Rencontres GdR DYCOEC, Nice, 5-6 février 2008 Spatio-temporal Dynamics of Spatio-temporal Dynamics of Nonlinear Mechano-chemical Nonlinear Mechano-chemical Processes Processes Driving Anisotropic Rhythmic Driving Anisotropic Rhythmic Contraction Contraction of Cardiac Myocytes of Cardiac Myocytes Philippe TRACQUI CNRS, Laboratoire TIMC-IMAG, Equipe Dynacell Institut de l’Ingénierie et de l’Information de Santé, In 3 S, Grenoble, France http://www-timc.imag.fr/dynacell in collaboration with Jacques OHAYON
Spatio-temporal Dynamics of Nonlinear Mechano-chemical Processes Driving Anisotropic Rhythmic Contraction of Cardiac Myocytes. Philippe TRACQUI. in collaboration with Jacques OHAYON. CNRS, Laboratoire TIMC-IMAG, Equipe Dynacell Institut de l’Ingénierie et de l’Information de Santé, In 3 S, - PowerPoint PPT Presentation
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Rencontres GdR DYCOEC, Nice, 5-6 février 2008
Spatio-temporal Dynamics of Spatio-temporal Dynamics of Nonlinear Mechano-chemical Nonlinear Mechano-chemical
ContractionContractionof Cardiac Myocytes of Cardiac Myocytes
Philippe TRACQUI
CNRS, Laboratoire TIMC-IMAG, Equipe DynacellInstitut de l’Ingénierie et de l’Information de Santé, In3S,
Grenoble, France
http://www-timc.imag.fr/dynacell
in collaboration with Jacques OHAYON
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
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
Slide from the Physiome project presentationSlide from the Physiome project presentation(R. McLeod & P. Hunter)(R. McLeod & P. Hunter)
Slide from the Physiome project presentationSlide from the Physiome project presentation(R. McLeod & P. Hunter)(R. McLeod & P. Hunter)
GenesGenes ProteinsProteins Biophysical modelsBiophysical models Constitutive lawsConstitutive laws Organ modelOrgan model Whole body modelWhole body model
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)
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
A theoretical model of the A theoretical model of the cardiomyocyte self-sustained cardiomyocyte self-sustained
contractioncontraction
expression of Ca2+ 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
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
Modelling calcium waves propagation Modelling calcium waves propagation in cells and tissuesin cells and tissues
Dupont et al. 96
(Means et al., 2006)
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
Goldbeter et al. (PNAS, 1990)
Z: Cytosolic Ca2+ concentration
Y: Ca2+ concentration in the sarcoplasmic reticulum
A simplified one calcium -pool modelA simplified one calcium -pool model
€
dZ
dt= v0 +v1.β − v2 +v3 + k f .Y −k.Z
€
dY
dt= v2 −v3 −k f .Y
nn
n
MZK
ZV +=
222 .ν
ppA
p
mmR
m
M ZK
Z
YK
YV
++= ..33ν
Autocatalytic process responsible for temporal Autocatalytic process responsible for temporal oscillations: Calcium-Induced-Calcium-Release oscillations: Calcium-Induced-Calcium-Release
(CICR)(CICR)
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
0
1
2
3
4
5
6
7
8
9
10
1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5
longueur sarcomère en micronsSarcomere length SL (m)
Tension (kPa)
Passive tension as a function of the Passive tension as a function of the sarcomere length sarcomere length ((Cazorla et al., 2003Cazorla et al., 2003))
20 20 mm
Elastic properties of the cardiomyocyteElastic properties of the cardiomyocyte
Uniaxial stretching of the Uniaxial stretching of the cardiomyocytecardiomyocyte
Finite element simulation of the Finite element simulation of the cardiomyocyte spontaneous cardiomyocyte spontaneous
contractioncontraction
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
(Pustoc’h et al., Acta Biotheor. 2005)
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
Cardiomyocyte contraction driven by calcium waves originating Cardiomyocyte contraction driven by calcium waves originating from cell border (left) or from cell centre (right), as shown from cell border (left) or from cell centre (right), as shown
by videomicroscopy time-lapse observationsby videomicroscopy time-lapse observations
Saptio-temporal evolution of cytosolic calcium concentrations (Z(x,y,t))Saptio-temporal evolution of cytosolic calcium concentrations (Z(x,y,t))
Simulated self-sustained oscillating contraction of Simulated self-sustained oscillating contraction of an isolated cardiomyocytean isolated cardiomyocyte
Triggering calcium spark initiated on the left cell sideSoliton propagating from left to right in pace with cell shortening
Calcium spark initiated in the middle of the cellTwo solitary waves propagating in opposite directionsCell contracts at both ends simultaneously
Rencontres GdR DYCOEC, Nice, 5-6 février 2008
Conclusions and perspectivesConclusions 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”)