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