Limits to positional information in boundary-driven systems

TL;DR

This paper investigates the fundamental physical limits of positional information in boundary-driven systems, deriving a universal expression in near-equilibrium conditions and proposing it as an upper bound beyond linear response.

Contribution

It introduces a universal formula for positional information in boundary-driven systems and conjectures its role as an upper bound in non-linear regimes.

Findings

Derived a universal expression involving chemical potential and density gradients.

Supported the conjecture with analysis of various solvable systems.

Proposed the expression as an upper bound beyond linear response.

Abstract

Chemical gradients can be used by a particle to determine its position. This \textit{positional information} is of crucial importance, for example in developmental biology in the formation of patterns in an embryo. The central goal of this paper is to study the fundamental physical limits on how much positional information can be stored inside a system. To achieve this, we study positional information for general boundary-driven systems, and derive, in the near-equilibrium regime, a universal expression involving only the chemical potential and density gradients of the system. We also conjecture that this expression serves as an upper bound on the positional information of boundary driven systems beyond linear response. To support this claim, we test it on a broad range of solvable boundary-driven systems.