Accurate simulation of incompressible Carreau-type blood flow in aneurysmal vessels is challenging due to the nonlinear coupling between viscosity and shear rate and tortuous vascular geometries. In this paper, we develop a fully discrete second-order-in-time numerical method for the incompressible Carreau model relevant to large-artery hemodynamics. In space, we use a hybridizable discontinuous Galerkin (HDG) discretization with numerical traces on element interfaces, yielding locally conservative fluxes and allowing efficient static condensation of unknowns. In time, we employ a BDF2-based pressure-correction scheme together with a discrete gradient reconstruction and lifting operator for the nonlinear diffusion term, designed so that the fully discrete scheme satisfies a discrete analogue of the continuous energy law. We prove that the scheme is well posed and unconditionally energy stable. Numerical experiments verify second-order convergence in time and space, and include idealized fusiform and saccular aneurysm configurations that probe jets and recirculation regions, as well as patient-specific cerebral aneurysm geometries. These results demonstrate that the proposed numerical framework provides an accurate, robust tool for computing non-Newtonian blood flow fields and wall-shear-stress distributions in complex three-dimensional vascular domains.

Septins are a conserved family of cytoskeletal proteins known for sensing micron-scale membrane curvature via amphipathic helix (AH) domains. While cooperative interactions in septin assembly have been suggested, the molecular mechanisms governing membrane binding and assembly remain unclear. Building on prior findings, we use all-atom molecular dynamics simulations to examine how single and paired extended AH domains, derived from Cdc12, interact with lipid bilayers. We find that a single membrane-bound AH adopts a bent conformation upon membrane association. In solution, a second AH peptide preferentially interacts with the bound peptide through conserved salt bridges, favoring an antiparallel arrangement. Simulations of covalently linked AH tandems confirm the stability of this configuration. When two AH domains are membrane-bound, they induce localized lipid packing defects, reduce tail order, and exhibit slight peptide displacement on planar bilayers. These observations suggest a cooperative AH binding mechanism and are consistent with models in which lipid packing defects facilitate multivalent AH engagement in curved membrane environments. Our findings advance the mechanistic understanding of septin-membrane interactions and highlight the role of cooperative AH domain binding in stabilizing higher-order structures.

In eukaryotic cells, the nucleolus is a pivotal subnuclear organelle, instrumental in ribosomal RNA synthesis and nuclear organization. Although the unique viscoelastic properties of the nucleolus are associated with transient interactions between chromatin and regulatory proteins, the specific mechanistic details driving nucleolar phase separation and mechanical responses have remained largely undefined. In this study, we employ a computational approach to elucidate chromatin-protein interactions within the nucleolus of budding yeast, using a sophisticated bead-spring polymer model. This model integrates DNA and nucleolar architectures with dynamic simulations of interactions involving chromosomal structural maintenance proteins and rDNA transcriptional regulators through systematically varied cross-linking kinetics. Our findings reveal that modulations in protein-DNA interactions critically dictate the phase behavior, relaxation dynamics, and viscoelastic properties of the nucleolus, underscoring a complex but precise regulatory mechanism at play. Notably, protein-mediated bridging emerges as a critical factor enhancing nucleolar condensation and modulating stress relaxation, highlighting the transformative role of transient cross-linking in nuclear mechanics regulation. These insights not only deepen our understanding of nucleolar function but also open avenues for interventions in genetic engineering and disease therapeutics.

Amphipathic helices (AHs) are secondary structures that can facilitate binding of proteins to the membrane by folding into a helix with hydrophobic and hydrophilic faces that interact with the same surfaces in the lipid membrane. Septins are cytoskeletal proteins that preferentially bind to domains of micron-scale curvature on the cell membrane. Studies have shown that AH domains in septin are essential for curvature sensing. We present the first computational study of septin AH interactions with lipid bilayers. Using all-atom simulations and metadynamics-enhanced sampling, we study the effect of charge distribution at the flanking ends of septin AH on the energy for helical folding and its consequences on the binding configuration and affinity to the membrane. This is relevant to septins, since the net positive charge on the flanking C-terminal amino acids is a conserved property across several organisms. Simulations revealed that the energy barrier for folding in the neutral-capped AH is much larger than the charge-capped AH, leading to a small fraction of AH folding and integration to the membrane compared to a significantly folded configuration in the bound charge-capped AH. These observations are consistent with the binding measurements of synthetic AH constructs with variable helicity to lipid vesicles. Additionally, we examined an extended AH sequence including eight amino acids upstream and downstream of the AH to mimic the native protein. Again, simulations and experiments show that the extended peptide, with a net positive charge at C-terminus, adopts a strong helical configuration in solution, giving rise to a higher membrane affinity. Altogether, these results identify the energy cost for folding of AHs as a regulator of AH binding configuration and affinity and provide a basic template for parameterizing AH-membrane interactions as a starting point for the future multiscale simulations for septin-membrane interactions.

The pursuit of polymer nanocomposites (PNCs) that simultaneously exhibit high strength and toughness has long been hindered by the intrinsic trade-offs between these properties. Here, we introduce a groundbreaking strategy by integrating stiff nanorings (SNRs) into polymer melts, enabling unprecedented mechanical performance without relying on traditional cross-linking or filler reinforcement. Through advanced statistical rheological simulations, we reveal that threading polymer chains through SNRs transforms the melt into a gel-like hyperviscous fluid, despite the absence of permanent or transient cross-links. Under applied strain, the dynamic sliding of polymer chains along the constrained SNRs concentrates stress on the nanorings, effectively delaying chain relaxation and minimizing chain breakage. This innovative mechanism not only enhances both strength and toughness but also imparts exceptional viscoelastic properties, surpassing those of conventional polymer melts. Our findings establish SNRs as dynamic stress-dissipative units, offering a versatile and scalable platform for designing next-generation PNCs. This work opens new avenues for applications in extreme mechanical environments, from advanced manufacturing to biomedical engineering, and represents a paradigm shift in PNC science.

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 for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with 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 constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based 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.

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.

Our research investigates septin, a nano-scale protein capable of sensing shallow micron-scale curvatures in cellular membranes of the eukaryotes. Previous studies have identified the amphipathic helix (AH) domain as the required and sufficient molecular component for septin's curvature sensing. Our aim is to understand the structural and mechanical features of AH domains and lipid bilayers that contribute to AH binding to the bilayer, using all-atom molecular dynamics simulation. Our results show that the AH domain must fold from disordered state in solution to helical conformation, upon interactions with the lipid bilayer, to stay bound.

The assembly of long-range aligned structures of two-dimensional nanosheets (2DNSs) in polymer nanocomposites (PNCs) is in urgent need for the design of nanoelectronics and lightweight energy-storage materials of high conductivity for electricity or heat. These 2DNS are thin and exhibit thermal fluctuations, leading to an intricate interplay with polymers in which entropic effects can be exploited to facilitate a range of different assemblies. In molecular dynamics simulations of experimentally studied 2DNSs, we show that the layer-forming crystallization of 2DNSs is programmable by regulating the strengths and ranges of polymer-induced entropic depletion attractions between pairs of 2DNSs, as well as between single 2DNSs and a substrate surface, by exclusively tuning the temperature and size of the 2DNS. Enhancing the temperature supports the 2DNS-substrate depletion rather than crystallization of 2DNSs in the bulk, leading to crystallized layers of 2DNSs on the substrate surfaces. On the other hand, the interaction range of the 2DNS-2DNS depletion attraction extends further than the 2DNS-substrate attraction whenever the 2DNS size is well above the correlation length of the polymers, which results in a nonmonotonic dependence of the crystallization layer on the 2DNS size. It is demonstrated that the depletion-tuned crystallization layers of 2DNSs contribute to a conductive channel in which individual lithium ions (Li ions) migrate efficiently through the PNCs. This work provides statistical and dynamical insights into the balance between the 2DNS-2DNS and 2DNS-substrate depletion interactions in polymer-2DNS composites and highlights the possibilities to exploit depletion strategies in order to engineer crystallization processes of 2DNSs and thus to control electrical conductivity.

Septins are a class of cytoskeletal proteins that preferentially bind to domains of micron-scale curvature on the cell membrane. Studies have shown that amphipathic helix (AH) domains in septin oligomers are essential for septin curvature sensing. Yet, the underlying mechanochemical interactions that modulate this curvature sensing remain ambiguous. Here we use all-atom molecular dynamics alongside a metadynamics enhanced sampling approach to bridge the gap between time and length scales required to optimize and validate experimental design of amphipathic helices. Simulations revealed that the local charge on the termini of an 18-amino-acid AH peptide impacts its helical content and positioning within lipid membranes. These computational observations are confirmed with experiments measuring the binding of synthetic AH constructs with variable helical content and charged termini to lipid vesicles. Taken together, these results identify the helical content of amphipathic helices as a regulator of septin binding affinity to lipid membranes. Additionally, we examined an extended AH sequence including 8 amino acids upstream and downstream of the minimal 18-amino-acid-long AH domain to more closely mimic the native protein in simulations and experiments. Simulations and experiments show that the extended peptide sequence adopts a strong alpha-helical conformation when free in solution, giving rise to a higher affinity to lipid membranes than that of the shorter AH sequence. Together, these results provide insight into how the native septin proteins interact with membranes, and establish general design principles that can guide the interaction of future synthetic materials with lipid membranes in a programmable manner. STATEMENT OF SIGNIFICANCE Understanding how cells sense and react to their shape is necessary for numerous biological processes. Here we explore the interactions between amphipathic helices, a curvature sensing protein motif, and lipid membranes. Using molecular dynamics simulations, enhanced simulation sampling techniques, and experiments, we find that increasing the helical content of the amphipathic helix or adding charged capping sequences yields higher membrane binding affinity. Understanding these parameters for membrane-binding could enable us to interface and regulate native protein functions, as well as guide the design of synthetic curvature-sensing materials that can interact with and deform lipid membranes. ### Competing Interest Statement The authors have declared no competing interest.

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment.

Human respiratory mucus (HRM) is extremely soft, compelling passive microrheology for linear viscoelastic characterization. We focus this study on the use of passive microrheology to characterize HRM heterogeneity, a phenomenon in normal HRM that becomes extreme during cystic fibrosis (CF) disease. Specifically, a fraction of the mucin polymers comprising HRM phase-separate into insoluble structures, called flakes, dispersed in mucin-depleted solution. We first reconstitute HRM samples to the MUC5B:MUC5AC mucin ratios consistent with normal and CF clinical samples, which we show recapitulate progressive flake formation and heterogeneity. We then employ passive particle tracking with 200 nm and 1 mu m diameter beads in each reconstituted sample. To robustly analyze the tracking data, we introduce statistical denoising methods for low signal-to-noise tracking data within flakes, tested and verified using model-generated synthetic data. These statistical methods provide a fractional Brownian motion classifier of all successfully denoised, tracked beads in flakes and the dilute solution. From the ensemble of classifier data, per bead diameter and mucus sample, we then employ clustering methods to learn and infer multiple levels of heterogeneity: (i) tracked bead data within vs. outside flakes and (ii) within-flake data buried within or distinguishable from the experimental noise floor. Simulated data consistent with experimental data (within and outside flakes) are used to explore form(s) of the generalized Stokes-Einstein relation (GSER) that recover the dynamic moduli of homogeneous and heterogeneous truth sets of purely flakelike, dilute solution, and mixture samples. The appropriate form of GSER is applied to experimental data to show (i) flakes are heterogeneous with gel and sol domains; (ii) dilute solutions are heterogeneous with only sol domains; and (iii) flake and dilute solution properties vary with probe diameter.

Transient DNA loops occur throughout the genome due to thermal fluctuations of DNA and the function of SMC complex proteins such as condensin and cohesin. Transient crosslinking within and between chromosomes and loop extrusion by SMCs have profound effects on high-order chromatin organization and exhibit specificity in cell type, cell cycle stage, and cellular environment. SMC complexes anchor one end to DNA with the other extending some distance and retracting to form a loop. How cells regulate loop sizes and how loops distribute along chromatin are emerging questions. To understand loop size regulation, we employed bead–spring polymer chain models of chromatin and the activity of an SMC complex on chromatin. Our study shows that (1) the stiffness of the chromatin polymer chain, (2) the tensile stiffness of chromatin crosslinking complexes such as condensin, and (3) the strength of the internal or external tethering of chromatin chains cooperatively dictate the loop size distribution and compaction volume of induced chromatin domains. When strong DNA tethers are invoked, loop size distributions are tuned by condensin stiffness. When DNA tethers are released, loop size distributions are tuned by chromatin stiffness. In this three-way interaction, the presence and strength of tethering unexpectedly dictates chromatin conformation within a topological domain.

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.

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.

Throughout the COVID-19 pandemic, an unprecedented level of clinical nasal swab data from around the globe has been collected and shared. Positive tests have consistently revealed viral titers spanning six orders of magnitude! An open question is whether such extreme population heterogeneity is unique to SARS-CoV-2 or possibly generic to viral respiratory infections. To probe this question, we turn to the computational modeling of nasal tract infections. Employing a physiologically faithful, spatially resolved, stochastic model of respiratory tract infection, we explore the statistical distribution of human nasal infections in the immediate 48 h of infection. The spread, or heterogeneity, of the distribution derives from variations in factors within the model that are unique to the infected host, infectious variant, and timing of the test. Hypothetical factors include: (1) reported physiological differences between infected individuals (nasal mucus thickness and clearance velocity); (2) differences in the kinetics of infection, replication, and shedding of viral RNA copies arising from the unique interactions between the host and viral variant; and (3) differences in the time between initial cell infection and the clinical test. Since positive clinical tests are often pre-symptomatic and independent of prior infection or vaccination status, in the model we assume immune evasion throughout the immediate 48 h of infection. Model simulations generate the mean statistical outcomes of total shed viral load and infected cells throughout 48 h for each “virtual individual”, which we define as each fixed set of model parameters (1) and (2) above. The “virtual population” and the statistical distribution of outcomes over the population are defined by collecting clinically and experimentally guided ranges for the full set of model parameters (1) and (2). This establishes a model-generated “virtual population database” of nasal viral titers throughout the initial 48 h of infection of every individual, which we then compare with clinical swab test data. Support for model efficacy comes from the sampling of infection dynamics over the virtual population database, which reproduces the six-order-of-magnitude clinical population heterogeneity. However, the goal of this study is to answer a deeper biological and clinical question. What is the impact on the dynamics of early nasal infection due to each individual physiological feature or virus–cell kinetic mechanism? To answer this question, global data analysis methods are applied to the virtual population database that sample across the entire database and de-correlate (i.e., isolate) the dynamic infection outcome sensitivities of each model parameter. These methods predict the dominant, indeed exponential, driver of population heterogeneity in dynamic infection outcomes is the latency time of infected cells (from the moment of infection until onset of viral RNA shedding). The shedding rate of the viral RNA of infected cells in the shedding phase is a strong, but not exponential, driver of infection. Furthermore, the unknown timing of the nasal swab test relative to the onset of infection is an equally dominant contributor to extreme population heterogeneity in clinical test data since infectious viral loads grow from undetectable levels to more than six orders of magnitude within 48 h.

Throughout the COVID-19 pandemic, positive nasal swab tests have revealed dramatic population heterogeneity in viral titers spanning 6 orders-of-magnitude. Our goal here is to probe potential drivers of infection outcome sensitivity arising from (i) physiological heterogeneity between hosts and (ii) host-variant heterogeneity in the detailed kinetics of cell infection and viral replication. Toward this goal, we apply global sensitivity methods (Partial Rank Correlation Coefficient analysis and Latin Hypercube Sampling) to a physiologically faithful, stochastic, spatial model of inhaled SARS-CoV-2 exposure and infection in the human respiratory tract. We focus on the nasal passage as the primary origin of respiratory infection and site of clinical testing, and we simulate the spatial and dynamic progression of shed viral load and infected cells in the immediate 48 hours post infection. We impose immune evasion, i.e., suppressed immune protection, based on the preponderance of clinical evidence that nasal infections occur rapidly post exposure, largely independent of immune status. Global sensitivity methods provide the de-correlated outcome sensitivities to each source of within-host heterogeneity, including the dynamic progression of sensitivities at 12, 24, 36, and 48 hours post infection. The results reveal a dynamic rank-ordering of the drivers of outcome sensitivity in early infection, providing insights into the dramatic population-scale outcome diversity during the COVID-19 pandemic. While we focus on SARS-CoV-2, the model and methods are applicable to any inhaled virus in the immediate 48 hours post infection.

The mucus lining of the human airway epithelium contains two gel-forming mucins, MUC5B and MUC5AC. During progression of cystic fibrosis (CF), mucus hyper-concentrates as its mucin ratio changes, coinciding with formation of insoluble, dense mucus flakes. We explore rheological heterogeneity of this pathology with reconstituted mucus matching three stages of CF progression and particle-tracking of 200 nm and 1 micron diameter beads. We introduce statistical data analysis methods specific to low signal-to-noise data within flakes. Each bead time series is decomposed into: (i) a fractional Brownian motion (fBm) classifier of the pure time-series signal; (ii) high-frequency static and dynamic noise; and (iii) low-frequency deterministic drift. Subsequent analysis focuses on the denoised fBm classifier ensemble from each mucus sample and bead diameter. Every ensemble fails a homogeneity test, compelling clustering methods to assess levels of heterogeneity. The first binary level detects beads within vs. outside flakes. A second binary level detects within-flake bead signals that can vs. cannot be disentangled from the experimental noise floor. We show all denoised ensembles, within- and outside-flakes, fail a homogeneity test, compelling additional clustering; next, all clusters with sufficient data fail a homogeneity test. These levels of heterogeneity are consistent with outcomes from a stochastic phase-separation process, and dictate applying the generalized Stokes-Einstein relation to each bead per cluster per sample, then frequency-domain averaging to assess rheological heterogeneity. Flakes exhibit a spectrum of gel-like and sol-like domains, outside-flake solutions a spectrum of sol-like domains, painting a rheological signature of the phase-separation process underlying flake-burdened mucus.

Background Mucus hyperconcentration in cystic fibrosis (CF) lung disease is marked by increases in both mucin and DNA concentration. Additionally, it has been shown that half of the mucins present in bronchial alveolar lavage fluid (BALF) from preschool-aged CF patients are present in as non-swellable mucus flakes. This motivates us to examine the utility of mucus flakes, as well as mucin and DNA concentrations in BALF as markers of infection and inflammation in CF airway disease. Methods In this study, we examined the mucin and DNA concentration, as well as mucus flake abundance, composition, and biophysical properties in BALF from three groups; healthy adult controls, and two CF cohorts, one preschool aged and the other school aged. BALFs were characterized via refractometry, PicoGreen, immunofluorescence microscopy, particle tracking microrheology, and fluorescence image tiling. Results Mucin and DNA BALF concentrations increased progressively from healthy young adult controls to preschool-aged people and school-aged people with CF. Notably, mucin concentrations were increased in bronchoalveolar lavage fluid (BALF) from preschool-aged patients with CF prior to decreased pulmonary function. Infrequent small mucus flakes were identified in normal subjects. A progressive increase in the abundance of mucus flakes in preschool and school-aged CF patients was observed. Compositionally, MUC5B dominated flakes from normal subjects, whereas an increase in MUC5AC was observed in people with CF, reflected in a reduced flaked MUC5B/MUC5AC mucin ratio. Conclusion These findings suggest mucus composition and flake properties are useful markers of inflammatory and infection-based changes in CF airways.