DOI: 10.5061/dryad.tb2rbnzx8
title: Myosin cross-bridge kinetics slow at longer muscle lengths during isometric contractions in intact soleus from mice

description: Muscle contraction results from force-generating cross-bridge interactions
 between myosin and actin. Cross-bridge cycling kinetics underlie
 fundamental contractile properties, such as active force production and
 energy utilization. Factors that influence cross-bridge kinetics at the
 molecular level propagate through the sarcomeres, cells, and tissue to
 modulate whole-muscle function. Conversely, movement and changes in muscle
 length can influence cross-bridge kinetics on the molecular level.
 Reduced, single-molecule and single-fiber experiments have shown that
 increasing the strain on cross-bridges may slow their cycling rate and
 prolong their attachment duration. However, whether these strain-dependent
 cycling mechanisms persist in intact muscle tissue, which encompasses more
 complex organization and passive elements, remains unclear. To investigate
 this multi-scale relationship, we adapted traditional step-stretch
 protocols for use with mouse soleus muscle during isometric tetanic
 contractions, enabling novel estimates of length-dependent cross-bridge
 kinetics in intact skeletal muscle. Compared to rates at optimal muscle
 length (Lo), we found that cross-bridge detachment rates increased by ~20%
 at 90% of Lo (shorter) and decreased by ~20% at 110% of Lo (longer). These
 data indicate that cross-bridge kinetics vary with whole-muscle length
 during intact, isometric contraction, which could intrinsically modulate
 force-generation and energetics, and suggests a multi-scale feedback
 pathway between whole-muscle function and cross-bridge activity.
description: Small step analysis
 Striated muscle responds to a
 sudden length increase with a force response that has classically been
 described by four phases (1–4). In phase 1, force rises instantaneously as
 attached cross-bridges and elastic elements are strained (Fig. 2,
 σ<sub>0</sub> to σ<sub>1</sub>). In phase 2, force
 decays as cross-bridges detach in a synchronized manner (Fig. 2,
 σ<sub>1</sub> to σ<sub>2</sub>). Next, force rises
 in phase 3 due to cross-bridge recruitment, and finally the force response
 plateaus at an elevated level (phase 4) due to passive properties (i.e.,
 of stretching tendon, connective tissue, titin and collagen) and changes
 in active (i.e. altered cross-bridge activity) biomechanical properties of
 the muscle at the new, longer muscle length. These phases are a
 time-domain representation of the same processes observed via
 smaller-amplitude length perturbation analysis (0.05-1.25% muscle length),
 in which frequency-dependent shifts in the elastic and viscous moduli
 (i.e. viscoelastic stress-strain stiffness response) describe enzymatic
 and mechanical properties of the muscle (5–7). Thus, the time-dependent
 modulus response, Y(t) (=σ(t)/ε(t), where σ(t) and ε(t) represent the
 muscle stress response and muscle strain as a function of time,
 respectively) a step-function change in muscle length can be characterized
 as described by Palmer <i>et al.</i> (7): 
 Y(t) =
 At<sup>-k</sup>-Be<sup>-2πbt</sup>+Ce<sup>-2πct</sup> (1) The molecular, cellular, and tissue characteristics described by Eq. 1 are outlined below, with this model appropriately describing Y(t) for the measured stress-strain response between σ<sub>1</sub> and σ<sub>final</sub>, with the initial time-point occurring at the onset of the strain stimulus (i.e. time=0 at t<sub>0</sub> for σ<sub>0</sub>)—as further described below and illustrated in Fig. 2. The A-process reflects the viscoelastic mechanical response of passive, structural elements in the muscle and holds no enzymatic dependence. Parameter <i>A</i> represents the combined mechanical stress of the muscle and tendon, while parameter <i>k</i> describes the viscoelasticity of these passive elements; a <i>k </i>value of 0 (minimum possible value for the fractional derivative) represents a purely elastic response and a <i>k</i> value of 1 represents a purely viscous response (8,9). The B- and C- processes characterize work-producing (cross-bridge recruitment) and work-absorbing (cross-bridge detachment) characteristics of the contracting muscle, respectively (7,10–12). Thus, these B- and C- processes are analogous to the work-producing and work-absorbing process described above during phase 3 for cross-bridge recruitment and phase 2 for cross-bridge detachment. The parameters <i>B</i> and <i>C</i> represent the mechanical stress from the cross-bridges, and the rate parameters <i>b</i> and <i>c</i> reflect cross-bridge kinetics (13). More specifically, molecular processes contributing to cross-bridge recruitment or force generation underlie the cross-bridge recruitment rate, 2π<i>b</i>, and processes contributing to cross-bridge detachment or force decay underlie the cross-bridge detachment rate, 2π<i>c</i>.   To best emulate physiological length changes, both the proximal and distal tendons of the muscle preparations were left intact. However, the tendons add an additional in-series elastic element that should be considered when applying small step analysis to ensure that the muscle (and not tendon) is primarily experiencing the perturbation. Using methods described by Cui et al. 2008 (14), we calculated tendon area and length to provide an estimate of tendon stiffness with: (2) where <i>E</i> is the elastic modulus (reported to be approximately 62 N/mm<sup>2</sup> for mouse soleus tendon (15)), <i>A<sub>T</sub></i> is calculated tendon area (0.59 mm<sup>2</sup>), and <i>l<sub>T</sub></i> is the calculated tendon length (5.67±0.14 mm) at L<sub>o</sub>. Therefore, we can roughly estimate an in-series elastic element with a stiffness of 6.45 N/mm. Our average L<sub>o</sub> was 15.22±0.37 mm, so a 1% length­-step stretched the MTU on average 0.15 mm. During this step, we measured an average rise in force (represented as phase 1) around 0.16 N, for MTU stiffness (K<sub>MTU</sub>) of 1.05 N/mm. Therefore, we can solve for the stiffness of the muscle (K<sub>M</sub>) using:        (3) which estimates K<sub>m</sub> to be on average 1.25 N/mm. These values suggest that the stiffness of the tendon is approximately five times that of the stiffness of the muscle, and thus we assume that for a given length increase, the muscle fibers experience the majority of the length change from the step-length perturbations imposed herein.   Animal models All procedures were approved by the Institutional Animal Care and Use Committee at Washington State University and complied with the <i>Guide for<sup> </sup>the Use and Care of Laboratory Animals</i> published by the National<sup> </sup>Institutes of Health. Male C57BL/6 mice (7 weeks old) were sourced from Simonsen Laboratories. Ten mice were anesthetized by isoflurane inhalation (3% volume in 95% O<sub>2</sub>-5% CO<sub>2</sub> flowing at 2 L/min), then a soleus muscle was removed, preserving as much of the proximal and distal tendons as possible. After removal, the whole MTU was immediately placed in the experimental chamber containing oxygenated Ringer’s solution.   Tetanic step procedure Soleus muscles were suspended in a temperature controlled, oxygenated chamber with the distal tendon sutured onto a force transducer (Aurora Scientific 407A, Aurora, ON), and the proximal tendon sutured onto a length controller (Aurora Scientific 305C, Aurora, ON). Muscles equilibrated with the Ringer’s solution (154 mM NaCl, 5.6 mM KCl, 1 mM MgCl<sub>2</sub>, 2.2 mM CaCl<sub>2</sub>, 10 mM glucose, 20 mM HEPES, pH 7.4, (16)) for at least 5 minutes. Muscles were field stimulated (Aurora scientific 701C, Aurora, ON) via parallel electrode plates along the length of the chamber at 20 V and 100 Hz to measure maximum isometric tetanic force (Figure 1A). Optimal MTU length (L<sub>o</sub>) was determined by tetanically stimulating the muscle at multiple lengths (minimum of 5 lengths, each followed by at least 3 minutes rest) to produce a force-length curve. L<sub>o</sub> was then defined as the length that generated maximum active force along the MTU force-length curve. Once L<sub>o</sub> was established, the MTU was set to one of three lengths: L<sub>o</sub>, 90% of L<sub>o</sub>, or 110% of L<sub>o</sub>. Tetanic contraction was then induced in the muscle for 2 seconds, with a length step (1% increase in MTU length) applied at 1 second and held for the remainder of the activation period (Figure 2). This procedure was then repeated for the remaining two lengths and then again for all three lengths at the other test temperature. The order of MTU length and temperature of the chamber (17°C or 27°C) was randomized for each experiment. After mechanical experiments were completed, muscle and tendons were separated, measured, and weighed to estimate the physiological cross-sectional area (CSA, (17)): (4) where <i>m</i> is muscle mass, θ is pennation angle (=8.5° for soleus muscle (18)), L<sub>f</sub> is fiber length calculated from fiber-to-muscle length ratio (=0.71 for soleus muscle (19)), and ρ is muscle density (=1.06 mg/mm<sup>3 </sup>(20)). Average soleus muscle CSA was 0.78±0.05 mm<sup>2</sup>. Force was then divided by the CSA to calculate stress.   Statistical analysis All data are listed as mean ± SEM. Sequential quadratic programming methods in Matlab (v. 9.4.0, The Mathworks, Natick MA) was used for constrained nonlinear least-squares fitting of Eq. 1 to moduli data for each muscle. Statistical analysis of experimental data were performed in SPSS (IBM Statistics, Chicago, IL), implementing linear mixed models with muscle length and temperature as repeated measures where appropriate. This approach matches data from the same muscle to provide more statistical power than a one-way ANOVA. First-order autoregression was assumed for the covariance structure and post-hoc analyses were performed using least-significant difference corrections where appropriate. Statistical significance is reported at p&lt;0.05.   <em>References</em> 1.        Huxley AF, Simmons RM. Proposed mechanism of force generation in striated muscle. Nature. 1971;233(5321):533–8. 2.        Ford LE, Huxley AF, Simmons RM. Tension responses to sudden length change in stimulated frog muscle fibres near slack length. J Physiol. 1977;269(2):441–515. 3.        Davis JS, Rodgers ME. Force generation and temperature-jump and length-jump tension transients in muscle fibers. Biophys J. 1995 May;68(5):2032–40. 4.        Huxley AF. Muscular contraction. J Physiol. 1974;243(1):1–43. 5.       Kawai M, Brandt PW. Sinusoidal analysis: a high resolution method for correlating biochemical reactions with physiological processes in activated skeletal muscles of rabbit, frog and crayfish. J Muscle Res Cell Motil. 1980 Sep;1(3):279–303. 6.     Tanner BCW, Wang Y, Maughan DW, Palmer BM. Measuring myosin cross-bridge attachment time in activated muscle fibers using stochastic vs. sinusoidal length perturbation analysis. J Appl Physiol. 2011;110(4):1101–8. 7.      Palmer BM, Suzuki T, Wang Y, Barnes WD, Miller MS, Maughan DW. Two-State Model of Acto-Myosin Attachment-Detachment Predicts C-Process of Sinusoidal Analysis. Biophys J. 2007;93(3):760–9. 8.        Palmer BM, Tanner BCW, Toth MJ, Miller MS. An inverse power-law distribution of molecular bond lifetimes predicts fractional derivative viscoelasticity in biological tissue. Biophys J. 2013 Jun;104(11):2540–52. 9.      Mulieri LA, Barnes WD, Leavett BJ, Ittleman FP, LeWinter MM, Alpert NR, et al. Alterations of myocardial dynamic stiffness implicating abnormal crossbridge function in human mitral regurgitation heart failure. Circ Res. 2002;90(1):66–72. 10.     Kawai M, Wray JS, Zhao Y. The effect of lattice spacing change on cross-bridge kinetics in chemically skinned rabbit psoas muscle fibers. I: Proportionality between the lattice spacing and the fiber width. Biophys J. 1993;64(1):187–96. 11.     Campbell KB, Chandra M, Kirkpatrick RD, Slinker BK, Hunter WC. Interpreting cardiac muscle force-length dynamics using a novel functional model. Am J Physiol Hear Circ Physiol. 2004;286:H1535-H1545. 12.     Kawai M, Halvorson HR. Two step mechanism of phosphate release and the mechanism of force generation in chemically skinned fibers of rabbit psoas muscle. Biophys J. 1991 Feb;59(February):329–42. 13.      Lymn RW, Taylor EW. Mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry. 1971;10(25):4617–24. 14.      Cui L, Perreault EJ, Maas H, Sandercock TG. Modeling short-range stiffness of feline lower hindlimb muscles. J Biomech. 2008;41(9):1945–52. 15.    Rigozzi S, Müller R, Snedeker JG. Local strain measurement reveals a varied regional dependence of tensile tendon mechanics on glycosaminoglycan content. J Biomech. 2009; 16.      Barton ER, Lynch G. Measuring isometric force of isolated mouse muscles in vitro. 2008;(Id):1–14. 17.      Sacks RD, Roy RR. Architecture of the hind limb muscles of cats: Functional significance. J Morphol. 1982 Aug 1;173(2):185–95. 18.     Burkholder TJ, Fingado B, Baron S, Lieber RL. Relationship between muscle fiber types and sizes and muscle architectural properties in the mouse hindlimb. J Morphol. 1994;221(2):177–90. 19.      Brooks S V, Faulkner JA. 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description: <em>MaxForce_ProcRSocB.csv</em>
 This file contains the force data obtained from each mouse (1
 soleus muscle), from each condition.  Animal_ID = The
 ID of the mouse used. MTU_Length = The length of
 the muscle-tendon unit at which force was
 measured (Max_ActForce). Frac_Lo = The fraction of
 Lo at which Max_ActForce was measured. 1 = Lo, 0.9 = 90%Lo, 1.1 =
 110%Lo. Temp = Temperature in celsius.
 CSA = Calculated cross-sectional area of the
 muscle. Max_ActForce = The maximal force of the
 muscle during tetanic stimulation at the given condition.
 Max_Stress =  Max_ActForce per CSA (mN /
 mm<sup>2</sup>)  
 <em>Step_Kinetics_ProcRSocB.csv</em>
 Paramaters from the data fits to Eq 1 (see methods) for each
 muscle at each condition.  Animal_ID = The ID of the
 mouse used. MTU_Length = The length of the
 muscle-tendon unit at which force was measured (Max_ActForce).
 Frac_Lo = The fraction of Lo at which Max_ActForce was
 measured. 1 = Lo, 0.9 = 90%Lo, 1.1 = 110%Lo. Temp =
 Temperature in celsius. t12half = Time for force to
 decay by 50% following the length step. Parameters
 A,k,B,b,C,c = Parameters acquired by fitting Eq 1 to the decay response
 following the length step.