Noise control for molecular computing

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.

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“…We can therefore assume that z x0 (0) ≥ 2β α 1 γ . By (37), it follows that as long as z x0 (t) ≥ 2β…”

Section: A3 Proof Of Propositionmentioning

confidence: 99%

“…Furthermore, as is the case in [18], their CRNs are fated to a state where no reactions can take place. Plesa et al [37] do not consider arbitrary distributions, but develop methods for controlling noise while preserving the mean behavior of the model in a certain limit.…”

Section: Introductionmentioning

confidence: 99%

Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions

Cappelletti

Ortiz-Muñoz

Anderson

et al. 2020

Theoretical Computer Science

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“…Manipulating the dynamics of cells in vivo, and designing their synthetic counterparts in vitro, are complementary goals of synthetic biology, both involving overcoming nonlinear, non-modular and stochastic nature of biochemical networks [2]. In particular, when biochemical systems are integrated into smaller-volume compartments, such as living or synthetic cells, the lower copy-numbers of some of the underlying species give rise to intrinsic noise [9][10][11][22][23][24][25][26]. The induced stochasticity requires theoretical and experimental methods (see section S1 in the electronic supplementary material and §5, respectively) which are more involved than their larger-volume (deterministic) counterparts [14,15,27].…”

Section: Introductionmentioning

confidence: 99%

“…Dynamics achieved under (quasi-) robust controllers are said to display (quasi-)robust adaptation, and plays important roles in biology, e.g. in cell signalling, glycolysis and chemokinesis [29][30][31][32][33][34]; the same is true for timescale separations (slow-fast dynamics), which underpin biochemical multi-stability, oscillations and bifurcations [22][23][24][25]27,[35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Quasi-robust control of biochemical reaction networks via stochastic morphing

Plesa

Stan

Ouldridge

et al. 2021

J. R. Soc. Interface.

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One of the main objectives of synthetic biology is the development of molecular controllers that can manipulate the dynamics of a given biochemical network that is at most partially known. When integrated into smaller compartments, such as living or synthetic cells, controllers have to be calibrated to factor in the intrinsic noise. In this context, biochemical controllers put forward in the literature have focused on manipulating the mean (first moment) and reducing the variance (second moment) of the target molecular species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the probability distribution modes (maxima). To bridge the gap, we put forward the stochastic morpher controller that can, under suitable timescale separations, morph the probability distribution of the target molecular species into a predefined form. The morphing can be performed at a lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at a higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robustness and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.

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“…Central to such differences is a relationship between multiple coexisting stable equilibria at the deterministic level (multistability) and coexisting maxima (modes) of the stationary probability distribution at the stochastic level (multimodality). In general, mutistability and multimodality, for both transient and long-term dynamics, do not imply each other for finite reactor volumes (such as in living cells) [13,14]. For example, even feedback-free gene-regulatory networks, involving only first-order reactions, which are deterministically unistable, may be stochastically mutimodal under a suitable time-scale separation between the gene switching and protein dynamics [15,16].…”

Section: Introductionmentioning

confidence: 99%

Noise-induced mixing and multimodality in reaction networks

2018

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We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory networks, and consist of a slow-subnetwork, describing conversions among the different gene states, and fast-subnetworks, describing biochemical interactions involving the gene products. We show that the long-term dynamics of such networks can consist of a unique attractor at the deterministic level (unistability), while the long-term probability distribution at the stochastic level may display multiple maxima (multimodality). The dynamical differences stem from a novel phenomenon we call noise-induced mixing, whereby the probability distribution of the gene products is a linear combination of the probability distributions of the fast-subnetworks which are 'mixed' by the slow-subnetworks. The results are applied in the context of systems biology, where noise-induced mixing is shown to play a biochemically important role, producing phenomena such as stochastic multimodality and oscillations.In this section, chemical reaction networks are defined [14,17,18,19], which are used to model the biochemical processes considered in this paper, together with their deterministic and stochastic dynamical models. We begin with some notation.Definition 2.1 Set R is the space of real numbers, R ≥ the space of nonnegative real numbers, and R > the space of positive real numbers. Similarly, Z is the space of integer numbers, Z ≥ the space of nonnegative integer numbers, and Z > the space of positive integer numbers. Euclidean vectors are denoted in boldface, x = (x 1 , x 2 , . . . , x m ) ∈ R m . The support of x is defined by supp(x) = {i ∈ {1, 2, . . . , m}|x i = 0}. Given a finite set S, we denote its cardinality by |S|.Definition 2.2 A chemical reaction network is a triple {S, C, R}, where (i) S = {S 1 , S 2 , . . . , S m } is the set of species of the network.

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Noise control for molecular computing

Cited by 13 publications

References 56 publications

Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions

Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions

Quasi-robust control of biochemical reaction networks via stochastic morphing

Noise-induced mixing and multimodality in reaction networks

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