Mechanisms controlling cell size and shape during isotropic cell spreading

Abstract

Cell motility is important for many developmental and physiological processes. Motility arises from interactions between physical forces at the cell surface membrane and the biochemical reactions that control the actin cytoskeleton. To computationally analyze how these factors interact, we built a three-dimensional stochastic model of the experimentally observed isotropic spreading phase of mammalian fibroblasts. The multiscale model is composed at the microscopic levels of three actin filament remodeling reactions that occur stochastically in space and time, and these reactions are regulated by the membrane forces due to membrane surface resistance (load) and bending energy. The macroscopic output of the model (isotropic spreading of the whole cell) occurs due to the movement of the leading edge, resulting solely from membrane force-constrained biochemical reactions. Numerical simulations indicate that our model qualitatively captures the experimentally observed isotropic cell-spreading behavior. The model predicts that increasing the capping protein concentration will lead to a proportional decrease in the spread radius of the cell. This prediction was experimentally confirmed with the use of Cytochalasin D, which caps growing actin filaments. Similarly, the predicted effect of actin monomer concentration was experimentally verified by using Latrunculin A. Parameter variation analyses indicate that membrane physical forces control cell shape during spreading, whereas the biochemical reactions underlying actin cytoskeleton dynamics control cell size (i.e., the rate of spreading). Thus, during cell spreading, a balance between the biochemical and biophysical properties determines the cell size and shape. These mechanistic insights can provide a format for understanding how force and chemical signals together modulate cellular regulatory networks to control cell motility.

Figure 1

Relationship between microscopic events and macroscopic whole-cell spreading behavior. (A) Evolution of a single family of filaments. (B) The 3D filament network at 30 s for [Arp2/3] = 0.1 μM and [capping protein] = 0.1 μM. The changing filaments from the previous reaction time step are shown in blue and the cell periphery is shown in red. (C) Projection of the changing filaments from B with the cell periphery. (D) The energy map shows the probability factor $e^{-\Delta E/k_{B}T}$ at 30 s. E–G are similar to B–D at 60 s. (D and E) Filament network at 30 and 60 s, respectively. Values on the axes represent (x,y,z) location.

Figure 2

Comparison of simulations and experiments regarding the characteristics of isotropic cell spreading. (A) Radius map from an average of 24 simulations for [Arp2/3] = 0.1 μM and [capping protein] = 0.1 μM. (B) Radius map from experiment, showing the full 30 min of spreading. (C) The velocity map from simulation shows isotropic spreading with a few pockets of zero velocity. (D) Velocity map of experiment. (E) Comparison of fold change in radius χ in experiment and simulation. (F) Comparison of circularity in experiment and simulation.

Figure 3

Effects of changing the capping protein on isotropic cell spreading, and the (A) fold change in radius and (B) circularity. (C) The final value of χ at 5 min correlates inversely with [Cap]. (D) Circularity at 5 min has a positive correlation with [Cap]. Actin concentration = 20 μM, and [Arp2/3] = 0.05 μM. (E) Increasing cytochalasin D decreases the cell-spreading radius. (F) The final value of χ at 5 min decreases with increasing cytochalasin D concentration.

Figure 4

Effects of membrane surface resistance and bending on isotropic cell spreading, and the (A) number of growing filaments, (B) filament density, (C) fold change in radius, and (D) circularity. [Actin] = 20 μM, [capping protein] = 0.1 μM, and [Arp2/3] = 0.1 μM.

Figure 5

Effect of changing levels of Arp2/3 concentration (in μM) on isotropic cell spreading. Effects of Arp2/3 concentration on the (A) number of growing filaments, (B) filament density, (C) fold change in radius, and (D) circularity are shown. (E) The final value of χ at 5 min correlates linearly with Arp2/3 concentration. (F) Circularity at 5 min has an inverse correlation with Arp2/3 concentration. Actin concentration was 20 μM and capping protein concentration was 0.05 μM.

Figure 6

Phase plots of the relationship between the ratio of capping protein/Arp2/3 and the change in radius or circularity. (A) Phase plot of χ as a function of capping protein and Arp2/3 concentrations μM; χ correlates negatively with α = [Cap]/[Arp2/3]. (B) Phase plot of circularity as a function of Arp2/3 and capping protein concentrations; C correlates positively with α = [Cap]/[Arp2/3].