Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction

Tanmoy Pal, Jonas Wessén, Suman Das, and Hue Sun Chan

Phys. Rev. E 103, 042406 – Published 9 April 2021

Abstract

Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, “fuzzy” molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.

Received 11 June 2020
Accepted 11 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042406

Physics Subject Headings (PhySH)

Biomolecular interactions Biomolecular self-assembly Biomolecular structure Compartmentalization Electrostatic interactions Excluded volume interaction Liquid-liquid phase transition Polymer behavior Supramolecular phase separation

Organelle

Polymers & Soft MatterPhysics of Living Systems

Authors & Affiliations

Tanmoy Pal, Jonas Wessén , Suman Das, and Hue Sun Chan ^*

Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada

^*To whom correspondence should be addressed: chan@arrhenius.med.utoronto.ca

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Vol. 103, Iss. 4 — April 2021

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Images

Figure 1
Polyampholytes studied in this work. Blue or red beads of “K”s (lysines) or “E”s (glutamic acids) carry $\pm 1$ protonic charges. The sv labels are those of Ref. [42].
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Figure 2
FTS-computed PDFs and mixing parameter $ξ_{p, q}$ for binary sv sequence mixtures. [(a)–(c)] Each $G_{p, p}, G_{q, q}$ (dashed, in color), and $G_{p, q}$ (solid, black) for the indicated $v$ is computed using a periodic $48^{3}$ mesh averaged over 30–40 independent runs (standard errors comparable to the plotting line width). Insets are illustrative snapshots of the real non-negative part of the density operators ${\tilde{ρ}}_{b, p}$ and ${\tilde{ρ}}_{b, q}$ depicted in different colors; the component species in the same snapshot are shown separately on the side. (d) $ξ_{p, q}$ is computed using a periodic $32^{3}$ mesh (averaged over 70–80 independent runs, solid lines) as well as the $48^{3}$ mesh (dashed lines) used for (a)–(c). Error bars represents standard errors of the mean.
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Figure 3
Cross sections of FTS droplets of binary sv sequence mixtures illustrating the interplaying roles of sequence charge pattern mismatch and generic excluded volume in mixing or demixing of polyampholyte species. Shown here along the (a), (b), and (c) columns are two-dimensional slides through the droplet center of mass in the $x − y$ (top), $y − z$ (middle), and $x − z$ (bottom) planes of the three FTS droplets depicted, respectively, in Figs. 2–2 for (a) sv28 and sv1 at $v = 0.068 b^{3}$ , (b) sv28 and sv25 at the same $v = 0.068 b^{3}$ , and (c) sv28 and sv1 at a reduced $v = 0.0068 b^{3}$ . Density contours for the two sv sequence components $p, q$ in a given mixture are similarly color coded as in Fig. 2: sv28: blue, sv1: red, and sv25: green. The contours for species $p$ ( $q$ ) are curves of constant bead density, where “bead density” here in a FTS snapshot means the real non-negative part of the density operator, viz., ${Re}_{+} ({\tilde{ρ}}_{b, p / q} (r))$ where ${Re}_{+} (u) \equiv [Re (u) + sgn (Re (u))] / 2$ for any complex number $u$ . (Among all snapshots considered, $Re ({\tilde{ρ}}_{b, p} (r)) < - 0.01 b^{- 3}$ occurs only for $< 2 %$ of the mesh points). The contours are evenly spaced from $Re ({\tilde{ρ}}_{b, p}), Re ({\tilde{ρ}}_{b, q}) = 0$ (transparent) to ${Re}_{+} ({\tilde{ρ}}_{b, p}) = max {{Re}_{+} ({\tilde{ρ}}_{b, p})}$ $[{Re}_{+} ({\tilde{ρ}}_{b, q}) = max {{Re}_{+} ({\tilde{ρ}}_{b, q})}]$ (opaque) where $max {{Re}_{+} ({\tilde{ρ}}_{b, p})}$ $[max {{Re}_{+} ({\tilde{ρ}}_{b, q})}]$ is the maximum density of species $p$ ( $q$ ) in a given snapshot.
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Figure 4
MD-simulated LLPS of binary sv sequence mixtures. (a) Excluded volume interactions in FTS (blue) for $v / b^{3} = 0.102, 0.068, 0.034$ , and 0.0068 (top to bottom, independent of $T^{*}$ ) and in MD (brown) for $r_{0} = a_{0}$ (solid) and $r_{0} = a_{0} / 2$ (dashed) at $T^{*} = 0.6$ (insets show relative sizes of the LJ spheres). [(b)–(d)] MD-simulated polyampholyte densities of binary mixtures, $ρ (z) s$ for different sv sequences are colored differently (as indicated) here and in the snapshots (on the side) of the rectangular periodic simulation boxes (wherein $z$ is the vertical coordinate), each harboring a condensed droplet. [(e)–(g)] $G_{p, q}$ of the MD systems in (b)–(d), respectively [same line style as Fig. 2–2]. Droplet snapshots (insets) are visualized [83] here with chains at periodic boundaries unwrapped.
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Figure 5
Cross-sectional views of FTS and MD snapshots of binary mixtures of polyampholytes afford a consistent picture of sequence- and excluded-volume-dependent droplet organization. Column (a): FTS density distributions on one of the two-dimensional planes in Fig. 3 through each droplet's center of mass. Column (b): Corresponding cut-out views of the MD droplets shown inside the periodic simulation boxes in Figs. 4–4 at one half of the box dimension extending perpendicularly into the page. Two different representations are used to visualize the sv28-sv1 droplet with full excluded volume (top two rows; $v = 0.068 b^{3}, r_{0} = a_{0}$ ). Upper row: sv1 and sv28 are depicted, respectively, in red and blue. Lower row: The negatively and positively charged beads in sv28 are depicted, respectively, in red and blue, whereas the corresponding beads in sv1 are depicted in pink and cyan. The color code for the sv28-sv25 mixture at full excluded volume (third row from top; $v = 0.068 b^{3}, r_{0} = a_{0}$ ) and the sv28-sv1 mixture with reduced excluded volume (bottom row; $v = 0.0068 b^{3}, r_{0} = a_{0} / 2$ ) follows that in Figs. 2 and 4.
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