FIGURE 1:

Components of the stochastic reaction-diffusion-dynamics model implemented in the CellDynaMo package: (A) Schematic of the model. 1) Centrosomes (green); 2) MTs (green); 3) KTs (orange) on which the Ndc80 complexes are bound to MTs with their KT-associated domains are labeled (orange beads); 4) chromosomes (CHs); 5) Ndc80 KT–MT links; 6) chromokinesin (CK) modeled as two harmonically coupled beads with one bead connected to a CH arm and the other bead connected to a MT; 7) blue space is phosphatase (enzyme dephosphorylating Ndc80), which is uniformly distributed in the cell interior; 8) Aurora B kinase (enzyme phosphorylating Ndc80) described by the spherical gradient of its concentration with the central maximum in the space between the KTs (red cloud); and 9) cell boundary (black) is modeled as a repulsive potential for all cell components. Components 1–6 and 9 are described using the Langevin dynamics in the overdamped (Brownian diffusion) limit (see Supplemental Eqs. S14–S17; see also Table 1 and Supplemental Table S2); components 5–8 are modeled using the reaction-diffusion master equation (see Supplemental Eq. S1; see also Supplemental Tables S1 and S2). (B) Snapshot in 3D from the CellDynaMo-based simulation that shows all the components. (C) More detailed representation of cylindrical potential (for cylindrical segments of MTs or CH arms) including stretching, bending, and excluded volume interactions between cylinders. Each beginning and end of the cylinder are connected by harmonic springs (shown in yellow). Transparent areas show the excluded volume of each structure. At the intersection point of these volumes, each cylinder is divided into two parts, parametrized by u ∈ [0, 1] and s ∈ [0, 1] (see Supplemental Eq. S2). (D) More detailed MT–CH interaction interface. A cylinder-based scheme is used in the CellDynaMo force field to model MTs and CH arms. Transparent areas show the excluded volume of each structure. CK is represented as a harmonic potential between two beads on the surfaces of bound cylinders (see Supplemental Eq. S8). Positions of the beads are determined by stochastic chemical reactions and force-velocity relationship (see SM). (E) Types of KT–MT attachments are illustrated by examples coming from snapshots taken from the simulations.