Micro- to macro-phase separation transition in sequence-defined coacervates

Magnetic tweezers characterization of the entropic elasticity of intrinsically disordered proteins and peptoids

Understanding the conformational behavior of biopolymers is essential to unlocking knowledge of their biophysical mechanisms and functional roles. Single-molecule force spectroscopy can provide a unique perspective on this by exploiting entropic elasticity to uncover key biopolymer structural parameters. A particularly powerful approach involves the use of magnetic tweezers, which can easily generate lower stretching forces (0.1-20 pN). For forces at the low end of this range, the elastic response of biopolymers is sensitive to excluded volume effects, and they can be described by Pincus blob elasticity model that allow robust extraction of the Flory polymer scaling exponent. Here, we detail protocols for the use of magnetic tweezers for force-extension measurements of intrinsically disordered proteins and peptoids. We also discuss procedures for fitting low-force elastic curves to the predictions of polymer physics models to extract key conformational parameters.

Polymer sequence design via molecular simulation-based active learning

Molecular-scale interactions and chemical structures offer an enormous opportunity to tune material properties. However, designing materials from their molecular scale is a grand challenge owing to the practical limitations in exploring astronomically large design spaces using traditional experimental or computational methods. Advancements in data science and machine learning have produced a host of tools and techniques that can address this problem and facilitate the efficient exploration of large search spaces. In this work, a blended approach integrating physics-based methods, machine learning techniques and uncertainty quantification is implemented to effectively screen a macromolecular sequence space and design target structures. Here, we survey and assess the efficacy of data-driven methods within the framework of active learning for a challenging design problem, viz., sequence optimization of a copolymer. We report the impact of surrogate models, kernels, and initial conditions on the convergence of the active learning method for the sequence design problem. This work establishes optimal strategies and hyperparameters for efficient inverse design of polymer sequences via active learning.

Multiscale Modeling of Protein-RNA Condensation in and Out of Equilibrium

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.

Field theory description of ion association in re-entrant phase separation of polyampholytes

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.

Tuning Formation of Protein-DNA Coacervates by Sequence and Environment

The high concentration of nucleic acids and positively charged proteins in the cell nucleus provides many possibilities for complex coacervation. We consider a prototypical mixture of nucleic acids together with the polycationic C-terminus of histone H1 (CH1). Using a minimal coarse-grained model that captures the shape, flexibility, and charge distributions of the molecules, we find that coacervates are readily formed at physiological ionic strengths, in agreement with experiment, with a progressive increase in local ordering at low ionic strength. Variation of the positions of charged residues in the protein tunes phase separation: for well-mixed or only moderately blocky distributions of charge, there is a modest increase of local ordering with increasing blockiness that is also associated with an increased propensity to phase separate. This ordering is also associated with a slowdown of rotational and translational diffusion in the dense phase. However, for more extreme blockiness (and consequently higher local charge density), we see a qualitative change in the condensed phase to become a segregated structure with a dramatically increased ordering of the DNA. Naturally occurring proteins with these sequence properties, such as protamines in sperm cells, are found to be associated with very dense packing of nucleic acids.

Advances in the Structural Design of Polyelectrolyte Complex Micelles

Polyelectrolyte complex micelles (PCMs) are a unique class of self-assembled nanoparticles that form with a core of associated polycations and polyanions, microphase-separated from neutral, hydrophilic coronas in aqueous solution. The hydrated nature and structural and chemical versatility make PCMs an attractive system for delivery and for fundamental polymer physics research. By leveraging block copolymer design with controlled self-assembly, fundamental structure-property relationships can be established to tune the size, morphology, and stability of PCMs precisely in pursuit of tailored nanocarriers, ultimately offering storage, protection, transport, and delivery of active ingredients. This perspective highlights recent advances in predictive PCM design, focusing on (i) structure-property relationships to target specific nanoscale dimensions and shapes and (ii) characterization of PCM dynamics primarily using time-resolved scattering techniques. We present several vignettes from these two emerging areas of PCM research and discuss key opportunities for PCM design to advance precision medicine.

The effect of ion pairs on coacervate-driven self-assembly of block polyelectrolytes

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 K_aa and K_ac, respectively. We give a detailed analysis about how the binding strength K_ac and K_aa 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 K_aa, K_ac, and charged block composition f_a is analyzed in depth. The obtained phase diagrams are in good agreement with currently existing experimental and theoretical results.

Ion Pairing and the Structure of Gel Coacervates

A scaling model for the structure of coacervates is presented for mixtures of oppositely-charged polyelectrolytes of both symmetric and asymmetric charge-densities for different degrees of electrostatic strength and levels of added salt. At low electrostatic strengths, weak coacervates, with the energy of electrostatic interactions between charges less than the thermal energy, k B T, are liquid. At higher electrostatic strengths, strong coacervates are gels with crosslinks formed by ion pairs of opposite charges bound to each other with energy higher than k B T. Charge-symmetric coacervates are formed for mixtures of oppositely-charged polyelectrolytes with equal and opposite charge-densities. While charge-symmetric weak coacervates form a semidilute polymer solution with a correlation length equal to the electrostatic blob size, charge-symmetric strong coacervates form reversible gels with a correlation length on the order of the distance between bound ion pairs. Charge-asymmetric coacervates are formed from mixtures of oppositely-charged polyelectrolytes with different charge-densities. While charge-asymmetric weak coacervates form double solutions with two correlation lengths and qualitatively different chain conformations of polycations and polyanions, charge-asymmetric strong coacervates form bottlebrush and star-like gels. Unlike liquid coacervates, for which an increase in the concentration of added salt screens electrostatic interactions, causing structural rearrangement and eventually leads to their dissolution, the salt does not affect the structure of strong coacervates until ion pairs dissociate and the gel disperses.

Comparing Zwitterionic and PEG Exteriors of Polyelectrolyte Complex Micelles

A series of model polyelectrolyte complex micelles (PCMs) was prepared to investigate the consequences of neutral and zwitterionic chemistries and distinct charged cores on the size and stability of nanocarriers. Using aqueous reversible addition-fragmentation chain transfer (RAFT) polymerization, we synthesized a well-defined diblock polyelectrolyte system, poly(2-methacryloyloxyethyl phosphorylcholine methacrylate)-block-poly((vinylbenzyl) trimethylammonium) (PMPC-PVBTMA), at various neutral and charged block lengths to compare directly against PCM structure-property relationships centered on poly(ethylene glycol)-block-poly((vinylbenzyl) trimethylammonium) (PEG-PVBTMA) and poly(ethylene glycol)-block-poly(l-lysine) (PEG-PLK). After complexation with a common polyanion, poly(sodium acrylate), the resulting PCMs were characterized by dynamic light scattering (DLS) and small angle X-ray scattering (SAXS). We observed uniform assemblies of spherical micelles with a diameter ~1.5-2× larger when PMPC-PVBTMA was used compared to PEG-PLK and PEG-PVBTMA via SAXS and DLS. In addition, PEG-PLK PCMs proved most resistant to dissolution by both monovalent and divalent salt, followed by PEG-PVBTMA then PMPC-PVBTMA. All micelle systems were serum stable in 100% fetal bovine serum over the course of 8 h by time-resolved DLS, demonstrating minimal interactions with serum proteins and potential as in vivo drug delivery vehicles. This thorough study of the synthesis, assembly, and characterization of zwitterionic polymers in PCMs advances the design space for charge-driven micelle assemblies.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

Polymer science has been driven by ever-increasing molecular complexity, as polymer synthesis expands an already-vast palette of chemical and architectural parameter space. Copolymers represent a key example, where simple homopolymers have given rise to random, alternating, gradient, and block copolymers. Polymer physics has provided the insight needed to explore this monomer sequence parameter space. The future of polymer science, however, must contend with further increases in monomer precision, as this class of macromolecules moves ever closer to the sequence-monodisperse polymers that are the workhorses of biology. The advent of sequence-defined polymers gives rise to opportunities for material design, with increasing levels of chemical information being incorporated into long-chain molecules; however, this also raises questions that polymer physics must address. What properties uniquely emerge from sequence-definition? Is this circumstance-dependent? How do we define and think about sequence dispersity? How do we think about a hierarchy of sequence effects? Are more sophisticated characterization methods, as well as theoretical and computational tools, needed to understand this class of macromolecules? The answers to these questions touch on many difficult scientific challenges, setting the stage for a rich future for sequence-defined polymers in polymer physics.