Fixed-budget simulation method for growing cell populations

TL;DR

This paper introduces a novel fixed-budget stochastic simulation method for growing cell populations that maintains constant computational complexity and is proven to be statistically consistent, enabling efficient analysis of large biological systems.

Contribution

The paper presents the FKG-SSA, a new simulation algorithm that uses a fixed number of cells, ensuring efficiency and consistency for growing populations.

Findings

The method maintains constant computational complexity regardless of population size.

The FKG-SSA is statistically consistent and reliable.

Numerical examples demonstrate the effectiveness of the approach.

Abstract

Investigating the dynamics of growing cell populations is crucial for unraveling key biological mechanisms in living organisms, with many important applications in therapeutics and biochemical engineering. Classical agent-based simulation algorithms are often inefficient for these systems because they track each individual cell, making them impractical for fast (or even exponentially) growing cell populations. To address this challenge, we introduce a novel stochastic simulation approach based on a Feynman-Kac-like representation of the population dynamics. This method, named the Feynman-Kac-inspired Gillespie's Stochastic Simulation Algorithm (FKG-SSA), always employs a fixed number of independently simulated cells for Monte Carlo computation of the system, resulting in a constant computational complexity regardless of the population size. Furthermore, we theoretically show the statistical consistency of the proposed method, indicating its accuracy and reliability. Finally, a couple of biologically relevant numerical examples are presented to illustrate the approach. Overall, the proposed FKG-SSA effectively addresses the challenge of simulating growing cell populations, providing a solid foundation for better analysis of these systems.