Evaluation of the sliding distance in shortening muscles and in polymerizing actin from Hill's force-velocity equation

The relationship derived earlier between the sliding distance, Deltal(m), and a/P(0), the characteristic parameter of Hill's force-velocity equation for muscle contraction, was re-formulated in order to get a more general relationship which can be applied also to other biological mechano-chemical energy converters: alpha x Deltal(m)=phi (0)(a/P(0))Deltal(m)=-Deltag where Deltag is the free energy change accompanying the hydrolysis of one ATP molecule while alpha and phi (0) are, respectively, the average forces developed by a myosin head-actin complex which are responsible for shortening and for isometric tension generation. These two molecular forces are different in magnitude and in nature and it is demonstrated that alpha , not phi (0), is the true contractile force. The values of alpha and of phi (0) have been calculated for three muscles. The equation has been successfully applied to actin polymerization-based motility. The value of Deltag in different muscles under different environmental conditions can be easily determined from this equation with the value of Deltal(m) derived experimentally.     

Two rigor states in skinned crayfish single muscle fibers

We studied the tension and stiffness of crayfish skinned single muscle fibers during and after the induction of rigor by removal of MgATP (substrate). We found that the rigor state is not unique but depends on the condition of the muscle before rigor. Fibers induced into rigor with a minimum of activation (low rigor) develop a small tension and moderate stiffness, while those entering rigor during maximum activation (high rigor) maintain near peak tension (80%) and develop a high stiffness. These rigor states are insensitive to Ca addition or deletion but they are partially interconvertible by length change. Stiffness changes when the rigor muscle length is varied, a condition in which the number of attached cross-rigor muscle length is varied, a condition in which the number of attached cross-bridges cannot change, and high-rigor muscle becomes less stiff than low-rigor muscle when the former is brought to the same tension by length release. The sensitivity of low, high, or length-released high-rigor muscles to trace substrate concentration (less than muM) differs, and rigor at lower strain is more suscepitible to substrate.     

Mutual contact of murine erythroleukemia cells activates depolarizing cation channels, whereas contact with extracellular substrata activates hyperpolarizing Ca2+-dependent K+ channels

This study deals with the modulation of the plasma membrane potential (delta psi p) of murine erythroleukemia (MEL) cells by cell-substratum or cell-cell contact. delta psi p was determined by measuring the distribution of tetraphenylphosphonium (TPP+) across the plasma membrane; it appeared strongly, and inversely, influenced by the two types of cell contacts. Contact with the culture surface produced a delta psi p hyperpolarization directly proportional to average distance among the ideal centers of the cells on this surface (d) within the range 10-80 microns. A detailed mathematical analysis of the function delta psi p = f(d) is presented, as well as experiments involving the use of ionophores (valinomycin and A23187) and the conditioning of the culture surface. We concluded that the d-dependent hyperpolarization (dDH) was the result of a complex interplay between the activating properties of substratum on Ca2+-dependent K+ channels (KCa) and some substratum-adherent factors that are shed by MEL cells and antagonize KCa activation (substratum-attached cellular factors = SACF). By contrast, contact of the cells with each other, obtained by incubating MEL cells at d smaller than the average cell diameter (phi = 10 microns), produced a marked delta psi p depolarization. This intercellular contact-dependent depolarization (ICDD) was unaffected by valinomycin; it was abolished by substituting Na+ in the external medium with a nondiffusible cation (choline), which shows that ICDD was sustained by Na+ influxes, probably mediated by stretch-activated (s.a.) cation channels.     

Hydrostatic compression in glycerinated rabbit muscle fibers.

Glycerinated muscle fibers isolated from rabbit psoas muscle, and a number of other nonmuscle elastic fibers including glass, rubber, and collagen, were exposed to hydrostatic pressures of up to 10 MPa (100 Atm) to determine the pressure sensitivity of their isometric tension. The isometric tension of muscle fibers in the relaxed state (passive tension) was insensitive to increased pressure, whereas the muscle fiber tension in rigor state increased linearly with pressure. The tension of all other fiber types (except rubber) also increased with pressure; the rubber tension was pressure insensitive. The pressure sensitivity of rigor tension was 2.3 kN/m2/MPa and, in comparison with force/extension relation determined at atmospheric pressure, the hydrostatic compression in rigor muscle fibers was estimated to be 0.03% Lo/MPa. As reported previously, the active muscle fiber tension is depressed by increased pressure. The possible underlying basis of the different pressure-dependent tension behavior in relaxed, rigor, and active muscle is discussed.     

Depolarization of In Situ Mitochondria Due to Hydrogen Peroxide-Induced Oxidative Stress in Nerve Terminals

Mitochondrial membrane potential (delta psi(m)) was determined in intact isolated nerve terminals using the membrane potential-sensitive probe JC-1. Oxidative stress induced by H2O2 (0.1-1 mM) caused only a minor decrease in delta psi(m). When complex I of the respiratory chain was inhibited by rotenone (2 microM), delta psi(m) was unaltered, but on subsequent addition of H2O2, delta psi(m) started to decrease and collapsed during incubation with 0.5 mM H2O2 for 12 min. The ATP level and [ATP]/[ADP] ratio were greatly reduced in the simultaneous presence of rotenone and H2O2. H2O2 also induced a marked reduction in delta psi(m) when added after oligomycin (10 microM), an inhibitor of F0F1-ATPase. H2O2 (0.1 or 0.5 mM) inhibited alpha-ketoglutarate dehydrogenase and decreased the steady-state NAD(P)H level in nerve terminals. It is concluded that there are at least two factors that determine delta psi(m) in the presence of H2O2: (a) The NADH level reduced owing to inhibition of alpha-ketoglutarate dehydrogenase is insufficient to ensure an optimal rate of respiration, which is reflected in a fall of delta psi(m) when the F0F1-ATPase is not functional. (b) The greatly reduced ATP level in the presence of rotenone and H2O2 prevents maintenance of delta psi(m) by F0F1-ATPase. The results indicate that to maintain delta psi(m) in the nerve terminal during H2O2-induced oxidative stress, both complex I and F0F1-ATPase must be functional. Collapse of delta psi(m) could be a critical event in neuronal injury in ischemia or Parkinson's disease when H2O2 is generated in excess and complex I of the respiratory chain is simultaneously impaired.     

Simultaneous measurements of proton motive force, delta pH, membrane potential, and H+/O ratios in intact Escherichia coli.

An instrument is described that enables the simultaneous monitoring of proton motive force (PMF), membrane potential (delta psi), the delta pH across a membrane, oxidase activity, proton movements, and H+/O ratios. We have studied the relationship existing among these parameters of energy transduction as a critical condition is changed during an experiment. The major findings are: (a) In the pH range of 4.5 to 7.5, increasing the external pH causes an increase in delta psi, internal pH, and oxidase activity, a decrease in H+/O ratio, and a peak-plateau in PMF from pH 5.5 to 6.6 where delta pH is converted to delta psi. (b) An increase in [K+] from 1 to 100 mM, in the presence of 0.5 microM valinomycin, causes the conversion of delta psi to delta pH, a gradual decline in PMF and an increase in H+/O ratio, internal pH, and oxidase activity. (c) Increasing valinomycin concentration from 0 to 2.5 microM, in the presence of 50 mM [K+], causes a decline in delta psi from 125 to 0 mV, and an increase in delta pH from 35 to 70 mV. From 2.5 to 10 microM, the delta pH and the PMF (which it solely represents), stay constant, H+/O ratio increases mainly from 0 to 0.5 microM and much more slowly from 2.5 to 10 microM. (d) Oxygen at only 10% of its concentration in air-saturated buffer can support the generation of 90% or more of the delta psi, delta pH, and PMF generated in an air-saturated solution. (e) The return of extruded protons to the cell (referred to here as "suck-back") represents a complicated process driven by delta psi and influenced by a variety of factors. (f) H+/O ratios measured by the kinetic technique used here are much higher than those measured by standard oxygen pulse techniques.     

Gradation of the magnitude of the electrochemical proton gradient in Mycoplasma cells

The results presented show that in Mycoplasma mycoides var. Capri, regulation of glucose uptake by its non-metabolizable analogue methyl alpha-D-glucoside, can be used to control intracellular ATP content. This in turn leads to a control of the rate of proton extrusion catalysed by the Mg2+-dependent ATPase (phi (cHxN)2C H+) and the respective amplitudes of the components of delta mu H+. When Mycoplasma cells are incubated with 10 mM methyl alpha-D-glucoside, the amplitude of phi (cHxN)2C H+, of the electrical potential delta psi and of the chemical gradient delta pH become continuous functions of external glucose concentration within the limits of the non-energized and fully energized states. Analysis of the relationships between graduated amplitudes of delta psi, delta pH and phi (cHxN) 2C H+ show that the primary form of energy stored by a delta mu H+ generator is the electrical potential.     

Effects of K+ on the proton motive force of Bradyrhizobium sp. strain 32H1.

In previous studies, respiring Bradyrhizobium sp. strain 32H1 cells grown under 0.2% O2, conditions that derepress N2 fixation, were found to have a low proton motive force of less than -121 mV, because of a low membrane potential (delta psi). In contrast, cells grown under 21% O2, which do not fix N2, had high proton motive force values of -175 mV or more, which are typical of respiring bacteria, because of high delta psi values. In the present study, we found that a delta psi of 0 mV in respiring cells requires growth in relatively high-[K+] media (8 mM), low O2 tension, and high internal [K+]. When low-[O2], high-[K+]-grown cells were partially depleted of K+, the delta psi was high. When cells were grown under 21% O2 or in media low in K+ (50 microM K+), the delta psi was again high. The transmembrane pH gradient was affected only slightly by varying the growth or assay conditions. In addition, low-[O2], high-[K+]-grown cells had a greater proton permeability than did high-[O2]-grown cells. To explain these findings, we postulate that cells grown under conditions that derepress N2 fixation contain an electrogenic K+/H+ antiporter that is responsible for the dissipation of the delta psi. The consequence of this alteration in K+ cycling is rerouting of proton circuits so that the putative antiporter becomes the major pathway for H+ influx, rather than the H+-ATP synthase.     

New control of mitochondrial membrane potential and ROS formation--a hypothesis

A new control of mitochondrial membrane potential delta(psi)m and formation of reactive oxygen species (ROS) is presented, based on allosteric ATP-inhibition of cytochrome c oxidase at high intramitochondrial ATP/ADP ratios. Since the rate of ATP synthesis by the ATP synthase is already maximal at low membrane potentials (100-120 mV), the ATP/ADP ratio will also be maximal at this delta(psi)m (at constant rate of ATP consumption). Therefore the control of respiration by the ATP/ADP-ratio keeps delta(psi)m low. In contrast, the known 'respiratory control' leads to an inhibition of respiration only at high delta(psi)m values (150-200 mV) which cause ROS formation. ATP-inhibition of cytochrome c oxidase is switched on and off by reversible phosphorylation (via cAMP and calcium, respectively). We propose that 'stress hormones' which increase intracellular [Ca2+] also increase delta(psi)m and ROS formation, which promote degenerative diseases and accelerate aging.     

Effect of ATP concentration and pH on rigor tension development and dissociation of rigor complex in glycerinated rabbit psoas muscle fiber

Isometric rigor tension development of glycerinated rabbit psoas muscle fibers in a medium, due to the formation of rigor complexes, was estimated at varying ATP concentrations from 0 to 2.5 mM and pH values from 6.75 to 8.20. The dissociation of rigor complexes was also estimated under the same conditions. When muscle fibers developed rigor tension from the relaxed and rigor states, the magnitude of rigor tension increased with increasing concentration of ATP. Transition between rigor and relaxation in single fibers occurred discontinuously at constant levels (critical levels) of ATP which were determined by pH. The critical concentrations of ATP necessary for inducing the transitions between rigor and relaxed states were also increased exponentially with increased pH. Incomplete repetition of tension development by the same fiber was also observed. This incomplete reversibility was divided into two types: one which showed a decay in rigor tension and another which showed no decay. The reason for the incomplete reversibility was discussed.     

Study of the mechanics and small-angle equatorial x-ray pattern of the frog skeletal muscle during transition and rigor at different temperatures

Mechanical characteristics and low-angle equatorial X-ray patterns from frog sartorius muscle passing into iodoacetate rigor under isometric conditions at temperatures 2 degrees-25 degrees C were studied. It is ascertained that during the rigor tension development at all the temperatures Z-reflection intensity increases and those of the (10), (11), (20), (21) and (30) reflections decrease. The last three reflections disappear then still in the phase of the rigor tension development. It is found that the sarcomere lengths remain not always invariable, especially at high temperatures, when the muscle passes into rigor, and can both decrease and increase in the sample place which is investigated by means of X-ray diffraction method. It is shown that the decrease of the I10/I11 relation in some experiments at high temperatures is only due to the sarcomere length decrease. The merging time of the Z and (11) reflections depends both on the temperature and on the sarcomere length change. Thus essential changes correlated with the rigor tension development, and resulted in the Z-reflection intensity increase take place in tetragonal lattice of Z-band and in the I-band region located near Z-band. In A-band the hexagonal lattice order change for the worse is marked only. It is proposed that the mechanism of the rigor tension development differs from that of tension development in ordinary contraction of the skeletal muscle.     

Tension responses to increased hydrostatic pressure in glycerinated rabbit psoas muscle fibres

A method developed to study the effect of increased hydrostatic pressure on the isometric tension of a single muscle fibre is described and experiments done at room temperature (18-22 degrees C) on glycerinated rabbit psoas muscle fibres are presented. Increase of pressure (range 1-10 MPa) caused little change in tension transducer response when a muscle fibre was relaxed. However, there was a reversible depression of isometric tension with an increase of pressure when a fibre was maximally calcium-activated or in rigor; the depression was around 15% for active tension and 30% for rigor tension, for an increase of pressure of 10 MPa (ca. 100 atm).     

Intracellular mitochondrial membrane potential as an indicator of hepatocyte energy metabolism: further evidence for thermodynamic control of metabolism

The lipophilic triphenylmethylphosphonium cation (TPMP+) has been employed to measure delta psi m, the electrical potential across the inner membrane of the mitochondria of intact hepatocytes. The present studies have examined the validity of this technique in hepatocytes exposed to graded concentrations of inhibitors of mitochondrial energy transduction. Under these conditions, TPMP+ uptake allows a reliable measure of delta psi m in intracellular mitochondria, provided that the ratio [TPMP+]i/[TPMP+]e is greater than 50:1 and that at the end of the incubation more than 80% of the hepatocytes exclude Trypan blue. Hepatocytes, staining with Trypan blue, incubated in the presence of Ca2+, do not concentrate TPMP+. The relationships between delta psi m and two other indicators of cellular energy state, delta GPc and Eh, or between delta psi m and J0, were examined in hepatocytes from fasted rats by titration with graded concentrations of inhibitors of mitochondrial energy transduction. Linear relationships were generally observed between delta psi m and delta GPc, Eh or J0 over the delta psi m range of 120-160 mV, except in the presence of carboxyatractyloside or oligomycin, where delta psi m remained constant. Both the magnitude and the direction of the slope of the observed relationships depended upon the nature of the inhibitor. Hepatocytes from fasted rats synthesized glucose from lactate or fructose, and urea from ammonia, at rates which were generally linear functions of the magnitude of delta psi m, except in the presence of oligomycin or carboxyatractyloside. Linear relationships were also observed between delta psi m and the rate of formation of lactate in cells incubated with fructose and in hepatocytes from fed rats. The linear property of these force-flow relationships is taken as evidence for the operation of thermodynamic regulatory mechanisms within hepatocytes.     

Assignment of protein backbone resonances using connectivity, torsion angles and 13Cα chemical shifts

A program is presented which will return the most probable sequence location for a short connected set of residues in a protein given just (13)C(alpha) chemical shifts (delta((13)C(alpha))) and data restricting the phi and psi backbone angles. Data taken from both the BioMagResBank and the Protein Data Bank were used to create a probability density function (PDF) using a multivariate normal distribution in delta((13)C(alpha)), phi, and psi space for each amino acid residue. Extracting and combining probabilities for particular amino acid residues in a short proposed sequence yields a score indicative of the correctness of the proposed assignment. The program is illustrated using several proteins for which structure and (13)C(alpha) chemical shift data are available.     

Crystal structure and conformation of a highly constrained linear tetrapeptide Boc-Leu-dehydro Phe-Ala-Leu-OCH3.

The conformation of a tetrapeptide containing a dehydro amino acid, delta ZPhe, in its sequence has been determined in the crystalline state using X-ray crystallographic techniques. The tetrapeptide, Boc-Leu-delta ZPhe-Ala-Leu-OCH3, crystallizes in the orthorhombic space group P2(1)2(1)2(1) with four molecules in a unit cell of dimensions a = 11.655(1) A, b = 15.698(6) A and c = 18.651(3) A V = 3414.9 A and Dcalc = 1.12 g/cm-3. The asymmetric unit contains one tetrapeptide molecule, C30H46N4O7, a total of 41 nonhydrogen atoms. The structure was determined using the direct methods program SHELXS86 and refined to an R-factor of 0.049 for 3347 reflections (I3.0(I). The linear tetrapeptide in the crystal exhibits a double bend of the Type III-I, with Leu1 (phi = -54.1 degrees, psi = -34.5 degrees) and delta ZPhe2 (phi = -59.9 degrees, psi = -17.1 degrees) as the corner residues of Type III turn and delta ZPhe2 (phi = -59.9 degrees, psi = -17.1 degrees) and Ala3 (phi = -80.4 degrees, psi = 0.5 degrees) residues occupying the corners of Type I turn, with delta ZPhe as the common residue in the double bend. The turn structures are further stabilized by two intramolecular 4----1 type hydrogen bonds.     

Transgenic UCP1 in white adipocytes modulates mitochondrial membrane potential

To test if mitochondrial uncoupling in white adipocytes is responsible for obesity resistance of the aP2-Ucp transgenic mice expressing ectopic uncoupling protein 1 (UCPI) in white fat, mitochondrial membrane potential (delta psi(m)) was estimated by flow cytometry in adipocytes isolated from gonadal fat. Ectopic UCP1 (approximately 0.8 mol UCP1/mol respiratory chain) decreased the delta psi(m) and rendered the potential sensitive to GDP and fatty acids. These ligands of UCP1 had no effect on delta psi(m) in white adipocytes from non-transgenic mice, suggesting that the function of endogenous UCP2 in adipocytes was not affected. The results support the hypothesis that mitochondrial uncoupling in white fat may prevent development of obesity.     

Radial forces within muscle fibers in rigor

Considering the widely accepted cross-bridge model of muscle contraction (Huxley. 1969. Science [Wash. D. C.]. 164:1356-1366), one would expect that attachment of angled cross-bridges would give rise to radial as well as longitudinal forces in the muscle fiber. These forces would tend, in most instances, to draw the myofilaments together and to cause the fiber to decrease in width. Using optical techniques, we have observed significant changes in the width of mechanically skinned frog muscle fibers when the fibers are put into rigor by deleting ATP from the bathing medium. Using a high molecular weight polymer polyvinylpyrrolidone (PVP-40; number average mol. wt. (Mn) = 40,000) in the bathing solution, we were able to estimate the magnitude of the radial forces by shrinking the relaxed fiber to the width observed with rigor induction. With rigor, fiber widths decreased up to approximately 10%, with shrinking being greater at shorter sarcomere spacing and at lower PVP concentrations. At higher PVP concentrations, some fibers actually swelled slightly. Radial pressures seen with rigor in 2 and 4% PVP ranged up to 8.9 x 10(3) N/m2. Upon rigor induction, fibers exerted a longitudinal force of approximately 1 x 10(5) N/m2 that was inhibited by high PVP concentrations (greater than or equal to 13%). In very high PVP concentrations (greater than or equal to 20%), fibers exerted an anomalous force, independent of ATP, which ranged up to 6 x 10(4) N/m2 at 60% PVP. Assuming that all the radial force is the result of cross- bridge attachment, we calculated that rigor cross-bridges exert a radial force of 0.2 x 1.2 x 10(-9) N per thick filament in sarcomeres near rest length. This force is of roughly the same order of magnitude as the longitudinal force per thick filament in rigor contraction or in maximal (calcium-activated) contraction of skinned fibers in ATP- containing solutions. Inasmuch as widths of fibers stretched well beyond overlap of thick and thin filaments decreased with rigor, other radially directed forces may be operating in parallel with cross-bridge forces.     

Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.     

Stability of membrane potential in heart mitochondria: single mitochondrion imaging

Mitochondrial membrane potential (delta psi(m)) plays an important role in cellular activity. Although delta psi(m) of intracellular mitochondria are relatively stable, the recent experiments with isolated mitochondria demonstrate that individual mitochondria show frequent fluctuations of delta psi(m). The current study is performed to investigate the factors that stabilize delta psi(m) in cells by observing delta psi(m) of individual isolated mitochondria with fluorescence microscopy. Here, we report that (1) the transient depolarizations are also induced for mitochondria in plasma membrane permeabilized cells, (2) almost all mitochondria isolated from porcine hearts show the transient depolarizations that is enhanced with the net efflux of protons from the matrix to the intermembrane space, and (3) ATP and ADP significantly inhibit the transient depolarizations by plural mechanisms. These results suggest that the suppression of acute alkalinization of the matrix together with the presence of ATP and ADP contributes to the stabilization of delta psi(m) in cells.     

Empirical torsional potential functions from protein structure data. Phi- and psi-potentials for non-glycyl amino acid residues.

The torsional potential functions Vt(phi) and Vt(psi) around single bonds N--C alpha and C alpha--C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (phi, psi)-plane with the value of Vtot(phi, psi), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in L-configuration, are Vt(phi) = 1.0 cos (phi + 60 degrees); Vt(psi) = 0.5 cos (psi + 60 degrees) - 1.0 cos (2 psi + 30 degrees) - 0.5 cos (3 psi + 30 degrees). The dipeptide energy maps Vtot(phi, psi) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line psi = 0 degrees. These functions derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.