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 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 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 Genetic recombination as a generalised gradient flow

2021 ◽  
Author(s):  
Frederic Alberti
Keyword(s):  
Arbitrary Number ◽  
Genetic Recombination ◽  
Reaction Network ◽  
Gradient Flow ◽  
Mass Action ◽  
Gradient System ◽  
Gradient Structure ◽  
Law Of Mass Action ◽  
Reversible Chemical Reaction ◽  
Time Partitioning

AbstractIt is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.

scholarly journals How is the effectiveness of immune surveillance impacted by the spatial distribution of spreading infections?

2015 ◽  
Vol 370 (1675) ◽  
pp. 20140289 ◽  
Author(s):  
Ulrich D. Kadolsky ◽  
Andrew J. Yates
Keyword(s):  
Spatial Distribution ◽  
Immune Surveillance ◽  
Critical Density ◽  
Search Time ◽  
Handling Time ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Expected Time ◽  
Target Ratio ◽  
Infected Cells

What effect does the spatial distribution of infected cells have on the efficiency of their removal by immune cells, such as cytotoxic T lymphocytes (CTL)? If infected cells spread in clusters, CTL may initially be slow to locate them but subsequently kill more rapidly than in diffuse infections. We address this question using stochastic, spatially explicit models of CTL interacting with different patterns of infection. Rather than the effector : target ratio, we show that the relevant quantity is the ratio of a CTL's expected time to locate its next target (search time) to the average time it spends conjugated with a target that it is killing (handling time). For inefficient (slow) CTL, when the search time is always limiting, the critical density of CTL (that required to control 50% of infections, C * ) is independent of the spatial distribution and derives from simple mass-action kinetics. For more efficient CTL such that handling time becomes limiting, mass-action underestimates C * , and the more clustered an infection the greater is C * . If CTL migrate chemotactically towards targets the converse holds— C * falls, and clustered infections are controlled most efficiently. Real infections are likely to spread patchily; this combined with even weak chemotaxis means that sterilizing immunity may be achieved with substantially lower numbers of CTL than standard models predict.

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