Chaos out of internal noise in the collective dynamics of diffusively coupled cells

Abstract.We study the transition from stochasticity to determinism in calcium oscillations via diffusive coupling of individual cells that are modeled by stochastic simulations of the governing reaction-diffusion equations. As expected, the stochastic solutions gradually converge to their deterministic limit as the number of coupled cells increases. Remarkably however, although the strict deterministic limit dictates a fully periodic behavior, the stochastic solution remains chaotic even for large numbers of coupled cells if the system is set close to an inherently chaotic regime. On the other hand, the lack of proximity to a chaotic regime leads to an expected convergence to the fully periodic behavior, thus suggesting that near-chaotic states are presently a crucial predisposition for the observation of noise-induced chaos. Our results suggest that chaos may exist in real biological systems due to intrinsic fluctuations and uncertainties characterizing their functioning on small scales.

[1]  Zhonghuai Hou,et al.  Internal noise stochastic resonance for intracellular calcium oscillations in a cell system. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Matjaž Perc,et al.  Periodic calcium waves in coupled cells induced by internal noise , 2007 .

[3]  D. Gillespie.  Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[4]  M Claret,et al.  Coordinated intercellular calcium waves induced by noradrenaline in rat hepatocytes: dual control by gap junction permeability and agonist , 1997, The EMBO journal.

[5]  Matjaz Perc,et al.  Irregularity test for very short electrocardiogram (ECG) signals as a method for predicting a successful defibrillation in patients with ventricular fibrillation. , 2007, Translational research : the journal of laboratory and clinical medicine.

[6]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[7]  Gao,et al.  Noise-induced chaos in an optically injected semiconductor laser model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Ursula Kummer,et al.  Transition from stochastic to deterministic behavior in calcium oscillations. , 2005, Biophysical journal.

[9]  B. M. Fulk.  MATH , 1992 .

[10]  S. Schuster,et al.  Modelling of simple and complex calcium oscillations , 2002 .

[11]  B. Wolf,et al.  Modellbildung in der biologie , 1992, Naturwissenschaften.

[12]  M. Falcke.  Reading the patterns in living cells —the physics of ca2+ signaling , 2004 .

[13]  M. Perc.  Nonlinear time series analysis of the human electrocardiogram , 2005 .

[14]  G. Donaldson,et al.  The chaotic behaviour of resting human respiration. , 1992, Respiration physiology.

[15]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[16]  M. Kraus,et al.  Crosstalk between cellular morphology and calcium oscillation patterns. Insights from a stochastic computer model. , 1996, Cell calcium.

[17]  Quan Liu,et al.  A mesoscopic stochastic mechanism of cytosolic calcium oscillations. , 2007, Biophysical chemistry.

[18]  Matjaž Perc,et al.  From stochasticity to determinism in the collective dynamics of diffusively coupled cells , 2006 .

[19]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[20]  H. Herzel,et al.  SUBHARMONICS, BIPHONATION, AND DETERMINISTIC CHAOS IN MAMMAL VOCALIZATION , 1998 .

[21]  D. T. Kaplan,et al.  Direct test for determinism in a time series. , 1992, Physical review letters.

[22]  R Toral,et al.  Stochastic effects in intercellular calcium spiking in hepatocytes. , 2001, Journal of theoretical biology.

[23]  K Prank,et al.  Precision of intracellular calcium spike timing in primary rat hepatocytes. , 2005, Systems biology.

[24]  A Goldbeter,et al.  Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5-trisphosphate signal in a model for intracellular Ca2+ oscillations , 1999, Bulletin of mathematical biology.

[25]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[26]  P. Jung,et al.  Optimal intracellular calcium signaling. , 2002, Physical review letters.

[27]  Wen-Wen Tung,et al.  Noise-induced Hopf-bifurcation-type sequence and transition to chaos in the lorenz equations. , 2002, Physical review letters.

[28]  B. Huberman,et al.  Fluctuations and simple chaotic dynamics , 1982 .

[29]  Aleksander S Popel,et al.  Monte Carlo simulations of VEGF binding to cell surface receptors in vitro. , 2005, Biochimica et biophysica acta.

[30]  P. Cobbold,et al.  Phorbol ester and sperm activate mouse oocytes by inducing sustained oscillations in cell Ca2+ , 1985, Nature.

[31]  Ying-Cheng Lai,et al.  Transition to chaos in continuous-time random dynamical systems. , 2002, Physical review letters.

[32]  Curtis W. Sabrosky,et al.  How Many Insects Are There , 1953 .

[33]  Jianbo Gao,et al.  When Can Noise Induce Chaos , 1999 .

[34]  D. D. Dixon,et al.  Piecewise deterministic dynamics from the application of noise to singular equations of motion , 1995 .

[35]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[36]  Chunbiao Gan,et al.  Noise-Induced Chaos in Duffing Oscillator with Double Wells , 2006 .

[37]  Houwen Xin,et al.  Internal stochastic resonance in a model system for intracellular calcium oscillations , 2001 .

[38]  J. A. Stewart,et al.  Nonlinear Time Series Analysis , 2015 .

[39]  James P. Crutchfield,et al.  Fluctuations and the onset of chaos , 1980 .

[40]  M. Perc.  The dynamics of human gait , 2005 .