scholarly journals Noise control for molecular computing

2018 ◽  
Vol 15 (144) ◽  
pp. 20180199 ◽  
Author(s):  
Tomislav Plesa ◽  
Konstantinos C. Zygalakis ◽  
David F. Anderson ◽  
Radek Erban
Keyword(s):  
Stochastic Dynamics ◽  
Noise Control ◽  
Reaction System ◽  
Reaction Network ◽  
Intrinsic Noise ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Interdisciplinary Field ◽  
Biochemical Systems

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production–decay reaction system, and on an exotic system displaying bistability. For the production–decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.

scholarly journals Training an asymmetric signal perceptron through reinforcement in an artificial chemistry

2014 ◽  
Vol 11 (93) ◽  
pp. 20131100 ◽  
Author(s):  
Peter Banda ◽  
Christof Teuscher ◽  
Darko Stefanovic
Keyword(s):  
State Of The Art ◽  
Chemical Species ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Dna Strand Displacement ◽  
Autonomous Adaptation ◽  
Biochemical Systems ◽  
Dna Strand ◽  
Logic Functions ◽  
Application Specific

State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be reprogrammed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. In this paper, we begin addressing these challenges with a novel chemical perceptron that can solve all 14 linearly separable logic functions. The system performs asymmetric chemical arithmetic, learns through reinforcement and supports both Michaelis–Menten as well as mass-action kinetics. To enable cascading of the chemical perceptrons, we introduce thresholds that amplify the outputs. The simplicity of our model makes an actual wet implementation, in particular by DNA-strand displacement, possible.

scholarly journals A structural property for reduction of biochemical networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anika Küken ◽  
Philipp Wendering ◽  
Damoun Langary ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Model Reduction ◽  
Structural Property ◽  
Large Scale ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Reduced Models ◽  
Metabolic Phenotypes ◽  
Genome Scale

AbstractLarge-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

scholarly journals A general technique for the detection of switch-like bistability in chemical reaction networks governed by mass action kinetics with conservation laws

2020 ◽  
Author(s):  
Brandon C Reyes ◽  
Irene Otero-Muras ◽  
Vladislav A Petyuk
Keyword(s):  
Conservation Laws ◽  
Signaling Pathways ◽  
Chemical Reaction ◽  
Reaction Network ◽  
Mass Action ◽  
Numerical Continuation ◽  
Reaction Networks ◽  
General Technique ◽  
Bistable Switch ◽  
Mass Action Kinetics

AbstractBackgroundTheoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws.ResultsIn this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves 1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, 2) minimization of the objective function to search for conditions resulting in a zero eigenvalue 3) computation of a confidence level that describes if the global minimum has been found and 4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability.ConclusionsWe have developed a variation of an optimization-based method for discovery of bistability, which is not limited to the structure of the chemical reaction network. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

The Gompertz model revisited and modified using reaction networks: Mathematical analysis

BIOMATH ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 2110023
Author(s):  
Svetoslav Marinov Markov
Keyword(s):  
Exponential Decay ◽  
Mathematical Analysis ◽  
Reaction Network ◽  
Gompertz Model ◽  
Mass Action ◽  
Reaction Networks ◽  
Data Sets ◽  
Growth Data ◽  
Mass Action Kinetics ◽  
Additional Degree

In the present work we discuss the?usage of the framework of chemical reaction networks for the construction of dynamical models and their mathematical analysis. To this end, the process of construction of reaction-network-based models via mass action kinetics is introduced and illustrated on several familiar examples,?such as the exponential (radioactive) decay, the logistic and the Gompertz models. Our final goal is to modify the reaction network of the classic Gompertz model in a natural way using certain features of the exponential decay and the logistic models. The growth function of the obtained new Gompertz-type hybrid model possesses an additional degree of freedom (one more rate parameter) and is thus more flexible when applied to numerical simulation of measurement and experimental data sets. More specifically, the ordinate (height) of the inflection point of the new generalized Gompertz model can vary in the interval (0, 1/e], whereas the respective height of the classic Gompertz model is fixed at 1/e (assuming the height of the upper asymptote is one). It is shown that?the new model is a generalization of both the classic Gompertz model and the one-step exponential decay model.?Historically the Gompertz function has been first used for statistical/insurance purposes, much later this function has been applied to simulate biological growth data sets coming from various fields of science, the reaction network approach explains and unifies the two approaches.

scholarly journals Deciphering noise amplification and reduction in open chemical reaction networks

2018 ◽  
Author(s):  
Fabrizio Pucci ◽  
Marianne Rooman
Keyword(s):  
Differential Equation ◽  
Molecular Species ◽  
Dynamical Behavior ◽  
Intrinsic Noise ◽  
Mass Action ◽  
Model Systems ◽  
Reaction Networks ◽  
Mass Action Kinetics ◽  
Noise Amplification ◽  
The Impact

AbstractThe impact of fluctuations on the dynamical behavior of complex biological systems is a longstanding issue, whose understanding would elucidate how evolutionary pressure tends to modulate intrinsic noise. Using the Itō stochastic differential equation formalism, we performed analytic and numerical analyses of model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. For networks of zero deficiency, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated and their Fano factors are Poissonian. Systems of higher deficiency have non-equilibrium steady states and non-zero reaction fluxes flowing between the complexes. When they model homooligomerization, the noise on each species is reduced when the flux flows from the oligomers of lowest to highest degree, and amplified otherwise. In the case of hetero-oligomerization systems, only the noise on the highest-degree species shows this behavior.

scholarly journals Dynamic analysis of biochemical network using complex network method

2015 ◽  
Vol 19 (4) ◽  
pp. 1249-1253 ◽  
Author(s):  
Shuqiang Wang ◽  
Yanyan Shen ◽  
Jinxing Hu ◽  
Ning Li ◽  
Dewei Zeng
Keyword(s):  
Complex Network ◽  
Reaction System ◽  
Reaction Network ◽  
Reaction Model ◽  
Mass Action ◽  
Biochemical Reaction ◽  
Biochemical Network ◽  
Initial State ◽  
Complex Network Theory ◽  
Linear Differential

In this study, the stochastic biochemical reaction model is proposed based on the law of mass action and complex network theory. The dynamics of biochemical reaction system is presented as a set of non-linear differential equations and analyzed at the molecular-scale. Given the initial state and the evolution rules of the biochemical reaction system, the system can achieve homeostasis. Compared with random graph, the biochemical reaction network has larger information capacity and is more efficient in information transmission. This is consistent with theory of evolution.

REGISTER MACHINE COMPUTATIONS ON BINARY NUMBERS BY OSCILLATING AND CATALYTIC CHEMICAL REACTIONS MODELLED USING MASS-ACTION KINETICS

2009 ◽  
Vol 20 (03) ◽  
pp. 411-426 ◽  
Author(s):  
THOMAS HINZE ◽  
RAFFAEL FASSLER ◽  
THORSTEN LENSER ◽  
PETER DITTRICH
Keyword(s):  
Theoretical Perspective ◽  
Reaction Network ◽  
Logic Gates ◽  
Mass Action ◽  
Machine Model ◽  
Mass Action Kinetics ◽  
Fast Switching ◽  
Register Machine ◽  
Dynamical Simulations ◽  
Concerted Reaction

Biocomputing emerged as a promising paradigm capable of coping efficiently with challenges of programming decentralized but concerted reaction systems. The chemical programming metaphor subsumes different encoding techniques into molecular or spatial structures in conjunction with artificial reaction networks. Here, a variety of supplementary assumptions like predefined polymeric sequences or availability of inhibiting reactions is frequently used. Inspired by the idea to build chemical computers based on minimal requirements in chemistry from a theoretical perspective, we introduce a pure chemical register machine model operating on binary numbers. The register machine architecture is composed of reaction network motifs acting as fast switching logic gates, oscillators, and self-reproducible bit storage units. The dynamical machine behavior consistently employs mass-action kinetics. Two case studies, calculating the maximum of three natural numbers as well as numerical addition, illustrate the practicability of the design along with dynamical simulations.

scholarly journals Stochastic analysis of biochemical reaction networks with absolute concentration robustness

2014 ◽  
Vol 11 (93) ◽  
pp. 20130943 ◽  
Author(s):  
David F. Anderson ◽  
Germán A. Enciso ◽  
Matthew D. Johnston
Keyword(s):  
State Space ◽  
Stationary Distribution ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Fine Tuning ◽  
Mass Action ◽  
Absolute Concentration ◽  
Biochemical Reaction Networks ◽  
Discrete State ◽  
Quasi Stationary Distribution

It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.

scholarly journals Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

2021 ◽  
Author(s):  
Yun Min Song ◽  
Hyukpyo Hong ◽  
Jae Kyoung Kim
Keyword(s):  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Mass Action ◽  
Elementary Functions ◽  
Deterministic Models ◽  
Bistable Switch ◽  
Elementary Reactions ◽  
Reversible Binding ◽  
Reaction Functions ◽  
Biochemical Systems

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary functions are derived by applying the quasi-steady-state approximation(QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems.In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA,developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation.

scholarly journals Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

2021 ◽  
Vol 17 (10) ◽  
pp. e1008952
Author(s):  
Yun Min Song ◽  
Hyukpyo Hong ◽  
Jae Kyoung Kim
Keyword(s):  
Stochastic Dynamics ◽  
Elementary Reaction ◽  
Stochastic Simulations ◽  
Mass Action ◽  
Deterministic Models ◽  
Elementary Reactions ◽  
Reversible Binding ◽  
Deterministic Systems ◽  
Reaction Functions ◽  
Biochemical Systems

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary reaction functions are derived by applying the quasi-steady-state approximation (QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems. In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA, developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation. To facilitate the framework, we provide a user-friendly open-source computational package, ASSISTER, that automatically performs the present framework.

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