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Research Article

Robust nonequilibrium pathways to microcompartment assembly

View ORCID ProfileGrant M. Rotskoff and View ORCID ProfilePhillip L. Geissler
  1. aCourant Institute of Mathematical Sciences, New York University, New York, NY 10002;
  2. bDepartment of Chemistry, University of California, Berkeley, CA 94720

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PNAS June 19, 2018 115 (25) 6341-6346; first published June 4, 2018; https://doi.org/10.1073/pnas.1802499115
Grant M. Rotskoff
aCourant Institute of Mathematical Sciences, New York University, New York, NY 10002;
bDepartment of Chemistry, University of California, Berkeley, CA 94720
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  • ORCID record for Grant M. Rotskoff
Phillip L. Geissler
bDepartment of Chemistry, University of California, Berkeley, CA 94720
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  • For correspondence: geissler@berkeley.edu
  1. Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved May 4, 2018 (received for review February 9, 2018)

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    Fig. 1.

    Model dynamics of microcompartment assembly. (A) Cargo monomers (green spheres) in our molecular model occupy sites of an FCC lattice, experiencing short-ranged attraction to their nearest neighbors and also to protein monomers composing the shell. Each shell monomer corresponds to a triangle in a discretized shell (gray) that resists bending and stretching according to an elastic Hamiltonian. Closure of the shell requires the presence of topological defects in the triangulated surface, vertices that are connected to only five neighbors. Red spheres in A and B highlight the locations of these defects. (B) A fully assembled microcompartment includes at least 12 of these defects. In B and E, we show the boundary of the cargo droplet as a translucent green surface. (C) At early time t in the assembly process, high curvature of the cargo droplet limits shell growth to an area that is relatively flat while maintaining contact with the cargo. (D) Droplet growth reduces curvature until encapsulation becomes thermodynamically favorable and kinetically facile (Movie S1). (E) The nearly closed shell effectively halts cargo aggregation, but the approach to a simply connected envelope proceeds slowly as defects reposition and combine to heal grain boundaries.

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    Fig. 2.

    Minimalist model for dynamics of cargo growth and encapsulation. (A) Our phenomenological model resolves only the radius R of a cargo droplet and the polar angle θ of a spherical cap that coats it. As in Fig. 1, the green spherical droplet represents the cargo, and the gray coating represents the shell. Black contours indicate lines of constant free energy F(R,θ). Green lines show the course of 10 kinetic Monte Carlo trajectories under conditions favorable for microcompartment assembly (kc0/ks0=0.001, all other parameters given in SI Appendix, section S4). Several structures along the assembly trajectory are shown near the corresponding values of R and θ. Encapsulation is thermodynamically favorable for R>R* (lower dashed line). The free energy barrier to encapsulation is smaller than the thermal energy kBT for R>R‡ (Eq. S43) (dotted-dashed line). (B) Histograms of microcompartment radius when θ reaches π (at which point dynamics cease). Ten thousand independent trajectories were collected for kc0/ks0 = 0.1, 0.01, and 0.001. Radius values are given in a unit of length ℓ that is comparable to the shell monomer size (Eq. S37).

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    Fig. 3.

    Structural variation among microcompartments generated by our molecular model. As in Fig. 1, the cargo is shown in green, the shell is shown in gray, and topological defects are shown in red. (A) Structures from the ensemble evincing the distinct regimes of sphericity and faceting. Note that two-dimensional projections can obscure some of the variation. (B) Typical assemblies are not substantially elongated, indicated by a histogram of the sphericity α (SI Appendix, section S7). (C) Faceting necessitates relatively sharp angles between shell monomers surrounding a fivefold defect (SI Appendix, section S7). A histogram of this angle ⟨θdefect⟩ (averaged over all defects in an assembled structure) underscores the typically strong faceting visible in A.

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    • Download Movie_S01 (MP4) - Simulations were visualized using the VMD software package [2]. In order to clearly show the shell structure, only occupied lattice sites that are above a distance cutoff of 1.5l0 are shown in our visualizations. The cargo is depicted either as density isosurfaces or spheres centered at the lattice sites. In the Movie S1, the shell is depicted as dynamic bonds with a distance cutoff of 1:5l0; which leads to unconnected vertices appearing bonded in some frames.
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Robust nonequilibrium pathways to microcompartment assembly
Grant M. Rotskoff, Phillip L. Geissler
Proceedings of the National Academy of Sciences Jun 2018, 115 (25) 6341-6346; DOI: 10.1073/pnas.1802499115

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Robust nonequilibrium pathways to microcompartment assembly
Grant M. Rotskoff, Phillip L. Geissler
Proceedings of the National Academy of Sciences Jun 2018, 115 (25) 6341-6346; DOI: 10.1073/pnas.1802499115
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Proceedings of the National Academy of Sciences: 115 (25)
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