Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (\ie cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses

An Oscillatory Contractile Pole-Force Component Dominates the Traction Forces Exerted by Migrating Amoeboid Cells

We used principal component analysis to dissect the mechanics of chemotaxis of amoeboid cells into a reduced set of dominant components of cellular traction forces and shape changes. The dominant traction force component in wild-type cells accounted for ~40% of the mechanical work performed by these cells, and consisted of the cell attaching at front and back contracting the substrate towards its centroid (pole-force). The time evolution of this pole-force component was responsible for the periodic variations of cell length and strain energy that the cells underwent during migration. We identified four additional canonical components, reproducible from cell to cell, overall accounting for an additional ~20% of mechanical work, and associated with events such as lateral protrusion of pseudopodia. We analyzed mutant strains with contractility defects to quantify the role that non-muscle Myosin II (MyoII) plays in amoeboid motility. In MyoII essential light chain null cells the polar-force component remained dominant. On the other hand, MyoII heavy chain null cells exhibited a different dominant traction force component, with a marked increase in lateral contractile forces, suggesting that cortical contractility and/or enhanced lateral adhesions are important for motility in this cell line. By compressing the mechanics of chemotaxing cells into a reduced set of temporally-resolved degrees of freedom, the present study may contribute to refined models of cell migration that incorporate cell-substrate interactions

Force and shape coordination in amoeboid cell motility

Cell motility plays an essential role in many physiological and pathological processes, yet we still lack information about the spatio-temporal coordination between regulatory biochemical processes and mechanics of cell migration. This dissertation has investigated the mechanics of amoeboid cell migration through intensive analysis of the traction forces exerted and shapes adopted by single Dictyostelium discoideum cells migrating chemotactically, focusing on wild-type (WT) and contractility-defective cells lacking either protein myosin II (mhcA⁻) or the myosin II essential light chains (mlcE⁻). We have developed an improved traction force cytometry method to calculate cell traction stresses which considers the finite thickness of the substrate. We have shown that the strain energy exerted by locomoting cells on the substrate evolves quasi-periodically and correlates with cell length, and thus it can be used as a quantitative indicator of the cell motility cycle. The periodicity (T) of the oscillations in the traction forces correlates strongly with the average velocity of migration (V) of cells according to the hyperbolic law V T=[lambda], where the constant [lambda] is independent of the strain analyzed and corresponds to the average distance a cell travels per cycle. Given the quasi-periodic character of both cell length and strain energy, we have performed a phase statistical analysis to obtain a spatio-temporal representation of the canonical motility cycle divided into four phases: protrusion, contraction, retraction, and relaxation. This analysis has elucidated the role that protein myosin II plays in enhancing the kinetics of the four stages of the cycle and in controlling the spatial distribution of the traction forces regulating that process. We have used principal component analysis to dissect the mechanics of locomotion of amoeboid cells into a reduced set of dominant components of cellular traction forces and shape changes. The dominant traction force component accounts for 40% of the strain energy performed by these cells, and its temporal evolution correlates with the quasi-periodic variations of cell length and strain energy exerted on the substrate. Finally, we have developed two analytic assays for the calculation of cell traction stresses in configurations of interest to further understand the mechanosensing machinery of cell