Free Volume in Membranes: Viscosity or Tension?

Many papers have used fluorescent probe diffusion to infer membrane viscosity but the measurement is actually an assay of the free volume of the membrane. The free volume is also related to the membrane tension. Thus, changes in probe mobility refer equally well to changes in membrane tension. In complicated structures like cell membranes, it appears more intuitive to consider variations in free volume as referring to the effect of domains structures and interactions with the cytoskeleton than changes in viscosity since tension is a state variable and viscosity is not.

[Mechanosensitivity of gramicidin A channels in semispherical bilayer membranes at constant tension].

Mechanoelectrical transduction in gramicidin A channels was studied in macroscopic planar lipid bilayer membranes bulged at constant tension. We found a supralinear increase in the single channel activity, which was proportional to the square of membrane radius but could not be accounted for by the increase in membrane surface area or by recruitment of new channels. When being extrapolated to biological membranes, these observations may suggest that the activity of permeability of ion channels can be influenced simply by changing the shape of the membrane, with or without stretching.

[New poly-(3-hydroxybutyrate)-based systems for controlled release of dipyridamole and indomethacin].

New poly-(3-hydroxybutyrate)-based systems for controlled release of anti-inflammatory and antithrombogenic drugs have been studied. The release occurs via two mechanisms (diffusion and degradation) operating simultaneously. Dipyridamole and indomethacin diffusion processes determine the rate of the release at the early stages of the contact of the system with the environment (the first 6-8 days). The coefficient of the release diffusion of a drug depends on its nature, the thickness of the poly-(3-hydroxybutyrate) films containing the drug, the concentrations of dipyridamole and indomethacin, and the molecular weight of the poly-(3-hydroxybutyrate). The results obtained are critical for developing systems of release of diverse drugs, thus, enabling the attainment of the requisite physiological effects on tissues and organs of humans.

Role of membrane curvature in mechanoelectrical transduction: ion carriers nonactin and valinomycin sense changes in integral bending energy.

We describe the phenomenon of mechanoelectrical transduction in macroscopic lipid bilayer membranes modified by two cation-selective ionophores, valinomycin and nonactin. We found that bulging these membranes, while maintaining the membrane tension constant, produced a marked supralinear increase in specific carrier-mediated conductance. Analyses of the mechanisms involved in mechanoelectrical transduction induced by the imposition of a hydrostatic pressure gradient or by an amphipathic compound chlorpromazine reveal similar changes in the charge carrier motility and carrier reaction rates at the interface(s). Furthermore, the relative change in membrane conductance was independent of membrane diameter, but was directly proportional to the square of membrane curvature, thus relating the observed phenomena to the bilayer bending energy. Extrapolated to biological membranes, these findings indicate that ion transport in cells can be influenced simply by changing shape of the membrane, without a change in membrane tension.

Thermodynamics of mechanosensitivity.

Mechanosensitivity of ion channels is conventionally interpreted as being driven by a change of their in-plane cross-sectional area A(msc). This, however, does not include any factors relating to membrane stiffness, thickness, spontaneous curvature or changes in channel shape, length or stiffness. Because the open probability of a channel is sensitive to all these factors, we constructed a general thermodynamic formalism. These equations provide the basis for the analysis of the behaviour of mechanosensitive channels in lipids of different geometric and chemical properties such as the hydrophobic mismatch at the boundary between the protein and lipid or the effects of changes in the bilayer intrinsic curvature caused by the adsorption of amphipaths. This model predicts that the midpoint gamma(1/2) and the slope(1/2) of the gating curve are generally not independent. Using this relationship, we have predicted the line tension at the channel/lipid border of MscL as approximately 10 pN, and found it to be much less than the line tension of aqueous pores in pure lipid membranes. The MscL channel appears quite well matched to its lipid environment. Using gramicidin as a model system, we have explained its observed conversion from stretch-activated to stretch-inactivated gating as a function of bilayer thickness and composition.

The invagination of excess surface area by shrinking neurons.

Over most of their surface, neurons are surrounded by a narrow extracellular gap across which they make adhesive cell-cell contacts. Thus constrained, how do they regulate their geometry when osmotically perturbed? Specifically, are there any interesting consequences of local osmosis in such conditions? Using confocal imaging of shrinking neurons in culture, we observe water exiting into the cell-substratum gap. This water efflux generates a hydrostatic pressure that, at discrete (low adhesion) sites, causes the neuron's excess plasma membrane to invaginate, thus compensating for shrinkage with a pseudo-intracellular volume. To identify the minimal requirements of the process, a compartment/flux model was constructed. It comprises, essentially, a large liposome adhering in a labyrinthine fashion to a substratum. The model predicts that invaginations form at the cell-substratum interface under the influence of local osmosis, provided that adhesion across the gap is neither too tight nor too loose. Local osmosis in the central nervous system, in contrast to epithelia, is usually considered a mishap, not a physiological opportunity. We postulate, however, that local osmotic forces acting in conjunction with confined extracellular spaces could be harnessed in service of surface area, shape, and volume regulation when intense neural activity alters a neuron's osmotic balance.

Modeling of the drug delivery from a hydrophilic transdermal therapeutic system across polymer membrane.

A mathematical simulation is presented which describes the in vitro drug delivery kinetics from hydrophilic adhesive water-soluble poly-N-vinylpyrrolidone (PVP)-polyethylene glycol (PEG) matrices of transdermal therapeutic systems (TTS) across skin-imitating hydrophobic Carbosil membranes. Propranolol is employed as the test drug. The contributions of the following physicochemical determinants to drug delivery rate control have been estimated: the drug diffusion coefficients both in the matrix and the membrane; the membrane-matrix drug partition coefficient: the drug concentration in the matrix and the membrane thickness. Drug transfer from the hydrophilic matrix across the membrane is shown to be controlled by the drug partitioning from the matrix into the membrane. The best correlation between simulation data and experimental results is obtained when the effect of membrane hydration is taken into consideration during in vitro drug release.

Kinetic control of guanine nucleotide binding to soluble Galpha(q).

Binding of guanine nucleotides to heterotrimeric G proteins is controlled primarily by kinetic factors, such as the release of bound GDP, rather than by affinity alone. Detergent-solubilized Galpha(q) displays unusual guanine nucleotide binding properties in comparison with other G protein alpha subunits. Under conditions where most G proteins bind nearly stoichiometric GTPgammaS in 5-30 min at micromolar nucleotide concentrations, GTPgammaS binding to Galpha(q) is slow (>1 hr to completion), markedly substoichiometric, and dependent upon high concentrations of nucleotide (0.1 to 0.2 mM). Although the latter two properties suggest low affinity, GTPgammaS dissociation is immeasurably slow under commonly used conditions. We found that purified Galpha(q) can bind stoichiometric GTPgammaS, but that binding is controlled kinetically by a combination of factors. GDP (or IDP) dissociated slowly from Galpha(q), but the dissociation rate increased linearly with the concentration of (NH4)2SO4 up to 0.75 M (approximately 20-fold acceleration). The resulting GDP-free Galpha(q) was labile to rapid and irreversible denaturation, however (rate constant > or = 1 min(-1) at 20 degrees). Denaturation competed kinetically with relatively slow GTPgammaS association, such that stoichiometric binding was only attained at 100 microM GTPgammaS. These findings reconcile the slowly reversible binding of GTPgammaS to Galpha(q) with the other behaviors that suggested lower affinity, and point out that events subsequent to GDP dissociation can markedly influence the rates and extents of guanine nucleotide binding to G protein alpha subunits. Understanding these interactions allowed the direct, accurate quantitation of active Galpha(q) by a simple GTPgammaS binding assay in the presence of (NH4)2SO4, and similarly can prevent underestimation of the concentrations of other G proteins.

Biomechanics of stretch-induced beading.

To account for the beading of myelinated fibers, and axons of unmyelinated nerve fibers as well of neurites of cultured dorsal root ganglia caused by mild stretching, a model is presented. In this model, membrane tension and hydrostatic pressure are the basic factors responsible for axonal constriction, which causes the movement of axonal fluid from the constricted regions into the adjoining axon, there giving rise to the beading expansions. Beading ranges from a mild undulation, with the smallest degree of stretch, to more globular expansions and narrow intervening constrictions as stretch is increased: the degree of constriction is physically limited by the compaction of the cytoskeleton within the axons. The model is a general one, encompassing the possibility that the membrane skeleton, composed mainly of spectrin and actin associated with the inner face of the axolemma, could be involved in bringing about the constrictions and beading.

Biophysical and functional consequences of receptor-mediated nerve fiber transformation.

Stimulation of the nervous system by substance P, a G protein-coupled receptor, and subsequent receptor internalization causes dendrites to change their shape from homogeneous cylinders to a heterogeneous string of swollen varicosities (beads) connected by thin segments. In this paper we have analyzed this phenomenon and propose quantitative mechanisms to explain this type of physical shape transformation. We developed a mathematical solution to describe the relationship between the initial radius of a cylindrical nerve fiber and the average radii of the subsequently created varicosities and connecting segments, as well as the periodicity of the varicosities along the nerve fiber. Theoretical predictions are in good agreement with our own and published experimental data from dorsal root ganglion neurons, spinal cord, and brain. Modeling the electrical properties of these beaded fibers has led to an understanding of the functional biophysical consequences of nerve fiber transformation. Several hypotheses for how this shape transformation can be used to process information within the nervous system have been put forth.

Electrical double layers at the oil/water interface.

This review presents the historical development and current status of the theory of the electrical double layer at a liquid/liquid interface. It gives rigorous thermodynamic definitions of all basic concepts related to liquid interfaces and to the electrical double layer. The difference between the surface of a solid electrode and the interface of two immiscible electrolyte solutions (ITIES) is analyzed in connection to their electrical properties. The most important classical relationships for the electrical double layer are presented and critically discussed. The generalized adsorption isotherm is derived. After a short review of the classical Gouy-Chapman and Verwey-Niessen models, more recent developments of the double layer theory are presented. These include effects of variable dielectric permittivity, nonlocal electrostatics, hydration forces, the modified Poisson-Boltzmann equation and the ion-dipole plasma. The relative merits of different theories are estimated by comparing them with computer simulation of the ITIES and electrical double layer. Special attention is given to the structure of ITIES and its variation due to adsorption of ions and amphiphilic molecules.

Membrane transport mechanisms probed by capacitance measurements with megahertz voltage clamp.

We have used capacitance measurements with a 1-microsecond voltage clamp technique to probe electrogenic ion-transporter interactions in giant excised membrane patches. The hydrophobic ion dipicrylamine was used to test model predictions for a simple charge-moving reaction. The voltage and frequency dependencies of the apparent dipicrylamine-induced capacitance, monitored by 1-mV sinusoidal perturbations, correspond to single charges moving across 76% of the membrane field at a rate of 9500 s-1 at 0 mV. For the cardiac Na,K pump, the combined presence of cytoplasmic ATP and sodium induces an increase of apparent membrane capacitance which requires the presence of extracellular sodium. The dependencies of capacitance changes on frequency, voltage, ATP, and sodium verify that phosphorylation enables a slow, 300- to 900-s-1, pump transition (the E1-E2 conformational change), which in turn enables fast, electrogenic, extracellular sodium binding reactions. For the GAT1 (gamma-aminobutyric acid,Na,Cl) cotransporter, expressed in Xenopus oocyte membrane, we find that chloride binding from the cytoplasmic side, and probably sodium binding from the extracellular side, results in a decrease of membrane capacitance monitored with 1- to 50-kHz perturbation frequencies. Evidently, ion binding by the GAT1 transporter suppresses an intrinsic fast charge movement which may originate from a mobility of charged residues of the transporter binding sites. The results demonstrate that fast capacitance measurements can provide new insight into electrogenic processes closely associated with ion binding by membrane transporters.

The secretory granule matrix-electrolyte interface: a homologue of the p-n rectifying junction.

When placed at the tip of a glass micropipette electrode the polymeric matrix of the secretory granule behaves like a diode. The measured current was 100-fold greater at negative potentials compared to positive potentials, and up to sixfold greater than that measured with the pipette alone. By manipulating the geometry of the electric field we show that these electrical properties result from focusing an electric field at the gel-electrolyte interface. We also show, by using pulsed-laser imaging with fluorescein as the ionic probe, that there is a rapid accumulation and depletion of ions at the gel-electrolyte interface. A voltage pulse of -9 V applied to the gel caused a severalfold increase in the fluorescence intensity within 5 ms. This correlated with an increase in the measured current (approximately 1 microA). In contrast, within 5 ms of applying +9 V we recorded a decrease in the fluorescence intensity, which paralleled the twofold decrease in the measured current. This is similar to a p-n junction where an applied voltage causes the accumulation and depletion of charge carriers. Using synthetic gels (diameter 3-6 microns) with different charge characteristics we observed no rectification of the current with neutral gels and confirmed that rectification and amplification of the current were dependent on the fixed charge within a gel. In addition, we modeled the conduction at the gel-electrolyte interface using the Nernst-Planck electrodiffusion equation and accurately fitted the experimental current-voltage relationships. This study provides some insight into how biological interfaces may function. For example, we suggest that neurotransmitter release during exocytosis could be regulated by voltage-induced accumulation and depletion of ions at the interface between the secretory granule and the fusion pore.

Modeling the active process of the cochlea: phase relations, amplification, and spontaneous oscillation.

The high sensitivity and sharp frequency selectivity of acoustical signal transduction in the cochlea suggest that an active process pumps energy into the basilar membrane's oscillations. This function is generally attributed to outer hair cells, but its exact mechanism remains uncertain. Several classical models of amplification represent the load upon the basilar membrane as a single mass. Such models encounter a fundamental difficulty, however: the phase difference between basilar-membrane movement and the force generated by outer hair cells inhibits, rather than amplifies, the modeled basilar-membrane oscillations. For this reason, modelers must introduce artificially either negative impedance or an appropriate phase shift, neither of which is justified by physical analysis of the system. We consider here a physical model based upon the recent demonstration that the basilar membrane and reticular lamina can move independently, albeit with elastic coupling through outer hair cells. The mechanical model comprises two resonant masses, representing the basilar membrane and the reticular lamina, coupled through an intermediate spring, the outer hair cells. The spring's set point changes in response to displacement of the reticular lamina, which causes deflection of the hair bundles, variation of outer hair cell length and, hence, force production. Depending upon the frequency of the acoustical input, the basilar membrane and reticular lamina can oscillate either in phase or in counterphase. In the latter instance, the force produced by hair cells leads basilar-membrane oscillation, energy is pumped into basilar-membrane movement, and an external input can be strongly amplified. The model is also capable of producing spontaneous oscillation. In agreement with experimental observations, the model describes mechanical relaxation of the basilar membrane after electrical stimulation causes outer hair cells to change their length.

The voltage-activated hydrogen ion conductance in rat alveolar epithelial cells is determined by the pH gradient.

Voltage-activated H+ currents were studied in rat alveolar epithelial cells using tight-seal whole-cell voltage clamp recording and highly buffered, EGTA-containing solutions. Under these conditions, the tail current reversal potential, Vrev, was close to the Nernst potential, EH, varying 52 mV/U pH over four delta pH units (delta pH = pHo - pHi). This result indicates that H+ channels are extremely selective, PH/PTMA > 10(7), and that both internal and external pH, pHi, and pHo, were well controlled. The H+ current amplitude was practically constant at any fixed delta pH, in spite of up to 100-fold symmetrical changes in H+ concentration. Thus, the rate-limiting step in H+ permeation is pH independent, must be localized to the channel (entry, permeation, or exit), and is not bulk diffusion limitation. The instantaneous current-voltage relationship exhibited distinct outward rectification at symmetrical pH, suggesting asymmetry in the permeation pathway. Sigmoid activation kinetics and biexponential decay of tail currents near threshold potentials indicate that H+ channels pass through at least two closed states before opening. The steady state H+ conductance, gH, as well as activation and deactivation kinetic parameters were all shifted along the voltage axis by approximately 40 mV/U pH by changes in pHi or pHo, with the exception of the fast component of tail currents which was shifted less if at all. The threshold potential at which H+ currents were detectably activated can be described empirically as approximately 20-40(pHo-pHi) mV. If internal and external protons regulate the voltage dependence of gH gating at separate sites, then they must be equally effective. A simpler interpretation is that gating is controlled by the pH gradient, delta pH. We propose a simple general model to account for the observed delta pH dependence. Protonation at an externally accessible site stabilizes the closed channel conformation. Deprotonation of this site permits a conformational change resulting in the appearance of a protonation site, possibly the same one, which is accessible via the internal solution. Protonation of the internal site stabilizes the open conformation of the channel. In summary, within the physiological range of pH, the voltage dependence of H+ channel gating depends on delta pH and not on the absolute pH.

Gating-spring models of mechanoelectrical transduction by hair cells of the internal ear.

A sensory receptor of the internal ear, or hair cell, responds to sound or acceleration when this mechanical stimulus deflects the cell's mechanosensitive organelle, or hair bundle. The gating-spring model posits that mechanoelectrical transduction occurs as mechanical force is transmitted through an elastic element, or gating spring, to the molecular gate of each transduction channel; increased tension in the gating spring then promotes the channel's transition from a closed to an open state. Electrophysiological and micromechanical data from a variety of hair cells, both in vivo and in vitro, confirm that the stimulus dependence of channel open probability and bundle stiffness are quantitatively consistent with the model. The results accord still better, however, with an extended formulation including channel transitions among one open and two closed states. In addition to providing a derivation of this three-state model, this review delineates several experimentally testable predictions of gating-spring models.

Two different rigor complexes of myosin subfragment 1 and actin.

Our previous titration and cross-linking experiments showed that myosin subfragment 1 (S1) can bind to one or two monomers in F-actin [Andreev, O. A., & Borejdo, J. (1991) Biochem. Biophys. Res. Commun. 177, 350-356; (1992a) J. Muscle Res. Cell Motil. 13, 523-533; (1992b) Biochem. Biophys. Res. Commun. 188, 94-101]. In the present work we used a sedimentation method to extend these studies to equilibrium binding and a stopped flow method to investigate its kinetics. Both equilibrium and kinetic data indicated the existence of two different rigor complexes. On the basis of these data we developed a model which suggested that binding of S1 to F-actin occurred in two steps: (i) initial rapid binding to one monomer of F-actin, A + M<==>A.M and (ii) a consequent slow binding to a neighboring monomer, A.M + A<==>A.M.A, where A stands for actin and M for myosin subfragment 1. The second reaction can proceed only if the neighboring actin site is unoccupied. The model fit the equilibrium and kinetic binding data with equilibrium constants K1 = 6 x 10(6) M-1 and K2 = 4 and kinetic constants k+1 = 10.5 x 10(6) M-1 s-1, k-1 = 1.75 s-1, k+2 = 0.8 s-1, and k-2 = 0.2 s-1, where the subscripts refer to the reactions i and ii. These results corroborate our hypothesis that myosin head can make two types of complexes with F-actin and support our speculation that during a power stroke in contracting muscle a myosin head may first bind to one and then to two actins.

Auditory illusions and the single hair cell.

Like our other senses, the auditory system can produce illusions. Prominent among these are distortion products: when listening to two tones, one of frequency f1 and the second of a higher frequency f2, an individual may hear not only these primary tones, but also a difference tone of frequency f2 - f1, a sum tone of frequency f2 + f1, and combination tones of frequencies such as 2f1 - f2 and 2f2 - f1. Discovered by Tartini early in the eighteenth century, these illusory sounds are sufficiently conspicuous that they were employed to carry melodies in classical compositions. Distortion products originate within the cochlea, where they manifest themselves in the basilar membrane's vibration. Here we demonstrate distortion products in individual hair cells of the bullfrog's sacculus, where they emerge from a nonlinearity inherent in the mechanoelectrical transduction process. In addition to offering an explanation for cochlear distortion products, our results suggest that the mechanical properties of hair bundles significantly influence the basilar membrane's motion.