Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

TL;DR

This paper introduces a geometric path integral framework to analyze multiscale biological systems and phenotype robustness, translating biological questions into complex numerical properties of a robustness function.

Contribution

It proposes a novel geometric path integral approach to model phenotype robustness and extends the concept to complex-valued functions, providing a new mathematical language for systems biology.

Findings

Path integral formalism can model phenotype robustness.

The approach links molecular networks to phenotypic outcomes.

Application to centipede leg number demonstrates practical utility.

Abstract

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes.