Simple mechanochemistry describes the dynamics of kinesin molecules

Recently, Block and coworkers [Visscher, K., Schnitzer, M. J., & Block, S. M. (1999) Nature (London) 400, 184–189 and Schnitzer, M. J., Visscher, K. & Block, S. M. (2000) Nat. Cell Biol. 2, 718–723] have reported extensive observations of individual kinesin molecules moving along microtubules in vitro under controlled loads, F = 1 to 8 pN, with [ATP] = 1 μM to 2 mM. Their measurements of velocity, V, randomness, r, stalling force, and mean run length, L, reveal a need for improved theoretical understanding. We show, presenting explicit formulae that provide a quantitative basis for comparing distinct molecular motors, that their data are satisfactorily described by simple, discrete-state, sequential stochastic models. The simplest (N = 2)-state model with fixed load-distribution factors and kinetic rate constants concordant with stopped-flow experiments, accounts for the global (V, F, L, [ATP]) interdependence and, further, matches relative acceleration observed under assisting loads. The randomness, r(F,[ATP]), is accounted for by a waiting-time distribution, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{1}^{+}}}\end{equation*}\end{document}(t), [for the transition(s) following ATP binding] with a width parameter ν ≡ 〈t〉2/〈(Δt)2〉≃2.5, indicative of a dispersive stroke of mechanicity ≃0.6 or of a few (≳ν − 1) further, kinetically coupled states: indeed, N = 4 (but not N = 3) models do well. The analysis reveals: (i) a substep of d0 = 1.8–2.1 nm on ATP binding (consistent with structurally based suggestions); (ii) comparable load dependence for ATP binding and unbinding; (iii) a strong load dependence for reverse hydrolysis and subsequent reverse rates; and (iv) a large (≳50-fold) increase in detachment rate, with a marked load dependence, following ATP binding.

Electric Field–directed Cell Motility Involves Up-regulated Expression and Asymmetric Redistribution of the Epidermal Growth Factor Receptors and Is Enhanced by Fibronectin and Laminin

Wounding corneal epithelium establishes a laterally oriented, DC electric field (EF). Corneal epithelial cells (CECs) cultured in similar physiological EFs migrate cathodally, but this requires serum growth factors. Migration depends also on the substrate. On fibronectin (FN) or laminin (LAM) substrates in EF, cells migrated faster and more directly cathodally. This also was serum dependent. Epidermal growth factor (EGF) restored cathodal-directed migration in serum-free medium. Therefore, the hypothesis that EGF is a serum constituent underlying both field-directed migration and enhanced migration on ECM molecules was tested. We used immunofluorescence, flow cytometry, and confocal microscopy and report that 1) EF exposure up-regulated the EGF receptor (EGFR); so also did growing cells on substrates of FN or LAM; and 2) EGFRs and actin accumulated in the cathodal-directed half of CECs, within 10 min in EF. The cathodal asymmetry of EGFR and actin staining was correlated, being most marked at the cell–substrate interface and showing similar patterns of asymmetry at various levels through a cell. At the cell–substrate interface, EGFRs and actin frequently colocalized as interdigitated, punctate spots resembling tank tracks. Cathodal accumulation of EGFR and actin did not occur in the absence of serum but were restored by adding ligand to serum-free medium. Inhibition of MAPK, one second messenger engaged by EGF, significantly reduced EF-directed cell migration. Transforming growth factor β and fibroblast growth factor also restored cathodal-directed cell migration in serum-free medium. However, longer EF exposure was needed to show clear asymmetric distribution of the receptors for transforming growth factor β and fibroblast growth factor. We propose that up-regulated expression and redistribution of EGFRs underlie cathodal-directed migration of CECs and directed migration induced by EF on FN and LAM.

Electric field-induced reorganization of two-component supported bilayer membranes

Application of electric fields tangent to the plane of a confined patch of fluid bilayer membrane can create lateral concentration gradients of the lipids. A thermodynamic model of this steady-state behavior is developed for binary systems and tested with experiments in supported lipid bilayers. The model uses Flory’s approximation for the entropy of mixing and allows for effects arising when the components have different molecular areas. In the special case of equal area molecules the concentration gradient reduces to a Fermi–Dirac distribution. The theory is extended to include effects from charged molecules in the membrane. Calculations show that surface charge on the supporting substrate substantially screens electrostatic interactions within the membrane. It also is shown that concentration profiles can be affected by other intermolecular interactions such as clustering. Qualitative agreement with this prediction is provided by comparing phosphatidylserine- and cardiolipin-containing membranes.