[HG_AP] Reaction Networks for Protein Condensation in terms of Spatial Effects and Nucleation Threshold
ABSTRACT
Protein condensation is a fundamental process in cell biology, and its dynamics vary between 2D cell membranes and the 3D cytoplasm. In this study, we model variations that depend on spatial dimensions. Using Stochastic Reaction Networks and the Deficiency Zero Theorem, we derive an analytical expression for a stationary distribution in closed form. By integrating First Passage Time theory with Smoluchowski reaction dynamics, we demonstrate that nucleation can occur at lower protein concentrations on 2D membrane surfaces than in 3D environments, thereby facilitating condensation. Furthermore, we investigate how spatial dimensionality affects the first formation time of large droplets as observed in experimental data. Finally, we propose a method based on First Passage Time to quantify threshold numbers from biological data.
