Determination of active forces in actomyosin systems as inverse source problems for the Stokes equation

TL;DR

This paper develops a mathematical framework to identify forces in active biological systems like actomyosin networks by solving inverse source problems for the Stokes equation, using microscopy data.

Contribution

It introduces a novel inverse problem approach to determine forces from fluid flow data in active gels, including analysis of incomplete data and regularization techniques.

Findings

Successfully applied methods to synthetic data.

Validated approach with experimental microscopy data.

Provided insights into force distributions in actomyosin systems.

Abstract

The identification of forces and stresses is a central task in biophysics research: Knowledge on forces is key to understanding dynamic processes in active biological systems that are able to self-organize and display emergent properties by converting energy into mechanical work. The aim of this paper is to identify forces generated by a filament-motor network of F-actin and myosin -- actomyosin -- and exerted on the surrounding fluid, therefore causing a fluid flow. In particular, we evaluate optical microscopy data stemming from two different physical settings, confined and non-confined active gels. As a theoretical model, we use the Stokes equation together with an incompressibility condition and suitable boundary conditions reflecting the physical settings. The problem of determining the forces from knowledge on the fluid flow is formulated as an inverse source problem. Due to experimental limitations, only incomplete data are available. We provide a rigorous analysis of the forward problems and the impact of missing data, derive the adjoints of the forward operators needed for regularization, and demonstrate our methods on both synthetic and experimentally measured data.