Figure 1. Single-cell construction and dynamics.

(a) A schematic depiction of the components of a single cell in our model. Two symmetric cell halves with semicircular poles and long edges are constrained to align using a ball-and-groove type connection. Each cell half has mass m (assumed to remain constant during cell growth) and center of mass located at the center of its semicircular pole. Growth expansion forces are generated by connecting the two cell halves to a virtual linear spring (with spring constant k) along the cell’s long axis, and then extending the rest length, R, of the virtual spring. (bc) Expansion speed (magnitude of the difference between the velocities of the two cell halves) and spring compression (difference between rest length R and cell length ℓ) for a single cell with $\dot{R}=0.1$ μm min⁻¹ and a 10-fold increase in normalized resistive damping parameter γ (see Appendix for normalization details). Simulation data (boxes) match analytical solutions (curves). Increasing γ (orange traces) lengthens the time required for expansion speed and spring compression to reach steady state ( $\tau =\frac{\gamma }{2k}$ is the time constant for the first-order system). Larger steady-state spring compression monitors the increased mechanical load felt by the growing cell when the damping coefficient is higher.