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Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions. Polymers (Basel) 2022; 14:polym14204421. [PMID: 36297998 PMCID: PMC9612006 DOI: 10.3390/polym14204421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Revised: 10/03/2022] [Accepted: 10/04/2022] [Indexed: 11/17/2022] Open
Abstract
The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters.
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Lin YH, Brady JP, Chan HS, Ghosh K. A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes. J Chem Phys 2020; 152:045102. [PMID: 32007034 DOI: 10.1063/1.5139661] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles. LLPS of neutral homopolymers is quite well described by theory, but it has been a challenge to develop general theories for the LLPS of heteropolymers involving charge-charge interactions. Here, we present a theory that combines a random-phase-approximation treatment of polymer density fluctuations and an account of intrachain conformational heterogeneity based on renormalized Kuhn lengths to provide predictions of LLPS properties as a function of pH, salt, and charge patterning along the chain sequence. Advancing beyond more limited analytical approaches, our LLPS theory is applicable to a wide variety of charged sequences ranging from highly charged polyelectrolytes to neutral or nearly neutral polyampholytes. This theory should be useful in high-throughput screening of protein and other sequences for their LLPS propensities and can serve as a basis for more comprehensive theories that incorporate nonelectrostatic interactions. Experimental ramifications of our theory are discussed.
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Affiliation(s)
- Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Jacob P Brady
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Kingshuk Ghosh
- Department of Physics and Astronomy, University of Denver, Colorado, Colorado 80208, USA
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Molecular design of self-coacervation phenomena in block polyampholytes. Proc Natl Acad Sci U S A 2019; 116:8224-8232. [PMID: 30948640 DOI: 10.1073/pnas.1900435116] [Citation(s) in RCA: 77] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Coacervation is a common phenomenon in natural polymers and has been applied to synthetic materials systems for coatings, adhesives, and encapsulants. Single-component coacervates are formed when block polyampholytes exhibit self-coacervation, phase separating into a dense liquid coacervate phase rich in the polyampholyte coexisting with a dilute supernatant phase, a process implicated in the liquid-liquid phase separation of intrinsically disordered proteins. Using fully fluctuating field-theoretic simulations using complex Langevin sampling and complementary molecular-dynamics simulations, we develop molecular design principles to connect the sequenced charge pattern of a polyampholyte with its self-coacervation behavior in solution. In particular, the lengthscale of charged blocks and number of connections between oppositely charged blocks are shown to have a dramatic effect on the tendency to phase separate and on the accessible chain conformations. The field and particle-based simulation results are compared with analytical predictions from the random phase approximation (RPA) and postulated scaling relationships. The qualitative trends are mostly captured by the RPA, but the approximation fails catastrophically at low concentration.
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Kudaibergenov SE, Nuraje N. Intra- and Interpolyelectrolyte Complexes of Polyampholytes. Polymers (Basel) 2018; 10:E1146. [PMID: 30961071 PMCID: PMC6403860 DOI: 10.3390/polym10101146] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Revised: 10/08/2018] [Accepted: 10/09/2018] [Indexed: 12/12/2022] Open
Abstract
At present, a large amount of research from experimental and theoretical points of view has been done on interpolyelectrolyte complexes formed by electrostatic attractive forces and/or interpolymer complexes stabilized by hydrogen bonds. By contrast, relatively less attention has been given to polymer⁻polymer complex formation with synthetic polyampholytes (PA). In this review the complexation of polyampholytes with polyelectrolytes (PE) is considered from theoretical and application points of view. Formation of intra- and interpolyelectrolyte complexes of random, regular, block, dendritic polyampholytes are outlined. A separate subsection is devoted to amphoteric behavior of interpolyelectrolyte complexes. The realization of the so-called "isoelectric effect" for interpolyelectrolyte complexes of water-soluble polyampholytes, amphoteric hydrogels and cryogels with respect to surfactants, dye molecules, polyelectrolytes and proteins is demonstrated.
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Affiliation(s)
- Sarkyt E Kudaibergenov
- Laboratory of Functional Polymers, Institute of Polymer Materials and Technology, Almaty 050013, Kazakhstan.
| | - Nurxat Nuraje
- Department of Chemical Engineering, Texas Tech University, Lubbock TX 79409-3121, Box 43121, USA.
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Das S, Eisen A, Lin YH, Chan HS. A Lattice Model of Charge-Pattern-Dependent Polyampholyte Phase Separation. J Phys Chem B 2018; 122:5418-5431. [DOI: 10.1021/acs.jpcb.7b11723] [Citation(s) in RCA: 66] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Suman Das
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Adam Eisen
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Mathematics & Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Molecular Medicine, Hospital for Sick Children, Toronto, Ontario M5G 0A4, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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Lin YH, Song J, Forman-Kay JD, Chan HS. Random-phase-approximation theory for sequence-dependent, biologically functional liquid-liquid phase separation of intrinsically disordered proteins. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.09.090] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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Lin YH, Forman-Kay JD, Chan HS. Sequence-Specific Polyampholyte Phase Separation in Membraneless Organelles. PHYSICAL REVIEW LETTERS 2016; 117:178101. [PMID: 27824447 DOI: 10.1103/physrevlett.117.178101] [Citation(s) in RCA: 180] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 05/05/2023]
Abstract
Liquid-liquid phase separation of charge- and/or aromatic-enriched intrinsically disordered proteins (IDPs) is critical in the biological function of membraneless organelles. Much of the physics of this recent discovery remains to be elucidated. Here, we present a theory in the random phase approximation to account for electrostatic effects in polyampholyte phase separations, yielding predictions consistent with recent experiments on the IDP Ddx4. The theory is applicable to any charge pattern and thus provides a general analytical framework for studying sequence dependence of IDP phase separation.
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Affiliation(s)
- Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
- Molecular Structure and Function Program, Hospital for Sick Children, 686 Bay Street, Toronto, Ontario M5G 0A4, Canada
| | - Julie D Forman-Kay
- Department of Biochemistry, University of Toronto, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
- Molecular Structure and Function Program, Hospital for Sick Children, 686 Bay Street, Toronto, Ontario M5G 0A4, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
- Department of Molecular Genetics, University of Toronto, Toronto, 1 King's College Circle, Ontario M5S 1A8, Canada
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Jiang H, Adidharma H. Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: Polyampholyte and polyelectrolyte solutions. J Chem Phys 2014; 141:174906. [DOI: 10.1063/1.4900985] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Arndt MC, Sadowski G. Thermodynamic Model for Polyelectrolyte Hydrogels. J Phys Chem B 2014; 118:10534-42. [DOI: 10.1021/jp501798x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Markus C. Arndt
- Laboratory of Thermodynamics,
Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, Emil-Figge-Str. 70, 44227 Dortmund, Germany
| | - Gabriele Sadowski
- Laboratory of Thermodynamics,
Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, Emil-Figge-Str. 70, 44227 Dortmund, Germany
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Pizio O, Sokołowski S. Restricted primitive model for electrolyte solutions in slit-like pores with grafted chains: Microscopic structure, thermodynamics of adsorption, and electric properties from a density functional approach. J Chem Phys 2013; 138:204715. [DOI: 10.1063/1.4807777] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Borówko M, Sokołowski S, Staszewski T, Sokołowska Z, Ilnytskyi JM. Adsorption of ions on surfaces modified with brushes of polyampholytes. J Chem Phys 2012; 137:074707. [DOI: 10.1063/1.4745200] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
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Hynninen AP, Panagiotopoulos AZ. Simulations of phase transitions and free energies for ionic systems. Mol Phys 2008. [DOI: 10.1080/00268970802112160] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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