Field-theoretic simulations of random copolymers with structural rigidity

Development of hybrid coarse-grained atomistic models for rapid assessment of local structuring of polymeric semiconductors

Decades of work in the field of computational study of semiconducting polymers using atomistic models illustrate the challenges of generating equilibrated models for this class of materials. While adopting a coarse-grained model can be helpful, the process of developing a suitable model is particularly non-trivial and time-consuming for semiconducting polymers due to a large number of different interactions with some having an anisotropic nature. This work introduces a procedure for the rapid generation of a hybrid model for semiconducting polymers where atoms of secondary importance (those in the alkyl side chains) are transformed into coarse-grained beads to reduce the computational cost of generating an equilibrated structure. The parameters are determined from easy-to-equilibrate simulations of very short oligomers and the model is constructed to enable a very simple back-mapping procedure to reconstruct geometries with atomistic resolution. The model is illustrated for three related polymers containing DPP (diketopyrrolopyrrole) to evaluate the transferability of the potential across different families of polymers. The accuracy of the model, determined by comparison with the results of fully equilibrated simulations of the same material before and after back-mapping, is fully satisfactory for two out of the three cases considered. We noticed that accuracy can be determined very early in the workflow so that it is easy to assess when the deployment of this method is advantageous. The hybrid representation can be used to evaluate directly the electronic properties of structures sampled by the simulations.

Topological Constraints with Optimal Length Promote the Formation of Chromosomal Territories at Weakened Degree of Phase Separation

It is generally agreed that the nuclei of eukaryotic cells at interphase are partitioned into disjointed territories, with distinct regions occupied by certain chromosomes. However, the underlying mechanism for such territorialization is still under debate. Here we model chromosomes as coarse-grained block copolymers and to investigate the effect of loop domains (LDs) on the formation of compartments and territories based on dissipative particle dynamics. A critical length of LDs, which depends sensitively on the length of polymeric blocks, is obtained to minimize the degree of phase separation. This also applies to the two-polymer system: The critical length not only maximizes the degree of territorialization but also minimizes the degree of phase separation. Interestingly, by comparing with experimental data, we find the critical length for LDs and the corresponding length of blocks to be respectively very close to the mean length of topologically associating domains (TADs) and chromosomal segments with different densities of CpG islands for human chromosomes. The results indicate that topological constraints with optimal length can contribute to the formation of territories by weakening the degree of phase separation, which likely promotes the chromosomal flexibility in response to genetic regulations.

Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory

Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.

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.

Designing Electrostatic Interactions via Polyelectrolyte Monomer Sequence

Charged polymers are ubiquitous in biological systems because electrostatic interactions can drive complicated structure formation and respond to environmental parameters such as ionic strength and pH. In these systems, function emerges from sophisticated molecular design; for example, intrinsically disordered proteins leverage specific sequences of monomeric charges to control the formation and function of intracellular compartments known as membraneless organelles. The role of a charged monomer sequence in dictating the strength of electrostatic interactions remains poorly understood despite extensive evidence that sequence is a powerful tool biology uses to tune soft materials. In this article, we use a combination of theory, experiment, and simulation to establish the physical principles governing sequence-driven control of electrostatic interactions. We predict how arbitrary sequences of charge give rise to drastic changes in electrostatic interactions and correspondingly phase behavior. We generalize a transfer matrix formalism that describes a phase separation phenomenon known as "complex coacervation" and provide a theoretical framework to predict the phase behavior of charge sequences. This work thus provides insights into both how charge sequence is used in biology and how it could be used to engineer properties of synthetic polymer systems.

Bottom-up modeling of chromatin segregation due to epigenetic modifications

Predicting how epigenetic marks control the 3D organization of the genome is key to understanding how these marks regulate gene expression. We show that a physical model of a chromosome with experimentally measured local interactions segregates into euchromatin- and heterochromatin-like phases. The model reproduces many of the features of the large-scale organization of the chromosome as measured by Hi-C. Our work provides an estimate of the amount of epigenetic marking needed to segregate a gene into heterochromatin.

We use a chromosome-scale simulation to show that the preferential binding of heterochromatin protein 1 (HP1) to regions high in histone methylation (specifically H3K9me3) results in phase segregation and reproduces features of the observed Hi-C contact map. Specifically, we perform Monte Carlo simulations with one computational bead per nucleosome and an H3K9me3 pattern based on published ChIP-seq signals. We implement a binding model in which HP1 preferentially binds to trimethylated histone tails and then oligomerizes to bridge together nucleosomes. We observe a phase reminiscent of heterochromatin—dense and high in H3K9me3—and another reminiscent of euchromatin—less dense and lacking H3K9me3. This segregation results in a plaid contact probability map that matches the general shape and position of published Hi-C data. Analysis suggests that a roughly 20-kb segment of H3K9me3 enrichment is required to drive segregation into the heterochromatic phase.

Fluctuation Effects in Semiflexible Diblock Copolymers

We present a simulation study of the equilibrium thermodynamic behavior of semiflexible diblock copolymer melts. Using discretized wormlike chains and field-theoretic Monte Carlo, we find that concentration fluctuations play a critical role in controlling phase transitions of semiflexible diblock copolymers. Polymer flexibility and aspect ratio control the order-disorder transition Flory-Huggins parameter χ_ODTN. For polymers with low aspect ratios, fluctuations strongly elevate the phase transition χ_ODTN at finite molecular weights. For high aspect-ratio polymers, chain semiflexibility decreases the phase transition χ_ODTN. We find that the simulated phase behavior agrees well with our recently developed fluctuation theory based on wormlike chain configurations and a one-loop treatment of concentration fluctuations.

Self-assembly in densely grafted macromolecules with amphiphilic monomer units: diagram of states

By means of computer modelling, the self-organization of dense planar brushes of macromolecules with amphiphilic monomer units was addressed and their state diagram was constructed. The diagram of states includes the following regions: disordered position of monomer units with respect to each other, strands composed of a few polymer chains and lamellae with different domain spacing. The transformation of lamellae structures with different domain spacing occurred within the intermediate region and could proceed through the formation of so-called parking garage structures. The parking garage structure joins the lamellae with large (on the top of the brushes) and small (close to the grafted surface) domain spacing, which appears like a system of inclined locally parallel layers connected with each other by bridges. The parking garage structures were observed for incompatible A and B groups in selective solvents, which result in aggregation of the side B groups and dense packing of amphiphilic macromolecules in the restricted volume of the planar brushes.

Sequence and entropy-based control of complex coacervates

Biomacromolecules rely on the precise placement of monomers to encode information for structure, function, and physiology. Efforts to emulate this complexity via the synthetic control of chemical sequence in polymers are finding success; however, there is little understanding of how to translate monomer sequence to physical material properties. Here we establish design rules for implementing this sequence-control in materials known as complex coacervates. These materials are formed by the associative phase separation of oppositely charged polyelectrolytes into polyelectrolyte dense (coacervate) and polyelectrolyte dilute (supernatant) phases. We demonstrate that patterns of charges can profoundly affect the charge–charge associations that drive this process. Furthermore, we establish the physical origin of this pattern-dependent interaction: there is a nuanced combination of structural changes in the dense coacervate phase and a 1D confinement of counterions due to patterns along polymers in the supernatant phase.

Monomer sequence is an emerging tool to precisely encode information (and thus structure and function) into polymer systems. Here the authors use sequence-control in complex coacervates to understand how monomer sequence translates to physical material properties.