Modeling identifies variability in SARS-CoV-2 uptake and eclipse phase by infected cells as principal drivers of extreme variability in nasal viral load in the 48 h post infection.

The SARS-CoV-2 coronavirus continues to evolve with scores of mutations of the spike, membrane, envelope, and nucleocapsid structural proteins that impact pathogenesis. Infection data from nasal swabs, nasal PCR assays, upper respiratory samples, ex vivo cell cultures and nasal epithelial organoids reveal extreme variabilities in SARS-CoV-2 RNA titers within and between the variants. Some variabilities are naturally prone to clinical testing protocols and experimental controls. Here we focus on nasal viral load sensitivity arising from the timing of sample collection relative to onset of infection and from heterogeneity in the kinetics of cellular infection, uptake, replication, and shedding of viral RNA copies. The sources of between-variant variability are likely due to SARS-CoV-2 structural protein mutations, whereas within-variant population variability is likely due to heterogeneity in cellular response to that particular variant. With the physiologically faithful, agent-based mechanistic model of inhaled exposure and infection from (Chen et al., 2022), we perform statistical sensitivity analyses of the progression of nasal viral titers in the first 0-48 h post infection, focusing on three kinetic mechanisms. Model simulations reveal shorter latency times of infected cells (including cellular uptake, viral RNA replication, until the onset of viral RNA shedding) exponentially accelerate nasal viral load. Further, the rate of infectious RNA copies shed per day has a proportional influence on nasal viral load. Finally, there is a very weak, negative correlation of viral load with the probability of infection per virus-cell encounter, the model proxy for spike-receptor binding affinity.

The power of weak, transient interactions across biology: A paradigm of emergent behavior.

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus.

Modeling insights into SARS-CoV-2 respiratory tract infections prior to immune protection.

Mechanistic insights into human respiratory tract (RT) infections from SARS-CoV-2 can inform public awareness as well as guide medical prevention and treatment for COVID-19 disease. Yet the complexity of the RT and the inability to access diverse regions pose fundamental roadblocks to evaluation of potential mechanisms for the onset and progression of infection (and transmission). We present a model that incorporates detailed RT anatomy and physiology, including airway geometry, physical dimensions, thicknesses of airway surface liquids (ASLs), and mucus layer transport by cilia. The model further incorporates SARS-CoV-2 diffusivity in ASLs and best-known data for epithelial cell infection probabilities, and, once infected, duration of eclipse and replication phases, and replication rate of infectious virions. We apply this baseline model in the absence of immune protection to explore immediate, short-term outcomes from novel SARS-CoV-2 depositions onto the air-ASL interface. For each RT location, we compute probability to clear versus infect; per infected cell, we compute dynamics of viral load and cell infection. Results reveal that nasal infections are highly likely within 1-2 days from minimal exposure, and alveolar pneumonia occurs only if infectious virions are deposited directly into alveolar ducts and sacs, not via retrograde propagation to the deep lung. Furthermore, to infect just 1% of the 140 m2 of alveolar surface area within 1 week, either 103 boluses each with 106 infectious virions or 106 aerosols with one infectious virion, all physically separated, must be directly deposited. These results strongly suggest that COVID-19 disease occurs in stages: a nasal/upper RT infection, followed by self-transmission of infection to the deep lung. Two mechanisms of self-transmission are persistent aspiration of infected nasal boluses that drain to the deep lung and repeated rupture of nasal aerosols from infected mucosal membranes by speaking, singing, or cheering that are partially inhaled, exhaled, and re-inhaled, to the deep lung.

A hybrid discrete-continuum model of immune responses to SARS-CoV-2 infection in the lung alveolar region, with a focus on interferon induced innate response.

We develop a lattice-based, hybrid discrete-continuum modeling framework for SARS-CoV-2 exposure and infection in the human lung alveolar region, or parenchyma, the massive surface area for gas exchange. COVID-19 pneumonia is alveolar infection by the SARS-CoV-2 virus significant enough to compromise gas exchange. The modeling framework orchestrates the onset and progression of alveolar infection, spatially and temporally, beginning with a pre-immunity baseline, upon which we superimpose multiple mechanisms of immune protection conveyed by interferons and antibodies. The modeling framework is tunable to individual profiles, focusing here on degrees of innate immunity, and to the evolving infection-replication properties of SARS-CoV-2 variant strains. The model employs partial differential equations for virion, interferon, and antibody concentrations governed by diffusion in the thin fluid coating of alveolar cells, species and lattice interactions corresponding to sources and sinks for each species, and multiple immune protections signaled by interferons. The spatial domain is a two-dimensional, rectangular lattice of alveolar type I (non-infectable) and type II (infectable) cells with a stochastic, species-concentration-governed, switching dynamics of type II lattice sites from healthy to infected. Once infected, type II cells evolve through three phases: an eclipse phase during which RNA copies (virions) are assembled; a shedding phase during which virions and interferons are released; and then cell death. Model simulations yield the dynamic spread of, and immune protection against, alveolar infection and viral load from initial sites of exposure. We focus in this paper on model illustrations of the diversity of outcomes possible from alveolar infection, first absent of immune protection, and then with varying degrees of four known mechanisms of interferon-induced innate immune protection. We defer model illustrations of antibody protection to future studies. Results presented reinforce previous recognition that interferons produced solely by infected cells are insufficient to maintain a high efficacy level of immune protection, compelling additional mechanisms to clear alveolar infection, such as interferon production by immune cells and adaptive immunity (e.g., T cells). This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Statistical mechanics of chromosomes: in vivo and in silico approaches reveal high-level organization and structure arise exclusively through mechanical feedback between loop extruders and chromatin substrate properties.

The revolution in understanding higher order chromosome dynamics and organization derives from treating the chromosome as a chain polymer and adapting appropriate polymer-based physical principles. Using basic principles, such as entropic fluctuations and timescales of relaxation of Rouse polymer chains, one can recapitulate the dominant features of chromatin motion observed in vivo. An emerging challenge is to relate the mechanical properties of chromatin to more nuanced organizational principles such as ubiquitous DNA loops. Toward this goal, we introduce a real-time numerical simulation model of a long chain polymer in the presence of histones and condensin, encoding physical principles of chromosome dynamics with coupled histone and condensin sources of transient loop generation. An exact experimental correlate of the model was obtained through analysis of a model-matching fluorescently labeled circular chromosome in live yeast cells. We show that experimentally observed chromosome compaction and variance in compaction are reproduced only with tandem interactions between histone and condensin, not from either individually. The hierarchical loop structures that emerge upon incorporation of histone and condensin activities significantly impact the dynamic and structural properties of chromatin. Moreover, simulations reveal that tandem condensin-histone activity is responsible for higher order chromosomal structures, including recently observed Z-loops.

Experimental Data and PBPK Modeling Quantify Antibody Interference in PEGylated Drug Carrier Delivery.

Physiologically-based pharmacokinetic (PBPK) modeling is a popular drug development tool that integrates physiology, drug physicochemical properties, preclinical data, and clinical information to predict drug systemic disposition. Since PBPK models seek to capture complex physiology, parameter uncertainty and variability is a prevailing challenge: there are often more compartments (e.g., organs, each with drug flux and retention mechanisms, and associated model parameters) than can be simultaneously measured. To improve the fidelity of PBPK modeling, one approach is to search and optimize within the high-dimensional model parameter space, based on experimental time-series measurements of drug distributions. Here, we employ Latin Hypercube Sampling (LHS) on a PBPK model of PEG-liposomes (PL) that tracks biodistribution in an 8-compartment mouse circulatory system, in the presence (APA+) or absence (naïve) of anti-PEG antibodies (APA). Near-continuous experimental measurements of PL concentration during the first hour post-injection from the liver, spleen, kidney, muscle, lung, and blood plasma, based on PET/CT imaging in live mice, are used as truth sets with LHS to infer optimal parameter ranges for the full PBPK model. The data and model quantify that PL retention in the liver is the primary differentiator of biodistribution patterns in naïve versus APA+ mice, and spleen the secondary differentiator. Retention of PEGylated nanomedicines is substantially amplified in APA+ mice, likely due to PL-bound APA engaging specific receptors in the liver and spleen that bind antibody Fc domains. Our work illustrates how applying LHS to PBPK models can further mechanistic understanding of the biodistribution and antibody-mediated clearance of specific drugs.

Centromere tethering confines chromosome domains.

The organization of chromosomes into territories plays an important role in a wide range of cellular processes, including gene expression, transcription, and DNA repair. Current understanding has largely excluded the spatiotemporal dynamic fluctuations of the chromatin polymer. We combine in vivo chromatin motion analysis with mathematical modeling to elucidate the physical properties that underlie the formation and fluctuations of territories. Chromosome motion varies in predicted ways along the length of the chromosome, dependent on tethering at the centromere. Detachment of a tether upon inactivation of the centromere results in increased spatial mobility. A confined bead-spring chain tethered at both ends provides a mechanism to generate observed variations in local mobility as a function of distance from the tether. These predictions are realized in experimentally determined higher effective spring constants closer to the centromere. The dynamic fluctuations and territorial organization of chromosomes are, in part, dictated by tethering at the centromere.

Convolutional neural networks automate detection for tracking of submicron-scale particles in 2D and 3D.

Particle tracking is a powerful biophysical tool that requires conversion of large video files into position time series, i.e., traces of the species of interest for data analysis. Current tracking methods, based on a limited set of input parameters to identify bright objects, are ill-equipped to handle the spectrum of spatiotemporal heterogeneity and poor signal-to-noise ratios typically presented by submicron species in complex biological environments. Extensive user involvement is frequently necessary to optimize and execute tracking methods, which is not only inefficient but introduces user bias. To develop a fully automated tracking method, we developed a convolutional neural network for particle localization from image data, comprising over 6,000 parameters, and used machine learning techniques to train the network on a diverse portfolio of video conditions. The neural network tracker provides unprecedented automation and accuracy, with exceptionally low false positive and false negative rates on both 2D and 3D simulated videos and 2D experimental videos of difficult-to-track species.

Transient crosslinking kinetics optimize gene cluster interactions.

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5kbp domains (genes) in the nucleolus on Chromosome XII; and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling predictions.

Observation of transition cascades in sheared liquid crystalline polymers.

We report on the shear rheology of liquid crystalline solutions composed of charged, rodlike polymers that form supramolecular assemblies dispersed in water. Under steady shear, we observe shear thickening behavior, followed by a hesitation in the viscosity accompanied by an extremely narrow range of negative first normal stress difference. The Peclet number (Pe, shear rate normalized by rod rotational diffusivity) for the onset of shear thickening is in agreement with previous, high-resolution numerical simulations of the Doi-Edwards-Hess kinetic theory. We interrogate these dynamic responses through shear step-down experiments, revealing a complex evolution of transient responses. Detailed analysis of the stress transients provides compelling evidence that the principal axis of the rod orientational distribution, the nematic director, undergoes a cascade of transitions and coexistence of periodic states known as kayaking, tumbling, and wagging, before transitioning to steady flow alignment above a critical shear rate.

Antibody-Mediated Immobilization of Virions in Mucus.

Antibodies have been shown to hinder the movement of herpes simplex virus virions in cervicovaginal mucus, as well as other viruses in other mucus secretions. However, it has not been possible to directly observe the mechanisms underlying this phenomenon, so the nature of virion-antibody-mucin interactions remain poorly understood. In this work, we analyzed thousands of virion traces from single particle tracking experiments to explicate how antibodies must cooperate to immobilize virions for relatively long time periods. First, using a clustering analysis, we observed a clear separation between two classes of virion behavior: freely diffusing and immobilized. While the proportion of freely diffusing virions decreased with antibody concentration, the magnitude of their diffusivity did not, implying an all-or-nothing dichotomy in the pathwise effect of the antibodies. Proceeding under the assumption that all binding events are reversible, we used a novel switch-point detection method to conclude that there are very few, if any, state switches on the experimental timescale of 20 s. To understand this slow state switching, we analyzed a recently proposed continuous-time Markov chain model for binding kinetics and virion movement. Model analysis implied that virion immobilization requires cooperation by multiple antibodies that are simultaneously bound to the virion and mucin matrix and that there is an entanglement phenomenon that accelerates antibody-mucin binding when a virion is immobilized. In addition to developing a widely applicable framework for analyzing multistate particle behavior, this work substantially enhances our mechanistic understanding of how antibodies can reinforce a mucus barrier against passive invasive species.

Pathological mucus and impaired mucus clearance in cystic fibrosis patients result from increased concentration, not altered pH.

Cystic fibrosis (CF) is a recessive genetic disease that is characterised by airway mucus plugging and reduced mucus clearance. There are currently alternative hypotheses that attempt to describe the abnormally viscous and elastic mucus that is a hallmark of CF airways disease, including: 1) loss of CF transmembrane regulator (CFTR)-dependent airway surface volume (water) secretion, producing mucus hyperconcentration-dependent increased viscosity, and 2) impaired bicarbonate secretion by CFTR, producing acidification of airway surfaces and increased mucus viscosity.A series of experiments was conducted to determine the contributions of mucus concentration versus pH to the rheological properties of airway mucus across length scales from the nanoscopic to macroscopic.For length scales greater than the nanoscopic, i.e. those relevant to mucociliary clearance, the effect of mucus concentration dominated over the effect of airway acidification.Mucus hydration and chemical reduction of disulfide bonds that connect mucin monomers are more promising therapeutic approaches than alkalisation.

RIGID GRAPH COMPRESSION: MOTIF-BASED RIGIDITY ANALYSIS FOR DISORDERED FIBER NETWORKS.

Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph theoretic property of rigidity to model mechanical reinforcement in composites with stiff rod-like particles. We develop an efficient algorithmic approach called rigid graph compression (RGC) to describe the transition from floppy to rigid in disordered fiber networks ("rod-hinge systems"), which form the reinforcing phase in many composite systems. To establish RGC on a firm theoretical foundation, we adapt rigidity matroid theory to identify primitive topological network motifs that serve as rules for composing interacting rigid particles into larger rigid components. This approach is computationally efficient and stable, because RGC requires only topological information about rod interactions (encoded by a sparse unweighted network) rather than geometrical details such as rod locations or pairwise distances (as required in rigidity matroid theory). We conduct numerical experiments on simulated two-dimensional rod-hinge systems to demonstrate that RGC closely approximates the rigidity percolation threshold for such systems, through comparison with the pebble game algorithm (which is exact in two dimensions). Importantly, whereas the pebble game is derived from Laman's condition and is only valid in two dimensions, the RGC approach naturally extends to higher dimensions.

Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures - Part I: Idealized Axisymmetric Swirling Flow.

A multi-mode nonlinear constitutive model for mucus is constructed directly from micro- and macro-rheology experimental data on cell culture mucus, and a numerical algorithm is developed for the culture geometry and idealized cilia driving conditions. This study investigates the roles that mucus rheology, wall effects, and HBE culture geometry play in the development of flow profiles and the shape of the air-mucus interface. Simulations show that viscoelasticity captures normal stress generation in shear leading to a peak in the air-mucus interface at the middle of the culture and a depression at the walls. Linear and nonlinear viscoelastic regimes can be observed in cultures by varying the hurricane radius and mean rotational velocity. The advection-diffusion of a drug concentration dropped at the surface of the mucus flow is simulated as a function of Peclet number.

Modeling the Excess Cell Surface Stored in a Complex Morphology of Bleb-Like Protrusions.

Cells transition from spread to rounded morphologies in diverse physiological contexts including mitosis and mesenchymal-to-amoeboid transitions. When these drastic shape changes occur rapidly, cell volume and surface area are approximately conserved. Consequently, the rounded cells are suddenly presented with a several-fold excess of cell surface whose area far exceeds that of a smooth sphere enclosing the cell volume. This excess is stored in a population of bleb-like protrusions (BLiPs), whose size distribution is shown by electron micrographs to be skewed. We introduce three complementary models of rounded cell morphologies with a prescribed excess surface area. A 2D Hamiltonian model provides a mechanistic description of how discrete attachment points between the cell surface and cortex together with surface bending energy can generate a morphology that satisfies a prescribed excess area and BLiP number density. A 3D random seed-and-growth model simulates efficient packing of BLiPs over a primary rounded shape, demonstrating a pathway for skewed BLiP size distributions that recapitulate 3D morphologies. Finally, a phase field model (2D and 3D) posits energy-based constitutive laws for the cell membrane, nematic F-actin cortex, interior cytosol, and external aqueous medium. The cell surface is equipped with a spontaneous curvature function, a proxy for the cell surface-cortex couple, that is a priori unknown, which the model "learns" from the thin section transmission electron micrograph image (2D) or the "seed and growth" model image (3D). Converged phase field simulations predict self-consistent amplitudes and spatial localization of pressure and stress throughout the cell for any posited stationary morphology target and cell compartment constitutive properties. The models form a general framework for future studies of cell morphological dynamics in a variety of biological contexts.

Kinetic attractor phase diagrams of active nematic suspensions: the dilute regime.

Large-scale simulations by the authors of the kinetic-hydrodynamic equations for active polar nematics revealed a variety of spatio-temporal attractors, including steady and unsteady, banded (1d) and cellular (2d) spatial patterns. These particle scale activation-induced attractors arise at dilute nanorod volume fractions where the passive equilibrium phase is isotropic, whereas all previous model simulations have focused on the semi-dilute, nematic equilibrium regime and mostly on low-moment orientation tensor and polarity vector models. Here we extend our previous results to complete attractor phase diagrams for active nematics, with and without an explicit polar potential, to map out novel spatial and dynamic transitions, and to identify some new attractors, over the parameter space of dilute nanorod volume fraction and nanorod activation strength. The particle-scale activation parameter corresponds experimentally to a tunable force dipole strength (so-called pushers with propulsion from the rod tail) generated by active rod macromolecules, e.g., catalysis with the solvent phase, ATP-induced propulsion, or light-activated propulsion. The simulations allow 2d spatial variations in all flow and orientational variables and full spherical orientational degrees of freedom; the attractors correspond to numerical integration of a coupled system of 125 nonlinear PDEs in 2d plus time. The phase diagrams with and without the polar interaction potential are remarkably similar, implying that polar interactions among the rodlike particles are not essential to long-range spatial and temporal correlations in flow, polarity, and nematic order. As a general rule, above a threshold, low volume fractions induce 1d banded patterns, whereas higher yet still dilute volume fractions yield 2d patterns. Again as a general rule, varying activation strength at fixed volume fraction induces novel dynamic transitions. First, stationary patterns saturate the instability of the isotropic state, consisting of discrete 1d banded or 2d cellular patterns depending on nanorod volume fraction. Increasing activation strength further induces a sequence of attractor bifurcations, including oscillations superimposed on the 1d and 2d stationary patterns, a uniform translational motion of 1d and 2d oscillating patterns, and periodic switching between 1d and 2d patterns. These results imply that active macromolecular suspensions are capable of long-range spatial and dynamic organization at isotropic equilibrium concentrations, provided particle-scale activation is sufficiently strong.

Transient antibody-mucin interactions produce a dynamic molecular shield against viral invasion.

Given the difficulty in finding a cure for HIV/AIDS, a promising prevention strategy to reduce HIV transmission is to directly block infection at the portal of entry. The recent Thai RV144 trial offered the first evidence that an antibody-based vaccine may block heterosexual HIV transmission. Unfortunately, the underlying mechanism(s) for protection remain unclear. Here we theoretically examine a hypothesis that builds on our recent laboratory observation: virus-specific antibodies (Ab) can trap individual virions in cervicovaginal mucus (CVM), thereby reducing infection in vivo. Ab are known to have a weak-previously considered inconsequential-binding affinity with the mucin fibers that constitute CVM. However, multiple Ab can bind to the same virion at the same time, which markedly increases the overall Ab-mucin binding avidity, and creates an inheritable virion-mucin affinity. Our model takes into account biologically relevant length and timescales, while incorporating known HIV-Ab affinity and the respective diffusivities of viruses and Ab in semen and CVM. The model predicts that HIV-specific Ab in CVM leads to rapid formation and persistence of an HIV concentration front near the semen/CVM interface, far from the vaginal epithelium. Such an HIV concentration front minimizes the flux of HIV virions reaching target cells, and maximizes their elimination upon drainage of genital secretions. The robustness of the result implies that even exceedingly weak Ab-mucin affinity can markedly reduce the flux of virions reaching target cells. Beyond this specific application, the model developed here is adaptable to other pathogens, mucosal barriers, and geometries, as well as kinetic and diffusional effects, providing a tool for hypothesis testing and producing quantitative insights into the dynamics of immune-mediated protection.

Micro-heterogeneity metrics for diffusion in soft matter.

Passive particle tracking of diffusive paths in soft matter, coupled with analysis of the path data, is firmly established as a fundamental methodology for characterization of both diffusive transport properties (the focus here) and linear viscoelasticity. For either focus, particle time series are typically analyzed by ensemble averaging over paths, a perfectly natural protocol for homogeneous materials or for applications where mean properties are sufficient. Many biological materials, however, are heterogeneous over length scales above the probe diameter, and the implications of heterogeneity for biologically relevant transport properties (e.g. diffusive passage times through a complex fluid layer) motivate this paper. Our goals are three-fold: first, to detect heterogeneity as reflected by the ensemble path data; second, to further decompose the ensemble of particle paths into statistically distinct clusters; and third, to fit the path data in each cluster to a model for the underlying stochastic process. After reviewing current best practices for detection and assessment of heterogeneity in diffusive processes, we introduce our strategy toward the first two goals with methods from the statistics and machine learning literature that have not found application thus far to passive particle tracking data. We apply an analysis based solely on the path data that detects heterogeneity and yields a decomposition of particle paths into statistically distinct clusters. After these two goals are achieved, one can then pursue model-fitting. We illustrate these heterogeneity metrics on diverse datasets: for numerically generated and experimental particle paths, with tunable and unknown heterogeneity, on numerical models for simple diffusion and anomalous sub-diffusion, and experimentally on sucrose, hyaluronic acid, agarose, and human lung culture mucus solutions.

Benchmarking the Immersed Boundary Method for Viscoelastic Flows.

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological fluid dynamics and other modeling scenarios in which a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems involving viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constitutive equation. In the viscoelastic context, however, relatively little work has explored the accuracy or convergence properties of this numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using either the idealized Oldroyd-B constitutive model or the more physcially realistic, polymer-entanglementbased Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.

Transient crosslinking controls the condensate formation pathway within chromatin networks.

The network structure of densely packed chromatin within the nucleus of eukaryotic cells acts in concert with nonequilibrium processes. Using statistical physics simulations, we explore the control provided by transient crosslinking of the chromatin network by structural-maintenance-of-chromosome (SMC) proteins over (i) the physical properties of the chromatin network and (ii) condensate formation of embedded molecular species. We find that the density and lifetime of transient SMC crosslinks regulate structural relaxation modes and tune the sol-vs-gel state of the chromatin network, which imparts control over the kinetic pathway to condensate formation. Specifically, lower density, shorter-lived crosslinks induce sollike networks and a droplet-fusion pathway, whereas higher density, longer-lived crosslinks induce gellike networks and an Ostwald-ripening pathway.