The model comprises three major early endocytic proteins:

1) Clathrin

2) AP2

3) FCHo2.

We modeled the membrane as a 36 × 36 hexagonal lattice, and proteins can bind at the vertices of the lattice. We assume the following interactions:

1) FCHo2 can bind to the membrane with an energy of EFCHo2.

2) Two FCHo2 proteins bound at neighboring sites interact with an energy EFCHo2–FCHo2.

3) If FCHo2 and AP2 are bound at the same site, they interact with an energy EFCHo2–AP2.

4) When FCHo2 interacts with AP2 (if they are bound at the same site), AP2 gets activated. AP2 stays activated as long as it is bound to the membrane, even if FCHo2 unbinds.

5) Nonactivated AP2 binds to the membrane with a low-energy EAP2, while the activated AP2 binds to the membrane more strongly (36), with an energy EAP2–act such that |EAP2| << |EAP2–act | (see values of the parameters in table S1).

6) Clathrin can bind to the membrane only if AP2 is already present at the same site. Clathrin and AP2 interact with an energy EAP2–cl.

7) If two clathrin proteins are bound at neighboring sites, then they interact with an energy Ecl–cl.

All values of the parameters used in the model are reported in table S1. Each FCHo2 unit binding to the membrane in the model is considered to be a dimer, as FCHo2 forms stable dimers (24). We allowed both FCHo2 and clathrin to form higher-order structures by associating an attractive pairwise interaction between any pair of neighboring FCHo2 dimers or any pair of neighboring clathrin molecules. To account for the tendency of clathrin to form higher-order structures, stronger attractive energy between pairs of neighboring clathrin molecule was used in the model (see table S1).

The number of AP2 and clathrin proteins present in the simulations was fixed to a number of 180 each. Different simulations were performed with a different number of FCHo2 proteins available, from 5 to 50, to investigate the effect of FCHo2 on the formation of clathrin clusters. The simulations were performed as follows. At each time step, for each of the endocytic proteins, one of the proteins in the pool is selected at random. If the selected protein is unbound, then a site on the lattice is selected at random. If the site is already occupied by a protein of the same kind, then nothing happens. If no protein of the same species is bound at the selected site, then the selected protein binds to the membrane at that site. However, as discussed above, clathrin can bind only if AP2 is present. If the selected protein is already bound, then it can unbind with a probability exp(Etot), where Etot is the total energy of the bound protein, taking into account all the contributions from the interactions listed above (all interactions are considered additive). Simulations were performed for a total of 108 steps, and snapshots were recorded every 1000 steps. A total of 100 simulations were performed for each of the different choices for the number of FCHo2 proteins. In each simulation, the formation of clathrin clusters as a function of time was monitored as follows. In each snapshot, clusters were detected by considering the connectivity of clathrin interactions on the lattice. The trajectories of the center of mass of each cluster consisting of more than 10 clathrin proteins and lasting more than 5 × 106 steps were recorded, and the size of the cluster as a function of time was monitored.

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