Rigidity enhances a magic-number effect in polymer phase separation

Xu, Bai; He, Guanhua; Weiner, Benjamin; Ronceray, Pierre; Meir, Yigal; Jonikas, Martin C.; Wingreen, Ned S.

doi:10.1038/s41467-020-15395-6

Cited by 56 publications

(66 citation statements)

References 35 publications

(50 reference statements)

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“…2A), which corresponds to a monomer-monomer dissociation constant K d = 0.4mM. This value is consistent with the onset K d of 1-2.5mM estimated from 3D lattice simulations with one polymer and one rigid component [8].…”

Section: Discussionsupporting

confidence: 87%

“…where c d1 , c d2 , and c b are the solutions of Eqs. 7and (8). Equations (7), (8), and (13) form a complete set which predicts the free-energy density of the two-component associative polymer system at given total monomer concentrations, c 1 and c 2 , of the two species.…”

Section: Dimer-gel Theory Resultsmentioning

confidence: 99%

“…To give a concrete example of the above analysis, we extract the values of K d for dimers from simulations, choose a value of K b for independent bonds close to the dissociation constant of a pair of monomers (see Supplemental Material for details), and numerically solve Eqs. (7) and (8) for c d1 , c d2 , and c b to find the fraction of monomers in dimers and independent bonds for all concentrations (c 1 , c 2 ). We find that indeed for polymers of equal valence, dimers are favored at low concentrations and independent bonds at high concentrations.…”

Section: Dimer-gel Theory Resultsmentioning

confidence: 99%

“…Previous simulations [5,8] of average cluster size in such two-component systems revealed a striking phenomenon -for sufficiently strong binding, the formation of large clusters is suppressed when the valence of one species equals or is an integral multiple of the valence of the other species, favoring the formation of small stable oligomers instead of a condensate. The phenomenon reminiscent of the exact filling of atomic shells leading to the unreactive noble gases was termed the "magic-number" effect.…”

Section: Introductionmentioning

confidence: 99%

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Decoding the physical principles of two-component biomolecular phase separation

Zhang

Weiner

Meir

et al. 2020

Preprint

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Cells possess a multiplicity of non-membrane bound compartments, which form via liquid-liquid phase separation. These condensates assemble and dissolve as needed to enable central cellular functions. One important class of condensates is those composed of two associating polymer species that form one-to-one specific bonds. What are the physical principles that underlie phase separation in such systems? To address this question, we employed coarse-grained molecular dynamics simulations to examine how the phase boundaries depend on polymer valence, stoichiometry, and binding strength. We discovered a striking phenomenon -- for sufficiently strong binding, phase separation is suppressed at rational polymer stoichiometries, which we termed the magic-ratio effect. We further developed an analytical dimer-gel theory that confirmed the magic-ratio effect and disentangled the individual roles of polymer properties in shaping the phase diagram. Our work provides new insights into the factors controlling the phase diagrams of biomolecular condensates, with implications for natural and synthetic systems.

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Section: Discussionsupporting

confidence: 87%

Section: Dimer-gel Theory Resultsmentioning

confidence: 99%

Section: Dimer-gel Theory Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decoding the physical principles of two-component biomolecular phase separation

Zhang

Weiner

Meir

et al. 2020

Preprint

Self Cite

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“…and Rubisco [20,21]. At unequal stoichiometries the energetic penalty for misalignments is reduced because excess scaffolds are available to bind one of the sticky ends, which facilitates the formation of longer complexes.…”

Section: Resultsmentioning

confidence: 99%

Structure-function properties in disordered condensates

Bhandari

Cotten

Kim

et al. 2020

Preprint

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Biomolecular condensates appear throughout the cell serving a wide variety of functions. Many condensates appear to form by the assembly of multivalent molecules, which produce phase separated networks with liquid-like properties. These networks then recruit client molecules, with the total composition providing functionality. Here we use a model system of poly-SUMO and poly-SIM proteins to understand client-network interactions and find that the structure of the network plays a strong role in defining client recruitment, and thus functionality. The basic unit of assembly in this system is a zipper-like filament composed of alternating poly-SUMO and poly-SIM molecules.These filaments have defects of unsatisfied bonds that allow for both the formation of a 3D network and the recruitment of clients. The filamentous structure constrains the scaffold stoichiometries and the distribution of client recruitment sites that the network can accommodate. This results in a non-monotonic client binding response that can be tuned independently by the client valence and binding energy. These results show how the interactions within liquid states can be disordered yet still contain structural features that provide functionality to the condensate. I. INTRODUCTIONMany cellular structures have been shown to form by the spontaneous condensation of biomolecules into liquidlike states [1,2], often through liquid-liquid phase transitions. While these condensates may contain hundreds of different molecules, typically only a small number of molecules with high interaction valence and high connectivity to other molecules in the structure contribute strongly to phase separation [3][4][5]. These are said to have scaffoldlike properties depending on how strongly they promote phase separation. The remaining molecules, which exhibit client-like properties, are recruited through interactions with scaffolds [6,7]. Together, the collection of molecules in a condensate determines its functionality.Since the molecules driving phase separation are multivalent, polymer-like species, many treatments of condensate formation are based on polymer theories [8][9][10][11]. In particular, scaffold condensation can be understood as the interaction between attractive stickers separated by inert spacers [11,12]. These efforts explain universal features of condensates, such as how multivalency can amplify the effect of weak interactions to tune the phase coexistence line to within physiologically relevant regions of phase space (e.g. physiological concentrations) [8]. However, there are also many non-universal features of biomolecular condensates. Experiments are revealing a striking diversity of functions performed by condensates [2,7,[13][14][15][16], and each of these assemblies will be under evolutionary pressure to optimize its specific function. This begs the question of how the disordered network of interactions within a liquid structure can affect its properties.

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Ubiquitin‐Modulated Phase Separation of Shuttle Proteins: Does Condensate Formation Promote Protein Degradation?

Dao

Castañeda

2020

BioEssays

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Liquid-liquid phase separation (LLPS) has recently emerged as a possible mechanism that enables ubiquitin-binding shuttle proteins to facilitate the degradation of ubiquitinated substrates via distinct protein quality control (PQC) pathways. Shuttle protein LLPS is modulated by multivalent interactions among their various domains as well as heterotypic interactions with polyubiquitin chains. Here, the properties of three different shuttle proteins (hHR23B, p62, and UBQLN2) are closely examined, unifying principles for the molecular determinants of their LLPS are identified, and how LLPS is connected to their functions is discussed. Evidence supporting LLPS of other shuttle proteins is also found. In this review, it is proposed that shuttle protein LLPS leads to spatiotemporal regulation of PQC activities by mediating the recruitment of PQC machinery (including proteasomes or autophagic components) to biomolecular condensates, assembly/disassembly of condensates, selective enrichment of client proteins, and extraction of ubiquitinated proteins from condensates in cells.

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Rigidity enhances a magic-number effect in polymer phase separation

Cited by 56 publications

References 35 publications

Decoding the physical principles of two-component biomolecular phase separation

Decoding the physical principles of two-component biomolecular phase separation

Structure-function properties in disordered condensates

Ubiquitin‐Modulated Phase Separation of Shuttle Proteins: Does Condensate Formation Promote Protein Degradation?

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