Chathranee Jayathilaka

arXiv2026

Mathematical modeling of biochemical signal propagation in many-stage enzymatic pathways

Biochemical signalling cascades transduce extracellular stimuli into cellular responses through sequences of discrete, node-to-node activations. While signal fidelity depends critically on local interaction kinetics, the mechanisms governing information propagation in realistic, highly variable kinetic contexts remain poorly understood. In this paper, we develop a mathematical framework for travelling waves in canonical feed-forward pathways governed by nonlinear Michaelis-Menten-type kinetics. For uniform pathways, we characterise the complete steady-state landscape and demonstrate that activation bias (the contribution of the binary states of each node to downstream activation) between connected nodes acts as a key bifurcation parameter dictating wave existence. Extending this framework to heterogeneous networks, we show how parameter gradients and random kinetic variations distort wavefronts and induce heavy fluctuations in propagation speed. To recover predictable signal transmission, we introduce a novel reciprocal-velocity spatial rescaling technique. We demonstrate that this coordinate transformation inherently absorbs local kinetic variations, effectively smoothing wave velocities and preserving wavefront profiles without requiring bespoke parameter tuning or continuous limits. Finally, by testing the framework's limits against extreme parameter variability, we reveal how severe kinetic bottlenecks lead to functional pathway fragmentation, offering a mathematically justified basis for rational model reduction in complex biochemical networks.

math.DS↗

arXiv2023

Reduction of a biochemical network mathematical model by means of approximating activators and inhibitors as perfect inverse relationships

Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions from the identification of topological features, for example positive and negative feedback loops. These topological features are usually identified under the presumption that activation and inhibition are inverse relationships. The conclusions are often drawn without quantitative analysis, instead relying on rules of thumb. We investigate the extent to which a model needs to prescribe inhibition and activation as true inverses before models behave idiosyncratically; quantitatively dissimilar to networks with similar typologies formed by swapping inhibitors as the inverse of activators. The purpose of the study is to determine under what circumstances rudimentary qualitative assessment of network structure can provide reliable conclusions as to the quantitative behaviour of the network and how appropriate is it to treat activator and inhibitor relationships as opposite in nature.

math.DS↗