Andrew J. Spakowitz

Multiple studies of block copolymer micelle fragmentation have revealed a surprising compressed exponential time dependence of relaxation toward the equilibrium size, following exp[(–t/τ)n], with n ≈ 2. We present a simple two-step kinetic model that quantitatively explains the mechanistic origin of the apparent compressed exponential behavior. In this model, as-prepared micelles evolve toward steady-state micelles via metastable, “peanut-shaped” intermediates. Concentrations of the three states are obtained as a function of time by coupling simple rate laws. The initial and final sizes are known from experiments. The size of the intermediates is estimated by modelling them as prolate ellipsoids, leading to a radius about 2% larger than that of the as-prepared micelles. The two rate constants, k1 and k2, for the formation and decomposition of the intermediate state, respectively, are estimated by fitting experimental data, while providing the sizes of the three states as input. Fitting reveals that k1 and k2 need to be very similar (within a factor of about 2) to observe the apparent compressed exponential dynamics. Equivalent magnitudes of k1 and k2 suggest that the intermediate state is metastable with a finite lifetime and not a transition state, an inference that is supported by the appearance of the peanut-shaped intermediates in previously conducted in-situ TEM experiments. Calculations also indicate that the relative population of the intermediate state reaches a peak value of 20–40%, which should facilitate further imaging of intermediates via TEM. We are not aware of a current theory for block copolymer micelle fragmentation that proposes passage through a metastable intermediate, so this question certainly merits further examination.

The performance of conjugated polymers (CPs) in optoelectronic devices is strongly influenced by nematic ordering, which enhances charge transport through improved molecular alignment. Traditional worm-like chain models predict only uniaxial nematic phases due to rotational averaging about the chain backbone, and cannot capture the biaxial nematic behavior observed in ribbon-like molecules, such as CPs with π-conjugation backbones. We recently developed the ribbon-like chain (RLC) model, which includes anisotropic bending and twist stiffness, and provides a framework for studying both uniaxial and biaxial nematic ordering. Here, we present a self-consistent field theory for biaxial nematic phases in solutions of RLCs, by adopting Maier–Saupe-type interactions. The existing work for rigid rods, rigid ribbons, and twistable ribbons are shown to correspond to the variety of limits of our model. The phase diagrams evaluated for RLCs with finite stiffness values reveal that twist stiffness plays a disproportionately important role compared to bending stiffness, while molecular weight effects reflect a competition between energetics and conformational entropy. The results provide a foundation for coarse-grained simulations that can predict nematic ordering in specific CP chemistries and guide the rational design of high-performance organic electronic materials.

The development of three‐dimensional (3D) in vitro tissue culture models is critical for biomedical research. Hydrogel‐based systems have become preferred scaffolds for 3D models, as they have tunable viscoelastic properties, which are well‐known to influence cell morphology and function. Particularly, reversible hydrogel crosslinks formed through dynamic covalent chemistry (DCC) can introduce viscoelastic behavior including stress relaxation. However, traditional strategies to increase relaxation rates in DCC gels rely on faster bond kinetics, resulting in faster erosion rates that prevent their use for long‐term 3D culture. As an alternative strategy, we explore the use of molecular parameters (specifically molecular weight and degree of functionalization) to carefully control hydrogel stiffness and stress relaxation behavior, creating different combinations of mechanics, while preventing rapid erosion. To aid in interpreting our measurements, we develop and validate a modified theoretical model of gel viscoelasticity to account for additional relaxation process, applying it to a two‐component DCC gel composed of modified hyaluronic acid and elastin‐like protein. Finally, we utilize this tunable gel platform to explore the impact of scaffold viscoelasticity on encapsulated human neural progenitor cells. In summary, this work expands the molecular design space of DCC hydrogels to achieve tunable viscoelastic properties for 3D in vitro models.

We present a self-consistent polyelectrolyte field theory that reveals the impact of solvent polarity and polymer semiflexibility on polyelectrolyte solution thermodynamic behavior. Our approach incorporates a microscopic treatment of the solvent dipolar field and focuses on the importance of the charge separation distance in the dipole solvent. Consequently, this leads to an inhomogeneous dielectric medium at microscopic length scales and a significant free-energy contribution that manifests as the insolubility of uncharged species in a polar solvent. We then add the Born solvation energies of each charged species to account for their inherent solubility. Using this updated theory, which incorporates quadratic-order concentration fluctuation corrections, we generate phase diagrams for oppositely charged polyelectrolyte solutions that display phase re-entrant behavior for weakly charged polyelectrolytes and capture phase behavior consistent with recent experimental findings.

Using a polymer field-theoretic model, we study copolymer solutions with two distinct chemical moieties that bind heterogeneously along the copolymer chains, enabling adaptive self-assembly by tuning the binder species concentration.

The spatial organization of chromatin is governed by epigenetic factors, including epigenetic marks and the reader proteins that bind them. By dictating the accessibility of genomic loci, epigenetic factors contribute to the physical regulation of gene expression, enabling diverse cellular phenotypes to be encoded by a shared genome in an individual. Epigenetic dysregulation can lead to aberrations in chromatin architecture, contributing to diseases such as neurological disorders and cancers. Despite the known importance of chromatin organization for human health, the physical mechanisms governing chromatin folding remain underspecified. In this work, we develop a physical model of chromatin organization based on contributions from multiple epigenetic factors. Using our model, we evaluate how conditions in the nuclear environment and crosstalk between epigenetic marks affect the compartmentalization of chromatin into dense heterochromatin and loose euchromatin. Our results emphasize the role of reader protein binding in chromatin compartmentalization. We show that reader proteins interact through an indirect mechanism facilitated by the shared chromatin “scaffold” to which they bind. Under a scenario where reader proteins compete for binding sites, we find that indirect interactions affect the program adopted by the chromatin fiber. By isolating indirect modes of epigenetic crosstalk, we demonstrate how the interplay between epigenetic patterning and environmental factors influences chromatin architecture.

Genome function requires regulated genome motion. However, tools to directly observe this motion in vivo have been limited in coverage and resolution. Here we introduce an approach to tile mammalian chromosomes with self-mapping fluorescent labels and track them at ultraresolution. We find that sequences separated by submegabase distances transition to proximity in tens of seconds. This rapid search is dependent on cohesin and is exhibited only within domains. Domain borders act as kinetic impediments to this search process, rather than structural boundaries. The genomic separation–dependent scaling of the search time for cis interactions violated predictions of diffusion, suggesting motor-driven folding. We also uncover cohesin-dependent processive motion at 2.7 kilobases per second. Together, these multiscale dynamics reveal the organization of the genome into kinetically associated domains.

The 3D organization of the genome—in particular, which two regions of DNA are in contact with each other—plays a role in regulating gene expression. Several factors influence genome 3D organization. Nucleosomes (where ∼100 base pairs of DNA wrap around histone proteins) bend, twist, and compactify chromosomal DNA, altering its polymer mechanics. How much does the positioning of nucleosomes between gene loci influence contacts between those gene loci? And to what extent are polymer mechanics responsible for this? To address this question, we combine a stochastic polymer mechanics model of chromosomal DNA including twists and wrapping induced by nucleosomes with two data-driven pipelines. The first estimates nucleosome positioning from ATAC-seq data in regions of high accessibility. Most of the genome is low accessibility, so we combine this with a novel image analysis method that estimates the distribution of nucleosome spacing from electron microscopy data. There are no fit parameters in the biophysical model. We apply this method to IL-6, IL-15, CXCL9, and CXCL10, inflammatory marker genes in macrophages, before and after inflammatory stimulation, and compare the predictions with contacts measured by conformation capture experiments (4C-seq). We find that within a 500-kb genomic region, polymer mechanics with nucleosomes can explain 71% of close contacts. These results suggest that, while genome contacts on 100 kb scales are multifactorial, they may be amenable to mechanistic, physical explanation. Our work also highlights the role of nucleosomes, not just at the loci of interest, but between them, and not just the total number of nucleosomes, but their specific placement. The method generalizes to other genes, and can be used to address whether a contact is under active regulation by the cell (e.g. a macrophage during inflammatory stimulation).

DNA methylation is a crucial epigenetic modification that orchestrates chromatin remodelers that suppress transcription, and aberrations in DNA methylation result in a variety of conditions such as cancers and developmental disorders. While it is understood that methylation occurs at CpG-rich DNA regions, it is less understood how distinct methylation profiles are established within various cell types. In this work, we develop a molecular-transport model that depicts the genomic exploration of DNA methyltransferase within a multiscale DNA environment, incorporating biologically relevant factors like methylation rate and CpG density to predict how patterns are established. Our model predicts DNA methylation-state correlation distributions arising from the transport and kinetic properties that are crucial for the establishment of unique methylation profiles. We model the methylation correlation distributions of nine cancerous human cell types to determine how these properties affect the epigenetic profile. Our theory is capable of recapitulating experimental methylation patterns, suggesting the importance of DNA methyltransferase transport in epigenetic regulation. Through this work, we propose a mechanistic description for the establishment of methylation profiles, capturing the key behavioral characteristics of methyltransferase that lead to aberrant methylation.