A comparison of mathematical models for polarization of single eukaryotic cells in response to guided cues

Abstract

Polarization, a primary step in the response of an individual eukaryotic cell to a spatial stimulus, has attracted numerous theoretical treatments complementing experimental studies in a variety of cell types. While the phenomenon itself is universal, details differ across cell types, and across classes of models that have been proposed. Most models address how symmetry breaking leads to polarization, some in abstract settings, others based on specific biochemistry. Here, we compare polarization in response to a stimulus (e.g., a chemoattractant) in cells typically used in experiments (yeast, amoebae, leukocytes, keratocytes, fibroblasts, and neurons), and, in parallel, responses of several prototypical models to typical stimulation protocols. We find that the diversity of cell behaviors is reflected by a diversity of models, and that some, but not all models, can account for amplification of stimulus, maintenance of polarity, adaptation, sensitivity to new signals, and robustness.

Figure 1. Schematic diagrams for proposed cell polarity mechanisms.

Slow-diffusing (local) components are shown on the “cell membrane” (shaded), while fast-diffusing (global) components are shown in the interior of the cell (not to scale). S, signal; A, activator; I, inhibitor (unless otherwise indicated). (a) Model with a short-range activator and long-range inhibitor. See , . (b) Model with substrate depletion. See , . (c) A three-component model based on mutual inhibition . F and B mutually inhibit each other and activate the global inhibitor. (Note: models (a–c) have Turing instabilities and we refer to these as “Turing-type” models.) (d) Local excitation, global inhibition (LEGI) . The signal has identical effect on A and I, which together regulate a downstream response element (R). (e) Balanced inactivation mechanism . S activates A and B, which produces B_m. B_m and A are mutual inhibitors. (f) The wave-pinning mechanism . S affects a local membrane-bound activator (A ^*), which is produced autocatalytically from its cytosolic substrate (A).

Figure 2. Comparison of polarization behavior of four models.

Columns: (left to right) the wave-pinning (WP) system (2) , Goryachev's (GOR) system (4) , the Otsuji (OT) system (3) , and the LEGI system (5) . Rows: the stimuli used: (a) single localized stimulus, (b) two competing local stimuli at opposite ends of the cell, (c) persistent graded stimuli of various strengths, (d) graded stimulus and its reversal, (e) noisy initial conditions, (f) increase in cell size. (See Methods for details.)