A probabilistic model for ligand-cytoskeleton transmembrane adhesion: predicting the behavior of microspheres on the surface of migrating cells

Stability and exponential convergence of continuous-time Markov chains

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

Stability and exponential convergence of continuous-time Markov chains

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

A molecular clutch between the actin flow and N-cadherin adhesions drives growth cone migration

The adhesion molecule N-cadherin plays important roles in the development of the nervous system, in particular by stimulating axon outgrowth, but the molecular mechanisms underlying this effect are mostly unknown. One possibility, the so-called "molecular clutch" model, could involve a direct mechanical linkage between N-cadherin adhesion at the membrane and intracellular actin-based motility within neuronal growth cones. Using live imaging of primary rat hippocampal neurons plated on N-cadherin-coated substrates and optical trapping of N-cadherin-coated microspheres, we demonstrate here a strong correlation between growth cone velocity and the mechanical coupling between ligand-bound N-cadherin receptors and the retrograde actin flow. This relationship holds by varying ligand density and expressing mutated N-cadherin receptors or small interfering RNAs to perturb binding to catenins. By restraining microsphere motion using optical tweezers or a microneedle, we further show slippage of cadherin-cytoskeleton bonds at low forces, and, at higher forces, local actin accumulation, which strengthens nascent N-cadherin contacts. Together, these data support a direct transmission of actin-based traction forces to N-cadherin adhesions, through catenin partners, driving growth cone advance and neurite extension.

Regulation of N-cadherin dynamics at neuronal contacts by ligand binding and cytoskeletal coupling

N-cadherin plays a key role in axonal outgrowth and synaptogenesis, but how neurons initiate and remodel N-cadherin-based adhesions remains unclear. We addressed this issue with a semiartificial system consisting of N-cadherin coated microspheres adhering to cultured neurons transfected for N-cadherin-GFP. Using optical tweezers, we show that growth cones are particularly reactive to N-cadherin coated microspheres, which they capture in a few seconds and drag rearward. Such strong coupling requires an intact connection between N-cadherin receptors and catenins. As they move to the basis of growth cones, microspheres slow down while gradually accumulating N-cadherin-GFP, demonstrating a clear delay between bead coupling to the actin flow and receptor recruitment. Using FRAP and photoactivation, N-cadherin receptors at bead-to-cell contacts were found to continuously recycle, consistently with a model of ligand-receptor reaction not limited by membrane diffusion. The use of N-cadherin-GFP receptors truncated or mutated in specific cytoplasmic regions show that N-cadherin turnover is exquisitely regulated by catenin partners. Turnover rates are considerably lower than those obtained previously in single molecule studies, demonstrating an active regulation of cadherin bond kinetics in intact cells. Finally, spontaneous neuronal contacts enriched in N-cadherin exhibited similar turnover rates, suggesting that such dynamics of N-cadherin may represent an intrinsic mechanism underlying the plasticity of neuronal adhesions.

NrCAM coupling to the cytoskeleton depends on multiple protein domains and partitioning into lipid rafts

NrCAM is a cell adhesion molecule of the L1 family that is implicated in the control of axonal growth. Adhesive contacts may promote advance of the growth cone by triggering the coupling of membrane receptors with the F-actin retrograde flow. We sought to understand the mechanisms leading to clutching the F-actin at the site of ligand-mediated clustering of NrCAM. Using optical tweezers and single particle tracking of beads coated with the ligand TAG-1, we analyzed the mobility of NrCAM-deletion mutants transfected in a neuroblastoma cell line. Deletion of the cytoplasmic tail did not prevent the coupling of NrCAM to the actin flow. An additional deletion of the FNIII domains to remove cis-interactions, was necessary to abolish the rearward movement of TAG-1 beads, which instead switched to a stationary behavior. Next, we showed that the actin-dependent retrograde movement of NrCAM required partitioning into lipid rafts as indicated by cholesterol depletion experiments using methyl-beta-cyclodextrin. Recruitment of the raft component caveolin-1 was induced at the adhesive contact between the cell surface and TAG-1 beads, indicating that enlarged rafts were generated. Photobleaching experiments showed that the lateral mobility of NrCAM increased with raft dispersion in these contact areas, further suggesting that TAG-1-coated beads induced the coalescence of lipid rafts. In conclusion, we propose that anchoring of NrCAM with the retrograde actin flow can be triggered by adhesive contacts via cooperative processes including interactions with the cytoplasmic tail, formation of cis-complex via the FNIII repeats, and lipid raft aggregation.

Retrograde flow rate is increased in growth cones from myosin IIB knockout mice

Growth cones of myosin-IIB-knockout mice have reduced outgrowth rates and traction force. There is a close relationship between traction force, retrograde flow and forward advance of growth cones. All three activities appear to be at least partially myosin dependent. Therefore, we have now tested for differences in retrograde flow rates between growth cones from myosin-IIB-knockout mice and their normal littermates. By placing nerve-growth-factor-coated silica beads on the surface of growth cones with laser tweezers, or by tracking GFP-myosin IIA spots, we found that the retrograde flow rate was increased more than two fold in the knockout growth cones compared with the wild type. These data suggest that both myosin IIA and IIB normally contribute to retrograde flow and the properties of the flow are strongly influenced by myosin IIB because of its location and abundance. However, in the absence of myosin IIB, myosin IIA takes over this function. The change in retrograde flow rate may reflect the difference in functional properties of these two myosins. Knockout growth cones also exhibited reduced stability of lamellipodia, possibly as a partial consequence of this increased retrograde flow rate. In addition, microtubules penetrated a shorter distance into filopodia, which suggests that the increase in flow rate may adversely affect the microtubule-dependent maturation of filopodia. Taken together these data support the idea that the forward advance of the growth cone is myosin II dependent and involves multiple myosin II isoforms.