CALCIUM MOVEMENT IN THE SARCOMERE AND ITS CONNECTION TO MUSCLE CONTRACTION: A PILOT STUDY Neil Goldsmith A Thesis Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE November 2008 Committee: Dr. Lewis Fulcher, Advisor Dr. Ronald Scherer Dr. Donald Cooper Dr. John Laird ii ABSTRACT Dr. Lewis Fulcher, Advisor The human body uses calcium as an activator for muscle contraction. A muscle contraction begins with the release of calcium from the terminal cisternae into the sarcomere. The interaction of calcium with myoplasmic proteins then causes the muscle to contract. A biophysical model of the sarcomere will be developed in order to use the model to connect chemical concentrations with force production by the muscle. Since the sarcomere is the base contractile unit of muscle, it should therefore be the appropriate starting point for such a model. The model includes calcium release, diffusion, binding, and uptake. Magnesium concentrations are also modeled as they compete for calcium binding sites on parvalbumin, ATP, and troponin. The binding of calcium to troponin is of special importance because it results in unblocking of the actin sites. The actin will then interact with myosin in a multi-step process that is well understood but poorly quantified. This interaction leads to contraction of the sarcomere and thus the production of force. iii Dedication To my grandmother. Someone once told her I could do anything... and she never let me forget it. iv Acknowledgement I gratefully and thankfully acknowledge the Physics department at Bowling Green State University. I would like to personally thank Dr. Fulcher whose unending curiosity serves as an example of what scientist should be. I would also like to thank Dr. Laird. He always had time to listen and a wise word of advice to offer. v TABLE OF CONTENTS Page CHAPTER 1. INTRODUCTION ............................. 1 CHAPTER 2. MUSCLE DATA .............................. 16 2.1 Overviewofmuscletensiondata. .... 16 2.1.1 Twitch measurements in the canine vocalis . ..... 18 2.1.2 Tetanic contraction in the canine vocalis . ...... 21 2.1.3 Twitch contraction in canine posterior cricoarytenoid muscle . 22 2.1.4 Twitch contraction in thyroarytenoid muscle . ....... 24 2.2 Overviewofbiochemicaldata . ... 25 2.2.1 ATP utilization and its temperature dependence . ....... 26 2.2.2 Effects of strain on actomyosin kinetics . ..... 27 CHAPTER 3. SUMMARY OF EARLIER MODELS .................. 29 3.1 CannellandAllenmodel . .. .. 32 3.2 Baylor and Hollingworth’s 1998 model . ..... 35 3.3 Baylor and Hollingworth’s 2007 model . ..... 38 3.4 Shortenetal’s2007model . .. 42 CHAPTER 4. THE PRESENT MODEL ......................... 44 4.1 Geometry ..................................... 44 4.2 SERCApump................................... 46 4.3 Calciumrelease .................................. 48 4.4 Diffusion...................................... 49 4.5 Kinetics ...................................... 50 vi CHAPTER 5. RESULTS AND DISCUSSION ...................... 52 5.1 Results....................................... 52 5.2 Towardsabettermodel ............................. 59 REFERENCES ....................................... 63 vii LIST OF FIGURES Figure Page 1.1 Muscleorganization.............................. .. 2 1.2 Exampletwitch .................................. 4 1.3 Dualtwitch .................................... 4 1.4 Steady frequency stimulus contraction . ....... 5 1.5 Externalviewofsarcomeres . ... 7 1.6 Myosinpowerstroke ............................... 8 1.7 Cannell and Allen’s model geometry . .... 10 1.8 Comparison of BH07 calcium release to Shorten et al.’s calcium release . 12 1.9 Force production kinetic scheme . ..... 12 1.10 Shorten et al’s model vs. experimental data . ........ 13 1.11 Titze’s predicted muscle tension curve vs. experimentaldata ......... 14 2.1 Example twitch with metric overlay . ..... 18 2.2 50% relaxation time versus strain in the canine vocalis . ........... 19 2.3 Force versus elongation in canine vocalis . ........ 20 2.4 Mean contraction time for various species . ........ 22 2.5 Temperatureeffectontwitch. ... 23 2.6 Latencytimeofatwitch ............................ 24 2.7 Twitch of a canine thyroarytenoid muscle . ....... 25 2.8 Temperature dependence of resting force and ATP utilization......... 27 3.1 Sarcoplasmic calcium depletion . ..... 39 3.2 SERCAkineticscheme .............................. 40 4.1 SERCA models theoretical comparison . ..... 47 viii 5.1 Surface graphs of calcium concentration gradient . ........... 55 5.2 Spatially averaged calcium concentration during a twitch........... 57 5.3 Force producing crossbridge concentration for a twitch ............ 58 5.4 Force producing crossbridge concentration for multiple twitches . 59 ix LIST OF TABLES Table Page 3.1 Half-sarcomeredimensions.. ..... 32 3.2 Crank’s finite difference approximation equations. ........... 34 3.3 Reaction constants and concentrations of chemicals and proteins from Ref. [11]. 35 3.4 Diffusionconstants ............................... 37 3.5 Constants and total concentrations of chemicals and proteins from Ref. [13] . 37 3.6 Concentration of myoplasmic constituents . ........ 40 3.7 Rate constants for reactions shown in Fig. 3.2 and the troponin-calcium bind- ingreaction .................................... 41 3.8 Rateconstantsforforceproduction . ...... 42 4.1 Half-sarcomere dimensions in present model . ........ 45 4.2 Rate constants for reactions in the present model . ......... 50 1 CHAPTER 1 INTRODUCTION Figure 1.1 shows a top-down organizational view of skeletal muscle. The present study will focus on the myofibril, an element of the muscle fiber, but some features at levels above the myofibril are important to note. The tendons and to a lesser degree the epimysium, perimysium, and blood vessels all add an elastic nature to the muscle. This elastic nature is an important feature of the muscle because it allows the muscle to contract without moving the limb to which it is attached. In the following pages data for isometric and isotonic muscle contractions will be presented. Some care is needed to understand the isometric contraction since the muscle length does not change. In this situation the muscle shortens while the elastic elements are lengthened until the force of the contraction is balanced by the pull of the elastic elements. This allows the contracting parts of the muscle to shorten without moving the attached load. Since parts of the muscle shorten, it is not truly an isometric contraction. A second type of muscle contraction is carried out under isotonic conditions. In an isotonic contraction the muscle contracts against a finite, constant load. In this situation the muscle will develop tension equal to the load, the elastic elements will transfer that force to the load, and the load will move. This would be the type of contraction where one picks up a weight with a slow uniform motion. A sphincter muscle serves as an example of an intermediate type of contraction. A sphincter is a ringlike muscle that serves to close bodily passages through contraction. Sphincter muscles are not anchored to a load so they do not perform an isotonic contraction, and they are required to reduce their size to close the passage that passes through them, thus their contraction cannot be considered isometric. Our understanding of a muscle that undergoes a contraction that is neither isotonic or isometric is important because the muscles of interest for this thesis are all skeletal muscles of the larynx and in voiced sounds they are required to perform in a manner that has elements 2 Figure 1.1: Organizational levels of skeletal muscle, taken from Raul654, Deglr6328, and Rama [1]. of both isometric and isotonic contractions. Some examples are the lateral cricoarytenoid and the posterior cricoarytenoid. The lateral cricoarytenoid muscle rotates the arytenoid cartilage medially when it contracts, which relaxes and adducts the vocal folds [2]. The posterior cricoarytenoid is an antagonistic muscle to the lateral cricoarytenoid. The posterior cricoarytenoid rotates the vocal process of the arytenoid cartilage laterally and abducts the vocal folds [2]. In both of these cases the muscle creates a tension in a pseudo-isometric manner, until it has created enough force to move the load to which the muscle is attached, and then it contracts in a pseudo-isotonic fashion. Finally, when the muscle has moved the 3 attached load to the desired position it returns to a pseudo-isometric contraction. In the first instance, the isometric contraction is not a true isometric contraction because the load it is acting against is not infinite, and the muscle is shortening even though the load is not moving. Once the muscle has generated sufficient force, then it will start to move the load. As the load is moved it will become greater either by the stretching of an antagonist muscle or the elongation of an attached elastic element such as a ligament or a tendon. This makes the load variable, which means that the contraction is not isotonic. Once the force of the load reaches the force of the muscle, the muscle returns to a state similar to an isometric contraction. Again, it is not a true isometric contraction because the muscle will constantly be tensing and relaxing instead of holding a steady length. The force these laryngeal muscles exert in response to a stimulus has been measured. The force has even been measured in vivo [3,4], which