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.

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.

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.

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.

Active random forces can drive differential cellular positioning and enhance motor-driven transport.

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.

Swimming bacteria power microspin cycles.

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.

Measuring DNA content in live cells by fluorescence microscopy.

BACKGROUND: Live-cell fluorescence microscopy (LCFM) is a powerful tool used to investigate cellular dynamics in real time. However, the capacity to simultaneously measure DNA content in cells being tracked over time remains challenged by dye-associated toxicities. The ability to measure DNA content in single cells by means of LCFM would allow cellular stage and ploidy to be coupled with a variety of imaging directed analyses. Here we describe a widely applicable nontoxic approach for measuring DNA content in live cells by fluorescence microscopy. This method relies on introducing a live-cell membrane-permeant DNA fluorophore, such as Hoechst 33342, into the culture medium of cells at the end of any live-cell imaging experiment and measuring each cell's integrated nuclear fluorescence to quantify DNA content. Importantly, our method overcomes the toxicity and induction of DNA damage typically caused by live-cell dyes through strategic timing of adding the dye to the cultures; allowing unperturbed cells to be imaged for any interval of time before quantifying their DNA content. We assess the performance of our method empirically and discuss adaptations that can be implemented using this technique. RESULTS: Presented in conjunction with cells expressing a histone 2B-GFP fusion protein (H2B-GFP), we demonstrated how this method enabled chromosomal segregation errors to be tracked in cells as they progressed through cellular division that were later identified as either diploid or polyploid. We also describe and provide an automated Matlab-derived algorithm that measures the integrated nuclear fluorescence in each cell and subsequently plots these measurements into a cell cycle histogram for each frame imaged. The algorithm's accurate assessment of DNA content was validated by parallel flow cytometric studies. CONCLUSIONS: This method allows the examination of single-cell dynamics to be correlated with cellular stage and ploidy in a high-throughput fashion. The approach is suitable for any standard epifluorescence microscope equipped with a stable illumination source and either a stage-top incubator or an enclosed live-cell incubation chamber. Collectively, we anticipate that this method will allow high-resolution microscopic analysis of cellular processes involving cell cycle progression, such as checkpoint activation, DNA replication, and cellular division.

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.

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.

A minimal actomyosin-based model predicts the dynamics of filopodia on neuronal dendrites.

Dendritic filopodia are actin-filled dynamic subcellular structures that sprout on neuronal dendrites during neurogenesis. The exploratory motion of the filopodia is crucial for synaptogenesis, but the underlying mechanisms are poorly understood. To study filopodial motility, we collected and analyzed image data on filopodia in cultured rat hippocampal neurons. We hypothesized that mechanical feedback among the actin retrograde flow, myosin activity, and substrate adhesion gives rise to various filopodial behaviors. We formulated a minimal one-dimensional partial differential equation model that reproduced the range of observed motility. To validate our model, we systematically manipulated experimental correlates of parameters in the model: substrate adhesion strength, actin polymerization rate, myosin contractility, and the integrity of the putative microtubule-based barrier at the filopodium base. The model predicts the response of the system to each of these experimental perturbations, supporting the hypothesis that our actomyosin-driven mechanism controls dendritic filopodia dynamics.

The induction of endoreduplication and polyploidy by elevated expression of 14-3-3γ.

Several studies have demonstrated that specific 14-3-3 isoforms are frequently elevated in cancer and that these proteins play a role in human tumorigenesis. 14-3-3γ, an isoform recently demonstrated to function as an oncoprotein, is overexpressed in a variety of human cancers; however, its role in promoting tumorigenesis remains unclear. We previously reported that overexpression of 14-3-3γ caused the appearance of polyploid cells, a phenotype demonstrated to have profound tumor promoting properties. Here we examined the mechanism driving 14-3-3γ-induced polyploidization and the effect this has on genomic stability. Using FUCCI probes we showed that these polyploid cells appeared when diploid cells failed to enter mitosis and subsequently underwent endoreduplication. We then demonstrated that 14-3-3γ-induced polyploid cells experience significant chromosomal segregation errors during mitosis and observed that some of these cells stably propagate as tetraploids when isolated cells were expanded into stable cultures. These data lead us to conclude that overexpression of the 14-3-3γ promotes endoreduplication. We further investigated the role of 14-3-3γ in human NSCLC samples and found that its expression is significantly elevated in polyploid tumors. Collectively, these results suggests that 14-3-3γ may promote tumorigenesis through the production of a genetically unstable polyploid intermediate.

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.

An immersed boundary method for two-phase fluids and gels and the swimming of Caenorhabditis elegans through viscoelastic fluids.

The swimming of microorganisms typically involves the undulation or rotation of thin, filamentary objects in a fluid or other medium. Swimming in Newtonian fluids has been examined extensively, and only recently have investigations into microorganism swimming through non-Newtonian fluids and gels been explored. The equations that govern these more complex media are often nonlinear and require computational algorithms to study moderate to large amplitude motions of the swimmer. Here, we develop an immersed boundary method for handling fluid-structure interactions in a general two-phase medium, where one phase is a Newtonian fluid and the other phase is viscoelastic (e.g., a polymer melt or network). We use this algorithm to investigate the swimming of an undulating, filamentary swimmer in 2D (i.e., a sheet). A novel aspect of our method is that it allows one to specify how forces produced by the swimmer are distributed between the two phases of the fluid. The algorithm is validated by comparing theoretical predictions for small amplitude swimming in gels and viscoelastic fluids. We show how the swimming velocity depends on material parameters of the fluid and the interaction between the fluid and swimmer. In addition, we simulate the swimming of Caenorhabditis elegans in viscoelastic fluids and find good agreement between the swimming speeds and fluid flows in our simulations and previous experimental measurements. These results suggest that our methodology provides an accurate means for exploring the physics of swimming through non-Newtonian fluids and gels.

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.

Junctional angle of a bihanded helix.

Helical filaments having sections of reversed chirality are common phenomena in the biological realm. The apparent angle between the two sections of opposite handedness provides information about the geometry and elasticity of the junctional region. In this paper, the governing differential equations for the local helical axis are developed, and asymptotic solutions of the governing equations are solved by perturbation theory. The asymptotic solutions are compared with the corresponding numerical solutions, and the relative error at second order is found to be less than 1.5% over a range of biologically relevant curvature and torsion values from 0 to 1/2 in dimensionless units.

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.

Causes of retrograde flow in fish keratocytes.

Confronting motile cells with obstacles doubling as force sensors we tested the limits of the driving actin and myosin machinery. We could directly measure the force necessary to stop actin polymerization as well as the force present in the retrograde actin flow. Combined with detailed measurements of the retrograde flow velocity and specific manipulation of actin and myosin we found that actin polymerization and myosin contractility are not enough to explain the cells behavior. We show that ever-present depolymerization forces, a direct entropic consequence of actin filament recycling, are sufficient to fill this gap, even under heavy loads.

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.