Biophysical Journal Volume 110 February 2016 521–522
521
New and Notable Finally, We Can Relax: A New Generation of Muscle Models that Incorporate Sarcomere Compliance Michael Regnier1,2,3,* and Yuanhua Cheng1 1
Department of Bioengineering, 2Center for Cardiovascular Biology, and 3Institute for Stem Cell and Regenerative Medicine, University of Washington, Seattle, Washington
Relaxation is an important property of muscle activity, but is much less studied or understood than contraction. For skeletal muscle, relaxation is important for motor control of movement, breathing, and posture. For cardiac muscle, relaxation is critically important for diastolic function, allowing effective filling with blood for pumping (systole), during normal activity but especially so when heart rate increases during activity or stress. In both skeletal and cardiac muscle, contraction and relaxation occur in networks of myofibrils organized in parallel bundles (Fig. 1 A). Myofibrils are the subcellular organelles that produce cell and tissue force and shortening. They are composed of sarcomeres which, in turn, are composed of thin and thick filaments that contain the contractile proteins myosin and actin, as well as protein complexes that regulate the switching on and off of contractile activity (Fig. 1 B). Sarcomeres are arranged end to end in series within the myofibrils, with ~50 in a row in cardiac muscle cells and up to hundreds in a row for skeletal muscle cells. Myofibril relaxation is a complex phenomenon involving both inter- and intrasarcomere components. To study it experimentally requires custom-built apparatus designed to hold on to the
Submitted December 17, 2015, and accepted for publication December 21, 2015. *Correspondence: [email protected] Editor: James Sellers. Ó 2016 by the Biophysical Society 0006-3495/16/02/0521/2
small dimensions of myofibrils (1– 2 mm width, 40–70 mm length), rapid solution switching, and the ability to monitor picoNewton levels of tension with kinetics in the millisecond timescale. Relaxation of myofibrils from isometric tension occurs in two phases (Fig. 1 C). There is an initial slow, linear phase that is relatively small in amplitude and is thought to reflect the rate of myosin detachment from actin (cross-bridge) detachment. This is followed by a much larger and faster relaxation phase when tension decays to the resting baseline. This phase is thought to reflect multiple compliance components including heterogeneity in cross-bridge detachment within and between sarcomeres, heterogeneity in sarcomere lengths such as shortening of sarcomeres in the middle that stretches sarcomeres at the ends of myofibrils, and series elastic components from proteins such as titin and protein complexes, primarily the Z-disks (1–3). The complex, multicomponent nature of the fast phase of relaxation, where most of the force decay occurs, has made it difficult to determine mechanisms experimentally. An alternative approach is to develop computational models that account for cross-bridge cycling and detachment, and for the various compliances within and between the sarcomeres of myofibrils. Even this approach has been attempted by few, and none to date have adequately accounted for myofilament compliances as well as intersarcomere compliances along the myofibril. In this edition of the Biophysical Journal, Dr. Kenneth Campbell (4) has made an initial attempt to do just this with computational simulations of relaxation. The model accounts for both cross-bridges and series compliance. Cross-bridges are simulated using the two-state Huxley model, governed by rates for myosin attachment to actin and force (tension) development (f) and a cross-bridge detachment rate (g). Both force and these rates are dependent of the strain in the myosin
head and elasticity of the thin and thick filaments. Compliance in myofibrils can come from elasticity of thin and thick filaments, titin, and, perhaps Zdisk protein complexes. The Campbell model varies elasticity of the thin and thick filaments. By varying the compliance of these elements, he demonstrates the time course of both the early, slow linear phase followed by the dominant rapid phase of relaxation seen in myofibril studies. This is due, at least in part, to compliant realignment of myosin binding sites on actin filaments, which has previously been reported to also influence cooperative myosin binding during contractile activation (5). The stretch of filaments also results in detachment of myosin due to stretching of cross-bridges into positions that increase strain-dependent detachment rates. Campbell found that this two-phase relaxation did not occur in a very rigid system, with no compliance, where relaxation occurred as a slow exponential decline in force. However, the stretch of filaments needed to simulate myofibril relaxation was 10 times greater than that measured experimentally, suggesting there are other compliant features. There are several potential sources that could limit the reliance of filament stretching to explain two-phase relaxation. The Campbell model simplifies the half-sarcomere to single thin and thick filaments, while there is threedimensional architecture in the myofilament lattice, thus the probability of myosin binding sites on actin is likely reduced considerably (6). Additionally, simulating myosin as a single, linear spring (as opposed to one containing an elastic, torsional component that occurs in myosin head movement) may also limit myosin binding probability as well as overestimate the stretching of filaments. Given these limitations, the Campbell model is a valuable step forward
http://dx.doi.org/10.1016/j.bpj.2015.12.025
522
Regnier and Cheng
incomplete relaxation (7). Other recent studies suggest that at least some mutations associated with hypertrophic cardiomyopathy impair the ability of cardiac muscle to relax more swiftly during b-adrenergic stimulation (8), when heart rate has increased, making it a potential contributing factor in diastolic dysfunction. REFERENCES 1. Poggesi, C., C. Tesi, and R. Stehle. 2005. Sarcomeric determinants of striated muscle relaxation kinetics. Pflugers Arch. 449: 505–517. 2. de Tombe, P. P., A. Belus, ., C. Poggesi. 2007. Myofilament calcium sensitivity does not affect cross-bridge activation-relaxation kinetics. Am. J. Physiol. Regul. Integr. Comp. Physiol. 292:R1129–R1136.
FIGURE 1 (A) Cartoon model of a muscle bundle (left) and a single myofibril (right). (B) Cartoon model of myofilaments arrangement in the sarcomere. (C) An example tension trace (at pCa 4.0) for isolated rat LV cardiac myofibril. (Inset) Closeup of slow phase of relaxation demonstrating how the rate (kREL,slow) and duration (tREL,slow) values of slow phase are measured. To see this figure in color, go online.
in developing new tools to understand the complex structure-function behavior of striated muscle relaxation. He has followed the rule that models should be constructed as simple as possible to explain the measurements being simulated. He has clearly demonstrated that series elasticity is required to explain the complex behavior of myofibril relaxation, and that there is a range of compliances that allow the predominant rapid rate of cross-bridge detachment and relaxation. It is clear that additional complexity of structure, geometry, and protein function will be needed in
Biophysical Journal 110(3) 521–522
future models, but the Campbell model is a good starting point for future iterations. There is considerable potential for this model and future, more complete models to impact our understanding of the mechanisms of contractile dysfunctions that occur with diseases, particularly those resulting from mutations in proteins of the sarcomere contractile lattice. For example, there is growing evidence that mutations in myosin associated with diseases of congenital contracture of limb skeletal muscle may result at least partially from altered relaxation kinetics and
3. Kreutziger, K. L., N. Piroddi, ., M. Regnier. 2008. Thin filament Ca2þ binding properties and regulatory unit interactions alter kinetics of tension development and relaxation in rabbit skeletal muscle. J. Physiol. 586:3683– 3700. 4. Campbell, K. S. 2016. Compliance accelerates relaxation in striated muscle by allowing myosin heads to move relative to actin. Biophys. J. 110:661–668. 5. Tanner, B. C., T. L. Daniel, and M. Regnier. 2012. Filament compliance influences cooperative activation of thin filaments and the dynamics of force production in skeletal muscle. PLOS Comput. Biol. 8:e1002506. 6. Tanner, B. C., T. L. Daniel, and M. Regnier. 2007. Sarcomere lattice geometry influences cooperative myosin binding in muscle. PLOS Comput. Biol. 3:e115. 7. Racca, A. W., A. E. Beck, ., M. Regnier. 2015. The embryonic myosin R672C mutation that underlies Freeman-Sheldon syndrome impairs cross-bridge detachment and cycling in adult skeletal muscle. Hum. Mol. Genet. 24:3348–3358. 8. Cheng, Y., V. Rao, ., M. Regnier. 2015. Troponin I mutations R146G and R21C alter cardiac troponin function, contractile properties and modulation by PKA-mediated phosphorylation. J. Biol. Chem. 290:27749– 27766.
521
New and Notable Finally, We Can Relax: A New Generation of Muscle Models that Incorporate Sarcomere Compliance Michael Regnier1,2,3,* and Yuanhua Cheng1 1
Department of Bioengineering, 2Center for Cardiovascular Biology, and 3Institute for Stem Cell and Regenerative Medicine, University of Washington, Seattle, Washington
Relaxation is an important property of muscle activity, but is much less studied or understood than contraction. For skeletal muscle, relaxation is important for motor control of movement, breathing, and posture. For cardiac muscle, relaxation is critically important for diastolic function, allowing effective filling with blood for pumping (systole), during normal activity but especially so when heart rate increases during activity or stress. In both skeletal and cardiac muscle, contraction and relaxation occur in networks of myofibrils organized in parallel bundles (Fig. 1 A). Myofibrils are the subcellular organelles that produce cell and tissue force and shortening. They are composed of sarcomeres which, in turn, are composed of thin and thick filaments that contain the contractile proteins myosin and actin, as well as protein complexes that regulate the switching on and off of contractile activity (Fig. 1 B). Sarcomeres are arranged end to end in series within the myofibrils, with ~50 in a row in cardiac muscle cells and up to hundreds in a row for skeletal muscle cells. Myofibril relaxation is a complex phenomenon involving both inter- and intrasarcomere components. To study it experimentally requires custom-built apparatus designed to hold on to the
Submitted December 17, 2015, and accepted for publication December 21, 2015. *Correspondence: [email protected] Editor: James Sellers. Ó 2016 by the Biophysical Society 0006-3495/16/02/0521/2
small dimensions of myofibrils (1– 2 mm width, 40–70 mm length), rapid solution switching, and the ability to monitor picoNewton levels of tension with kinetics in the millisecond timescale. Relaxation of myofibrils from isometric tension occurs in two phases (Fig. 1 C). There is an initial slow, linear phase that is relatively small in amplitude and is thought to reflect the rate of myosin detachment from actin (cross-bridge) detachment. This is followed by a much larger and faster relaxation phase when tension decays to the resting baseline. This phase is thought to reflect multiple compliance components including heterogeneity in cross-bridge detachment within and between sarcomeres, heterogeneity in sarcomere lengths such as shortening of sarcomeres in the middle that stretches sarcomeres at the ends of myofibrils, and series elastic components from proteins such as titin and protein complexes, primarily the Z-disks (1–3). The complex, multicomponent nature of the fast phase of relaxation, where most of the force decay occurs, has made it difficult to determine mechanisms experimentally. An alternative approach is to develop computational models that account for cross-bridge cycling and detachment, and for the various compliances within and between the sarcomeres of myofibrils. Even this approach has been attempted by few, and none to date have adequately accounted for myofilament compliances as well as intersarcomere compliances along the myofibril. In this edition of the Biophysical Journal, Dr. Kenneth Campbell (4) has made an initial attempt to do just this with computational simulations of relaxation. The model accounts for both cross-bridges and series compliance. Cross-bridges are simulated using the two-state Huxley model, governed by rates for myosin attachment to actin and force (tension) development (f) and a cross-bridge detachment rate (g). Both force and these rates are dependent of the strain in the myosin
head and elasticity of the thin and thick filaments. Compliance in myofibrils can come from elasticity of thin and thick filaments, titin, and, perhaps Zdisk protein complexes. The Campbell model varies elasticity of the thin and thick filaments. By varying the compliance of these elements, he demonstrates the time course of both the early, slow linear phase followed by the dominant rapid phase of relaxation seen in myofibril studies. This is due, at least in part, to compliant realignment of myosin binding sites on actin filaments, which has previously been reported to also influence cooperative myosin binding during contractile activation (5). The stretch of filaments also results in detachment of myosin due to stretching of cross-bridges into positions that increase strain-dependent detachment rates. Campbell found that this two-phase relaxation did not occur in a very rigid system, with no compliance, where relaxation occurred as a slow exponential decline in force. However, the stretch of filaments needed to simulate myofibril relaxation was 10 times greater than that measured experimentally, suggesting there are other compliant features. There are several potential sources that could limit the reliance of filament stretching to explain two-phase relaxation. The Campbell model simplifies the half-sarcomere to single thin and thick filaments, while there is threedimensional architecture in the myofilament lattice, thus the probability of myosin binding sites on actin is likely reduced considerably (6). Additionally, simulating myosin as a single, linear spring (as opposed to one containing an elastic, torsional component that occurs in myosin head movement) may also limit myosin binding probability as well as overestimate the stretching of filaments. Given these limitations, the Campbell model is a valuable step forward
http://dx.doi.org/10.1016/j.bpj.2015.12.025
522
Regnier and Cheng
incomplete relaxation (7). Other recent studies suggest that at least some mutations associated with hypertrophic cardiomyopathy impair the ability of cardiac muscle to relax more swiftly during b-adrenergic stimulation (8), when heart rate has increased, making it a potential contributing factor in diastolic dysfunction. REFERENCES 1. Poggesi, C., C. Tesi, and R. Stehle. 2005. Sarcomeric determinants of striated muscle relaxation kinetics. Pflugers Arch. 449: 505–517. 2. de Tombe, P. P., A. Belus, ., C. Poggesi. 2007. Myofilament calcium sensitivity does not affect cross-bridge activation-relaxation kinetics. Am. J. Physiol. Regul. Integr. Comp. Physiol. 292:R1129–R1136.
FIGURE 1 (A) Cartoon model of a muscle bundle (left) and a single myofibril (right). (B) Cartoon model of myofilaments arrangement in the sarcomere. (C) An example tension trace (at pCa 4.0) for isolated rat LV cardiac myofibril. (Inset) Closeup of slow phase of relaxation demonstrating how the rate (kREL,slow) and duration (tREL,slow) values of slow phase are measured. To see this figure in color, go online.
in developing new tools to understand the complex structure-function behavior of striated muscle relaxation. He has followed the rule that models should be constructed as simple as possible to explain the measurements being simulated. He has clearly demonstrated that series elasticity is required to explain the complex behavior of myofibril relaxation, and that there is a range of compliances that allow the predominant rapid rate of cross-bridge detachment and relaxation. It is clear that additional complexity of structure, geometry, and protein function will be needed in
Biophysical Journal 110(3) 521–522
future models, but the Campbell model is a good starting point for future iterations. There is considerable potential for this model and future, more complete models to impact our understanding of the mechanisms of contractile dysfunctions that occur with diseases, particularly those resulting from mutations in proteins of the sarcomere contractile lattice. For example, there is growing evidence that mutations in myosin associated with diseases of congenital contracture of limb skeletal muscle may result at least partially from altered relaxation kinetics and
3. Kreutziger, K. L., N. Piroddi, ., M. Regnier. 2008. Thin filament Ca2þ binding properties and regulatory unit interactions alter kinetics of tension development and relaxation in rabbit skeletal muscle. J. Physiol. 586:3683– 3700. 4. Campbell, K. S. 2016. Compliance accelerates relaxation in striated muscle by allowing myosin heads to move relative to actin. Biophys. J. 110:661–668. 5. Tanner, B. C., T. L. Daniel, and M. Regnier. 2012. Filament compliance influences cooperative activation of thin filaments and the dynamics of force production in skeletal muscle. PLOS Comput. Biol. 8:e1002506. 6. Tanner, B. C., T. L. Daniel, and M. Regnier. 2007. Sarcomere lattice geometry influences cooperative myosin binding in muscle. PLOS Comput. Biol. 3:e115. 7. Racca, A. W., A. E. Beck, ., M. Regnier. 2015. The embryonic myosin R672C mutation that underlies Freeman-Sheldon syndrome impairs cross-bridge detachment and cycling in adult skeletal muscle. Hum. Mol. Genet. 24:3348–3358. 8. Cheng, Y., V. Rao, ., M. Regnier. 2015. Troponin I mutations R146G and R21C alter cardiac troponin function, contractile properties and modulation by PKA-mediated phosphorylation. J. Biol. Chem. 290:27749– 27766.
