Ground States of Crystalline Caps: Generalized Jellium on Curved Space

Li, Siyu; Zandi, Roya; Travesset, Alex; Grason, Gregory M.

doi:10.1103/physrevlett.123.145501

Cited by 44 publications

(50 citation statements)

References 47 publications

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“…One possible explanation is that interactions between the assembling proteins bias the pathways toward proper capsids. A recent model based on continuum elasticity theory (28) proposes that coat proteins adopt the correct configurations in the capsid as it grows in order to minimize the elastic stress. This model predicts that the number of proteins in the growing capsid should increase monotonically with time, a prediction that is consistent with our measurements of the growth phase.…”

Section: Discussionmentioning

confidence: 99%

Measurements of the self-assembly kinetics of individual viral capsids around their RNA genome

Garmann

Goldfain

Manoharan

2019

Proc. Natl. Acad. Sci. U.S.A.

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Self-assembly is widely used by biological systems to build functional nanostructures, such as the protein capsids of RNA viruses. But because assembly is a collective phenomenon involving many weakly interacting subunits and a broad range of timescales, measurements of the assembly pathways have been elusive. We use interferometric scattering microscopy to measure the assembly kinetics of individual MS2 bacteriophage capsids around MS2 RNA. By recording how many coat proteins bind to each of many individual RNA strands, we find that assembly proceeds by nucleation followed by monotonic growth. Our measurements reveal the assembly pathways in quantitative detail and also show their failure modes. We use these results to critically examine models of the assembly process.

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Section: Discussionmentioning

confidence: 99%

Measurements of the self-assembly kinetics of individual viral capsids around their RNA genome

Garmann

Goldfain

Manoharan

2019

Proc. Natl. Acad. Sci. U.S.A.

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“…Following the results of Ref. [52,53], we assume that pentamers grow linearly with the capsid area, so the pentameric For ks = 400kBT , it takes 78 steps for a pentamer to move and "correct" its location such that the cap has only 25 trimers when the pentamer formed in the "wrong" position dissociates. We note that each MC move involves any attempt to move any trimer or vertex through diffusion, growth or detachment.…”

Section: Hydrophobic Interactionmentioning

confidence: 99%

How a Virus Circumvents Energy Barriers to Form Symmetric Shells

Panahandeh

Marichal

et al. 2020

ACS Nano

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Previous self-assembly experiments on a model icosahedral plant virus have shown that, under physiological conditions, capsid proteins initially bind to the genome through an en masse mechanism and form nucleoprotein complexes in a disordered state, which raises the questions as to how virions are assembled into a highly ordered structure in the host cell. Using small-angle X-ray scattering, we find out that a disorder-order transition occurs under physiological conditions upon an increase in capsid protein concentrations. Our cryo-transmission electron microscopy reveals closed spherical shells containing in vitro transcribed viral RNA even at pH 7.5, in marked contrast with the previous observations. We use Monte Carlo simulations to explain this disorder-order transition and find that, as the shell grows, the structures of disordered intermediates in which the distribution of pentamers does not belong to the icosahedral subgroups become energetically so unfavorable that the caps can easily dissociate and reassemble overcoming the energy barriers for the formation of perfect icosahedral shells. In addition, we monitor the growth of capsids under the condition that the nucleation and growth is the dominant pathway and show that the key for the disorder-order transition in both en masse and nucleation and growth pathways lies in the strength of elastic energy compared to the other forces in the system including protein-protein interactions and the chemical potential of free subunits. Our findings explain, at least in part, why perfect virions with icosahedral order form under different conditions including physiological ones.

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“…Thus, the form of the Helfrich energy is sufficient to describe the equilibrium bending energy of the spherical shells that we consider. However, we note that the inter-defect interactions can have a significant effect on the energy landscape and preferred geometry of assembly intermediates [104, 105], and thus would be important to consider for assembly pathways and kinetics.…”

Section: Supplementary Informationmentioning

confidence: 99%

“…Previous modeling studies have elucidated the assembly of empty icosahedral shells [69–95], the effect of an interior template such as a nanoparticle or RNA molecule on shell assembly[76, 82–84, 96–118], and how the interplay between template curvature and shell elasticity can control its size [76, 104, 105]. However, the many-molecule scaffold-cargo complex within a microcompartment does not have a specific size or morphology, and thus requires new models.…”

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confidence: 99%

Mechanisms of scaffold-mediated microcompartment assembly and size-control

Mohajerani

Sayer

Christopher

et al. 2020

Preprint

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This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by long flexible scaffold proteins that have weak multivalent interactions with the cargo. We describe a minimal model for the thermodynamics and dynamics of assembly of a protein shell around cargo and scaffold molecules, with scaffold-mediated cargo coalescence and encapsulation. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target new molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.

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Ground States of Crystalline Caps: Generalized Jellium on Curved Space

Cited by 44 publications

References 47 publications

Measurements of the self-assembly kinetics of individual viral capsids around their RNA genome

Measurements of the self-assembly kinetics of individual viral capsids around their RNA genome

How a Virus Circumvents Energy Barriers to Form Symmetric Shells

Mechanisms of scaffold-mediated microcompartment assembly and size-control

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