Abstract
High-performance computing approaches that combine molecular-scale and macroscale continuum mechanics have long been anticipated in various fields. Such approaches may enrich our understanding of the links between microscale molecular mechanisms and macroscopic properties in the continuum. However, there have been few successful examples to date owing to various difficulties associated with overcoming the large spatial (from 1 nm to 10 cm) and temporal (from 1 ns to 1 ms) gaps between the two scales. In this paper, we propose an efficient parallel scheme to couple a microscopic model using Langevin dynamics for a protein motor with a finite element continuum model of a beating heart. The proposed scheme allows us to use a macroscale time step that is an order of magnitude longer than the microscale time step of the Langevin model, without loss of stability or accuracy. This reduces the overhead required by the imbalanced loads of the microscale computations and the communication required when switching between scales. An example of the Langevin dynamics model that demonstrates the usefulness of the coupling approach is the molecular mechanism of the actomyosin system, in which the stretch-activation phenomenon can be successfully reproduced. This microscopic Langevin model is coupled with a macroscopic finite element ventricle model. In the numerical simulations, the Langevin dynamics model reveals that a single sarcomere can undergo spontaneous oscillation (15 Hz) accompanied by quick lengthening due to cooperative movements of the myosin molecules pulling on the common Z-line. Also, the coupled simulations using the ventricle model show that the stretch-activation mechanism contributes to the synchronization of the quick lengthening of the sarcomeres at the end of the systolic phase. By comparing the simulation results given by the molecular model with and without the stretch-activation mechanism, we see that this synchronization contributes to maintaining the systolic blood pressure by providing sufficient blood volume without slowing the diastolic process.
Highlights
With the advances in computational science made possible by improvements in hardware technology, it is possible to create multi-scale simulation models of the heart in which the macroscopic behaviors of the beating heart can be reproduced and analyzed based on molecular mechanisms of the excitationcontraction coupling process (Kerckhoffs et al, 2007; Gurev et al, 2011; Sugiura et al, 2012)
A molecular dynamics simulation of actomyosin should be coupled with a macroscopic finite element model of the heart because with such a model the impact of mutations in the myosin molecules on cardiac function can be directly assessed
This is a simplification of the behavior of real myosin molecules experiencing thermal fluctuations, and we have recently reported that a model with an energy landscape possessing wide minima can reproduce experimental findings with higher accuracy (Marcucci et al, 2016)
Summary
With the advances in computational science made possible by improvements in hardware technology, it is possible to create multi-scale simulation models of the heart in which the macroscopic behaviors of the beating heart can be reproduced and analyzed based on molecular mechanisms of the excitationcontraction coupling process (Kerckhoffs et al, 2007; Gurev et al, 2011; Sugiura et al, 2012). It is not possible to perform such simulations even with the best available high-performance computers, and current multi-scale heart simulators usually adopt state-transition models of crossbridge cycling In these models, the rate constants for transitions between states are governed by the energy of each state (Huxley and Simmons, 1971), but the minimum in the energy landscape corresponding to each state ignores its width in the infinitely-sharp minimum approximation, in which the angle of each lever arm is fixed in the most stable configuration. The Kramers-Smoluchovski approximation (Gardiner, 2004) was used to obtain the rate constants of the transitions between the multiple states, which were given by discretizing the one-dimensional range of the Parameter
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