Unraveling biochemical spatial patterns: machine learning approaches to the inverse problem of Turing patterns

TL;DR

This paper presents machine learning methods, including physics-informed neural networks, to solve the inverse problem of Turing pattern formation in noisy biological and chemical systems, enabling better understanding and engineering of spatial patterns.

Contribution

It introduces a noise-robust machine learning approach, combining least squares and physics-informed neural networks, to analyze and engineer Turing patterns in biological systems.

Findings

Neural networks can effectively handle noisy pattern data.

The approach successfully applied to experimental chemical patterns.

Machine learning enhances control over synthetic biological patterns.

Abstract

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since high levels of noise corrupt the patterns and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application through a prototype involving an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.