1
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Cao Y, Chao Y, Shum HC. Affinity-Controlled Partitioning of Biomolecules at Aqueous Interfaces and Their Bioanalytic Applications. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024:e2409362. [PMID: 39171488 DOI: 10.1002/adma.202409362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2024] [Indexed: 08/23/2024]
Abstract
All-aqueous phase separation systems play essential roles in bioanalytical and biochemical applications. Compared to conventional oil and organic solvent-based systems, these systems are characterized by their rich bulk and interfacial properties, offering superior biocompatibility. In particular, phase separation in all-aqueous systems facilitates the creation of compartments with specific physicochemical properties, and therefore largely enhances the accessibility of the systems. In addition, the all-aqueous compartments have diverse affinities, with an important property known as partitioning, which can concentrate (bio)molecules toward distinct immiscible phases. This partitioning affinity imparts all-aqueous interfaces with selective permeability, enabling the controlled enrichment of target (bio)molecules. This review introduces the basic principles and applications of partitioning-induced interfacial phenomena in a typical all-aqueous system, namely aqueous two-phase systems (ATPSs); these applications include interfacial chemical reactions, bioprinting, and assembly, as well as bio-sensing and detection. The primary challenges associated with designing all-aqueous phase separation systems and several future directions are also discussed, such as the stabilization of aqueous interfaces, the handling of low-volume samples, and exploration of suitable ATPSs compositions with the efficient protocol.
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Affiliation(s)
- Yang Cao
- Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, 999077, China
- Advanced Biomedical Instrumentation Centre, Hong Kong Science Park, Shatin, New Territories, Hong Kong SAR, 999077, China
| | - Youchuang Chao
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China
| | - Ho Cheung Shum
- Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, 999077, China
- Advanced Biomedical Instrumentation Centre, Hong Kong Science Park, Shatin, New Territories, Hong Kong SAR, 999077, China
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2
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Noguchi H, van Wijland F, Fournier JB. Cycling and spiral-wave modes in an active cyclic Potts model. J Chem Phys 2024; 161:025101. [PMID: 38973763 DOI: 10.1063/5.0221050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2024] [Accepted: 06/24/2024] [Indexed: 07/09/2024] Open
Abstract
We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant state cycles via nucleation and growth, while spiral waves are formed at high energy. For large systems, a discontinuous transition occurs from these cyclic homogeneous phases to spiral waves, while the opposite transition is absent. Conversely, these two modes can coexist for small systems. The waves can be reproduced by a continuum theory, and the transition can be understood from the competition between nucleation and growth.
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Affiliation(s)
- Hiroshi Noguchi
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Cité & CNRS, 75013 Paris, France
| | - Jean-Baptiste Fournier
- Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Cité & CNRS, 75013 Paris, France
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3
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Cao Z, Wolynes PG. Motorized chain models of the ideal chromosome. Proc Natl Acad Sci U S A 2024; 121:e2407077121. [PMID: 38954553 PMCID: PMC11252987 DOI: 10.1073/pnas.2407077121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 06/06/2024] [Indexed: 07/04/2024] Open
Abstract
An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.
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Affiliation(s)
- Zhiyu Cao
- Center for Theoretical Biological Physics, Rice University, Houston, TX77005
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Peter G. Wolynes
- Center for Theoretical Biological Physics, Rice University, Houston, TX77005
- Department of Chemistry, Rice University, Houston, TX77005
- Department of Physics, Rice University, Houston, TX77005
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4
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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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5
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Ziethen N, Zwicker D. Heterogeneous nucleation and growth of sessile chemically active droplets. J Chem Phys 2024; 160:224901. [PMID: 38856073 DOI: 10.1063/5.0207761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Accepted: 05/19/2024] [Indexed: 06/11/2024] Open
Abstract
Droplets are essential for spatially controlling biomolecules in cells. To work properly, cells need to control the emergence and morphology of droplets. On the one hand, driven chemical reactions can affect droplets profoundly. For instance, reactions can control how droplets nucleate and how large they grow. On the other hand, droplets coexist with various organelles and other structures inside cells, which could affect their nucleation and morphology. To understand the interplay of these two aspects, we study a continuous field theory of active phase separation. Our numerical simulations reveal that reactions suppress nucleation while attractive walls enhance it. Intriguingly, these two effects are coupled, leading to shapes that deviate substantially from the spherical caps predicted for passive systems. These distortions result from anisotropic fluxes responding to the boundary conditions dictated by the Young-Dupré equation. Interestingly, an electrostatic analogy of chemical reactions confirms these effects. We thus demonstrate how driven chemical reactions affect the emergence and morphology of droplets, which could be crucial for understanding biological cells and improving technical applications, e.g., in chemical engineering.
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Affiliation(s)
- Noah Ziethen
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
| | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
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6
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Chew PY, Joseph JA, Collepardo-Guevara R, Reinhardt A. Aromatic and arginine content drives multiphasic condensation of protein-RNA mixtures. Biophys J 2024; 123:1342-1355. [PMID: 37408305 PMCID: PMC11163273 DOI: 10.1016/j.bpj.2023.06.024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Revised: 06/20/2023] [Accepted: 06/30/2023] [Indexed: 07/07/2023] Open
Abstract
Multiphasic architectures are found ubiquitously in biomolecular condensates and are thought to have important implications for the organization of multiple chemical reactions within the same compartment. Many of these multiphasic condensates contain RNA in addition to proteins. Here, we investigate the importance of different interactions in multiphasic condensates comprising two different proteins and RNA using computer simulations with a residue-resolution coarse-grained model of proteins and RNA. We find that in multilayered condensates containing RNA in both phases, protein-RNA interactions dominate, with aromatic residues and arginine forming the key stabilizing interactions. The total aromatic and arginine content of the two proteins must be appreciably different for distinct phases to form, and we show that this difference increases as the system is driven toward greater multiphasicity. Using the trends observed in the different interaction energies of this system, we demonstrate that we can also construct multilayered condensates with RNA preferentially concentrated in one phase. The "rules" identified can thus enable the design of synthetic multiphasic condensates to facilitate further study of their organization and function.
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Affiliation(s)
- Pin Yu Chew
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Jerelle A Joseph
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey
| | - Rosana Collepardo-Guevara
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom; Department of Physics, University of Cambridge, Cambridge, United Kingdom; Department of Genetics, University of Cambridge, Cambridge, United Kingdom.
| | - Aleks Reinhardt
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom.
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7
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Hegde O, Li T, Sharma A, Borja M, Jacobs WM, Rogers WB. Competition between Self-Assembly and Phase Separation Governs High-Temperature Condensation of a DNA Liquid. PHYSICAL REVIEW LETTERS 2024; 132:208401. [PMID: 38829088 DOI: 10.1103/physrevlett.132.208401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2023] [Revised: 03/21/2024] [Accepted: 04/19/2024] [Indexed: 06/05/2024]
Abstract
In many biopolymer solutions, attractive interactions that stabilize finite-sized clusters at low concentrations also promote phase separation at high concentrations. Here we study a model biopolymer system that exhibits the opposite behavior, whereby self-assembly of DNA oligonucleotides into finite-sized, stoichiometric clusters tends to inhibit phase separation. We first use microfluidics-based experiments to map a novel phase transition in which the oligonucleotides condense as the temperature increases at high concentrations of divalent cations. We then show that a theoretical model of competition between self-assembly and phase separation quantitatively predicts changes in experimental phase diagrams arising from DNA sequence perturbations. Our results point to a general mechanism by which self-assembly shapes phase boundaries in complex biopolymer solutions.
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Affiliation(s)
- Omkar Hegde
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Tianhao Li
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Anjali Sharma
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Marco Borja
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - William M Jacobs
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - W Benjamin Rogers
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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8
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Meng L, Mao S, Lin J. Heterogeneous elasticity drives ripening and controls bursting kinetics of transcriptional condensates. Proc Natl Acad Sci U S A 2024; 121:e2316610121. [PMID: 38489385 PMCID: PMC10962985 DOI: 10.1073/pnas.2316610121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Accepted: 02/10/2024] [Indexed: 03/17/2024] Open
Abstract
Many biomolecular condensates, including transcriptional condensates, are formed in elastic mediums. In this work, we study the nonequilibrium condensate dynamics in a chromatin-like environment modeled as a heterogeneous elastic medium. We demonstrate that the ripening process in such an elastic medium exhibits a temporal power-law scaling of the average condensate radius, depending on the local stiffness distribution and different from Ostwald ripening. Moreover, we incorporate an active process to model the dissolution of transcriptional condensates upon RNA accumulation. Intriguingly, three types of kinetics of condensate growth emerge, corresponding to constitutively expressed, transcriptional-bursting, and silenced genes. Furthermore, the simulated burst frequency decreases exponentially with the local stiffness, through which we infer a lognormal distribution of local stiffness in living cells using the transcriptome-wide distribution of burst frequency. Under the inferred stiffness distribution, the simulated distributions of bursting kinetic parameters agree reasonably well with the experimental data. Our findings reveal the interplay between biomolecular condensates and elastic mediums, yielding far-reaching implications for gene expression.
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Affiliation(s)
- Lingyu Meng
- Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing100871, China
| | - Sheng Mao
- Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing100871, China
| | - Jie Lin
- Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing100871, China
- Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing100871, China
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9
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Kumar A, Safran SA. Fluctuations and Shape Dependence of Microphase Separation in Systems with Long-Range Interactions. PHYSICAL REVIEW LETTERS 2023; 131:258401. [PMID: 38181373 DOI: 10.1103/physrevlett.131.258401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 11/14/2023] [Indexed: 01/07/2024]
Abstract
The combination of phase separation and long-ranged, effective, Coulomb interactions results in microphase separation. We predict the sizes and shapes of such microdomains and uniquely their dependence on the macroscopic sample shape which also affects the effective interfacial tension of fluctuations of the lamellar phase. These are applied to equilibrium salt solutions and block copolymers. Nonequilibrium phase separation in the presence of chemical reactions (e.g., cellular condensates) is mapped to the Coulomb theory to which our predictions apply. In some cases, the effective interfacial tension can be ultralow.
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Affiliation(s)
- Amit Kumar
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Samuel A Safran
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
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10
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Weyer H, Brauns F, Frey E. Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory. Phys Rev E 2023; 108:064202. [PMID: 38243507 DOI: 10.1103/physreve.108.064202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 08/29/2023] [Indexed: 01/21/2024]
Abstract
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.
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Affiliation(s)
- Henrik Weyer
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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11
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Decayeux J, Fries J, Dahirel V, Jardat M, Illien P. Isotropic active colloids: explicit vs. implicit descriptions of propulsion mechanisms. SOFT MATTER 2023; 19:8997-9005. [PMID: 37965908 DOI: 10.1039/d3sm00763d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of activity. Here, we take advantage of a recent two-dimensional model of isotropic active particles whose propulsion originates from the interactions between solute particles in the bath. The colloid catalyzes a chemical reaction in its vicinity, which results in a local phase separation of solute particles, and the density fluctuations of solute particles cause the enhanced diffusion of the colloid. In this paper, we investigate an assembly of such active particles, using (i) an explicit model, where the microscopic dynamics of the solute particles is accounted for; and (ii) an implicit model, whose parameters are inferred from the explicit model at infinite dilution. In the explicit solute model, the long-time diffusion coefficient of the active colloids strongly decreases with density, an effect which is not captured by the derived implicit model. This suggests that classical models, which usually decouple pair interactions from activity, fail to describe collective dynamics in active colloidal systems driven by solute-solute interactions.
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Affiliation(s)
- Jeanne Decayeux
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Jacques Fries
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Vincent Dahirel
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Marie Jardat
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
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12
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Celora GL, Blossey R, Münch A, Wagner B. Counterion-controlled phase equilibria in a charge-regulated polymer solution. J Chem Phys 2023; 159:184902. [PMID: 37942872 DOI: 10.1063/5.0169610] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 10/17/2023] [Indexed: 11/10/2023] Open
Abstract
We study phase equilibria in a minimal model of charge-regulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonation-deprotonation processes in the presence of a dissolved acid, whose anions serve as screening counterions. We explicitly account for variability in the polymers' charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counter-ions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes uni-modal and multi-modal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for non-linear responses to the solution acidity: Re-entrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions.
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Affiliation(s)
- Giulia L Celora
- Department of Mathematics, University College London, 25 Gordon Street, London WC1H 0AY, United Kingdom
| | - Ralf Blossey
- Univ. Lille, CNRS, UMR 8576 - UGSF - Unité de Glycobiologie Structurale et Fonctionnelle, F-59000 Lille, France
| | - Andreas Münch
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Barbara Wagner
- Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany
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13
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Osmanović D, Franco E. Chemical reaction motifs driving non-equilibrium behaviours in phase separating materials. J R Soc Interface 2023; 20:20230117. [PMID: 37907095 PMCID: PMC10618056 DOI: 10.1098/rsif.2023.0117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 10/11/2023] [Indexed: 11/02/2023] Open
Abstract
Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviours of a phase separating system is difficult to fully predict theoretically. In this paper, we analyse a mean field theory coupling CRNs to a combined system of phase separating and non-phase separating materials and analyse how the properties of the CRNs affect different classes of non-equilibrium behaviour: microphase separation or temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by statistical analysis of the Jacobians, of which the most important motifs are negative feedback of the phase separating component and combined inhibition/activation by the non-phase separating components. We then identify CRN motifs that are likely to yield microphase by examining randomly generated networks and parameters. Molecular sequestration of the phase separating motif is shown to be the most robust towards yielding microphase separation. Subsequently, we find that dynamics of the phase separating species is promoted most easily by inducing oscillations in the diffusive components coupled to the phase separating species. Our results provide guidance towards the design of CRNs that manage the formation, dissolution and organization of compartments.
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Affiliation(s)
- Dino Osmanović
- Department of Mechanical and Aerospace Engineering, University of California, Los Angeles 90095, CA, USA
| | - Elisa Franco
- Department of Mechanical and Aerospace Engineering, University of California, Los Angeles 90095, CA, USA
- Department of Bioengineering, University of California, Los Angeles 90095, CA, USA
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14
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Cho Y, Jacobs WM. Nonequilibrium interfacial properties of chemically driven fluids. J Chem Phys 2023; 159:154101. [PMID: 37843057 DOI: 10.1063/5.0166824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 09/26/2023] [Indexed: 10/17/2023] Open
Abstract
Chemically driven fluids can demix to form condensed droplets that exhibit phase behaviors not observed at equilibrium. In particular, nonequilibrium interfacial properties can emerge when the chemical reactions are driven differentially between the interior and exterior of the phase-separated droplets. Here, we use a minimal model to study changes in the interfacial tension between coexisting phases away from equilibrium. Simulations of both droplet nucleation and interface roughness indicate that the nonequilibrium interfacial tension can either be increased or decreased relative to its equilibrium value, depending on whether the driven chemical reactions are accelerated or decelerated within the droplets. Finally, we show that these observations can be understood using a predictive theory based on an effective thermodynamic equilibrium.
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Affiliation(s)
- Yongick Cho
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - William M Jacobs
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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15
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Späth F, Maier AS, Stasi M, Bergmann AM, Halama K, Wenisch M, Rieger B, Boekhoven J. The Role of Chemically Innocent Polyanions in Active, Chemically Fueled Complex Coacervate Droplets. Angew Chem Int Ed Engl 2023; 62:e202309318. [PMID: 37549224 DOI: 10.1002/anie.202309318] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2023] [Revised: 08/04/2023] [Accepted: 08/07/2023] [Indexed: 08/09/2023]
Abstract
Complex coacervation describes the liquid-liquid phase separation of oppositely charged polymers. Active coacervates are droplets in which one of the electrolyte's affinity is regulated by chemical reactions. These droplets are particularly interesting because they are tightly regulated by reaction kinetics. For example, they serve as a model for membraneless organelles that are also often regulated by biochemical transformations such as post-translational modifications. They are also a great protocell model or could be used to synthesize life-they spontaneously emerge in response to reagents, compete, and decay when all nutrients have been consumed. However, the role of the unreactive building blocks, e.g., the polymeric compounds, is poorly understood. Here, we show the important role of the chemically innocent, unreactive polyanion of our chemically fueled coacervation droplets. We show that the polyanion drastically influences the resulting droplets' life cycle without influencing the chemical reaction cycle-either they are very dynamic or have a delayed dissolution. Additionally, we derive a mechanistic understanding of our observations and show how additives and rational polymer design help to create the desired coacervate emulsion life cycles.
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Affiliation(s)
- Fabian Späth
- Department of Chemistry, School of Natural Sciences, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Anton S Maier
- WACKER-Chair of Macromolecular Chemistry, Catalysis Research Center, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Michele Stasi
- Department of Chemistry, School of Natural Sciences, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Alexander M Bergmann
- Department of Chemistry, School of Natural Sciences, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Kerstin Halama
- WACKER-Chair of Macromolecular Chemistry, Catalysis Research Center, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Monika Wenisch
- Department of Chemistry, School of Natural Sciences, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Bernhard Rieger
- WACKER-Chair of Macromolecular Chemistry, Catalysis Research Center, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
| | - Job Boekhoven
- Department of Chemistry, School of Natural Sciences, Technical University of Munich, Lichtenbergstrasse 4, 85748, Garching, Germany
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16
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Häfner G, Müller M. Reaction-driven assembly: controlling changes in membrane topology by reaction cycles. SOFT MATTER 2023; 19:7281-7292. [PMID: 37605887 DOI: 10.1039/d3sm00876b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/23/2023]
Abstract
Chemical reaction cycles are prototypical examples how to drive systems out of equilibrium and introduce novel, life-like properties into soft-matter systems. We report simulations of amphiphilic molecules in aqueous solution. The molecule's head group is permanently hydrophilic, whereas the reaction cycle switches the molecule's tail from hydrophilic (precursor) to hydrophobic (amphiphile) and vice versa. The reaction cycle leads to an arrest in coalescence and results in uniform vesicle sizes that can be controlled by the reaction rate. Using a continuum description and particle-based simulation, we study the scaling of the vesicle size with the reaction rate. The chemically active vesicles are inflated by precursor, imparting tension onto the membrane and, for specific parameters, stabilize pores.
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Affiliation(s)
- Gregor Häfner
- Institute for Theoretical Physics, Georg-August University, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
- Max Planck School Matter to Life, Jahnstraße 29, 69120 Heidelberg, Germany
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
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17
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Lauber N, Tichacek O, Narayanankutty K, De Martino D, Ruiz-Mirazo K. Collective catalysis under spatial constraints: Phase separation and size-scaling effects on mass action kinetics. Phys Rev E 2023; 108:044410. [PMID: 37978605 DOI: 10.1103/physreve.108.044410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
Chemical reactions are usually studied under the assumption that both substrates and catalysts are well-mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the demixing of catalysts could lead to the formation of microenvironments that influence the kinetics of a linear (multistep) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of a collection of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial "hitting times" to reach the catalysts condensate. We finally test this approach by considering open nonlinear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behavior, providing a possible explanation for the marginal role that this complex dynamic behavior plays in real metabolisms.
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Affiliation(s)
- Nino Lauber
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain
- Department of Philosophy, University of the Basque Country, 20018 Donostia-San Sebastian, Spain
| | - Ondrej Tichacek
- Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, 160 00 Prague, Czech Republic
| | - Krishnadev Narayanankutty
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Department of Molecular Biology and Biochemistry, University of the Basque Country, 48940 Leioa, Spain
| | - Daniele De Martino
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Ikerbasque Foundation, 48009 Bilbao, Spain
| | - Kepa Ruiz-Mirazo
- Biofisika Institute (CSIC, UPV/EHU), 48940 Leioa, Spain
- Department of Philosophy, University of the Basque Country, 20018 Donostia-San Sebastian, Spain
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18
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Aslyamov T, Avanzini F, Fodor É, Esposito M. Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability. PHYSICAL REVIEW LETTERS 2023; 131:138301. [PMID: 37832019 DOI: 10.1103/physrevlett.131.138301] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Accepted: 08/30/2023] [Indexed: 10/15/2023]
Abstract
We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out of equilibrium by external chemostats. We find analytically that these instabilities can be of two types: instabilities caused by intermolecular energetic interactions (E type), and instabilities caused by multimolecular out-of-equilibrium chemical reactions (R type). Furthermore, we identify a class of chemical reaction networks, containing unimolecular networks but also extending beyond them, that can only undergo E-type instabilities. We illustrate our analytical findings with numerical simulations on two reaction-diffusion models, each displaying one of the two types of instability and generating stable patterns.
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Affiliation(s)
- Timur Aslyamov
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Francesco Avanzini
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
- Department of Chemical Sciences, University of Padova, Via F. Marzolo, 1, I-35131 Padova, Italy
| | - Étienne Fodor
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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19
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Luo C, Zwicker D. Influence of physical interactions on spatiotemporal patterns. Phys Rev E 2023; 108:034206. [PMID: 37849174 DOI: 10.1103/physreve.108.034206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Accepted: 08/31/2023] [Indexed: 10/19/2023]
Abstract
Spatiotemporal patterns are often modeled using reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusive motion. Such descriptions neglect physical interactions between constituents, which might affect resulting patterns. To overcome this, we study how physical interactions affect cyclic dominant reactions, like the seminal rock-paper-scissors game, which exhibits spiral waves for ideal diffusion. Generalizing diffusion to incorporate physical interactions, we find that weak interactions change the length- and time scales of spiral waves, consistent with a mapping to the complex Ginzburg-Landau equation. In contrast, strong repulsive interactions typically generate oscillating lattices, and strong attraction leads to an interplay of phase separation and chemical oscillations, like droplets co-locating with cores of spiral waves. Our work suggests that physical interactions are relevant for forming spatiotemporal patterns in nature, and it might shed light on how biodiversity is maintained in ecological settings.
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Affiliation(s)
- Chengjie Luo
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
| | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
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20
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Lan C, Kim J, Ulferts S, Aprile-Garcia F, Weyrauch S, Anandamurugan A, Grosse R, Sawarkar R, Reinhardt A, Hugel T. Quantitative real-time in-cell imaging reveals heterogeneous clusters of proteins prior to condensation. Nat Commun 2023; 14:4831. [PMID: 37582808 PMCID: PMC10427612 DOI: 10.1038/s41467-023-40540-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 07/26/2023] [Indexed: 08/17/2023] Open
Abstract
Our current understanding of biomolecular condensate formation is largely based on observing the final near-equilibrium condensate state. Despite expectations from classical nucleation theory, pre-critical protein clusters were recently shown to form under subsaturation conditions in vitro; if similar long-lived clusters comprising more than a few molecules are also present in cells, our understanding of the physical basis of biological phase separation may fundamentally change. Here, we combine fluorescence microscopy with photobleaching analysis to quantify the formation of clusters of NELF proteins in living, stressed cells. We categorise small and large clusters based on their dynamics and their response to p38 kinase inhibition. We find a broad distribution of pre-condensate cluster sizes and show that NELF protein cluster formation can be explained as non-classical nucleation with a surprisingly flat free-energy landscape for a wide range of sizes and an inhibition of condensation in unstressed cells.
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Affiliation(s)
- Chenyang Lan
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- BIOSS and CIBSS Signalling Research Centres, University of Freiburg, Freiburg, Germany
- PicoQuant GmbH, Rudower Chaussee 29, 12489, Berlin, Germany
| | - Juhyeong Kim
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
| | - Svenja Ulferts
- Institute of Experimental and Clinical Pharmacology and Toxicology, University of Freiburg, Freiburg, Germany
| | | | - Sophie Weyrauch
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Spemann Graduate School of Biology and Medicine (SGBM), University of Freiburg, Freiburg, Germany
- Faculty of Chemistry and Pharmacology, University of Freiburg, Freiburg, Germany
| | | | - Robert Grosse
- Institute of Experimental and Clinical Pharmacology and Toxicology, University of Freiburg, Freiburg, Germany
| | - Ritwick Sawarkar
- Medical Research Council (MRC), University of Cambridge, Cambridge, CB2 1QR, United Kingdom
| | - Aleks Reinhardt
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, United Kingdom.
| | - Thorsten Hugel
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany.
- BIOSS and CIBSS Signalling Research Centres, University of Freiburg, Freiburg, Germany.
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21
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Menou L, Luo C, Zwicker D. Physical interactions in non-ideal fluids promote Turing patterns. J R Soc Interface 2023; 20:20230244. [PMID: 37434500 PMCID: PMC10336379 DOI: 10.1098/rsif.2023.0244] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 06/23/2023] [Indexed: 07/13/2023] Open
Abstract
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.
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Affiliation(s)
- Lucas Menou
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, Göttingen 37077, Germany
| | - Chengjie Luo
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, Göttingen 37077, Germany
| | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, Göttingen 37077, Germany
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22
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Ziethen N, Kirschbaum J, Zwicker D. Nucleation of Chemically Active Droplets. PHYSICAL REVIEW LETTERS 2023; 130:248201. [PMID: 37390433 DOI: 10.1103/physrevlett.130.248201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 05/10/2023] [Indexed: 07/02/2023]
Abstract
Driven chemical reactions can control the macroscopic properties of droplets, like their size. Such active droplets are critical in structuring the interior of biological cells. Cells also need to control where and when droplets appear, so they need to control droplet nucleation. Our numerical simulations demonstrate that reactions generally suppress nucleation if they stabilize the homogeneous state. An equilibrium surrogate model reveals that reactions increase the effective energy barrier of nucleation, enabling quantitative predictions of the increased nucleation times. Moreover, the surrogate model allows us to construct a phase diagram, which summarizes how reactions affect the stability of the homogeneous phase and the droplet state. This simple picture provides accurate predictions of how driven reactions delay nucleation, which is relevant for understanding droplets in biological cells and chemical engineering.
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Affiliation(s)
- Noah Ziethen
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17 37077, Göttingen, Germany
| | - Jan Kirschbaum
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17 37077, Göttingen, Germany
| | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17 37077, Göttingen, Germany
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23
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Goychuk A, Kannan D, Chakraborty AK, Kardar M. Polymer folding through active processes recreates features of genome organization. Proc Natl Acad Sci U S A 2023; 120:e2221726120. [PMID: 37155885 PMCID: PMC10194017 DOI: 10.1073/pnas.2221726120] [Citation(s) in RCA: 17] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 04/02/2023] [Indexed: 05/10/2023] Open
Abstract
From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.
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Affiliation(s)
- Andriy Goychuk
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Deepti Kannan
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Arup K. Chakraborty
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139
- Ragon Institute of Massachusetts General Hospital, Massachusetts Institute of Technology and Harvard University, Cambridge, MA02139
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
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24
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Demarchi L, Goychuk A, Maryshev I, Frey E. Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence. PHYSICAL REVIEW LETTERS 2023; 130:128401. [PMID: 37027840 DOI: 10.1103/physrevlett.130.128401] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 02/03/2023] [Indexed: 06/19/2023]
Abstract
Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.
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Affiliation(s)
- Leonardo Demarchi
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Ivan Maryshev
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 München, Germany
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25
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Cho Y, Jacobs WM. Tuning Nucleation Kinetics via Nonequilibrium Chemical Reactions. PHYSICAL REVIEW LETTERS 2023; 130:128203. [PMID: 37027881 DOI: 10.1103/physrevlett.130.128203] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Accepted: 02/21/2023] [Indexed: 06/19/2023]
Abstract
Unlike fluids at thermal equilibrium, biomolecular mixtures in living systems can sustain nonequilibrium steady states, in which active processes modify the conformational states of the constituent molecules. Despite qualitative similarities between liquid-liquid phase separation in these systems, the extent to which the phase-separation kinetics differ remains unclear. Here we show that inhomogeneous chemical reactions can alter the nucleation kinetics of liquid-liquid phase separation in a manner that is consistent with classical nucleation theory, but can only be rationalized by introducing a nonequilibrium interfacial tension. We identify conditions under which nucleation can be accelerated without changing the energetics or supersaturation, thus breaking the correlation between fast nucleation and strong driving forces that is typical of phase separation and self-assembly at thermal equilibrium.
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Affiliation(s)
- Yongick Cho
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - William M Jacobs
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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