Control of Turing patterns and their usage as sensors, memory arrays, and logic gates

Muzika, František; Schreiber, Igor

doi:10.1063/1.4825379

Cited by 14 publications

(23 citation statements)

References 49 publications

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“…In our previous work, an array of two coupled cells (Muzika et al, 2014) and a linear array of three coupled cells (Muzika and Schreiber, 2013) were described through bifurcation diagrams in the parameter plane of σ M and σ inh and in the parameter plane of σ inh and k ADP at fixed q. In the following we use the same parameter planes.…”

Section: Stability and Bifurcation Analysis Bifurcation Scenariosmentioning

confidence: 99%

“…In our previous chemical computing system (Muzika and Schreiber, 2013;Muzika et al, 2014), simultaneous perturbations with T = 100 s are used, which seems to be the minimum perturbation length to achieve transitions under given model parameters (the system shows large amplitude oscillations with the shortest period T = 50.29 s). There are also small amplitude oscillations, which are visible through superposition with large amplitude oscillations, having period T ≈ 400 s. When the system is carefully perturbed by a positive perturbation for a proper time length T, it is possible to induce discrete Turing patterns by perturbation of only one cell in the case of a non-cyclic array.…”

Section: Tautology and Contradictionmentioning

confidence: 99%

“…The induced Turing pattern is resistant to positive perturbation A i ≤ 1.2 and negative perturbation A i ≥ −0.5 therefore such a device can be used as a tautology function in the first cell and a contradiction function in the second cell. In a system composed of advanced cellular assemblages, it can be used as the basic true/false device necessary for knockout perturbations (Muzika and Schreiber, 2013;Muzika et al, 2014), see sections Logic Gates, Advanced Cellular Assemblages Design.…”

Section: Tautology and Contradictionmentioning

confidence: 99%

“…Following these findings, in our previous work we examined the case of equal transport rate coefficients of activator and inhibitor using a core model of (Goldbeter and Moran, 1984) glycolysis as an oscillatory reaction. We identified coexisting discrete Turing patterns in linear arrays of two and three coupled cells (Muzika and Schreiber, 2013;Muzika et al, 2014) and applied targeted perturbations to perform basic logical functions. In our experimental research, we substituted membrane by a reciprocal peristaltic pumping to form a cyclic array of four coupled subsystems where the reaction of yeast extract and Dglucose took place (Muzika et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

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Advanced Chemical Computing Using Discrete Turing Patterns in Arrays of Coupled Cells

2020

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We examine dynamical switching among discrete Turing patterns that enable chemical computing performed by mass-coupled reaction cells arranged as arrays with various topological configurations: three coupled cells in a cyclic array, four coupled cells in a linear array, four coupled cells in a cyclic array, and four coupled cells in a branched array. Each cell is operating as a continuous stirred tank reactor, within which the glycolytic reaction takes place, represented by a skeleton inhibitor-activator model where ADP plays the role of activator and ATP is the inhibitor. The mass coupling between cells is assumed to be operating in three possible transport regimes: (i) equal transport coefficients of the inhibitor and activator (ii) slightly faster transport of the activator, and (iii) strongly faster transport of the inhibitor. Each cellular array is characterized by two pairs of tunable parameters, the rate coefficients of the autocatalytic and inhibitory steps, and the transport coefficients of the coupling. Using stability and bifurcation analysis we identified conditions for occurrence of discrete Turing patterns associated with non-uniform stationary states. We found stable symmetric and/or asymmetric discrete Turing patterns coexisting with stable uniform periodic oscillations. To switch from one of the coexisting stable regimes to another we use carefully targeted perturbations, which allows us to build systems of logic gates specific to each topological type of the array, which in turn enables to perform advanced modes of chemical computing. By combining chemical computing techniques in the arrays with glycolytic excitable channels, we propose a cellular assemblage design for advanced chemical computing.

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Section: Stability and Bifurcation Analysis Bifurcation Scenariosmentioning

confidence: 99%

Section: Tautology and Contradictionmentioning

confidence: 99%

Section: Tautology and Contradictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Advanced Chemical Computing Using Discrete Turing Patterns in Arrays of Coupled Cells

2020

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“…This observation motivates investigation on computational strategies based on enzymatic processes characterized by a complex, nonlinear chemical kinetics and exhibiting a rich variety of stationary spatio-temporal patterns. [2][3][4] Enzymatic systems can accept and transform information in the form of chemical substrates with particular properties that meet the binding specificity criteria of a selected enzyme. The input information can be coded in concentrations of specific molecules that undergo catalyzing reactions leading to products with different properties than that of input reagents.…”

Section: Introductionmentioning

confidence: 99%

How many enzyme molecules are needed for discrimination oriented applications?

Górecki

Górecka

Nowakowski

et al. 2016

Phys. Chem. Chem. Phys.

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Chemical reactions establish a molecular mechanism for information processing in living organisms. Here we consider a simple enzymatic reaction model that can be used to discriminate parameters characterizing periodic reagent inflow. Numerical simulations based on the kinetic equations show that there exist a range of inflow frequencies and amplitudes in which the time evolution of the system is very sensitive to small changes in the values of these parameters. However, the kinetic equations are derived for the thermodynamic limit, whereas in a real biological medium, like a cell, the number of enzyme molecules is an integer and finite. We use stochastic simulations to estimate discriminator reliability as a function of the number of enzyme molecules involved. For systems with 10 000 molecules the functionality predicted by kinetic equations is confirmed. If the number of molecules is decreased to 100, discrimination becomes unreliable.

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