Thick-to-thin filament surface distance modulates cross-bridge kinetics in Drosophila flight muscle

Bayesian Estimation of Muscle Mechanisms and Therapeutic Targets Using Variational Autoencoders

Cardiomyopathies, often caused by mutations in genes encoding muscle proteins, are traditionally treated by phenotyping hearts and addressing symptoms post irreversible damage. With advancements in genotyping, early diagnosis is now possible, potentially introducing earlier treatment. However, the intricate structure of muscle and its myriad proteins make treatment predictions challenging. Here we approach the problem of estimating therapeutic targets for a mutation in mouse muscle using a spatially explicit half sarcomere muscle model. We selected 9 rate parameters in our model linked to both small molecules and cardiomyopathy-causing mutations. We then randomly varied these rate parameters and simulated an isometric twitch for each combination to generate a large training dataset. We used this dataset to train a Conditional Variational Autoencoder (CVAE), a technique used in Bayesian parameter estimation. Given simulated or experimental isometric twitches, this machine learning model is able to then predict the set of rate parameters which are most likely to yield that result. We then predict the set of rate parameters associated with twitches from control mice with the cardiac Troponin C (cTnC) I61Q variant and control twitches treated with the myosin activator Danicamtiv, as well as model parameters that recover the abnormal I61Q cTnC twitches.

SIGNIFICANCE

Machine learning techniques have potential to accelerate discoveries in biologically complex systems. However, they require large data sets and can be challenging in high dimensional systems such as cardiac muscle. In this study, we combined experimental measures of cardiac muscle twitch forces with mechanistic simulations and a newly developed mixture of Bayesian inference with neural networks (in autoencoders) to solve the inverse problem of determining the underlying kinetics for observed force generation by cardiac muscle. The autoencoders are trained on millions of simulations spanning parameter spaces that correspond to the mechanochemistry of cardiac sarcomeres. We apply the trained model to experimental data in order to infer parameters that can explain a diseased twitch and ways to recover it.

The structural and functional effects of myosin regulatory light chain phosphorylation are amplified by increases in sarcomere length and [Ca2+]

Precise regulation of sarcomeric contraction is essential for normal cardiac function. The heart must generate sufficient force to pump blood throughout the body, but either inadequate or excessive force can lead to dysregulation and disease. Myosin regulatory light chain (RLC) is a thick-filament protein that binds to the neck of the myosin heavy chain. Post-translational phosphorylation of RLC (RLC-P) by myosin light chain kinase is known to influence acto-myosin interactions, thereby increasing force production and Ca2+-sensitivity of contraction. Here, we investigated the role of RLC-P on cardiac structure and function as sarcomere length and [Ca2+] were altered. We found that at low, non-activating levels of Ca2+, RLC-P contributed to myosin head disorder, though there were no effects on isometric stress production and viscoelastic stiffness. With increases in sarcomere length and Ca2+-activation, the structural changes due to RLC-P become greater, which translates into greater force production, greater viscoelastic stiffness, slowed myosin detachment rates and altered nucleotide handling. Altogether, these data suggest that RLC-P may alter thick-filament structure by releasing ordered, off-state myosin. These more disordered myosin heads are available to bind actin, which could result in greater force production as Ca2+ levels increase. However, prolonged cross-bridge attachment duration due to slower ADP release could delay relaxation long enough to enable cross-bridge rebinding. Together, this work further elucidates the effects of RLC-P in regulating muscle function, thereby promoting a better understanding of thick-filament regulatory contributions to cardiac function in health and disease. KEY POINTS: Myosin regulatory light chain (RLC) is a thick-filament protein in the cardiac sarcomere that can be phosphorylated (RLC-P), and changes in RLC-P are associated with cardiac dysfunction and disease. This study assesses how RLC-P alters cardiac muscle structure and function at different sarcomere lengths and calcium concentrations. At low, non-activating levels of Ca2+, RLC-P contributed to myofilament disorder, though there were no effects on isometric stress production and viscoelastic stiffness. With increases in sarcomere length and Ca2+-activation, the structural changes due to RLC-P become greater, which translates into greater force production, greater viscoelastic stiffness, slower myosin detachment rate and altered cross-bridge nucleotide handling rates. This work elucidates the role of RLC-P in regulating muscle function and facilitates understanding of thick-filament regulatory protein contributions to cardiac function in health and disease.

Disruption of Z-Disc Function Promotes Mechanical Dysfunction in Human Myocardium: Evidence for a Dual Myofilament Modulatory Role by Alpha-Actinin 2

The ACTN2 gene encodes α-actinin 2, located in the Z-disc of the sarcomeres in striated muscle. In this study, we sought to investigate the effects of an ACTN2 missense variant of unknown significance (p.A868T) on cardiac muscle structure and function. Left ventricular free wall samples were obtained at the time of cardiac transplantation from a heart failure patient with the ACTN2 A868T heterozygous variant. This variant is in the EF 3-4 domain known to interact with titin and α-actinin. At the ultrastructural level, ACTN2 A868T cardiac samples presented small structural changes in cardiomyocytes when compared to healthy donor samples. However, contractile mechanics of permeabilized ACTN2 A868T variant cardiac tissue displayed higher myofilament Ca2+ sensitivity of isometric force, reduced sinusoidal stiffness, and faster rates of tension redevelopment at all Ca2+ levels. Small-angle X-ray diffraction indicated increased separation between thick and thin filaments, possibly contributing to changes in muscle kinetics. Molecular dynamics simulations indicated that while the mutation does not significantly impact the structure of α-actinin on its own, it likely alters the conformation associated with titin binding. Our results can be explained by two Z-disc mediated communication pathways: one pathway that involves α-actinin's interaction with actin, affecting thin filament regulation, and the other pathway that involves α-actinin's interaction with titin, affecting thick filament activation. This work establishes the role of α-actinin 2 in modulating cross-bridge kinetics and force development in the human myocardium as well as how it can be involved in the development of cardiac disease.

Cardiac troponin T N-domain variant destabilizes the actin interface resulting in disturbed myofilament function

Missense variant Ile79Asn in human cardiac troponin T (cTnT-I79N) has been associated with hypertrophic cardiomyopathy and sudden cardiac arrest in juveniles. cTnT-I79N is located in the cTnT N-terminal (TnT1) loop region and is known for its pathological and prognostic relevance. A recent structural study revealed that I79 is part of a hydrophobic interface between the TnT1 loop and actin, which stabilizes the relaxed (OFF) state of the cardiac thin filament. Given the importance of understanding the role of TnT1 loop region in Ca2+ regulation of the cardiac thin filament along with the underlying mechanisms of cTnT-I79N-linked pathogenesis, we investigated the effects of cTnT-I79N on cardiac myofilament function. Transgenic I79N (Tg-I79N) muscle bundles displayed increased myofilament Ca2+ sensitivity, smaller myofilament lattice spacing, and slower crossbridge kinetics. These findings can be attributed to destabilization of the cardiac thin filament's relaxed state resulting in an increased number of crossbridges during Ca2+ activation. Additionally, in the low Ca2+-relaxed state (pCa8), we showed that more myosin heads are in the disordered-relaxed state (DRX) that are more likely to interact with actin in cTnT-I79N muscle bundles. Dysregulation of the myosin super-relaxed state (SRX) and the SRX/DRX equilibrium in cTnT-I79N muscle bundles likely result in increased mobility of myosin heads at pCa8, enhanced actomyosin interactions as evidenced by increased active force at low Ca2+, and increased sinusoidal stiffness. These findings point to a mechanism whereby cTnT-I79N weakens the interaction of the TnT1 loop with the actin filament, which in turn destabilizes the relaxed state of the cardiac thin filament.

Nanometer-scale structure differences in the myofilament lattice spacing of two cockroach leg muscles correspond to their different functions

Muscle is highly organized across multiple length scales. Consequently, small changes in the arrangement of myofilaments can influence macroscopic mechanical function. Two leg muscles of a cockroach have identical innervation, mass, twitch responses, length-tension curves and force-velocity relationships. However, during running, one muscle is dissipative (a 'brake'), while the other dissipates and produces significant positive mechanical work (bifunctional). Using time-resolved X-ray diffraction in intact, contracting muscle, we simultaneously measured the myofilament lattice spacing, packing structure and macroscopic force production of these muscles to test whether structural differences in the myofilament lattice might correspond to the muscles' different mechanical functions. While the packing patterns are the same, one muscle has 1 nm smaller lattice spacing at rest. Under isometric stimulation, the difference in lattice spacing disappeared, consistent with the two muscles' identical steady-state behavior. During periodic contractions, one muscle undergoes a 1 nm greater change in lattice spacing, which correlates with force. This is the first identified structural feature in the myofilament lattice of these two muscles that shares their whole-muscle dynamic differences and quasi-static similarities.

Structural and functional impact of troponin C-mediated Ca2+ sensitization on myofilament lattice spacing and cross-bridge mechanics in mouse cardiac muscle

Acto-myosin cross-bridge kinetics are important for beat-to-beat regulation of cardiac contractility; however, physiological and pathophysiological mechanisms for regulation of contractile kinetics are incompletely understood. Here we explored whether thin filament-mediated Ca²⁺ sensitization influences cross-bridge kinetics in permeabilized, osmotically compressed cardiac muscle preparations. We used a murine model of hypertrophic cardiomyopathy (HCM) harboring a cardiac troponin C (cTnC) Ca²⁺-sensitizing mutation, Ala8Val in the regulatory N-domain. We also treated wild-type murine muscle with bepridil, a cTnC-targeting Ca²⁺ sensitizer. Our findings suggest that both methods of increasing myofilament Ca²⁺ sensitivity increase cross-bridge cycling rate measured by the rate of tension redevelopment (k_TR); force per cross-bridge was also enhanced as measured by sinusoidal stiffness and I_1,1/I_1,0 ratio from X-ray diffraction. Computational modeling suggests that Ca²⁺ sensitization through this cTnC mutation or bepridil accelerates k_TR primarily by promoting faster cross-bridge detachment. To elucidate if myofilament structural rearrangements are associated with changes in k_TR, we used small angle X-ray diffraction to simultaneously measure myofilament lattice spacing and isometric force during steady-state Ca²⁺ activations. Within in vivo lattice dimensions, lattice spacing and steady-state isometric force increased significantly at submaximal activation. We conclude that the cTnC N-domain controls force by modulating both the number and rate of cycling cross-bridges, and that the both methods of Ca²⁺ sensitization may act through stabilization of cTnC's D-helix. Furthermore, we propose that the transient expansion of the myofilament lattice during Ca²⁺ activation may be an additional factor that could increase the rate of cross-bridge cycling in cardiac muscle. These findings may have implications for the pathophysiology of HCM.

Altered myofilament structure and function in dogs with Duchenne muscular dystrophy cardiomyopathy

AIM

Duchenne Muscular Dystrophy (DMD) is associated with progressive depressed left ventricular (LV) function. However, DMD effects on myofilament structure and function are poorly understood. Golden Retriever Muscular Dystrophy (GRMD) is a dog model of DMD recapitulating the human form of DMD.

OBJECTIVE

The objective of this study is to evaluate myofilament structure and function alterations in GRMD model with spontaneous cardiac failure.

METHODS AND RESULTS

We have employed synchrotron X-rays diffraction to evaluate myofilament lattice spacing at various sarcomere lengths (SL) on permeabilized LV myocardium. We found a negative correlation between SL and lattice spacing in both sub-epicardium (EPI) and sub-endocardium (ENDO) LV layers in control dog hearts. In the ENDO of GRMD hearts this correlation is steeper due to higher lattice spacing at short SL (1.9μm). Furthermore, cross-bridge cycling indexed by the kinetics of tension redevelopment (ktr) was faster in ENDO GRMD myofilaments at short SL. We measured post-translational modifications of key regulatory contractile proteins. S-glutathionylation of cardiac Myosin Binding Protein-C (cMyBP-C) was unchanged and PKA dependent phosphorylation of the cMyBP-C was significantly reduced in GRMD ENDO tissue and more modestly in EPI tissue.

CONCLUSIONS

We found a gradient of contractility in control dogs' myocardium that spreads across the LV wall, negatively correlated with myofilament lattice spacing. Chronic stress induced by dystrophin deficiency leads to heart failure that is tightly associated with regional structural changes indexed by increased myofilament lattice spacing, reduced phosphorylation of regulatory proteins and altered myofilament contractile properties in GRMD dogs.

Multiscale and Multiaxial Mechanics of Vascular Smooth Muscle

Mathematical models can facilitate an integrative understanding of the complexity underlying biological structure and function, but they must be informed and validated by empirical data. Uniaxial contraction of an arterial ring is a well-used in vitro approach for studying characteristics of smooth muscle contractility even though this experimental arrangement does not mimic the in vivo vascular geometry or loading. In contrast, biaxial contraction of an inflated and axially extended excised vessel provides broader information, both passive and active, under more realistic conditions. Few investigations have compared these two in vitro approaches directly, namely how their results overlap, how they differ, or if each provides unique complementary information. Toward this end, we present, to our knowledge, a new multiscale mathematical model of arterial contractility accounting for structural and functional constituents at molecular, cellular, and tissue levels. The artery is assumed to be a thick-walled incompressible cylinder described by an anisotropic model of the extracellular matrix and, to our knowledge, novel model of smooth muscle contractility. The latter includes a 3D structural sensitivity to deformation, including microscale muscle filament overlap and filament lattice spacing. The overall model captures uniaxial and biaxial experimental contraction data, which was not possible when accounting for filament overlap alone. The model also enables parameter sensitivity studies, which confirmed that uniaxial contraction tests are not as efficient as biaxial tests for identifying changes in vascular smooth muscle function.

Myosin MgADP Release Rate Decreases as Sarcomere Length Increases in Skinned Rat Soleus Muscle Fibers

Actin-myosin cross-bridges use chemical energy from MgATP hydrolysis to generate force and shortening in striated muscle. Previous studies show that increases in sarcomere length can reduce thick-to-thin filament spacing in skinned muscle fibers, thereby increasing force production at longer sarcomere lengths. However, it is unclear how changes in sarcomere length and lattice spacing affect cross-bridge kinetics at fundamental steps of the cross-bridge cycle, such as the MgADP release rate. We hypothesize that decreased lattice spacing, achieved through increased sarcomere length or osmotic compression of the fiber via dextran T-500, could slow MgADP release rate and increase cross-bridge attachment duration. To test this, we measured cross-bridge cycling and MgADP release rates in skinned soleus fibers using stochastic length-perturbation analysis at 2.5 and 2.0 μm sarcomere lengths as pCa and [MgATP] varied. In the absence of dextran, the force-pCa relationship showed greater Ca²⁺ sensitivity for 2.5 vs. 2.0 μm sarcomere length fibers (pCa₅₀ = 5.68 ± 0.01 vs. 5.60 ± 0.01). When fibers were compressed with 4% dextran, the length-dependent increase in Ca²⁺ sensitivity of force was attenuated, though the Ca²⁺ sensitivity of the force-pCa relationship at both sarcomere lengths was greater with osmotic compression via 4% dextran compared to no osmotic compression. Without dextran, the cross-bridge detachment rate slowed by ∼15% as sarcomere length increased, due to a slower MgADP release rate (11.2 ± 0.5 vs. 13.5 ± 0.7 s^-1). In the presence of dextran, cross-bridge detachment was ∼20% slower at 2.5 vs. 2.0 μm sarcomere length due to a slower MgADP release rate (10.1 ± 0.6 vs. 12.9 ± 0.5 s^-1). However, osmotic compression of fibers at either 2.5 or 2.0 μm sarcomere length produced only slight (and statistically insignificant) slowing in the rate of MgADP release. These data suggest that skeletal muscle exhibits sarcomere-length-dependent changes in cross-bridge kinetics and MgADP release that are separate from, or complementary to, changes in lattice spacing.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

Mechano-chemical Interactions in Cardiac Sarcomere Contraction: A Computational Modeling Study

We developed a model of cardiac sarcomere contraction to study the calcium-tension relationship in cardiac muscle. Calcium mediates cardiac contraction through its interactions with troponin (Tn) and subsequently tropomyosin molecules. Experimental studies have shown that a slight increase in intracellular calcium concentration leads to a rapid increase in sarcomeric tension. Though it is widely accepted that the rapid increase is not possible without the concept of cooperativity, the mechanism is debated. We use the hypothesis that there exists a base level of cooperativity intrinsic to the thin filament that is boosted by mechanical tension, i.e. a high level of mechanical tension in the thin filament impedes the unbinding of calcium from Tn. To test these hypotheses, we developed a computational model in which a set of three parameters and inputs of calcium concentration and sarcomere length result in output tension. Tension as simulated appeared in good agreement with experimentally measured tension. Our results support the hypothesis that high tension in the thin filament impedes Tn deactivation by increasing the energy required to detach calcium from the Tn. Given this hypothesis, the model predicted that the areas with highest tension, i.e. closest to the Z-disk end of the single overlap region, show the largest concentration of active Tn's.

Increased Titin Compliance Reduced Length-Dependent Contraction and Slowed Cross-Bridge Kinetics in Skinned Myocardial Strips from Rbm (20ΔRRM) Mice

Titin is a giant protein spanning from the Z-disk to the M-band of the cardiac sarcomere. In the I-band titin acts as a molecular spring, contributing to passive mechanical characteristics of the myocardium throughout a heartbeat. RNA Binding Motif Protein 20 (RBM20) is required for normal titin splicing, and its absence or altered function leads to greater expression of a very large, more compliant N2BA titin isoform in Rbm20 homozygous mice (Rbm20^ΔRRM) compared to wild-type mice (WT) that almost exclusively express the stiffer N2B titin isoform. Prior studies using Rbm20^ΔRRM animals have shown that increased titin compliance compromises muscle ultrastructure and attenuates the Frank-Starling relationship. Although previous computational simulations of muscle contraction suggested that increasing compliance of the sarcomere slows the rate of tension development and prolongs cross-bridge attachment, none of the reported effects of Rbm20^ΔRRM on myocardial function have been attributed to changes in cross-bridge cycling kinetics. To test the relationship between increased sarcomere compliance and cross-bridge kinetics, we used stochastic length-perturbation analysis in Ca²⁺-activated, skinned papillary muscle strips from Rbm20^ΔRRM and WT mice. We found increasing titin compliance depressed maximal tension, decreased Ca²⁺-sensitivity of the tension-pCa relationship, and slowed myosin detachment rate in myocardium from Rbm20^ΔRRM vs. WT mice. As sarcomere length increased from 1.9 to 2.2 μm, length-dependent activation of contraction was eliminated in the Rbm20^ΔRRM myocardium, even though myosin MgADP release rate decreased ~20% to prolong strong cross-bridge binding at longer sarcomere length. These data suggest that increasing N2BA expression may alter cardiac performance in a length-dependent manner, showing greater deficits in tension production and slower cross-bridge kinetics at longer sarcomere length. This study also supports the idea that passive mechanical characteristics of the myocardium influence ensemble cross-bridge behavior and maintenance of tension generation throughout the sarcomere.

Myosin MgADP release rate decreases at longer sarcomere length to prolong myosin attachment time in skinned rat myocardium

Cardiac contractility increases as sarcomere length increases, suggesting that intrinsic molecular mechanisms underlie the Frank-Starling relationship to confer increased cardiac output with greater ventricular filling. The capacity of myosin to bind with actin and generate force in a muscle cell is Ca(2+) regulated by thin-filament proteins and spatially regulated by sarcomere length as thick-to-thin filament overlap varies. One mechanism underlying greater cardiac contractility as sarcomere length increases could involve longer myosin attachment time (ton) due to slowed myosin kinetics at longer sarcomere length. To test this idea, we used stochastic length-perturbation analysis in skinned rat papillary muscle strips to measure ton as [MgATP] varied (0.05-5 mM) at 1.9 and 2.2 μm sarcomere lengths. From this ton-MgATP relationship, we calculated cross-bridge MgADP release rate and MgATP binding rates. As MgATP increased, ton decreased for both sarcomere lengths, but ton was roughly 70% longer for 2.2 vs. 1.9 μm sarcomere length at maximally activated conditions. These ton differences were driven by a slower MgADP release rate at 2.2 μm sarcomere length (41 ± 3 vs. 74 ± 7 s(-1)), since MgATP binding rate was not different between the two sarcomere lengths. At submaximal activation levels near the pCa50 value of the tension-pCa relationship for each sarcomere length, length-dependent increases in ton were roughly 15% longer for 2.2 vs. 1.9 μm sarcomere length. These changes in cross-bridge kinetics could amplify cooperative cross-bridge contributions to force production and thin-filament activation at longer sarcomere length and suggest that length-dependent changes in myosin MgADP release rate may contribute to the Frank-Starling relationship in the heart.

Kinetics of cardiac myosin isoforms in mouse myocardium are affected differently by presence of myosin binding protein-C

We tested whether cardiac myosin binding protein-C (cMyBP-C) affects myosin cross-bridge kinetics in the two cardiac myosin heavy chain (MyHC) isoforms. Mice lacking cMyBP-C (t/t) and transgenic controls (WT(t/t)) were fed L-thyroxine (T4) to induce 90/10% expression of α/β-MyHC. Non-transgenic (NTG) and t/t mice were fed 6-n-propyl-2-thiouracil (PTU) to induce 100% expression of β-MyHC. Ca(2+)-activated, chemically-skinned myocardium underwent length perturbation analysis with varying [MgATP] to estimate the MgADP release rate (k(-ADP)) and MgATP binding rate (k(+ATP)). Values for (k(-ADP)) were not significantly different between t/t(T4) (102.2 ± 7.0 s(-1)) and WT(t/t)(T4) (91.3 ± 8.9 s(-1)), but k(+ATP)) was lower in t/t(T4) (165.9 ± 12.5 mM(-1) s(-1)) compared to WT(t/t)(T4) (298.6 ± 15.7 mM(-1) s(-1), P < 0.01). In myocardium expressing β-MyHC, values for k(-ADP) were higher in t/t(PTU) (24.8 ± 1.0 s(-1)) compared to NTG(PTU) (15.6 ± 1.3 s(-1), P < 0.01), and k(+ATP) was not different. At saturating [MgATP], myosin detachment rate approximates k(-ADP), and detachment rate decreased as sarcomere length (SL) was increased in both t/t(T4) and WT(t/t)(T4) with similar sensitivities to SL. In myocardium expressing β-MyHC, detachment rate decreased more as SL increased in t/t(PTU) (21.5 ± 1.3 s(-1) at 2.2 μm and 13.3 ± 0.9 s(-1) at 3.3 μm) compared to NTGPTU (15.8 ± 0.3 s(-1) at 2.2 μm and 10.9 ± 0.3 s(-1) at 3.3 μm) as detected by repeated-measures ANOVA (P < 0.01). These findings suggest that cMyBP-C reduces MgADP release rate for β-MyHC, but not for α-MyHC, even as the number of cMyBP-C that overlap with the thin filament is reduced to zero. Therefore, cMyBP-C appears to affect β-MyHC kinetics independent of its interaction with the thin filament.

The nebulin repeat protein Lasp regulates I-band architecture and filament spacing in myofibrils

With just two nebulin repeats, the Drosophila protein Lasp controls muscle thin filament length and filament spacing.

Mutations in nebulin, a giant muscle protein with 185 actin-binding nebulin repeats, are the major cause of nemaline myopathy in humans. Nebulin sets actin thin filament length in sarcomeres, potentially by stabilizing thin filaments in the I-band, where nebulin and thin filaments coalign. However, the precise role of nebulin in setting thin filament length and its other functions in regulating power output are unknown. Here, we show that Lasp, the only member of the nebulin family in Drosophila melanogaster, acts at two distinct sites in the sarcomere and controls thin filament length with just two nebulin repeats. We found that Lasp localizes to the Z-disc edges to control I-band architecture and also localizes at the A-band, where it interacts with both actin and myosin to set proper filament spacing. Furthermore, introducing a single amino acid change into the two nebulin repeats of Lasp demonstrated different roles for each domain and established Lasp as a suitable system for studying nebulin repeat function.

An inverse power-law distribution of molecular bond lifetimes predicts fractional derivative viscoelasticity in biological tissue

Viscoelastic characteristics of many materials falling under the category of soft glassy substances, including biological tissue, often exhibit a mechanical complex modulus Y(ω) well described by a fractional derivative model: Y(ω) = E(iω/ϕ)k, where E = a generalized viscoelastic stiffness; i = (-1)1/2; ω = angular frequency; ϕ = scaling factor; and k = an exponent valued between 0 and 1. The term "fractional derivative" refers to the value of k: when k = 0 the viscoelastic response is purely elastic, and when k = 1 the response is purely viscous. We provide an analytical derivation of the fractional derivative complex modulus based on the hypothesis that the viscoelastic response arises from many intermittent molecular crosslinks, whose lifetimes longer than a critical threshold lifetime, tcrit, are distributed with an inverse power law proportional to t-(k+2). We demonstrate that E is proportional to the number and stiffness of crosslinks formed at any moment; the scaling factor ϕ is equivalent to reciprocal of tcrit; and the relative mean lifetime of the attached crosslinks is inversely proportional to the parameter k. To test whether electrostatic molecular bonds could be responsible for the fractional derivative viscoelasticity, we used chemically skinned human skeletal muscle as a one-dimensional model of a soft glassy substance. A reduction in ionic strength from 175 to 110 mEq resulted in a larger E with no change in k, consistent with a higher probability of interfilament molecular interactions. Thick to thin filament spacing was reduced by applying 4% w/v of the osmolyte Dextran T500, which also resulted in a larger E, indicating a greater probability of crosslink formation in proportion to proximity. A 10°C increase in temperature resulted in an increase in k, which corresponded to a decrease in cross-bridge attachment lifetime expected with higher temperatures. These theoretical and experimental results suggest that the fractional derivative viscoelasticity observed in some biological tissue arises as a mechanical consequence of electrostatic interactions, whose longest lifetimes are distributed with an inverse power law.

Myofilament lattice structure in presence of a skeletal myopathy-related tropomyosin mutation

Human tropomyosin mutations deregulate skeletal muscle contraction at the cellular level. One key feature is the slowing of the kinetics of force development. The aim of the present study was to characterize the potential underlying molecular mechanisms by recording and analyzing the X-ray diffraction patterns of human membrane-permeabilized muscle cells expressing a particular β-tropomyosin mutation (E41K). During resting conditions, the d1,0 lattice spacing, Δ1,0 and I1,1 to I1,0 ratio were not different from control values. These results suggest that, in presence of the E41K β-tropomyosin mutation, the myofilament lattice geometry is well maintained and therefore may not have any detrimental influence on the contraction mechanisms and thus, on the rate of force generation.