A Design Principle for an Autonomous Post-translational Pattern Formation

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  • Sugai Shuhei S
    Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Japan
  • Ode Koji L
    Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Japan Laboratory for Synthetic Biology, RIKEN Quantitative Biology Center, Japan
  • Ueda Hiroki R
    Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Japan Laboratory for Synthetic Biology, RIKEN Quantitative Biology Center, Japan

抄録

<p>Reversible phosphorylation is one of the most abundant forms of posttranslational modification in living organisms. To describe such enzymatic reactions, Michaelis-Menten (MM) kinetics is often applied. This scheme can, despite its simplicity, display many complex behaviors; the known examples are ultrasensitivity, bistability, travelling waves, and limit-cycle oscillation. However, it was unknown whether a temporally stable differentiation including spatial pattern could also arise from this MM-approximated reversible phosphorylation scheme. Previous models for biochemical pattern formation often assumed complex molecular/cellular networks, or pre-patterns, to trigger or amplify pattern formation. This theoretical study, however, shows that a system composed of one substrate with two phosphorylation sites and a pair of kinase and phosphatase can generate autonomous differentiation, including complex stripe patterns and cluster splitting.</p><p>In our model, all (de-)phosphorylation reactions are described with reaction-diffusion equations with MM kinetics, and all species freely diffuse without pre-existing gradients. Computational simulation upon >23,000,000 randomly generated parameter sets revealed the design motifs of cyclic reaction and enzyme sequestration by slow-diffusing substrates. These motifs constitute short-range positive and long-range negative feedback loops to induce Turing instability. Through a bifurcation analysis, it was found that the width and height of spatial patterns can be controlled independently by distinct reaction-diffusion processes. Stochastic molecular simulation, which tracks individual molecules, confirmed the existence of the two reaction cycles.</p><p>Furthermore, by substituting mean-field approximation for the diffusion terms in the reaction-diffusion equations, cluster splitting was observed from homogeneous cells with identical reaction kinetics and initial values. The mathematical requirements for Turing instability and cluster splitting in our scheme were highly homologous; in fact, the ranges of parameters to meet each of the two requirements were highly similar.</p><p>Our result shows that multisite reversible post-translational modification can be a ubiquitous source for various patterns without complex regulations such as pre-patterns or autocatalytic regulation of enzymes. The simplicity and generality of our reversible phosphorylation model provides a framework to investigate a biochemical source of autonomous pattern formation and to synthesize a de novo molecular network to generate patterns.</p><p>Ref: Sugai et al. Cell Reports. 19. 863-8211;874 (2017)</p>

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