# Investigating local negative feedback of Rac activity by mathematical models and cell-motility simulations

## TL;DR

This paper uses mathematical models and simulations to show how Rac and its inhibitor help cells maintain polarization and respond to directional cues.

## Contribution

The study introduces a minimal Rac-inhibitor-PIP3 circuit model that explains optogenetic data and improves gradient sensing in dynamic conditions.

## Key findings

- The Rac-inhibitor-PIP3 circuit explains optogenetic data and exotic cell trajectories.
- The model is minimal and improves gradient sensing under noisy or dynamic conditions.
- Simulations reveal how signaling components influence cell responses to stimuli.

## Abstract

How do cells maintain robust, yet flexible polarization for directed motion? Recent optogenetic experiments by Town and Weiner on neutrophil-like HL-60 cells strongly point to the essential role of a Rac-inhibitor (downstream of the small GTPase Rac) in shaping requisite negative feedback that allows cells to respond to rapidly changing directional cues. Here we adapt a previous mathematical model for cell polarity to model interactions of Rac, its putative inhibitor, and upstream PIP3 (a product of the optogenetically stimulated PI3K). We fit parameters in our partial differential equation (PDE) model to temporal and spatial experimental data. Cell shapes, motility, and stimulus responses are modeled in 2D simulations, with PDEs solved along the cell edge. We show that the Rac-inhibitor-PIP3 circuit accounts for the optogenetic data (including exotic cell trajectories), that it is the minimal circuit to do so, and that it improves gradient sensing under noisy or dynamic conditions.

•A mathematical model for Rac GTPase and its inhibitor is simulated along a cell edge•Model parameters are fit to data for optogenetically stimulated neutrophils•Simulations of cell motility reveal roles of signaling components in cell responses•Full model accounts for cell paths in local to global stimulation protocol

A mathematical model for Rac GTPase and its inhibitor is simulated along a cell edge

Model parameters are fit to data for optogenetically stimulated neutrophils

Simulations of cell motility reveal roles of signaling components in cell responses

Full model accounts for cell paths in local to global stimulation protocol

Cell biology; Mathematical biosciences