Approximation for Cooperative Interactions of a Spatially-Detailed Cardiac Sarcomere Model

We developed a novel ordinary differential equation (ODE) model, which produced results that correlated well with the Monte Carlo (MC) simulation when applied to a spatially-detailed model of the cardiac sarcomere. Configuration of the novel ODE model was based on the Ising model of myofilaments, with the “co-operative activation” effect introduced to incorporate nearest-neighbor interactions. First, a set of parameters was estimated using arbitrary Ca transient data to reproduce the combinational probability for the states of three consecutive regulatory units, using single unit probabilities for central and neighboring units in the MC simulation. The parameter set thus obtained enabled the calculation of the state transition of each unit using the ODE model with reference to the neighboring states. The present ODE model not only provided good agreement with the MC simulation results but was also capable of reproducing a wide range of experimental results under both steady-state and dynamic conditions including shortening twitch. The simulation results suggested that the nearest-neighbor interaction is a reasonable approximation of the cooperativity based on end-to-end interactions. Utilizing the modified ODE model resulted in a reduction in computational costs but maintained spatial integrity and co-operative effects, making it a powerful tool in cardiac modeling

Sarcomere length-dependent Ca2+ activation in skinned rabbit psoas muscle fibers: coordinated regulation of thin filament cooperative activation and passive force

In skeletal muscle, active force production varies as a function of sarcomere length (SL). It has been considered that this SL dependence results simply from a change in the overlap length between the thick and thin filaments. The purpose of this study was to provide a systematic understanding of the SL-dependent increase in Ca2+ sensitivity in skeletal muscle, by investigating how thin filament “on–off” switching and passive force are involved in the regulation. Rabbit psoas muscles were skinned, and active force measurements were taken at various Ca2+ concentrations with single fibers, in the short (2.0 and 2.4 μm) and long (2.4 and 2.8 μm) SL ranges. Despite the same magnitude of SL elongation, the SL-dependent increase in Ca2+ sensitivity was more pronounced in the long SL range. MgADP (3 mM) increased the rate of rise of active force and attenuated SL-dependent Ca2+ activation in both SL ranges. Conversely, inorganic phosphate (Pi, 20 mM) decreased the rate of rise of active force and enhanced SL-dependent Ca2+ activation in both SL ranges. Our analyses revealed that, in the absence and presence of MgADP or Pi, the magnitude of SL-dependent Ca2+ activation was (1) inversely correlated with the rate of rise of active force, and (2) in proportion to passive force. These findings suggest that the SL dependence of active force in skeletal muscle is regulated via thin filament “on–off” switching and titin (connectin)-based interfilament lattice spacing modulation in a coordinated fashion, in addition to the regulation via the filament overlap

Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions

We propose a reduced ODE model for the mechanical activation of cardiac myofilaments, which is based on explicit spatial representation of nearest-neighbour interactions. Our model is derived from the cooperative Markov Chain model of Washio et al. (Cell Mol Bioeng 5(1):113–126, 2012), under the assumption of conditional independence of specific sets of events. This physically motivated assumption allows to drastically reduce the number of degrees of freedom, thus resulting in a significantly large computational saving. Indeed, the original Markov Chain model involves a huge number of degrees of freedom (order of (Formula presented.)) and is solved by means of the Monte Carlo method, which notoriously reaches statistical convergence in a slow fashion. With our reduced model, instead, numerical simulations can be carried out by solving a system of ODEs, reducing the computational time by more than 10, 000 times. Moreover, the reduced model is accurate with respect to the original Markov Chain model. We show that the reduced model is capable of reproducing physiological steady-state force–calcium and force–length relationships with the observed asymmetry in apparent cooperativity near the calcium level producing half activation. Finally, we also report good qualitative and quantitative agreement with experimental measurements under dynamic conditions

Cardiac Tissue Structure, Properties, and Performance: A Materials Science Perspective

From an engineering perspective, many forms of heart disease can be thought of as a reduction in biomaterial performance, in which the biomaterial is the tissue comprising the ventricular wall. In materials science, the structure and properties of a material are recognized to be interconnected with performance. In addition, for most measurements of structure, properties, and performance, some processing is required. Here, we review the current state of knowledge regarding cardiac tissue structure, properties, and performance as well as the processing steps taken to acquire those measurements. Understanding the impact of these factors and their interactions may enhance our understanding of heart function and heart failure. We also review design considerations for cardiac tissue property and performance measurements because, to date, most data on cardiac tissue has been obtained under non-physiological loading conditions. Novel measurement systems that account for these design considerations may improve future experiments and lead to greater insight into cardiac tissue structure, properties, and ultimately performance