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Chemical Memory with Discrete Turing Patterns Appearing in the Glycolitic Reaction

Version 1.0

Górecki, Jerzy; Muzika, František, 2023, "Chemical Memory with Discrete Turing Patterns Appearing in the Glycolitic Reaction", https://doi.org/10.18150/EWF30H, RepOD, V1

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Description

abstract: Memory is an essential element of information processing devices. We investigated a network formed by just 3 interacting nodes representing continuously stirred tank reactors (CSTRs) where the glycolytic reaction proceeds as a potential realization of a chemical memory unit. Our study was based on the 2-variable computational model of the reaction. The model parameters were selected such that the system has a stable limit cycle and several distinct, discrete Turing patterns characterized by stationary concentrations at the nodes. In our interpretation, oscillations represent a blank memory unit, and Turing patterns code information. The considered memory can preserve information on one of 6 different symbols.  The time evolution of the nodes was individually controlled by the inflow of ATP. We demonstrated that information could be written with a simple and short perturbation of the inflow. The perturbation applies to one or two nodes only, and it is symbol specific. The memory can be erased with identical inflow perturbation applied to all nodes.  We believe the idea of pattern-coded memory applies to other reaction networks that allow for discrete Turing patterns. Moreover, it hints at the experimental realization of memory in a simple system with glycolytic reaction.

(2023-03)
Subject
Chemistry; Engineering; Mathematical Sciences
Keyword

chemical computing, memory, oscillations, discrete Turing pattern, glycolytic reaction

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description.txt
Plain Text - 9.9 KB - Apr 19, 2023 - 17 Downloads
MD5: 39802e40be1ba486f90c634a64a7cb0b
License: CC0 Creative Commons Zero 1.0
file with descriptions
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model.txt
Plain Text - 2.5 KB - Apr 19, 2023 - 18 Downloads
MD5: 2316749808295df86897a6195fb40557
License: CC0 Creative Commons Zero 1.0
file "model.txt" Contains model part of 3 coupled cells written in fortran. This file text has to be inserted into model.f in the program CONT, but can be used with any programming language after proper modifications.
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Fig1.pdf
Adobe PDF - 16.5 KB - Apr 19, 2023 - 14 Downloads
MD5: 8505b25bc0795361147a2703ea2d8ee0
License: CC0 Creative Commons Zero 1.0
The geometry of a network considered as a chemical memory. Big circles represent network nodes (CSTRs) where the glycolytic reaction occurs/proceeds. The following figures use the same node color to plot time-dependent concentrations of reagents. Dark green arrows interlinking nodes represent the solution flows represented by the last two terms on Eqs.3 and 4. Colored arrows directed towards the nodes mark time-dependent inflows of ATP (the first term on the right side of Eq. 1).
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Fig2.pdf
Adobe PDF - 214.7 KB - Apr 19, 2023 - 12 Downloads
MD5: 0a96be7f0a9cfda8a5d8f7c75335294e
License: CC0 Creative Commons Zero 1.0
The bifurcation diagram for three coupled CSTRs with a cyclic geometry of connections illustrated in Fig. \ref{fig:1} in the phase space of parameters $\sigma_{inh}$ and $\sigma_M$. The system of Equations 3, 4 is solved with $ k_D = 0.1 s^{-1} $. The line coding: red curve - the Hopf bifurcation line, blue curve — symmetry breaking bifurcation line, green curve — limit point curve/line. The solid line indicates change of stability at the line crossing. The is no no change of stability between regions separated by a dashed line. The notation $N-M$ indicates that there are $N$ stationary states in the region of which $M$ are stable. The asterisk symbol marks location of parameter values used in our simulations of a chemical memory simulations ($\sigma_{inh} = 80 s^{-1}$ and $\sigma_M = 200 s^{-1}$
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Fig2.zip
ZIP Archive - 206.5 MB - Apr 19, 2023 - 12 Downloads
MD5: 6ece7464d78bd78f8709182264cf3c00
License: CC0 Creative Commons Zero 1.0
file "Figure2.zip" Contains a list of files to plot a bifurcation diagram for three coupled CSTRs in a cyclic array for sigma_inh=80 s-1, sigma_M =200 s-1, kd=0.1 s-1, ny = 1.84 s-1. contains files: "hcontplt.s" contains data set for stable Hopf bifurcation curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient,column #9 represents omega which is associated with a bifurcation eigenvalue i*omega, column #10 represents an arch (see manual for program CONT), column #11 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "hcontplt.u" contains data set for unstable Hopf bifurcation curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient,column #9 represents omega which is associated with a bifurcation eigenvalue i*omega, column #10 represents an arch (see manual for program CONT), column #11 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "hcontplt (2).s" contains data set for stable Hopf bifurcation curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient,column #9 represents omega which is associated with a bifurcation eigenvalue i*omega, column #10 represents an arch (see manual for program CONT), column #11 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "hcontplt (2).u" contains data set for unstable Hopf bifurcation curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient,column #9 represents omega which is associated with a bifurcation eigenvalue i*omega, column #10 represents an arch (see manual for program CONT), column #11 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "bcontplt.u" contains data set for unstable branch point curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "bcontplt (2).u" contains data set for unstable branch point curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "lcontplt.u" contains data set for unstable limit point curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "lcontplt (2).u" contains data set for unstable limit point curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents stability sign (-1 is stable, +1 unstable, 0 stability changing bifurcation point). "hh (2).b" contains data points for intersection of two Hopf bifurcation curves, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents omega which is associated with a bifurcation eigenvalue i*omega,column #10 represents an arch (see manual for program CONT), column #11 represents bifurcation point type. "hvlinter.b" contains data points for intersection of Hopf bifurcation curve with branch/limit point curve, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient, column #8 represents autoctalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents bifurcation point type; for 11 column version, the additional column #9 represents omega which is associated with a bifurcation eigenvalue i*omega "bt.b" contains data points of Bogdanov-Takens bifurcation, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents bifurcation point type. "bt (2).b" contains data points of Bogdanov-Takens bifurcation, odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents inhibition rate coeffient,column #8 represents autocatalysis rate coeffient, column #9 represents an arch (see manual for program CONT), column #10 represents bifurcation point type. "mustr.gnu" - file for plotting the bifurcation diagram in Gnuplot
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fig3.pdf
Adobe PDF - 212.6 KB - Apr 19, 2023 - 18 Downloads
MD5: 9df4ed0eb03c1c6fdbb692e3fda23296
License: CC0 Creative Commons Zero 1.0
The process of erasing memory loaded with the $A$ symbol. a) the inflow combined with perturbation applied to all nodes $\nu_i(t), i=1,~3 $(the black curve, $\alpha = 0.1$, $t_0 = 500$, $dt = 200$ and $\beta = 0.2$. ) compared with the inflow characterizing unperturbed memory (the red curve $\nu_0 \equiv 1.84 s^{-1}$). The pairs of sub-figures (b,c), (d,e) and (f,g) show the time evolution of $x(t)$ and $y(t)$ in all nodes before, during and after the perturbation . The color coding is the same as in Fig. \ref{fig:1}
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figure3.zip
ZIP Archive - 975.0 KB - Apr 19, 2023 - 18 Downloads
MD5: c322c70e75a2950ae8295d293126d029
License: CC0 Creative Commons Zero 1.0
file "Figure3.zip" Contains a list of files to plot the process of erasing memory loaded with the A symbol. a) the inflow combined with perturbation applied to all nodes νi (t), i = 1, 3 contains files: "contplt.txt" odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents time of the simulation "contfunct.txt" column #1 represents time of the simulation, column #2 represents nu_1 (t), column #3 represents nu_2 (t), column #4 represents nu_3 (t) "matematica.pdf" - file for solving the eqations and plotting the figure
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fig4.pdf
Adobe PDF - 194.8 KB - Apr 19, 2023 - 18 Downloads
MD5: e4d0941c251a8e557c2b8d82cda3e790
License: CC0 Creative Commons Zero 1.0
The process of erasing memory loaded with the $Z$ symbol. a) the inflow combined with perturbation applied to all nodes $\nu_i(t), i=1,~3 $(the black curve, $\alpha = 1.0$, $t_0 = 500$, $dt = 100$ and $\beta = 0.2$. ) compared with the inflow characterizing unperturbed memory (the red curve $\nu_0 \equiv 1.84 s^{-1}$). The pairs of sub-figures (b,c), (d,e) and (f,g) show the time evolution of $x(t)$ and $y(t)$ in all nodes before, during and after the perturbation . The color coding is the same as in Fig. \ref{fig:1}
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figure4.zip
ZIP Archive - 945.0 KB - Apr 19, 2023 - 18 Downloads
MD5: c5fa4900051a27bda683e46ffbbfb58b
License: CC0 Creative Commons Zero 1.0
file "Figure4.zip" Contains a list of files to plot The process of erasing memory loaded with the Z symbol. a) the inflow combined with perturbation applied to all nodes νi (t), i = 1, 3 contains files: "contplt.txt" odd columns represent stationary concentrations of ATP in cells from 1 to 3(last column is column #5), even columns represent stationary concentrations of ADP in cells from 1 to 3(last column is column #6), column #7 represents time of the simulation "contfunct.txt" column #1 represents time of the simulation, column #2 represents nu_1 (t), column #3 represents nu_2 (t), column #4 represents nu_3 (t) "matematica.pdf" - file for solving the eqations and plotting the figure
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fig6.pdf
Adobe PDF - 206.9 KB - Apr 19, 2023 - 12 Downloads
MD5: a53f379728046144add537b9a35227a1
License: CC0 Creative Commons Zero 1.0
The process of writing the $Z$ symbol into the blank memory. a) the blue line shows $\nu_1(t) $ ($\alpha = 0.5$, $t_0 = 500$, $dt =200$ and $\beta = 0.2$ ), the green line presents $\nu_2(t) $ ($\alpha = 1.9$, $t_0 = 500$, $dt =700$ and $\beta = 0.2$ ), the inflow at the node \#3 is unperturbed ($\nu_3(t) \equiv 1.84 s^{-1}$). The pairs of sub-figures (b,c), (d,e) and (f,g) show the time evolution of $x(t)$ and $y(t)$ in all nodes before, during and after the perturbation . The color coding is the same as in Fig. \ref{fig:1}
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