Motile cells explore their surrounding milieu by extending thin dynamic protrusions, or filopodia. The growth of filopodia is driven by actin filament bundles that polymerize underneath the cell membrane. We compute the mechanical and dynamical features of the protrusion growth process by explicitly incorporating the flexible plasma membrane. We find that a critical number of filaments are needed to generate net filopodial growth. Without external influences, the filopodium can extend indefinitely up to the buckling length of the F-actin bundle. Dynamical calculations show that the protrusion speed is enhanced by the thermal fluctuations of the membrane; a filament bundle encased in a flexible membrane grows much faster. The protrusion speed depends directly on the number and spatial arrangement of the filaments in the bundle and whether the filaments are tethered to the membrane. Filopodia also attract each other through distortions of the membrane. Spatially close filopodia will merge to form a larger one. Force-velocity relationships mimicking micromanipulation experiments testing our predictions are computed.

Summary The shape of walled cells such as fungi, bacteria and plants are determined by the cell wall. Models for cell morphogenesis postulate that the effects of turgor pressure and mechanical properties of the cell wall can explain the shapes of these diverse cell types [1–6]. However, in general, these models await validation through quantitative experiments. Fission yeast Schizosaccharomyces pombe are rod-shaped cells that grow by tip extension and then divide medially through formation of a cell wall septum. Upon cell separation after cytokinesis, the new cell ends adopt a rounded morphology. Here, we show that this shape is generated by a very simple mechanical-based mechanism in which turgor pressure inflates the elastic cell wall in the absence of cell growth. This process is independent of actin and new cell wall synthesis. To model this morphological change, we first estimate the mechanical properties of the cell wall using several approaches. The lateral cell wall behaves as an isotropic elastic material with a Young’s modulus of 50 ± 10 MPa inflated by a turgor pressure estimated to be 1.5 ± 0.2 MPa. Based upon these parameters, we develop a quantitative mechanical-based model for new end formation, which reveals that the cell wall at the new end expands into its characteristic rounded shape in part because it is softer than the mature lateral wall. These studies provide a simple example of how turgor pressure expands the elastic cell wall to generate a particular cell shape.

Lamellipodium extension, incorporating actin filament dynamics and the cell membrane, is simulated in three dimensions. The actin filament network topology and the role of actin-associated proteins such as Arp2/3 are examined. We find that the orientational pattern of the filaments is in accord with the experimental data only if the spatial orientation of the Arp2/3 complex is restricted during each branching event. We hypothesize that branching occurs when Arp2/3 is bound to Wiskott-Aldrich syndrome protein (WASP), which is in turn bound to Cdc42 signaling complex; Arp2/3 binding geometry is restricted by the membrane-bound complex. Using mechanical and energetic arguments, we show that any membrane protein that is conical or trapezoidal in shape preferentially resides at the curved regions of the plasma membrane. We hypothesize that the transmembrane receptors involved in the recruitment of Cdc42/WASP complex has this property and concentrate at the leading edge. These features, combined with the mechanical properties of the cell membrane, explain why lamellipodium is a flat organelle.

In hair cells, although mechanotransduction channels have been localized to tips of shorter stereocilia of the mechanically sensitive hair bundle, little is known about how force is transmitted to the channel. Here, we use a biophysical model of the membrane-channel complex to analyze the nature of the gating spring compliance and channel arrangement. We use a triangulated surface model and Monte Carlo simulation to compute the deformation of the membrane under the action of tip link force. We show that depending on the gating spring stiffness, the compliant component of the gating spring arises from either the membrane alone or a combination of the membrane and a tether that connects the channel to the actin cytoskeleton. If a bundle is characterized by relatively soft gating springs, such as those of the bullfrog sacculus, the need for membrane reinforcement by channel tethering then depends on membrane parameters. With stiffer gating springs, such as those from rat outer hair cells, the channel must be tethered for all biophysically realistic parameters of the membrane. We compute the membrane forces (resultants), which depend on membrane tension, bending modulus, and curvature, and show that they can determine the fate of the channel.

The effective spectroscopic Hamiltonian fitted to experiment by Troellsch and Temps (Z. Phys. Chem. 2001, 215, 207) and describing high vibrational excitation to bound and resonant states is used in conjunction with methods of nonlinear classical dynamics and semiclassical mechanics to extract, for all of the observed highly excited resonance levels in polyad 8, the molecular motions upon which they are quantized. Two types of interlaced dynamically distinct ladders of states are revealed. The rungs of these ladders intersperse, making the spectra complex. The resonant 2:2:1 frequency ratio of the DC and CO stretches and the bend, respectively, is what causes the complexity and is what caused past attempts at interpretation to be at best incomplete. All states are assigned with physically meaningful quantum numbers corresponding to quasiconserved quantities. Most interestingly, it is pointed out that much of the information and assignment can be done without any calculations at all, using only the qualitative ideas from nonlinear, semiclassical, and quantum mechanics, along with the information supplied by the experimentalist.