Closing the loop between microstructure and charge transport in conjugated polymers by combining microscopy and simulation.

A grand challenge in materials science is to identify the impact of molecular composition and structure across a range of length scales on macroscopic properties. We demonstrate a unified experimental-theoretical framework that coordinates experimental measurements of mesoscale structure with molecular-level physical modeling to bridge multiple scales of physical behavior. Here we apply this framework to understand charge transport in a semiconducting polymer. Spatially-resolved nanodiffraction in a transmission electron microscope is combined with a self-consistent framework of the polymer chain statistics to yield a detailed picture of the polymer microstructure ranging from the molecular to device relevant scale. Using these data as inputs for charge transport calculations, the combined multiscale approach highlights the underrepresented role of defects in existing transport models. Short-range transport is shown to be more chaotic than is often pictured, with the drift velocity accounting for a small portion of overall charge motion. Local transport is sensitive to the alignment and geometry of polymer chains. At longer length scales, large domains and gradual grain boundaries funnel charges preferentially to certain regions, creating inhomogeneous charge distributions. While alignment generally improves mobility, these funneling effects negatively impact mobility. The microstructure is modified in silico to explore possible design rules, showing chain stiffness and alignment to be beneficial while local homogeneity has no positive effect. This combined approach creates a flexible and extensible pipeline for analyzing multiscale functional properties and a general strategy for extending the accesible length scales of experimental and theoretical probes by harnessing their combined strengths.

Physical modeling of the heritability and maintenance of epigenetic modifications.

We develop a predictive theoretical model of the physical mechanisms that govern the heritability and maintenance of epigenetic modifications. This model focuses on a particular modification, methylation of lysine-9 of histone H3 (H3K9), which is one of the most representative and critical epigenetic marks that affects chromatin organization and gene expression. Our model combines the effect of segregation and compaction on chromosomal organization with the effect of the interaction between proteins that compact the chromatin (heterochromatin protein 1) and the methyltransferases that affect methyl spreading. Our chromatin model demonstrates that a block of H3K9 methylations in the epigenetic sequence determines the compaction state at any particular location in the chromatin. Using our predictive model for chromatin compaction, we develop a methylation model to address the reestablishment of the methylation sequence following DNA replication. Our model reliably maintains methylation over generations, thereby establishing the robustness of the epigenetic code.

Semiflexible polymer solutions. II. Fluctuations and Frank elastic constants.

We study the collective elastic behavior of semiflexible polymer solutions in a nematic liquid-crystalline state using polymer field theory. Our polymer field-theoretic model of semiflexible polymer solutions is extended to include second-order fluctuation corrections to the free energy, permitting the evaluation of the Frank elastic constants based on orientational order fluctuations in the nematic state. Our exact treatment of wormlike chain statistics permits the evaluation of behavior from the nematic state, thus accurately capturing the impact of single-chain behavior on collective elastic response. Results for the Frank elastic constants are presented as a function of aligning field strength and chain length, and we explore the impact of conformation fluctuations and hairpin defects on the twist, splay, and bend moduli. Our results indicate that the twist elastic constant Ktwist is smaller than both bend and splay constants (Kbend and Ksplay, respectively) for the entire range of polymer rigidity. Splay and bend elastic constants exhibit regimes of dominance over the range of chain stiffness, where Ksplay > Kbend for flexible polymers (large-N limit) while the opposite is true for rigid polymers. Theoretical analysis also suggests the splay modulus tracks exactly to that of the end-to-end distance in the transverse direction for semiflexible polymers at intermediate to large-N. These results provide insight into the role of conformation fluctuations and hairpin defects on the collective response of polymer solutions.

Bottom-up modeling of chromatin segregation due to epigenetic modifications.

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.

Chromatin Compaction Leads to a Preference for Peripheral Heterochromatin.

A layer of dense heterochromatin is found at the periphery of the nucleus. Because this peripheral heterochromatin functions as a repressive phase, mechanisms that relocate genes to the periphery play an important role in regulating transcription. Using Monte Carlo simulations, we show that an interaction that attracts euchromatin and heterochromatin equally to the nuclear envelope will still preferentially locate heterochromatin to the nuclear periphery. This observation considerably broadens the class of possible interactions that result in peripheral positioning to include boundary interactions that either weakly attract all chromatin or strongly bind to a randomly chosen 0.05% of nucleosomes. The key distinguishing feature of heterochromatin is its high chromatin density with respect to euchromatin. In our model, this densification is caused by heterochromatin protein 1's preferential binding to histone H3 tails with a methylated lysine at the ninth residue, a hallmark of heterochromatin. We find that a global rearrangement of chromatin to place heterochromatin at the nuclear periphery can be accomplished by attaching a small subset of loci, even if these loci are uncorrelated with heterochromatin. Hence, factors that densify chromatin determine which genomic regions condense to form peripheral heterochromatin.

Geometrical Heterogeneity Dominates Thermal Fluctuations in Facilitating Chromatin Contacts.

Within a living cell, the myriad of proteins that bind DNA introduce heterogeneously spaced kinks into an otherwise semiflexible DNA double helix. To investigate the effects of heterogeneous nucleosome binding on chromatin organization, we extend the wormlike chain model to include statistically spaced, rigid kinks. On timescales where nucleosome positions are fixed, we find that the probability of chromatin loop formation can vary by up to six orders of magnitude between two sets of nucleosome positions drawn from the same distribution. On longer timescales, we show that continuous rerandomization due to nucleosome turnover results in chromatin tracing out an effective WLC with a dramatically smaller Kuhn length than bare DNA. Together, these observations demonstrate that nucleosome spacing acts as the primary source of the structural heterogeneity that dominates local and global chromatin organization.

Polymer Semiflexibility Induces Nonuniversal Phase Transitions in Diblock Copolymers.

The order-disorder phase transition and the associated phase diagrams of semiflexible diblock copolymers are investigated using the wormlike chain model, incorporating concentration fluctuations. The free energy up to quartic order in concentration fluctuations is developed with chain-rigidity-dependent coefficients, evaluated using our exact results for the wormlike chain model, and a one-loop renormalization treatment is used to account for fluctuation effects. The chain length N and the monomer aspect ratio α directly control the strength of immiscibility (defined by the Flory-Huggins parameter χ) at the order-disorder transition and the resulting microstructures at different chemical compositions f_{A}. When monomers are infinitely thin (i.e., large aspect ratio α), the finite chain length N lowers the χN at the phase transition. However, fluctuation effects become important when chains have a finite radius, and a decrease in the chain length N elevates the χN at the phase transition. Phase diagrams of diblock copolymers over a wide range of N and α are calculated based on our fluctuation theory. We find that both finite N and α enhance the stability of the lamellar phase above the order-disorder transition. Our results demonstrate that polymer semiflexibility plays a dramatic role in the phase behavior, even for large chain lengths (e.g., N≈100).

Field-theoretic simulations of random copolymers with structural rigidity.

Copolymers play an important role in a range of soft-materials applications and biological phenomena. Prevalent works on block copolymer phase behavior use flexible chain models and incorporate interactions using a mean-field approximation. However, when phase separation takes place on length scales comparable to a few monomers, the structural rigidity of the monomers becomes important. In addition, concentration fluctuations become significant at short length scales, rendering the mean-field approximation invalid. In this work, we use simulation to address the role of finite monomer rigidity and concentration fluctuations in microphase segregation of random copolymers. Using a field-theoretic Monte-Carlo simulation of semiflexible polymers with random chemical sequences, we generate phase diagrams for random copolymers. We find that the melt morphology of random copolymers strongly depends on chain flexibility and chemical sequence correlation. Chemically anti-correlated copolymers undergo first-order phase transitions to local lamellar structures. With increasing degree of chemical correlation, this first-order phase transition is softened, and melts form microphases with irregular shaped domains. Our simulations in the homogeneous phase exhibit agreement with the density-density correlation from mean-field theory. However, conditions near a phase transition result in deviations between simulation and mean-field theory for the density-density correlation and the critical wavemode. Chain rigidity and sequence randomness lead to frustration in the segregated phase, introducing heterogeneity in the resulting morphologies.

Observation of surface plasmon polariton pumping of optical eigenmodes of gold-decorated gallium nitride nanowires.

The photocurrent of individual gallium nitride (GaN) nanowires decorated with Au nanoparticles as function of the wavelength of light (405 nm (blue), 532 nm (green), and 632.8 nm (red)) and nanowire diameter (80 to 400 nm) is reported. The photocurrent scales with photon energy but oscillates with nanowire diameter. The oscillations are described in terms of the scattering of surface plasmon polaritons into allowed transverse magnetic electromagnetic modes of the nanowire that have maximum intensities in the undepleted region of the nanowire. These oscillations do not occur below a nanowire diameter of ~200 nm due to the depletion layer formed at the Au-GaN interface, which completely depletes the nanowire, that is, there is an insufficient density of carriers that can be excited into the conduction band. On the basis of estimations of the depletion depth and solutions of the Helmholtz equation, the maxima in the photocurrent for d > 200 nm are assigned to the two lowest azimuthally symmetric transverse magnetic eigenmodes: (m = 0, n = 1) and (m = 0, n = 2), which have maximum electric field intensities within the undepleted region of the GaN nanowire. The outcome of this work could have far reaching implications on the development of nanophotonics.

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 χODTN. For polymers with low aspect ratios, fluctuations strongly elevate the phase transition χODTN at finite molecular weights. For high aspect-ratio polymers, chain semiflexibility decreases the phase transition χODTN. 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.