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Cell migration on two-dimensional substrates is typically characterized by lamellipodia at the leading edge, mature focal adhesions and spread morphologies. These observations result from adherent cell migration studies on stiff, elastic substrates, because most cells do not migrate on soft, elastic substrates. However, many biological tissues are soft and viscoelastic, exhibiting stress relaxation over time in response to a deformation. Here, we have systematically investigated the impact of substrate stress relaxation on cell migration on soft substrates. We observed that cells migrate minimally on substrates with an elastic modulus of 2 kPa that are elastic or exhibit slow stress relaxation, but migrate robustly on 2-kPa substrates that exhibit fast stress relaxation. Strikingly, migrating cells were not spread out and did not extend lamellipodial protrusions, but were instead rounded, with filopodia protrusions extending at the leading edge, and exhibited small nascent adhesions. Computational models of cell migration based on a motor-clutch framework predict the observed impact of substrate stress relaxation on cell migration and filopodia dynamics. Our findings establish substrate stress relaxation as a key requirement for robust cell migration on soft substrates and uncover a mode of two-dimensional cell migration marked by round morphologies, filopodia protrusions and weak adhesions., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

Cell migration and traction are essential to many biological phenomena, and one of their key features is sensitivity to substrate stiffness, which biophysical models, such as the motor-clutch model and the cell migration simulator can predict and explain. However, these models have not accounted for the finite size of adhesions, the spatial distribution of forces within adhesions. Here, we derive an expression that relates varying adhesion radius ( R) and spatial distribution of force within an adhesion (described by s) to the effective substrate stiffness ( κ sub ), as a function of the Young's modulus of the substrate ( E Y ), which yields the relation, κ sub = R s E Y , for two-dimensional cell cultures. Experimentally, we found that a cone-shaped force distribution ( s = 1.05) can describe the observed displacements of hydrogels deformed by adherent U251 glioma cells. Also, we found that the experimentally observed adhesion radius increases linearly with the cell protrusion force, consistent with the predictions of the motor-clutch model with spatially distributed clutches. We also found that, theoretically, the influence of one protrusion on another through a continuous elastic environment is negligible. Overall, we conclude cells can potentially control their own interpretation of the mechanics of the environment by controlling adhesion size and spatial distribution of forces within an adhesion., (© 2019 Wiley Periodicals, Inc.)

Glioblastoma is a primary malignant brain tumor characterized by highly infiltrative glioma cells. Vasculature and white matter tracts are considered to be the preferred and fastest routes for glioma invasion through brain tissue. In this study, we systematically quantified the routes and motility of the U251 human glioblastoma cell line in mouse brain slices by multimodal imaging. Specifically, we used polarization-sensitive optical coherence tomography to delineate nerve fiber tracts while confocal fluorescence microscopy was used to image cell migration and brain vasculature. Somewhat surprisingly, we found that in mouse brain slices, U251 glioma cells do not follow white matter tracts but rather preferentially migrate along vasculature in both gray and white matter. In addition, U251 cell motility is ∼2-fold higher in gray matter than in white matter (91 vs. 43 μm 2 /h), with a substantial fraction (44%) of cells in both regions invading without close association with vasculature. Interestingly, within both regions, the rates of migration for the perivascular and televascular routes of invasion were indistinguishable. Furthermore, by imaging of local vasculature deformation dynamics during cell migration, we found that U251 cells are capable of exerting traction forces that locally pull on their environment, suggesting the applicability of a "motor-clutch"-based model for migration in vivo. Overall, by quantitatively analyzing the migration dynamics along the diverse pathways followed by invading U251 glioma cells as observed by our multimodal imaging approach, our studies suggest that effective antiinvasive strategies will need to simultaneously limit parallel routes of both perivascular and televascular invasion through both gray and white matter., (Copyright © 2019 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Microtubule-targeting agents (MTAs) are widely used chemotherapy drugs capable of disrupting microtubule-dependent cellular functions, such as division and migration. We show that two clinically approved MTAs, paclitaxel and vinblastine, each suppress stiffness-sensitive migration and polarization characteristic of human glioma cells on compliant hydrogels. MTAs influence microtubule dynamics and cell traction forces by nearly opposite mechanisms, the latter of which can be explained by a combination of changes in myosin motor and adhesion clutch number. Our results support a microtubule-dependent signaling-based model for controlling traction forces through a motor-clutch mechanism, rather than microtubules directly relieving tension within F-actin and adhesions. Computational simulations of cell migration suggest that increasing protrusion number also impairs stiffness-sensitive migration, consistent with experimental MTA effects. These results provide a theoretical basis for the role of microtubules and mechanisms of MTAs in controlling cell migration., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

Understanding how cells migrate in fibrous environments is important in wound healing, immune function, and cancer progression. A key question is how fiber orientation and network geometry influence cell movement. Here we describe a quantitative, modeling-based approach toward identifying the mechanisms by which cells migrate in fibrous geometries having well controlled orientation. Specifically, U251 glioblastoma cells were seeded onto non-electrospinning Spinneret based tunable engineering parameters fiber substrates that consist of networks of suspended 400 nm diameter nanofibers. Cells were classified based on the local fiber geometry and cell migration dynamics observed by light microscopy. Cells were found in three distinct geometries: adhering two a single fiber, adhering to two parallel fibers, and adhering to a network of orthogonal fibers. Cells adhering to a single fiber or two parallel fibers can only move in one dimension along the fiber axis, whereas cells on a network of orthogonal fibers can move in two dimensions. We found that cells move faster and more persistently in 1D geometries than in 2D, with cell migration being faster on parallel fibers than on single fibers. To explain these behaviors mechanistically, we simulated cell migration in the three different geometries using a motor-clutch based model for cell traction forces. Using nearly identical parameter sets for each of the three cases, we found that the simulated cells naturally replicated the reduced migration in 2D relative to 1D geometries. In addition, the modestly faster 1D migration on parallel fibers relative to single fibers was captured using a correspondingly modest increase in the number of clutches to reflect increased surface area of adhesion on parallel fibers. Overall, the integrated modeling and experimental analysis shows that cell migration in response to varying fibrous geometries can be explained by a simple mechanical readout of geometry via a motor-clutch mechanism.

Cell migration is the physical movement of cells and is responsible for the extensive cellular invasion and metastasis that occur in high-grade tumors. Motivated by decades of direct observation of cell migration via light microscopy, theoretical models have emerged to capture various aspects of the fundamental physical phenomena underlying cell migration. Yet, the motility mechanisms actually used by tumor cells during invasion are still poorly understood, as is the role of cellular interactions with the extracellular environment. In this chapter, we review key physical principles of cytoskeletal self-assembly and force generation, membrane tension, biological adhesion, hydrostatic and osmotic pressures, and their integration in mathematical models of cell migration. With the goal of modeling-driven cancer therapy, we provide examples to guide oncologists and physical scientists in developing next-generation models to predict disease progression and treatment.

Cell migration, which is central to many biological processes including wound healing and cancer progression, is sensitive to environmental stiffness, and many cell types exhibit a stiffness optimum, at which migration is maximal. Here we present a cell migration simulator that predicts a stiffness optimum that can be shifted by altering the number of active molecular motors and clutches. This prediction is verified experimentally by comparing cell traction and F-actin retrograde flow for two cell types with differing amounts of active motors and clutches: embryonic chick forebrain neurons (ECFNs; optimum ∼1 kPa) and U251 glioma cells (optimum ∼100 kPa). In addition, the model predicts, and experiments confirm, that the stiffness optimum of U251 glioma cell migration, morphology and F-actin retrograde flow rate can be shifted to lower stiffness by simultaneous drug inhibition of myosin II motors and integrin-mediated adhesions.

While several studies link the cell-surface marker CD44 to cancer progression, conflicting results show both positive and negative correlations with increased CD44 levels. Here, we demonstrate that the survival outcomes of genetically induced glioma-bearing mice and of high-grade human glioma patients are biphasically correlated with CD44 level, with the poorest outcomes occurring at intermediate levels. Furthermore, the high-CD44-expressing mesenchymal subtype exhibited a positive trend of survival with increased CD44 level. Mouse cell migration rates in ex vivo brain slice cultures were also biphasically associated with CD44 level, with maximal migration corresponding to minimal survival. Cell simulations suggest that cell-substrate adhesiveness is sufficient to explain this biphasic migration. More generally, these results highlight the potential importance of non-monotonic relationships between survival and biomarkers associated with cancer progression., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

The mechanical stiffness of a cell's environment exerts a strong, but variable, influence on cell behavior and fate. For example, different cell types cultured on compliant substrates have opposite trends of cell migration and traction as a function of substrate stiffness. Here, we describe how a motor-clutch model of cell traction, which exhibits a maximum in traction force with respect to substrate stiffness, may provide a mechanistic basis for understanding how cells are tuned to sense the stiffness of specific microenvironments. We find that the optimal stiffness is generally more sensitive to clutch parameters than to motor parameters, but that single parameter changes are generally only effective over a small range of values. By contrast, dual parameter changes, such as coordinately increasing the numbers of both motors and clutches offer a larger dynamic range for tuning the optimum. The model exhibits distinct regimes: at high substrate stiffness, clutches quickly build force and fail (so-called frictional slippage), whereas at low substrate stiffness, clutches fail spontaneously before the motors can load the substrate appreciably (a second regime of frictional slippage). Between the two extremes, we find the maximum traction force, which occurs when the substrate load-and-fail cycle time equals the expected time for all clutches to bind. At this stiffness, clutches are used to their fullest extent, and motors are therefore resisted to their fullest extent. The analysis suggests that coordinate parameter shifts, such as increasing the numbers of motors and clutches, could underlie tumor progression and collective cell migration., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

A major goal of liver tissue engineering is to understand how the constituent cell types interact to achieve liver-specific structure and function. Here we show that hepatocytes migrate toward and adhere to endothelial vascular structures formed on Matrigel in vitro, and that hepatocyte recruitment is dependent on endothelium-derived hepatocyte growth factor. The hepatocyte-decorated endothelial vascular structures resemble In vivo sinusoids containing plate-like structures, bile canaliculi, and a lumen. The sinusoid-like structures retained cytochrome P450 expression and activity, in addition to stable albumin expression and secretion rate for over 2 months in vitro. The stability of the sinusoid-like structures was dependent on the presence of vimentin-positive fibroblasts in culture. The sinusoid-like structures formed by hepatocytes and pure populations of endothelial cells collapsed after 10 days in culture. In contrast, culture of hepatocytes with fibroblast-contaminated human dermal microvascular endothelial cells or a combination of human umbilical vein endothelial cells and normal human dermal fibroblasts resulted in stable sinusoid-like structures surrounded by a fibroblastic capsule that maintained liver specific functions for several months in vitro. These results demonstrate that specification of endothelial cell position ultimately determines hepatocyte position in vitro, suggesting that similar interactions might occur In vivo. The novelty of the culture's sinusoid-like organization and long-term function suggest a new model for the study of liver toxicity, ischemia/reperfusion injury, and fibrosis.