"Patchiness" in mechanical stiffness across a tumor as an early-stage marker for malignancy.

Mechanical phenotyping of tumors, either at an individual cell level or tumor cell population level is gaining traction as a diagnostic tool. However, the extent of diagnostic and prognostic information that can be gained through these measurements is still unclear. In this work, we focus on the heterogeneity in mechanical properties of cells obtained from a single source such as a tissue or tumor as a potential novel biomarker. We believe that this heterogeneity is a conventionally overlooked source of information in mechanical phenotyping data. We use mechanics-based in-silico models of cell-cell interactions and cell population dynamics within 3D environments to probe how heterogeneity in cell mechanics drives tissue and tumor dynamics. Our simulations show that the initial heterogeneity in the mechanical properties of individual cells and the arrangement of these heterogenous sub-populations within the environment can dictate overall cell population dynamics and cause a shift towards the growth of malignant cell phenotypes within healthy tissue environments. The overall heterogeneity in the cellular mechanotype and their spatial distributions is quantified by a "patchiness" index, which is the ratio of the global to local heterogeneity in cell populations. We observe that there exists a threshold value of the patchiness index beyond which an overall healthy population of cells will show a steady shift towards a more malignant phenotype. Based on these results, we propose that the "patchiness" of a tumor or tissue sample, can be an early indicator for malignant transformation and cancer occurrence in benign tumors or healthy tissues. Additionally, we suggest that tissue patchiness, measured either by biochemical or biophysical markers, can become an important metric in predicting tissue health and disease likelihood just as landscape patchiness is an important metric in ecology.

Interactions between ploidy and resource availability shape clonal interference at initiation and recurrence of glioblastoma.

Glioblastoma (GBM) is the most aggressive form of primary brain tumor. Complete surgical resection of GBM is almost impossible due to the infiltrative nature of the cancer. While no evidence for recent selection events have been found after diagnosis, the selective forces that govern gliomagenesis are strong, shaping the tumor's cell composition during the initial progression to malignancy with late consequences for invasiveness and therapy response. We present a mathematical model that simulates the growth and invasion of a glioma, given its ploidy level and the nature of its brain tissue micro-environment (TME), and use it to make inferences about GBM initiation and response to standard-of-care treatment. We approximate the spatial distribution of resource access in the TME through integration of in-silico modelling, multi-omics data and image analysis of primary and recurrent GBM. In the pre-malignant setting, our in-silico results suggest that low ploidy cancer cells are more resistant to starvation-induced cell death. In the malignant setting, between first and second surgery, simulated tumors with different ploidy compositions progressed at different rates. Whether higher ploidy predicted fast recurrence, however, depended on the TME. Historical data supports this dependence on TME resources, as shown by a significant correlation between the median glucose uptake rates in human tissues and the median ploidy of cancer types that arise in the respective tissues (Spearman r = -0.70; P = 0.026). Taken together our findings suggest that availability of metabolic substrates in the TME drives different cell fate decisions for cancer cells with different ploidy and shapes GBM disease initiation and relapse characteristics.

Kinesin and myosin motors compete to drive rich multiphase dynamics in programmable cytoskeletal composites.

The cellular cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable nonequilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton's versatile reconfigurability, programmed by interactions between its constituents, makes it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate-far from the composite cytoskeleton in cells. Here, we engineer actin-microtubule (MT) composites, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or MTs has an opposite effect. Our minimal advection-diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and demixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the nonequilibrium dynamics across all composites and timescales can be organized into three classes-slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.

Modeling collective cell behavior in cancer: Perspectives from an interdisciplinary conversation.

Collective cell behavior contributes to all stages of cancer progression. Understanding how collective behavior emerges through cell-cell interactions and decision-making will advance our understanding of cancer biology and provide new therapeutic approaches. Here, we summarize an interdisciplinary discussion on multicellular behavior in cancer, draw lessons from other scientific disciplines, and identify future directions.

Differences in cell death and division rules can alter tissue rigidity and fluidization.

Tissue mechanical properties such as rigidity and fluidity, and changes in these properties driven by jamming-unjamming transitions (UJT), have come under recent highlight as mechanical markers of health and disease in various biological processes including cancer. However, most analyses of these mechanical properties and UJT have sidestepped the effect of cellular death and division in these systems. Cellular apoptosis (programmed cell death) and mitosis (cell division) can drive significant changes in tissue properties. The balance between the two is crucial in maintaining tissue function, and an imbalance between the two is seen in situations such as cancer progression, wound healing and necrosis. In this work we investigate the impact of cell death and division on tissue mechanical properties, by incorporating specific mechanosensitive triggers of cell death and division based on the size and geometry of the cell within in silico models of tissue dynamics. Specifically, we look at cell migration, tissue response to external stress, tissue extrusion propensity and self-organization of different cell types within the tissue, as a function of cell death and division and the rules that trigger these events. We find that not only do cell death and division events significantly alter tissue mechanics when compared to systems without these events, but that the choice of triggers driving these cell death and division events also alters the predicted tissue mechanics and overall system behavior.

Robotic end-to-end fusion of microtubules powered by kinesin.

The active assembly of molecules by nanorobots has advanced greatly since "molecular manufacturing"­that is, the use of nanoscale tools to build molecular structures­was proposed. In contrast to a catalyst, which accelerates a reaction by smoothing the potential energy surface along the reaction coordinate, molecular machines expend energy to accelerate a reaction relative to the baseline provided by thermal motion and forces. Here, we design a nanorobotics system to accelerate end-to-end microtubule assembly by using kinesin motors and a circular confining chamber. We show that the mechanical interaction of kinesin-propelled microtubules gliding on a surface with the walls of the confining chamber results in a nonequilibrium distribution of microtubules, which increases the number of end-to-end microtubule fusion events 20-fold compared with microtubules gliding on a plane. In contrast to earlier nanorobots, where a nonequilibrium distribution was built into the initial state and drove the process, our nanorobotic system creates and actively maintains the building blocks in the concentrated state responsible for accelerated assembly through the adenosine triphosphate­fueled generation of force by kinesin-1 motor proteins. This approach can be used in the future to develop biohybrid or bioinspired nanorobots that use molecular machines to access nonequilibrium states and accelerate nanoscale assembly.

Adhesion strength and contractility enable metastatic cells to become adurotactic.

Significant changes in cell stiffness, contractility, and adhesion, i.e., mechanotype, are observed during a variety of biological processes. Whether cell mechanics merely change as a side effect of or driver for biological processes is still unclear. Here, we sort genotypically similar metastatic cancer cells into strongly adherent (SA) versus weakly adherent (WA) phenotypes to study how contractility and adhesion differences alter the ability of cells to sense and respond to gradients in material stiffness. We observe that SA cells migrate up a stiffness gradient, or durotax, while WA cells largely ignore the gradient, i.e., adurotax. Biophysical modeling and experimental validation suggest that differences in cell migration and durotaxis between weakly and strongly adherent cells are driven by differences in intra-cellular actomyosin activity. These results provide a direct relationship between cell phenotype and durotaxis and suggest how, unlike other senescent cells, metastatic cancer cells navigate against stiffness gradients.

Power Law Behavior in Protein Desorption Kinetics Originating from Sequential Binding and Unbinding.

The study of protein adsorption at the single molecule level has recently revealed that the adsorption is reversible, but with a long-tailed residence time distribution which can be approximated with a sum of exponential functions putatively related to distinct adsorption sites. Here it is proposed that the shape of the residence time distribution results from an adsorption process with sequential and reversible steps that contribute to overall binding strength resembling "zippering". In this model, the survival function of the residence time distribution of single proteins varies from an exponential distribution for a single adsorption step to a power law distribution with exponent -1/2 for a large number of adsorption steps. The adsorption of fluorescently labeled fibrinogen to glass surfaces is experimentally studied with single molecule imaging. The experimental residence time distribution can be readily fit by the proposed model. This demonstrates that the observed long residence times can arise from stepwise adsorption rather than rare but strong binding sites and provides guidance for the control of protein adsorption to biomaterials.

Computational models of migration modes improve our understanding of metastasis.

Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell-extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.

To lead or to herd: optimal strategies for 3D collective migration of cell clusters.

Cells migrating in clusters play a significant role in a number of biological processes such as embryogenesis, wound healing, and tumor metastasis during cancer progression. A variety of environmental and biochemical factors can influence the collective migration of cells with differing degrees of cell autonomy and inter-cellular coupling strength. For example, weakly coupled cells can move collectively under the influence of contact guidance from neighboring cells or the environment. Alternatively strongly coupled cells might follow one or more leader cells to move as a single cohesive unit. Additionally, chemical and mechanical signaling between these cells may alter the degree of coupling and determine effective cluster sizes. Being able to understand this collective cell migration process is critical in the prediction and manipulation of outcomes of key biological processes. Here we focus on understanding how various environmental and cellular factors influence small clusters of cells migrating collectively within a 3D fibrous matrix. We combine existing knowledge of single-cell migration in 2D and 3D environments, prior experimental observations of cell-cell interactions and collective migration, and a newly developed stochastic model of cell migration in 3D matrices, to simulate the migration of cell clusters in different physiologically relevant environments. Our results show that based on the extracellular environment and the strength of cell-cell mechanical coupling, two distinct optimal approaches to driving collective cell migration emerge. The ability to effectively employ these two distinct migration strategies might be critical for cells to collectively migrate through the heterogeneous tissue environments within the body.

Cell Adhesiveness Serves as a Biophysical Marker for Metastatic Potential.

Tumors are heterogeneous and composed of cells with different dissemination abilities. Despite significant effort, there is no universal biological marker that serves as a metric for metastatic potential of solid tumors. Common to disseminating cells from such tumors, however, is the need to modulate their adhesion as they detach from the tumor and migrate through stroma to intravasate. Adhesion strength is heterogeneous even among cancer cells within a given population, and using a parallel plate flow chamber, we separated and sorted these populations into weakly and strongly adherent groups; when cultured under stromal conditions, this adhesion phenotype was stable over multiple days, sorting cycles, and common across all epithelial tumor lines investigated. Weakly adherent cells displayed increased migration in both two-dimensional and three-dimensional migration assays; this was maintained for several days in culture. Subpopulations did not show differences in expression of proteins involved in the focal adhesion complex but did exhibit intrinsic focal adhesion assembly as well as contractile differences that resulted from differential expression of genes involved in microtubules, cytoskeleton linkages, and motor activity. In human breast tumors, expression of genes associated with the weakly adherent population resulted in worse progression-free and disease-free intervals. These data suggest that adhesion strength could potentially serve as a stable marker for migration and metastatic potential within a given tumor population and that the fraction of weakly adherent cells present within a tumor could act as a physical marker for metastatic potential. SIGNIFICANCE: Cancer cells exhibit heterogeneity in adhesivity, which can be used to predict metastatic potential.

Correction: A stochastic algorithm for accurately predicting path persistence of cells migrating in 3D matrix environments.

[This corrects the article DOI: 10.1371/journal.pone.0207216.].

A stochastic algorithm for accurately predicting path persistence of cells migrating in 3D matrix environments.

Cell mobility plays a critical role in immune response, wound healing, and the rate of cancer metastasis and tumor progression. Mobility within a three-dimensional (3D) matrix environment can be characterized by the average velocity of cell migration and the persistence length of the path it follows. Computational models that aim to predict cell migration within such 3D environments need to be able predict both of these properties as a function of the various cellular and extra-cellular factors that influence the migration process. A large number of models have been developed to predict the velocity of cell migration driven by cellular protrusions in 3D environments. However, prediction of the persistence of a cell's path is a more tedious matter, as it requires simulating cells for a long time while they migrate through the model extra-cellular matrix (ECM). This can be a computationally expensive process, and only recently have there been attempts to quantify cell persistence as a function of key cellular or matrix properties. Here, we propose a new stochastic algorithm that can simulate and analyze 3D cell migration occurring over days with a computation time of minutes, opening new possibilities of testing and predicting long-term cell migration behavior as a function of a large variety of cell and matrix properties. In this model, the matrix elements are generated as needed and stochastically based on the biophysical and biochemical properties of the ECM the cell migrates through. This approach significantly reduces the computational resources required to track and calculate cell matrix interactions. Using this algorithm, we predict the effect of various cellular and matrix properties such as cell polarity, cell mechanoactivity, matrix fiber density, matrix stiffness, fiber alignment, and fiber binding site density on path persistence of cellular migration and the mean squared displacement of cells over long periods of time.

Mechanosensing of shear by Pseudomonas aeruginosa leads to increased levels of the cyclic-di-GMP signal initiating biofilm development.

Biofilms are communities of sessile microbes that are phenotypically distinct from their genetically identical, free-swimming counterparts. Biofilms initiate when bacteria attach to a solid surface. Attachment triggers intracellular signaling to change gene expression from the planktonic to the biofilm phenotype. For Pseudomonas aeruginosa, it has long been known that intracellular levels of the signal cyclic-di-GMP increase upon surface adhesion and that this is required to begin biofilm development. However, what cue is sensed to notify bacteria that they are attached to the surface has not been known. Here, we show that mechanical shear acts as a cue for surface adhesion and activates cyclic-di-GMP signaling. The magnitude of the shear force, and thereby the corresponding activation of cyclic-di-GMP signaling, can be adjusted both by varying the strength of the adhesion that binds bacteria to the surface and by varying the rate of fluid flow over surface-bound bacteria. We show that the envelope protein PilY1 and functional type IV pili are required mechanosensory elements. An analytic model that accounts for the feedback between mechanosensors, cyclic-di-GMP signaling, and production of adhesive polysaccharides describes our data well.

Variability and host density independence in inductions-based estimates of environmental lysogeny.

Temperate bacterial viruses (phages) may enter a symbiosis with their host cell, forming a unit called a lysogen. Infection and viral replication are disassociated in lysogens until an induction event such as DNA damage occurs, triggering viral-mediated lysis. The lysogen-lytic viral reproduction switch is central to viral ecology, with diverse ecosystem impacts. It has been argued that lysogeny is favoured in phages at low host densities. This paradigm is based on the fraction of chemically inducible cells (FCIC) lysogeny proxy determined using DNA-damaging mitomycin C inductions. Contrary to the established paradigm, a survey of 39 inductions publications found FCIC to be highly variable and pervasively insensitive to bacterial host density at global, within-environment and within-study levels. Attempts to determine the source(s) of variability highlighted the inherent complications in using the FCIC proxy in mixed communities, including dissociation between rates of lysogeny and FCIC values. Ultimately, FCIC studies do not provide robust measures of lysogeny or consistent evidence of either positive or negative host density dependence to the lytic-lysogenic switch. Other metrics are therefore needed to understand the drivers of the lytic-lysogenic decision in viral communities and to test models of the host density-dependent viral lytic-lysogenic switch.

The spatial profiles and metabolic capabilities of microbial populations impact the growth of antibiotic-resistant mutants.

Antibiotic resistance adversely affects clinical and public health on a global scale. Using the opportunistic human pathogen Pseudomonas aeruginosa, we show that increasing the number density of bacteria, on agar containing aminoglycoside antibiotics, can non-monotonically impact the survival of antibiotic-resistant mutants. Notably, at high cell densities, mutant survival is inhibited. A wide range of bacterial species can inhibit antibiotic-resistant mutants. Inhibition results from the metabolic breakdown of amino acids, which results in alkaline by-products. The consequent increase in pH acts in conjunction with aminoglycosides to mediate inhibition. Our work raises the possibility that the manipulation of microbial population structure and nutrient environment in conjunction with existing antibiotics could provide therapeutic approaches to combat antibiotic resistance.

Modeling the mechanics of cancer: effect of changes in cellular and extra-cellular mechanical properties.

Malignant transformation, though primarily driven by genetic mutations in cells, is also accompanied by specific changes in cellular and extra-cellular mechanical properties such as stiffness and adhesivity. As the transformed cells grow into tumors, they interact with their surroundings via physical contacts and the application of forces. These forces can lead to changes in the mechanical regulation of cell fate based on the mechanical properties of the cells and their surrounding environment. A comprehensive understanding of cancer progression requires the study of how specific changes in mechanical properties influences collective cell behavior during tumor growth and metastasis. Here we review some key results from computational models describing the effect of changes in cellular and extra-cellular mechanical properties and identify mechanistic pathways for cancer progression that can be targeted for the prediction, treatment, and prevention of cancer.

How changes in cell mechanical properties induce cancerous behavior.

Tumor growth and metastasis are ultimately mechanical processes involving cell migration and uncontrolled division. Using a 3D discrete model of cells, we show that increased compliance as observed for cancer cells causes them to grow at a much faster rate compared to surrounding healthy cells. We also show how changes in intercellular binding influence tumor malignancy and metastatic potential. These findings suggest that changes in the mechanical properties of cancer cells is the proximate cause of uncontrolled division and migration and various biochemical factors drive cancer progression via this mechanism.

An adsorption-based model for pulse duration in resistive-pulse protein sensing.

We have been investigating an electrochemical single-molecule counting experiment called nanopore resistive-pulse sensing. The sensor element is a conically shaped gold nanotube embedded in a thin polymeric membrane. We have been especially interested in counting protein molecules using these nanotube sensors. This is accomplished by placing the nanotube membrane between two electrolyte solutions, applying a transmembrane potential difference, and measuring the resulting ionic current flowing through the nanopore. In simplest terms, when a protein molecule enters and translocates the nanopore, it transiently blocks the ion current, resulting in a downward current pulse. We have found that the duration of such current-pulses are many orders of magnitude longer than the electrophoretic transport time of the protein through the nanotube detection zone. We develop here a simple model that accounts for this key, and previously explained, observation. This model assumes that the protein molecule engages in repeated adsorption/desorption events to/from the nanotube walls as it translocates through the detection zone. This model not only accounts for the long pulse duration but also for the triangular shape of the current pulse and the increase in the standard deviation of the pulse duration with increasing protein size. Furthermore, the results of our analyses are in general agreement with results obtained from other investigations of protein adsorption to surfaces. This includes the observations that smaller proteins stick more readily to the surface but remain adsorbed for shorter times than larger proteins. In addition, the sticking probabilities calculated from our data are in general agreement with results obtained from other methods.

Two-stage capture employing active transport enables sensitive and fast biosensors.

Nanoscale sensors enable the detection of analytes with improved signal-to-noise ratio but suffer from mass transport limitations. Molecular shuttles, assembled from, e.g., antibody-functionalized microtubules and kinesin motor proteins, can selectively capture analytes from solution and deliver the analytes to a sensor patch. This two-stage process can accelerate mass transport to nanoscale biosensors and facilitate the rapid detection of analytes. Here, the possible increase of the signal-to-noise ratio is calculated, and the optimal layout of a system which integrates active transport is determined.