Aggregation-fragmentation model of robust concentration gradient formation

Stochastic reaction networks in dynamic compartment populations

Many biochemical processes in living systems take place in compartmentalized environments, where individual compartments can interact with each other and undergo dynamic remodeling. Studying such processes through mathematical models poses formidable challenges because the underlying dynamics involve a large number of states, which evolve stochastically with time. Here we propose a mathematical framework to study stochastic biochemical networks in compartmentalized environments. We develop a generic population model, which tracks individual compartments and their molecular composition. We then show how the time evolution of this system can be studied effectively through a small number of differential equations, which track the statistics of the population. Our approach is versatile and renders an important class of biological systems computationally accessible.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

Aggregation and fragmentation in liquids with dispersed nanoparticles

Nanoparticle-induced aggregation and fragmentation phenomena in liquid media are investigated by applying a model of preferential attachment of dispersing molecules to randomly chosen nanoparticles and larger particles, each containing a single nanoparticle.

Simplified Analysis for the Association of a Constrained Receptor to an Oscillating Ligand

The stability of a bond cluster upon oscillated loads under physiological conditions is strongly regulated by the kinetics of association and dissociation of a single bond, which can play critical roles in cell–matrix adhesion, cell–cell adhesion, etc. Here, we obtain a simplified analysis for the bond association process of a constrained receptor to an oscillating ligand due to its diffusion-independence, which can facilitate the potential multiscale studies in the future. Based on the analysis, our results indicate that the mean passage time for bond association intriguingly saturates at high oscillating frequencies, and there can also surprisingly exist optimal bond elasticity for bond association. This work can bring important insights into understanding of the behaviors of bond cluster under cyclic loads at the level of a single bond.