Protein-coat dynamics and cluster phases in intracellular trafficking

Abstract

Clustering of membrane proteins is a hallmark of biological membranes' lateral organization and crucial to their function. However, the physical properties of these protein aggregates remain poorly understood. Ensembles of coat proteins, the example considered here, are necessary for intracellular transport in eukaryotic cells. Assembly and disassembly rates for coat proteins involved in intracellular vesicular trafficking must be carefully controlled: their assembly deforms the membrane patch and drives vesicle formation, yet the protein coat must rapidly disassemble after vesiculation. Motivated by recent experimental findings for protein-coat dynamics, we study a dynamical Ising-type model for coat assembly and disassembly, and demonstrate how simple dynamical rules generate a robust, steady-state distribution of protein clusters (corresponding to intermediate budded shapes) and how cluster sizes are controlled by the kinetics. We interpret the results in terms of both vesiculation and the coupling to cargo proteins.

Figure 1

A snapshot of the system showing clusters formed by particle aggregation. Particles representing coat units diffuse on an underlying hexagonal lattice; they associate and dissociate at rates given by k_on and k_off, respectively.

Figure 2

(A) Snapshots of a portion of the system at different values of k_on, k_off. The interaction strength is J = 4.0 in Figs. (i)-(iv), and J = 1.6 in Figs. (v) and (vi). The parameters are (i) k_on = 3 × 10⁻⁶, k_off = 5 × 10⁻⁵, (ii) k_on = 3 × 10⁻⁶, k_off = 1×10⁻⁶, (iii) k_on = 3×10⁻⁵, k_off = 5×10⁻⁴, (iv) k_on = 3×10⁻⁵, k_off = 1×10⁻⁴, (v) k_on = 3 × 10⁻⁶, k_off = 5 × 10⁻⁵, and (vi) k_on = 3 × 10⁻⁶, k_off = 1 × 10⁻⁵. We note that all snapshots shown here correspond to J > J_c, and that lower values of J (provided J > J_c) lead to larger (though fewer) clusters and to a larger fraction of particles existing as monomers. (B) The distribution of cluster size at different values of the interaction strength J, with k_on = 3×10⁻⁶ and k_off = 5×10⁻⁵. We find that the peak cluster size increases as J decreases (provided J > J_c), even though the height of the peak goes down, consistent with the previous observation that a larger fraction of particles exist as monomers at lower values of J.

Figure 3

The aggregation number as a function of the dissociation rate. The association rate is 3 × 10⁻⁶. For dissociation rates less 3 × 10⁻⁴, the data are well described by a power law (dotted line) with exponent −1.06. For dissociation rates larger than this (association-rate dependent) crossover, the aggregation number asymptotes to 1. Inset: Peak size as a function of the dissociation rate. The association rate is 3 × 10⁻⁶. The points are fitted to a power law (dotted line), with exponent −1.00.

Figure 4

The aggregation number as a function of density. At low densities, the aggregation number approaches 1 and a quadratic fit of the form 1 + ½(ρ/c)² is shown. Inset: The average density of the system as a function of the dissociation rate. The association rate is 3 × 10⁻⁴. A crossover at dissociation rate 1.5 × 10⁻² separates high-density from low-density scaling, with associated exponents of −0.49 and −0.30, respectively. Since at low dissociation rates, the density is expected to asymptote to 1, the domain of validity of that scaling behavior is correspondingly circumscribed.