Theoretical analysis of the adaptive contractile behaviour of a single cardiomyocyte cultured on elastic substrates with varying stiffness.

In vivo, cardiomyocytes interact with surrounding extracellular matrix while performing periodically a contractile behaviour, which is the main determinant of heart performance. As extracellular substrates with easily tunable stiffness properties, polyacrylamide gels (PAGs) provide valuable flexible media for studying in vitro the dynamical behaviour of cardiomyocytes responding to stiffness variations of their surrounding environment. We propose in this paper an original mechano-chemical model of the cardiac cell contraction that sheds light on the adaptive response of cardiomyocytes evidenced recently in the experiments of Qin et al. [2007. Dynamical stress characterization and energy evaluation of single cardiac myocyte actuating on flexible substrate. Biochem. Biophys. Res. Commun. 360, 352-356]. The model links the amplitude of the extracellular PAGs strain fields to the spatio-temporal variation of the intracellular stresses in every part of the cell during the sarcomeres contraction-relaxation. In a continuum mechanics framework, we derived a unified description of the sarcomere-length dependence of intracellular active stress and of its control by anisotropic calcium diffusion and autocatalytic calcium release from the sarcoplasmic reticulum. Taking benefit of our previous work on the characterization of mechanical properties of PAGs with varying stiffness, we were thus able to evaluate the active intracellular stress exerted by the cardiomyocyte on flexible PAGs with different and known Young's moduli. Interestingly, we were able to explain the intriguing increase of maximal cellular stress observed experimentally when substrate stiffness is increased. By providing an evaluation of the whole-field cell stresses and strains, this integrative approach of cardiomyocyte contraction provides a reliable basis for further analysis of additional cooperativity and mechanotransduction mechanisms involved in cell contractility regulation, notably in physiological and pathological situations where modifications of cardiac performance are linked to varied stiffness of the cardiomyocytes environment.