[Paper Review] Robust nonequilibrium pathways to microcompartment assembly

Grant M. Rotskoff, Phillip L. Geissler|arXiv (Cornell University)|Aug 25, 2017

Bacteriophages and microbial interactions3 citations

TL;DR

This paper proposes a robust nonequilibrium pathway for microcompartment assembly in cyanobacteria, where cargo condensation drives shell formation through a kinetic mechanism rather than equilibrium thermodynamics. Simulations show that shell nucleation occurs at a critical cargo radius, with elastic shell dynamics and topological defects enabling the formation of faceted, carboxysome-like structures with narrow size distributions, revealing key control variables for nanoscale encapsulation.

ABSTRACT

Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that posit microcompartments as stable equilibrium arrangements of the constituent proteins. Here we describe a different mechanism for microcompartment assembly, one that is fundamentally nonequilibrium and yet highly reliable. This pathway is revealed by simulations of a molecular model resolving the size and shape of a cargo droplet, and the extent and topography of an elastic shell. The resulting metastable microcompartment structures closely resemble those of carboxysomes, with a narrow size distribution and faceted shells. The essence of their assembly dynamics can be understood from a simpler mathematical model that combines elements of classical nucleation theory with continuum elasticity. These results highlight important control variables for achieving nanoscale encapsulation in general, and for modulating the size and shape of carboxysomes in particular.

Motivation & Objective

• To understand the dynamic pathway of bacterial microcompartment assembly, particularly carboxysomes, which are structurally similar to viral capsids but functionally distinct.
• To challenge the prevailing assumption that microcompartment assembly follows equilibrium thermodynamics, as seen in viral capsid models.
• To identify the physical and kinetic drivers that enable reliable, size-controlled encapsulation of metabolic enzymes in microcompartments.
• To quantify the role of shell elasticity, curvature, and topological defects in determining the final structure and size distribution of microcompartments.

Proposed method

• Simulates a molecular model of microcompartment assembly with cargo monomers on an FCC lattice and a triangulated elastic shell governed by a continuum elasticity Hamiltonian.
• Models shell formation using a kinetic Monte Carlo approach with nucleation barriers derived from classical nucleation theory.
• Introduces a critical radius $ R^{lat} $ at which the activation free energy for shell nucleation equals thermal energy ($ k_B T $), marking the onset of stable growth.
• Uses bond orientational order parameters ($ Q_6 $, $ \hat{W}_{10} $) and a defect-based faceting parameter to quantify icosahedral symmetry and structural morphology.
• Defines an effective radius $ R_{\text{eff}} = \left(\frac{3N_c}{4\pi}\right)^{1/3} $ to compare simulated and experimental size distributions.
• Analyzes the role of topological defects (fivefold vertices) in enabling closure of the shell and healing of grain boundaries.

Experimental results

Research questions

• RQ1 Can microcompartment assembly be explained by a nonequilibrium kinetic pathway rather than equilibrium thermodynamics?
• RQ2 What determines the critical size at which shell nucleation becomes favorable and kinetically accessible?
• RQ3 How do elastic shell properties and topological defects influence the size, shape, and stability of assembled microcompartments?
• RQ4 Why do microcompartments exhibit a narrow size distribution despite the absence of a strong curvature preference in shell proteins?
• RQ5 To what extent do structural features like facets and icosahedral symmetry emerge from kinetic and elastic constraints rather than local protein preferences?

Key findings

• Shell nucleation occurs at a critical cargo radius $ R^{lat} $, where the activation free energy for nucleation equals thermal energy ($ k_B T $), marking the transition to stable growth.
• The resulting microcompartments exhibit a narrow size distribution, closely matching experimental data from Iancu et al. (2010), with effective radii consistent across simulations and observations.
• Despite the absence of intrinsic curvature preference in shell proteins, the final structures display distinct faceting and icosahedral symmetry, driven by elastic energy minimization and defect dynamics.
• The distribution of $ Q_6 $ and $ \hat{W}_{10} $ indicates that while ideal icosahedra are rare, the structures are morphologically consistent with carboxysomes observed in tomograms.
• The faceting parameter $ \langle \theta_{\text{defect}} \rangle $ confirms that high curvature at fivefold defects drives the formation of flat facets, enabling efficient encapsulation.
• The pathway is robust to variations in protein-cargo interactions and shell elasticity, suggesting a general mechanism for reliable nanoscale encapsulation.