PhD Defence Matteo Giani

modeling the self-assembly of clathrin coats 

The assembly of clathrin coats in the presence of adaptor proteins was studied through computer simulations using coarse-grained models and through statistical mechanics. Adopting a reductionist approach based on recent experimental results, we aimed at reproducing and studying the minimal conditions that lead to the successful formation of aggregates, and at investigating the molecular properties and mechanisms required by the assembly process both in bulk conditions and at a membranous surface. In order to tackle this challenging task, coarse-grained models  were used to describe all the assembly units involved in the simulations presented in this thesis. These models are based on the available structural data and are engineered to capture the key elements and behavior of the modeled proteins.

In the first chapter, we introduce a coarse grained model of adaptor proteins, inspired by and representing the AP2 complex. The latter, the second most abundant component of endocytic coats after clathrin, is known to play a fundamental role in promoting and assisting the creation of coats at the cytosolic surface of the membrane. It is reported to be able to trigger polymerization of clathrin triskelia in physiological conditions of salt and pH, under which purified clathrin triskelia do not spontaneously self-assemble. The interaction between APs and clathrin were modeled throughout this thesis through a click potential, introduced for the first time in this chapter. The characteristics of the AP model, and of this interaction, have been tuned to reproduce the existing experimental assembly data of an AP2 and clathrin mixture. Our computer simulations provide novel insights into the role of AP2 in the self-assembly of clathrin cages and suggest that the mechanical properties of adaptor proteins are of fundamental importance.  In the same chapter, we also developed a statistical mechanical

theory that describes the equilibrium concentration of clathrin cages as a function of the other assembly variables and parameters, such as the protein concentrations and interaction strengths.

This theoretical model has been further developed in the third chapter, in order to explicitly take into account the effect of the flexibility of the clathrin triskelion, previously neglected. The main aim of the chapter is to investigate the equilibrium properties of clathrin cages resulting from the aggregation process, with emphasis on their size in the absence and in the presence of adaptor proteins. In order to perform this study, the essential features and characteristics of clathrin and AP2s are captured through a small number of effective parameters, and the number of allowed aggregates is determined on the base of geometrical considerations and arguments. The model is able to capture the key mechanisms determining the experimentally known ability of AP2s to influence the size of a clathrin cage, and thus to shape the resulting cage size distribution.

In the fourth chapter, we introduce a triangulated mesh model for an elastic membrane to investigate the formation of clathrin/AP2 coats at the cytosolic face of a cellular membrane. The model parameters are tuned to reproduce the typical properties of a biological membrane within the computational limits imposed by our simulations. In order to be able to extract the dynamical behavior associated to the aggregation process from the simulations, we make use of a compact Rotational Brownian Dynamics algorithm that uses quaternions to describe rotations, recently developed within the group.  In the same spirit that led to the development of the statistical-mechanical model accompanying the simulations of the second chapter, we developed a Langmuir-like adsorption model for the clathrin/AP complex at the membrane. Through the combination of simulations and theory, we characterize the mechanisms by which an initial nucleation point constituted by a small number of assembly units is stabilized through a cooperative effect between APs and clathrin at the membrane surface. We furthermore describe and predict the conditions under which this nucleation point is able to grow into a hemispherical clathrin coat.  

In all the simulations performed in the fourth chapter , the growth of the clathrin coat halts upon reaching a hemispherical configuration, hinting towards the existence of an activation barrier in the free energy profile associated with the assembly of a clathrin coat at the membrane. The fifth chapter is devoted to investigating and computing the free energy profile by means of constrained Brownian Dynamics simulations. The free energy is here expressed and computed as a function of a reaction coordinate by integrating the average constraint force.  Our results confirm the existence of a free energy barrier, implying the action of other endocytic components, possibly other membrane-bending proteins, at a specific step of the assembly process.