152 research outputs found
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Coarse-graining stochastic biochemical networks: adiabaticity and fast simulations
We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscoplc, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenhelmer approximation in quantum mechanics, follows from the stochastic path Integral representation of the cumulant generating function of reaction events. In applications with a small number of chemIcal reactions, It produces analytical expressions for cumulants of chemical fluxes between the slow variables. This allows for a low-dimensional, Interpretable representation and can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we derive the coarse-grained description for a chain of biochemical reactions, and show that the coarse-grained and the microscopic simulations are in an agreement, but the coarse-gralned simulations are three orders of magnitude faster
Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice
The Berry phase and the pump flux in stochastic chemical kinetics
We study a classical two-state stochastic system in a sea of substrates and
products (absorbing states), which can be interpreted as a single
Michaelis-Menten catalyzing enzyme or as a channel on a cell surface. We
introduce a novel general method and use it to derive the expression for the
full counting statistics of transitions among the absorbing states. For the
evolution of the system under a periodic perturbation of the kinetic rates, the
latter contains a term with a purely geometrical (the Berry phase)
interpretation. This term gives rise to a pump current between the absorbing
states, which is due entirely to the stochastic nature of the system. We
calculate the first two cumulants of this current, and we argue that it is
observable experimentally
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
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