An electrostatic mechanism closely reproducing observed behavior in the bacterial flagellar motor.

A mechanism coupling the transmembrane flow of protons to the rotation of the bacterial flagellum is studied. The coupling is accomplished by means of an array of tilted rows of positive and negative charges around the circumference of the rotor, which interacts with a linear array of proton binding sites in channels. We present a rigorous treatment of the electrostatic interactions using minimal assumptions. Interactions with the transition states are included, as well as proton-proton interactions in and between channels. In assigning values to the parameters of the model, experimentally determined structural characteristics of the motor have been used. According to the model, switching and pausing occur as a consequence of modest conformational changes in the rotor. In contrast to similar approaches developed earlier, this model closely reproduces a large number of experimental findings from different laboratories, including the nonlinear behavior of the torque-frequency relation in Escherichia coli, the stoichiometry of the system in Streptococcus, and the pH-dependence of swimming speed in Bacillus subtilis.

Genesis of the ultradian rhythm of GH secretion: a new model unifying experimental observations in rats.

Growth hormone (GH) induces growth in animals and humans and also has important metabolic functions. The GH neuroendocrine axis consists of a signaling cascade from the hypothalamus to the pituitary, the liver, and peripheral tissues, including two major feedback mechanisms. GH is secreted from the pituitary into the circulating blood according to the effect on the somatotrophs of two hypothalamic peptides, GH-releasing hormone (GHRH) and its antagonist, somatostatin (SRIF). The typical GH profile in the male rat shows secretory episodes every 3.3 h, which are subdivided into two peaks. Focusing on the mechanisms for generation of this ultradian GH rhythm, we simulated the time course of GH secretion under a variety of conditions. The model that we propose is based on feedback of GH on its own release mediated both by GH receptors on SRIF neurons in the brain and by a delayed SRIF release into both the brain and portal blood. SRIF, with a resultant periodicity of 3.3 h, affects both the somatotroph cells in the pituitary and the GHRH neurons in the hypothalamus. The secretion of GHRH is postulated to occur in an approximately 1-h rhythm modulated by the level of SRIF in the hypothalamus. The model predicts a possible mechanism for the feminization of the male GH rhythm by sex steroids and vice versa, and suggests experiments that might reveal the proposed intrinsic 1-h GHRH rhythm.

Fumarate modulates bacterial flagellar rotation by lowering the free energy difference between the clockwise and counterclockwise states of the motor.

Switching flagellar rotation from one direction to another is an essential part of bacterial chemotaxis. Fumarate has been shown to possess the capacity to restore to flagella of cytoplasm-free, CheY-containing bacterial envelopes the ability to switch directions and to increase the probability of reversal in intact cells. Neither the target of fumarate action nor the mechanism of function is known. To distinguish between the two potential targets of fumarate, the response regulator CheY and the flagellar switch-motor complex, we compared flagellar rotation between isogenic strains that lacked CheY and had either low or high levels of fumarate. The difference in the fumarate levels was due to a deletion of the genes encoding the enzymes that synthesize and metabolize fumarate; succinate dehydrogenase and fumarase, respectively. The strains were in a gutted background (i.e. a background deleted for the cytoplasmic chemotaxis proteins and some of the receptors), and switching was achieved by carrying out the measurements at 2.5 degreesC, where it has been demonstrated that gutted cells switch spontaneously. The flagellar rotation of the strain with the highest level of fumarate was the most clockwise-biased and had the highest reversal frequency, indicating that fumarate is effective even in the absence of CheY. Fumarate reduced the free energy difference of the counterclockwise-to-clockwise transition and had no appreciable effect on the activation energy of this transition. Similar observations were made at room temperature, provided that intracellular CheY was present. In a wild-type background, both mutants made rings on semi-solid agar typical of normal chemotaxis. Taken together, the results suggest that the target of fumarate is the switch-motor complex, that fumarate acts by increasing the probability of the clockwise state, and that a fumarate level as low as that found in succinate dehydrogenase mutants is sufficient for normal chemotaxis.

Bacterial chemotaxis: unsolved mystery of the flagellar switch.

Impressive progress has been made in understanding the mechanism of bacterial chemotaxis and function of the flagellar motor, but how the direction of rotation is reversed by the 'flagellar switch'--a central step in chemotaxis--remains obscure and calls for new experimental approaches.

Temperature-induced switching of the bacterial flagellar motor.

Chemotaxis signaling proteins normally control the direction of rotation of the flagellar motor of Escherichia coli. In their absence, a wild-type motor spins exclusively counterclockwise. Although the signaling pathway is well defined, relatively little is known about switching, the mechanism that enables the motor to change direction. We found that switching occurs in the absence of signaling proteins when cells are cooled to temperatures below about 10 degrees C. The forward rate constant (for counterclockwise to clockwise, CCW to CW, switching) increases and the reverse rate constant (for CW to CCW switching) decreases as the temperature is lowered. At about -2 degrees C, most motors spin exclusively CW. At temperatures for which reversals are frequent enough to generate a sizable data set, both CCW and CW interval distributions appear to be exponential. From the rate constants we computed equilibrium constants and standard free energy changes, and from the temperature dependence of the standard free energy changes we determined standard enthalpy and entropy changes. Using transition-state theory, we also calculated the activation free energy, enthalpy, and entropy. We conclude that the CW state is preferred at very low temperatures and that it is relatively more highly bonded and restricted than the CCW state.

Chemical oscillations arise solely from kinetic nonlinearity and hence can occur near equilibrium.

A minimal kinetic scheme for a system displaying sustained chemical oscillations is presented. The system is isothermal, and all steps in the scheme are kinetically reversible. The oscillations are analyzed and the crucial points elucidated. Both positive and negative feedback, if properly introduced, support oscillations, provided the state responsible for feedback is optimally buffered. It is shown that the requisite nonlinearity is introduced at the kinetic level because of feedback regulation and not, as is usually assumed, by large affinities that introduce nonlinearity at the thermodynamic level. Hence, sustained oscillations may occur near equilibrium.

Fluctuations in rotation rate of the flagellar motor of Escherichia coli.

The purpose of this work was to study the changes in rotation rate of the bacterial motor and to try to discriminate between various sources of these changes with the aim of understanding the mechanism of force generation better. To this end Escherichia coli cells were tethered and videotaped with brief stroboscopic light flashes. The records were scanned by means of a computerized motion analysis system, yielding cell size, radius of rotation, and accumulated angle of rotation as functions of time for each cell selected. In conformity with previous studies, fluctuations in the rotation rate of the flagellar motor were invariably found. Employing an exclusively counterclockwise rotating mutant ("gutted" RP1091 strain) and using power spectral density, autocorrelation and residual mean square angle analysis, we found that a simple superposition of rotational diffusion on a steady rotary motion is insufficient to describe the observed rotation. We observed two additional rotational components, one fluctuating (0.04-0.6 s) and one oscillating (0.8-7 s). However, the effective rotational diffusion coefficient obtained after taking these two components into account generally exceeded that calculated from external friction by two orders of magnitude. This is consistent with a model incorporating association and dissociation of force-generating units.

Rotational asymmetry of Escherichia coli flagellar motor in the presence of arsenate.

The flagellar motor of Escherichia coli (E. coli) is driven by a proton-motive force (PMF), hence it was of interest to determine whether the motor is symmetrical in the sense that it can be rotated by any polarity of PMF. For this purpose the cells had to be deenergized first. Conventional deenergization procedures caused irreversible loss of motility, presumably due to ATP-dependent degradative processes. However, E. coli cells deenergized by incubation with arsenate manifested a slow, reversible depletion of PMF. In this procedure there was a sufficiently long time window, during which a considerable proportion of the cells lost their motility and could be made to rotate again by an artificially-imposed PMF. The motors of these cells rotated in response to any PMF polarity, but positive and negative polarities rotated different sub-populations of cells and the direction was almost exclusively counterclockwise. The reason for the unidirectionality of the rotation was not the intervention of the chemotaxis system. A number of potential reasons are suggested. One is the arsenate effect on the motor function found previously [Margolin, Y., Barak, R. and Eisenbach, M. (1994) J. Bacteriol. 176, 5547-5549]. A possible interaction between arsenate and the motor is discussed.

Temporal segregation in signalling: a novel mechanism in human neutrophils.

The ability of neutrophils to carry out chemotaxis in response to low chemoattractant concentrations, but arrest their motility when exposed to higher concentrations of the same substance, has fascinated investigators for years. By analyzing the temporal characteristics of the morphological responses, corresponding to chemotaxis and cell arrest, we have recently discovered that the choice between them is made by transduction of the continuous binding process into either single or multiple stimuli within defined time intervals, initiating chemotaxis or cell arrest, respectively. Both experimental and theoretical lines of evidence are presented to support the validity of this unique mechanism.

Pausing, switching and speed fluctuation of the bacterial flagellar motor and their relation to motility and chemotaxis.

Wild-type Escherichia coli and Salmonella typhimurium cells, tethered to glass by their flagella, rotate with brief intermittent pauses, the prevalence of which is decreased by attractants and increased by repellents. By attaching latex beads to filaments of a S. typhimurium mutant having straight rather than helical flagella, it was established that the flagella on free cells also pause intermittently. Pausing is therefore an intrinsic feature of the motor and not an artifact associated with tethering. In tethered cells of wild-type strains and non-chemotactic mutants defective in transducers, chemotaxis proteins, or the flagellar switch, both the classical response to chemotactic stimuli (change in direction of rotation from counterclockwise to clockwise or vice versa), and the pausing response to such stimuli, were linked together. No separate signal for pausing was found. In comparing different strains under different stimulation conditions, it was found that cells that never reversed seldom if ever paused, while cells that reversed frequently paused frequently. It is suggested that pausing is the result of futile switching events. A modified description of tumbling and chemotaxis is provided in which pausing, as well as reversal, has a role. Suppression of reversals and pauses by attractant stimuli commonly resulted in an increase in the speed of counterclockwise rotation; this may be because of suppression of pauses or reversals that are too brief to be detected. The clockwise rotation rate of unstimulated cells, which commonly was faster than their counterclockwise rate, was not further increased by repellent stimuli. The rotation rate of any given cell under any given condition was found to fluctuate on all time-scales measured. The study also revealed that some of the common repellents of E. coli and S. typhimurium slow down or stop the motor; these effects are not mediated by the chemotaxis machinery or intracellular pH.

Dynamics of a tightly coupled mechanism for flagellar rotation. Bacterial motility, chemiosmotic coupling, protonmotive force.

The bacterial flagellar motor is a molecular engine that couples the flow of protons across the cytoplasmic membrane to rotation of the flagellar filament. We analyze the steady-state behavior of an explicit mechanical model in which a fixed number of protons carries the filament through one revolution. Predictions of this model are compared with experimentally determined relationships between protonmotive force, proton flux, torque, and speed. All such tightly coupled mechanisms produce the same torque when the motor is stalled but vary greatly in their behavior at high speed. The speed at zero load predicted by our model is limited by the rates of association and dissociation of protons at binding sites on the rotor and by the mobility of force generators containing transmembrane channels that interact with these sites. Our analysis suggests that more could be learned about the motor if it were driven by an externally applied torque backwards (at negative speed) or forwards at speeds greater than the zero-load speed.

Water movement: does thermodynamic interpretation distort reality?

In a recent theoretical analysis of water flow, Finkelstein (Water Movement Through Lipid Bilayers, Pores, and Plasma Membranes: Theory and Reality, 1987) has attacked the contributions of irreversible thermodynamics, stating that "the thermodynamic treatment of uphill water flow completely distorts reality." Instead he presents a mechanistic formulation. For a porous membrane, water flow is attributed to convection generated by a favorable hydrostatic pressure gradient within pores, even when in the presence of permeant solutes water moves against its chemical potential gradient; water flow may "drag", solute, to an extent determined by the solute partition coefficient, but the possibility that solute flow may drag water is excluded. We argue that this formulation violates the second law of thermodynamics. Water cannot move against its chemical potential gradient because of the influence of only part of the chemical potential gradient. Furthermore, the proposed mechanism requires that at one of the membrane-solution interfaces water must move against both its concentration gradient and the hydrostatic pressure gradient. Also considered by Finkelstein is the nature of the reflection coefficient sigma, a kinetic variable, which he concludes can be evaluated (in a porous membrane) by measurement of the (equilibrium) solute partition coefficient. We claim that in general it is not possible to evaluate a kinetic variable from measurements of equilibrium parameters alone. A valid kinetic analysis must incorporate the contribution of all coupled flows.

Light-induced conductivity changes of purple membrane suspensions in strong electrolytes.

Measurements have been made of the modulated light-induced changes in conductivity and the associated relaxation times of bacteriorhodopsin in a variety of strong electrolytes, both unbuffered and buffered. The effects of pH and temperature variation have been studied as well as the effect of adding valinomycin. Two relaxation times can be distinguished: a fast lifetime associated with protonation-deprotonation, and a slow lifetime associated with ion binding. The ion-binding effects appear to be cation specific.

Interaction of furosemide with lipid membranes.

The interaction of furosemide with different phospholipids was investigated. Its influence on the lipid structure was inferred from its effect on the phase transition properties of lipids and on the conductance of planar bilayer membranes. The thermotropic properties of dipalmitoyl phosphatidylcholine, phosphatidylethanolamine (natural), dipalmitoyl phosphatidylethanolamine, brain sphingomyelin, brain cerebrosides and phosphatidylserine in the presence and absence of furosemide were investigated by differential scanning calorimetry. The modifying effect of furosemide seems to be strongest on phosphatidylethanolamine (natural) and sphingomyelin bilayers. The propensity of furosemide to decrease the electrical resistance of planar lipid membranes was also studied and it is shown that the drug facilitates the transport of ions. Partition coefficients of furosemide between lipid bilayers and water were measured.

Energy coupling and thermokinetic balancing in enzyme kinetics. Microscopic reversibility and detailed balance revisited.

A survey of the development of the concepts of microscopic reversibility and detailed balancing is given. Considerable confusion surrounds these concepts. To obviate this, an unambiguous relation is presented that holds under all conditions and for which we propose the term "thermokinetic balancing." The utility of this relation, which in contrast to detailed balancing is independent of reactant and product concentrations, is demonstrated in a detailed discussion of the kinetics and thermodynamics of the calcium-transporting ATPase according to the principles worked out by Hill. This includes a critical analysis of the different concepts advocated by Jencks and Tanford. The advantage of thermokinetic balancing over detailed balancing is illustrated by examples, high-lighting the relationship of these procedures to standard free energies and basic free energies.

Consequences of detailed balance in a model for sensory adaptation based on ligand-induced receptor modification.

A model for exact sensory adaptation has been published by Segel and co-workers in several papers [e.g., Knox, B. E., Devreotes, P. N., Goldbeter, A. & Segel, L. A. (1986) Proc. Natl. Acad. Sci. USA 83, 2345-2349]. The model comprises a pair of states whose relative probabilities are determined by the binding of a ligand. A second pair of states related by the same ligand binding is accessible as a consequence of either a conformational change or a "covalent modification." By taking proper account of detailed balance, we show that the notion of covalent modification in this context includes three cases, two of which involve dissipation of metabolic energy. The condition for exact adaptation is dependent on metabolite concentrations in all cases of covalent modification. The performance of the model is critically examined on thermodynamic and kinetic grounds.