Stochastic Chemical Reaction Networks for Robustly Approximating Arbitrary Probability Distributions

Abstract

We show that discrete distributions on the $d$-dimensional non-negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks. We begin by providing a class of detailed balanced networks and prove that they can approximate any discrete distribution to any desired accuracy. However, these detailed balanced constructions rely on the ability to initialize a system precisely, and are therefore susceptible to perturbations in the initial conditions. We therefore provide another construction based on the ability to approximate point mass distributions and prove that this construction is capable of approximating arbitrary discrete distributions for any choice of initial condition. In particular, the developed models are ergodic, so their limit distributions are robust to a finite number of perturbations over time in the counts of molecules.

References in corpus (12)

• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
• Stochastic thermodynamics of chemical reaction networks
• Steady-state fluctuations of a genetic feedback loop: an exact solution
• Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws
• Transitions Induced by the Discreteness of Molecules in a Small Autocatalytic System
• Product-form Poisson-like distributions and complex balanced reaction systems
• Chemical Boltzmann Machines
• Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness
• Systems of branching, annihilating, and coalescing particles
• Time-dependent product-form Poisson distributions for reaction networks with higher order complexes
• A stochastic molecular scheme for an artificial cell to infer its environment from partial observations

Cited by in corpus (1)

• Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks