapid calcium transients, the shift in the activation-inactivation mechanism contributes to the phasic behavior. During an

2+ 2+ increase in [Ca ]i, the activation mechanisms cause contraction and during [Ca ]i decrease, the inactivation mechanisms become predominant and cause relaxation. As discussed in Chapters 3 and 4, the ratio of activities of MLCK and MLCP influence the level of myosin phosphorylation and hence the active force (Gong et al., 1992a).

The regulation of this ratio by any change in MLCK activity, MLCP activity, or both, can lead to the observed behavior of myosin phosphorylation and force. One potential

Ca2+ desensitizing mechanism reported in the literature is the Ca2+/CaM dependent protein kinase II (CaMKII) regulated phosphorylation of MLCK (Tansey et al., 1992;

Stull et al., 1993; Tansey et al., 1994; Word et al., 1994; Murahashi et al., 1999).

142

5.2. Hypothesis 1 – Calcium desensitization through MLCK

phosphorylation

Purified myosin light chain kinase is phosphorylated at a specific serine site A (serine

512) in the regulatory domain by activated Ca2+/CaM dependent protein kinase II

(CaMKII) (Ikebe and Reardon, 1990). From peptide sequencing studies, the phosphorylation site is believed to be in proximity to the CaM binding site (Tansey et al., 1992). The phosphorylation of MLCK at the specific serine site has been found to

2+ result in reduced affinity of the enzyme for (Ca )4CaM and the dissociation constant

(Kd) has been found to increase by approximately 25 times compared to the non- phosphorylated MLCK (Kasturi et al., 1993; Hong et al., 2009). Non-phosphorylated

MLCK is a high affinity target protein of CaM with a Kd approximately 1 nM and also

CaM bound to MLCK has been shown to bind Ca2+ at its C-terminal site at a faster rate with enhanced affinity (Johnson et al., 1996).

Goeckeler et al. (2000) and Conti et al. (1981) have identified and characterized more than one kinase with MLCK as one of their substrates. Their studies mainly point towards cAMP-dependent protein kinase, CaMKII and PKC. However the catalytic properties of the kinases have been reported to vary. Among the various kinases,

2+ CaMKII activation has been found to be dependent on (Ca )4CaM for its activation.

Experiments done under calcium depleted conditions and KCl stimulation, have shown CaMKII activation to be Ca2+ dependent (Tansey et al., 1992; Tansey et al.,

1994). Hence, the kinase and its activity are likely to play a role in Ca2+ dependent desensitization.

143

2+ Tansey et.al. (1994) showed that MLCK activity declined when the [Ca ]i was increased in steps from 0.01 to 2 microM with each step at various intervals (30, 60 and 120 seconds). A significant observation was that MLCK phosphorylation happened at significantly greater Ca2+ concentrations compared to the Ca2+ concentration required for MLCK activation. This was attributed to the greater

2+ concentration of (Ca )4CaM being required for activation of CaMKII relative to

2+ MLCK. As [Ca ]i was increased, activity ratio for MLCK decreased. The decrease was higher for the time interval of 60 seconds compared to 30 seconds after increasing

2+ [Ca ]i. The MLCK activity ratios measured at 60 seconds and 120 seconds interval were the same indicating a steady state had been reached at 60 seconds.

It has been shown that MLCK bound to CaM cannot be phosphorylated by CaMKII

(Ikebe and Reardon, 1990; Tansey et al., 1992; Tansey et al., 1994). Hence it is possible that under the condition where MLCK is in excess to a limited level of free

CaM, the free unbound MLCK is phosphorylated by activated CaMKII. With a high

Ca2+ concentration, CaMKII would be in competition with MLCK for binding to

2+ (Ca )4CaM. In addition, phosphorylation of MLCK reduces its affinity for

2+ 2+ (Ca )4CaM, allowing for more (Ca )4CaM to be bound to CaMKII (Kasturi et al.,

1993; Hong et al., 2009). Hence phosphorylation of the unbound MLCK would alter the activation dynamics of the myosin light chain kinase and subsequently affect the level of myosin phosphorylation.

CaMKII activation is known to be Ca2+ dependent and the observed phosphorylation of MLCK by CaMKII has been widely hypothesized to be a Ca2+ dependent negative feedback loop on MLCK activation and hence MLC20 phosphorylation (Stull et al.,

1993; Tansey et al., 1994). Hence the mechanism of MLCK phosphorylation has been

144 integrated with the main pathway model (Chapter 3) to test the hypothesis that MLCK phosphorylation alters the Ca2+ sensitivity of force at high Ca2+ concentrations. Two

Ca2+ signals (Figure 5.1 and Figure 5.11) reported in the experimental work of Ozaki et al. (1991a) have been used as inputs to the model to observe the dynamics of

MLCK activation in the presence and absence of MLCK phosphorylation. The objective here is to show that MLCK phosphorylation could be a possible mechanism for Ca2+ desensitization in SMCs during high and sustained Ca2+ transients.

5.2.1. MLCK phosphorylation pathway

The reaction pathway that describes the Ca2+ dependent phosphorylation of MLCK is shown in Figure 5.2. The section of the Figure 5.2 in red shows the reactions leading to MLCK phosphorylation that has been added to the model to account for calcium

2+ desensitization at higher [Ca ]i levels.

145

2+ Ca CaMfree

2+ (Ca )4CaM

CaMKII

2+ (Ca )4CaM-CaMKII

MLCK MLCK P Phosphatase

2+ 2+ (Ca )4CaM-MLCK (Ca )4CaM-MLCK P

Myosin Myosin P Myosin Light Chain Phosphatase (MLCP)

Figure 5.2. Reaction scheme showing phosphorylation of MLCK catalysed by CaMKII 2+ and binding of phosphorylated MLCK to (Ca )4CaM.

The approach reported by Lukas (2004b) was used to model the Ca2+ dependent phosphorylation of MLCK. In this model, the parameters of the enzyme kinetics of

MLCK phosphorylation are made a direct function of Ca2+.

2+ (Ca )4-CaM-CaMKII

Kfwd

MLCK MLCKp

Krev Phosphatase

Figure 5.3. Reaction scheme showing phosphorylation of MLCK catalysed by the CaMKII and dephosphorylation by unknown phosphatase.

146

Using mass action kinetics, the reaction scheme shown in Figure 5.3 was defined by the Equation 5.1. The forward reaction with rate constant Kfwd defining the phosphorylation of MLCK was assumed to follow Henri-Michaelis-Menten kinetics.

(5.1)

y1 and y2 are the parameters

determining the Ca2+ dependence of MLCK phosphorylation. CaMKII activation by

2+ 2+ increase in Ca is represented by the parameter Vmax. Increase in [Ca ]i, in addition to causing MLCK activation (Module I) also leads to phosphorylation of MLCK as

2+ shown in Figure 5.3. Phosphorylated MLCK then binds to (Ca )4CaM as shown in

2+ the reaction scheme in Figure 5.4 to form (Ca )4CaM-MLCKp. In the absence of experimental data on the dephosphorylation kinetics of MLCK, the dephosphorylation reaction of MLCK in Figure 5.3 was modelled with a fixed rate constant.

Kfwd

2+ 2+ MLCKp + (Ca )4CaM (Ca )4CaM-MLCKp

Krev

Figure 5.4. Reaction scheme showing binding of phosphorylated MLCK to (Ca2+)4CaM.

147

(5.2)

Equations 5.1 and 5.2 define the negative feedback mechanism due to MLCK phosphorylation. At higher calcium concentrations, MLCK phosphorylation will be driven forward, as shown in Figure 5.3, and the phosphorylated MLCK binds to

2+ (Ca )4CaM (Figure 5.4) with reduced affinity as compared to unphosphorylated

MLCK. The values of the parameters were estimated by fitting to experimental result shown in Figure 5.1 and the resulting values are reported in Table 5.1.

Table 5.1. Parameters involved in the MLCK phosphorylation pathway described by Equations 5.2 and 5.3.

Reaction Parameters Ref

-1 y1 = 3 s

y2 = 0.6 µM MLCK ↔ MLCKp Fitted Km = 0.5 µM -1 Krev = 0.05 s

(Johnson et al., -1 -1 Kfwd = 2 µM s 1996; Lukas, 2+ ↔ 2+ MLCKp + (Ca )4CaM (Ca )4CaM-MLCKp -1 Krev = 0.1 s 2004b; Hong et al., 2009)

148

5.2.2. Results and Discussion

Figure 5.1 shows the contractile behavior of canine antral SM when intracellular

2+ + 2+ [Ca ]i was increased by increasing the external K concentration. [Ca ]i increased rapidly, reached a maximum within 1 minute and reached a plateau like phase with a slow decay rate for around five minutes. Muscle tension also increased, reached a maximum at about two minutes and then decreased before the onset of significant

2+ decline in [Ca ]i.

2+ The model was simulated with the [Ca ]i input signal shown in Figure 5.1. The force behavior predicted by the model is given in Figure 5.5. In the experimental result shown in Figure 5.1, the maximum force value attained during the plateau like slow

2+ declining phase of [Ca ]i was 5 times the peak force value achieved during the initial rapid Ca2+ transients. Without MLCK phosphorylation, the model predicted a maximum force value 29 times the peak force value achieved during rapid Ca2+ transient (Figure 5.5A). However in the presence of MLCK phosphorylation, the maximum force value produced decreased to 13 times the peak force value in the initial the rapid Ca2+ transient (Figure 5.5B). This shows that MLCK phosphorylation did indeed reduce the force reponse to Ca2+ at high Ca2+ levels as seen in Figure 5.5.

In terms of the temporal response and shape, the results from the model with MLCK phosphorylation showed better qualitative agreement with experimental force behavior compared to the model without MLCK phosphorylation. The rate of force development during the induced Ca2+ transient (from one to six minutes in Figure 5.5) was slower in the model with MLCK phosphorylation compared to the model without

MLCK phosphorylation reaction.

149

Without MLCK With MLCK phosphorylation phosphorylation

3 3 N (%) 0.3 A B 0.3 [Ca2+] (microM) N (%) [Ca2+] (microM)

2 2

0.2 0.2

N (%) N N (%) N

1 1

0.1 0.1

[Calcium] (microM) [Calcium] [Calcium] (microM) [Calcium]

0 0 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time (min) Time (min)

1 C Ca2+ 1 D Ca2+ N 0.8 N 0.8

0.6 0.6

0.4 0.4

Fraction of maximum of Fraction Fraction of maximum of Fraction 0.2 0.2

0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time (min) Time (min)

Figure 5.5. Effect of MLCK phosphorylation on the simulated force behavior for 2+ a given [Ca ]i signal. A) Normalized force (N) produced by the model without MLCK phosphorylation, B) Normalized force (N) produced by the model in the presence of MLCK phosphorylation mechanism and C) &D) Normalized force is shown as fraction of maximum value in the absence and presence of MLCK phosphorylation mechanism respectively. MLCK phosphorylation leads to 2+ desensitization producing less force at high [Ca ]i levels with no significant effect on the response to rapid Ca2+ transients.

150

The force response in the presence of MLCK phosphorylation can be attributed to the

2+ 2+ formation of the active MLCK pool ((Ca )4CaM-MLCK and (Ca )4CaM-MLCKp) as shown in Figure 5.6B. In the presence of high sustained Ca2+, MLCK is

2+ phosphorylated as shown in Figure 5.6A. MLCK binds to (Ca )4CaM rapidly while

2+ MLCKp binds to (Ca )4CaM with reduced affinity. Phosphorylation causes a shift in

2+ 2+ the Ca sensitivity of MLCK by reducing its affinity to (Ca )4CaM. This is shown by

2+ the time lag in the formation of the (Ca )4CaM-MLCKp complex. It was noted that

2+ MLCK phosphorylation and formation of (Ca )4CaM-MLCKp are not significant during the rapid Ca2+ transients.

10 0.1 [(Ca2+) CaM-MLCK] [MLCK ] 0.3 4 0.3 p [(Ca2+) CaM-MLCK ] 4 p A [Ca2+] B [(Ca2+)]

8

0.2 0.2 ] (microM) ]

e 0.05

] (microM) ]

v

i

t

p

c a 6

0.1 0.1

[MLCK

[Calcium] (microM) [Calcium]

[Calcium] (microM) [Calcium] [MLCK

4 0 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time (min) Time (min)

Figure 5.6. Effect of MLCK phosphorylation mechanism on the activation of 2+ MLCK. A) MLCK phosphorylation (solid line) and B) formation (Ca )4CaM- 2+ 2+ MLCK (solid line) and (Ca )4CaM-MLCKp (dashed line) for a given Ca signal (dotted line) are shown. Ca2+ dependent MLCK phosphorylation and reduced 2+ affinity of phosphorylated MLCK to (Ca )4CaM leads to slow formation of 2+ 2+ (Ca )4CaM-MLCKp compared to the rapid formation of (Ca )4CaM-MLCK.

Figure 5.7 shows the effect of MLCK phosphorylation mechanism on the activation of

MLCK. At sustained high Ca2+ levels, phosphorylation of MLCK leads to lower levels of MLCK activation.

151

5 with MLCK phosphorylation

without MLCK phosphorylation

4

e v

i 3

t

c a

MLCK 2

percentage of total MLCK total of percentage 1

0 1 2 3 4 5 6 Time (min)

Figure 5.7. Effect of myosin phosphorylation on MLCK activation at sustained 2+ high Ca concentration. Concentration of MLCKactive complex as a percentage of total MLCK for a given Ca2+ input shown in Figure 5.6 is shown in the presence (solid line) and absence (dashed line) of MLCK phosphorylation mechanism. It can be seen that MLCK phosphorylation affects both the magnitude and temporal dynamics of MLCK activation.

It should be noted here that reduced affinity of phosphorylated MLCK becomes important under the condition of limited free intracellular CaM and competitive binding of other high affinity target proteins to CaM. MLCK cannot be phosphorylated at the regulatory site by a kinase when it is bound to CaM. If there is excess CaM, it would inhibit MLCK phosphorylation by binding to MLCK. Hence the hypothesis presented here would not hold under the condition of excess free CaM. If free intracellular CaM is present in limited levels, as has been shown by experimental studies (Persechini and Stemmer, 2002), the model predictions indicate that MLCK

2+ phosphorylation regulates the Ca sensitivity of MLC20 phosphorylation and hence

152 force production in SMCs. The distribution and concentration of CaM and MLCK

(free vs. bound) is important in this regulation. Thus according to this model, Ca2+ positively regulates MLC20 phosphorylation via MLCK activation and negatively regulates MLC20 phosphorylation via activation of CaMKII and down regulation of

MLCK activation at higher Ca2+ levels. According to Tansey et al. (1994), this model represents a unique cellular mechanism that involves a decrease in Ca2+ sensitivity rather than a decrease in Ca2+ per se.

The model results support the hypothesis that MLCK phosphorylation, by acting as a negative control mechanism for myosin light chain phosphorylation, affects the contractile response. The Ca2+ activation properties of MLCK regulate the myosin light chain phosphorylation. The activation properties of MLCK are in turn regulated by the Ca2+ activation properties of CaMKII which phosphorylates MLCK. There is notable lack of data for the Ca2+ activation properties of CaMKII in smooth muscle cells. Once the data becomes available, the model can be extended to include the

CaMKII activation pathway.

At present the dephosphorylation of MLCK has been modelled with a fixed rate constant due to the lack of data on dephosphorylation kinetics of MLCK. However in vitro studies have shown that type 2A protein phosphatase and type 1 protein phosphatase were able to dephosphorylate MLCK at specific sites (Nomura et al.,

1992). A protein phosphatase fraction isolated from smooth muscle actomyosin was characterized to contain multiple protein phosphatases capable of dephosphorylating phosphorylated MLCK with unique site specificities and catalytic properties. The isolation of such protein phosphatase shows that the phosphatases could possibly have an effect on the regulation of the activity of MLCK. These findings open new avenues

153 for investigation of the role of various phosphatases in contraction of SMCs. Once kinetic data on dephosphorylation of MLCK is available, the current model can be improved by replacing the fixed dephosphorylation rate constant with suitable enzyme kinetic reaction.

Though many biochemical studies have been done on the phosphorylation of MLCK by CaMKII, only limited data is available on the quantitative relationship between calcium and active force generation relative to MLC20 phosphorylation with and without MLCK phosphorylation (Tansey et al., 1994). Hence a pathway model with

MLCK phosphorylation such as this one would be useful to predict the effect of

MLCK phosphorylation on myosin phosphorylation and active force.

5.3. Hypothesis 2 – Calcium desensitization through MLCP

activation

2+ MLCK phosphorylation caused desensitization of force to a sustained [Ca ]i signal the relaxation was more rapid in the experimental results (Figure 5.1) compared to the model predictions (Figure 5.5). The regulation of MLCP and its activation by smooth muscle specific protein telokin was discussed in the previous chapter (Chapter 4).

Biochemical studies have identified phosphorylation sites on telokin and phosphorylation of telokin at a specific serine site (serine 13) by cellular kinases such as the cyclic nucleotide-activated protein kinase(s) has been suggested to enhance its ability to increase the activity of MLCP (Wu et al., 1998; Krymsky et al., 2001;

Walker et al., 2001; Choudhury et al., 2004). Addition of phosphorylated

154 recombinant telokin has been shown to be more potent in inducing relaxation than non-phosphorylated telokin (Khromov et al., 2006).

It has also been suggested that active MLCK causes slow phosphorylation of telokin

(Sobieszek et al., 2005; Hong et al., 2009). Hence it is possible that under high and

2+ sustained [Ca ]i conditions, phosphorylation of telokin causes increased activation of

MLCP leading to desensitization to Ca2+. Given that telokin can be phosphorylated and phosphorylated telokin is a more potent relaxing agent, it appears that this may be

2+ a possible mechanism for [Ca ]i desensitization. Hence enhanced activation of MLCP is hypothesized as a mechanism for calcium desensitization in phasic SMCs.

5.3.1. Enhanced MLCP activation model

The slow activation of MLCP in response to a sustained maintenance of high calcium concentration was modelled with the same approach as used for the MLCP activation during a rapid Ca2+ transient as shown in Equation 5.3.

(5.3)

The parameters control the concentration of MLCP, with A2 controlling the amplitude of activation and ω2 (=1/τ) representing the time constant of MLCP activation.

∆[MLCP] on the right hand side of the Equation 5.3 is the concentration of MLCP in response to the normal rapid calcium transients defined by different set of parameters

(Section 4.3) and shows the activation of MLCP by telokin under normal calcium transients. The parameters A2 and ω2 describe the enhancement in the activation of

155

MLCP i.e., more MLCP is activated by phosphorylated telokin with slower kinetics in addition to the MLCP activation described in Section 4.3. This method was used due to the unavailability of experimental data regarding the exact mechanism of activation of MLCP by telokin and quantitative details on the phosphorylation of telokin and enhancement of the activation ability of telokin upon its phosphorylation. The parameter values were estimated by fitting the model to the experimental force curve shown in Figure 5.1. A limiting condition of total MLCP equal to total MLCK (10

µM) was assumed in the estimation of the parameters. The estimated values of A2 and

-1 ω2 were 5 and 60 s respectively.

5.3.2. Results and Discussion

2+ A slow decline in [Ca ]i leads to slow enhancement in the activation of MLCP as shown in Figure 5.8.

The effect of the enhanced activation was not significant during rapid Ca2+ transients.

2+ A 14.7% increase in [MLCP] during the slow declining phase of [Ca ]i decreased the magnitude of maximum force achieved by 10% compared to the maximum force achieved without the enhanced MLCP activation shown in Figure 5.9A. Normalized force from the model with and without the enhanced MLCP activation mechanism are expressed as a fraction of their maximum value to compare the temporal dynamics of force (Figure 5.9B).

156

10 [MLCP] with 0.3 enhanced activation [MLCP] without enhanced activation [Ca2+] 0.2

5

[MLCP] (microM) [MLCP] 0.1 [Calcium] (microM) [Calcium]

0 0 0 1 2 3 4 5 6 7 Time (min)

Figure 5.8. Concentration of MLCP for a given Ca2+ signal (dotted line) in the presence (solid line) and absence (dashed line) of the enhanced MLCP activation reaction (Equation 5.3).

2+ N with MLCK and [Ca ] p 1 N with MLCK and 0.8 A enhanced MLCP 0.3 B p activation enhanced MLCP activation 0.8 N with only MLCK N with only MLCK p p 0.6 0.2 0.6

0.4 N (%) N 0.4

0.1 [Calcium] (microM) [Calcium]

0.2 maximum of Fraction 0.2

0 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time (min) Time (min)

Figure 5.9. Effect of enhanced MLCP activation on the normalized force behavior for a given Ca2+ signal (dotted line). Enhanced MLCP activation caused further desensitization by decreasing the magnitude of maximum force achieved by 10% as shown in (A) and did not have any significant effect on the temporal dynamics of the force behavior as seen in (B).

157

The extended model with MLCK phosphorylation and enhanced MLCP activation

2+ 2+ was simulated with a prescribed rapid Ca transient with a [Ca ]max of 0.3 µM and the results are shown in Figure 5.10. The presence of desensitization mechanism reduced the amplitude of the peak force and did not have a significant effect on the temporal dynamics of the force behavior for the rapid Ca2+ transient. With a prescribed

2+ 2+ rapid Ca transient with a [Ca ]max of 0.8 µM, normalized force of 11% was achieved. As suggested by Word et al. (1994) and Yagi et al. (1988), the desensitizing

2+ mechanims can be attributed to the dissociation in the coupling of [Ca ]i and force production observed during the activation of single gastric smooth muscle cells.

5 2+ With desensitization mechanism [Ca ] 0.3 1 A Without desensitization mechanism B N with desentization mechanism 4 [Ca2+] 0.8 N without desensitization mechanism 0.2

3 0.6 N (%) N 2 0.4

0.1

[Calcium] (microM) [Calcium] Fraction of maximum of Fraction 1 0.2

0 0 0 0 5 10 15 0 5 10 15 Time (second) Time (second)

Figure 5.10. Simulated normalized force behavior for a prescribed Ca2+ transient (dotted line). The presence of desensitization mechanisms reduced the amplitude of the peak force as seen in (A) and did not have a significant effect on the temporal dynamics of the force behavior as seen in (B).

2+ The model was also tested with an another [Ca ]i input signal reported by Ozaki et al.

(1991a) (Figure 5.11). In Figure 5.11, Ca2+ depletion in the external solution with

EGTA caused decrease of Ca2+ below the resting levels. However the tension did not decrease and was maintained at the resting state. Addition of Ca2+ to the external

158

2+ solution progressively caused an increase in [Ca ]i and restored the contractions. It should be noted that contraction was initiated below the initial resting Ca2+ value.

Ozaki et al. (1991a and 1993) has argued that the threshold for contraction depends on

2+ 2+ the basal resting [Ca ]i condition. A decrease in resting [Ca ]i caused a decrease in

2+ 2+ the [Ca ]i threshold for contraction due to a change in Ca sensitivity as shown in

2+ 2+ Figure 5.11. Cumulative addition of [Ca ]i further increased intracellular [Ca ]i and subsequently muscle tension. However the the fall in tension preceded the fall in

2+ [Ca ]i. Similar results have also been reported in ileal SM (Himpens et al., 1988;

Himpens et al., 1989). These results show that the contractile response gets desensitized or sensitized to Ca2+ as a function of amplitude and rate of change of Ca2+.

Figure 5.11. Experimental results from canine antral smooth muscle showing changes in Ca2+ and muscle tension in response to Ca2+ depletion and re-addition.

The experimental maximum force value attained was 2 times the peak force value of the rapid Ca2+ transient. Without any desensitizing mechanisms, the model predicted a maximum force value 17 times the peak force value achieved during rapid Ca2+ transient (Figure 5.12). However in the presence of desensitizing mechanisms, the maximum force value produced was only 9 times the peak force value corresponding to the rapid Ca2+ transient (Figure 5.12). Though exact quantitative match to

159 experimental result could not be achieved at this stage, it is evident that the two mechanisms, MLCK phosphorylation and MLCP activation, act as negative feedback controls and cause desensitization to Ca2+.

Ozaki et al. (1991a) suggested that the Ca2+ desensitization observed was time

2+ dependent. During the relatively rapid increases of [Ca ]i, there is a steep relationship

2+ 2+ between Ca and the contractile response, but slow increases in [Ca ]i during maintained K+ depolarizations lead to activation of desensitizing mechanisms that

2+ diminish the contractile response for a given increase in [Ca ]i (Ozaki et al., 1991a).

Ozaki et al. (1991a) has argued that a shift in the activation-inactivation balance

2+ during the slow declining phase of [Ca ]i leads to the observed force behavior.

2+ In the current model, rapid increase in [Ca ]i leads to rapid MLCK activation and

2+ initiation of contraction. When [Ca ]i reaches a plateau like slow declining phase, phosphorylation of MLCK and enhanced activation of MLCP are induced. While

MLCK phosphorylation reduces the activation rate of MLCK and hence myosin light chain phosphorylation, higher MLCP activation levels accelerate myosin light chain dephosphorylation. This forms a two step negative feedback mechanism on the active force production.

160

3 With Without 2+ desensitization mechanism desensitization mechanism [Ca ] 2.5 0.3

2 0.2

1.5 N (%) N

1

0.1 (microM) [Calcium]

0.5

0 0 0 1 2 3 4 5 6 7 8 9 10 11 Time (min)

Figure 5.12.Simulated normalized force for a given experimental Ca2+ signal (dotted line) in the presence (solid line) and absence (dashed line) of desensitizing mechanisms. Without any desensitizing mechanisms , the model predicted a maximum force value 17 times the peak force value achieved during rapid Ca2+ transient. However in the presence of desensitizing mechanisms, the maximum force value produced was only 9 times the peak force value corresponding to the rapid Ca2+ transient. This indicates the desensitization of force to Ca2+.

N with N without 2+ desensitization mechanism desensitization mechanism Ca 1

0.8

0.6

0.4 Fraction of maximum of Fraction 0.2

0

0 1 2 3 4 5 6 7 8 9 10 11 Time (min)

Figure 5.13. Simulated normalized force for a given experimental Ca2+ signal (dotted line), expressed as a fraction of the maximum value, in the presence (solid line) and absence (dashed line) of desensitizing mechanisms. The figure shows the effect of the desensitizing mechanisms on the temporal dynamics of force behavior.

161

5.4. Summary

Though MLCK activation is the primary mechanism in the active force production in

SMC, the results reported here suggest that the relationship between Ca2+ and active force may be subject to secondary regulation from an extended network of kinases and phosphatases. Activation of desensitization processes is evident from the experimental results. However, the exact molecular mechanisms are not yet clear. From the various pathways and molecular species observed in vitro, only suggestive claims have been made on what could be the mechanism of calcium desensitization. Work done by

Tansey et al. (1992 and 1994), Stull et al. (1993) and Word et al. (1994) support the hypothesis that the regulation of MLCK through its phosphorylation regulates the

Ca2+ sensitivity of force in phasic SMCs. Ozaki et al. (1991a) and Choudhury et al.

(2004), suggest that MLCP activation leads to Ca2+ desensitization in phasic smooth muscles. Hence one or more pathways could be acting in tandem or separately in vivo to cause the calcium desensitization. Events related to filament re-organization have also been reported to play role in the calcium sensitization process (Murahashi et al.,

1999). It has been suggested that dynamic changes in the actin cytoskeleton regulate the development of mechanical tension and the material properties of smooth muscle cells. Actin polymerization has been found to affect the muscle tension by increasing the number or stiffness of attachments of actomyosin assemblies to membrane-dense plaques and cytoplasmic-dense bodies (Gerthoffer and Gunst, 2001). Cytoskeletal remodeling and mechanotransduction pathways regulated by various cellular proteins like integrins, focal adhesion kinase (FAK), and small heat shock protein (HSP27) have been found to mediate adaptive responses of the SM cytoskeleton to various stimuli (Gunst and Zhang, 2008).

162

In summary, two potential mechanisms for Ca2+ induced Ca2+ desensitization have been identified from the literature and quantitatively described. First one is the phosphorylation of MLCK by CaMKII and the second mechanism is the enhanced

MLCP activation by phosphorylated telokin. The two mechanisms have been shown

2+ to reduce the force response to a given [Ca ]i and can be attributed to the desensitization phenomenon observed in phasic smooth muscle cells.

There is convincing evidence in the literature that Ca2+-CaM mediated MLCK activation and the resultant myosin light chain phosphorylation is the central mechanism in active contraction of SMC. Gene knockout studies and studies with specific inhibitory agents (e.g., wortmannin) have established the role of MLCK in the overall cell function (Burke et al., 1996; He et al., 2008). Targeted deletion of MLCK in adult mouse smooth muscle resulted in severe gut dysmotility characterized by weak peristalsis, dilation of the digestive tract and reduction of faeces excretion and food intake (He et al., 2008). These studies establish the significance of a cellular reaction in the physiological context. However, there is no conclusive evidence for the role of Ca2+ desensitizing mechanisms in the physiological setting. Whole cell and tissue level experiments have shown the presence of a phenomenon called Ca2+ desensitization. From the observation that MLCK is being phosphorylation by cellular kinases and MLCK phosphorylation regulates its activation negatively, it has been hypothesized to be a Ca2+ desensitizing mechanism. More studies are still required to investigate the effect of MLCK phosphorylation on the contractility of GI muscles.

163

6. Conclusion

The main aim of this thesis was to investigate the relationship between intracellular

Ca2+ concentration and force in gastric SMCs. By describing the biochemical reactions linking Ca2+ to contraction, the phasic contractile behavior of gastric SMCs has been simulated. The simulation results have been compared to experimental recordings and good qualitative agreement has been found. The various modules of the model and their effect on the force response capture their regulatory role in the smooth muscle cell function. This model has accounted for the specific properties of

SMCs exhibiting phasic contractile behavior.

A pathway for active contraction has been developed and quantitatively described. In this modelling study, data from isolated experiments have been collated and placed in a physiologically relevant scheme. This thesis in addition to contributing towards an in silico model which will serve as a useful tool for understanding gastric physiology in health and disease, also helps to identify the key areas where further experimental investigation is needed for a better understanding of the problem.

In the multiscale modelling of GI system, a cellular level model for SM contraction would play a significant role in the development of tissue level and organ scale models to study gastric motility. Although generic models of SM contraction and models for other SM types (e.g., airway, vascular which are primarily tonic SM) have been developed previously, this study has led to a model that is specific for phasic gastric SM. MLCP regulation by telokin has been modelled for the first time. MLCK phosphorylation and MLCP activation pathways have been investigated in a

164 physiological context of Ca2+ desensitization and the regulatory effect of kinase- phosphatase network on the active contractile response of a SMC has been discussed.

6.1. Limitations and Future Work

In the model, actual force values are not estimated. What is being estimated is the number of cross bridges for a given total myosin concentration. Gestrelius and

Borgstrom (Gestrelius and Borgstrom, 1986) have proposed a formulation for active force as a function of normalized number of cross-bridges available for interaction with actin, the stiffness of a cross-bridge and average cross-bridge extension

(Equation 2.8). Such a mathematical formulation to calculate active force from the number of cross-bridges is necessary to validate the model against experimental force data without any normalization. Existing literature on the mechanical properties of cross-bridge will be useful for this purpose.

Based on literature evidence and to account for the rapid decline of force in the experimental results compared to model predictions, MLCP regulation was included in the model. Though MLCP regulation has been widely reported in the literature, there are no quantitative reports on cellular concentration of MLCP and kinetic studies on its regulatory pathways. Hence a biochemical reaction based approach similar to

MLCK activation pathway could not be drawn for MLCP regulation. A bottom up approach of predicting MLCP behavior from the force behavior was used and a feedback equation based on electronic filters was hypothesized. Once the reaction scheme for telokin mediated MLCP activation is available, the feedback equation can be replaced with the reaction kinetics.

165

Dephosphorylation of MLCK (Chapter 5) has been modelled with a fixed rate constant. Though some studies have identified cellular phosphatases dephosphorylating phosphorylated MLCK, quantitative properties of the phosphatases are still unknown (Nomura et al., 1992). With further characterization of MLCK specific phosphatases, the dephosphorylation kinetics in Equation 5.1 can be modelled with phosphatase enzyme kinetics.

In the estimation of the parameter values, one of the two scenarios, either problem of over fitting or under-constrained estimation can arise. In this study, over-fitting of the model was not possible due to limited GI specific data. The problem of under- constrained estimation was avoided by using suitable data from other cells types where GI specific data was not available. For example, module I was predominantly fitted using data from HEK cells. However Module II has been built and validated using canine gastric antrum SM data. Experimental data from human GI SM will hopefully be available in the future and enable human GI specific models.

The most important future work would be to integrate this model to electrical models of GI SM and use it in tissue and organ level descriptions to study GI motility. The motivation for the work also stems from multiscale modelling studies done to study the electrical activity throughout the stomach and the experimental studies on contractile response for a given electrical stimuli. To understand how electrical activity regulates the motility function in GI, the intracellular Ca2+ profile from experimental studies and electrical models have to be linked to contraction. Integrative models at different levels of biological organisation, from genes to the whole organism via gene regulatory networks, protein pathways, cell function, and tissue and

166 whole organ function will provide a framework for understanding physiology and pathophysiology.

167

Appendix I

Equations in the model

1. Module I : Model for Ca2+ dependent MLCK activation

Reactions Equations

1

2

3

4

5

6

168

Reactions Equations

7

8

9

10

11

169

2. Module II : Model for myosin phosphorylation and cross-bridge formation

(fraction of total myosin)

Number of cross-bridges,

Normalized number of cross-bridges,

170

3. Input calcium transient

4. MLCP regulation model

5. Model for Ca2+ induced Ca2+ desensitization

5.1. MLCK phosphorylation model

Reaction Equation

MLCK ↔ MLCKp

MLCKp + 2+ (Ca )4CaM ↔ 2+ (Ca )4CaM-MLCKp

171

5.2. Enhanced MLCP activation model

172

Appendix II

Values of the model parameters

1. Module I : Model for Ca2+ dependent MLCK activation

kf kr Kd Reaction (µM-1s-1) (s-1) (µM)

1 2.3 2.4 1.043

2 160 500 3.125

3 2.8 2.4 0.857

4 100 253* 2.53#

5 5 15 3

6 27.6* 55.2# 2

7 201.81* 0.222# 0.0011

8 840 45.36 0.054

9 12.8 64# 5*

10 2.3 0.39 0.1696

11 160 36.8# 0.23*

Note: *- parameters estimated through fitting. #- the parameter calculated from the other two values.

173

2. Module II : Model for myosin phosphorylation and cross-bridge formation

Parameter Values

-1 kcat_MLCKactive 47 s

Km_MLCKactive 10 µM

-1 K3 39.577 s

K4 K3/4

-1 kcat _MLCP 30 s

Km_MLCP 14.3 µM

-1 K7 29.333 s

[MLCP] 7.703 µM

3. Input calcium transient

Parameter Value

2+ [Ca ]r 0.1 µM

2+ [Ca ]max 0.6 µM

t1 0 s

t2 2 s

t3 20 s k 0.4 s-1

4. MLCP regulation model

-1 A2 = 27.4 and 2 = 2.5 s

174

5. Model for Ca2+ induced Ca2+ desensitization

5.1. MLCK phosphorylation model

Reaction Parameters

-1 y1 = 3 s

y2 = 0.6 µM MLCK ↔ MLCKp Km = 0.5 µM -1 Krev = 0.05 s

-1 -1 2+ 2+ Kfwd = 2 µM s MLCKp + (Ca )4CaM ↔ (Ca )4CaM-MLCKp -1 Krev = 0.1 s

5.2. Enhanced MLCP activation model

-1 A2 = 5 and 2 = 60 s

175

6. Steady state concentration of the species at resting Ca2+ concentration of 0.1

µM.

Species Initial concentration (µM) CaM 0.721

2+ (Ca )2CaMC 0.002

2+ (Ca )2CaMN 0.001

2+ (Ca )4CaM 0.0

CaM-BP 3.484

BP 14.516

MLCK 7.946

CaM-MLCK 1.146

2+ (Ca )2CaMC-MLCK 0.168

2+ (Ca )4CaM-MLCK 0.007

M 44.954

Mp 0.005

AMp 0.005

AM 0.003

176

Awards

 Awarded “Young Investigator Award – Silver” under the Tissue Mechanics

Theme at the 6th World Congress of Biomechanics held at Singapore from 1st

to 6th August 2010.

Publications

Journal Publications

 Gajendiran V and Buist ML, “A quantitative description of active force

generation in gastrointestinal smooth muscle”. International Journal for

Numerical Methods in Biomedical Engineering, 2011, Volume 27, Issue 3,

p450–460.

 Du P, Poh YC, Lim JL, Gajendiran V, O’Grady G, Buist ML, Pullan AJ,

and Cheng LK, “A Preliminary Model of Gastrointestinal Electromechanical

Coupling”. IEEE Trans Biomed Eng, 2011, Volume 58, Issue 12, p3491 - 3495.

177

International Conferences

 Gajendiran V and Buist ML. “A Mathematical Model of Active Force

Production in Gastric Smooth Muscle Cells”. Poster presentation at

Neurogastroenterology and Motility Joint International Meeting, Boston

(USA), 26 Aug- 29 Aug 2010.

 Gajendiran V and Buist ML. “Mathematical Modelling of Myosin Light

Chain Kinase (MLCK) Activation and Active Force Production in Gastric

Smooth Muscle Cells”. Oral Presentation at the 6th World Congress of

Biomechanics, Singapore, 1 Aug – 6 Aug 2010.

 Gajendiran V and Buist ML. “A Mathematical Model to Study the Regulation

of Active Stress Production in GI Smooth Muscle”. Poster presentation at the

13th International Conference on Biomedical Engineering. Singapore, 3 Dec- 6

Dec 2008. IFMBE Proceedings, 2009, Volume 23, Track 5, p1696-1699.

Local Conferences and Seminars

 Gajendiran V and Buist ML. “A Mathematical Model of the Regulation of

Active Stress Production in Gastrointestinal Smooth Muscle”. Oral

presentation at the 3rd East Asian Pacific Student Workshop on Nano-

Biomedical Engineering. Singapore, 21 Dec- 22 Dec 2009.

178

 Gajendiran V. “A Mathematical Model of Active Force Production in Gastric

Smooth Muscle Cells”. Oral presentation at the Graduate Students’ Seminars,

Division of Bioengineering, NUS, Singapore. 26 Mar, 2010.

 Gajendiran V. “Mathematical Modeling of Mechanical Activity of

Gastrointestinal Smooth Muscle”. Oral presentation at the Graduate Students’

Seminars, Division of Bioengineering, NUS, Singapore. 27 Feb, 2009.

179

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