Using Multiscale Simulations as a Tool to Interpret Equatorial X-ray Fiber Diffraction Patterns from Skeletal Muscle.

Synchrotron small-angle X-ray diffraction is the method of choice for nm-scale structural studies of striated muscle under physiological conditions and on millisecond time scales. The lack of generally applicable computational tools for modeling X-ray diffraction patterns from intact muscles has been a significant barrier to exploiting the full potential of this technique. Here, we report a novel "forward problem" approach using the spatially explicit computational simulation platform MUSICO to predict equatorial small-angle X-ray diffraction patterns and the force output simultaneously from resting and isometrically contracting rat skeletal muscle that can be compared to experimental data. The simulation generates families of thick-thin filament repeating units, each with their individually predicted occupancies of different populations of active and inactive myosin heads that can be used to generate 2D-projected electron density models based on known Protein Data Bank structures. We show how, by adjusting only a few selected parameters, we can achieve a good correspondence between experimental and predicted X-ray intensities. The developments presented here demonstrate the feasibility of combining X-ray diffraction and spatially explicit modeling to form a powerful hypothesis-generating tool that can be used to motivate experiments that can reveal emergent properties of muscle.

Computational Modeling on Drugs Effects for Left Ventricle in Cardiomyopathy Disease.

Cardiomyopathy is associated with structural and functional abnormalities of the ventricular myocardium and can be classified in two major groups: hypertrophic (HCM) and dilated (DCM) cardiomyopathy. Computational modeling and drug design approaches can speed up the drug discovery and significantly reduce expenses aiming to improve the treatment of cardiomyopathy. In the SILICOFCM project, a multiscale platform is developed using coupled macro- and microsimulation through finite element (FE) modeling of fluid-structure interactions (FSI) and molecular drug interactions with the cardiac cells. FSI was used for modeling the left ventricle (LV) with a nonlinear material model of the heart wall. Simulations of the drugs' influence on the electro-mechanics LV coupling were separated in two scenarios, defined by the principal action of specific drugs. We examined the effects of Disopyramide and Dygoxin which modulate Ca2+ transients (first scenario), and Mavacamten and 2-deoxy adenosine triphosphate (dATP) which affect changes of kinetic parameters (second scenario). Changes of pressures, displacements, and velocity distributions, as well as pressure-volume (P-V) loops in the LV models of HCM and DCM patients were presented. Additionally, the results obtained from the SILICOFCM Risk Stratification Tool and PAK software for high-risk HCM patients closely followed the clinical observations. This approach can give much more information on risk prediction of cardiac disease to specific patients and better insight into estimated effects of drug therapy, leading to improved patient monitoring and treatment.

Effect of Myosin Isoforms on Cardiac Muscle Twitch of Mice, Rats and Humans.

To understand how pathology-induced changes in contractile protein isoforms modulate cardiac muscle function, it is necessary to quantify the temporal-mechanical properties of contractions that occur under various conditions. Pathological responses are much easier to study in animal model systems than in humans, but extrapolation between species presents numerous challenges. Employing computational approaches can help elucidate relationships that are difficult to test experimentally by translating the observations from rats and mice, as model organisms, to the human heart. Here, we use the spatially explicit MUSICO platform to model twitch contractions from rodent and human trabeculae collected in a single laboratory. This approach allowed us to identify the variations in kinetic characteristics of α- and ß-myosin isoforms across species and to quantify their effect on cardiac muscle contractile responses. The simulations showed how the twitch transient varied with the ratio of the two myosin isoforms. Particularly, the rate of tension rise was proportional to the fraction of α-myosin present, while the ß-isoform dominated the rate of relaxation unless α-myosin was >50%. Moreover, both the myosin isoform and the Ca2+ transient contributed to the twitch tension transient, allowing two levels of regulation of twitch contraction.

Effect of Active Lengthening and Shortening on Small-Angle X-ray Reflections in Skinned Skeletal Muscle Fibres.

Our purpose was to use small-angle X-ray diffraction to investigate the structural changes within sarcomeres at steady-state isometric contraction following active lengthening and shortening, compared to purely isometric contractions performed at the same final lengths. We examined force, stiffness, and the 1,0 and 1,1 equatorial and M3 and M6 meridional reflections in skinned rabbit psoas bundles, at steady-state isometric contraction following active lengthening to a sarcomere length of 3.0 µm (15.4% initial bundle length at 7.7% bundle length/s), and active shortening to a sarcomere length of 2.6 µm (15.4% bundle length at 7.7% bundle length/s), and during purely isometric reference contractions at the corresponding sarcomere lengths. Compared to the reference contraction, the isometric contraction after active lengthening was associated with an increase in force (i.e., residual force enhancement) and M3 spacing, no change in stiffness and the intensity ratio I1,1/I1,0, and decreased lattice spacing and M3 intensity. Compared to the reference contraction, the isometric contraction after active shortening resulted in decreased force, stiffness, I1,1/I1,0, M3 and M6 spacings, and M3 intensity. This suggests that residual force enhancement is achieved without an increase in the proportion of attached cross-bridges, and that force depression is accompanied by a decrease in the proportion of attached cross-bridges. Furthermore, the steady-state isometric contraction following active lengthening and shortening is accompanied by an increase in cross-bridge dispersion and/or a change in the cross-bridge conformation compared to the reference contractions.

The effect of variable troponin C mutation thin filament incorporation on cardiac muscle twitch contractions.

One of the complexities of understanding the pathology of familial forms of cardiac diseases is the level of mutation incorporation in sarcomeres. Computational models of the sarcomere that are spatially explicit offer an approach to study aspects of mutational incorporation into myofilaments that are more challenging to get at experimentally. We studied two well characterized mutations of cardiac TnC, L48Q and I61Q, that decrease or increase the release rate of Ca2+ from cTnC, k-Ca, resulting in HCM and DCM respectively [1]. Expression of these mutations in transgenic mice was used to provide experimental data for incorporation of 30 and 50% (respectively) into sarcomeres. Here we demonstrate that fixed length twitch contractions of trabeculae from mice containing mutant differ from WT; L48Q trabeculae have slower relaxation while I61Q trabeculae have markedly reduced peak tension. Using our multiscale modelling approach [2] we were able to describe the tension transients of WT mouse myocardium. Tension transients for the mutant cTnCs were simulated with changes in k-Ca, measured experimentally for each cTnC mutant in whole troponin complex, a change in the affinity of cTnC for cTnI, and a reduction in the number of detached crossbridges available for binding. A major advantage of the multiscale explicit 3-D model is that it predicts the effects of variable mutation incorporation, and the effects of variations in mutation distribution within thin filaments in sarcomeres. Such effects are currently impossible to explore experimentally. We explored random and clustered distributions of mutant cTnCs in thin filaments, as well as distributions of individual thin filaments with only WT or mutant cTnCs present. The effects of variable amounts of incorporation and non-random distribution of mutant cTnCs are more marked for I61Q than L48Q cTnC. We conclude that this approach can be effective for study on mutations in multiple proteins of the sarcomere. SUMMARY: A challenge in experimental studies of diseases is accounting for the effect of variable mutation incorporation into myofilaments. Here we use a spatially explicit computational approach, informed by experimental data from transgenic mice expressing one of two mutations in cardiac Troponin C that increase or decrease calcium sensitivity. We demonstrate that the model can accurately describe twitch contractions for the data and go on to explore the effect of variable mutant incorporation and localization on simulated cardiac muscle twitches.

Multiscale modeling of twitch contractions in cardiac trabeculae.

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

Estimation of Forces on Actin Filaments in Living Muscle from X-ray Diffraction Patterns and Mechanical Data.

Many biological processes are triggered or driven by mechanical forces in the cytoskeletal network, but these transducing forces have rarely been assessed. Striated muscle, with its well-organized structure provides an opportunity to assess intracellular forces using small-angle X-ray fiber diffraction. We present a new methodology using Monte Carlo simulations of muscle contraction in an explicit 3D sarcomere lattice to predict the fiber deformations and length changes along thin filaments during contraction. Comparison of predicted diffraction patterns to experimental meridional X-ray reflection profiles allows assessment of the stepwise changes in intermonomer spacings and forces in the myofilaments within living muscle cells. These changes along the filament length reflect the effect of forces from randomly attached crossbridges. This approach enables correlation of the molecular events, such as the current number of attached crossbridges and the distributions of crossbridge forces to macroscopic measurements of force and length changes during muscle contraction. In addition, assessments of fluctuations in local forces in the myofilaments may reveal how variations in the filament forces acting on signaling proteins in the sarcomere M-bands and Z-discs modulate gene expression, protein synthesis and degradation, and as well to mechanisms of adaptation of muscle in response to changes in mechanical loading.

Myosin motor domains carrying mutations implicated in early or late onset hypertrophic cardiomyopathy have similar properties.

Hypertrophic cardiomyopathy (HCM) is a common genetic disorder characterized by left ventricular hypertrophy and cardiac hyper-contractility. Mutations in the ß-cardiac myosin heavy chain gene (ß-MyHC) are a major cause of HCM, but the specific mechanistic changes to myosin function that lead to this disease remain incompletely understood. Predicting the severity of any ß-MyHC mutation is hindered by a lack of detailed examinations at the molecular level. Moreover, because HCM can take ≥20 years to develop, the severity of the mutations must be somewhat subtle. We hypothesized that mutations that result in early onset disease would have more severe changes in function than do later onset mutations. Here, we performed steady-state and transient kinetic analyses of myosins carrying one of seven missense mutations in the motor domain. Of these seven, four were previously identified in early onset cardiomyopathy screens. We used the parameters derived from these analyses to model the ATP-driven cross-bridge cycle. Contrary to our hypothesis, the results indicated no clear differences between early and late onset HCM mutations. Despite the lack of distinction between early and late onset HCM, the predicted occupancy of the force-holding actin·myosin·ADP complex at [Actin] = 3 Kapp along with the closely related duty ratio (the fraction of myosin in strongly attached force-holding states), and the measured ATPases all changed in parallel (in both sign and degree of change) compared with wildtype (WT) values. Six of the seven HCM mutations were clearly distinct from a set of previously characterized DCM mutations.

The ATPase cycle of human muscle myosin II isoforms: Adaptation of a single mechanochemical cycle for different physiological roles.

Striated muscle myosins are encoded by a large gene family in all mammals, including humans. These isoforms define several of the key characteristics of the different striated muscle fiber types, including maximum shortening velocity. We have previously used recombinant isoforms of the motor domains of seven different human myosin isoforms to define the actin·myosin cross-bridge cycle in solution. Here, we present data on an eighth isoform, the perinatal, which has not previously been characterized. The perinatal is distinct from the embryonic isoform, appearing to have features in common with the adult fast-muscle isoforms, including weak affinity of ADP for actin·myosin and fast ADP release. We go on to use a recently developed modeling approach, MUSICO, to explore how well the experimentally defined cross-bridge cycles for each isoform in solution can predict the characteristics of muscle fiber contraction, including duty ratio, shortening velocity, ATP economy, and load dependence of these parameters. The work shows that the parameters of the cross-bridge cycle predict many of the major characteristics of each muscle fiber type and raises the question of what sequence changes are responsible for these characteristics.

Nebulin and titin modulate cross-bridge cycling and length-dependent calcium sensitivity.

Various mutations in the structural proteins nebulin and titin that are present in human disease are known to affect the contractility of striated muscle. Loss of nebulin is associated with reduced actin filament length and impairment of myosin binding to actin, whereas titin is thought to regulate muscle passive elasticity and is likely involved in length-dependent activation. Here, we sought to assess the modulation of muscle function by these sarcomeric proteins by using the computational platform muscle simulation code (MUSICO) to quantitatively separate the effects of structural changes, kinetics of cross-bridge cycling, and calcium sensitivity of the thin filaments. The simulations show that variation in thin filament length cannot by itself account for experimental observations of the contractility in nebulin-deficient muscle, but instead must be accompanied by a decreased myosin binding rate. Additionally, to match the observed calcium sensitivity, the rate of TnI detachment from actin needed to be increased. Simulations for cardiac muscle provided quantitative estimates of the effects of different titin-based passive elasticities on muscle force and activation in response to changes in sarcomere length and interfilament lattice spacing. Predicted force-pCa relations showed a decrease in both active tension and sensitivity to calcium with a decrease in passive tension and sarcomere length. We conclude that this behavior is caused by partial redistribution of the muscle load between active muscle force and titin-dependent passive force, and also by redistribution of stretch along the thin filament, which together modulate the release of TnI from actin. These data help advance understanding of how nebulin and titin mutations affect muscle function.

Nebulin stiffens the thin filament and augments cross-bridge interaction in skeletal muscle.

Nebulin is a giant sarcomeric protein that spans along the actin filament in skeletal muscle, from the Z-disk to near the thin filament pointed end. Mutations in nebulin cause muscle weakness in nemaline myopathy patients, suggesting that nebulin plays important roles in force generation, yet little is known about nebulin's influence on thin filament structure and function. Here, we used small-angle X-ray diffraction and compared intact muscle deficient in nebulin (using a conditional nebulin-knockout, Neb cKO) with control (Ctrl) muscle. When muscles were activated, the spacing of the actin subunit repeat (27 Å) increased in both genotypes; when converted to thin filament stiffness, the obtained value was 30 pN/nm in Ctrl muscle and 10 pN/nm in Neb cKO muscle; that is, the thin filament was approximately threefold stiffer when nebulin was present. In contrast, the thick filament stiffness was not different between the genotypes. A significantly shorter left-handed (59 Å) thin filament helical pitch was found in passive and contracting Neb cKO muscles, as well as impaired tropomyosin and troponin movement. Additionally, a reduced myosin mass transfer toward the thin filament in contracting Neb cKO muscle was found, suggesting reduced cross-bridge interaction. We conclude that nebulin is critically important for physiological force levels, as it greatly stiffens the skeletal muscle thin filament and contributes to thin filament activation and cross-bridge recruitment.

Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice.

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

X-ray diffraction from nonuniformly stretched helical molecules.

The fibrous proteins in living cells are exposed to mechanical forces interacting with other subcellular structures. X-ray fiber diffraction is often used to assess deformation and movement of these proteins, but the analysis has been limited to the theory for fibrous molecular systems that exhibit helical symmetry. However, this approach cannot adequately interpret X-ray data from fibrous protein assemblies where the local strain varies along the fiber length owing to interactions of its molecular constituents with their binding partners. To resolve this problem a theoretical formulism has been developed for predicting the diffraction from individual helical molecular structures nonuniformly strained along their lengths. This represents a critical first step towards modeling complex dynamical systems consisting of multiple helical structures using spatially explicit, multi-scale Monte Carlo simulations where predictions are compared with experimental data in a 'forward' process to iteratively generate ever more realistic models. Here the effects of nonuniform strains and the helix length on the resulting magnitude and phase of diffraction patterns are quantitatively assessed. Examples of the predicted diffraction patterns of nonuniformly deformed double-stranded DNA and actin filaments in contracting muscle are presented to demonstrate the feasibly of this theoretical approach.

Cooperative regulation of myosin-S1 binding to actin filaments by a continuous flexible Tm-Tn chain.

The regulation of striated muscle contraction involves cooperative interactions between actin filaments, myosin-S1 (S1), tropomyosin (Tm), troponin (Tn), and calcium. These interactions are modeled by treating overlapping tropomyosins as a continuous flexible chain (CFC), weakly confined by electrostatic interactions with actin. The CFC is displaced locally in opposite directions on the actin surface by the binding of either S1 or Troponin I (TnI) to actin. The apparent rate constants for myosin and TnI binding to and detachment from actin are then intrinsically coupled via the CFC model to the presence of neighboring bound S1s and TnIs. Monte Carlo simulations at prescribed values of the CFC stiffness, the CFC's degree of azimuthal confinement, and the angular displacements caused by the bound proteins were able to predict the stopped-flow transients of S1 binding to regulated F-actin. The transients collected over a large range of calcium concentrations could be well described by adjusting a single calcium-dependent parameter, the rate constant of TnI detachment from actin, k(-I). The resulting equilibrium constant K(B) ≡ 1/K(I) varied sigmoidally with the free calcium, increasing from 0.12 at low calcium (pCa >7) to 12 at high calcium (pCa <5.5) with a Hill coefficient of ~2.15. The similarity of the curves for excess-actin and excess-myosin data confirms their allosteric relationship. The spatially explicit calculations confirmed variable sizes for the cooperative units and clustering of bound myosins at low calcium concentrations. Moreover, inclusion of negative cooperativity between myosin units predicted the observed slowing of myosin binding at excess-myosin concentrations.

The Hill model for binding myosin S1 to regulated actin is not equivalent to the McKillop-Geeves model.

The Hill two-state cooperativity model and the McKillop-Geeves (McK-G) three-state model predict very similar binding traces of myosin subfragment 1 (S1) binding to regulated actin filaments in the presence and absence of calcium, and both fit the experimental data reasonably well [Chen et al., Biophys. J., 80, 2338-2349]. Here, we compared the Hill model and the McK-G model for binding myosin S1 to regulated actin against three sets of experimental data: the titration of regulated actin with S1 and the kinetics of S1 binding of regulated actin with either excess S1 to actin or excess actin to S1. Each data set was collected for a wide range of specified calcium concentrations. Both models were able to generate reasonable fits to the time course data and to titration data. The McK-G model can fit all three data sets with the same calcium-concentration-sensitive parameters. Only K(B) and K(T) show significant calcium dependence, and the parameters have a classic pCa curve. A unique set of the Hill model parameters was extremely difficult to estimate from the best fits of multiple sets of data. In summary, the McK-G cooperativity model more uniquely resolves parameters estimated from kinetic and titration data than the Hill model, predicts a sigmoidal dependence of key parameters with calcium concentration, and is simpler and more suitable for practical use.

Derivation of a finite-element model of lingual deformation during swallowing from the mechanics of mesoscale myofiber tracts obtained by MRI.

To demonstrate the relationship between lingual myoarchitecture and mechanics during swallowing, we performed a finite-element (FE) simulation of lingual deformation employing mesh aligned with the vector coordinates of myofiber tracts obtained by diffusion tensor imaging with tractography in humans. Material properties of individual elements were depicted in terms of Hill's three-component phenomenological model, assuming that the FE mesh was composed of anisotropic muscle and isotropic connective tissue. Moreover, the mechanical model accounted for elastic constraints by passive and active elements from the superior and inferior directions and the effect of out-of-plane muscles and connective tissue. Passive bolus effects were negligible. Myofiber tract activation was simulated over 500 ms in 1-ms steps following lingual tip association with the hard palate and incorporated specifically the accommodative and propulsive phases of the swallow. Examining the displacement field, active and passive muscle stress, elemental stretch, and strain rate relative to changes of global shape, we demonstrate that lingual reconfiguration during these swallow phases is characterized by (in sequence) the following: 1) lingual tip elevation and shortening in the anterior-posterior direction; 2) inferior displacement related to hyoglossus contraction at its inferior-most position; and 3) dominant clockwise rotation related to regional contraction of the genioglossus and contraction of the hyoglossus following anterior displacement. These simulations demonstrate that lingual deformation during the indicated phases of swallowing requires temporally patterned activation of intrinsic and extrinsic muscles and delineate a method to ascertain the mechanics of normal and pathological swallowing.

Resolving myoarchitectural disarray in the mouse ventricular wall with diffusion spectrum magnetic resonance imaging.

The myoarchitecture of the ventricular wall provides a structural template dictating tissue-scale patterns of mechanical function. We studied whether myofiber tract imaging performed with MR diffusion spectrum imaging (DSI) tractography has the capacity to resolve abnormalities of ventricular myoarchitecture in a model of congenital hypertrophic cardiomyopathy (HCM) associated with the ablation of myosin binding protein-C (MyBP-C). Homozygous MyBP-C knockout mice were generated by deletion of exons 3-10 from the endogenous MyBP-C gene. Fiber alignment in the left ventricular wall of wild type mice was depicted through DSI tractography (and confirmed by multi-slice two-photon microscopy) as a set of helical structures whose angles display a continuous transition from negative in the subepicardium to positive in the subendocardium. In contrast, the hearts obtained from the MyBP-C knockouts displayed substantial myoarchitectural disarray, characterized by a loss of voxel-to-voxel orientational coherence for fibers principally located in the mid-myocardium-subendocardium and impairment of the transmural progression of helix angles. These results substantiate the use of DSI tractography in determining myoarchitectural disarray in models of cardiomyopathy and suggest a biological association between myofilament expression, cardiac fiber alignment, and torsional rotation in the setting of congenital HCM.

Resolution and uniqueness of estimated parameters of a model of thin filament regulation in solution.

The estimation of chemical kinetic rate constants for any non-trivial model is complex due to the nonlinear effects of second order chemical reactions. We developed an algorithm to accomplish this goal based on the Damped Least Squares (DLS) inversion method and then tested the effectiveness of this method on the McKillop-Geeves (MG) model of thin filament regulation. The kinetics of MG model is defined by a set of nonlinear ordinary differential equations (ODEs) that predict the evolution of troponin-tropomyosin-actin and actin-myosin states. The values of the rate constants are estimated by integrating these ODEs numerically and fitting them to a series of stopped-flow pyrene fluorescence transients of myosin-S1 fragment binding to regulated actin in solution. The accuracy and robustness of the estimated rate constants are evaluated for DLS and two other methods, namely quasi-Newton (QN) and simulated annealing (SA). The comparison of these methods revealed that SA provides the best estimates of the model parameters because of its global optimization scheme. However it converges slowly and does quantify the uniqueness of the estimated parameters. On the other hand the QN method converges rapidly but only if the initial guess of the parameters is close to the optimum values, otherwise it diverges. Overall, the DLS method proves to be the most convenient method. It converges fast and was able to provide excellent estimates of kinetic parameters. Furthermore, DLS provides the model resolution matrix, which quantifies the interdependence of model parameters thereby evaluating the uniqueness of their estimated values. This property is essential for estimating of the dependence of the model parameters on experimental conditions (e.g. Ca(2+) concentration) when it is assessed from noisy experimental data such as pyrene fluorescence from stopped-flow transients. The advantages of the DLS method observed in this study should be further examined in other physicochemical systems to firmly establish the observed effectiveness of DSL vs. the other parameter estimation methods.

Remodeling of integrated contractile tissues and its dependence on strain-rate amplitude.

Here we investigate the origin of relaxation times governing the mechanical response of an integrated contractile tissue to imposed cyclic changes of length. When strain-rate amplitude is held constant as frequency is varied, fast events are accounted for by actomyosin cross-bridge cycling, but slow events reveal relaxation processes associated with ongoing cytoskeletal length adaptation. Although both relaxation regimes are innately nonlinear, these regimes are unified and their positions along the frequency axis are set by the imposed strain-rate amplitude.

Thermodynamic origin of cooperativity in actomyosin interactions: the coupling of short-range interactions with actin bending stiffness in an Ising-like model.

We present Monte Carlo simulations for a molecular motor system found in virtually all eukaryotic cells, the acto-myosin motor system, composed of a group of organic macromolecules. Cell motors were mapped to an Ising-like model, where the interaction field is transmitted through a tropomyosin polymer chain. The presence of Ca2+ induces tropomyosin to block or unblock binding sites of the myosin motor leading to its activation or deactivation. We used the Metropolis algorithm to find the transient and the equilibrium states of the acto-myosin system composed of solvent, actin, tropomyosin, troponin, Ca2+, and myosin-S1 at a given temperature, including the spatial configuration of tropomyosin on the actin filament surface. Our model describes the short- and long-range cooperativity during actin-myosin binding which emerges from the bending stiffness of the tropomyosin complex. We found all transition rates between the states only using the interaction energy of the constituents. The agreement between our model and experimental data also supports the recent theory of flexible tropomyosin.