# Emergent Homeostasis and Degeneracy From Multi‐Dimensional Attractors

## TL;DR

The paper suggests that biological homeostasis can emerge from complex interactions rather than relying solely on control mechanisms.

## Contribution

A new perspective on homeostasis is proposed, based on multi-dimensional attractor manifolds rather than traditional control theory.

## Key findings

- Homeostasis can emerge from high-dimensional interactions forming stable manifolds.
- Degenerate states on manifolds allow flexibility while maintaining function.
- Control circuits may be low-dimensional projections of complex systems.

## Abstract

Biological systems maintain homeostasis, ensuring stability in the face of internal and external perturbations and counteracting stochastic noise. Traditionally, this is understood through the lens of control mechanisms designed to offset variations and maintain certain quantities near functionally desired set points. Here, we propose an alternative perspective to understand homeostasis: the collective dynamics perspective, in which homeostasis emerges spontaneously from high‐dimensional interactions, creating limiting manifolds in phase space. These multi‐dimensional attractor manifolds can constrain many components collectively, eliminating the need for explicit control of individual variables. The presence of null directions on a manifold allows for degenerate states that can add flexibility while preserving functionality. Using single‐cell growth and division homeostasis as a test case, we develop and support our perspective by models and meta‐analysis of numerous single‐cell datasets across organisms and conditions. Importantly, we do not reject the control‐theory perspective but rather suggest that control circuit models can be seen as low‐dimensional projections of a more complex, multi‐dimensional system.

Biological systems maintain homeostasis—stability to perturbations. Control theory (right) describes this as designed regulatory circuits that maintain set points. We propose that homeostasis can emerge from collective dynamics that generate stable attracting manifolds (left). Perturbations displace trajectories, but dynamics restore them to the manifold. Degenerate directions allow variability without loss of function.