1
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An Y, Gao T, Wang T, Zhang D, Bharti B. Effects of charge asymmetry on the liquid-liquid phase separation of polyampholytes and their condensate properties. SOFT MATTER 2024. [PMID: 39044475 DOI: 10.1039/d4sm00532e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/25/2024]
Abstract
Liquid-liquid phase separation (LLPS) is the mechanism underlying the formation of bio-molecular condensates which are important compartments regulating intra- and extra-cellular functions. Electrostatic interactions are some of the important driving forces of the LLPS behaviors of biomolecules. However, the understanding of the electrostatic interactions is still limited, especially in the mixtures of biomolecules with different charge patterns. Here, we focus on the electrostatic interactions in mixtures of charge-asymmetric and charge-symmetric polyampholytes and their roles in the phase separation behaviors. We build charge-asymmetric and charge-symmetric model proteins consisting of both glutamic acid (E, negatively charged) and lysine (K, positively charged), i.e. polyampholytes of E35K15 (charge asymmetric) and E25K25 (charge symmetric). Pure E25K25 can undergo LLPS. To investigate the effects of charge-asymmetric polyampholytes on the mixtures of E25K25/E35K15, we perform coarse-grained simulations to determine their phase separation. The charge-asymmetric polyampholyte E35K15 is resistant to the LLPS of the mixtures of E25K25/E35K15. The condensate density decreases with the molar fraction of E35K15 increasing to 0.4, and no LLPS occurs at the molar fraction of 0.5 and above. This can be attributed to the electrostatic repulsion between the negatively charged E35K15 polymers. We further investigate the effects of charge asymmetry on the conformations and properties of the condensates. The E35K15 polymers in the condensates exhibit a more collapsed state as the molar fraction of E35K15 increases. However, the conformation of E25K25 polymers changes slightly across different condensates. The surface tensions of condensates decline with the increase of the molar fraction of E35K15 polymers, while the diffusivity of polymers in the condensed phases is enhanced. This work elucidates the role of charge-asymmetric polyampholytes in determining the LLPS behaviours of binary mixtures of charge-symmetric and charge-asymmetric proteins as well as the properties of condensed phases.
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Affiliation(s)
- Yaxin An
- Department of Chemical Engineering, Louisiana State University, USA.
| | - Tong Gao
- Department of Chemical Engineering, Louisiana State University, USA.
| | - Tianyi Wang
- Department of Chemical Engineering, Louisiana State University, USA.
| | - Donghui Zhang
- Department of Chemistry, Louisiana State University, USA
| | - Bhuvnesh Bharti
- Department of Chemical Engineering, Louisiana State University, USA.
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2
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Dinic J, Tirrell MV. Effects of Charge Sequence Pattern and Lysine-to-Arginine Substitution on the Structural Stability of Bioinspired Polyampholytes. Biomacromolecules 2024; 25:2838-2851. [PMID: 38567844 PMCID: PMC11094733 DOI: 10.1021/acs.biomac.4c00002] [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] [Received: 01/01/2024] [Revised: 03/17/2024] [Accepted: 03/18/2024] [Indexed: 05/14/2024]
Abstract
A comprehensive study focusing on the combined influence of the charge sequence pattern and the type of positively charged amino acids on the formation of secondary structures in sequence-specific polyampholytes is presented. The sequences of interest consisting exclusively of ionizable amino acids (lysine, K; arginine, R; and glutamic acid, E) are (EKEK)5, (EKKE)5, (ERER)5, (ERRE)5, and (EKER)5. The stability of the secondary structure was examined at three pH values in the presence of urea and NaCl. The results presented here underscore the combined prominent effects of the charge sequence pattern and the type of positively charged monomers on secondary structure formation. Additionally, (ERRE)5 readily aggregated across a wide range of pH. In contrast, sequences with the same charge pattern, (EKKE)5, as well as the sequences with the equivalent amino acid content, (ERER)5, exhibited no aggregate formation under equivalent pH and concentration conditions.
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Affiliation(s)
- Jelena Dinic
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60637, United States
- Center
for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Matthew V. Tirrell
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60637, United States
- Center
for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
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3
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Sementa D, Dave D, Fisher RS, Wang T, Elbaum-Garfinkle S, Ulijn RV. Sequence-Tunable Phase Behavior and Intrinsic Fluorescence in Dynamically Interacting Peptides. Angew Chem Int Ed Engl 2023; 62:e202311479. [PMID: 37934145 DOI: 10.1002/anie.202311479] [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: 08/09/2023] [Revised: 10/31/2023] [Accepted: 11/06/2023] [Indexed: 11/08/2023]
Abstract
A conceptual framework towards understanding biological condensed phases is emerging, derived from biological, biomimetic, and synthetic sequences. However, de novo peptide condensate design remains a challenge due to an incomplete understanding of the structural and interactive complexity. We designed peptide modules based on a simple repeat motif composed of tripeptide spacers (GSG, SGS, GLG) interspersed with adhesive amino acids (R/H and Y). We show, using sequence editing and a combination of computation and experiment, that n→π* interactions in GLG backbones are a dominant factor in providing sufficient backbone structure, which in turn regulates the water interface, collectively promoting liquid droplet formation. Moreover, these R(GLG)Y and H(GLG)Y condensates unexpectedly display sequence-dependent emission that is a consequence of their non-covalent network interactions, and readily observable by confocal microscopy.
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Affiliation(s)
- Deborah Sementa
- Advanced Science Research Center (ASRC) at the Graduate Center, City University of New York (CUNY), 85 St Nicholas Terrace, New York, NY 10031, USA
| | - Dhwanit Dave
- Advanced Science Research Center (ASRC) at the Graduate Center, City University of New York (CUNY), 85 St Nicholas Terrace, New York, NY 10031, USA
- Ph.D. Programs in Biochemistry and Chemistry, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA
- Department of Chemistry, Hunter College, City University of New York (CUNY), 695 Park Avenue, New York, NY 10065, USA
| | - Rachel S Fisher
- Advanced Science Research Center (ASRC) at the Graduate Center, City University of New York (CUNY), 85 St Nicholas Terrace, New York, NY 10031, USA
| | - Tong Wang
- Advanced Science Research Center (ASRC) at the Graduate Center, City University of New York (CUNY), 85 St Nicholas Terrace, New York, NY 10031, USA
| | - Shana Elbaum-Garfinkle
- Advanced Science Research Center (ASRC) at the Graduate Center, City University of New York (CUNY), 85 St Nicholas Terrace, New York, NY 10031, USA
| | - Rein V Ulijn
- Advanced Science Research Center (ASRC) at the Graduate Center, City University of New York (CUNY), 85 St Nicholas Terrace, New York, NY 10031, USA
- Ph.D. Programs in Biochemistry and Chemistry, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA
- Department of Chemistry, Hunter College, City University of New York (CUNY), 695 Park Avenue, New York, NY 10065, USA
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4
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Lee NK, Chae MK, Jung Y, Johner A, Joanny JF. Polyelectrolytes: From Seminal Works to the Influence of the Charge Sequence. Polymers (Basel) 2023; 15:4593. [PMID: 38232020 PMCID: PMC10708673 DOI: 10.3390/polym15234593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Revised: 11/19/2023] [Accepted: 11/27/2023] [Indexed: 01/19/2024] Open
Abstract
We propose a selected tour of the physics of polyelectrolytes (PE) following the line initiated by de Gennes and coworkers in their seminal 1976 paper. The early works which used uniform charge distributions along the PE backbone achieved tremendous progress and set most milestones in the field. Recently, the focus has shifted to the role of the charge sequence. Revisited topics include PE complexation and polyampholytes (PA). We develop the example of a random PE in poor solvent forming pearl-necklace structures. It is shown that the pearls typically adopt very asymmetric mass and charge distributions. Individual sequences do not necessarily reflect the ensemble statistics and a rich variety of behaviors emerges (specially for PA). Pearl necklaces are dynamic structures and switch between various types of pearl-necklace structures, as described for both PE and PA.
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Affiliation(s)
- Nam-Kyung Lee
- Department of Physics and Astronomy, Sejong University, Seoul 05006, Republic of Korea;
| | - Min-Kyung Chae
- National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea;
| | - Youngkyun Jung
- Supercomputing Center, Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea;
| | - Albert Johner
- Institut Charles Sadron CNRS-Unistra, 6 rue Boussingault, 67083 Strasbourg, France
| | - Jean-Francois Joanny
- Institut Curie, Physique des cellules et Cancer, Collège de France Soft Matter and Biophysics Chair, 11, PSL University, Place Marcelin-Berthelot, 75231 Paris, France;
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5
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Quah T, Delaney KT, Fredrickson GH. Assessment of the partial saddle point approximation in field-theoretic polymer simulations. J Chem Phys 2023; 159:164103. [PMID: 37873956 DOI: 10.1063/5.0173047] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Accepted: 10/06/2023] [Indexed: 10/25/2023] Open
Abstract
Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a "sign problem" associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the sign problem. Although CL is exact in principle, it can be difficult to stabilize in strongly fluctuating systems. An alternate approach for blends or block copolymers with two segment species is to make a "partial saddle point approximation" (PSPA) in which the stiff pressure-like field is constrained to its mean-field value, eliminating the sign problem in the remaining field theory, allowing for traditional (real) sampling methods. The consequences of the PSPA are relatively unknown, and direct comparisons between the two methods are limited. Here, we quantitatively compare thermodynamic observables, order-disorder transitions, and periodic domain sizes predicted by the two approaches for a weakly compressible model of AB diblock copolymers. Using Gaussian fluctuation analysis, we validate our simulation observations, finding that the PSPA incorrectly captures trends in fluctuation corrections to certain thermodynamic observables, microdomain spacing, and location of order-disorder transitions. For incompressible models with contact interactions, we find similar discrepancies between the predictions of CL and PSPA, but these can be minimized by regularization procedures such as Morse calibration. These findings mandate caution in applying the PSPA to broader classes of soft-matter models and systems.
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Affiliation(s)
- Timothy Quah
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Glenn H Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
- Materials Department, University of California, Santa Barbara, California 93106, USA
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6
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Jedlinska ZM, Riggleman RA. The effect of monomer polarizability on the stability and salt partitioning in model coacervates. SOFT MATTER 2023; 19:7000-7010. [PMID: 37668019 DOI: 10.1039/d3sm00706e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/06/2023]
Abstract
Coacervation of charged polymer chains has been a topic of major interest in both polymer and biological sciences, as it is a subset of a phenomenon called liquid-liquid phase separation (LLPS). In this process the polymer-rich phase separates from the polymer-lean supernatant while still maintaining its liquid-like properties. LLPS has been shown to play a crucial role in cellular homeostasis by driving the formation of membraneless organelles. It also has the potential to be harnessed to aid in novel therapeutical applications. Recent studies have demonstrated that there is no one simple mechanism which drives LLPS, which is instead a result of the combined effect of electrostatic, dipolar, hydrophobic, and other weak interactions. Using coarse-grained polymer simulations we investigate the relatively unexplored effects of monomer polarizability and spatially varying dielectric constant on LLPS propensity, and these factors affect the properties of the resulting condensates. In order to produce spatial variations in the dielectric constant, all our simulations include explicit solvent and counterions. We demonstrate that polarizability has only a minor effect on the bulk behaviour of the condensates but plays a major role when ion partitioning and microstructure are considered. We observe that the major contribution comes from the nature of the neutral blocks as endowing them with an induced dipole changes their character from hydrophobic to hydrophilic. We hypothesize that the results of this work can aid in guiding future studies concerned with LLPS by providing a general framework and by highlighting important factors which influence LLPS.
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Affiliation(s)
- Zuzanna M Jedlinska
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, USA
| | - Robert A Riggleman
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, USA.
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7
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Sinha NJ, Cunha KC, Murphy R, Hawker CJ, Shea JE, Helgeson ME. Competition between β-Sheet and Coacervate Domains Yields Diverse Morphologies in Mixtures of Oppositely Charged Homochiral Polypeptides. Biomacromolecules 2023; 24:3580-3588. [PMID: 37486022 DOI: 10.1021/acs.biomac.3c00361] [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: 07/25/2023]
Abstract
Biomolecular assembly processes involving competition between specific intermolecular interactions and thermodynamic phase instability have been implicated in a number of pathological states and technological applications of biomaterials. As a model for such processes, aqueous mixtures of oppositely charged homochiral polypeptides such as poly-l-lysine and poly-l-glutamic acid have been reported to form either β-sheet-rich solid-like precipitates or liquid-like coacervate droplets depending on competing hydrogen bonding interactions. Herein, we report studies of polypeptide mixtures that reveal unexpectedly diverse morphologies ranging from partially coalescing and aggregated droplets to bulk precipitates, as well as a previously unreported re-entrant liquid-liquid phase separation at high polypeptide concentration and ionic strength. Combining our experimental results with all-atom molecular dynamics simulations of folded polypeptide complexes reveals a concentration dependence of β-sheet-rich secondary structure, whose relative composition correlates with the observed macroscale morphologies of the mixtures. These results elucidate a crucial balance of interactions that are important for controlling morphology during coacervation in these and potentially similar biologically relevant systems.
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Affiliation(s)
- Nairiti J Sinha
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, United States
- Materials Department and Materials Research Laboratory, University of California Santa Barbara, Santa Barbara, California 93106, United States
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Keila Cristina Cunha
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Robert Murphy
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Craig J Hawker
- Materials Department and Materials Research Laboratory, University of California Santa Barbara, Santa Barbara, California 93106, United States
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Matthew E Helgeson
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, United States
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8
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Lequieu J. Combining particle and field-theoretic polymer models with multi-representation simulations. J Chem Phys 2023; 158:244902. [PMID: 37377157 DOI: 10.1063/5.0153104] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Accepted: 05/30/2023] [Indexed: 06/29/2023] Open
Abstract
Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.
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Affiliation(s)
- Joshua Lequieu
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA
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9
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Shi WH, Adhikari RS, Asthagiri DN, Marciel AB. Influence of Charge Block Length on Conformation and Solution Behavior of Polyampholytes. ACS Macro Lett 2023; 12:195-200. [PMID: 36695540 DOI: 10.1021/acsmacrolett.2c00665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
We investigate the effect of charge block length on polyampholyte chain conformation and phase behavior using small-angle X-ray scattering (SAXS) and implicit-solvent molecular simulations. To this end, we use solid phase peptide synthesis to precision-tailor a series of polyampholytes consisting of l-glutamic acid (E) and l-lysine (K) monomers arranged in alternating blocks from 2 to 16 monomers. We observe that the polyampholytes tend to phase separate as block size increases. With addition of NaCl, phase separated polyampholytes exhibit a salting-in effect dependent on charge block length. Fourier-transform infrared (FTIR) spectroscopy reveals the presence of intramolecular hydrogen bonds that are disrupted upon the addition of NaCl, implicating both electrostatic interactions and hydrogen bonding in the phase behavior. SAXS spectra at no-added salt conditions show minimal dependence of charge block length on the radius of gyration (Rg) for soluble polyampholytes, but local chain stiffening is found to be dependent on charge block length. With increasing NaCl, consistent with electrostatic screening, all polyampholytes expand and behave as neutral or swollen chains in good solvent conditions. Molecular simulations are qualitatively consistent with experiments. Implications for understanding intracellular condensates and material design are noted.
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Affiliation(s)
- Winnie H Shi
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas77005, United States
| | - Rohan S Adhikari
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas77005, United States
| | | | - Amanda B Marciel
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas77005, United States
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10
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Chae MK, Lee NK, Jung Y, Johner A. Shape Fluctuations of Random Polyampholyte and Intrinsically Disordered Protein Sequences. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Min-Kyung Chae
- Department of Physics and Astronomy, Sejong University, Seoul05006, Korea
- National Institute for Mathematical Sciences, Daejeon34047, South Korea
| | - Nam-Kyung Lee
- Department of Physics and Astronomy, Sejong University, Seoul05006, Korea
| | - Youngkyun Jung
- Supercomputing Center, Korea Institute of Science and Technology Information, Daejeon34141, Korea
| | - Albert Johner
- Institut Charles Sadron CNRS─Unistra, Universite de Strasbourg, F-67000Strasbourg, France
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11
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Lin YH, Wessén J, Pal T, Das S, Chan HS. Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins. Methods Mol Biol 2023; 2563:51-94. [PMID: 36227468 DOI: 10.1007/978-1-0716-2663-4_3] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.
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Affiliation(s)
- Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
- Molecular Medicine, Hospital for Sick Children, Toronto, ON, Canada
| | - Jonas Wessén
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
| | - Tanmoy Pal
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada.
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12
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Najafi S, McCarty J, Delaney KT, Fredrickson GH, Shea JE. Field-Theoretic Simulation Method to Study the Liquid-Liquid Phase Separation of Polymers. Methods Mol Biol 2023; 2563:37-49. [PMID: 36227467 DOI: 10.1007/978-1-0716-2663-4_2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Liquid-liquid phase separation (LLPS) is a process that results in the formation of a polymer-rich liquid phase coexisting with a polymer-depleted liquid phase. LLPS plays a critical role in the cell through the formation of membrane-less organelles, but it also has a number of biotechnical and biomedical applications such as drug confinement and its targeted delivery. In this chapter, we present a computational efficient methodology that uses field-theoretic simulations (FTS) with complex Langevin (CL) sampling to characterize polymer phase behavior and delineate the LLPS phase boundaries. This approach is a powerful complement to analytical and explicit-particle simulations, and it can serve to inform experimental LLPS studies. The strength of the method lies in its ability to properly sample a large ensemble of polymers in a saturated solution while including the effect of composition fluctuations on LLPS. We describe the approaches that can be used to accurately construct phase diagrams of a variety of molecularly designed polymers and illustrate the method by generating an approximation-free phase diagram for a classical symmetric diblock polyampholyte.
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Affiliation(s)
- Saeed Najafi
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA, USA
- Materials Research Laboratory, University of California, Santa Barbara, CA, USA
| | - James McCarty
- Department of Chemistry, Western Washington University, Bellingham, WA, USA
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, CA, USA
| | - Glenn H Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, CA, USA
- Department of Chemical Engineering, University of California, Santa Barbara, CA, USA
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA, USA.
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
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13
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Laghmach R, Malhotra I, Potoyan DA. Multiscale Modeling of Protein-RNA Condensation in and Out of Equilibrium. Methods Mol Biol 2023; 2563:117-133. [PMID: 36227470 PMCID: PMC11186142 DOI: 10.1007/978-1-0716-2663-4_5] [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] [Indexed: 06/16/2023]
Abstract
A vast number of intracellular membraneless bodies also known as biomolecular condensates form through a liquid-liquid phase separation (LLPS) of biomolecules. To date, phase separation has been identified as the main driving force for a membraneless organelles such as nucleoli, Cajal bodies, stress granules, and chromatin compartments. Recently, the protein-RNA condensation is receiving increased attention, because it is closely related to the biological function of cells such as transcription, translation, and RNA metabolism. Despite the multidisciplinary efforts put forth to study the biophysical properties of protein-RNA condensates, there are many fundamental unanswered questions regarding the mechanism of formation and regulation of protein-RNA condensates in eukaryotic cells. Major challenges in studying protein-RNA condensation stem from (i) the molecular heterogeneity and conformational flexibility of RNA and protein chains and (ii) the nonequilibrium nature of transcription and cellular environment. Computer simulations, bioinformatics, and mathematical models are uniquely positioned for shedding light on the microscopic nature of protein-RNA phase separation. To this end, there is an urgent need for innovative models with the right spatiotemporal resolution for confronting the experimental observables in a comprehensive and physics-based manner. In this chapter, we will summarize the currently emerging research efforts, which employ atomistic and coarse-grained molecular models and field theoretical models to understand equilibrium and nonequilibrium aspects of protein-RNA condensation.
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Affiliation(s)
- Rabia Laghmach
- Department of Chemistry, Iowa State University, Ames, IA, USA
| | - Isha Malhotra
- Department of Chemistry, Iowa State University, Ames, IA, USA
| | - Davit A Potoyan
- Department of Chemistry, Iowa State University, Ames, IA, USA.
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14
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Chen X, Chen EQ, Yang S. Multiphase Coacervation of Polyelectrolytes Driven by Asymmetry of Charged Sequence. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Xu Chen
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, China
| | - Er-Qiang Chen
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, China
| | - Shuang Yang
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, China
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15
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Wessén J, Das S, Pal T, Chan HS. Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions. J Phys Chem B 2022; 126:9222-9245. [PMID: 36343363 DOI: 10.1021/acs.jpcb.2c06181] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.
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Affiliation(s)
- 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
| | - Tanmoy Pal
- 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
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16
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Nguyen M, Sherck N, Shen K, Edwards CER, Yoo B, Köhler S, Speros JC, Helgeson ME, Delaney KT, Shell MS, Fredrickson GH. Predicting Polyelectrolyte Coacervation from a Molecularly Informed Field-Theoretic Model. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- My Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Kevin Shen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Chelsea E. R. Edwards
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - Brian Yoo
- BASF Corporation, Tarrytown, New York 10591, United States
| | | | - Joshua C. Speros
- California Research Alliance (CARA) by BASF, Berkeley, California 94720, United States
| | - Matthew E. Helgeson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
- Department of Materials, University of California, Santa Barbara, California 93106, United States
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17
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Le ML, Grzetic DJ, Delaney KT, Yang KC, Xie S, Fredrickson GH, Chabinyc ML, Segalman RA. Electrostatic Interactions Control the Nanostructure of Conjugated Polyelectrolyte–Polymeric Ionic Liquid Blends. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- My Linh Le
- Materials Department, University of California, Santa Barbara, California 93106, United States
| | - Douglas J. Grzetic
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Kai-Chieh Yang
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Shuyi Xie
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Materials Department, University of California, Santa Barbara, California 93106, United States
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Michael L. Chabinyc
- Materials Department, University of California, Santa Barbara, California 93106, United States
| | - Rachel A. Segalman
- Materials Department, University of California, Santa Barbara, California 93106, United States
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
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18
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Dinic J, Schnorenberg MR, Tirrell MV. Sequence-Controlled Secondary Structures and Stimuli Responsiveness of Bioinspired Polyampholytes. Biomacromolecules 2022; 23:3798-3809. [PMID: 35969881 DOI: 10.1021/acs.biomac.2c00666] [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: 11/28/2022]
Abstract
A comprehensive study focusing on the influence of the sequence charge pattern on the secondary structure preferences of annealed polyampholytes and their responsiveness to external stimuli is presented. Two sequences are designed composed entirely of ionizable amino acids (charge fraction, f = 1) and an equal number of positive and negative charges (f+ = f- = 0.5) with distinct charge patterns consisting of lysine and glutamic acid monomers. The study reveals that the sequence charge pattern has a significant influence on the secondary structure preferences of polyampholytes at physiological pH. Furthermore, it shows that external stimuli such as pH, ionic strength, and solvent dielectric constant can be used to modulate the secondary structure of the two studied sequences. The observed secondary structure transformations for the two sequences are also substantially different from those determined for uniformly charged homo-polypeptides under matching conditions.
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Affiliation(s)
- Jelena Dinic
- Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Mathew R Schnorenberg
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew V Tirrell
- Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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19
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Abstract
There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.
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20
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Rumyantsev AM, Johner A, Tirrell MV, de Pablo JJ. Unifying Weak and Strong Charge Correlations within the Random Phase Approximation: Polyampholytes of Various Sequences. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00569] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Artem M. Rumyantsev
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Albert Johner
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, Strasbourg 67034, France
| | - Matthew V. Tirrell
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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21
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Sahoo A, Lee PY, Matysiak S. Transferable and Polarizable Coarse Grained Model for Proteins─ProMPT. J Chem Theory Comput 2022; 18:5046-5055. [PMID: 35793442 DOI: 10.1021/acs.jctc.2c00269] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The application of classical molecular dynamics (MD) simulations at atomic resolution (fine-grained level, FG), to most biomolecular processes, remains limited because of the associated computational complexity of representing all the atoms. This problem is magnified in the presence of protein-based biomolecular systems that have a very large conformational space, and MD simulations with fine-grained resolution have slow dynamics to explore this space. Current transferable coarse grained (CG) force fields in literature are either limited to only peptides with the environment encoded in an implicit form or cannot capture transitions into secondary/tertiary peptide structures from a primary sequence of amino acids. In this work, we present a transferable CG force field with an explicit representation of the environment for accurate simulations with proteins. The force field consists of a set of pseudoatoms representing different chemical groups that can be joined/associated together to create different biomolecular systems. This preserves the transferability of the force field to multiple environments and simulation conditions. We have added electronic polarization that can respond to environmental heterogeneity/fluctuations and couple it to protein's structural transitions. The nonbonded interactions are parametrized with physics-based features such as solvation and partitioning free energies determined by thermodynamic calculations and matched with experiments and/or atomistic simulations. The bonded potentials are inferred from corresponding distributions in nonredundant protein structure databases. We present validations of the CG model with simulations of well-studied aqueous protein systems with specific protein fold types─Trp-cage, Trpzip4, villin, WW-domain, and β-α-β. We also explore the applications of the force field to study aqueous aggregation of Aβ 16-22 peptides.
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Affiliation(s)
- Abhilash Sahoo
- Biophysics Program, University of Maryland, College Park, Maryland 20742, United States
| | - Pei-Yin Lee
- Chemical Physics Program, University of Maryland, College Park, Maryland 20742, United States
| | - Silvina Matysiak
- Fischell Department of Bioengineering, University of Maryland, College Park, Maryland 20742, United States
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22
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Weyman A, Mavrantzas VG, Öttinger HC. Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations. J Chem Phys 2022; 156:224115. [PMID: 35705412 DOI: 10.1063/5.0090333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We discuss the functional inverse problem in field-theoretic simulations for realistic pairwise potentials such as the Morse potential (widely used in particle simulations as an alternative to the 12-6 Lennard-Jones one), and we propose the following two solutions: (a) a numerical one based on direct inversion on a regular grid or deconvolution and (b) an analytical one by expressing attractive and repulsive contributions to the Morse potential as higher-order derivatives of the Dirac delta function; the resulting system of ordinary differential equations in the saddle-point approximation is solved numerically with appropriate model-consistent boundary conditions using a Newton-Raphson method. For the first time, exponential-like, physically realistic pair interactions are analytically treated and incorporated into a field-theoretic framework. The advantages and disadvantages of the two approaches are discussed in detail in connection with numerical findings from test simulations for the radial distribution function of a monatomic fluid at realistic densities providing direct evidence for the capability of the analytical method to resolve structural features down to the Angstrom scale.
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Affiliation(s)
- Alexander Weyman
- Polymer Physics, Department of Materials, ETH Zürich, CH-8093 Zurich, Switzerland
| | - Vlasis G Mavrantzas
- Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, CH-8092 Zurich, Switzerland
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23
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Chen S, Zhang P, Wang ZG. Complexation between Oppositely Charged Polyelectrolytes in Dilute Solution: Effects of Charge Asymmetry. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00339] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Shensheng Chen
- Division of Chemistry and Chemical Engineering, California Institute of Technology, 1200 E California Blvd., Pasadena, California 91125, United States
| | - Pengfei Zhang
- State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Center for Advanced Low-Dimension Materials, College of Materials and Engineering, Donghua University, Shanghai 201620, China
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, 1200 E California Blvd., Pasadena, California 91125, United States
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24
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Ghosh K, Huihui J, Phillips M, Haider A. Rules of Physical Mathematics Govern Intrinsically Disordered Proteins. Annu Rev Biophys 2022; 51:355-376. [PMID: 35119946 PMCID: PMC9190209 DOI: 10.1146/annurev-biophys-120221-095357] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.
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Affiliation(s)
- Kingshuk Ghosh
- Department of Physics and Astronomy, University of Denver, Denver, Colorado, USA,Molecular and Cellular Biophysics Program, University of Denver, Denver, Colorado, USA
| | - Jonathan Huihui
- Department of Physics and Astronomy, University of Denver, Denver, Colorado, USA
| | - Michael Phillips
- Department of Physics and Astronomy, University of Denver, Denver, Colorado, USA
| | - Austin Haider
- Molecular and Cellular Biophysics Program, University of Denver, Denver, Colorado, USA
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25
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Wessén J, Pal T, Chan HS. Field theory description of ion association in re-entrant phase separation of polyampholytes. J Chem Phys 2022; 156:194903. [DOI: 10.1063/5.0088326] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion-pairs through an association reaction. A field theory description of the system, that treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is hereby given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently show evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion-association. As an illustration of the ramifications of our theoretical framework, several polyampholyte concentration vs ion concentration phase diagrams under constant temperature conditions are presented to elucidate the dependence of phase separation behavior on polyampholyte sequence charge pattern as well as ion-pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.
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Affiliation(s)
- Jonas Wessén
- Department of Biochemsitry, University of Toronto, Canada
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26
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Madinya JJ, Sing CE. Hybrid Field Theory and Particle Simulation Model of Polyelectrolyte–Surfactant Coacervation. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00187] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Jason J. Madinya
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, 600 S. Matthews Ave., Urbana, Illinois 61820, United States
| | - Charles E. Sing
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, 600 S. Matthews Ave., Urbana, Illinois 61820, United States
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27
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Nilsson D, Bozorg B, Mohanty S, Söderberg B, Irbäck A. Limitations of field-theory simulation for exploring phase separation: The role of repulsion in a lattice protein model. J Chem Phys 2022; 156:015101. [PMID: 34998327 DOI: 10.1063/5.0070412] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid-liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.
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Affiliation(s)
- Daniel Nilsson
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Behruz Bozorg
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Sandipan Mohanty
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Bo Söderberg
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Anders Irbäck
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
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28
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Ylitalo AS, Balzer C, Zhang P, Wang ZG. Electrostatic Correlations and Temperature-Dependent Dielectric Constant Can Model LCST in Polyelectrolyte Complex Coacervation. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c02000] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Andrew S. Ylitalo
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Christopher Balzer
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Pengfei Zhang
- State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Center for Advanced Low-Dimension Materials, College of Material Science and Engineering, Donghua University, Shanghai 201620, China
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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29
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Abstract
Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples-random charge densities and periodic charge densities-with different scaling properties. Under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.
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Affiliation(s)
- Kevin S Silmore
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Rajeev Kumar
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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30
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Sinha NJ, Langenstein MG, Pochan DJ, Kloxin CJ, Saven JG. Peptide Design and Self-assembly into Targeted Nanostructure and Functional Materials. Chem Rev 2021; 121:13915-13935. [PMID: 34709798 DOI: 10.1021/acs.chemrev.1c00712] [Citation(s) in RCA: 85] [Impact Index Per Article: 28.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Peptides have been extensively utilized to construct nanomaterials that display targeted structure through hierarchical assembly. The self-assembly of both rationally designed peptides derived from naturally occurring domains in proteins as well as intuitively or computationally designed peptides that form β-sheets and helical secondary structures have been widely successful in constructing nanoscale morphologies with well-defined 1-d, 2-d, and 3-d architectures. In this review, we discuss these successes of peptide self-assembly, especially in the context of designing hierarchical materials. In particular, we emphasize the differences in the level of peptide design as an indicator of complexity within the targeted self-assembled materials and highlight future avenues for scientific and technological advances in this field.
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Affiliation(s)
- Nairiti J Sinha
- Department of Materials Science and Engineering, University of Delaware, Newark, Delaware 19716, United States
| | - Matthew G Langenstein
- Department of Materials Science and Engineering, University of Delaware, Newark, Delaware 19716, United States
| | - Darrin J Pochan
- Department of Materials Science and Engineering, University of Delaware, Newark, Delaware 19716, United States
| | - Christopher J Kloxin
- Department of Materials Science and Engineering, University of Delaware, Newark, Delaware 19716, United States.,Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States
| | - Jeffery G Saven
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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31
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Li M, Zhuang B, Yu J. Sequence–Conformation Relationship of Zwitterionic Peptide Brushes: Theories and Simulations. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01229] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Minglun Li
- School of Materials Science and Engineering, Nanyang Technological University, 639798 Singapore
| | - Bilin Zhuang
- Division of Science, Yale-NUS College, 138527 Singapore
| | - Jing Yu
- School of Materials Science and Engineering, Nanyang Technological University, 639798 Singapore
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32
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Nassar R, Dignon GL, Razban RM, Dill KA. The Protein Folding Problem: The Role of Theory. J Mol Biol 2021; 433:167126. [PMID: 34224747 PMCID: PMC8547331 DOI: 10.1016/j.jmb.2021.167126] [Citation(s) in RCA: 41] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 06/21/2021] [Accepted: 06/26/2021] [Indexed: 10/20/2022]
Abstract
The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.
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Affiliation(s)
- Roy Nassar
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY, USA; Department of Chemistry, Stony Brook University, Stony Brook, NY, USA
| | - Gregory L Dignon
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY, USA
| | - Rostam M Razban
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY, USA
| | - Ken A Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY, USA; Department of Chemistry, Stony Brook University, Stony Brook, NY, USA; Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA.
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33
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Tian WD, Ghasemi M, Larson RG. Extracting free energies of counterion binding to polyelectrolytes by molecular dynamics simulations. J Chem Phys 2021; 155:114902. [PMID: 34551524 DOI: 10.1063/5.0056853] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We use all-atom molecular dynamics simulations to extract ΔGeff, the free energy of binding of potassium ions K+ to the partially charged polyelectrolyte poly(acrylic acid), or PAA, in dilute regimes. Upon increasing the charge fraction of PAA, the chains adopt more extended conformations, and simultaneously, potassium ions bind more strongly (i.e., with more negative ΔGeff) to the highly charged chains to relieve electrostatic repulsions between charged monomers along the chains. We compare the simulation results with the predictions of a model that describes potassium binding to PAA chains as a reversible reaction whose binding free energy (ΔGeff) is adjusted from its intrinsic value (ΔG) by electrostatic correlations, captured by a random phase approximation. The bare or intrinsic binding free energy ΔG, which is an input in the model, depends on the binding species and is obtained from the radial distribution function of K+ around the charged monomer of a singly charged, short PAA chain in dilute solutions. We find that the model yields semi-quantitative predictions for ΔGeff and the degree of potassium binding to PAA chains, α, as a function of PAA charge fraction without using fitting parameters.
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Affiliation(s)
- Wen-de Tian
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Mohsen Ghasemi
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Ronald G Larson
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
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34
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Trindade SG, da Silveira NP, Loh W. Aggregation Behavior of Asymmetric Diblock Polyampholyte in Aqueous Solution over a Wide Range of pH and Ionic Strength. MACROMOL CHEM PHYS 2021. [DOI: 10.1002/macp.202100141] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Suelen G. Trindade
- Institute of Chemistry University of Campinas (UNICAMP) P.O. Box 6154 Campinas São Paulo 13083‐970 Brazil
| | - Nádya P. da Silveira
- Institute of Chemistry Federal University of Rio Grande do Sul (UFRGS) P.O. Box 9500 Porto Alegre Rio Grande do Sul 90650‐001 Brazil
| | - Watson Loh
- Institute of Chemistry University of Campinas (UNICAMP) P.O. Box 6154 Campinas São Paulo 13083‐970 Brazil
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35
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Chen X, Chen EQ, Shi AC, Yang S. Multiphase Coacervates Driven by Electrostatic Correlations. ACS Macro Lett 2021; 10:1041-1047. [PMID: 35549117 DOI: 10.1021/acsmacrolett.1c00282] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
The liquid-liquid phase separation of a polyelectrolyte solution containing one type of negatively and two types of positively charged polymers with different charge densities is studied theoretically by random phase approximation (RPA). It is predicted that multicoacervate phases could coexist, driven purely by electrostatic correlations. The asymmetry of the linear charge density could induce an effective immiscibility between two positively charged polyelectrolytes, leading to the multiphase separation. Adding salt will induce the disappearance of the dilute phase, forming two coexisting complex phases, instead of fusion between coacervates. Raising temperature could either induce a two coexisting complex phase, or a dilute phase coexisting with a coacervate phase, depending on the bulk concentration. Our predictions are in good agreement with experiments and provide insights in the further designing of the multiphase coacervation system.
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Affiliation(s)
- Xu Chen
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Center for Soft Mater Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Er-Qiang Chen
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Center for Soft Mater Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Shuang Yang
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Center for Soft Mater Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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36
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Rumyantsev A, Johner A, de Pablo JJ. Sequence Blockiness Controls the Structure of Polyampholyte Necklaces. ACS Macro Lett 2021; 10:1048-1054. [PMID: 34476121 PMCID: PMC8397398 DOI: 10.1021/acsmacrolett.1c00318] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 07/20/2021] [Indexed: 12/14/2022]
Abstract
A scaling theory of statistical (Markov) polyampholytes is developed to understand how sequence correlations, that is, the blockiness of positive and negative charges, influences conformational behavior. An increase in the charge patchiness leads to stronger correlation attractions between oppositely charged monomers, but simultaneously, it creates a higher charge imbalance in the polyampholyte. A competition between effective short-range attractions and long-range Coulomb repulsions induces globular, pearl-necklace, or fully stretched chain conformations, depending on the average length of the block of like charges. The necklace structure and the underlying distribution of the net charge are also controlled by the sequence. Sufficiently long blocks allow for charge migration from globular beads (pearls) to strings, thereby providing a nonmonotonic change in the number of necklace beads as the blockiness increases. The sequence-dependent structure of polyampholyte necklaces is confirmed by molecular dynamics simulations. The findings presented here provide a framework for understanding the sequence-encoded conformations of synthetic polyampholytes and intrinsically disordered proteins (IDPs).
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Affiliation(s)
- Artem
M. Rumyantsev
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60637, United States
| | - Albert Johner
- Institut
Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 Rue du Loess, Strasbourg, 67034 Cedex
2, France
| | - Juan J. de Pablo
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60637, United States
- Center
for Molecular Engineering, Argonne National
Laboratory, Lemont, Illinois 60439, United
States
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37
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Dinic J, Marciel AB, Tirrell MV. Polyampholyte physics: Liquid–liquid phase separation and biological condensates. Curr Opin Colloid Interface Sci 2021. [DOI: 10.1016/j.cocis.2021.101457] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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38
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Knoerdel AR, Blocher McTigue WC, Sing CE. Transfer Matrix Model of pH Effects in Polymeric Complex Coacervation. J Phys Chem B 2021; 125:8965-8980. [PMID: 34328340 DOI: 10.1021/acs.jpcb.1c03065] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Oppositely charged polyelectrolytes can undergo an associative phase separation, in a process known as polymeric complex coacervation. This phenomenon is driven by the electrostatic attraction between polyanion and polycation species, leading to the formation of a polymer-dense coacervate phase and a coexisting polymer-dilute supernatant phase. There has been significant recent interest in the physical origin and features of coacervation; yet notably, experiments often use weak polyelectrolytes the charge state of which depends on solution pH, while theoretical or computational efforts typically assume strong polyelectrolytes that remain fully charged. There have been only a few efforts to address this limitation, and thus there has been little exploration of how pH can affect complex coacervation. In this paper, we modify a transfer matrix theory of coacervation to account for acid-base equilibria, taking advantage of its ability to directly account for some local ion correlations that will affect monomer charging. We show that coacervation can stabilize the charged state of a weak polyelectrolyte via the proximity of oppositely charged monomers, and can lead to asymmetric phase diagrams where the positively and negatively charged polyelectrolytes exhibit different behaviors near the pKa of either chain. Specifically, there is a partitioning of one of the salt species to a coacervate to maintain electroneutrality when one of the polyelectrolytes is only partially charged. This results in the depletion of the same salt species in the supernatant, and overall can suppress phase separation. We also demonstrate that, when one of the species is only partially charged, mixtures that are off-stoichiometric in volume fraction but stoichiometric in charge exhibit the greatest propensity to form coacervate phases.
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Affiliation(s)
- Ashley R Knoerdel
- Program in Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Whitney C Blocher McTigue
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Charles E Sing
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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39
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Sherck N, Shen K, Nguyen M, Yoo B, Köhler S, Speros JC, Delaney KT, Shell MS, Fredrickson GH. Molecularly Informed Field Theories from Bottom-up Coarse-Graining. ACS Macro Lett 2021; 10:576-583. [PMID: 35570772 DOI: 10.1021/acsmacrolett.1c00013] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.
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Affiliation(s)
- Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Kevin Shen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - My Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Brian Yoo
- BASF Corporation, Tarrytown, New York 10591, United States
| | | | - Joshua C. Speros
- California Research Alliance (CARA) by BASF, Berkeley, California 94720, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
- Department of Materials, University of California, Santa Barbara, California 93106, United States
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40
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Wessén J, Pal T, Das S, Lin YH, Chan HS. A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates. J Phys Chem B 2021; 125:4337-4358. [PMID: 33890467 DOI: 10.1021/acs.jpcb.1c00954] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs. To gain insight into this LLPS-induced dielectric heterogeneity, addressing in particular whether a low-dielectric condensed phase entails more favorable LLPS than that posited by assuming IDP electrostatic interactions are uniformly modulated by the higher dielectric constant of the pure solvent, we consider a simplified multiple-chain model of polyampholytes immersed in explicit solvents that are either polarizable or possess a permanent dipole. Notably, simulated phase behaviors of these systems exhibit only minor to moderate differences from those obtained using implicit-solvent models with a uniform relative permittivity equals to that of pure solvent. Buttressed by theoretical treatments developed here using random phase approximation and polymer field-theoretic simulations, these observations indicate a partial compensation of effects between favorable solvent-mediated interactions among the polyampholytes in the condensed phase and favorable polyampholyte-solvent interactions in the dilute phase, often netting only a minor enhancement of overall LLPS propensity from the very dielectric heterogeneity that arises from the LLPS itself. Further ramifications of this principle are discussed.
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Affiliation(s)
- Jonas Wessén
- Department of Biochemistry, University of Toronto, Medical Sciences Building-5th Floor, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
| | - Tanmoy Pal
- Department of Biochemistry, University of Toronto, Medical Sciences Building-5th Floor, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Medical Sciences Building-5th Floor, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
| | - Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Medical Sciences Building-5th Floor, 1 King's College Circle, 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, Medical Sciences Building-5th Floor, 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada
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41
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Jiang J, Chen EQ, Yang S. The effect of ion pairs on coacervate-driven self-assembly of block polyelectrolytes. J Chem Phys 2021; 154:144903. [PMID: 33858167 DOI: 10.1063/5.0044845] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The incorporation of oppositely charged polyelectrolytes into a block copolymer system can lead to formation of microphase separated nanostructures driven by the electrostatic complex between two oppositely charged blocks. It is a theoretical challenge to build an appropriate model to handle such coacervate-driven self-assembly, which should capture the strong electrostatic correlations for highly charged polymers. In this paper, we develop the self-consistent field theory considering the ion paring effect to predict the phase behavior of block polyelectrolytes. In our model, two types of ion pairs, the binding between two oppositely charged monomers and the binding between charged monomers and counterions, are included. Their strength of formation is controlled by two parameters Kaa and Kac, respectively. We give a detailed analysis about how the binding strength Kac and Kaa and salt concentration affect the self-assembled nanostructure of diblock polyelectrolyte systems. The results show that the binding between two oppositely charged blocks provides driven force for microphase separation, while the binding between charged monomers and counterions competes with the polyion pairing and thus suppresses the microphase separation. The addition of salt has a shielding effect on the charges of polymers, which is a disadvantage to microphase separation. The phase diagrams as a function of polymer concentration and salt concentration at different situations are constructed, and the influence of Kaa, Kac, and charged block composition fa is analyzed in depth. The obtained phase diagrams are in good agreement with currently existing experimental and theoretical results.
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Affiliation(s)
- Jiadi Jiang
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering and Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry, Peking University, Beijing 100871, People's Republic of China
| | - Er-Qiang Chen
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering and Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry, Peking University, Beijing 100871, People's Republic of China
| | - Shuang Yang
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering and Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry, Peking University, Beijing 100871, People's Republic of China
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42
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Luengo GS, Fameau AL, Léonforte F, Greaves AJ. Surface science of cosmetic substrates, cleansing actives and formulations. Adv Colloid Interface Sci 2021; 290:102383. [PMID: 33690071 DOI: 10.1016/j.cis.2021.102383] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Revised: 02/04/2021] [Accepted: 02/06/2021] [Indexed: 12/22/2022]
Abstract
The development of shampoo and cleansing formulations in cosmetics is at a crossroads due to consumer demands for better performing, more natural products and also the strong commitment of cosmetic companies to improve the sustainability of cosmetic products. In order to go beyond traditional formulations, it is of great importance to clearly establish the science behind cleansing technologies and appreciate the specificity of cleansing biological surfaces such as hair and skin. In this review, we present recent advances in our knowledge of the physicochemical properties of the hair surface from both an experimental and a theoretical point of view. We discuss the opportunities and challenges that newer, sustainable formulations bring compared to petroleum-based ingredients. The inevitable evolution towards more bio-based, eco-friendly ingredients and sustainable formulations requires a complete rethink of many well-known physicochemical principles. The pivotal role of digital sciences and modelling in the understanding and conception of new ingredients and formulations is discussed. We describe recent numerical approaches that take into account the specificities of the hair surface in terms of structuration, different methods that study the adsorption of formulation ingredients and finally the success of new data-driven approaches. We conclude with practical examples on current formulation efforts incorporating bio-surfactants, controlling foaming and searching for new rheological properties.
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43
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Wang X, Zhang P, Tian L. Spatiotemporal organization of coacervate microdroplets. Curr Opin Colloid Interface Sci 2021. [DOI: 10.1016/j.cocis.2021.101420] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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44
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Pal T, Wessén J, Das S, Chan HS. Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction. Phys Rev E 2021; 103:042406. [PMID: 34005864 DOI: 10.1103/physreve.103.042406] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 03/11/2021] [Indexed: 06/12/2023]
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.
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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
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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45
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Rumyantsev AM, Jackson NE, Johner A, de Pablo JJ. Scaling Theory of Neutral Sequence-Specific Polyampholytes. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02515] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Artem M. Rumyantsev
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Nicholas E. Jackson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Albert Johner
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 Rue du Loess, Strasbourg, 67034 Cedex 2, France
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
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46
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Affiliation(s)
- Nam-Kyung Lee
- Department of Physics and Astronomy, Sejong University, Seoul 05006, Korea
| | - Youngkyun Jung
- Supercomputing Center, Korea Institute of Science and Technology Information, Daejeon 34141, Korea
| | - Albert Johner
- Institut Charles Sadron CNRS-Unistra, 6 rue Boussingault, Strasbourg Cedex 67083, France
| | - Jean-François Joanny
- Collège de France, 11, place Marcelin-Berthelot, Paris Cedex 05 75231, France
- Physico-chimie Curie, Institut Curie, PSL University, Paris Cedex 05 75248, France
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47
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Grzetic DJ, Delaney KT, Fredrickson GH. Electrostatic Manipulation of Phase Behavior in Immiscible Charged Polymer Blends. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00095] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Douglas J. Grzetic
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Departments of Chemical Engineering and Materials, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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48
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Schuster BS, Regy RM, Dolan EM, Kanchi Ranganath A, Jovic N, Khare SD, Shi Z, Mittal J. Biomolecular Condensates: Sequence Determinants of Phase Separation, Microstructural Organization, Enzymatic Activity, and Material Properties. J Phys Chem B 2021; 125:3441-3451. [PMID: 33661634 DOI: 10.1021/acs.jpcb.0c11606] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
This perspective article highlights recent progress and emerging challenges in understanding the formation and function of membraneless organelles (MLOs). A long-term goal in the MLO field is to identify the sequence-encoded rules that dictate the formation of compositionally controlled biomolecular condensates, which cells utilize to perform a wide variety of functions. The molecular organization of the different components within a condensate can vary significantly, ranging from a homogeneous mixture to core-shell droplet structures. We provide many examples to highlight the richness of the observed behavior and potential research directions for improving our mechanistic understanding. The tunable environment within condensates can, in principle, alter enzymatic activity significantly. We examine recent examples where this was demonstrated, including applications in synthetic biology. An important question about MLOs is the role of liquid-like material properties in biological function. We discuss the need for improved quantitative characterization tools and the development of sequence-structure-dynamics relationships.
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Affiliation(s)
- Benjamin S Schuster
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Roshan Mammen Regy
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Elliott M Dolan
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States.,Institute for Quantitative Biomedicine, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Aishwarya Kanchi Ranganath
- Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Nina Jovic
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Sagar D Khare
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States.,Institute for Quantitative Biomedicine, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Zheng Shi
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Jeetain Mittal
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
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49
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Kudaibergenov SE. Synthetic and natural polyampholytes: Structural and behavioral similarity. POLYM ADVAN TECHNOL 2021. [DOI: 10.1002/pat.5145] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Sarkyt E. Kudaibergenov
- Institute of Polymer Materials and Technology Atyrau Kazakhstan
- Laboratory of Engineering Profile Satbayev University Almaty Kazakhstan
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50
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Bari KJ, Prakashchand DD. Fundamental Challenges and Outlook in Simulating Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins. J Phys Chem Lett 2021; 12:1644-1656. [PMID: 33555894 DOI: 10.1021/acs.jpclett.0c03404] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Intrinsically disordered proteins (IDPs) populate an ensemble of dynamic conformations, making their structural characterization by experiments challenging. Many IDPs undergo liquid-liquid phase separation into dense membraneless organelles with myriad cellular functions. Multivalent interactions in low-complexity IDPs promote the formation of these subcellular coacervates. While solution NMR, Förster resonance energy transfer (FRET), and small-angle X-ray scattering (SAXS) studies on IDPs have their own challenges, recent computational methods draw a rational trade-off to characterize the driving forces underlying phase separation. In this Perspective, we critically evaluate the scope of approximation-free field theoretic simulations, well-tempered ensemble methods, enhanced sampling techniques, coarse-grained force fields, and slab simulation approaches to offer an improved understanding of phase separation. A synergy between simulation length scale and model resolution would reduce the existing caveats and enable theories of polymer physics to elucidate finer details of liquid-liquid phase separation (LLPS). These computational advances offer promise for rigorous characterization of the IDP proteome and designing peptides with tunable material and self-assembly properties.
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Affiliation(s)
- Khandekar Jishan Bari
- Center for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500107, India
- Department of Chemical Sciences, Indian Institute of Science Education and Research, Berhampur, Odisha 760010, India
| | - Dube Dheeraj Prakashchand
- Center for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500107, India
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