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. * These authors contributed equally.

Quasi-robust control of biochemical reaction networks via stochastic morphing

“…In this paper, we have instead combined high-gain feedback control with noise-induced mixing to systematically morph probability distributions into any predefined shape, with a particular focus on multi-modality/multi-stability. On the other hand, the higher-resolution stochastic morpher shares some similarities with the work presented in [63], where Kronecker-delta distributions are also implemented using timescale separations and catalysis similar to [25,64]. However, while we have realized Kronecker-delta distributions with experimentally feasible bi-molecular networks, implementations from [63] involve higher than bi-molecular networks.…”

“…However, while we have realized Kronecker-delta distributions with experimentally feasible bi-molecular networks, implementations from [63] involve higher than bi-molecular networks. In electronic supplementary material, section S4, using the results from [28], we have proved that the bi-molecular construction put forward in this paper reduces in an appropriate limit to the higher-molecular one from [63]. Furthermore, in this paper, we have focused on biochemical control, involving combining multiple biochemical networks together, some of which are black-box (unknown), in order to achieve suitable dynamical behaviours.…”

“…Furthermore, in this paper, we have focused on biochemical control, involving combining multiple biochemical networks together, some of which are black-box (unknown), in order to achieve suitable dynamical behaviours. Therefore, our analyses take into a consideration realistic effects biochemical networks experience in applications, such as retro-activity [52,65]; such effects have not been included in [63].…”

On reaction network implementations of neural networks

“…There is a growing interest in synthetic chemical reaction networks that carry out some pre-determined task [1][2][3][4][5][6][7][8][9][10][11][12][13]. The field that develops and analyses these networks often goes by the name 'computation with chemical reaction networks'.…”

Programming and simulating chemical reaction networks on a surface

“…Conversely, some computational schemes are possible with stochastic CRNs but not with deterministic CRNs. For example, stochastic CRNs can directly represent complex probability distributions [23], perform probabilistic inference [24], and use the CRN's inherent stochasticity to help solve combinatorial search problems [25].…”