When neurons undergo dramatic shape and volume changes, how is surface area adjusted appropriately? The membrane tension hypothesis-namely that high tensions favor recruitment of membrane to the surface whereas low tensions favor retrieval-provides a simple conceptual framework for surface area homeostasis. With membrane tension and area in a feedback loop, tension extremes may be averted even during excessive mechanical load variations. We tested this by measuring apparent membrane tension of swelling and shrinking Lymnaea neurons. With hypotonic medium (50%), tension that was calculated from membrane tether forces increased from 0.04 to as much as 0.4 mN/m, although at steady state, swollen-cell tension (0.12 mN/m) exceeded controls only threefold. On reshrinking in isotonic medium, tension reduced to 0.02 mN/m, and at the substratum, membrane invaginated, creating transient vacuolelike dilations. Swelling increased membrane tension with or without BAPTA chelating ytoplasmic Ca2+, but with BAPTA, unmeasurably large (although not lytic) tension surges occurred in approximately two-thirds of neurons. Furthermore, in unarborized neurons voltage-clamped by perforated-patch in 50% medium, membrane capacitance increased 8%, which is indicative of increasing membrane area. The relatively damped swelling–tension responses of Lymnaea neurons (no BAPTA) were consistent with feedback regulation. BAPTA did not alter resting membrane tension, but the large surges during swelling of BAPTA-loaded neurons demonstrated that 50% medium was inherently treacherous and that tension regulation was impaired by subnormal cytoplasmic [Ca2+]. However, neurons did survive tension surges in the absence of Ca2+ signaling. The mechanism to avoid hightension rupture may be the direct tension-driven recruitment of membrane stores.

The small GTPase racE is essential for cytokinesis in Dictyostelium. We found that this require- ment is restricted to cells grown in suspension. When attached to a substrate, racE null cells form an actomyosin contractile ring and complete cytokinesis normally. Nonetheless, racE null cells fail completely in cytokinesis when in suspension. To understand this conditional requirement for racE, we developed a method to observe cytokinesis in suspension. Using this approach, we found that racE null cells attempt cytokinesis in suspension by forming a contractile ring and cleavage furrow. However, the cells form multiple blebs and fail incytokinesis by regression of the cleavage furrow. We believe this phenotype is caused by the extremely low level of cortical tension found in racE null cells com- pared to wild-type cells. The reduced cortical tension of racE null cells is not caused by a decrease in their content of F-actin. Instead, mitotic racE null cells contain abnormal F-actin aggregates. These results suggest that racE is essential for the organization of the cortical cytoskeleton to maintain proper cortical integrity. This function of racE is independent of attachment to a sub- strate, but can be bypassed by other signaling pathways induced by adhesion to a substrate.

Membrane tethers are extracted at constant velocity from neuronal growth cones using a force generated by a laser tweezers trap. A thermodynamic analysis shows that as the tether is extended, energy is stored in the tether as bending and adhesion energies and in the cell body as "nonlocal" bending. It is postulated that energy is dissipated by three viscous mechanisms including membrane flow, slip between the two monolayers that form the bilayer, and slip between membrane and cytoskeleton. The analysis predicts and the experiments show a linear relation between tether force and tether velocity. Calculations based on the analytical results and the experimental measurements of a tether radius of ～0.2 μm and a tether force at zero velocity of ～8 pN give a bending modulus for the tether of 2.7×10-19 N-m and an extraordinarily small "apparent surface tension" in the growth cone of 0.003 mN/m, where the apparent surface tension is the sum of the far-field, in-plane tension and the energy of adhesion. Treatments with cytochalasin B and D, ethanol, and nocodazole affect the apparent surface tension but not bending. ATP depletion affects neither, whereas large concentrations of DMSO affect both. Under conditions of flow, data are presented to show that the dominant viscous mechanism comes from the slip that occurs when the membrane flows over the cytoskeleton. ATP depletion and the treatment with DMSO cause a dramatic drop in the effective viscosity. If it is postulated that the slip between membrane and cytoskeleton occurs in a film of water, then this water film has a mean thickness of only ～10 A.

The plasma membrane of most cells is drawn tightly over the cytoskeleton of the cell, resulting in a significant tension being developed in the membrane. The tension in the membrane can be calculated fi-om the force required to separate it ffom the cytoskeleton; and the force itself can be measured rapidly by using laser tweezers. Recent observations indicate that decreasing membrane tension stimulates endocytosis and increasing tension stimulates secretion. Thus, membrane tension provides a simple physical mechanism to control the area of the plasma membrane. Here, we speculate that tension is a global parameter that the cell uses to control physically plasma membrane dynamics, cell shape and cell motility.

Many cell phenomena involve major morphological changes, particularly in mitosis and the process of cell migration. For cells or neuronal growth cones to migrate, they must extend the leading edge of the plasma membrane as a lamellipodium or filopodium. During extension of filopodia, membrane must move across the surface creating shear and flow. Intracellular biochemical processes driving extension must work against the membrane mechanical properties, but the forces required to extend growth cones have not been measured. In this paper, laser optical tweezers and a nanometer-level analysis system were used to measure the neuronal growth cone membrane mechanical properties through the extension of filopodia-like tethers with IgG-coated beads. Although the probability of a bead attaching to the membrane was constant irrespective of treatment; the probability of forming a tether with a constant force increased dramatically with cytochalasin B or D and dimethylsulfoxide (DMSO). These are treatments that alter the organization of the actin cytoskeleton. The force required to hold a tether at zero velocity (F0) was greater than forces generated by single molecular motors, kinesin and myosin; and F0 decreased with cytochalasin B or D and DMSO in correlation with the changes in the probability of tether formation. The force of the tether on the bead increased linearly with the velocity of tether elongation. From the dependency of tether force on velocity of tether formation, we calculated a parameter related to membrane viscosity, which decreased with cytochalasin B or D, ATP depletion, nocodazole, and DMSO. These results indicate that the actin cytoskeleton affects the membrane mechanical properties, including the force required for membrane extension and the viscoelastic behavior.