Predictive landscapes hidden beneath biological cellular automata

TL;DR

This paper reviews recent advances in identifying predictive energy-like landscapes for cellular automata models of living systems, offering a promising approach to understand complex biological dynamics without extensive parameterization.

Contribution

It synthesizes recent research on discovering low-dimensional predictive landscapes for cellular automata, addressing the complexity and parameter challenges in modeling living systems.

Findings

Predictive landscapes enable low-dimensional representations of cellular automata dynamics.

Cellular automata models can qualitatively describe biological features effectively.

Recent methods help overcome the complexity of discrete dynamical systems in biology.

Abstract

To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious "parameter problem": models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge by discovering a predictive "landscape" that yield low-dimensional representations of cellular automata dynamics. We review these studies.