UNIVERSITY OF CALGARY. An Examination of Sarcomere Length Non-uniformities in Actively Stretched Muscle. Myofibrils. Kaleena Rachile Johnston A THESIS

Transcription

1 UNIVERSITY OF CALGARY An Examination of Sarcomere Length Non-uniformities in Actively Stretched Muscle Myofibrils by Kaleena Rachile Johnston A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN KINESIOLOGY CALGARY, ALBERTA APRIL, 2015 Kaleena Rachile Johnston 2015

2 Abstract Residual force enhancement (RFE) is a characteristic of skeletal muscle describing the increase in isometric steady-state force following an active stretch, compared to the force of an isometric contraction at the same final length. It has been argued that RFE is a result of unstable sarcomeres on the descending limb of the force-length relationship, causing long, weak sarcomeres to lengthen more than short, strong sarcomeres when a myofibril is actively stretched, as described by the Sarcomere Length Non-uniformity Theory (SLNT). While the SLNT is currently the most popular explanation for RFE, its primary predictions have never been experimentally tested. In this research we performed experiments on rabbit psoas muscle myofibrils, comparing isometric contractions to isometric contractions following active stretch in order to examine the predictions of the SLNT. The results suggest that, while sarcomere length non-uniformities may play a role, the SLNT does not fully capture the mechanism of RFE. ii

3 Acknowledgements I would like to express my appreciation and sincere thanks to the following: Dr. Walter Herzog for being my supervisor and for offering unparalleled knowledge and support throughout this degree. Dr. Darren Stefanyshyn and Dr. Michael Walsh for serving on my supervisory committee and providing guidance to me. Dr. Doug Syme (Internal-External Examiner) and Dr. Brent Edwards (Neutral Chair) for serving on my examination committee. AITF Graduate Student Scholarship Program and NSERC CREATE Training Program for Biomedical Engineers of the 21 st Century for providing major funding throughout this degree. Dr. Tim Leonard, Dr. Venus Joumaa, and Mike DuVall for providing knowledge and advice throughout this degree and for reading my thesis and offering excellent feedback. Azim Jinha, Hoa Nguyen, and Andrzej Stano for all of the many times they helped build and fix the programs and equipment needed to perform this work. Dawn Martin for helping with tissue harvesting and all of the highly enjoyable banter. My family, especially Brad, Lynne, and Kale Johnston and Dave Watson, for their unwavering love and support, and especially their encouraging words whenever I was in need. Amanda Lottermoser and the members of the Herzog Lab group for making the lab a great place to work and for offering much appreciated feedback throughout this degree. The PPP for all of the great times that helped keep me sane throughout this process. iii

4 Table of Contents Abstract... ii Acknowledgements... iii Table of Contents... iv List of Tables... vi List of Figures and Illustrations... vii List of Symbols, Abbreviations and Nomenclature...x Epigraph... xi CHAPTER ONE: INTRODUCTION...1 CHAPTER TWO: LITERATURE REVIEW Muscle hierarchy and architecture Force production Passive force production Active force production: the Cross-Bridge Theory Force-length relationship History dependence of skeletal muscle Increased force during active stretch Increased force following active stretch: residual force enhancement Sarcomere Length Non-uniformity Theory Description of the Sarcomere Length Non-uniformity Theory Predictions of the Sarcomere Length Non-uniformity Theory Uniform sarcomere lengths in isometric contractions Active stretch results in sarcomere length non-uniformities Force-enhanced state exhibits popped sarcomeres Summary Purpose Hypotheses...22 CHAPTER THREE: METHODS Microscope and apparatus setup Specimen harvesting Isolation of single myofibrils Experimental protocol Length and force measurements Statistical analyses...30 CHAPTER FOUR: RESULTS Mean sarcomere lengths Force Predictions of the Sarcomere Length Non-uniformity Theory Sarcomere length distribution in isometric contractions Sarcomere length distribution following active stretch Popped sarcomeres in the force-enhanced state...43 iv

5 CHAPTER FIVE: DISCUSSION Objective Predictions of the Sarcomere Length Non-uniformity Theory Sarcomere length distribution in isometric contractions Sarcomere length distribution following active stretch Popped sarcomeres in the force-enhanced state Limitations Considerations for residual force enhancement based on previous research Future directions Conclusion...54 REFERENCES...56 APPENDIX A: SOLUTIONS...63 APPENDIX B: RAW DATA...64 v

6 List of Tables Table 4.1 Mean sarcomere lengths, SDs of the mean sarcomere lengths, and forces for each of the steady states within the 12 myofibrils Table 4.2 Individual myofibril data for the isometric and force-enhanced states and the amount of RFE exhibited. The numbers in brackets in the myofibril column indicate which of the eight rabbits each myofibril came from Table 4.3 Summary of the variables required to assess the predictions of the SLNT for each individual myofibril and the mean. Values denoted by an asterisk (*) are those that align with the SLNT vi

7 List of Figures and Illustrations Figure 2.1 Schematic image of the hierarchical structure of skeletal muscle. Structural levels are labeled in bold on the right of the diagram and connective tissue sheaths are labeled and indicated on the left. Adapted from Herzog (2007) Figure 2.2 Schematic diagram of a sarcomere (Z-line to adjacent Z-line), indicating the thin (actin) and thick (myosin) filaments and titin. Various regions of the sarcomere are also labeled, including the A- and I-bands, which are responsible for the dark and light regions, respectively, when viewing a myofibril in phase contrast microscopy. Rabbit psoas muscle myosin filaments are 1.65 µm long, actin filaments are 1.08 µm long (Herzog, Kamal, & Clarke, 1992) Figure 2.3 Schematic diagram of the 1957 Cross-Bridge Theory. Myosin filament cross-bridge attachment site (M) oscillates about its equilibrium positon (O) and can attach to actin filament fixed attachment site (A). Following attachment, tension in the cross-bridge causes M-A to move towards O, resulting in the sliding of the actin filament relative to the myosin filament according to the directions indicated by the arrows. Adapted from A. F. Huxley (1957) Figure 2.4 Rate functions of attachment (f) and detachment (g) for M-A (Figure 2.3) cross-bridge attachments as a function of the distance (x) from the equilibrium position (O) to the actin filament attachment site. Adapted from A. F. Huxley (1957) Figure 2.5 Schematic diagram of the 1971 Cross-Bridge Theory. Interaction between the myosin and actin filaments occurs at the myosin head (H) which extends from the myosin filament via the AB link. The full line shows H in the first stable position, with M1A1 and M2A2 attachments made. The dashed line shows H in the second stable position (M2A2 and M3A3 attached), following a rotation of H about B. Adapted from A. F. Huxley and Simmons (1971) Figure 2.6 Force-length relationship of rabbit psoas muscle identifying the ascending limb (blue), plateau (yellow), and descending limb (red). The points on the curve labelled A-E correspond to sarcomere lengths depicted on the right. The values on the graphs corresponding to points B-E are calculated from the lengths of the rabbit psoas filaments (myosin, m = 1.65 µm; actin, a = 1.08 µm), and the widths of the Z- line (z = 0.1 µm) and bare zone (b = 0.17 µm): B = m + z; C = a + a + z; D = a + b + a + z; E = a + m + a + z (Herzog et al., 1992; Walker & Schrodt, 1973). The grey dashed line on the graph indicates the sarcomere passive force production curve. Adapted from Gordon et al. (1966) Figure 2.7 Residual force enhancement (RFE) after active stretch of muscle. An isometric reference contraction at the final length is depicted by the grey lines. The black line indicates an initial isometric contraction at a shorter length (solid), followed by a stretch (dashed), and finally the isometric contraction following the active stretch (dotted) vii

8 Figure 2.8 Normalized forces obtained from purely isometric contractions (circles) and from isometric contractions following active stretches of different amplitudes (squares). Black dashed lines indicate initial lengths of each stretched condition. Vertical grey lines indicate that sarcomeres at the same final lengths (110, 115, and 120 %) can produce different amounts of steady-state isometric force. Values approximated from Rassier and Herzog (2004) Figure 2.9 Diagram of Morgan's (1990, 1994) popping sarcomere hypothesis. A and B represent the average sarcomere lengths and associated forces of a short (A) and long (B) isometric contraction. During an active stretch from an average sarcomere length of A to B, some sarcomeres are only slightly stretched (C1), whereas a few others take on most of the length change (C2). These sarcomeres lengthen rapidly and eventually pop to a length beyond actin-myosin filament overlap, resulting in non-uniform sarcomere lengths. At this point, the tension of the sarcomeres at C2 is supported by passive forces. This allows the total force produced by the actively stretched muscle to be greater than the purely isometric contraction at the same final length (RFE) Figure 3.1 Schematic drawing of the experimental set-up. The diagram on the right depicts the microscopic field of view (not to scale). Adapted from Rassier, Herzog, and Pollack (2003) Figure 3.2 Photograph of a single myofibril with 10 A-bands (dark bands). The glass needle can be seen on the left and the cantilever pair on the right Figure 3.3 Experimental protocol depicting average sarcomere length changes throughout each experiment. The yellow star indicates the time point at which the myofibril was activated and the shaded yellow box signifies that the myofibril was active for the remainder of the experiment. Individual states that were of interest to this study are identified as passive short (purple), passive long (orange), isometric (blue), active short (green), and force-enhanced (red) Figure 4.1 Sarcomere length data for each of the 12 myofibrils. The isometric and force-enhanced states are represented in blue and red, respectively. The histograms on the left indicate frequencies of each sarcomere length (bins = 0.1 µm), with the vertical grey dashed line indicating the length at which a sarcomere would be considered popped beyond actin-myosin overlap. The graphs on the right show sarcomere length as a function of the sarcomere s position in the myofibril. The first sarcomere was closest to the needle attachment point and the last sarcomere was closest to the cantilever attachment point. Vertical arrows show the direction of the change in length between states, while a square marker indicates no change. The popped sarcomere length is indicated by the horizontal grey dashed line. Captions under each pair of graphs identify which myofibril is depicted (number corresponds to Table 4.2, Table 4.3, and Appendix B), the properties of that myofibril in relation to the three predictions of the SLNT, and the amount of RFE exhibited in the force-enhanced state viii

9 Figure 4.2 Correlations between the amounts of RFE versus sarcomere length nonuniformity. SD of the mean sarcomere lengths in the force-enhanced state had a non-significant, weak, positive correlation with RFE (r = 0.254, p = 0.426) (left). The increase in SD of the mean sarcomere lengths from the isometric to forceenhanced states had a non-significant, weak, negative correlation with RFE (r = , p = 0.328) (right). Marker labels on each graph indicate which myofibril is represented Figure 4.3 Correlation between the amounts of sarcomere length non-uniformity (SD of the mean sarcomere lengths) in the force-enhanced state versus the isometric state. A significant, strong, positive correlation was found (r = 0.906, p < 0.001). Marker labels indicate which myofibril is represented ix

10 List of Symbols, Abbreviations and Nomenclature Symbol RFE SLNT SD NA OD ID RPM PFE Definition Residual force enhancement Sarcomere Length Non-uniformity Theory Standard deviation Numerical aperture Outer diameter Inner diameter Revolutions per minute Passive force enhancement x

11 Epigraph The important thing is not to stop questioning. Curiosity has its own reason for existing. Albert Einstein xi

12 Chapter One: Introduction Skeletal muscle s main function is to produce force to allow movement of the body. Despite this significance and the vast amount of research that has been conducted within the field of skeletal muscle mechanics, many aspects of muscular contraction are still unknown. The current theory of muscle contraction, the Cross-Bridge Theory, was first proposed and defined mathematically by A. F. Huxley in Huxley s work at that time was influenced by his own findings, which were supported by others, that the A-band within a sarcomere does not significantly change length during contraction (A. F. Huxley & Niedergerke, 1954; H. E. Huxley & Hanson, 1954). From this result, he proposed that muscle contraction takes place via a sliding mechanism of the actin filaments into the spaces between the myosin filaments. This theory was then furthered by A. F. Huxley & Simmons (1971), through the development of a mathematical model of cross-bridge attachment involving the rotation of a myosin head to states of lower potential energy, resulting in a power stroke, and subsequent force production. The Cross-Bridge Theory has been rigorously analyzed and, to date, it is the generally accepted paradigm of muscle contraction (A. F. Huxley & Peachey, 1961; H. E. Huxley, 1969; Rayment et al., 1993; Sosa, Popp, Ouyang, & H. E. Huxley, 1994). Two important qualities of any theory are the assumptions upon which it is based and its ability to make accurate predictions. The assumptions of the Cross-Bridge Theory led to the prediction that for a given level of activation, force production is proportional to actinmyosin filament overlap, or total sarcomere length, which has been demonstrated experimentally for isometric contractions (Gordon, A. F. Huxley, & Julian, 1966). However, when tested after dynamic contractions, skeletal muscle displays history 1

13 dependent properties, which refer to the influence of a muscle s previous contractile history or conditions on the muscle s future force production abilities. One such property is residual force enhancement (RFE), which is defined as the excess amount of steady-state force exhibited during an isometric contraction following an active stretch, compared to the force observed during a purely isometric contraction at the same final length (Abbott & Aubert, 1952; Edman, Elzinga, & Noble, 1982). RFE has been demonstrated at all levels of muscle hierarchy, from whole muscle to individual sarcomeres; however, it cannot easily be explained by the Cross-Bridge Theory. The Sarcomere Length Non-uniformity Theory (SLNT) is currently the most popular explanation for RFE (Morgan, 1990, 1994). It is based on the idea that sarcomeres are unstable on the descending limb of the force-length relationship and support for this theory was provided by observations demonstrating that active stretching of muscle results in nonuniform sarcomere lengths (Bartoo, Popov, Fearn, & Pollack, 1993; Gordon et al., 1966; Hill, 1953; A. F. Huxley & Peachey, 1961; Julian & Morgan, 1979). Unfortunately, despite the popularity of the SLNT, the three main predictions of this theory have never been experimentally tested. Therefore, the objective of this thesis was to test the predictions of the SLNT by testing isolated myofibrils in a manner that allowed for the direct comparison between isometric and force-enhanced states. In order to gain a detailed understanding of the background of this thesis, Chapter 2 provides a review of the relevant literature, which discusses the current understanding of muscle mechanics, explains the phenomenon of RFE, and describes the SLNT. Chapter 3 outlines the specific methodology that was used in these experiments. Chapter 4 highlights the experimental results that are relevant to the SLNT. Finally, the thesis finishes with a 2

14 discussion (Chapter 5), which summarizes the findings of the research and discusses their implications on the SLNT, identifies limitations of this work, and suggests potential directions for future research. 3

15 Chapter Two: Literature Review 2.1 Muscle hierarchy and architecture There are three main types of muscle: skeletal, smooth, and cardiac. Skeletal and cardiac muscle demonstrate band-like patterns, known as striations. While cardiac and smooth muscles are controlled by the autonomic nervous system, skeletal muscle is the only type of muscle that is under direct voluntary control. Skeletal muscle is arranged in a hierarchical manner, with each structure contained within its own connective tissue sheath (Figure 2.1). A fascia and the epimysium surround the whole muscle. The epimysium is made up of irregularly distributed collagenous, reticular and elastic fibers, connective tissue cells, and fat cells. The whole muscle is composed of muscle fascicles, which are contained in the perimysium. The next structures are the muscle fibers, also known as the individual muscle cells. The fibers are surrounded by the thin endomysium, which is mainly composed of reticular fibers. Finally, fibers are made up of myofibrils, which are arranged in a parallel manner to each other and are contained within the sarcolemma (Herzog, 2007). 4

16 Muscle Fascia Epimysium Fascicle Muscle Fiber (Cell) Perimysium Endomysium Sarcolemma Myofibril Figure 2.1 Schematic image of the hierarchical structure of skeletal muscle. Structural levels are labeled in bold on the right of the diagram and connective tissue sheaths are labeled and indicated on the left. Adapted from Herzog (2007). Myofibrils are made up of individual sarcomeres, which are connected by Z-lines made up of structural proteins (Figure 2.2). Three main protein filaments, arranged in a specific geometry, make up the sarcomere. The thin filament is mainly composed of actin, but also includes tropomyosin and troponin. The thick filament, composed of myosin, lies central in the sarcomere and has extensions, or cross-bridges, on each side, which reach out towards the actin filaments. There are no cross-bridges in the center of the myosin filament, making up the bare region. The third protein filament of the sarcomere is titin. Titin extends from the Z-line to the center of the sarcomere, or the M-line, through direct anchoring to the myosin filament. Under phase contrast microscopy, a sarcomere is identified as having a dark central region known as the A-band (anisotropic), which is 5

17 flanked by two lighter regions known as the I-bands (isotropic). The A-band is defined by the length of the myosin filament, including the area where it is overlapped by the actin filament. The I-band includes the Z-line and the actin filament portion that is not overlapped by the myosin filament. The portion of the A-band that does not contain actin filaments is known as the H-zone. Length changes of skeletal muscle originate at the individual sarcomere level. This typically occurs through a change in the length of the I- band, by which the actin filaments slide into (shorten) or out of (lengthen) the spaces in between the myosin filaments (A. F. Huxley & Niedergerke, 1954; H. E. Huxley & Hanson, 1954). Sarcomere Actin Filament Myosin Filament M-line Titin Z-line I-band Bare Region H-zone A-band Z-line I-band Figure 2.2 Schematic diagram of a sarcomere (Z-line to adjacent Z-line), indicating the thin (actin) and thick (myosin) filaments and titin. Various regions of the sarcomere are also labeled, including the A- and I-bands, which are responsible for the dark and light regions, respectively, when viewing a myofibril in phase contrast microscopy. Rabbit psoas muscle myosin filaments are 1.65 µm long, actin filaments are 1.08 µm long (Herzog, Kamal, & Clarke, 1992). 6

18 2.2 Force production Arguably, the most important function of skeletal muscle is its ability to produce force. Skeletal muscle force can be produced in two ways: passively or actively. Both types of force have been demonstrated at all levels of skeletal muscle hierarchy, including isolated myofibrils, in which extracellular structures, such as connective tissue, are removed. Therefore, individual sarcomeres are considered the force producing units of muscle. In addition, due to the in-series mechanical connections between sarcomeres, each sarcomere along an isolated myofibril must hold the same amount of tension Passive force production Passive force production is considered the force that resists elongation of a sarcomere independent of the attributes of active force, which will be discussed in detail in the following section (Horowits, Kempner, Bisher, & Podolsky, 1986). The connective tissue sheaths surrounding the whole muscle, fascicles, and fibers, all provide a great amount of passive force in skeletal muscle; however, in an isolated myofibril, with all connective tissue removed, it is well accepted that passive force is a product of the elongation of the I-band portion of titin (Funatsu, Higuchi, & Ishiwata, 1990; Horowits et al., 1986; Horowits & Podolsky, 1987; Horowits, 1992; Linke, Popov, & Pollack, 1994; Wang, McCarter, Wright, Beverly, & Ramirez-Mitchell, 1991). Titin is considered to act as a nonlinear spring, with passive forces beginning at a sarcomere length of approximately 2.6 µm in rabbit psoas muscle and increasing exponentially as the sarcomere lengthens (Granzier, Kellermayer, Helmes, & Trombitás, 1997; Horowits, 1992; Ramsey & Street, 1941; Wang et al., 1991). Titin s passive elasticity also provides positional stabilization of the myosin 7

19 filament to the center of the sarcomere through the rigid attachment of titin to myosin (Funatsu et al., 1990; Horowits et al., 1986; Horowits & Podolsky, 1987) Active force production: the Cross-Bridge Theory Prior to 1954, it was believed that active force was produced by a sarcomere through the shortening of the A-band. In 1954, H. E. Huxley and Hanson and A. F. Huxley and Niedergerke published back-to-back articles in the scientific journal Nature demonstrating that this was incorrect; the myosin filament remains the same length upon activation. These findings were accompanied by suggestions that contraction was accomplished by a sliding of the actin filaments into the spaces in between the myosin filaments. Both articles furthered this idea, by proposing that force might be generated at various points within the region of actin-myosin overlap. With all of this under consideration, in 1957, A. F. Huxley presented the first version of the Cross-Bridge Theory of muscle contraction (Figure 2.3). His theory postulated that the myosin filaments have elastic sliding cross-bridges on the side of the filament, extending towards the actin filament. Huxley suggested that thermal agitation causes the crossbridges to oscillate about their equilibrium position (O). He believed that if the attachment point of a cross-bridge (M) came close enough to a fixed attachment point on the actin filament (A) then attachment would occur. Following M-A attachment, tension in the elastic link of the cross-bridge would result in a sliding of the actin filament relative to the myosin filament. In order to facilitate the active shortening property of muscle, Huxley accompanied this model with rate functions of M-A attachment and detachment, which are dependent upon the distance (x) of A from O (Figure 2.4). He proposed that the rate 8

20 function of attachment (f) increases linearly as x increases in the direction towards the nearest Z-line; while the rate function of detachment (g) also increases, but to a lesser extent. It was believed that f would be zero when the cross-bridge was on the opposite side of the O, but that on this side, g would be extremely large. These rate functions meant that an M-A attachment was only possible on the side of O that would result in muscle shortening and that following shortening, when M returns to O, detachment would occur. Myosin Filament Actin Filament O M x A Figure 2.3 Schematic diagram of the 1957 Cross-Bridge Theory. Myosin filament crossbridge attachment site (M) oscillates about its equilibrium positon (O) and can attach to actin filament fixed attachment site (A). Following attachment, tension in the cross-bridge causes M-A to move towards O, resulting in the sliding of the actin filament relative to the myosin filament according to the directions indicated by the arrows. Adapted from A. F. Huxley (1957). g O f g x Figure 2.4 Rate functions of attachment (f) and detachment (g) for M-A (Figure 2.3) crossbridge attachments as a function of the distance (x) from the equilibrium position (O) to the actin filament attachment site. Adapted from A. F. Huxley (1957). 9

21 In 1971, A. F. Huxley and Simmons modified the Cross-Bridge Theory by developing a mathematical model based on experimental observations of force transients during muscle length changes, which could not be explained by the 1957 model (Figure 2.5). They proposed that the myosin cross-bridges should be modeled as an instantaneously elastic link (AB) extending out from the myosin filament with a rotating head (H) at the end. The rotating head contains multiple combining sites (Mn) which are able to attach to corresponding sites on the actin filament (An). Stable positions occur when two consecutive MA sites are attached simultaneously and affinity between the myosin and actin sites increases from M1A1 to MnAn. This results in a favourable rotation of the head towards the final stable position (lowest potential energy state), resulting in a power stroke, or force production through the sliding of the actin filament. Following the final position, the binding and subsequent hydrolysis of ATP facilitates the detachment of the head from the actin filament, followed by its free rotation back to its initial position (Rayment et al., 1993). Many researchers have rigorously analyzed this theory and its many properties and to date it is still the prevailing paradigm of skeletal muscle active force production (A. F. Huxley & Peachey, 1961; H. E. Huxley, 1969; Rayment et al., 1993; Sosa et al., 1994). 10

22 Myosin Filament A B 1 B 2 H M 4 Actin Filament M 1 A 1 A 4 Figure 2.5 Schematic diagram of the 1971 Cross-Bridge Theory. Interaction between the myosin and actin filaments occurs at the myosin head (H) which extends from the myosin filament via the AB link. The full line shows H in the first stable position, with M1A1 and M2A2 attachments made. The dashed line shows H in the second stable position (M2A2 and M3A3 attached), following a rotation of H about B. Adapted from A. F. Huxley and Simmons (1971) Force-length relationship The Cross-Bridge Theory includes basic assumptions of the contraction of skeletal muscle. Three of these assumptions are that (1) the average force of each cross-bridge is the same, that (2) cross-bridges act independently of each other, and that (3) cross-bridges and attachment sites are uniformly dispersed on myosin and actin filaments, respectively. From these assumptions, the Cross-Bridge Theory predicts that sarcomere force production is proportional to the number of cross-bridges attached; therefore, force is proportional to the amount of overlap between the myosin and actin filaments within a sarcomere. This length-dependence prediction was previously suggested by multiple authors (Hill, 1953; Ramsey & Street, 1941), and was supported in 1954 by A. F. Huxley and Niedergerke, who related it to their proposed sliding filament theory. In 1966, Gordon, A. F. Huxley, and Julian provided experimental evidence confirming the association between the degree of myofilament overlap and isometric steady-state force, which is known as the force- 11

23 length relationship of muscle (Figure 2.6). These authors are highly credited for their work due to the support they provided linking various points of the force-length curve and specific degrees of actin-myosin filament overlap. As seen in Figure 2.6, the force-length relationship exhibits three distinct portions: the ascending limb (blue), the plateau (yellow) and the descending limb (red). The ascending limb consists of two parts: initially, the sarcomere is at a length at which the Z-lines are compressing the myosin filament and the actin filaments are fully overlapping each other (A), thus diminishing force production; as the sarcomere lengthens, actin filaments experience less overlap of each other, and the sarcomere reaches a length where the Z-lines are just in contact with the myosin filament (B); finally, the sarcomere reaches a length at which there is no actin-actin filament overlap (C). The plateau is characterized by the region which allows for maximal cross-bridge interactions, extending from point C to the length at which the actin filaments reach the edges of the bare region of the myosin filament (D). Beyond this point, extension of the sarcomere results in a loss of potential cross-bridge attachments due to less actin-myosin overlap. This defines the descending limb, which approaches zero active force production as the sarcomere reaches a length where there is no longer actin-myosin overlap (E). 12

24 Normalized Force 100 B C D A B C D 0 A E Sarcomere Length (µm) E Figure 2.6 Force-length relationship of rabbit psoas muscle identifying the ascending limb (blue), plateau (yellow), and descending limb (red). The points on the curve labelled A-E correspond to sarcomere lengths depicted on the right. The values on the graphs corresponding to points B-E are calculated from the lengths of the rabbit psoas filaments (myosin, m = 1.65 µm; actin, a = 1.08 µm), and the widths of the Z- line (z = 0.1 µm) and bare zone (b = 0.17 µm): B = m + z; C = a + a + z; D = a + b + a + z; E = a + m + a + z (Herzog et al., 1992; Walker & Schrodt, 1973). The grey dashed line on the graph indicates the sarcomere passive force production curve. Adapted from Gordon et al. (1966). 2.3 History dependence of skeletal muscle The force-length relationship of muscle has been tested by many research groups and found to be reasonably accurate for isometric contractions throughout all levels of the muscle hierarchy. However, muscle is dynamic in nature, often undergoing length changes throughout contractions. Therefore, it is necessary to study the properties of muscle under varying conditions Increased force during active stretch Active stretching, or eccentric contraction, of skeletal muscle results in an increase in force production that can be separated into two portions. The first increase in force occurs simultaneously with the increase in muscle length and is known as force enhancement 13

25 during stretch (Figure 2.7). This occurs as an initial rapid increase in force, followed by a slower increase that lasts until the end of the stretch. Force enhancement during stretch is stretch velocity- and amplitude-dependent: increased velocity and/or amplitude of stretch results in greater force production during stretch (Edman et al., 1982). This transient force property of muscle during active stretching was accounted for in the 1971 Cross-Bridge Theory (A. F. Huxley & Simmons, 1971) Increased force following active stretch: residual force enhancement Following the length change of an active stretch, skeletal muscle exhibits a gradual decay in force, as expected, but this force does not return to the predicted force value of the forcelength relationship for an isometric contraction at the final length of the muscle (Figure 2.7) (Abbott & Aubert, 1952; Cavagna & Citterio, 1974; Edman, Elzinga, & Noble, 1978; Edman et al., 1982). This increased force has been coined residual force enhancement (RFE) and it reaches steady-state after approximately 3 seconds following length change and persists to the end of a sustained contraction (Edman et al., 1982). RFE has been found to depend on initial length and amplitude of stretch, but it is independent of the stretch velocity (Abbott & Aubert, 1952; Edman et al., 1978, 1982; Sugi & Tsuchiya, 1988). 14

26 Relative Force RFE Relative Length Time Figure 2.7 Residual force enhancement (RFE) after active stretch of muscle. An isometric reference contraction at the final length is depicted by the grey lines. The black line indicates an initial isometric contraction at a shorter length (solid), followed by a stretch (dashed), and finally the isometric contraction following the active stretch (dotted). RFE introduces a conundrum into the Cross-Bridge Theory because it distinctly violates the force-length relationship, whereby sarcomeres that should exhibit the same amount of actin-myosin filament overlap are able to produce different amounts of force (for a given amount of activation) (Figure 2.8). In an attempt to explain this observation, within the constraints of the Cross-Bridge Theory, some researchers initially suggested that through active stretch, cross-bridge dynamics must be altered in a manner that permits extra crossbridge attachment. This hypothesis was tested through stiffness measurements, after which it was concluded that overall stiffness of the muscle was not significantly changed, thus the proportion of attached cross-bridges was likely unaltered (Edman et al., 1982; Julian & Morgan, 1979; Sugi & Tsuchiya, 1988). Therefore, RFE is unaccounted for in the mathematical model of the Cross-Bridge Theory. 15

27 Normalized Force Normalized Sarcomere Length Figure 2.8 Normalized forces obtained from purely isometric contractions (circles) and from isometric contractions following active stretches of different amplitudes (squares). Black dashed lines indicate initial lengths of each stretched condition. Vertical grey lines indicate that sarcomeres at the same final lengths (110, 115, and 120 %) can produce different amounts of steady-state isometric force. Values approximated from Rassier and Herzog (2004). Despite the uncertainty of the mechanism of RFE, previous researchers have demonstrated the occurrence of this phenomenon at all levels of the muscle hierarchy, from whole muscle to individual sarcomeres (Abbott & Aubert, 1952; Cavagna & Citterio, 1974; Edman et al., 1978, 1982; Herzog & Leonard, 2002; Joumaa, Leonard, & Herzog, 2008; Julian & Morgan, 1979; Leonard, DuVall, & Herzog, 2010; Morgan, Whitehead, Wise, Gregory, & Proske, 2000; D. Rassier, Herzog, & Pollack, 2003; D. Rassier & Pavlov, 2012; Sugi & Tsuchiya, 1988). An isolated myofibril preparation was first shown to exhibit RFE by Joumaa et al. (2008). Due to this, and other similar observations, it is accepted that RFE is a sarcomeric property of skeletal muscle (Leonard et al., 2010). Therefore, as isolated 16

28 myofibrils are capable of exhibiting RFE, and are thin enough to be rapidly maximally activated in solution via calcium influx, while retaining the natural structural organization of the contractile proteins of in vivo muscle and eliminating the effects of fatigue (Bartoo et al., 1993; Llewellyn, Barretto, Delp, & Schnitzer, 2008; Morgan et al., 2000), myofibrils are the ideal preparation to study the characteristics of RFE (Joumaa, Leonard, et al., 2008; Morgan, 1990, 1994). In addition, at the myofibril level, all sarcomeres must hold the same tension, which conveniently allows for the force that is measured at the end of the myofibril to be directly related to the length of each sarcomere (Bartoo et al., 1993; Herzog, Joumaa, & Leonard, 2010b; Joumaa, Leonard, et al., 2008). 2.4 Sarcomere Length Non-uniformity Theory Description of the Sarcomere Length Non-uniformity Theory Presently, the most popular explanation for RFE is the Sarcomere Length Non-uniformity Theory (SLNT), which arose from Morgan's (1990, 1994) popping sarcomere hypothesis. The foundation of the SLNT hinges on Hill's (1953) proposal that sarcomeres are inherently unstable on the descending limb of the force-length relationship due to the negative slope of the limb indicating that force decreases with increasing sarcomere length. Consequently, at sarcomere lengths along the descending limb, long sarcomeres are thought to be weak in comparison to shorter sarcomeres. The idea behind the SLNT is that active stretching of muscle along the descending limb results in sarcomere length nonuniformities, which leads to differential strengths between sarcomeres. This difference results in the long/weak sarcomeres becoming longer and weaker as they are unable to hold the tension of the other sarcomeres due to lengthening at high velocities. Eventually, these 17

29 sarcomeres are stretched beyond actin-myosin filament overlap, at which point they pop and their tension is sustained by passive forces equal to the active force being produced by the shorter/stronger sarcomeres (Morgan, 1990, 1994). Morgan (1990, 1994) predicts that this process continues with sequentially weaker sarcomeres popping until the end of the stretch. This allows a greater portion of the total length change to be taken up by the weaker sarcomeres through their rapid lengthening, while the stronger sarcomeres demonstrate smaller length changes (Abbott & Aubert, 1952). Following active stretch, Morgan (1994) suggests that sarcomeres exist at two distinct lengths, one shorter and one longer than the average sarcomere length. As a consequence, the final force exhibited is equal to the active force producing ability of the sarcomeres at the short length. This final force is inherently greater than the force associated with the average sarcomere length that presumably occurs in a purely isometric contraction, which does not involve the development of sarcomere length non-uniformities. This concept had been suggested previously by Edman et al. (1982). A visual representation of the SLNT is shown in Figure

30 Normalized Force 100 A C 1 RFE C 2 A B B C C 1 C 1 C 2 C 1 0 Sarcomere Length (µm) Figure 2.9 Diagram of Morgan's (1990, 1994) popping sarcomere hypothesis. A and B represent the average sarcomere lengths and associated forces of a short (A) and long (B) isometric contraction. During an active stretch from an average sarcomere length of A to B, some sarcomeres are only slightly stretched (C1), whereas a few others take on most of the length change (C2). These sarcomeres lengthen rapidly and eventually pop to a length beyond actin-myosin filament overlap, resulting in non-uniform sarcomere lengths. At this point, the tension of the sarcomeres at C2 is supported by passive forces. This allows the total force produced by the actively stretched muscle to be greater than the purely isometric contraction at the same final length (RFE) Predictions of the Sarcomere Length Non-uniformity Theory Uniform sarcomere lengths in isometric contractions Morgan (1990, 1994) predicts that isometric contractions on the descending limb of the force-length relationship will inherently involve sarcomere length non-uniformities due to the unstable negative slope of this portion of the relationship, and this has been observed experimentally by many researchers (Bartoo et al., 1993; Gordon et al., 1966; A. F. Huxley & Peachey, 1961; Joumaa, Leonard, et al., 2008; Julian & Morgan, 1979; Talbot & Morgan, 1996). Small variations in length may arise from differences in cross-sectional area of contractile material, or the number of attached cross-bridges, or a combination, all while allowing the sarcomeres to maintain the same tension (Morgan, 1990). Despite this, 19

31 in order for the mathematical models of the SLNT to hold true, sarcomeres in steady-state isometric contractions on the descending limb must be relatively uniform in length (Morgan, 1990, 1994; Zahalak, 1997). Sarcomere length distribution can be quantified by the standard deviation (SD) of the mean sarcomere length of a myofibril (Joumaa & Herzog, 2010), which more accurately represents the variation of sarcomere lengths than the previously used standard error of the mean (Telley et al., 2006). To date, the sarcomere length distribution during isometric contractions of isolated myofibrils on the descending limb has never been rigorously experimentally quantified (Joumaa, Leonard, et al., 2008) Active stretch results in sarcomere length non-uniformities The SLNT also predicts that actively stretched muscle will demonstrate an increase in sarcomere length non-uniformities in comparison to an isometric contraction at the same final length. Specifically, the SLNT predicts that following active stretch, there will be two distinct populations of sarcomere lengths: one shorter and one longer than the average sarcomere length (Morgan, 1994). Previous studies have found that sarcomere lengths are non-uniform following active stretch (Joumaa, Leonard, et al., 2008; D. Rassier et al., 2003); however, the sarcomere length distributions (SD) have never been experimentally quantified and compared for these states in the same myofibril at the same final length on the descending limb. Further, it has yet to be determined whether or not the isometric contraction following active stretch demonstrates the pseudo bi-modal sarcomere length distribution that is predicted by the SLNT. 20

32 Force-enhanced state exhibits popped sarcomeres The final prediction of the SLNT is that following active stretch some sarcomeres will be popped beyond actin-myosin filament overlap, which has been demonstrated in whole muscle preparations (Talbot & Morgan, 1996). Contrary to this, other research has suggested that it was possible to observe RFE in isolated myofibrils without popped sarcomeres (Telley et al., 2006); however, Morgan & Proske (2006) argue that the conditions required for sarcomere popping had not been met by these researchers. In addition, Telley et al. (2006) note that they only held the isometric contraction post-stretch for 1 second, during which the force was still in the transient phase. Therefore, the sarcomere dynamics identified were not those of a RFE state, so it is currently unknown if RFE is always accompanied by popped sarcomeres. 2.5 Summary RFE is a phenomenon that has been well observed at all levels of skeletal muscle hierarchy. Despite the widespread acceptance that RFE is a characteristic of sarcomeres, the current theory of muscle contraction, the Cross-Bridge Theory, cannot account for the increase in force observed in isometric contractions following active stretch compared to purely isometric contractions at the same final length. To date, the SLNT is the most popular explanation for RFE. This theory is based on a mathematical model with three main predictions: (1) sarcomeres in isometric contractions are uniform in length, (2) active stretch results in sarcomere length non-uniformities, and (3) the force-enhanced state exhibits sarcomeres at lengths that are popped beyond actin-myosin filament overlap. Unfortunately, previous research has never experimentally quantified the amount of 21

33 sarcomere length non-uniformity in a purely isometric state and a force-enhanced state at the same final length in a single myofibril. In addition, discrepancies exist amongst the evidence in regard to popped sarcomeres in the force-enhanced state. 2.6 Purpose The purpose of this research was to experimentally test the predictions of the SLNT through the comparison of isolated myofibrils in isometric contractions pre- and post-active stretch. 2.7 Hypotheses The following hypotheses were made in accordance with the SLNT: (1) Isometric contractions of myofibrils on the descending limb of the force-length relationship will have sarcomeres of uniform length (SD 0.1 µm, given the resolution of the system). (2) Following active stretch on the descending limb, myofibrils in isometric contractions exhibiting RFE will have more non-uniform sarcomere lengths (> 0.1 µm increase in SD) than in purely isometric contractions at the same final length. Specifically, the force-enhanced state will reveal a pseudo bi-modal distribution of sarcomere lengths. (3) Myofibrils exhibiting RFE will have sarcomeres that have popped beyond actinmyosin filament overlap (sarcomere length 4.0 µm). 22

34 Chapter Three: Methods 3.1 Microscope and apparatus setup A custom-built, bath-like chamber with a glass cover slip across the bottom was positioned on top of a moveable stage mounted on an inverted light microscope (Zeiss Axiovert 200M, Zeiss, Germany). The microscope had four Zeiss objectives: 5x (Numerical Aperture, NA, 0.15), 20x (NA 0.50), 40x (NA 0.75) and 100x oil immersion (NA 1.3) (Zeiss Immersol TM, 518F, Zeiss, Germany). All tests were conducted using the 100x oil immersion objective in phase-contrast illumination to allow for the visualization of sarcomere A- and I-bands. A Rolera Bolt camera (Quantitative Imaging Corp., Surrey, BC, Canada) attached to the microscope was used to record all of the experiments on StreamPix 5 Video Imaging software (NorPix Inc., Montreal, Canada) at 30 Hz (Figure 3.1). The optical resolution of this setup was 87 nm/pixel. To manipulate a myofibril, a 5 µl glass pipette (model# W625CF, Toshiba Corp., Japan) was pulled to a sharp-tipped, fused needle on a pipette puller (Model # 720, Kopf Instruments Ltd., Tujunga, CA, USA) and then placed in a holder attached to the microscope. Manual manipulation of the myofibril was accomplished using a hydraulic micro-manipulator (model# MMN-1, Narishige Co. Ltd., Japan). Automatic manipulation was accomplished using radial piezo-tubes (part# PZT-5H with 90 quadrants, Boston Piezo-Optics Inc., Bellingham, MA, USA), which were controlled through custom written software (LabVIEW, National Instruments Corp., Austin, TX, USA). One of a pair of custom-built nanofabricated silicon nitride cantilevers (Cornell Nano-scale Facility of Cornell University, Ithaca, NY, USA) with a stiffness of 132 nn/µm was attached to the 23

35 other side of the myofibril and was manipulated manually using a hydraulic micromanipulator (Fauver, Dunaway, Lilienfeld, Craighead, & Pollack, 1998). To activate the myofibril, a specialized jetted fluid delivery (Jacuzzi) technique was used. This technique delivered fluid via a glass pipette (outer diameter, OD: 1.5 mm; inner diameter, ID: 0.86 mm; Item #: BF , Sutter Instrument Co., Novato, CA, USA), which was custom pulled to a sharp, open tip using a two-step needle puller (Step 1 = 58.9, Step 2 = 43.4, Model PC-10 # 12009, Narishige Co. Ltd., Japan) and adjusted using a Microforge heater (MF-830-CA #12001, Narishige Co. Ltd., Japan) to an ID of approximately 0.18 mm. The needle was then glued (Super Fast Epoxy Cement, Elmer s Products Canada, Markham, Ontario, Canada) to polyethylene tubing (OD: 0.61 mm, ID: 0.28 mm, Cat: , Warner Instruments, Hamden, CT, USA) which was glued at the other end to a blunt needle (Monoject Aluminum Hub Blunt Needle, # , Kendall, Mansfield, MA, USA) to allow for syringe attachment (part# CABD309604, VWR Inc., Mississauga, Ontario, Canada) for fluid delivery. The Jacuzzi needle was manually positioned using a hydraulic micromanipulator. 24

36 Condenser Lens Needle Micromanipulator Lamp Cantilever Micromanipulator Jacuzzi Micromanipulator Lens Cantilever Pair Myofibril Data Acquisition Camera Mirror Needle Jacuzzi Needle Figure 3.1 Schematic drawing of the experimental set-up. The diagram on the right depicts the microscopic field of view (not to scale). Adapted from Rassier, Herzog, and Pollack (2003). 3.2 Specimen harvesting Ethics approval was granted by the Life and Environmental Sciences Animal Care Committee of the University of Calgary. Six month old female New Zealand White rabbits (Riemens Fur Ranches Ltd., Saint Agatha, Ontario, Canada) were euthanized by an intravenous injection of sodium pentobarbital (MTC Inc., Cambridge, Ontario, Canada). Small strips (approximately 2.5 cm long, 2-3 mm diameter) of rabbit psoas muscle were dissected using Dumont #3 forceps (Fine Science Tools Ltd., Vancouver, BC, Canada) and a #15 scalpel blade (VWR Inc. Mississauga, Ontario, Canada). Each strip was then tied (Black Braided Silk, Ref #SP120, LOOK, PA, USA) to a small wooden stick (Puritan Applicators, Ref # 807, Puritan Medical Products Co. LLC, Guilford, Maine, USA) to preserve the in-situ muscle length and the ends of the strips were cut to free the specimen. 25

37 Two of these specimens were then placed in a 15 ml centrifuge tube (Falcon-BD part# , VWR Inc., Mississauga, Ontario, Canada) containing 14 ml of rigor solution (see Appendix A for all solution compositions). These samples were then stored at 4 C (ph 7.0) for 6 hours. They were then transferred to a new 15 ml centrifuge tube containing a solution of fresh rigor solution and glycerol (50:50) and stored at 4 C (ph 7.0) for 16 hours. Finally, the samples were transferred to a new centrifuge tube containing fresh rigor solution and glycerol (50:50, 4 C, ph 7.0) and stored at -20 C for 10 to 20 days. Each of the preceding solutions contained one tablet of protease inhibitors (Complete, Roche Diagnostics, Montreal, Quebec, Canada) per 50 ml of rigor solution to minimize proteolytic activity and aid in the chemical isolation of myofibrils. 3.3 Isolation of single myofibrils On the day of each experiment, one muscle strip (still tied to the wooden stick) was placed in a centrifuge tube containing 14 ml of rigor solution (4 C, ph 7.0) on ice for 2 hours to remove excess glycerol from the sample. The sample was then transferred to a glass Petri dish (on ice) containing fresh rigor solution (4 C, ph 7.0). A small section of muscle tissue (approximately 5 mm long, 1 mm thick) was then cut from the middle region of the sample (between the sutures that were used to maintain the in-situ length) using a #15 scalpel blade. This muscle section was then added to 2.0 ml of rigor solution (4 C, ph 7.0) in a plastic homogenization tube (part# , Harvard Apparatus Inc., St-Laurent, Quebec, Canada) and blended in a tissue homogenizer (Model PRO250, Pro Scientific, Oxford, CT, USA) using the following sequence: twice for 5 seconds at 10,000 revolutions per minute (rpm), twice for 1 second at 13,200 rpm, five times for 1 second at 16,000 rpm, three times 26

38 for 1 second at 18,000 rpm, and six times for 1 second at 26,000 rpm. The homogenized solution containing rigor solution and suspended isolated myofibrils was then placed on ice for 1 hour to allow the heaviest myofibrils and connective tissue debris to settle to the bottom of the tube. 3.4 Experimental protocol A small amount of the homogenized solution (200 µl) was placed in the chamber on top of the microscope and allowed to stabilize for 10 minutes. This allowed the smallest myofibrils suspended in the solution to settle onto the coverslip. The rigor solution was then replaced by relaxing solution (room temperature, ph 7.0, Appendix A) through a vigorous flushing of the bath via two syringes attached to solution input and removal ports on the chamber. This removed any loose myofibrils that remained suspended in the solution, while leaving those that had settled onto the coverslip. A total of 12 myofibrils from 8 different rabbits were tested in the following manner. A single myofibril with good striation pattern and 5 23 sarcomeres in length was attached by one end to a glass needle by piercing the myofibril. The myofibril was then wrapped 180 around the glass needle to ensure adequate attachment. One of the pair of cantilevers was then glued (Dow Corning 3145 and :50 mixture, Midland, MI, USA) to the other end of the myofibril (Figure 3.2). The myofibril was then manually manipulated to a starting average length of 2.4 µm/sarcomere (passive short). The automated needle control software program was then started and it controlled the length of the myofibril throughout the experiment according to the protocol outlined in Figure 3.3. This involved passively stretching (0.1 µm/s/sarcomere) the myofibril to an average length of

39 µm/sarcomere (passive long). This average sarcomere length was chosen as it ensured that the sarcomeres would be at an average length along the descending limb of the force-length relationship, regardless of some compliance of the system, which resulted in slightly shorter individual sarcomere lengths. In addition, it has been suggested that the optimum sarcomere length for RFE is between 2.70 and 3.15 µm (Edman et al., 1982). The myofibril was then maximally activated via the Jacuzzi technique (room temperature, ph 7.0, pca = 3.12, Appendix A) and allowed to reach a steady-state (isometric) (Bartoo et al., 1993). The myofibril was then rapidly shortened (0.8 µm/s/sarcomere) to an average sarcomere length of 2.4 µm, held for 10 seconds (active short), and then stretched (0.1 µm/s/sarcomere) back to an average length of 3.2 µm/sarcomere (force-enhanced). The magnitude of stretch was slightly higher (3.4 µm/sarcomere) for the force-enhanced state in order to accommodate for the increase in force, which resulted in increased lever deflection. While shortening of the myofibril did result in some force depression, it has been previously shown that an isometric pause of at least 1 second in between active shortening followed by active stretching greatly reduces, if not eliminates depression effects on the subsequent RFE (Edman et al., 1982; D. Rassier & Herzog, 2004b). 5 µm Figure 3.2 Photograph of a single myofibril with 10 A-bands (dark bands). The glass needle can be seen on the left and the cantilever pair on the right. 28

40 Average Sarcomere Length (µm) Passive Long Passive Short Isometric Active Short Force-Enhanced Time (s) Figure 3.3 Experimental protocol depicting average sarcomere length changes throughout each experiment. The yellow star indicates the time point at which the myofibril was activated and the shaded yellow box signifies that the myofibril was active for the remainder of the experiment. Individual states that were of interest to this study are identified as passive short (purple), passive long (orange), isometric (blue), active short (green), and force-enhanced (red). 3.5 Length and force measurements Individual sarcomere lengths within each tested myofibril were quantified using a custom written software program in MATLAB (The Mathworks Inc., Natick, MA, USA). Sarcomere length was defined as the distance between centroids of adjacent A-bands, as identified visually and by the MATLAB software program (Herzog, Joumaa, & Leonard, 2010a; Herzog et al., 2010b; Joumaa & Herzog, 2010; Joumaa, Leonard, et al., 2008; Joumaa, Rassier, Leonard, & Herzog, 2007; Panchangam & Herzog, 2011; Pavlov, Novinger, & Rassier, 2009; D. Rassier et al., 2003; D. Rassier & Pavlov, 2012). The software program was also used to track the displacement of the attached cantilever relative to the unattached, or reference, cantilever. Force was then calculated by multiplying the displacement of the cantilever by its known stiffness (132 nn/µm). Individual sarcomere lengths and force were obtained throughout the course of each experiment at a frequency 29

41 of 3 Hz (every tenth video frame). This resulted in a full time-history trace for each of the 12 myofibrils tested. Through visual analysis of the time-history sarcomere length and force traces, the five steady states were determined. The steady states were: passive short, passive long, isometric, active short, and force-enhanced (Figure 3.3). Mean sarcomere length, SD of the mean sarcomere length, and force were obtained for each state and used in the statistical analyses of the data. 3.6 Statistical analyses Statistical analyses were performed to determine if sarcomere lengths were uniform in isometric contractions and if active stretch resulted in an increase in sarcomere length nonuniformities. The third prediction of the sarcomere length non-uniformity theory, that the force-enhanced state exhibits popped sarcomeres, was analyzed by determining if any individual sarcomeres within each myofibril had a length of 4.0 µm or greater. To analyze significance, a Friedman s ANOVA (α = 0.05) was conducted between the five steady states for each of the three dependent variables: mean sarcomere length, SD of the mean sarcomere length, and force. When significance was indicated, individual pairwise Wilcoxon Tests with a Bonferroni Correction (adjusted α = 0.005) were used to elucidate where significant differences had occurred. 30

42 Chapter Four: Results 4.1 Mean sarcomere lengths Mean values (± 1 SD) for the 12 myofibrils tested in each of the five determined steady states (passive short, passive long, isometric, active short, and force enhanced) are displayed in Table 4.1. Statistical analysis revealed no significant difference (α = 0.005) between mean sarcomere lengths in the isometric (mean ± 1 SD: 2.8 ± 0.3 µm) and forceenhanced (2.9 ± 0.3 µm) states (z = , p = 0.048). In addition, the mean sarcomere lengths in the isometric and force-enhanced states for each individual myofibril (see Raw Data in Appendix B) were either within 0.1 µm of each other, which is within the resolution of the system, or the force-enhanced state mean sarcomere length was greater, but not by more than 0.2 µm. These findings confirmed that, according to the force-length relationship, passive and active forces should have been similar between these two states. Table 4.1 Mean sarcomere lengths, SDs of the mean sarcomere lengths, and forces for each of the steady states within the 12 myofibrils. Steady State (n = 12) Mean Sarcomere Length (µm) Mean SD of the Mean Sarcomere Length (µm) Mean Force (nn) Passive Short 2.5 ± ± ± 3 Passive Long 3.1 ± ± ± 18 Isometric 2.8 ± ± ± 44 Active Short 2.1 ± ± ± 39 Force-Enhanced 2.9 ± ± ± 52 31

43 4.2 Force The isometric steady-state forces (127 ± 44 nn) were significantly greater than the passive forces (31 ± 18 nn) at similar lengths (z = , p = 0.002) (Table 4.1). In addition, the isometric forces were comparable to values observed by previous researchers for maximal contractions of isolated myofibrils along the descending limb of the force-length relationship (Herzog et al., 2010a, 2010b; Joumaa & Herzog, 2010; Joumaa, Leonard, et al., 2008; Leonard & Herzog, 2010; Pavlov et al., 2009), thus supporting that maximal activation was achieved. Following active stretch, RFE was observed in all of the myofibrils tested. Each myofibril exhibited a minimum force increase of 25 nn, which exceeded the resolution of the system (13 nn). The force enhanced states (174 ± 52 nn) demonstrated a mean force enhancement of 39 ± 15 % of the force produced in the isometric states, which was a significant increase (z = , p = 0.002) (Table 4.1 and Table 4.3). 4.3 Predictions of the Sarcomere Length Non-uniformity Theory Individual myofibril (n = 12) data for the isometric and force-enhanced states are presented in Table 4.2. Myofibril numbering remains consistent through all of the results presented. In addition, the number in brackets in the Myofibril column in Table 4.2 indicates which rabbit the myofibril came from. Table 4.3 provides a summary of the variables that were required to assess the predictions of the SLNT. Sarcomere length histograms for the isometric (blue) and force-enhanced (red) state for each myofibril are displayed in Figure 4.1 (left). In addition, Figure 4.1 (right) provides data on the lengths of each individual sarcomere along the myofibril. The x-axis of each graph represents sarcomere position 32

44 relative to the needle (x = 0) and cantilever (x = maximum) attachment points. The isometric (blue) and force-enhanced (red) state lengths are shown for each sarcomere and a vertical arrow depicts whether the sarcomere got shorter (down) or longer (up) from the isometric to the force-enhanced state. A square marker represents a sarcomere that was the same length in both states. Dotted grey lines on each of the graphs indicate the popping length of the sarcomeres. Table 4.2 Individual myofibril data for the isometric and force-enhanced states and the amount of RFE exhibited. The numbers in brackets in the myofibril column indicate which of the eight rabbits each myofibril came from. Myofibril (Rabbit) Number of Sarcomeres Isometric State Mean Length Force (µm) (nn) Force-Enhanced State Mean Length Force (µm) (nn) RFE (%) 1 (1) ± ± (1) ± ± (2) ± ± (3) ± ± (4) ± ± (5) ± ± (6) ± ± (7) ± ± (7) ± ± (5) ± ± (8) ± ± (2) ± ±

45 Table 4.3 Summary of the variables required to assess the predictions of the SLNT for each individual myofibril and the mean. Values denoted by an asterisk (*) are those that align with the SLNT. Myofibril Isometric SD (µm) Increase in SD (µm) Force- Enhanced SD (µm) Number of Popped Sarcomeres in Force- Enhanced State Number of Popped Sarcomeres in Isometric State 1 0.1* * * 1* * 4* * 3* * 3* * 1* * 1* * 2* * * Mean ± SD 0.7 ± ± ± ± 1 34

46 (1) Uniform sarcomere length distribution in the isometric state (SD = 0.1 µm); no increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.0 µm); and no popped sarcomeres. RFE = 33 % (2) Non-uniform sarcomere length distribution in the isometric state (SD = 0.3 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.2 µm); and no popped sarcomeres. RFE = 23 % 35

47 (3) Non-uniform sarcomere length distribution in the isometric state (SD = 0.5 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.3 µm); and one popped sarcomere in the force-enhanced state. RFE = 25 % (4) Non-uniform sarcomere length distribution in the isometric state (SD = 0.2 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.6 µm); and four popped sarcomeres in the force-enhanced state. RFE = 40 % 36

48 (5) Non-uniform sarcomere length distribution in the isometric state (SD = 0.7 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.4 µm); and three popped sarcomeres in the force-enhanced state, one of which was popped in the isometric state. RFE = 22 % (6) Non-uniform sarcomere length distribution in the isometric state (SD = 0.8 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.2 µm); and three popped sarcomeres in the force-enhanced state, two of which were popped in the isometric state. RFE = 33 % 37

49 (7) Non-uniform sarcomere length distribution in the isometric state (SD = 0.7 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.3 µm); and one popped sarcomere in the force-enhanced state, which was popped in the isometric state. RFE = 42 % (8) Non-uniform sarcomere length distribution in the isometric state (SD = 0.8 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.5 µm); and one popped sarcomere in the force-enhanced state, which was popped in the isometric state. RFE = 33 % 38

50 (9) Non-uniform sarcomere length distribution in the isometric state (SD = 1.6 µm); increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.6 µm); and two popped sarcomeres in the force-enhanced state, both of which were popped in the isometric state. RFE = 47 % (10) Non-uniform sarcomere length distribution in the isometric state (SD = 0.7 µm); no increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.1 µm); and one popped sarcomere in the force-enhanced state, which was popped in the isometric state. RFE = 47 % 39

51 (11) Non-uniform sarcomere length distribution in the isometric state (SD = 1.1 µm); no increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.0 µm); and one popped sarcomere in the force-enhanced state, which was popped in the isometric state. RFE = 78 % (12) Non-uniform sarcomere length distribution in the isometric state (SD = 0.6 µm); no increase in non-uniformity between the isometric and force-enhanced states (ΔSD = 0.0 µm); and no popped sarcomeres. RFE = 46 % Figure 4.1 Sarcomere length data for each of the 12 myofibrils. The isometric and forceenhanced states are represented in blue and red, respectively. The histograms on the left indicate frequencies of each sarcomere length (bins = 0.1 µm), with the vertical grey dashed line indicating the length at which a sarcomere would be considered popped beyond actinmyosin overlap. The graphs on the right show sarcomere length as a function of the sarcomere s position in the myofibril. The first sarcomere was closest to the needle attachment point and the last sarcomere was closest to the cantilever attachment point. Vertical arrows show the direction of the change in length between states, while a square marker indicates no change. The popped sarcomere length is indicated by the horizontal 40

52 grey dashed line. Captions under each pair of graphs identify which myofibril is depicted (number corresponds to Table 4.2, Table 4.3, and Appendix B), the properties of that myofibril in relation to the three predictions of the SLNT, and the amount of RFE exhibited in the force-enhanced state Sarcomere length distribution in isometric contractions For the 12 myofibrils tested, the mean sarcomere length in the isometric state was 2.8 ± 0.3 µm and the mean SD of the mean sarcomere length was 0.7 ± 0.4 µm (Table 4.1). Myofibril 1 was the only myofibril that exhibited a uniform sarcomere length distribution (SD 0.1 µm) in the isometric state. The remaining 11 myofibrils had a range of SDs from 0.2 to 1.1 µm, indicating non-uniform sarcomere length distributions in each of these myofibrils in the isometric state (Table 4.3 and Figure 4.1) Sarcomere length distribution following active stretch The mean increase in SD of the mean sarcomere length from the isometric state to the force-enhanced state was 0.3 ± 0.2 µm, ranging from 0.0 to 0.6 µm (Table 4.3), however, this was not significant (z = , p = 0.008). An increase in SD of more than 0.1 µm was seen in eight myofibrils (Myofibril 2-9), indicating an increase in sarcomere length non-uniformity between the two states. The pseudo bi-modal distribution was not demonstrated by any of the myofibrils. A non-significant, weak, positive correlation was found between RFE and the amount of sarcomere length non-uniformity in the forceenhanced state (r = 0.254, p = 0.426); while a non-significant, weak, negative correlation was found between RFE and the increase in sarcomere length non-uniformity between the isometric and force-enhanced states (r = , p = 0.328) (Figure 4.2). Despite the nonsignificant, weak correlations between RFE and non-uniformity, Figure 4.3 demonstrates 41

53 a significant, strong, positive correlation between sarcomere length non-uniformity in the force-enhanced state compared to the isometric state (r = 0.906, p < 0.001). Force Enhancement (%) r = p = Force-Enhanced State SD of the Mean Sarcomere Length (µm) r = p = Increase in SD from Isometric to Force-Enhanced State (µm) Figure 4.2 Correlations between the amounts of RFE versus sarcomere length nonuniformity. SD of the mean sarcomere lengths in the force-enhanced state had a nonsignificant, weak, positive correlation with RFE (r = 0.254, p = 0.426) (left). The increase in SD of the mean sarcomere lengths from the isometric to force-enhanced states had a non-significant, weak, negative correlation with RFE (r = , p = 0.328) (right). Marker labels on each graph indicate which myofibril is represented. 42

54 Force-Enhanced State SD of the Mean Sarcomere Length (µm) r = p < Isometric State SD of the Mean Sarcomere Length (µm) Figure 4.3 Correlation between the amounts of sarcomere length non-uniformity (SD of the mean sarcomere lengths) in the force-enhanced state versus the isometric state. A significant, strong, positive correlation was found (r = 0.906, p < 0.001). Marker labels indicate which myofibril is represented Popped sarcomeres in the force-enhanced state Nine of the myofibrils (Myofibril 3-11) exhibited at least one sarcomere that had popped beyond actin-myosin filament overlap (Table 4.3 and Figure 4.1). Of these nine, seven myofibrils (Myofibril 5-11) had at least one of the popped sarcomeres at a length beyond actin-myosin filament overlap in the isometric state (Figure 4.1). In addition, Appendix B shows that in three myofibrils (Myofibril 6, 8, and 9), one of the sarcomeres that was popped in both the isometric and force-enhanced states was also popped in the active short state. Overall, none of the 12 myofibrils that were tested satisfied all three of the predictions of the SLNT. Seven myofibrils (Myofibril 3-9) met two predictions: they exhibited an 43

55 increase in sarcomere length non-uniformity from the isometric state to the force-enhanced state, and they had popped sarcomeres. Myofibril 2 only met the prediction of an increase in non-uniformity between states, while Myofibrils 10 and 11 only had popped sarcomeres. Uniform sarcomere lengths in the isometric state was only demonstrated by Myofibril 1. Finally, Myofibril 12 did not satisfy any of the predictions of the SLNT. 44

56 Chapter Five: Discussion 5.1 Objective The objective of this research was to explore the phenomenon of RFE by experimentally testing three of the primary predictions of the SLNT: (1) Sarcomeres in isometric contractions are uniform in length; (2) Active stretch results in sarcomere length non-uniformities; and (3) The force-enhanced state exhibits sarcomeres at lengths that are popped beyond actin-myosin filament overlap. While the results found that none of the myofibrils tested met all three of these predictions, thereby introducing a flaw in the proposed SLNT, the implications of the findings on each of these predictions should be explored independently. Therefore, I will discuss these implications in detail within the context of the results obtained in this study. Following this, limitations of the methodology will be outlined. This will provide segue to a discussion of potential future directions regarding research aimed at identifying the underlying mechanism responsible for RFE, which will be accompanied by an overview of other possible mechanisms that have been investigated by other researchers Predictions of the Sarcomere Length Non-uniformity Theory Sarcomere length distribution in isometric contractions Despite the fact that the mathematical model of the SLNT predicts/requires uniform sarcomere lengths in isometric contractions, the finding that only one of the 12 myofibrils demonstrated this was not entirely unexpected. The crux of the SLNT hinges on Hill's (1953) notion of sarcomere length instability at lengths along the descending limb due to 45

57 the negative slope of this portion of the force-length relationship. In the proposal of the SLNT this inherent instability, resulting in small variations in length during isometric contractions, was noted as a main contributing factor for subsequent sarcomere length nonuniformities following stretch (Morgan, 1990, 1994). Therefore, the finding that sarcomere lengths were typically non-uniform in the isometric state aligned with these predictions, as well as the findings of previous research (Bartoo, Popov, Fearn, & Pollack, 1993; Gordon, A. F. Huxley, & Julian, 1966; A. F. Huxley & Peachey, 1961; Joumaa, Leonard, & Herzog, 2008; Julian & Morgan, 1979; Rassier, 2012; Talbot & Morgan, 1996; Telley et al., 2006). In contrast to Hill s suggestion, however, the experiments conducted here revealed that each myofibril had relatively stable sarcomere lengths, regardless of being at a length along the descending limb. While this represents one of the first times individual sarcomere lengths have been fully quantified in such contractions, sarcomere length stability in isometric contractions on the descending limb has been consistently observed by previous researchers (Edman et al., 1982; Herzog et al., 2010b; Joumaa, Leonard, et al., 2008; Rassier et al., 2003; Telley et al., 2006). With all of this in mind, a proposed mechanism of RFE should take into consideration the findings that isometric contractions on the descending limb of the force-length relationship can involve non-uniform, but stable, sarcomere lengths Sarcomere length distribution following active stretch The core prediction of the SLNT, that sarcomere lengths are more non-uniform following active stretch, was seen in eight of the 12 myofibrils. The specific nature of the nonuniformity, as described by the theory, is that in the force-enhanced state sarcomeres should 46

58 exist at two distinct lengths; this was not demonstrated by any of the myofibrils. Of the four myofibrils that did not increase in non-uniformity, there was high variability in the total amount of non-uniformity: one myofibril (Myofibril 1) had a SD of the mean sarcomere length of 0.1 µm, while another s (Myofibril 11) was 1.1 µm. These results directly oppose Morgan's (1990) prediction based on his mathematical model of the SLNT, which states that active stretching results in the development of extreme sarcomere length non-uniformities. In further discrepancy with the theory, it is suggested that a more nonuniform sarcomere length distribution should result in greater RFE, but the correlation between RFE and sarcomere length non-uniformity was not significant. A non-significant, weak correlation was also found between the increase in sarcomere length non-uniformity from the isometric to the force-enhanced state and RFE. These results suggest that while sarcomere length non-uniformities are often present in the force-enhanced state, the amount of non-uniformity does not seem to directly influence the total amount of RFE, which is supported by previous research (Telley et al., 2006). Variations in sarcomere lengths on the descending limb may simply be a result of a difference in the number of contractile elements between sarcomeres along a myofibril (Morgan, 1990). If this were the case, Joumaa et al. (2008) pointed out that upon active stretching, sarcomeres should maintain the same length ratios. While it was demonstrated in the current work that the amount of sarcomere length non-uniformity between the isometric and force-enhanced states are strongly and significantly correlated, the ratios of individual sarcomere lengths between states was not consistent, supporting the findings of Joumaa et al. (2008). 47

59 Hill s prediction of instability due to the negative slope of the descending limb, which was experimentally confirmed by Gordon et al. in 1966 for isometric contractions, serves as the foundation of the SLNT. In contrast, Allinger, Epstein, and Herzog (1996) concluded from their model and experimental observations that positive-stiffness on the descending limb will result in sarcomere length stability, despite the negative slope. Therefore, many researchers are in agreement that the dynamic behaviour of muscle, such as active stretching, should not be inferred from isometric observations (Rassier & Herzog, 2004a; Telley et al., 2006; ter Keurs, Iwazumi, & Pollack, 1978). From this and the presented results, sarcomere length non-uniformities in the force-enhanced state, as defined by the SLNT, should not be credited as the sole contributor to the development of RFE Popped sarcomeres in the force-enhanced state The final prediction of the SLNT, that the force-enhanced state exhibits popped sarcomeres, was satisfied by nine of the 12 myofibrils. In contrast with the SLNT, the other three myofibrils were able to demonstrate comparable amounts of RFE, despite all of the sarcomeres existing at lengths where actin-myosin filament overlap was still present. A similar result found by Telley et al. (2006) was dismissed by Morgan and Proske (2006) because there was a possibility that maximal activation had not been achieved. According to the results of Bartoo et al. (1993), however, maximal activation of rabbit psoas myofibrils is achieved at a pca of 5.5, which was exceeded by both Telley et al. (2006) and this study. Of the nine myofibrils that had popped sarcomeres, four myofibrils had more than one sarcomere popped beyond actin-myosin filament overlap. According to the SLNT, once a 48

60 sarcomere has popped, the tension within the sarcomere is supported by purely passive elements; therefore, all popped sarcomeres should be at the same length in the forceenhanced state (Morgan, 1990, 1994). This was not demonstrated in any of the four myofibrils. A total of 17 sarcomeres were popped in the nine myofibrils in the force-enhanced state. Nine of these sarcomeres, in seven myofibrils, were also at a popped length in the isometric state. An interesting result furthering this was that in the active short state between the isometric and force-enhanced states, six of these sarcomeres shortened to a length at which actin-myosin filament overlap was regained; the other three sarcomeres shortened slightly, but remained at popped lengths throughout these three states. This provides further evidence that the descending limb of the force-length relationship may not be unstable upon activation. Therefore, the mechanism of RFE needs to incorporate the possibility that sarcomeres may or may not reach lengths beyond actin-myosin filament overlap and that the myofibril exhibits stability despite average lengths along the descending limb. 5.2 Limitations Ideally, RFE would have been observed in myofibrils that were not previously actively shortened, as this resulted in force depression of all of the myofibrils in the active short state. With the main objective of this research being to compare sarcomere lengths in isometric and force-enhanced states, it was crucial that these states were exhibited in the same myofibril to allow for direct comparisons to be made. This could have been accomplished by relaxing the myofibrils in between the isometric and force-enhanced states, accompanied by a repeated isometric contraction following the force-enhanced 49

61 condition to ensure that force had not deteriorated between states. For the current study, this was not done because it has been shown previously that repeated cycles of activation and relaxation, particularly at lengths along the descending limb, result in force deterioration and increases in sarcomere length non-uniformity (Bartoo et al., 1993). Therefore, it was determined that a single activation protocol was acceptable given the objective of the research. In the future, if the activation-relaxation cyclical protocol for isolated myofibrils can be improved to eliminate these effects, this study could be repeated; however, it is predicted that similar results would be obtained. It has been suggested that half-sarcomere length non-uniformities may play a role in RFE (Campbell, Hatfield, & Campbell, 2011). Quantifying half-sarcomere lengths within the current study would have provided important insight into this hypothesis. Unfortunately, it is difficult to identify Z-lines consistently and continuously during dynamic testing without the use of fluorescently labelled antibodies. It may be beneficial for halfsarcomere lengths to be determined in the protocol used for this study; however, it is speculated that, similar to full sarcomeres, half-sarcomere length non-uniformities would not align with the SLNT. This speculation is in agreement with previous findings, as well as the fact that in order to fit the SLNT, half-sarcomere lengths would have to exist at two distinct lengths, which these results suggest they do not (Joumaa, Leonard, et al., 2008; Rassier & Pavlov, 2012; Telley et al., 2006). A potential major contributor to variation in sarcomere lengths along a myofibril is the distribution of titin isoforms. It has been demonstrated that the rabbit psoas muscle expresses two specific titin isoforms, a shorter, stiffer isoform (3295 kd), and a longer, more compliant one (3416 kd) (Neagoe, Opitz, Makarenko, & Linke, 2003; Prado et al., 50

62 2005). Both Neagoe et al. (2003) and Prado et al. (2005) found that in rabbit psoas fibers, the proportions of these two isoforms is approximately 70 % of the shorter and 30 % of the longer. Unfortunately it is currently unknown what the titin isoform distribution is at the individual rabbit psoas myofibril or sarcomere levels. Previous observations have shown that cardiac muscle half-sarcomeres can express more than one titin isoform (Trombitás, Wu, Labeit, Labeit, & Granzier, 2001). Therefore, it is hypothesized that the titin isoform distribution may vary among individual rabbit psoas sarcomeres and this variation would result in sarcomere length non-uniformities purely due to the passive force capabilities of the titin isoforms. It would be beneficial to quantify the variation in isoform proportion in individual rabbit psoas sarcomeres to determine if sarcomere length non-uniformities found in these results could be attributed to the variability in the expression of titin isoforms. Alternatively the experimental protocol used in this study could be repeated in skeletal muscle myofibrils that only express a single isoform of titin. Finally, this study utilized a single experimental protocol with no variations other than mean sarcomere length differences brought about by the compliance of the cantilevers. While this allowed for the comparison of myofibrils with mean sarcomere lengths on the descending limb of the force-length relationship ranging from 2.4 to 3.4 µm, no other variables were changed. Specifically, it would be interesting to determine if stretch velocity influences the development of sarcomere length non-uniformities, even though it has been found that stretch velocity does not affect the total amount of RFE (Abbott & Aubert, 1952; Edman et al., 1978; Sugi & Tsuchiya, 1988). It would also be useful to analyze contractions occurring in other physiologically relevant conditions, such as with varying final lengths (on the ascending limb, the plateau, and further down the descending 51

63 limb) or at submaximal activation levels, to see how these conditions affect sarcomere length non-uniformities in force-enhanced states. 5.3 Considerations for residual force enhancement based on previous research In addition to the direct evidence opposing the SLNT that was provided by the findings of this research, previous researchers have obtained results that contradict the mechanism proposed by this theory. For instance, the SLNT implies that RFE cannot occur on the ascending limb of the force-length relationship due to its inherent stability which would cause non-uniform sarcomeres to become uniform during stretch. This would result in the force-enhanced state producing the same amount of force as the isometric state at the same final length. However, RFE has been demonstrated on the ascending limb at different levels of the muscle hierarchy from whole muscle to myofibrils (Abbott & Aubert, 1952; Herzog & Leonard, 2002; Peterson, Rassier, & Herzog, 2004; Pun, Syed, & Rassier, 2010). In accordance with observations that all sarcomeres elongate during an active stretch, regardless of non-uniformities, the SLNT suggests that the isometric force following active stretch on the descending limb can never exceed the isometric force at the initial length (Edman et al., 1982; Herzog et al., 2010a; Julian & Morgan, 1979; Leonard & Herzog, 2010; Morgan, 1990; Panchangam & Herzog, 2011). Not only have observations been made where the final force exceeds the force at the initial length, but the force-enhanced state has been observed to produce forces above the plateau of the isometric force-length relationship, which is inherently impossible according to the SLNT (Lee & Herzog, 2008; Leonard & Herzog, 2010; Peterson et al., 2004; Pun et al., 2010). Finally, Leonard, DuVall, and Herzog (2010) obtained an average of 38 % RFE above the plateau of the force-length 52

64 relationship in single sarcomere experiments where, by definition, sarcomere length nonuniformity cannot exist. Therefore, future hypotheses of the mechanism responsible for RFE need to incorporate all of these experimental observations. 5.4 Future directions While the SLNT is currently the most popular explanation for RFE, the limitations of this theory have been noticed by other researchers and have led to proposals of other possible mechanisms. Aside from half-sarcomere dynamics, which were mentioned earlier, the most prevalent hypothesis is that the spring-like titin filament plays a role during activation, particularly noticeable during active stretch, as opposed to the previous notion that titin is purely a passive structure. The idea that RFE may involve the engagement of a passive element was suggested as early as 1978 (Edman et al., 1978; Edman & Tsuchiya, 1996). In 2002, passive force enhancement (PFE) was identified in whole muscle as an increase in the steady-state passive force following deactivation of an actively stretched muscle compared to the passive force following passive stretch or deactivation of an isometric contraction at the same final lengths (Herzog & Leonard, 2002). This observation has been supported by similar results in isolated myofibril preparations, leading to the proposal that, similar to RFE, PFE is a sarcomeric property (Joumaa et al., 2007). PFE, however, does not account for the entire increase in force production that is exhibited following active stretch (Joumaa et al., 2007; Rassier & Herzog, 2004b). Titin was identified as a potential contributor to PFE and RFE when observations were made that myofibrils exhibited a calcium-induced increase in stiffness even when crossbridge interactions were inhibited by both troponin C deletion and at lengths beyond actin- 53

65 myosin filament overlap, but not in preparations that had degraded titin (Joumaa, Rassier, Leonard, & Herzog, 2008; Leonard & Herzog, 2010). These observations support previous research indicating that titin has a calcium-based stiffness sensitivity (DuVall, Gifford, Amrein, & Herzog, 2013; Labeit et al., 2003; Tatsumi, Maeda, Hattori, & Takahashi, 2001). To further the idea of titin s role in active states, ample observations have been made in cardiac muscle, indicating that calcium not only increases the stiffness of titin by regulating the unfolding rates of specific sections of the protein, but also through facilitating interactions with other proteins within the sarcomere, such as the actin filaments (Granzier, Helmes, & Trombitás, 1996; Granzier et al., 1997; Granzier & Labeit, 2006; Labeit et al., 2003; Linke et al., 1997, 1994; Trombitás et al., 2000; Yamasaki et al., 2001). Similar results have been obtained in skeletal muscle, leading to various hypotheses of the exact mechanism of how titin may play a role in active force production and RFE (DuVall et al., 2013; Herzog, Leonard, Joumaa, DuVall, & Panchangam, 2012; Herzog & Leonard, 2002; Herzog, 2014a, 2014b; Joumaa, Rassier, et al., 2008; Leonard & Herzog, 2010; Nocella, Cecchi, Bagni, & Colombini, 2014; Powers et al., 2014; Rassier & Pavlov, 2012; Rassier et al., 2014; Wang et al., 1991). Future research should delve deeper into the elucidation of this mechanism as all of the current proposals hinge on indirect evidence. 5.5 Conclusion The phenomenon of RFE is not simply a product of the development of sarcomere length non-uniformities during active stretch in the manner proposed by the SLNT. More specifically, the SLNT attempts to explain RFE within the constraints of the force-length relationship predicted by the Cross-Bridge Theory; however, RFE seems to occur with 54

66 little, or highly inconsistent, regard for the degree of actin-myosin filament overlap, which provides sufficient explanation for force production during isometric contractions. It would be beneficial if future research focused on the elucidation of the mechanism behind RFE took an experimental approach rather than a modelling approach. It is evident from the results of this study and previous research that skeletal muscle contraction at the sarcomeric level is not fully understood. Consequently, mathematical models that are heavily based on assumptions may fail to incorporate details that are crucial to the development of RFE. A lot of research exists to support the idea that titin contributes to RFE, however, its exact role in active force production is currently unknown. Therefore, research aimed at identifying this role and its potential relation to sarcomere, or halfsarcomere length non-uniformities may ultimately lead to a progression in the identification of the mechanism responsible for RFE. 55

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74 APPENDIX A: SOLUTIONS A TRIS compatible ph meter and electrode (Corning Pinnacle 530, Corning Inc., Corning, NY, USA) and either 10 M potassium hydroxide or 40 % hydrochloric acid were used to ph adjust all of the solutions to ph = 7.0. The solutions used in the experiments in this thesis were a rigor solution, a relaxing solution, and an activating solution (Joumaa et al., 2007). Rigor solution (storage and homogenization): 50 mm 2-Amino-2-hydroxymethyl-propane- 1,3-diol (Tris), 100 mm sodium chloride, 2 mm potassium chloride, 2 mm magnesium chloride, 10 mm ethylene glycol bis(2-aminoethyl ether)-n,n,n N -tetraacetic acid (EGTA). Relaxing solution (passive state): 10 mm 3-(N-morpholino) propanesulfonic acid (MOPS), 64.4 mm potassium propionate, 9.45 mm sodium sulfate, 5.23 mm magnesium proprionate, 2 mm potassium EGTA, 7 mm adenosine 5 -triphosphate (ATP), 10 mm creatine phosphate. Activating solution (active state): 10 mm MOPS, 45.1 mm potassium propionate, 5.21 mm magnesium propionate, 9.27 mm sodium sulfate, 1 mm sodium EGTA, 7 mm ATP, 10 mm creatine phosphate, 0.75 mm calcium chloride (pca = 3.12). 63

75 APPENDIX B: RAW DATA The following pages contain individual sarcomere length and myofibril force time-history traces for each of the 12 myofibrils tested. Steady states for each myofibril are indicated, along with mean sarcomere lengths (mean ± SD) and forces for each state. The five steady states were passive short (purple), passive long (orange), isometric (blue), active short (green), and force-enhanced (red). The values to the right of each graph represent RFE (top) and the number of popped sarcomeres in the force-enhanced state (bottom). Axes scales are the same for all 12 graphs for comparative purposes. 64

76 Myofibril 1 65

77 Myofibril 2 66

78 Myofibril 3 67

79 Myofibril 4 68

80 Myofibril 5 69

81 Myofibril 6 70

82 Myofibril 7 71

83 Myofibril 8 72

84 Myofibril 9 73

85 Myofibril 10 74

86 Myofibril 11 75

87 Myofibril 12 76