In fluid dynamics, a classic calculation pertaining to suspensions of uniform spheres predicted that the variance of the velocity should diverge with system size. Experiments, on the other hand, find that while the variance grows with system size in small systems, it asymptotes to a fixed value for sufficiently large systems. Here, I show that this discrepancy between theory and experiment is resolved by accounting for the inertia of the particles. Using the unsteady Stokes' Green's functions, the leading order contribution to the variance is determined to be finite for systems of infinite extent.

Bladder, colon, gastric, prostate, and uterine cancers originate in organs surrounded by laminin-coated smooth muscle. In human prostate cancer, tumors that are organ confined, without extracapsular extension through muscle, have an overall cancer survival rate of up to 97% compared with 32% for metastatic disease. Our previous work modeling extracapsular extension reported the blocking of tumor invasion by mutation of a laminin-binding integrin called α6β1. Expression of the α6AA mutant resulted in a biophysical switch from cell-ECM (extracellular matrix) to cell-cell adhesion with drug sensitivity properties and an inability to invade muscle. Here we used different admixtures of α6AA and α6WT cells to test the cell heterogeneity requirements for muscle invasion. Time-lapse video microscopy revealed that tumor mixtures self-assembled into invasive networks in vitro, whereas α6AA cells assembled only as cohesive clusters. Invasion of α6AA cells into and through live muscle occurred using a 1:1 mixture of α6AA and α6WT cells. Electric cell-substrate impedance sensing measurements revealed that compared with α6AA cells, invasion-competent α6WT cells were 2.5-fold faster at closing a cell-ECM or cell-cell wound, respectively. Cell-ECM rebuilding kinetics show that an increased response occurred in mixtures since the response was eightfold greater compared with populations containing only one cell type. A synthetic cell adhesion cyclic peptide called MTI-101 completely blocked electric cell-substrate impedance sensing cell-ECM wound recovery that persisted in vitro up to 20 h after the wound. Treatment of tumor-bearing animals with 10 mg/kg MTI-101 weekly resulted in a fourfold decrease of muscle invasion by tumor and a decrease of the depth of invasion into muscle comparable to the α6AA cells. Taken together, these data suggest that mixed biophysical phenotypes of tumor cells within a population can provide functional advantages for tumor invasion into and through muscle that can be potentially inhibited by a synthetic cell adhesion molecule.

The dynamics of suspensions of particles has been an active area of research since Einstein first calculated the leading-order correction to the viscosity of a suspension of spherical particles (Einstein, Proc. R. Soc., vol. A102, 1906, pp. 161–179). Since then, researchers have strived to develop an accurate description of the behaviours of suspensions that goes beyond just leading order in the particle volume fraction. Here, we consider the low-Reynolds-number behaviour of a suspension of spherical particles. Working from the Green's functions for the flow due to a single particle, we derive a continuum-level description of the dynamics of suspensions. Our analysis corrects an error in the derivation of these equations in the work of Jackson (Chem. Engng Sci., vol. 52, 1997, pp. 2457–2469) and leads to stable equations of motion for the particles and fluid. In addition, our resulting equations naturally give the sedimentation speed for suspended particles and correct a separate error in the calculation by Batchelor (J. Fluid Mech., vol. 52, 1972, pp. 245–268). Using the pair-correlation function for hard spheres, we are able to compute the sedimentation speed out to seventh order in the volume fraction, which agrees with experimental data up to 30 %–35 %, and also get higher-order corrections to the suspension viscosity, which agree with experiments up to $\sim$ 15 %. Then, using the pair distribution for spheres in shear flow, we find alterations to both the first and second normal stresses.

Nearly all swimming bacteria have evolved to utilize external, helical, rotating appendages called flagella to achieve motility. These flagella are anchored into a cell wall which provides a structural rigidity during the swimming process. Contrary to this, a unique helical bacterium called spiroplasma has neither a cell wall nor flagella, yet still swims in water. Instead, this bacterium utilizes a set of actively deformable cytoskeletal filaments, internal to the cell, which allow for swimming motility.

Spiroplasma is a unique, helical bacterium that lacks a cell wall and swims using propagating helix hand inversions. These deformations are likely driven by a set of cytoskeletal filaments, but how remains perplexing. Here, we probe the underlying mechanism using a model where either twist or bend drive spiroplasma's chirality inversions. We show that Spiroplasma should wrap into plectonemes at different values of the length and external viscosity, depending on the mechanism. Then, by experimentally measuring the bending modulus of Spiroplasma and if and when plectonemes form, we show that Spiroplasma's helix hand inversions are likely driven by bending.

Bladder, colon, gastric, prostate, and uterine cancers originate from the organ’s epithelium, and each organ is surrounded by smooth muscle. In prostate cancer, organ-confined tumors, without extracapsular extension (ECE) through muscle, have a 5-year survival rate of 99% compared to 31% for metastatic disease. Previously, we modeled tumor cluster ECE and reported that a CRISPR-Cas9 integrin mutation (α6AA) blocked ECE by switching from a cell-ECM to a cell-cell biophysical phenotype. Since tumors are mosaics and migrate as heterogeneous drug-resistant populations, we tested the functional heterogeneity of the two biophysical cell phenotypes in ECE. Experimental procedures included the in vivo mouse xenograft model of ECE as a functional endpoint of muscle invasion, the MTT assay for cell survival, and using electric cell impedance sensing (ECIS) measurements to directly compare the biophysical properties of tumor cells expressing the invasion permissive α6WT integrin, cells expressing only the α6AA mutation, or a mixed population expressing both integrin types. The α6AA integrin mutation or α6KO knockout produced cells unable to invade into and through the smooth muscle of the mouse as compared to the α6WT integrin cells, as previously reported by us. The new unpublished results are that cell adhesion mediated drug resistance was detected in the α6AA population since their LD50 to Bortezomib, Gemcitabine, and Taxotere was shifted to 33.71nM, 64.66nM, and 5.77nM respectively from 16.29nM, 31.74nM, and 3.52nM in the α6WT cells as measured by MTT assay at 72 hours of incubation. In contrast, the α6AA cells were sensitized to the NAMPT inhibitor, FK866, with LD50 shifting from 27.46nM in α6WT to 7.354nM in the α6AA cells. A mixture of α6AA and α6WT cells allowed invasion into and through the muscle in the mouse of the mutant α6AA integrin cells that could not invade on their own. Examining the live cellular biophysical parameters revealed that the integrin mutation produced a 4-fold increase in cell-cell resistance (400Hz measurement) and a 12-fold recovery time delay in re-establishing a cell-cell resistance monolayer after wounding, with response complexity decreased two-fold. Cell-ECM resistance (40,000Hz measurement) in α6AA versus α6WT population was 1.5-fold decreased with a 6-fold recovery time delay in the cell-ECM resistance monolayer and response complexity decreased 2-fold. A heterogenous population containing up to a 4:1 proportion of α6AA to α6WT cells synergistically delayed cell-cell recovery time of the wounded monolayer up to 6-fold compared to the α6WT cells. Conversely, recovery of the wounded cell-ECM resistance monolayer with 1:1 or 4:1 mixture of α6AA cell only delayed recovery time by 1.5–1.7-fold. Taken together, these data suggest that a heterogenous tumor population provides functional advantages for drug-resistant tumor cells to invade and traverse the muscle barrier. Current work is ongoing to optimize the drug combinations to eliminate both phenotypes in the invasive tumor network and prevent ECE. Citation Format: Kendra D. Marr, Jaime M.C. Gard, William L. Harryman, Elijah J. Keeswood, Allan I. Paxson, Charles Wolgemuth, Lori A. Hazlehurst, Raymond B. Nagle, Anne E. Cress. Heterogeneity of cancer network biophysical phenotypes is required for tumor muscle invasion in vivo [abstract]. In: Proceedings of the AACR Special Conference: Advances in Prostate Cancer Research; 2023 Mar 15-18; Denver, Colorado. Philadelphia (PA): AACR; Cancer Res 2023;83(11 Suppl):Abstract nr B001.

Dendritic spines are the postsynaptic compartment of a neuronal synapse and are critical for synaptic connectivity and plasticity. A developmental precursor to dendritic spines, dendritic filopodia (DF), facilitate synapse formation by sampling the environment for suitable axon partners during neurodevelopment and learning. Despite the significance of the actin cytoskeleton in driving these dynamic protrusions, the actin elongation factors involved are not well characterized. We identified the Ena/VASP protein EVL as uniquely required for the morphogenesis and dynamics of DF. Using a combination of genetic and optogenetic manipulations, we demonstrated that EVL promotes protrusive motility through membrane-direct actin polymerization at DF tips. EVL forms a complex at nascent protrusions and DF tips with MIM/MTSS1, an I-BAR protein important for the initiation of DF. We proposed a model in which EVL cooperates with MIM to coalesce and elongate branched actin filaments, establishing the dynamic lamellipodia-like architecture of DF.

When an initially straight filament is immersed in a viscous fluid and rotated at one end, the fluid resists the rotational motion and causes a buildup of twist in the object. At a critical turning frequency, the object buckles due to the elastic stresses in the material. While this instability has been extensively studied over the past 25 years, these analyses have focused narrowly on filaments with circular cross sections near the onset of the instability. Here we explore the phase diagram for twirling filaments as a function of cross-sectional aspect ratio and rotational frequency. We find a large range of dynamic behaviors and even find that while filaments with circular cross sections transition directly from twirling to overwhirling, ribbonlike objects undergo a twirl-to-whirl transition, similar to what was originally predicted for rodlike objects. We show that the linear stability for rotating ribbons is equivalent to first order to that of cylindrical filaments. Hysteresis is also common, suggesting that there are multiple stable states in these systems. Finally, by comparing simulations using resistive force theory to immersed boundary methods, we identify the reason that these two methods have historically not agreed on the value of the critical turning frequency.

Filaments, rods, and beams are ubiquitous in biology and in many man-made products and structures. While a substantial amount of research has been done to understand the statics and dynamics of these long, thin objects, there remain many unanswered and unstudied problems related to the dynamics of bending and twisting filamentary objects. Simulating the general dynamics of these structures in 3D remains challenging. For example, the net force and torque on a free filament immersed in fluid at low Reynolds number must be zero. However, standard finite difference approaches will often fail to preserve the zero force and torque conditions. These numerical artifacts cause spurious rotations and translations that prohibit, or at least limit, their accuracy in simulating the dynamics of filaments, rods, and beams in these contexts (such as the free-swimming motion of a filamentary microorganism). Here we develop a finite volume discretization based on the Kirchoff equations that naturally guarantees the correct total integral of the forces and torques on filaments, rods, or beams. We then couple this discretization to resistive force theory to develop a stable, accurate dynamic algorithm of filament motion at low Reynolds number. We use a range of sample problems to highlight the utility, stability, and accuracy of this method. While our sample problems focus on low Reynolds number dynamics in the context of resistive force theory (RFT), our discretized finite volume algorithm is general and can be applied to inertial dynamics, immersed boundary methods, and boundary integral methods, as well.(c) 2022 Elsevier Inc. All rights reserved.

Synopsis The biological challenges facing humanity are complex, multi-factorial, and are intimately tied to the future of our health, welfare, and stewardship of the Earth. Tackling problems in diverse areas, such as agriculture, ecology, and health care require linking vast datasets that encompass numerous components and spatio-temporal scales. Here, we provide a new framework and a road map for using experiments and computation to understand dynamic biological systems that span multiple scales. We discuss theories that can help understand complex biological systems and highlight the limitations of existing methodologies and recommend data generation practices. The advent of new technologies such as big data analytics and artificial intelligence can help bridge different scales and data types. We recommend ways to make such models transparent, compatible with existing theories of biological function, and to make biological data sets readable by advanced machine learning algorithms. Overall, the barriers for tackling pressing biological challenges are not only technological, but also sociological. Hence, we also provide recommendations for promoting interdisciplinary interactions between scientists.

The level set method is a common approach for handling moving boundary problems, which allows a moving, irregular surface to be described implicitly on a Cartesian grid. This approach often requires reinitialization of the level set function and extrapolation of fields defined only on the interface. Because many applications in physics and engineering involve calculation of second derivatives of the interface curvature and fourth order derivatives of surface fields, accurate simulations of these problems require high-order methods for reinitialization and extrapolation. Here we build off WENO schemes for Hamilton–Jacobi equations to develop novel sixth-order accurate methods for reinitialization and extrapolation. We present numerical results in three dimensional spaces demonstrating fourth-order accuracy of the interfacial curvature and sixth-order accuracy for the extrapolated surface fields. We then show that the extrapolation scheme can be integrated into the closest point method for surface PDEs and present an example of computing geodesic curves on surfaces.

Cells are remarkable machines capable of performing an exquisite range of functions, many of which depend crucially on the activity of molecular motors that generate forces. Recent experiments have shown that intracellular random movements are not solely thermal in nature but also arise from stochasticity in the forces from these molecular motors. Here we consider the effects of these nonthermal random forces. We show that stochastic motor force not only enhances diffusion but also leads to size-dependent transport of objects that depends on the local density of the cytoskeletal filaments on which motors operate. As a consequence, we find that objects that are larger than the mesh size of the cytoskeleton should be attracted to regions of high cytoskeletal density, while objects that are smaller than the mesh size will preferentially avoid these regions. These results suggest a mechanism for size-based organelle positioning and also suggest that motor-driven random forces can additionally enhance motor-driven transport.

Over the past 50 years, the use of mathematical models, derived from physical reasoning, to describe molecular and cellular systems has evolved from an art of the few to a cornerstone of biological inquiry. George Oster stood out as a pioneer of this paradigm shift from descriptive to quantitative biology not only through his numerous research accomplishments, but also through the many students and postdocs he mentored over his long career. Those of us fortunate enough to have worked with George agree that his sharp intellect, physical intuition and passion for scientific inquiry not only inspired us as scientists but also greatly influenced the way we conduct research. We would like to share a few important lessons we learned from George in honor of his memory and with the hope that they may inspire future generations of scientists.

Dense suspensions of swimming bacteria are living fluids, an archetype of active matter. For example, Bacillus subtilis confined within a disc-shaped region forms a persistent stable vortex that counterrotates at the periphery. Here, we examined Escherichia coli under similar confinement and found that these bacteria, instead, form microspin cycles: a single vortex that periodically reverses direction on time scales of seconds. Using experimental perturbations of the confinement geometry, medium viscosity, bacterial length, density, and chemotaxis pathway, we show that morphological alterations of the bacteria transition a stable vortex into a periodically reversing one. We develop a mathematical model based on single-cell biophysics that quantitatively recreates the dynamics of these vortices and predicts that density gradients power the reversals. Our results define how microbial physics drives the active behavior of dense bacterial suspensions and may allow one to engineer novel micromixers for biomedical and other microfluidic applications.

Single, isolated epithelial cells move randomly; however, during wound healing, organism development, cancer metastasis, and many other multicellular phenomena, motile cells group into a collective and migrate persistently in a directed manner. Recent work has examined the physics and biochemistry that coordinates the motions of these groups of cells. Of late, two mechanisms have been touted as being crucial to the physics of these systems: leader cells and jamming. However, the actual importance of these to collective migration remains circumstantial. Fundamentally, collective behavior must arise from the actions of individual cells. Here, we show how biophysical activity of an isolated cell impacts collective dynamics in epithelial layers. Although many reports suggest that wound closure rates depend on isolated cell speed and/or leader cells, we find that these correlations are not universally true, nor do collective dynamics follow the trends suggested by models for jamming. Instead, our experimental data, when coupled with a mathematical model for collective migration, shows that intracellular contractile stress, isolated cell speed, and adhesion all play a substantial role in influencing epithelial dynamics, and that alterations in contraction and/or substrate adhesion can cause confluent epithelial monolayers to exhibit an increase in motility, a feature reminiscent of cancer metastasis. These results directly question the validity of wound-healing assays as a general means for measuring cell migration, and provide further insight into the salient physics of collective migration.