Stochastic approach to study the properties of the complex patterns observed in cytokine and T-cells interaction process

TL;DR

This paper models cytokine and T-cell interactions using a stochastic approach, revealing how large populations tend to form Poisson and normal patterns, indicating noise-driven dynamics and system attractors.

Contribution

It introduces a stochastic framework with a Master equation for cytokine-T-cell interactions, showing how population size influences pattern formation and noise effects.

Findings

Large populations exhibit Poisson distribution patterns.

Pattern transitions to normal distribution at high cytokine levels.

Cytokine dynamics are driven by noise, far from equilibrium.

Abstract

Patterns in complex systems store hidden information of the system which is needed to be explored. We present a simple model of cytokine and T-cells interaction and studied the model within stochastic framework by constructing Master equation of the system and solving it. The solved probability distribution function of the model show classical Poisson pattern in the large population limit $M,Z\rightarrow large$ indicating the system has the tendency to attract a large number small-scale random processes of the cytokine population towards the basin of attraction of the system by segregating from nonrandom processes. Further, in the large $\langle Z\rangle$ limit, the pattern transform to classical Normal pattern, where, uncorrelated small-scale fluctuations are wiped out to form a regular but memoryless spatiotemporal aggregated pattern. The estimated noise using Fano factor shows clearly that the cytokine dynamics is noise induced process driving the system far away from equilibrium.