Cell motility plays an essential role in many biological systems, but precise quantitative knowledge of the biophysical processes involved in cell migration is limited. Better measurements are needed to ultimately build models with predictive capabilities. We present an improved force cytometry method and apply it to the analysis of the dynamics of the chemotactic migration of the amoeboid form of Dictyostelium discoideum. Our explicit calculation of the force field takes into account the finite thickness of the elastic substrate and improves the accuracy and resolution compared with previous methods. This approach enables us to quantitatively study the differences in the mechanics of the migration of wildtype (WT) and mutant cell lines. The time evolution of the strain energy exerted by the migrating cells on their substrate is quasiperiodic and can be used as a simple indicator of the stages of the cell motility cycle. We have found that the mean velocity of migration v and the period of the strain energy T cycle are related through a hyperbolic law v ‫؍‬ L/T, where L is a constant step length that remains unchanged in mutants with adhesion or contraction defects. Furthermore, when cells adhere to the substrate, they exert opposing pole forces that are orders of magnitude higher than required to overcome the resistance from their environment.Dictyostelium ͉ myosin ͉ traction forces ͉ cytoskeleton ͉ chemotaxis

Mesenchymal stem cells (MSCs) respond to niche elasticity, which varies between and within tissues. Stiffness gradients result from pathological conditions but also occur through normal variation, e.g. muscle. MSCs undergo directed migration even in response to shallow stiffness gradients before differentiating. More refined gradients of both stiffness range and strength are needed to better understand mechanical regulation of migration in normal and disease pathologies. We describe polyacrylamide stiffness gradient fabrication using three distinct systems that generate stiffness gradients of physiological (1 Pa/µm), pathological (10 Pa/µm), and step (≥ 100Pa/um) strength spanning physiologically relevant stiffness for most soft tissue, i.e. 1–12 kPa. MSCs migrated to the stiffest region for each gradient. Time-lapse microscopy revealed that migration velocity scaled directly with gradient strength. Directed migration was reduced in the presence of the contractile agonist lysophosphatidic acid (LPA) and cytoskeletal-perturbing drugs nocodazole and cytochalasin; LPA- and nocodazole-treated cells remained spread and protrusive, while cytochalasin-treated cells did not. Untreated and nocodazole-treated cells spread in a similar manner, but nocodazole-treated cells had greatly diminished traction forces. These data suggest that actin is required for migration whereas microtubules are required for directed migration. The data also imply that in vivo, MSCs may have a more significant contribution to repairs in stiffer regions where they may preferentially accumulate.

We use a novel 3D inter-/intracellular force microscopy technique based on 3D traction force microscopy to measure the cell-cell junctional and intracellular tensions in subconfluent and confluent vascular endothelial cell (EC) monolayers under static and shear flow conditions. We found that z-direction cell-cell junctional tensions are higher in confluent EC monolayers than those in subconfluent ECs, which cannot be revealed in the previous 2D methods. Under static conditions, subconfluent cells are under spatially nonuniform tensions, whereas cells in confluent monolayers are under uniform tensions. The shear modulations of EC cytoskeletal remodeling, extracellular matrix (ECM) adhesions, and cell-cell junctions lead to significant changes in intracellular tensions. When a confluent monolayer is subjected to flow shear stresses with a high forward component comparable to that seen in the straight part of the arterial system, the intracellular and junction tensions preferentially increase along the flow direction over time, which may be related to the relocation of adherens junction proteins. The increases in intracellular tensions are shown to be a result of chemomechanical responses of the ECs under flow shear rather than a direct result of mechanical loading. In contrast, the intracellular tensions do not show a preferential orientation under oscillatory flow with a very low mean shear. These differences in the directionality and magnitude of intracellular tensions may modulate translation and transcription of ECs under different flow patterns, thus affecting their susceptibility for atherogenesis.cell alignment | endothelial monolayer | finite element method | fluid shear stress | junctional force B lood vessels are constantly exposed to hemodynamic forces imposed by the blood flow and pressure. Vascular endothelial cells (ECs), which line the inner blood vessel wall, bear the shear stress resulting from the blood flow. Responses of ECs to hemodynamic forces play significant roles in vascular homeostasis in health and disease. Atherosclerotic lesions are preferentially localized in regions, such as arterial branch points, where the ECs are subjected to disturbed flow consisting of flow separation, reversal, and reattachment (1-3). The reattachment area, which is exposed to a low shear stress magnitude and significant oscillatory reversal (i.e., the flow oscillates back and forth with little net direction), has random EC morphology and cytoskeletal organization, incomplete intercellular junctions, and pro-inflammatory and pro-atherogenic phenotypes (1). In contrast, ECs in the straight part of the arterial tree, which is generally spared from atherosclerosis, are exposed to high shear flow with a large net mean direction and have parallel cell orientation, aligned cytoskeletal fibers, and intact junctions. Studies on cultured ECs have advanced the knowledge of how different flow conditions regulate EC functions (1, 4, 5) and provided evidence for the biomedical importance of EC responses to flow shear. The b...

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 (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.