Crystallization of asymmetric patchy models for globular proteins in solution

Abstract

Asymmetric patchy particle models have recently been shown to describe the crystallization of small globular proteins with near-quantitative accuracy. Here, we investigate how asymmetry in patch geometry and bond energy generally impacts the phase diagram and nucleation dynamics of this family of soft matter models. We find the role of the geometry asymmetry to be weak, but the energy asymmetry to markedly interfere with the crystallization thermodynamics and kinetics. These results provide a rationale for the success and occasional failure of the proposal of George and Wilson for protein crystallization conditions as well as physical guidance for developing more effective protein crystallization strategies.

The glass-forming ability of model metal-metalloid alloys

“…We take a simpler geometric computational approach, where we model the covalent characteristics of metalloid atoms by arranging attractive patches on the surface of spherical particles to consider the directionality in covalently bonded structures. This patchy particle model has also been employed to study liquid stability [15], formation of quasicrystals [16], protein crystallization [17], and colloidal self-assembly [18,19].…”

Competition between Monomeric and Dimeric Crystals in Schematic Models for Globular Proteins

“…From the P2 1 2 1 2 1 lattice geometry, we obtain a lattice energy per particle e m = −3ε m for the monomeric crystal and e d = −(ε D +5ε d )/2 for the dimeric crystal. Note that although the assumption that all crystal contacts are identical is known not to be generally true, it nonetheless remains qualitatively robust in the limit of small interaction heterogeneity [21]. Without loss of generality, we adopt reduced units with length being given in units of σ, and energy and inverse temperature β = 1/k B T , where k B is the Boltzmann constant, in units of ε D .…”

“…21. The gas-liquid line of the phase diagram is obtained using the Gibbs ensemble method [25], and the critical temperature T c and density ρ c are extracted using the law of rectilinear diameters [26].…”

“…In this case, the crystal free energy is computed by integrating from an Einstein crystal [26], whose free energy is evaluated by a saddle point approximation [21], and the fluid free energy is in-tegrated from the ideal gas reference state. Free-energy integration over isotherms or isobars identifies the coexistence points between the fluid and the dimeric crystal, the fluid and the monomeric crystal, and the two crystals.…”

“…In these systems, successful crystallization is typically achieved in the region intermediate between the solubility line -above which the solution is stable-and the liquid-liquid critical point -below which the system precipitates into amorphous materials [16][17][18]. The observation that even spherical and rigid globular proteins are characterized by directional interactions (these interactions are notably responsible for the low packing fraction of protein crystals compared to atomic solids), however, soon led to the replacement of spherical symmetry with patchiness [19][20][21][22][23]. In patchy models, a protein is described as a spherical particle decorated with attractive patches that mimic the solutionmediated directional protein-protein interactions driving crystal assembly.…”