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Changiarath A, Arya A, Xenidis V, Padeken J, Stelzl LS. Sequence determinants of protein phase separation and recognition by protein phase-separated condensates through molecular dynamics and active learning. Faraday Discuss 2024. [PMID: 39319382 DOI: 10.1039/d4fd00099d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/26/2024]
Abstract
Elucidating how protein sequence determines the properties of disordered proteins and their phase-separated condensates is a great challenge in computational chemistry, biology, and biophysics. Quantitative molecular dynamics simulations and derived free energy values can in principle capture how a sequence encodes the chemical and biological properties of a protein. These calculations are, however, computationally demanding, even after reducing the representation by coarse-graining; exploring the large spaces of potentially relevant sequences remains a formidable task. We employ an "active learning" scheme introduced by Yang et al. (bioRxiv, 2022, https://doi.org/10.1101/2022.08.05.502972) to reduce the number of labelled examples needed from simulations, where a neural network-based model suggests the most useful examples for the next training cycle. Applying this Bayesian optimisation framework, we determine properties of protein sequences with coarse-grained molecular dynamics, which enables the network to establish sequence-property relationships for disordered proteins and their self-interactions and their interactions in phase-separated condensates. We show how iterative training with second virial coefficients derived from the simulations of disordered protein sequences leads to a rapid improvement in predicting peptide self-interactions. We employ this Bayesian approach to efficiently search for new sequences that bind to condensates of the disordered C-terminal domain (CTD) of RNA Polymerase II, by simulating molecular recognition of peptides to phase-separated condensates in coarse-grained molecular dynamics. By searching for protein sequences which prefer to self-interact rather than interact with another protein sequence we are able to shape the morphology of protein condensates and design multiphasic protein condensates.
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Affiliation(s)
- Arya Changiarath
- Institute of Physics, Johannes Gutenberg University (JGU) Mainz, Germany
| | - Aayush Arya
- Institute of Physics, Johannes Gutenberg University (JGU) Mainz, Germany
| | | | - Jan Padeken
- Institute of Molecular Biology (IMB) Mainz, Germany
| | - Lukas S Stelzl
- Institute of Molecular Biology (IMB) Mainz, Germany
- Institute of Molecular Physiology, Johannes Gutenberg University (JGU) Mainz, Germany.
- KOMET1, Institute of Physics, Johannes Gutenberg University (JGU) Mainz, Germany
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Pal T, Wessén J, Das S, Chan HS. Differential Effects of Sequence-Local versus Nonlocal Charge Patterns on Phase Separation and Conformational Dimensions of Polyampholytes as Model Intrinsically Disordered Proteins. J Phys Chem Lett 2024; 15:8248-8256. [PMID: 39105804 DOI: 10.1021/acs.jpclett.4c01973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/07/2024]
Abstract
Conformational properties of intrinsically disordered proteins (IDPs) are governed by a sequence-ensemble relationship. To differentiate the impact of sequence-local versus sequence-nonlocal features of an IDP's charge pattern on its conformational dimensions and its phase-separation propensity, the charge "blockiness" κ and the nonlocality-weighted sequence charge decoration (SCD) parameters are compared for their correlations with isolated-chain radii of gyration (Rgs) and upper critical solution temperatures (UCSTs) of polyampholytes modeled by random phase approximation, field-theoretic simulation, and coarse-grained molecular dynamics. SCD is superior to κ in predicting Rg because SCD accounts for effects of contact order, i.e., nonlocality, on dimensions of isolated chains. In contrast, κ and SCD are comparably good, though nonideal, predictors of UCST because frequencies of interchain contacts in the multiple-chain condensed phase are less sensitive to sequence positions than frequencies of intrachain contacts of an isolated chain, as reflected by κ correlating better with condensed-phase interaction energy than SCD.
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Affiliation(s)
- Tanmoy Pal
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Jonas Wessén
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Chemistry, Gandhi Institute of Technology and Management, Visakhapatnam, Andhra Pradesh 530045, India
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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3
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Chen F, Jacobs WM. Emergence of Multiphase Condensates from a Limited Set of Chemical Building Blocks. J Chem Theory Comput 2024. [PMID: 39078082 DOI: 10.1021/acs.jctc.4c00323] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/31/2024]
Abstract
Biomolecules composed of a limited set of chemical building blocks can colocalize into distinct, spatially segregated compartments known as biomolecular condensates. While many condensates are known to form spontaneously via phase separation, it has been unclear how immiscible condensates with precisely controlled molecular compositions assemble from a small number of chemical building blocks. We address this question by establishing a connection between the specificity of biomolecular interactions and the thermodynamic stability of coexisting condensates. By computing the minimum interaction specificity required to assemble condensates with target molecular compositions, we show how to design heteropolymer mixtures that produce compositionally complex condensates by using only a small number of monomer types. Our results provide insight into how compositional specificity arises in naturally occurring multicomponent condensates and demonstrate a rational algorithm for engineering complex artificial condensates from simple chemical building blocks.
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Affiliation(s)
- Fan Chen
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - William M Jacobs
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
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de Souza JP, Stone HA. Exact analytical solution of the Flory-Huggins model and extensions to multicomponent systems. J Chem Phys 2024; 161:044902. [PMID: 39046343 DOI: 10.1063/5.0215923] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2024] [Accepted: 06/17/2024] [Indexed: 07/25/2024] Open
Abstract
The Flory-Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at equilibrium have not been determined analytically, and numerical techniques are required that restrict the theory's ease of application. In this work, we derive an implicit analytical solution to the Flory-Huggins theory of one polymer in a solvent by applying a procedure that we call the implicit substitution method. While the solutions are implicit and in the form of composite variables, they can be mapped explicitly to a phase diagram in composition space. We apply the same formalism to multicomponent polymeric systems, where we find analytical solutions for polydisperse mixtures of polymers of one type. Finally, while complete analytical solutions are not possible for arbitrary mixtures, we propose computationally efficient strategies to map out coexistence curves for systems with many components of different polymer types.
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Affiliation(s)
- J Pedro de Souza
- Omenn-Darling Bioengineering Institute, Princeton University, Princeton, New Jersey 08544, USA
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Zhou HX, Kota D, Qin S, Prasad R. Fundamental Aspects of Phase-Separated Biomolecular Condensates. Chem Rev 2024; 124:8550-8595. [PMID: 38885177 PMCID: PMC11260227 DOI: 10.1021/acs.chemrev.4c00138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.
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Affiliation(s)
- Huan-Xiang Zhou
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
- Department of Physics, University of Illinois Chicago, Chicago, Illinois 60607, USA
| | - Divya Kota
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
| | - Sanbo Qin
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
| | - Ramesh Prasad
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
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Häfner G, Müller M. Reaction-Driven Diffusiophoresis of Liquid Condensates: Potential Mechanisms for Intracellular Organization. ACS NANO 2024; 18:16530-16544. [PMID: 38875706 PMCID: PMC11223496 DOI: 10.1021/acsnano.3c12842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Revised: 05/18/2024] [Accepted: 05/24/2024] [Indexed: 06/16/2024]
Abstract
The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted at the boundary, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, toward or away from fuel source and waste sink, depending on the product molecules' affinity toward fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.
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Affiliation(s)
- Gregor Häfner
- Georg-August
Universität Göttingen, Institut für Theoretische Physik, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
- Max
Planck School Matter to Life, Jahnstraße 29, 69120 Heidelberg, Germany
| | - Marcus Müller
- Georg-August
Universität Göttingen, Institut für Theoretische Physik, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
- Max
Planck School Matter to Life, Jahnstraße 29, 69120 Heidelberg, Germany
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Bot A, van der Linden E, Venema P. Phase Separation in Complex Mixtures with Many Components: Analytical Expressions for Spinodal Manifolds. ACS OMEGA 2024; 9:22677-22690. [PMID: 38826518 PMCID: PMC11137696 DOI: 10.1021/acsomega.4c00339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/10/2024] [Revised: 03/25/2024] [Accepted: 03/26/2024] [Indexed: 06/04/2024]
Abstract
The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N ≥ 2. Liquid-liquid phase separation is modeled using a virial expansion up to the second order of the concentrations of the components. Formal analytical expressions for the spinodal manifolds in N dimensions are derived, which simplify their calculation (by transforming the original problem into inequalities that can be evaluated numerically using linear programming techniques). In addition, a new expression is obtained to calculate the critical manifold and composition of the coexisting phases. The present analytical procedure complements previous attempts to handle spinodal decomposition for many components using a statistical approach based on random matrix theory. The results are relevant for predicting the effects of polydispersity on phase behavior in fields like polymer or food science and liquid-liquid phase separation in the cytosol of living cells.
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Affiliation(s)
- Arjen Bot
- Unilever
Foods Innovation Centre, Bronland 14, NL-6708 WH Wageningen, The Netherlands
- Laboratory
of Physics and Physical Chemistry of Foods, Department of Agrotechnology
and Food Sciences, Wageningen University
and Research, Bornse Weilanden 9, NL-6708 WG Wageningen, The Netherlands
| | - Erik van der Linden
- Laboratory
of Physics and Physical Chemistry of Foods, Department of Agrotechnology
and Food Sciences, Wageningen University
and Research, Bornse Weilanden 9, NL-6708 WG Wageningen, The Netherlands
| | - Paul Venema
- Laboratory
of Physics and Physical Chemistry of Foods, Department of Agrotechnology
and Food Sciences, Wageningen University
and Research, Bornse Weilanden 9, NL-6708 WG Wageningen, The Netherlands
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An Y, Webb MA, Jacobs WM. Active learning of the thermodynamics-dynamics trade-off in protein condensates. SCIENCE ADVANCES 2024; 10:eadj2448. [PMID: 38181073 PMCID: PMC10775998 DOI: 10.1126/sciadv.adj2448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 12/04/2023] [Indexed: 01/07/2024]
Abstract
Phase-separated biomolecular condensates exhibit a wide range of dynamic properties, which depend on the sequences of the constituent proteins and RNAs. However, it is unclear to what extent condensate dynamics can be tuned without also changing the thermodynamic properties that govern phase separation. Using coarse-grained simulations of intrinsically disordered proteins, we show that the dynamics and thermodynamics of homopolymer condensates are strongly correlated, with increased condensate stability being coincident with low mobilities and high viscosities. We then apply an "active learning" strategy to identify heteropolymer sequences that break this correlation. This data-driven approach and accompanying analysis reveal how heterogeneous amino acid compositions and nonuniform sequence patterning map to a range of independently tunable dynamic and thermodynamic properties of biomolecular condensates. Our results highlight key molecular determinants governing the physical properties of biomolecular condensates and establish design rules for the development of stimuli-responsive biomaterials.
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Affiliation(s)
- Yaxin An
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
| | - Michael A. Webb
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
| | - William M. Jacobs
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
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