Determinants of maximal force transmission in a motor-clutch model of cell traction in a compliant microenvironment.

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.

Shifting the optimal stiffness for cell migration.

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.

Biphasic Dependence of Glioma Survival and Cell Migration on CD44 Expression Level.

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.

Master equation-based analysis of a motor-clutch model for cell traction force.

Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell's optimum stiffness (i.e. the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on-off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours-days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.