Dynamics of membrane exchange of the plasma membrane and the lysis of isolated protoplasts during rapid expansions in area

Summary The plasma membrane of protoplasts isolated from rye leaves (Secale cereale L. cv. Puma) can withstand a maximum elastic stretching of about 2%. Larger area expansions involve the incorporation of new material into the membrane. The dynamics of this process during expansion from isotonic solutions and the probable frequency of lysis have been measured as a function of membrane tension in populations of protoplasts isolated from both cold-acclimated and nonacclimated plants. To a first approximation, both increase exponentially with tension. An analytical solution is reported for the membrane tension as a function of time during an arbitrary expansion in area.     

Physical Properties of Escherichia coli Spheroplast Membranes

We investigated the physical properties of bacterial cytoplasmic membranes by applying the method of micropipette aspiration to Escherichia coli spheroplasts. We found that the properties of spheroplast membranes are significantly different from that of laboratory-prepared lipid vesicles or that of previously investigated animal cells. The spheroplasts can adjust their internal osmolality by increasing their volumes more than three times upon osmotic downshift. Until the spheroplasts are swollen to their volume limit, their membranes are tensionless. At constant external osmolality, aspiration increases the surface area of the membrane and creates tension. What distinguishes spheroplast membranes from lipid bilayers is that the area change of a spheroplast membrane by tension is a relaxation process. No such time dependence is observed in lipid bilayers. The equilibrium tension-area relation is reversible. The apparent area stretching moduli are several times smaller than that of stretching a lipid bilayer. We conclude that spheroplasts maintain a minimum surface area without tension by a membrane reservoir that removes the excessive membranes from the minimum surface area. Volume expansion eventually exhausts the membrane reservoir; then the membrane behaves like a lipid bilayer with a comparable stretching modulus. Interestingly, the membranes cease to refold when spheroplasts lost viability, implying that the membrane reservoir is metabolically maintained.     

Correction

We investigated the physical properties of bacterial cytoplasmic membranes by applying the method of micropipette aspiration to Escherichia coli spheroplasts. We found that the properties of spheroplast membranes are significantly different from that of laboratory-prepared lipid vesicles or that of previously investigated animal cells. The spheroplasts can adjust their internal osmolality by increasing their volumes more than three times upon osmotic downshift. Until the spheroplasts are swollen to their volume limit, their membranes are tensionless. At constant external osmolality, aspiration increases the surface area of the membrane and creates tension. What distinguishes spheroplast membranes from lipid bilayers is that the area change of a spheroplast membrane by tension is a relaxation process. No such time dependence is observed in lipid bilayers. The equilibrium tension-area relation is reversible. The apparent area stretching moduli are several times smaller than that of stretching a lipid bilayer. We conclude that spheroplasts maintain a minimum surface area without tension by a membrane reservoir that removes the excessive membranes from the minimum surface area. Volume expansion eventually exhausts the membrane reservoir; then the membrane behaves like a lipid bilayer with a comparable stretching modulus. Interestingly, the membranes cease to refold when spheroplasts lost viability, implying that the membrane reservoir is metabolically maintained.     

TENSION AT THE HIGHLY STRETCHED SURFACE OF SEA-URCHIN EGGS*

Unfertilized eggs of the sea urchin, Paracentrotus lividus, were placed between two parallel plates and flattened by a definite force to 20% of their original diameter, with two-fold increase in their surface area. The resulting tension at their surface was calculated from the relation of force and deformation. In spite of this extensive stretching, the tension was found to be not more than 0.2 dyne/cm, while under conditions involving mild stretching (3%) the tension still amounted to 0.12 dyne/cm. These results do not support Mela's theory (7, 8), which predicts a transition of the mechanical properties of the egg surface from a ‘subelastic’ to ‘elastic’ state when the surface is stretched to beyond 34% of its initial area.     

Mechanical stresses in erythrocyte membranes (theoretical models)

The type of mechanical stresses that arise in erythrocyte membranes on exposure to catecholamines and steroid hormones is considered. Tensors of mechanical stresses and displacements were obtained for a membrane interacting with hormones. A possible mechanism of membrane rupture under mechanical stresses is discussed. Catecholamines and androgens increase the microviscosity of membranes, and alternating kink and stretching sites occur in the lipid membrane bilayer to produce a checker-wise pattern. The membrane becomes thinner in a stretching site (smectic A → smectic C transition). When tensile stresses increase further and exceed a certain critical value the membrane may rupture. It is possible that a gel phase L_β? → liquid crystalline phase L_α transition takes place in the stretching site of the lipid bilayer prior to disruption. The density of the lipid bilayer decreases in the process, pores form, and then cracks occur.     

Tension decrease during skin stretching in undermined versus not undermined skin: an experimental study in piglets

In a controlled study using 15 piglets, the efficacy of skin stretching using a skin stretching device was tested by quantifying the tension decrease during skin stretching in undermined and not undermined wounds. The viability of the skin margins was examined in both situations. Thirty standardized wounds was created: around 15 wounds on one flank, the surrounding skin was undermined; whereas around the 15 wounds on the opposite flank, the surrounding skin was not undermined. The force required to close the 9 x 9 cm defect was measured at the beginning, after undermining, and after 30 minutes of skin stretching. Also examined was the wound healing after 1 day and 1 week. A tension decrease of 3.02 N (13.6 percent reduction of the total force that is required to close the wound at the beginning) was seen due to undermining the surrounding skin. Skin stretching for 30 minutes without undermining the skin showed a tension decrease of 6.10 N (26.5 percent). Therefore, the tension decrease due to skin stretching was twice as high in comparison with undermining the skin margins alone. This has been statistically proven to be significant (-d (difference) = 3.08, 95 percent confidence interval = 2.16; 4.00, p < 0.001). When the undermined skin of the wound was stretched for 30 minutes, we measured a total tension decrease of 7.60 N (34.1 percent). There was a statistically significant but small difference in total tension decrease as a result of undermining combined with skin stretching in comparison with skin stretching without undermining (-d = 1.51, 95 percent confidence interval = 0.77; 2.23, p < 0.001). Undermining the surrounding skin involved cutting musculocutaneous perforating vessels. Looking at the viability of the skin, seven wounds, all found in the undermined group, showed skin necrosis after 1 week. Excessive seroma formation was seen in all wounds around which the skin was undermined. In the not undermined wounds, there were no problems in wound healing. In conclusion, skin stretching for only 30 minutes using a skin stretching device significantly reduces wound closing tension. The additional advantage of skin stretching over that of undermining alone is clearly shown. Undermining the wound margins before skin stretching gives a small additional tension decrease but has well-known complications, such as skin-edge necrosis and seroma formation.     

Do Cell Membranes Flow Like Honey or Jiggle Like Jello?

Cell membranes experience frequent stretching and poking: from cytoskeletal elements, from osmotic imbalances, from fusion and budding of vesicles, and from forces from the outside. Are the ensuing changes in membrane tension localized near the site of perturbation, or do these changes propagate rapidly through the membrane to distant parts of the cell, perhaps as a mechanical mechanism of long-range signaling? Literature statements on the timescale for membrane tension to equilibrate across a cell vary by a factor of ≈10⁶. This study reviews and discusses how apparently contradictory findings on tension propagation in cells can be evaluated in the context of 2D hydrodynamics and poroelasticity. Localization of tension in the cell membrane is likely critical in governing how membrane forces gate ion channels, set the subcellular distribution of vesicle fusion, and regulate the dynamics of cytoskeletal growth. Furthermore, in this study, it is proposed that cells can actively regulate the degree to which membrane tension propagates by modulating the density and arrangement of immobile transmembrane proteins. Also see the video abstract here https://youtu.be/T6K7AIAqqBs .     

Lipid phase transitions in fatty acid-homogeneous membranes of Acholeplasma laidlawii B

The thermotropic behaviour of fatty acid-homogeneous membranes of Acholeplasma laidlawii B was investigated by Fourier transform infrared spectroscopy. The organism was grown at 37°C in the presence of avidin, an inhibitor of fatty acid synthesis, in a medium supplemented with pentadecanoic acid-d₂₉; the enrichment of the membranes with this fatty acid was 95%. The temperature-dependent phase behaviour of the membranes was studied via the C–D stretching vibrational modes of the membrane lipids and was compared with that of the lipid extract. The high level of fatty acid homogeneity results in a sharp (for natural membranes) gel to liquid crystalline phase transition. The transition, in both the membranes and extracted lipids, is centered at about 6°C above the growth temperature. During the transition two principal liquid states are evident, one being more conformationally ordered than the other. The effect of proteins on the principal lipid phase transition is minimal. However, in the intact membranes there is evident a weaker, lower temperature transition, which is not evident in the extracted lipids.     

Excitation-contraction coupling in a barnacle muscle fiber as examined with voltage clamp technique

Relations between the membrane potential and the tension associated with changes in membrane potential were analyzed in barnacle giant muscle fibers by using voltage clamp techniques. With a step change in membrane potential the tension reaches its final level with a time course which is expressed by the difference of two exponential functions. The time constants τ₁ (0.2–0.4 sec at 23°C) and τ₂ (0.07–0.12 sec at 23°C) are independent of the new membrane potential at least for a relatively small membrane potential change while the final level of tension is a function of the potential. Decreasing the temperature increases both τ₁ and τ₂ (Q₁₀ = -2 to -3) and the increase of the tonicity of the external medium increases τ₁ but not τ₂. The final level of tension is related by an S-shaped curve to the membrane potential. The slope of the final tension-membrane potential curve increases with increasing external Ca concentration and is reduced when a small amount of transition metal ions is added to the medium. This suggests that the influx of Ca ions through the membrane is an important factor in the development of tension.     

Line tension and structure of raft boundary calculated from bending,tilt, and lateral compression/stretching

Bilayer thickness in membrane domains enriched with sphingomielin and cholesterol (known as “rafts”) is bigger than thickness of neighboring membrane. Monolayers need to deform to compensate the thicknesses difference in the vicinity of the raft boundary. Line tension of the boundary of rafts associated with elastic deformations originating from the compensation of the thickness mismatch is calculated in the frame-work of the elasticity theory. In the calculations deformations of splay, tilt and lateral stretching/compression are considered. It is assumed that raft consists of two monolayer domains situated in the different membrane monolayers; it is also assumed that the boundaries of domains can shift in the lateral direction with respect to relative to each other. Dependence of the boundary energy of raft on the value of the relative shift of the boundaries is calculated. It is shown that the boundary energy is minimal when shift is equal to 4.5 nm. Dependence of the optimal shift on the mismatch of the monolayer thicknesses of raft and surrounding membrane as well as membrane shape in the vicinity of boundary are calculated. The calculated values of line tension are in a good agreement with available experimental data. Taking into account deformation of stretching/compression increases the accuracy of calculations by 30%; this exceeds the uncertainty of the line tension measurements by modern techniques.     

Membrane Stretching Triggers Mechanosensitive Ca<Superscript>2+</Superscript> Channel Activation in <Emphasis Type="Italic">Chara</Emphasis>

In order to confirm that mechanosensitive Ca²⁺ channels are activated by membrane stretching, we stretched or compressed the plasma membrane of Chara by applying osmotic shrinkage or swelling of the cell by varying the osmotic potential of the bathing medium. Aequorin studies revealed that treatments causing membrane stretching induced a transient but large increase in cytoplasmic concentration of Ca²⁺ (Δ[Ca²⁺]_c). However, the observed Δ[Ca²⁺]_c decreased during the treatments, resulting in membrane compression. A second experiment was carried out to study the relationship between changes in membrane potential (ΔE _m) and stretching or compression of the plasma membrane. Significant ΔE _m values, often accompanied by an action potential, were observed during the initial exchange of the bathing medium from a hypotonic medium to a hypertonic one (plasmolysis). ΔE _m appears to be triggered by a partial stretching of the membrane as it was peeled from the cell wall. After plasmolysis, other exchanges from hypertonic to hypotonic media, with their accompanying membrane stretching, always induced large ΔE _m values and were often accompanied by an action potential. By contrast, action potentials were scarcely observed during other exchanges from hypotonic to hypertonic solutions (=membrane compression). Thus, we concluded that activation of the mechanosensitive channels is triggered by membrane stretching in Chara.     

An investigation of electrical breakdown of bimolecular lipid membranes

The investigation is concerned with the irreversible electrical breakdown of bimolecular lipid membranes, depending on the velocity of linear voltage scanning. It was found that the membrane breakdown potential depended on the velocity of electric field variation. For instance, at voltage scanning velocities of up to 0.1 V/s, the rupture of membrane from glycerol monooleate occurs at 0.20–0.25 V and, at velocities higher than 1 V/s, at 0.5–0.6 V. Then the film breakdown depending on lipid phase transition was studied. At high velocities of imposed voltage scanning, the disruption of the bimolecular lipid membranes was shown not to depend on their phase states; at the same time, at low velocities, one could note a slight difference in the stability of the films at temperatures higher and lower than those of the phase transition. Whereas transition from gel to liquid-crystalline state involves transition from an ordered to a less ordered membrane structure with a sharp increase in the number of defects in the membrane, the authors, conclude that the film breakdown in the second case occurs by the ‘defect’ mechanism suggested earlier. It was also assumed that, in certain cases involving low velocities of voltage scanning, membrane breakdown may occur because of variation in the interfacial tension and in the contact angle between the film and torus. Possible mechanisms of the membrane irreversible electrical breakdown at high velocities of voltage variation are discussed. It was shown that breakdown should occur as a result of membrane compression in an electric field by a mechanism previously examined. The elastic moduli of a number of membranes were calculated by the breakdown criterion suggested earlier. They were found to coincide with the results of other investigators and, depending on the type of lipid, to equal 10⁵–10⁶ Pa.     

The excitable fluid mosaic

The Fluid Mosaic Model by Singer & Nicolson proposes that biological membranes consist of a fluid lipid layer into which integral proteins are embedded. The lipid membrane acts as a two-dimensional liquid in which the proteins can diffuse and interact. Until today, this view seems very reasonable and is the predominant picture in the literature. However, there exist broad melting transitions in biomembranes some 10–20 degrees below physiological temperatures that reach up to body temperature. Since they are found below body temperature, Singer & Nicolson did not pay any further attention to the melting process. But this is a valid view only as long as nothing happens. The transition temperature can be influenced by membrane tension, pH, ionic strength and other variables. Therefore, it is not generally correct that the physiological temperature is above this transition. The control over the membrane state by changing the intensive variables renders the membrane as a whole excitable. One expects phase behavior and domain formation that leads to protein sorting and changes in membrane function. Thus, the lipids become an active ingredient of the biological membrane. The melting transition affects the elastic constants of the membrane. This allows for the generation of propagating pulses in nerves and the formation of ion-channel-like pores in the lipid membranes. Here we show that on top of the fluid mosaic concept there exists a wealth of excitable phenomena that go beyond the original picture of Singer & Nicolson.¹     

Effect of stress on the membrane capacitance of the auditory outer hair cell.

The membrane capacitance of the outer hair cell, which has unique membrane potential-dependent motility, was monitored during application of membrane tension. It was found that the membrane capacitance of the cell decreased when stress was applied to the membrane. This result is the opposite of stretching the lipid bilayer in the plasma membrane. It thus indicates the importance of some other capacitance component that decreases on stretching. It has been known that charge movement across the membrane can appear to be a nonlinear capacitance. If membrane stress at the resting potential restricts the movement of the charge associated with force generation, the nonlinear capacitance will decrease. Furthermore, less capacitance reduction by membrane stretching is expected when the membrane is already extended by the (hyperpolarizing) membrane potential. Indeed, it was found that at hyperpolarized potentials, the reduction of the membrane capacitance due to stretching is less. The capacitance change can be described by a two state model of a force-producing unit in which the free energy difference between the contracted and stretched states has both electrical and mechanical components. From the measured change in capacitance, the estimated difference in the membrane area of the unit between the two states is about 2 nm2.     

Lateral tensions and pressures in membranes and lipid monolayers

The effects of lateral tension on the properties of membranes are often explained in comparison with analogous experiments on monolayers, which yield more detailed data. To calculate the effects of changes in tension on the composition of, or incorporation of amphiphiles into membranes we examine (i) the fidelity of the monolayer analogy, (ii) the range of possible tensions in a membrane, and the way in which tensions arise and (iii) the equilibrium partitioning of amphiphiles between aqueous solution and a bilayer under tension. We argue that, at the same areas per molecule, a monolayer at an $\text{n-}\text{alkane}\text{/}\text{water}$ interface is a closer analogy of the lipid bilayer than a monolayer at an air/water interface. Next, we show from a thermodynamic argument that changes in membrane tension can affect the absorption of very large amphiphiles such as proteins, but that physiological tensions are unlikely to affect the absorption of lipids or drugs. Finally we consider the possibility that the measured bulk tension in a complicated membrane such as that of the erythrocyte may be larger than the local tension in the fluid mosaic portions, and suggest a model which explains the ability of the erythrocyte membrane to withstand much higher tensions than other biological membranes and lipid bilayers.     

Interaction of the cholesterol reducing agent simvastatin with zwitterionic DPPC and charged DPPG phospholipid membranes

Simvastatin is a lipid-lowering drug in the pharmaceutical group statins. Interaction of a drug with lipids may define its role in the system and be critical for its pharmacological activity. We examined the interactions of simvastatin with zwitterionic dipalmitoyl phosphatidylcholine (DPPC) and anionic dipalmitoyl phosphatidylglycerol (DPPG) multilamellar vesicles (MLVs) as a function of temperature at different simvastatin concentrations using Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC). The FTIR results indicate that the effect of simvastatin on membrane structure and dynamics depends on the type of membrane lipids. In anionic DPPG MLVs, high simvastatin concentrations (12, 18, 24 mol%) change the position of the CH₂ antisymmetric stretching mode to lower wavenumber values, implying an ordering effect. However, in zwitterionic DPPC MLVs, high concentrations of simvastatin disorder systems both in the gel and liquid crystalline phases. Moreover, in DPPG and DPPC MLVs, simvastatin has opposite dual effects on membrane dynamics. The bandwidth of the CH₂ antisymmetric stretching modes increases in DPPG MLVs, implying an increase in the dynamics, whereas it decreases in DPPC MLVs. Simvastatin caused broadening of the phase transition peaks and formation of shoulders on the phase transition peaks in DSC curves, indicating multi-domain formations in the phospholipid membranes. Because physical features of membranes such as lipid order and fluidity may be changed with the bioactivity of drugs, opposing effects of simvastatin on the order and dynamics of neutral and charged phospholipids may be critical to deduce the action mechanism of the drug and estimate drug-membrane interactions.     

Getting in shape and swimming: the role of cortical forces and membrane heterogeneity in eukaryotic cells

Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves—crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highly-simplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes. Such gradients can lead to a number of different characteristic cell shapes, and our first objective is to understand how different distributions of membrane tension influence the shape of cells in an inviscid quiescent fluid. We then analyze the effects of spatial variation in other membrane properties, and how they interact with tension gradients to determine the shape. We also study the effect of fluid–cell interactions and show how tension leads to cell movement, how the balance between tension gradients and a variable bending modulus determine the shape and direction of movement, and how the efficiency of movement depends on the properties of the fluid and the distribution of tension and bending modulus in the membrane.

     

Mechanosensitive Closed-Closed Transitions in Large Membrane Proteins: Osmoprotection and Tension Damping

Multiconformation membrane proteins are mechanosensitive (MS) if their conformations displace different bilayer areas. Might MS closed-closed transitions serve as tension buffers, that is, as membrane “spandex”? While bilayer expansion is effectively instantaneous, transitions of bilayer-embedded MS proteins are stochastic (thermally activated) so spandex kinetics would be critical. Here we model generic two-state (contracted/expanded) stochastic spandexes inspired by known bacterial osmovalves (MscL, MscS) then suggest experimental approaches to test for spandex-like behaviors in these proteins. Modeling shows: 1), spandex kinetics depend on the transition state location along an area reaction coordinate; 2), increasing membrane concentration of a spandex right-shifts its midpoint (= tension-Boltzmann); 3), spandexes with midpoints below the activating tension of an osmovalve could optimize osmovalve deployment (required: large midpoint, barrier near the expanded state); 4), spandexes could damp bilayer tension excursions (required: midpoint at target tension, and for speed, barrier halfway between the contracted and expanded states; the larger the spandex Δ-area, the more precise the maintenance of target tension; higher spandex concentrations damp larger amplitude strain fluctuations). One spandex species could not excel as both first line of defense for osmovalve partners and tension damper. Possible interactions among MS closed-closed and closed-open transitions are discussed for MscS- and MscL-like proteins.     

Gating of the mechanosensitive channel protein MscL: the interplay of membrane and protein

The mechanosensitive channel of large conductance (MscL) belongs to a family of transmembrane channel proteins in bacteria and functions as a safety valve that relieves the turgor pressure produced by osmotic downshock. MscL gating can be triggered solely by stretching of the membrane. This work reports an effort to understand this mechanotransduction by means of molecular dynamics (MD) simulation on the MscL of mycobacterium tuberculosis embedded in a palmitoyloleoylphosphatidylethanolamine membrane. Equilibrium MD under zero membrane tension produced a more compact protein structure, as measured by its radii of gyration, compared to the crystal structure, in agreement with previous experimental findings. Even under a large applied tension up to 1000 dyn/cm, the MscL lateral dimension largely remained unchanged after up to 20 ns of simulation. A nonequilibrium MD simulation of 3% membrane expansion showed a significant increase in membrane rigidity upon MscL inclusion, which can contribute to efficient mechanotransduction. Direct observation of channel opening was possible only when an explicit lateral bias force was applied to each of the five subunits of MscL in the radially outward direction. Using this force, open structures with a large pore of radius 10 Å could be obtained. The channel opening takes place in a stepwise manner and concurrently with the water chain formation across the channel, which occurs without direct involvement of protein hydrophilic residues. The N-terminal S1 helices stabilize the open structure, and the membrane asymmetry (different lipid density on the two leaflets of membrane) promotes channel opening.     

The sliding filament model of muscle contraction. II. The energetic and dynamical predictions of a quantum mechanical transducer model

A theoretical model of a molecular energy transducing unit designed for the production of mechanical work is constructed and its consequences examined and compared with the experimentally determined myothermal and dynamic properties of vertebrate striated muscle. The model rests on a number of independent assumptions which include: the almost instantaneous generation of mechanical force by the occurrence of a radiationless transition between vibronic states of the transducer (crossbridge) at a point of potential energy surface crossing; transmission of this force to the load via the active sites on the thin filament by means of non-bonding repulsive forces, no energy being required for detachment; “detachment” consists of a second radiationless transition at a lower energy point than the first force generating transition, the energy difference appearing largely as work. The method of force generation completely avoids problems such as the “force-rate dilemma” which occur repeatedly in any discussion where state populations are near-Boltzmann and also leads without further arbitrary assumptions to such concepts as “attached but non force-producing states” and strongly position dependent “attachment” and “detachment” rate constants since these can only be appreciable near potential energy surface crossings. The kinetics and energetics of a transducer of this type operating cyclically and converting ATP → ADP + P_i are considered and shown to lead to length-tension and energetic behaviour very similar to that exhibited by vertebrate striated muscle, both for contraction and stretching. The existence of a limiting tension for stretching is predicted by the model as is the decrease of the rate of enthalpy release rate below the isometric value. At the limiting tension the rate of enthalpy release by the transducers is virtually zero, as observed. However, the stretching only inhibits the ATP hydrolysis, the cyclic synthesis from ADP and work being impossible with this model. The response to rapid length step changes automatically contains the asymmetry observed experimentally (with respect to lengthening and shortening) and arbitrary assumptions over and above those giving adequate explanation of the steady-state properties are not required. The asymmetry arises mainly as a consequence of the non-bonded pushing action of the crossbridges. This same assumption predicts the occurrence of an asymmetric thermoelastic ratio for active muscle with respect to stretching and contraction. The quantitative aspects of the model are satisfactory as it simultaneously reconciles the numerical magnitudes of macroscopic quantities such as isometric tension, maximum contraction velocity, limiting tension sustainable on stretching, isometric heat rate and resting heat rate with molecular parameters such as the filament and crossbridge periodicities, molecular vibrational relaxation rates, recurrence times for the radiationless transitions occurring, etc. This is achieved without any parameter optimization and only a very much smaller number of unknown parameters than the number of observed results accounted for. Many of the entities occurring in the model cycle (vibronic states of crossbridges, ATP, etc.) appear to be in one-to-one correspondence with many of the kinetic entities postulated to account for the biochemical kinetic results obtained for the actomyosin ATPase system in vitro. Finally, the rigor state has to be viewed in a different way from the conventional one; on the basis that the present model states which are part of the contraction cycle but sparsely populated during the latter (and hence are of chemical kinetic but not dynamical importance) are heavily populated during the rigor state. The mechanical properties of the rigor state would then be determined by these molecular states which would be very short-lived during the contraction cycle. If this is correct the rigor state could yield much more information about inaccessible parts of the contraction cycle than is presently supposed. The model leads one to expect a rather different response to quick length step changes in the rigor state from that of the active state, in contrast to current interpretations in terms of a large number of attached crossbridges, unable to detach due to the absence of ATP.