Analytical approximations of the diffusive dispersion in fluid flows

We present a path-integral approach for finding solutions of the convection-diffusion equation with inhomogeneous fluid flow, which are notoriously difficult to solve. We derive a general approximate analytical solution of the convection-diffusion equation which is in principle applicable to arbitrary flow profiles. As examples, we apply this approximation to the diffusion in a linear shear flow and in a parabolic flow in infinite space, and to the diffusion in a linear shear flow over an impenetrable interface. This last case is particularly important for problems involving diffusive transport towards an interface with advection. We compare the analytical approximation with numerical solutions which are obtained from a conventional finite-element time-difference method

Enhanced dimerization drives ligand-independent activity of mutant EGFR in lung cancer.

Mutations within the epidermal growth factor receptor (EGFR/erbB1/Her1) are often associated with tumorigenesis. In particular, a number of EGFR mutants that demonstrate ligand-independent signaling are common in non-small cell lung cancer (NSCLC), including kinase domain mutations L858R (also called L834R) and exon 19 deletions (e.g. ΔL747-P753insS) which collectively make up nearly 90% of mutations in NSCLC. The molecular mechanisms by which these mutations confer constitutive activity remain unresolved. Using multiple subdiffraction-limit imaging modalities, we reveal the altered receptor structure and interaction kinetics of NSCLC-associated EGFR mutants. We applied two-color single quantum dot tracking to quantify receptor dimerization kinetics on living cells and show that, in contrast to wild type EGFR, mutants are capable of forming stable, ligand-independent dimers. Two-color super-resolution localization microscopy confirmed ligand-independent aggregation of EGFR mutants. Live cell FRET measurements revealed that the L858R kinase mutation alters ectodomain structure such that unliganded mutant EGFR adopts an extended, dimerization-competent conformation. Finally, mutation of the putative dimerization arm confirmed a critical role for ectodomain engagement in ligand-independent signaling. These data support a model in which dysregulated activity of NSCLC-associated kinase mutants is driven by coordinated interactions involving both the kinase and extracellular domains that lead to enhanced dimerization

Two-dimensional TIRF-SIM-traction force microscopy (2D TIRF-SIM-TFM)

Quantifying small, rapidly evolving forces generated by cells is a major challenge for the understanding of biomechanics and mechanobiology in health and disease. Traction force microscopy remains one of the most broadly applied force probing technologies but typically restricts itself to slow events over seconds and micron-scale displacements. Here, we improve >2-fold spatially and >10-fold temporally the resolution of planar cellular force probing compared to its related conventional modalities by combining fast two-dimensional total internal reflection fluorescence super-resolution structured illumination microscopy and traction force microscopy. This live-cell 2D TIRF-SIM-TFM methodology offers a combination of spatio-temporal resolution enhancement relevant to forces on the nano- and sub-second scales, opening up new aspects of mechanobiology to analysis