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Dynamically associating polymers have long been of interest due to their highly tunable viscoelastic behavior. Many applications leverage this tunability to create materials that have specific rheological properties, but designing such materials is an arduous, iterative process. Current models for dynamically associating polymers are phenomenological, assuming a structure for the relationship between association kinetics and network relaxation. We present the Brachiation model, a molecular-level theory of a polymer network with dynamic associations that is rooted in experimentally controllable design parameters, replacing the iterative experimental process with a predictive model for how experimental modifications to the polymer will impact rheological behavior. We synthesize hyaluronic acid chains modified with supramolecular host-guest motifs to serve as a prototypical dynamic network exhibiting tunable physical properties through control of polymer concentration and association rates. We use dynamic light scattering microrheology to measure the linear viscoelasticity of these polymers across six decades in frequency and fit our theory parameters to the measured data. The parameters are then altered by a magnitude corresponding to changes made to the experimental parameters and used to obtain new rheological predictions that match the experimental results well, demonstrating the ability for this theory to inform the design process of dynamically associating polymeric materials.

The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.

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.

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.

We present a theoretical model that demonstrates the integral role chromosome organization and structural mechanics play in the spreading of histone modifications involved in epigenetic regulation. Our model shows that heterogeneous nucleosome positioning, and the resulting position-dependent mechanical properties, must be included to reproduce several qualitative features of experimental data of histone methylation spreading around an artificially induced “nucleation site.” We show that our model recreates both the extent of spreading and the presence of a subdominant peak upstream of the transcription start site. Our model indicates that the spreading of epigenetic modifications is sensitive to heterogeneity in chromatin organization and the resulting variability in the chromatin’s mechanical properties, suggesting that nucleosome spacing can directly control the conferral of epigenetic marks by modifying the structural mechanics of the chromosome. It further illustrates how the physical organization of the DNA polymer may play a significant role in re-establishing the epigenetic code upon cell division.

Coarse-grained modeling tools are employed to simulate the mechanics of DNA loading within a nanoscale confinement and predict semiflexible polymer conformations within the confinement, providing design recommendations for DNA-sequencing devices. A workflow is developed to quantify competing requirements of efficiency and accuracy and extract metrics that guide design optimization. The mean first-passage time for DNA loading is calculated as a function of the nanochannel geometry and the applied electric field. We analyze the interplay between the free energy of confinement and the electric potential energy in achieving high-throughput, base-pair detection. The single-read probability is investigated as informative metrics for sequencing accuracy and for sensing-strategy design. High cost, low throughput, and low accuracy have so far limited the adoption of nanochannel analysis and other long-read technologies. Our work directly addresses these limitations with a systematic approach that is scalable to long molecules and complex geometries.

The pairing of homologous chromosomes (homologs) in meiosis is essential for distributing the correct numbers of chromosomes into haploid gametes. In budding yeast, pairing depends on the formation of 150-200 Spo11-mediated double-strand breaks (DSBs) that are distributed among 16 homolog pairs, but it is not known if all, or only a subset of these DSBs, contribute to the close juxtaposition of homologs. Having established a system to measure the position of fluorescently tagged chromosomal loci in 3D space over time, we analyzed locus trajectories to determine how frequently, and how long, loci spend colocalized or apart. Continuous imaging revealed highly heterogeneous cell-to-cell behavior of foci, with the majority of cells exhibiting a “mixed” phenotype where foci move into and out of proximity, even at late stages of prophase, suggesting that the axial structures of the synaptonemal complex may be more dynamic than anticipated. The observed plateaus of the mean-squared change in distance (MSCD) between foci informed the development of a biophysical model of two diffusing polymers that captures the loss of centromere linkages as cells enter meiosis, nuclear confinement, and the formation of Spo11-dependent linkages. The predicted number of linkages per chromosome in our theoretical model closely approximates the small number (~2-4) of estimated synapsis-initiation sites, suggesting that excess DSBs have negligible effects on the overall juxtaposition of homologs. These insights into the dynamic in-terchromosomal behavior displayed during homolog pairing demonstrate the power of combining time-resolvedin vivoanalysis with modeling at the granular level.Significance StatementEssential for sexual reproduction, meiosis is a specialized cell division required for the production of haploid gametes. Critical to this process is the pairing, recombination, and segregation of homologous chromosomes (homologs). While pairing and recombination are linked, it is not known how many linkages are sufficient to hold homologs in proximity. Here, we reveal that random diffusion and the placement of a small number of linkages are sufficient to establish the apparent “pairing” of homologs. We also show that colocalization between any two loci is more dynamic than anticipated. Our study is the first to provide observations of live interchromosomal dynamics during meiosis and illustrates the power of combining single-cell measurements with theoretical polymer modeling.

We present a path-integral formulation of the motion of a particle subjected to fluctuating active and thermal forces. This general framework predicts the statistical behavior associated with the stochastic trajectories of the particle, accounting for all possible realizations of Brownian and active forces, over an arbitrary potential landscape. Temporal correlations in the active forces result in non-Markovian statistics, necessitating the inclusion of a fixed active-force value at specified times within the statistical treatment. We specialize our theory to that of exponentially correlated active forces for a particle in a harmonic potential. We find the exact results for the statistical distributions for the initial position of the particle, accounting for the impact of the correlated active forces at all times prior to the initial time. Our theory is then used to find the two-point distribution for the active Brownian particle, which governs the joint probability that a particle begins and ends at specified locations. Analyses of the active Brownian statistics demonstrate that the impact of active forces can be interpreted through a time-dependent temperature whose influence depends on the competition of timescales of the active-force correlation and the relaxation time of the particle in the harmonic potential. The general results presented in this work are transferable to a broad range of nonequilibrium systems with active and Brownian motion, and the time-dependent temperature serves as a governing principle to describe the competition of timescales associated with active forces and internal relaxation processes.

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model’s ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.

We develop a theoretical model to predict the impact of nematic liquid-crystalline alignment on charge transport in conducting polymer materials. Using polymer field-theoretic modeling, we predict ...

Thick, viscous respiratory secretions are a major pathogenic feature of COVID-19, but the composition and physical properties of these secretions are poorly understood. We characterized the composition and rheological properties (i.e., resistance to flow) of respiratory secretions collected from intubated COVID-19 patients. We found the percentages of solids and protein content were greatly elevated in COVID-19 compared with heathy control samples and closely resembled levels seen in cystic fibrosis, a genetic disease known for thick, tenacious respiratory secretions. DNA and hyaluronan (HA) were major components of respiratory secretions in COVID-19 and were likewise abundant in cadaveric lung tissues from these patients. COVID-19 secretions exhibited heterogeneous rheological behaviors, with thicker samples showing increased sensitivity to DNase and hyaluronidase treatment. In histologic sections from these same patients, we observed increased accumulation of HA and the hyaladherin versican but reduced tumor necrosis factor–stimulated gene-6 staining, consistent with the inflammatory nature of these secretions. Finally, we observed diminished type I interferon and enhanced inflammatory cytokines in these secretions. Overall, our studies indicated that increases in HA and DNA in COVID-19 respiratory secretion samples correlated with enhanced inflammatory burden and suggested that DNA and HA may be viable therapeutic targets in COVID-19 infection.

We examine the relationship between the size of domains of epigenetic marks and the stability of those domains using our theoretical model that captures the physical mechanisms governing the maintenance of epigenetic modifications. We focus our study on histone H3 lysine-9 trimethylation, one of the most common and consequential epigenetic marks with roles in chromatin compaction and gene repression. Our model combines the effects of methyl spreading by methyltransferases and chromatin segregation into heterochromatin and euchromatin because of preferential heterochromatin protein 1 (HP1) binding. Our model indicates that, although large methylated domains are passed successfully from one chromatin generation to the next, small alterations to the methylation sequence are not maintained during chromatin replication. Using our predictive model, we investigate the size required for an epigenetic domain to persist over chromatin generations while surrounded by a much larger domain of opposite methylation and compaction state. We find that there is a critical size threshold in the hundreds-of-nucleosomes scale above which an epigenetic domain will be reliably maintained over generations. The precise size of the threshold differs for heterochromatic and euchromatic domains. Our results are consistent with natural alterations to the epigenetic sequence occurring during embryonic development and due to age-related epigenetic drift.

Invading breast cancer cells transform the mechanics of their surroundings across a panorama of time scales., Living tissues embody a unique class of hybrid materials in which active and thermal forces are inextricably linked. Mechanical characterization of tissues demands descriptors that respect this hybrid nature. In this work, we develop a microrheology-based force spectrum analysis (FSA) technique to dissect the active and passive fluctuations of the extracellular matrix (ECM) in three-dimensional (3D) cell culture models. In two different stromal models and a 3D breast cancer spheroid model, our FSA reveals emergent hybrid dynamics that involve both high-frequency stress stiffening and low-frequency fluidization of the ECM. We show that this is a general consequence of nonlinear coupling between active forces and the frequency-dependent viscoelasticity of stress-stiffening networks. In 3D breast cancer spheroids, this dual active stiffening and fluidization is tightly connected with invasion. Our results suggest a mechanism whereby breast cancer cells reconcile the seemingly contradictory requirements for both tension and malleability in the ECM during invasion.

We present a method for using dynamic light scattering in the single-scattering limit to measure the viscoelastic moduli of soft materials. This microrheology technique only requires a small sample volume of 12 μL to measure up to six decades in time of rheological behavior. We demonstrate the use of dynamic light scattering microrheology (DLSμR) on a variety of soft materials, including dilute polymer solutions, covalently-crosslinked polymer gels, and active, biological fluids. In this work, we detail the procedure for applying the technique to new materials and discuss the critical considerations for implementing the technique, including a custom analysis script for analyzing data output. We focus on the advantages of applying DLSμR to biologically relevant materials: breast cancer cells encapsulated in a collagen gel and cystic fibrosis sputum. DLSμR is an easy, efficient, and economical rheological technique that can guide the design of new polymeric materials and facilitate the understanding of the underlying physics governing behavior of naturally derived materials.

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.

The viscoelastic behavior of a physically crosslinked gel involves a spectrum of molecular relaxation processes, which at the single-chain level involve the chain undergoing transient hand-to-hand motion through the network. We develop a self-consistent theory for describing transiently associating polymer solutions that captures these complex dynamics. A single polymer chain transiently binds to a viscoelastic background that represents the polymer network formed by surrounding polymer chains. The viscoelastic background is described in the equation of motion as a memory kernel, which is self-consistently determined based on the predicted rheological behavior from the chain itself. The solution to the memory kernel is translated into rheological predictions of the complex modulus over a wide range of frequencies to capture the time-dependent behavior of a physical gel. Using the loss tangent predictions, a phase diagram is shown for the sol-gel transition of polymers with dynamic association affinities. This theory provides a predictive, molecular-level framework for the design of associating gels and supramolecular assemblies with targeted rheological properties.

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.

Summary Amphiphilic copolymers capable of extracting membrane proteins directly from lipid bilayers into “native nanodiscs” promise a simpler membrane protein sample preparation procedure for structural and functional studies. Unfortunately, the selection of nanodisc-forming copolymers is currently limited to molecules that are heterogeneous in terms of molecular weight and monomer sequence, limiting their efficacy in extracting membrane proteins. Here, we report the development of a highly alternating copolymer composed of acrylic acid and styrene by taking advantage of the fundamental reactivity ratios of these monomers. We show that these copolymers, which we term AASTY, are effective solubilizers of membrane proteins expressed in mammalian cells by virtue of their structured amphiphilicity. These AASTY copolymers are promising alternatives to styrene-maleic acid copolymers and provide a new chemical platform for structural and functional characterization of integral membrane proteins in native nanodiscs.

We present a field-theoretic model to predict the equilibrium thermodynamic behavior of semiflexible diblock copolymers and random copolymers in the presence of solvent. We find that in both systems polymer–solvent contacts dramatically influence the thermodynamic behavior with decreasing the copolymer segment length (i.e., molecular weight). When a copolymer has unequal monomer composition, both polymer length and solvent concentration have a strong influence on the phase transition spinodal and magnitude of the critical wave modes. Diblock copolymers exhibit an expanded region of the lamellar phase in the phase diagram with decreasing chain length and polymer concentration. Such effects suggest a breakdown of the dilute approximation for solutions of short diblock copolymers. Random copolymer solutions also exhibit changes in the phase-transition spinodal and critical wave mode at asymmetric chemical compositions. This effect is highly relevant to most random copolymer materials, since a monomer is typi...

Biomineralization, the process by which biological systems direct the synthesis of inorganic structures from organic templates, is an exquisite example of nanomaterial self-assembly in nature. Its products include the shells of mollusks and the bones and teeth of vertebrates. By comparison, conventional inorganic synthesis techniques provide limited control over inorganic nanomaterial architecture. Inspired by biomineralization in nature, over the last two decades, the field of biotemplating has emerged as a new paradigm for inorganic nanomaterial assembly, wherein researchers seek to design novel nano-structures in which inorganic nanomaterial synthesis is directed from an underlying biomolecular template. Here, we review the motivation, mechanistic understanding, progress, and challenges for the field of biotemplating. We highlight the interdisciplinary nature of this field, and survey a broad range of examples of bio-templated engineering: ranging from strategies that exploit the inherent capabilities of proteins in nature, to genetically-engineered systems that unlock new capabilities for self-assembly with biomolecules. We illustrate that the use of biological materials as templates for inorganic self-assembly holds tremendous potential for nanomaterial engineering, with applications that range from electronics and energy to medicine.

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.

The development of experimental techniques capable of probing the viscoelasticity of soft materials over a broad range of time scales is essential to uncovering the physics that governs their behavior. In this work, we develop a microrheology technique that requires only 12 μL of sample and is capable of resolving dynamic behavior ranging in time scales from 10–6 to 10 s. Our approach, based on dynamic light scattering in the single-scattering limit, enables the study of polymer gels and other soft materials over a vastly larger hierarchy of time scales than macrorheology measurements. Our technique captures the viscoelastic modulus of polymer hydrogels with a broad range of stiffnesses from 10 to 104 Pa. We harness these capabilities to capture hierarchical molecular relaxations in DNA and to study the rheology of precious biological materials that are impractical for macrorheology measurements, including decellularized extracellular matrices and intestinal mucus. The use of a commercially available benchtop setup that is already available to a variety of soft matter researchers renders microrheology measurements accessible to a broader range of users than existing techniques, with the potential to reveal the physics that underlies complex polymer hydrogels and biological materials., A broadly accessible microrheology technique is developed that reveals viscoelasticity across broad time scales for a variety of soft and biological materials.

Polymeric materials are ubiquitous in our daily lives, and they play a significant role in many technological applications. The general predictive framework for the behavior of soft polymeric materials can be divided into two vastly different approaches. Highly coarse-grained models capture polymers as flexible random walks, resulting in general predictions of physical behavior but lack chemical specificity. Detailed atomistic models contain molecular detail but are frequently computationally intractable for exhaustive materials discovery. In this perspective, we discuss theoretical models that successfully bridge these disparate approaches. We identify intermediate-scale physical models that are amenable to theoretical analyses while containing sufficient granular detail to capture a range of molecular-level processes. We then provide several problems in materials engineering and biological physics where multiscale physics is essential in their behavior.

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 between chromatin and the nuclear boundary need not be specific to heterochromatin in order to 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 small subset of loci. The key distinguishing feature of heterochromatin is its high chromatin density with respect to euchromatin. In our model this densification is caused by HP1’s preferential binding to H3K9me3 marked histone tails. We conclude that factors that are themselves unrelated to the nuclear periphery can determine which genomic regions condense to form heterochromatin and thereby control which regions are relocated to the periphery.

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 (WLC) model to include statistically spaced, rigid kinks. On time scales where nucleosome positions are fixed, we find that the probability of chromatin loop formation can differ by up to six orders of magnitude between two sets of nucleosome positions drawn from the same distribution. On longer time scales, we show that continuous re-randomization 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 heterogeneity in nucleosome spacing acts as the dominant source of chromatin elasticity and governs both local and global chromatin organization.

While transport in conjugated polymers has many similarities to that in crystalline inorganic materials, several key differences reveal the unique relationship between the morphology of polymer films and the charge mobility. We develop a model that directly incorporates the molecular properties of the polymer film and correctly predicts these unique transport features. At low degree of polymerization, the increase of the mobility with the polymer chain length reveals trapping at chain ends, and saturation of the mobility at high degree of polymerization results from conformational traps within the chains. Similarly, the inverse field dependence of the mobility reveals that transport on single polymer chains is characterized by the ability of the charge to navigate around kinks and loops in the chain. These insights emphasize the connection between the polymer conformations and the transport and thereby offer a route to designing improved device morphologies through molecular design and materials processing., Modeling of semiconducting polymer identifies the relationship between molecular order, morphology, and performance. We demonstrate that experimental anomalous charge transport reveals mechanisms of transport and pathways for materials optimization.

Random copolymers play an important role in a range of soft materials applications and biological phenomena. An individual monomer is typically a single chemical unit whose length is comparable to or less than a Kuhn length, resulting in a monomer segment that is structurally rigid at length scales of a segregated domain. Previous work on random copolymer phase segregation addresses the impact of correlations between the chemical identities along the chains for flexible polymers. In these works, a single monomer unit is effectively a large polymer block that behaves as a random walk without conformational correlation associated with semiflexibility. In our work, we develop a model of semiflexible random copolymers using the wormlike chain model to capture conformational correlation of the polymer chains. To address the thermodynamics of microphase segregation and the structure of the segregated domains, we develop a random phase approximation up to quartic order in density fluctuations that leverages our ...

The motion of chromosomal DNA is essential to many biological processes, including segregation, transcriptional regulation, recombination, and packaging. Physical understanding of these processes would be dramatically enhanced through predictive, quantitative modeling of chromosome dynamics of multiple loci. Using a polymer dynamics framework, we develop a prediction for the correlation in the velocities of two loci on a single chromosome or otherwise connected by chromatin. These predictions reveal that the signature of correlated motion between two loci can be identified by varying the lag time between locus position measurements. In general, this theory predicts that as the lag time interval increases, the dual-loci dynamic behavior transitions from being completely uncorrelated to behaving as an effective single locus. This transition corresponds to the timescale of the stress communication between loci through the intervening segment. This relatively simple framework makes quantitative predictions based on a single timescale fit parameter that can be directly compared to the in vivo motion of fluorescently labeled chromosome loci. Furthermore, this theoretical framework enables the detection of dynamically coupled chromosome regions from the signature of their correlated motion.

Significance 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.

Biological systems are equipped with a diverse repertoire of proteins that regulate DNA topology with precision that is beyond the reach of conventional polymer chemistry. Here, we harness the unique properties of topoisomerases to synthesize Olympic hydrogels formed by topologically interlinked DNA rings. Using dynamic light scattering microrheology to probe the viscoelasticity of DNA topological networks, we show that topoisomerase II enables the facile preparation of active, adenosine triphosphate--driven Olympic hydrogels that can be switched between liquid and solid states on demand. Our results provide a versatile system for engineering switchable topological materials that may be broadly leveraged to model the impact of topological constraints and active dynamics in the physics of chromosomes and other polymeric materials.

Semiconducting polymers play an important role in a wide range of optical and electronic material applications. It is widely accepted that the polymer ordering impacts charge transport in such devices. However, the connection between molecular ordering and device performance is difficult to predict due to the current need for a mathematical theory of the physics that dictate charge transport in semiconducting polymers. We present an analytical and computational description of semicrystalline conjugated polymer materials that captures the impact of polymer conformation on charge transport in heterogeneous thin films. We first develop an analytical theory for the statistical behavior of a polymer chain emanating from a crystallite, predicting the average distance to the first kink that would trap a charge. This analysis is used to define the conditions where percolation would lead to efficient transport through a semicrystalline material. We then establish a model that predicts the multiscale charge transport. This model is used to identify the speed limits of charge transport at short and long time scales for varying fraction of crystallinity. This work provides a rational framework to connect molecular organization to device performance.

We describe three optical tags, ArrayG, ArrayD and ArrayG/N, for intracellular tracking of single molecules over milliseconds to hours. ArrayG is a fluorogenic tag composed of a green fluorescent protein–nanobody array and monomeric wild-type green fluorescent protein binders that are initially dim but brighten ~26-fold on binding with the array. By balancing the rates of binder production, photobleaching and stochastic binder exchange, we achieve temporally unlimited tracking of single molecules. High-speed tracking of ArrayG-tagged kinesins and integrins for thousands of frames reveals novel dynamical features. Tracking of single histones at 0.5 Hz for >1 hour with the import competent ArrayG/N tag shows that chromosomal loci behave as Rouse polymers with visco-elastic memory and exhibit a non-Gaussian displacement distribution. ArrayD, based on a dihydrofolate reductase nanobody array and dihydrofolate reductase–fluorophore binder, enables dual-color imaging. The arrays combine brightness, fluorogenicity, fluorescence replenishment and extended fluorophore choice, opening new avenues for tracking single molecules in living cells. A genetically encoded array to amplify signals for live-cell single-molecule fluorescence imaging allows unlimited temporal resolution through exchange of fluorophores and can be used to monitor the dynamics of histones, kinesins and integrins.

Despite the innate complexity of the cell, emergent scale-invariant behavior is observed in many biological systems. We investigate one example of this phenomenon: the dynamics of large complexes in the bacterial cytoplasm. The observed dynamics of these complexes is scale invariant in three measures of dynamics: mean-squared displacement (MSD), velocity autocorrelation function, and the step-size distribution. To investigate the physical mechanism for this emergent scale invariance, we explore minimal models in which mobility is modeled as diffusion on a rough free-energy landscape in one dimension. We discover that all three scale-invariant characteristics emerge generically in the strong disorder limit. (Strong disorder is defined by the divergence of the ensemble-averaged hop time between lattice sites.) In particular, we demonstrate how the scale invariance of the relative step-size distribution can be understood from the perspective of extreme-value theory in statistics (EVT). We show that the Gumbel scale parameter is simply related to the MSD scaling parameter. The EVT mechanism of scale invariance is expected to be generic to strongly disordered systems and therefore a powerful tool for the analysis of other systems in biology and beyond.

Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in the load response of macroscopic structures, only when fluctuations can be neglected, whereas membranes, polymer brushes, filaments, and macromolecular chains undergo considerable Brownian fluctuations. We analyze here the buckling of a fluctuating semiflexible polymer experiencing a compressive load. Previous works rely on approximations to the polymer statistics, resulting in a range of predictions for the buckling transition that disagree on whether fluctuations elevate or depress the critical buckling force. In contrast, our theory exploits exact results for the statistical behavior of the worm-like chain model yielding unambiguous predictions about the buckling conditions and nature of the buckling transition. We find that a fluctuating polymer under compressive load requires a larger force to buckle than an elastic rod in the absence of fluctuations. The nature of the buckling transition exhibits a marked change from being distinctly second order in the absence of fluctuations to being a more gradual, compliant transition in the presence of fluctuations. We analyze the thermodynamic contributions throughout the buckling transition to demonstrate that the chain entropy favors the extended state over the buckled state, providing a thermodynamic justification of the elevated buckling force.

Storage and retrieval of the genetic information in cells is a dynamic process that requires the DNA to undergo dramatic structural rearrangements. DNA looping is a prominent example of such a structural rearrangement that is essential for transcriptional regulation in both prokaryotes and eukaryotes, and the speed of such regulations affects the fitness of individuals. Here, we examine the in vitro looping dynamics of the classic Lac repressor gene-regulatory motif. We show that both loop association and loop dissociation at the DNA-repressor junctions depend on the elastic deformation of the DNA and protein, and that both looping and unlooping rates approximately scale with the looping J factor, which reflects the system's deformation free energy. We explain this observation by transition state theory and model the DNA-protein complex as an effective worm-like chain with twist. We introduce a finite protein-DNA binding interaction length, in competition with the characteristic DNA deformation length scale, as the physical origin of the previously unidentified loop dissociation dynamics observed here, and discuss the robustness of this behavior to perturbations in several polymer parameters.

The ciliary permeability barrier is mechanistically distinct from other cellular diffusion barriers and allows soluble proteins under ∼100 kD in size to enter cilia in the absence of active transport., Specific proteins are concentrated within primary cilia, whereas others remain excluded. To understand the mechanistic basis of entry into cilia, we developed an in vitro assay using cells in which the plasma membrane was permeabilized, but the ciliary membrane was left intact. Using a diffusion-to-capture system and quantitative analysis, we find that proteins >9 nm in diameter (∼100 kD) are restricted from entering cilia, and we confirm these findings in vivo. Interference with the nuclear pore complex (NPC) or the actin cytoskeleton in permeabilized cells demonstrated that the ciliary diffusion barrier is mechanistically distinct from those of the NPC or the axon initial segment. Moreover, applying a mass transport model to this system revealed diffusion coefficients for soluble and membrane proteins within cilia that are compatible with rapid exploration of the ciliary space in the absence of active transport. Our results indicate that large proteins require active transport for entry into cilia but not necessarily for movement inside cilia.