Rotational Brownian dynamics simulations of clathrin cage formation.

The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.

Micellization model for the polymerization of clathrin baskets.

A thermodynamic model is used to investigate the conditions under which clathrin triskelions form polyhedral baskets. The analysis, which is similar to classical methods used to study micelle formation, relates clathrin basket energetics to system parameters linked to triskelial rigidity, the natural curvature of an isolated triskelion, and interactions between triskelial legs in the assembled polyhedra. Mathematical theory predicts that a minimal ("critical") clathrin concentration, C(C), needs to be surpassed in order for basket polymerization to occur, and indicates how C(C), and the amount of polymerized material, depend on the chosen parameters. Analytical expressions are obtained to indicate how changes in the parameters affect the sizes of the polyhedra which arise when the total clathrin concentration exceeds C(C). A continuum analytic approximation then is used to produce numerical results that illustrate the derived dependences.