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Quantitative modeling of diffusion-driven pattern formation in microRNA-regulated gene expression

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Abstract

MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs here. For three scenarios, (1) simple microRNA-based mRNA regulation with a graded response in output, (2) microRNA-based mRNA regulation resulting in bistability in the dynamics, and (3) a coordinated response of microRNA (miRNA), simultaneously regulating the mRNAs of two different pools, detailed dynamical analysis, as well as the reaction–diffusion scenario have been considered and analyzed in the steady state and for the transient dynamics further. We have observed persistent-temporal patterns, as a result of the dynamics of the motifs, that explain spatial gradients and relevant patterns formed by related proteins in development and phenotypic heterogenetic aspects in biological systems. Competitive effects of miRNA regulation have also been found to be capable to cause spatio-temporal patterns, persistent enough to direct developmental decisions. Under coordinated regulation, miRNAs are found to generate spatio-temporal patterning even from complete homogeneity in concentration of target protein, which may have impactful insights in choice of cell fates.

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  1. Link for the video is: https://youtu.be/C4zovgxtCpQ.

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Acknowledgements

PC and SG acknowledge the support by DST-INSPIRE, India, vide sanction Letter No. DST/INSPIRE/04/2017/002765 dated- 13.03.2019.

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Authors and Affiliations

  1. Department of Physics, National Institute of Technology Durgapur, Durgapur, India

    Priya Chakraborty & Sayantari Ghosh

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  1. Priya Chakraborty
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Correspondence to Priya Chakraborty.

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Appendix

Appendix

1.1 List of parameters:

For better clarity, we have given a list of parameters used in our entire manuscript hereby in Tables 1, 2 and 3.

Table 1 List of parameters for Model 1
Full size table
Table 2 List of parameters for Model 2
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Table 3 List of parameters for Model 3
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1.2 Model 2: Binary gene expression, temporal dynamics

To understand the temporal dynamics of the protein synthesized, we plot the time evolution curves of the protein starting from different initial conditions for three set of parameter values. For the parameter values of Fig. 14a, low synthesis state is the system’s stable steady state, starting from all initialization, the system converges to it. Similarly, 14c can be explained for its high synthesis stable state. However, the system has two steady states for the parameter value of 14b, and a bistable dynamics is shown in the output. Starting from different initial concentrations, the protein chooses any of its either low or high synthesis states, which one is more favorable and two drastic different concentrations coexist in output.

Fig. 14
figure 14

Time evolution curves of protein U for different initial conditions. x axis represents time and y axis represents the concentration of protein U. (a) The system is monostable with low synthesis state as a steady state. So for all initiation, protein U goes to its low synthesis stable state. (b) The system is bistable with two steady states. So with different initial conditions, the system chooses any of its nearest stable states and finally, we are left with two stable fixed states. (c) The system is monostable with its high synthesis stable state. All states from different initial conditions move to a single high synthesis stable state. Parameter \(\alpha\) has value 12 for (a), 13.3 for (b), 14 for (c). Rest of the parameter values for all (a)–(c) are \(\lambda =10,\; k=10,\;\delta =0.01,\;\phi =0.3\)

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Chakraborty, P., Ghosh, S. Quantitative modeling of diffusion-driven pattern formation in microRNA-regulated gene expression. Eur. Phys. J. Plus 138, 630 (2023). https://doi.org/10.1140/epjp/s13360-023-04258-w

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