Spatial Pattern Formation and Synchronization in Engineered Gene Networks: Insights from Reaction-Diffusion Modeling

Nada Abdul-Hassan Atiyah

Authors

Nada Abdul-Hassan Atiyah Al-Qadisiyah University, College of Education, Mathematics Department

Keywords:

Reaction-Diffusion Systems, Synthetic Biology, Turing Patterns, Spatiotemporal Dynamics, Partial Differential Equations, Mathematical Modeling, Multicellular Synchronization

Abstract

Synthetic biology constructs with distinctly different scenarios for approaches to synthetic gene regulation — Background systematic control of when and where synthetic genes are activated in apparently identical cells has result_fulltext Tired mechanisms generally see cells as sitting in an ideally mixed soup. That blatantly dismisses the fact that true biosynthetic tissue is loopy, clunky, thready reality. Objective would like to create a mathematical model, that is PDE based to predict the behavior of these spatial patterns against some change in physical environment. Methods created a reaction-diffusion model for two bodies. The first is about how activator interacts and repress quorum-sensing signals. I numerically solved the equations using a finite difference method and parameterized diffusion rates (speed of cell spreading) and numbers of cells. Fast Fourier Transforms were also used to interpret the periodic spatial patterns and measure Pearson correlation coefficients to quantify cell synchrony coordination. Results The three spatial behaviors were simulated. At a low level D = 0.01 the chemicals are fixed in stiff, stagnant configurations -- Add some diffusion (D = 0.10): chemical waves undulate through space in periodic waves -- Crank it to full throttle (D = 0.50, r=0.91) and we have a synchronized blinking population! Now strap a backwards feedback loop to that élan and it drops the spatial disorder 60%. I discovered how a neoburst of chemicals could change the system for all time from one state to another. It turns out that the speed of diffusion and how tightly cells pile one next to one other determines what your gene circuit does. Contrary to the deceptive complexity of heterogenous geometry, the maps I wrote up that reconcile this data would here be a primitive framework for biologically-inspired design—self-organizing systems or precise applications.

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