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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Spatio-temporal Dynamics of Nonlinear Mechano-chemical Processes Driving Anisotropic Rhythmic Contraction of Cardiac Myocytes Philippe TRACQUI CNRS, Laboratoire TIMC-IMAG, Equipe Dynacell Institut de lIngénierie et de lInformation de Santé, In 3 S, Grenoble, France in collaboration with Jacques OHAYON

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Mechanics is a key issue of heart function … … but still remains largely over simplified in analyses and models of cardiac cells and cardiac tissues dynamics Things are changing with the increasingly recognized importance of the transduction of mechanical signals (mechanotransduction) in cell signaling cascades There is a real need for the development of the mechanobiology of cardiac cells and tissues, notably through the development of theoretical models as the cell and tissue levels

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Slide from the Physiome project presentation (R. McLeod & P. Hunter) Genes Genes Proteins Proteins Biophysical models Biophysical models Constitutive laws Constitutive laws Organ model Organ model Whole body model Whole body model Genome Genome Protein Protein Physiology Physiology Structural Structural Bioeng. Materials Bioeng. Materials Clinical Clinical Modeling Hierarchies Databases Molecular Biology Physiology Bioengineering Clinical medicine

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Context: Analysis of excitation-contraction of isolated cardiac myocyte trough a multi-scale integrative approach of the structure and function relationships Aims: an analysis of the cardiac performance based on a relevant description of the Ca 2+ driven anosotropic and hyperelastic cardiomyocyte contraction a modelling basis for theoretical and quantitative analysis of the mechano-regulation of cardiomyocyte contraction by mechanotransduction processes Cellular level Tissue level Intracellular level

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Spontaneous contraction of rat cardiomyocyte size (110 x 20 m) Spontaneous contraction of an isolated cardiomyocyte The sarcomere as the contractile unit Mean experimental contraction period Mean experimental contraction duration 17,0 5,8 s1,5 0,4 s Mean experimental contraction amplitude ~ 8 m ( 7%)

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Associated calcium wave propagation Visualisation of the propagation of an intracellular calcium wave using Ca labelling with the fluorescent Fluo3 probe ( t = 268ms between two successive images, cell length :110 m)

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 A theoretical model of the cardiomyocyte self-sustained contraction expression of Ca 2+ oscillations in a domain of the parametric space where travelling waves may exist introduction of cytosolic Ca2+ variations in the formulation of an active stress tensor, taking into account cell architectural anisotropy consideration of cardiomyocyte hyperelastic properties with appropriate passive stress-strain relationship finite element simulation and experimental validation of the dynamical behaviour of the virtual cardiomyocyte in different contexts

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Modelling calcium waves propagation in cells and tissues Dupont et al. 96 (Means et al., 2006)

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Goldbeter et al. (PNAS, 1990) Z: Cytosolic Ca 2+ concentration Y: Ca 2+ concentration in the sarcoplasmic reticulum A simplified one calcium -pool model Autocatalytic process responsible for temporal oscillations: Calcium-Induced-Calcium-Release (CICR)

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Sarcomere length SL ( m) Tension (kPa) Passive tension as a function of the sarcomere length (Cazorla et al., 2003) 20 m Elastic properties of the cardiomyocyte Uniaxial stretching of the cardiomyocyte

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Constitutive stress-strain relationship (1): passive component a 1, a 2, cellular material constants I 1 is the first invariant of the right Cauchy- Green strain tensor C (I 1 =Tr(C)) The cardiomyocyte is considered as an hyperelastic incompressible medium with passive strain energy function

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Active anisotropic Cauchy stress tensor given by: (fs orientation of deformed fibers) Constitutive stress-strain relationship (2): active component with: with: Tmax maximal tension K(SL)=Ca half-maximal value n H Hill coefficient

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Interplay of calcium oscillations and cell contraction Calcium spatio-temporal dynamics (waves) Active and passive anisotropic mechanical behaviour Integrative mechano-biochemical model of the self- sustained cardiomyocyte contraction Model Variables Z(r,t), Y(r,t) and {u(r,t), v(r,t) } D diagonal diffusion tensor

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Finite element simulation of the cardiomyocyte spontaneous contraction Geometry extracted from real cell image Boundary conditions Stress free boundaries, localized zero displacement in the nucleus area No calcium fluxes (Neuman conditions) on the cell boundaries Permeability of the nucleus to cytosolic Ca (Pustoch et al., Acta Biotheor. 2005)

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Cardiomyocyte contraction driven by calcium waves originating from cell border (left) or from cell centre (right), as shown by videomicroscopy time-lapse observations Saptio-temporal evolution of cytosolic calcium concentrations (Z(x,y,t)) Simulated self-sustained oscillating contraction of an isolated cardiomyocyte Triggering calcium spark initiated on the left cell side Soliton propagating from left to right in pace with cell shortening Calcium spark initiated in the middle of the cell Two solitary waves propagating in opposite directions Cell contracts at both ends simultaneously

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Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Conclusions and perspectives A satisfactory and rather simple mechano-biochemical model of the isolated cardiomyocyte oscillatory contraction Amenable to theoretical analysis (bifurcation analysis of model dynamics) Exemplified mechanical aspects disregarded by reaction-diffusion models A quantitative framework for analysing the effect of local mechanotransduction processes (titin, endothelin,..) A basis for elaborating of a 2D virtual myocardium in which the global tissue response (arrhythmia, contraction inefficiency, …) to localized perturbations (ischemia, …) can be studied Acknowledgement: This work has been supported by a grant from the CNRS (ACI NIM MOCEMY)

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