dorsal/arxiv
View SchemaHeterogeneous Cell Population Dynamics: Equation-Free Uncertainty Quantification Computations
| Authors | Katherine A. Bold, Yu Zou, Ioannis G. Kevrekidis, Michael A. Henson |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0611001 |
| URL | https://arxiv.org/abs/q-bio/0611001 |
Abstract
We propose a computational approach to modeling the collective dynamics of populations of coupled heterogeneous biological oscillators. In contrast to Monte Carlo simulation, this approach utilizes generalized Polynomial Chaos (gPC) to represent random properties of the population, thus reducing the dynamics of ensembles of oscillators to dynamics of their (typically significantly fewer) representative gPC coefficients. Equation-Free (EF) methods are employed to efficiently evolve these gPC coefficients in time and compute their coarse-grained stationary state and/or limit cycle solutions, circumventing the derivation of explicit, closed-form evolution equations. Ensemble realizations of the oscillators and their statistics can be readily reconstructed from these gPC coefficients. We apply this methodology to the synchronization of yeast glycolytic oscillators coupled by the membrane exchange of an intracellular metabolite. The heterogeneity consists of a single random parameter, which accounts for glucose influx into a cell, with a Gaussian distribution over the population. Coarse projective integration is used to accelerate the evolution of the population statistics in time. Coarse fixed-point algorithms in conjunction with a Poincar\'e return map are used to compute oscillatory solutions for the cell population and to quantify their stability.
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"abstract": "We propose a computational approach to modeling the collective dynamics of\npopulations of coupled heterogeneous biological oscillators. In contrast to\nMonte Carlo simulation, this approach utilizes generalized Polynomial Chaos\n(gPC) to represent random properties of the population, thus reducing the\ndynamics of ensembles of oscillators to dynamics of their (typically\nsignificantly fewer) representative gPC coefficients. Equation-Free (EF)\nmethods are employed to efficiently evolve these gPC coefficients in time and\ncompute their coarse-grained stationary state and/or limit cycle solutions,\ncircumventing the derivation of explicit, closed-form evolution equations.\nEnsemble realizations of the oscillators and their statistics can be readily\nreconstructed from these gPC coefficients. We apply this methodology to the\nsynchronization of yeast glycolytic oscillators coupled by the membrane\nexchange of an intracellular metabolite. The heterogeneity consists of a single\nrandom parameter, which accounts for glucose influx into a cell, with a\nGaussian distribution over the population. Coarse projective integration is\nused to accelerate the evolution of the population statistics in time. Coarse\nfixed-point algorithms in conjunction with a Poincar\\\u0027e return map are used to\ncompute oscillatory solutions for the cell population and to quantify their\nstability.",
"arxiv_id": "q-bio/0611001",
"authors": [
"Katherine A. Bold",
"Yu Zou",
"Ioannis G. Kevrekidis",
"Michael A. Henson"
],
"categories": [
"q-bio.QM"
],
"title": "Heterogeneous Cell Population Dynamics: Equation-Free Uncertainty Quantification Computations",
"url": "https://arxiv.org/abs/q-bio/0611001"
},
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