dorsal/arxiv
View SchemaA variational approach to the stochastic aspects of cellular signal transduction
| Authors | Yueheng Lan, Peter G. Wolynes, Garegin A. Papoian |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0607025 |
| URL | https://arxiv.org/abs/q-bio/0607025 |
| DOI | 10.1063/1.2353835 |
| Journal | J. Chem. Phys. 125, 124106 (2006) |
Abstract
Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making more transparent the physical significance of the variational method. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.
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"abstract": "Cellular signaling networks have evolved to cope with intrinsic fluctuations,\ncoming from the small numbers of constituents, and the environmental noise.\nStochastic chemical kinetics equations govern the way biochemical networks\nprocess noisy signals. The essential difficulty associated with the master\nequation approach to solving the stochastic chemical kinetics problem is the\nenormous number of ordinary differential equations involved. In this work, we\nshow how to achieve tremendous reduction in the dimensionality of specific\nreaction cascade dynamics by solving variationally an equivalent quantum field\ntheoretic formulation of stochastic chemical kinetics. The present formulation\navoids cumbersome commutator computations in the derivation of evolution\nequations, making more transparent the physical significance of the variational\nmethod. We propose novel time-dependent basis functions which work well over a\nwide range of rate parameters. We apply the new basis functions to describe\nstochastic signaling in several enzymatic cascades and compare the results so\nobtained with those from alternative solution techniques. The variational\nansatz gives probability distributions that agree well with the exact ones,\neven when fluctuations are large and discreteness and nonlinearity are\nimportant. A numerical implementation of our technique is many orders of\nmagnitude more efficient computationally compared with the traditional Monte\nCarlo simulation algorithms or the Langevin simulations.",
"arxiv_id": "q-bio/0607025",
"authors": [
"Yueheng Lan",
"Peter G. Wolynes",
"Garegin A. Papoian"
],
"categories": [
"q-bio.QM",
"q-bio.MN"
],
"doi": "10.1063/1.2353835",
"journal_ref": "J. Chem. Phys. 125, 124106 (2006)",
"title": "A variational approach to the stochastic aspects of cellular signal transduction",
"url": "https://arxiv.org/abs/q-bio/0607025"
},
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