Biophysical phenotype mixtures reveal advantages for tumor muscle invasion in vivo.

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 α6ß1. 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.

Bend or Twist? What Plectonemes Reveal about the Mysterious Motility of Spiroplasma.

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.

Taking the Monte-Carlo gamble: How not to buckle under the pressure!

Consistent buckling distortions of a large membrane patch (200 × 200 Å) are observed during molecular dynamics (MD) simulations using the Monte-Carlo (MC) barostat in combination with a hard Lennard-Jones (LJ) cutoff. The buckling behavior is independent of both the simulation engine and the force field but requires the MC barostat-hard LJ cutoff combination. Similar simulations of a smaller patch (90 × 90 Å) do not show buckling, but do show a small, systematic reduction in the surface area accompanied by ~1 Å thickening suggestive of compression. We show that a mismatch in the way potentials and forces are handled in the dynamical equations versus the MC barostat results in a compressive load on the membrane. Moreover, a straightforward application of elasticity theory reveals that a minimal compression of the linear dimensions of the membrane, inversely proportional to the edge length, is required for buckling, explaining this differential behavior. We recommend always using LJ force or potential-switching when the MC barostat is employed to avoid undesirable membrane deformations.

Cellular Contraction Can Drive Rapid Epithelial Flows.

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.

New Continuum Approaches for Determining Protein-Induced Membrane Deformations.

The influence of the membrane on transmembrane proteins is central to a number of biological phenomena, notably the gating of stretch activated ion channels. Conversely, membrane proteins can influence the bilayer, leading to the stabilization of particular membrane shapes, topological changes that occur during vesicle fission and fusion, and shape-dependent protein aggregation. Continuum elastic models of the membrane have been widely used to study protein-membrane interactions. These mathematical approaches produce physically interpretable membrane shapes, energy estimates for the cost of deformation, and a snapshot of the equilibrium configuration. Moreover, elastic models are much less computationally demanding than fully atomistic and coarse-grained simulation methodologies; however, it has been argued that continuum models cannot reproduce the distortions observed in fully atomistic molecular dynamics simulations. We suggest that this failure can be overcome by using chemically and geometrically accurate representations of the protein. Here, we present a fast and reliable hybrid continuum-atomistic model that couples the protein to the membrane. We show that the model is in excellent agreement with fully atomistic simulations of the ion channel gramicidin embedded in a POPC membrane. Our continuum calculations not only reproduce the membrane distortions produced by the channel but also accurately determine the channel's orientation. Finally, we use our method to investigate the role of membrane bending around the charged voltage sensors of the transient receptor potential cation channel TRPV1. We find that membrane deformation significantly stabilizes the energy of insertion of TRPV1 by exposing charged residues on the S4 segment to solution.

Going with the Flow: Water Flux and Cell Shape during Cytokinesis.

Cell shape changes during cytokinesis in eukaryotic cells have been attributed to contractile forces from the actomyosin ring and the actomyosin cortex. Here we propose an additional mechanism where active pumping of ions and water at the cell poles and the division furrow can also achieve the same type of shape change during cytokinesis without myosin contraction. We develop a general mathematical model to examine shape changes in a permeable object subject to boundary fluxes. We find that hydrodynamic flows in the cytoplasm and the relative drag between the cytoskeleton network phase and the water phase also play a role in determining the cell shape during cytokinesis. Forces from the actomyosin contractile ring and cortex do contribute to the cell shape, and can work together with water permeation to facilitate cytokinesis. To influence water flow, we osmotically shock the cell during cell division, and find that the cell can actively adapt to osmotic changes and complete division. Depolymerizing the actin cytoskeleton during cytokinesis also does not affect the contraction speed. We also explore the role of membrane ion channels and pumps in setting up the spatially varying water flux.

Vancomycin Reduces Cell Wall Stiffness and Slows Swim Speed of the Lyme Disease Bacterium.

Borrelia burgdorferi, the spirochete that causes Lyme disease, is a tick-transmitted pathogen that requires motility to invade and colonize mammalian and tick hosts. These bacteria use a unique undulating flat-wave shape to penetrate and propel themselves through host tissues. Previous mathematical modeling has suggested that the morphology and motility of these spirochetes depends crucially on the flagellar/cell wall stiffness ratio. Here, we test this prediction using the antibiotic vancomycin to weaken the cell wall. We found that low to moderate doses of vancomycin (≤2.0 µg/mL for 24 h) produced small alterations in cell shape and that as the dose was increased, cell speed decreased. Vancomycin concentrations >1.0 µg/mL also inhibited cell growth and led to bleb formation on a fraction of the cells. To quantitatively assess how vancomycin affects cell stiffness, we used optical traps to bend unflagellated mutants of B. burgdorferi. We found that in the presence of vancomycin, cell wall stiffness gradually decreased over time, with a 40% reduction in the bending stiffness after 36 h. Under the same conditions, the swimming speed of wild-type B. burgdorferi slowed by ∼15%, with only marginal changes to cell morphology. Interestingly, our biophysical model for the swimming dynamics of B. burgdorferi suggested that cell speed should increase with decreasing cell stiffness. We show that this discrepancy can be resolved if the periplasmic volume decreases as the cell wall becomes softer. These results provide a testable hypothesis for how alterations of cell wall stiffness affect periplasmic volume regulation. Furthermore, since motility is crucial to the virulence of B. burgdorferi, the results suggest that sublethal doses of antibiotics could negatively impact spirochete survival by impeding their swim speed, thereby enabling their capture and elimination by phagocytes.

Flagellar motility of the pathogenic spirochetes.

Bacterial pathogens are often classified by their toxicity and invasiveness. The invasiveness of a given bacterium is determined by how capable the bacterium is at invading a broad range of tissues in its host. Of mammalian pathogens, some of the most invasive come from a group of bacteria known as the spirochetes, which cause diseases, such as syphilis, Lyme disease, relapsing fever and leptospirosis. Most of the spirochetes are characterized by their distinct shapes and unique motility. They are long, thin bacteria that can be shaped like flat-waves, helices, or have more irregular morphologies. Like many other bacteria, the spirochetes use long, helical appendages known as flagella to move; however, the spirochetes enclose their flagella in the periplasm, the narrow space between the inner and outer membranes. Rotation of the flagella in the periplasm causes the entire cell body to rotate and/or undulate. These deformations of the bacterium produce the force that drives the motility of these organisms, and it is this unique motility that likely allows these bacteria to be highly invasive in mammals. This review will describe the current state of knowledge on the motility and biophysics of these organisms and provide evidence on how this knowledge can inform our understanding of spirochetal diseases.

The unique paradigm of spirochete motility and chemotaxis.

Spirochete motility is enigmatic: It differs from the motility of most other bacteria in that the entire bacterium is involved in translocation in the absence of external appendages. Using the Lyme disease spirochete Borrelia burgdorferi (Bb) as a model system, we explore the current research on spirochete motility and chemotaxis. Bb has periplasmic flagella (PFs) subterminally attached to each end of the protoplasmic cell cylinder, and surrounding the cell is an outer membrane. These internal helix-shaped PFs allow the spirochete to swim by generating backward-moving waves by rotation. Exciting advances using cryoelectron tomography are presented with respect to in situ analysis of cell, PF, and motor structure. In addition, advances in the dynamics of motility, chemotaxis, gene regulation, and the role of motility and chemotaxis in the life cycle of Bb are summarized. The results indicate that the motility paradigms of flagellated bacteria do not apply to these unique bacteria.

Physical Mechanisms of Cancer in the Transition to Metastasis.

Whether a tumor is metastatic is one of the most significant factors that influence the prognosis for a cancer patient. The transition from a nonmetastatic tumor to a metastatic one is accompanied by a number of genetic and proteomic changes within the tumor cells. These protein-level changes conspire to produce behavioral changes in the cells: cells that had been relatively stationary begin to move, often as a group. In this study we ask the question of what cell-level biophysical changes are sufficient to initiate evasion away from an otherwise static tumor. We use a mathematical model developed to describe the biophysics of epithelial tissue to explore this problem. The model is first validated against in vitro wound healing experiments with cancer cell lines. Then we simulate the behavior of a group of mutated cells within a sea of healthy tissue. We find that moderate increases in adhesion between the cell and extracellular matrix (ECM) accompanied by a decrease in cell-cell adhesion and/or Rho family of small GTPase activation can cause a group of cells to break free from a tumor and spontaneously migrate. This result may explain why some metastatic cells have been observed to upregulate integrin, downregulate cadherin, and activate Rho family signaling.

On the Quantification of Cellular Velocity Fields.

The application of flow visualization in biological systems is becoming increasingly common in studies ranging from intracellular transport to the movements of whole organisms. In cell biology, the standard method for measuring cell-scale flows and/or displacements has been particle image velocimetry (PIV); however, alternative methods exist, such as optical flow constraint. Here we review PIV and optical flow, focusing on the accuracy and efficiency of these methods in the context of cellular biophysics. Although optical flow is not as common, a relatively simple implementation of this method can outperform PIV and is easily augmented to extract additional biophysical/chemical information such as local vorticity or net polymerization rates from speckle microscopy.

The heterogeneous motility of the Lyme disease spirochete in gelatin mimics dissemination through tissue.

The Lyme disease spirochete Borrelia burgdorferi exists in nature in an enzootic cycle that involves the arthropod vector Ixodes scapularis and mammalian reservoirs. To disseminate within and between these hosts, spirochetes must migrate through complex, polymeric environments such as the basement membrane of the tick midgut and the dermis of the mammal. To date, most research on the motility of B. burgdorferi has been done in media that do not resemble the tissue milieus that B. burgdorferi encounter in vivo. Here we show that the motility of Borrelia in gelatin matrices in vitro resembles the pathogen's movements in the chronically infected mouse dermis imaged by intravital microscopy. More specifically, B. burgdorferi motility in mouse dermis and gelatin is heterogeneous, with the bacteria transitioning between at least three different motility states that depend on transient adhesions to the matrix. We also show that B. burgdorferi is able to penetrate matrices with pore sizes much smaller than the diameter of the bacterium. We find a complex relationship between the swimming behavior of B. burgdorferi and the rheological properties of the gelatin, which cannot be accounted for by recent theoretical predictions for microorganism swimming in gels. Our results also emphasize the importance of considering borrelial adhesion as a dynamic rather than a static process.

Spatiotemporal evolution of erythema migrans, the hallmark rash of Lyme disease.

To elucidate pathogen-host interactions during early Lyme disease, we developed a mathematical model that explains the spatiotemporal dynamics of the characteristic first sign of the disease, a large (≥5-cm diameter) rash, known as an erythema migrans. The model predicts that the bacterial replication and dissemination rates are the primary factors controlling the speed that the rash spreads, whereas the rate that active macrophages are cleared from the dermis is the principle determinant of rash morphology. In addition, the model supports the clinical observations that antibiotic treatment quickly clears spirochetes from the dermis and that the rash appearance is not indicative of the efficacy of the treatment. The quantitative agreement between our results and clinical data suggest that this model could be used to develop more efficient drug treatments and may form a basis for modeling pathogen-host interactions in other emerging infectious diseases.

Elasticity and biochemistry of growth relate replication rate to cell length and cross-link density in rod-shaped bacteria.

In rod-shaped bacteria, cell morphology is correlated with the replication rate. For a given species, cells that replicate faster are longer and have less cross-linked cell walls. Here, we propose a simple mechanochemical model that explains the dependence of cell length and cross-linking on the replication rate. Our model shows good agreement with existing experimental data and provides further evidence that cell wall synthesis is mediated by multienzyme complexes; however, our results suggest that these synthesis complexes only mediate glycan insertion and cross-link severing, whereas recross-linking is performed independently.

Viscous dynamics of Lyme disease and syphilis spirochetes reveal flagellar torque and drag.

The spirochetes that cause Lyme disease (Borrelia burgdorferi) and syphilis (Treponema pallidum) swim through viscous fluids, such as blood and interstitial fluid, by undulating their bodies as traveling, planar waves. These undulations are driven by rotation of the flagella within the periplasmic space, the narrow (∼20-40 nm in width) compartment between the inner and outer membranes. We show here that the swimming speeds of B. burgdorferi and T. pallidum decrease with increases in viscosity of the external aqueous milieu, even though the flagella are entirely intracellular. We then use mathematical modeling to show that the measured changes in speed are consistent with the exertion of constant torque by the spirochetal flagellar motors. Comparison of simulations, experiments, and a simple model for power dissipation allows us to estimate the torque and resistive drag that act on the flagella of these major spirochetal pathogens.

Processivity of peptidoglycan synthesis provides a built-in mechanism for the robustness of straight-rod cell morphology.

The propagation of cell shape across generations is remarkably robust in most bacteria. Even when deformations are acquired, growing cells progressively recover their original shape once the deforming factors are eliminated. For instance, straight-rod-shaped bacteria grow curved when confined to circular microchambers, but straighten in a growth-dependent fashion when released. Bacterial cell shape is maintained by the peptidoglycan (PG) cell wall, a giant macromolecule of glycan strands that are synthesized by processive enzymes and cross-linked by peptide chains. Changes in cell geometry require modifying the PG and therefore depend directly on the molecular-scale properties of PG structure and synthesis. Using a mathematical model we quantify the straightening of curved Caulobacter crescentus cells after disruption of the cell-curving crescentin structure. We observe that cells straighten at a rate that is about half (57%) the cell growth rate. Next we show that in the absence of other effects there exists a mathematical relationship between the rate of cell straightening and the processivity of PG synthesis-the number of subunits incorporated before termination of synthesis. From the measured rate of cell straightening this relationship predicts processivity values that are in good agreement with our estimates from published data. Finally, we consider the possible role of three other mechanisms in cell straightening. We conclude that regardless of the involvement of other factors, intrinsic properties of PG processivity provide a robust mechanism for cell straightening that is hardwired to the cell wall synthesis machinery.

EVL and MIM/MTSS1 regulate actin cytoskeletal remodeling to promote dendritic filopodia in neurons.

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.

Swimming dynamics of the lyme disease spirochete.

The Lyme disease spirochete, Borrelia burgdorferi, swims by undulating its cell body in the form of a traveling flat wave, a process driven by rotating internal flagella. We study B. burgdorferi's swimming by treating the cell body and flagella as linearly elastic filaments. The dynamics of the cell are then determined from the balance between elastic and resistive forces and moments. We find that planar, traveling waves only exist when the flagella are effectively anchored at both ends of the bacterium and that these traveling flat waves rotate as they undulate. The model predicts how the undulation frequency is related to the torque from the flagellar motors and how the stiffness of the cell body and flagella affect the undulations and morphology.

Crawling cells can close wounds without purse strings or signaling.

When a gash or gouge is made in a confluent layer of epithelial cells, the cells move to fill in the "wound." In some cases, such as in wounded embryonic chick wing buds, the movement of the cells is driven by cortical actin contraction (i.e., a purse string mechanism). In adult tissue, though, cells apparently crawl to close wounds. At the single cell level, this crawling is driven by the dynamics of the cell's actin cytoskeleton, which is regulated by a complex biochemical network, and cell signaling has been proposed to play a significant role in directing cells to move into the denuded area. However, wounds made in monolayers of Madin-Darby canine kidney (MDCK) cells still close even when a row of cells is deactivated at the periphery of the wound, and recent experiments show complex, highly-correlated cellular motions that extend tens of cell lengths away from the boundary. These experiments suggest a dominant role for mechanics in wound healing. Here we present a biophysical description of the collective migration of epithelial cells during wound healing based on the basic motility of single cells and cell-cell interactions. This model quantitatively captures the dynamics of wound closure and reproduces the complex cellular flows that are observed. These results suggest that wound healing is predominantly a mechanical process that is modified, but not produced, by cell-cell signaling.

A general computational framework for the dynamics of single- and multi-phase vesicles and membranes.

The dynamics of thin, membrane-like structures are ubiquitous in nature. They play especially important roles in cell biology. Cell membranes separate the inside of a cell from the outside, and vesicles compartmentalize proteins into functional microregions, such as the lysosome. Proteins and/or lipid molecules also aggregate and deform membranes to carry out cellular functions. For example, some viral particles can induce the membrane to invaginate and form an endocytic vesicle that pulls the virus into the cell. While the physics of membranes has been extensively studied since the pioneering work of Helfrich in the 1970's, simulating the dynamics of large scale deformations remains challenging, especially for cases where the membrane composition is spatially heterogeneous. Here, we develop a general computational framework to simulate the overdamped dynamics of membranes and vesicles. We start by considering a membrane with an energy that is a generalized functional of the shape invariants and also includes line discontinuities that arise due to phase boundaries. Using this energy, we derive the internal restoring forces and construct a level set-based algorithm that can stably simulate the large-scale dynamics of these generalized membranes, including scenarios that lead to membrane fission. This method is applied to solve for shapes of single-phase vesicles using a range of reduced volumes, reduced area differences, and preferred curvatures. Our results match well the experimentally measured shapes of corresponding vesicles. The method is then applied to explore the dynamics of multiphase vesicles, predicting equilibrium shapes and conditions that lead to fission near phase boundaries.