Multiscale modeling of twitch contractions in cardiac trabeculae

© 2021 Mijailovich et al. 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

Modeling the Actin.myosin ATPase cross-bridge cycle for skeletal and cardiac muscle myosin isoforms

Modeling the complete actin.myosin ATPase cycle has always been limited by the lack of experimental data concerning key steps of the cycle, because these steps can only be defined at very low ionic strength. Here, using human ?-cardiac myosin-S1, we combine published data from transient and steady-state kinetics to model a minimal eight-state ATPase cycle. The model illustrates the occupancy of each intermediate around the cycle and how the occupancy is altered by changes in actin concentration for [actin] = 1–20Km. The cycle can be used to predict the maximal velocity of contraction (by motility assay or sarcomeric shortening) at different actin concentrations (which is consistent with experimental velocity data) and predict the effect of a 5 pN load on a single motor. The same exercise was repeated for human ?-cardiac myosin S1 and rabbit fast skeletal muscle S1. The data illustrates how the motor domain properties can alter the ATPase cycle and hence the occupancy of the key states in the cycle. These in turn alter the predicted mechanical response of the myosin independent of other factors present in a sarcomere, such as filament stiffness and regulatory proteins. We also explore the potential of this modeling approach for the study of mutations in human ?-cardiac myosin using the hypertrophic myopathy mutation R453C. Our modeling, using the transient kinetic data, predicts mechanical properties of the motor that are compatible with the single-molecule study. The modeling approach may therefore be of wide use for predicting the properties of myosin mutations

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

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

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto

One Stop Shop como modelo de integración de servicios públicos dentro del marco de la Post Nueva Gestión Pública

El objetivo de este documento es establecer una relación entre el modelo One-Stop-Shop y la manera en que los Estados se están buscando entregar de sus servicios bajo modelos enfocados en el ciudadano. Para ello, se abordó la discusión entre la Nueva Gestión Pública y la Post Nueva Gestión Pública para establecer si esta última es una continuación o establece una ruptura del antiguo modelo. Asimismo, se describió la evolución de la prestación de servicios públicos hasta llegar al modelo de prestación de servicios públicos enfocado en el ciudadano que desarrolla el Nuevo Servicio Público. Además, se describió el Whole of government cuyo enfoque de integración en la prestación de servicios fue decisivo para dar paso al desarrollo del modelo One-Stop-Shop en distintos países del mundo, incluido el Perú

Identificación de factores críticos para la implementación exitosa del Gobierno Digital en el Perú desde la perspectiva de actores relacionados al Poder Ejecutivo

El presente estudio busca identificar los factores críticos que permitan facilitar la implementación y desarrollo del Gobierno Digital en el Estado Peruano utilizando una matriz de variables y factores, la cual fue construida utilizando distintos estudios e investigaciones basadas en experiencias internacionales de Gobierno Digital y posteriormente validada por especialistas nacionales e internacionales en el tema. Esta investigación posee un enfoque metodológico del tipo cualitativo con alcance exploratorio-descriptivo, el cual permitió identificar, en un primer momento, un gran número de factores y variables que posteriormente fueron agrupadas en 7 factores (los cuales contienen 22 variables y 20 sub-variables) para que sean evaluadas por expertos en Gobierno Digital con el fin de otorgarles su nivel de criticidad correspondiente. Para este objetivo, se estructuró una guía de entrevistas semi estructurada como herramienta de recojo de información con la que se realizaron 21 entrevistas a profundidad a expertos en Gobierno Digital quienes están o estuvieron relacionados con entidades del Poder Ejecutivo peruano. A partir de la información recopilada de las entrevistas, se determinó el nivel de criticidad de cada uno de los factores identificados, así como los principales hallazgos relacionados a cada uno de estos. Finalmente, como resultado del análisis, se determinaron 4 factores críticos que facilitan la implementación del Gobierno Digital en el Perú. Adicionalmente, se logró identificar 3 niveles de priorización, los cuales contienen a los siete factores identificados

Distributed multi-scale muscle simulation in a hybrid MPI–CUDA computational environment

We present Mexie, an extensible and scalable software solution for distributed multi-scale muscle simulations in a hybrid MPI–CUDA environment. Since muscle contraction relies on the integration of physical and biochemical properties across multiple length and time scales, these models are highly processor and memory intensive. Existing parallelization efforts for accelerating multi-scale muscle simulations imply the usage of expensive large-scale computational resources, which produces overwhelming costs for the everyday practical application of such models. In order to improve the computational speed within a reasonable budget, we introduce the concept of distributed calculations of multi-scale muscle models in a mixed CPU–GPU environment. The concept is applied to a two-scale muscle model, in which a finite element macro model is coupled with the microscopic Huxley kinetics model. Finite element calculations of a continuum macroscopic model take place strictly on the CPU, while numerical solutions of the partial differential equations of Huxley’s cross-bridge kinetics are calculated on both CPUs and GPUs. We present a modular architecture of the solution, along with an internal organization and a specific load balancer that is aware of memory boundaries in such a heterogeneous environment. Solution was verified on both benchmark and real-world examples, showing high utilization of involved processing units, ensuring high scalability. Speed-up results show a boost of two orders of magnitude over any previously reported distributed multi-scale muscle models. This major improvement in computational feasibility of multi-scale muscle models paves the way for new discoveries in the field of muscle modeling and future clinical applications.Author's versio