Juan C. del Álamo

Scaling of the energy spectra of turbulent channels

The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Reτ = 1900. It is found, and explained, that their scaling is anomalous in several respects, including a square-root behaviour of their width with respect to their length, and a velocity scaling of the largest modes with the centreline velocity Uc. It is shown that this implies a logarithmic correction to the k −1 energy spectrum, and that it leads to a scaling of the total fluctuation intensities away from the wall which agrees well with the mixed scaling of de Graaff & Eaton (2000) at intermediate Reynolds numbers, but which tends to a pure scaling with Uc at very large ones.

Spectra of the very large anisotropic scales in turbulent channels

The spectra of numerically simulated channels at Reτ=180 and Reτ=550 in very large boxes are described and analyzed. They support a model in which the u-structures can be decomposed in two components. The first one is formed by structures of size λx≳5 h, λz≈2 h, which span most of the channel height, and penetrate into the buffer layer. The second one has maximum intensity in the near-wall region, where it is highly anisotropic and scales in inner units. It widens, lengthens, and becomes more isotropic in the outer layer, where it scales with h. The cospectrum exhibits an analogous quasi-isotropic range, whose width grows linearly with wall distance. At the present Reynolds numbers, nothing can be said about a possible streamwise similarity, due to limited scale separation. An extensive set of statistics from the simulations is downloadable from ftp://torroja.dmt.upm.es/channels.

Linear energy amplification in turbulent channels

We study the temporal stability of the Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. Friction Reynolds numbers up to Re τ =2×10 4 are considered. All the eigensolutions of the problem are damped, but initial perturbations with wavelengths λ x > λ z can grow temporarily before decaying. The most amplified solutions reproduce the organization of turbulent structures in actual channels, including their self-similar spreading in the logarithmic region. The typical widths of the near-wall streaks and of the large-scale structures of the outer layer, λ + z = 100 and λ z /h = 3, are predicted well. The dynamics of the most amplified solutions is roughly the same regardless of the wavelength of the perturbations and of the Reynolds number. They start with a wall-normal v event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear (uv < 0). The resulting u fluctuations grow significantly and last longer than the v ones, and contain nearly all the kinetic energy at the instant of maximum amplification.

Spatio-temporal analysis of eukaryotic cell motility by improved force cytometry

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 wild-type (WT) and mutant cell lines. The time evolution of the strain energy exerted by the migrating cells on their substrate is quasi-periodic 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.

Mesenchymal stem cell durotaxis depends on substrate stiffness gradient strength

Mesenchymal stem cells (MSCs) respond to the elasticity of their environment, which varies between and within tissues. Stiffness gradients within tissues can result from pathological conditions, but also occur through normal variation, such as in muscle. MSC migration can be directed by shallow stiffness gradients before differentiating. Gradients with fine control over substrate compliance - both in range and rate of change (strength) - are needed to better understand mechanical regulation of MSC migration in normal and diseased states. We describe polyacrylamide stiffness gradient fabrication using three distinct systems, generating stiffness gradients of physiological (1 Pa/μm), pathological (10 Pa/μm), and step change (≥ 100Pa/μm) strength. All gradients spanned a range of physiologically relevant elastic moduli for soft tissues (1-12 kPa). MSCs migrated to the stiffest region on each gradient. Time-lapse microscopy revealed that migration velocity correlated directly with gradient strength. Directed migration was reduced in the presence of the contractile agonist lysophosphatidic acid (LPA) and cytoskeleton-perturbing drugs nocodazole and cytochalasin. LPA- and nocodazole-treated cells remained spread and protrusive on the substrate, while cytochalasin-treated cells did not. Nocodazole-treated cells spread in a similar manner to untreated cells, but exhibited greatly diminished traction forces. These data suggest that a functional actin cytoskeleton is required for migration whereas microtubules are required for directed migration. The data also imply that, in vivo, MSCs may preferentially accumulate in regions of high elastic modulus and make a greater contribution to tissue repairs in these locations.

Myosin II Is Essential for the Spatiotemporal Organization of Traction Forces during Cell Motility

Amoeboid motility results from pseudopod protrusions and retractions driven by traction forces of cells. We propose that the motor and actin-crosslinking functions of MyoII differentially control the temporal and spatial distribution of the traction forces, and establish mechanistic relationships between these distributions, enabling cells to move.

Roles of cell confluency and fluid shear in 3-dimensional intracellular forces in endothelial cells

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 non-uniform 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 chemo-mechanical 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.

Turbulence modification by stable stratification in channel flow

Direct numerical simulations of stably stratified, turbulent channel flow at low to moderate Reynolds number have been performed using large computational boxes and considering a wide range of stratification levels. For weak stratification or high Reynolds number, the turbulence is affected by buoyancy in the core of the channel, but the near-wall region differs little from the neutral case. With strong stratification, large laminar patches appear in the near-wall region and turbulent momentum and buoyancy fluxes vanish in the core of the channel. With increasing stratification, the near-wall streaks remain essentially unmodified, while large-scale global modes are damped. In the central region, internal gravity waves are dominant. In addition, there is an intermediate outer layer where the dynamics of the turbulent structures is governed by local fluxes. In this region, energy spectra collapse when using local Obukhov scaling.

Anisotropic rheology and directional mechanotransduction in vascular endothelial cells

Adherent cells remodel their cytoskeleton, including its directionality, in response to directional mechanical stimuli with consequent redistribution of intracellular forces and modulation of cell function. We analyzed the temporal and spatial changes in magnitude and directionality of the cytoplasmic creep compliance (Γ) in confluent cultures of bovine aortic endothelial cells subjected to continuous laminar flow shear stresses. We extended particle tracking microrheology to determine at each point in the cytoplasm the principal directions along which Γ is maximal and minimal. Under static condition, the cells have polygonal shapes without specific alignment. Although Γ of each cell exhibits directionality with varying principal directions, Γ averaged over the whole cell population is isotropic. After continuous laminar flow shear stresses, all cells gradually elongate and the directions of maximal and minimal Γ become, respectively, parallel and perpendicular to flow direction. This mechanical alignment is accompanied by a transition of the cytoplasm to be more fluid-like along the flow direction and more solid-like along the perpendicular direction; at the same time Γ increases at the downstream part of the cells. The resulting directional anisotropy and spatial inhomogeneity of cytoplasmic rheology may play an important role in mechanotransduction in adherent cells by providing a means to sense the direction of mechanical stimuli.

In situ mechanotransduction via vinculin regulates stem cell differentiation

Human mesenchymal stem cell (hMSC) proliferation, migration, and differentiation have all been linked to extracellular matrix stiffness, yet the signaling pathway(s) that are necessary for mechanotransduction remain unproven. Vinculin has been implicated as a mechanosensor in vitro, but here we demonstrate its ability to also regulate stem cell behavior, including hMSC differentiation. RNA interference‐mediated vinculin knockdown significantly decreased stiffness‐induced MyoD, a muscle transcription factor, but not Runx2, an osteoblast transcription factor, and impaired stiffness‐mediated migration. A kinase binding accessibility screen predicted a cryptic MAPK1 signaling site in vinculin which could regulate these behaviors. Indeed, reintroduction of vinculin domains into knocked down cells indicated that MAPK1 binding site‐containing vinculin constructs were necessary for hMSC expression of MyoD. Vinculin knockdown does not appear to interfere with focal adhesion assembly, significantly alter adhesive properties, or diminish cell traction force generation, indicating that its knockdown only adversely affected MAPK1 signaling. These data provide some of the first evidence that a force‐sensitive adhesion protein can regulate stem cell fate. Stem Cells 2013;31:2467–2477