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.

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.

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.

The Axes of Life: A Roadmap for Understanding Dynamic Multiscale Systems.

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.

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.

Biophysics at the coffee shop: lessons learned working with George Oster.

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.

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.

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.

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.