A balancing domain decomposition by constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical bidomain and monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues, and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, and hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.

Allosteric molecules provide a powerful means to modulate protein function. However, the effect of such ligands on distal orthosteric sites cannot be easily described by classical docking methods. Here, we applied machine learning (ML) approaches to expose the links between local dynamic patterns and different degrees of allosteric inhibition of the ATPase function in the molecular chaperone TRAP1. We focused on 11 novel allosteric modulators with similar affinities to the target but with inhibitory efficacy between the 26.3 and 76%. Using a set of experimentally related local descriptors, ML enabled us to connect the molecular dynamics (MD) accessible to ligand-bound (perturbed) and unbound (unperturbed) systems to the degree of ATPase allosteric inhibition. The ML analysis of the comparative perturbed ensembles revealed a redistribution of dynamic states in the inhibitor-bound versus inhibitor-free systems following allosteric binding. Linear regression models were built to quantify the percentage of experimental variance explained by the predicted inhibitor-bound TRAP1 states. Our strategy provides a comparative MD–ML framework to infer allosteric ligand functionality. Alleviating the time scale issues which prevent the routine use of MD, a combination of MD and ML represents a promising strategy to support in silico mechanistic studies and drug design.

In this work, we investigate the influence of cardiac tissue deformation on re-entrant wave dynamics. We have developed a 3D strongly coupled electro-mechanical Bidomain model posed on an ideal monoventricular geometry, including fiber direction anisotropy and stretch-activated currents (SACs). The cardiac mechanical deformation influences the bioelectrical activity with two main mechanical feedback: (a) the geometric feedback (GEF) due to the presence of the deformation gradient in the diffusion coefficients and in a convective term depending on the deformation rate and (b) the mechano-electric feedback (MEF) due to SACs. Here, we investigate the relative contribution of these two factors with respect to scroll wave stability. We extend the previous works [Keldermann et al., Am. J. Physiol. Heart Circ. Physiol. 299, H134–H143 (2010) and Hu et al., PLoS One 8(4), e60287 (2013)] that were based on the Monodomain model and a simple non-selective linear SAC, while here we consider the full Bidomain model and both selective and non-selective components of SACs. Our simulation results show that the stability of cardiac scroll waves is influenced by MEF, which in case of low reversal potential of non-selective SACs might be responsible for the onset of ventricular fibrillation; GEF increases the scroll wave meandering but does not determine the scroll wave stability.