Changing the direction of flagellar rotation in bacteria by modulating the ratio between the rotational states of the switch protein FliM

One of the major questions in bacterial chemotaxis is how the switch, which controls the direction of flagellar rotation, functions. It is well established that binding of the signaling molecule CheY to the switch protein FliM shifts the rotation from the default direction, counterclockwise, to clockwise. How this shift is done is still a mystery. Our aim in this study was to determine the correlation between the fraction of FliM molecules in the clockwise state (i.e. occupied by CheY) and the probability of clockwise rotation. For this purpose we gradually expressed, from a plasmid, a clockwise FliM mutant protein in cells that express, from the chromosome, wild-type FliM but no chemotaxis proteins. We verified that plasmid-borne FliM exchanges chromosomal FliM in the switch. Surprisingly, a substantial clockwise probability was not obtained before the large majority of the FliM molecules in the switch were clockwise molecules. Thereafter, the rise in clockwise probability was very steep. These results suggest that an increase in the clockwise probability requires a high level of FliM occupancy by CheY approximately P. They further suggest that the steep increase in clockwise rotation upon increasing CheY levels, reported in several studies, is due, at least in part, to cooperativity of post-binding interactions within the switch. We also carried out the inverse experiment, in which wild-type FliM was gradually expressed in a background of a clockwise fliM mutant. In this case, the level of the clockwise mutant protein, required for establishing a certain clockwise probability, was lower than in the original experiment. If our system (in which the ratio between the rotational states of FliM in the switch is established by slow exchange) and the native system (in which the ratio is established by fast changes in FliM occupancy) are comparable, the results suggest that hysteresis is involved in the switch function. Such a situation might reflect a damping mechanism, which prevents a situation in which fluctuations in the phosphorylation level of CheY throw the switch from one direction of rotation to the other.     

Modeling of Hysteresis in Gene Regulatory Networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.     

A Mechanism of Modulating the Direction of Flagellar Rotation in Bacteria by Fumarate and Fumarate Reductase

Fumarate, an electron acceptor in anaerobic respiration of Escherichia coli, has an additional function of assisting the flagellar motor to shift from counterclockwise to clockwise rotation, with a consequent modulation of the bacterial swimming behavior. Fumarate transmits its effect to the motor via the fumarate reductase complex (FrdABCD), shown to bind to FliG—one of the motor’s switch proteins. How binding of the FrdABCD respiratory enzyme to FliG enhances clockwise rotation and how fumarate is involved in this activity have remained puzzling. Here we show that the FrdA subunit in the presence of fumarate is sufficient for binding to FliG and for clockwise enhancement. We further demonstrate by in vitro binding assays and super-resolution microscopy in vivo that the mechanism by which fumarate-occupied FrdA enhances clockwise rotation involves its preferential binding to the clockwise state of FliG (FliG_cw). Continuum electrostatics combined with docking analysis and conformational sampling endorsed the experimental conclusions and suggested that the FrdA–FliG_cw interaction is driven by the positive electrostatic potential generated by FrdA and the negatively charged areas of FliG. They further demonstrated that fumarate changes FrdA’s conformation to one that can bind to FliG_cw. These findings also show that the reason for the failure of the succinate dehydrogenase flavoprotein SdhA (an almost-identical analog of FrdA shown to bind to FliG equally well) to enhance clockwise rotation is that it has no binding preference for FliG_cw. We suggest that this mechanism is physiologically important as it can modulate the magnitude of ΔG⁰ between the clockwise and counterclockwise states of the motor to tune the motor to the growth conditions of the bacteria.     

Hysteresis modeling for calcium-mediated ciliary beat frequency in airway epithelial cells

A hysteresis model is proposed to describe calcium-mediated Ciliary beat frequency (CBF) in airway epithelial cells. In this dynamic model, the kinetics of coupling between calcium and CBF is posited as a two-step configuration. First, Ca²⁺ directly binds to or indirectly acts on the axonemal proteins to modulate the activity of axonemal proteins. This step can be modeled by a Hill function in biochemistry. In the second step, the activity of axonemal proteins interacts with the sliding velocity of axonemal microtubules, the equivalent to regulating the CBF. The well-known Bouc-Wen model for hysteresis in mechanical engineering, which can only generate the stable clockwise hysteresis loops, is modified to describe the counter clockwise hysteresis loops commonly observed in the biological experiments. Based upon this new hysteresis model, the dynamic behavior of calcium-regulated CBF in epithelial airway cells is investigated through simulation studies. The numerical results demonstrate that the CBF dynamics in airway epithelial cells predicted by the hysteresis model is more consistent with the experimental observations than that predicted by previous static model in the literature.     

Noise underlies switching behavior of the bacterial flagellum

We report the switching behavior of the full bacterial flagellum system that includes the filament and the motor in wild-type Escherichia coli cells. In sorting the motor behavior by the clockwise bias, we find that the distributions of the clockwise (CW) and counterclockwise (CCW) intervals are either exponential or nonexponential with long tails. At low bias, CW intervals are exponentially distributed and CCW intervals exhibit long tails. At intermediate CW bias (0.5) both CW and CCW intervals are mainly exponentially distributed. A simple model suggests that these two distinct switching behaviors are governed by the presence of signaling noise within the chemotaxis network. Low noise yields exponentially distributed intervals, whereas large noise yields nonexponential behavior with long tails. These drastically different motor statistics may play a role in optimizing bacterial behavior for a wide range of environmental conditions.     

In vitro growth properties of Xenopus retinal neurons undergo developmental modulation

To determine whether Xenopus retinal neurons undergo intrinsic developmental changes in growth properties, retinal explants from embryos and tadpoles of different stages were grown on laminin, fibronectin, and collagen I in serum-free media. Growth was assayed in terms of a neurite growth index (NGI) and the appearance of clockwise bundles, or a clockwise growth index (CGI). The first neurites from stage 25 optic vesicles are pioneers and display a unique growth phenotype; they emerge rapidly, survive for a short time, show little substrate preferences for growth (they grow almost as well on BSA as they do on laminin and fibronectin), and form no clockwise bundles under any conditions. Neurites from progressively older retinas (stages 32-37) share with stage 25 neurites the rapid outgrowth pattern, but begin to show substrate preferences and clockwise growth. From stage 40 to 50, the mature growth pattern is expressed; a lag in initial outgrowth, long-term survival, distinct substrate preferences (they grow 10 times better on laminin and fibronectin than on BSA) and display robust clockwise growth patterns on laminin and fibronectin. The acquisition of clockwise growth is independent of optic fiber contact with the tectum or exposure to diffusible factors from mature brain tissues. The results suggest that retinal neurons undergo developmental modulation of surface adhesive properties and/or cytoskeletal organization.     

Clockwise and counterclockwise hysteresis characterize state changes in the same aquatic ecosystem

Incremental increases in a driver variable, such as nutrients or detritus, can trigger abrupt shifts in aquatic ecosystems that may exhibit hysteretic dynamics and a slow return to the initial state. A model system for understanding these dynamics is the microbial assemblage that inhabits the cup‐shaped leaves of the pitcher plant Sarracenia purpurea. With enrichment of organic matter, this system flips within three days from an oxygen‐rich state to an oxygen‐poor state. In a replicated greenhouse experiment, we enriched pitcher‐plant leaves at different rates with bovine serum albumin (BSA), a molecular substitute for detritus. Changes in dissolved oxygen (DO) and undigested BSA concentration were monitored during enrichment and recovery phases. With increasing enrichment rates, the dynamics ranged from clockwise hysteresis (low), to environmental tracking (medium), to novel counter‐clockwise hysteresis (high). These experiments demonstrate that detrital enrichment rate can modulate a diversity of hysteretic responses within a single aquatic ecosystem, and suggest different management strategies may be needed to mitigate the effects of high vs. low rates of detrital enrichment.     

Both CheA and CheW are required for reconstitution of chemotactic signaling in Escherichia coli.

If cells of Escherichia coli deleted for genes that specify transducers and all known cytoplasmic chemotaxis proteins are reconstituted with CheA, CheW, and CheY, they spin their flagella alternately clockwise and counterclockwise. If the aspartate receptor also is present, clockwise rotation is suppressed upon addition of aspartate. If either CheA or CheW is absent, the fraction of time that the flagella spin clockwise is reduced and responses to aspartate do not occur.     

Regulation of Switching Frequency and Bias of the Bacterial Flagellar Motor by CheY and Fumarate

The effect of CheY and fumarate on switching frequency and rotational bias of the bacterial flagellar motor was analyzed by computer-aided tracking of tethered Escherichia coli. Plots of cells overexpressing CheY in a gutted background showed a bell-shaped correlation curve of switching frequency and bias centering at about 50% clockwise rotation. Gutted cells (i.e., with cheA to cheZ deleted) with a low CheY level but a high cytoplasmic fumarate concentration displayed the same correlation of switching frequency and bias as cells overexpressing CheY at the wild-type fumarate level. Hence, a high fumarate level can phenotypically mimic CheY overexpression by simultaneously changing the switching frequency and the bias. A linear correlation of cytoplasmic fumarate concentration and clockwise rotation bias was found and predicts exclusively counterclockwise rotation without switching when fumarate is absent. This suggests that (i) fumarate is essential for clockwise rotation in vivo and (ii) any metabolically induced fluctuation of its cytoplasmic concentration will result in a transient change in bias and switching probability. A high fumarate level resulted in a dose-response curve linking bias and cytoplasmic CheY concentration that was offset but with a slope similar to that for a low fumarate level. It is concluded that fumarate and CheY act additively presumably at different reaction steps in the conformational transition of the switch complex from counterclockwise to clockwise motor rotation.     

Microtubule polarity in Sertoli cells: a model for microtubule-based spermatid transport

Bundles of microtubules occur adjacent to ectoplasmic specializations (ESs) that line Sertoli cell crypts and support developing spermatids. These microtubules are oriented parallel to the direction of spermatid movement during spermatogenesis. We propose a model in which ESs function as vehicles, and microtubules as tracks, for microtubule-based transport of spermatids through the seminiferous epithelium. Microtubule polarity provides the basis for the direction of force generation by available mechanoenzymes. As part of a more general study designed to investigate the potential role of microtubule-based transport during spermatogenesis, we have studied the polarity of cytoplasmic microtubules of Sertoli cells. Rat testis blocks were incubated in a lysis/decoration buffer, with and without exogenous purified bovine brain tubulin. This treatment results in the decoration of endogenous microtubules with curved tubulin protofilament sheets (seen as hooks in cross section). The direction of curvature of the hooks indicates microtubule polarity; that is, clockwise hooks are seen when viewing microtubules from the plus to the minus end. We found that, in Sertoli cells, most of the hooks were orientated in the same direction. Significantly, when viewed from the base of the epithelium, hooks pointed in a clockwise direction. The clockwise direction of dynein arms on axonemes of sperm tails, in the same section, provided an internal check of the section orientation. Electron micrographs of fields of seminiferous epithelium were assembled into montages for quantitative analysis of microtubule polarity. Our data indicate that Sertoli cell cytoplasmic microtubules are of uniform polarity and are orientated with their minus ends toward the cell periphery. These observations have significant implications for our proposed model of microtubule-based transport of spermatids through the seminiferous epithelium.     

Control of speed modulation (chemokinesis) in the unidirectional rotary motor of Sinorhizobium meliloti

Swimming cells of Sinorhizobium meliloti are driven by flagella that rotate only clockwise. They can modulate rotary speed (achieve chemokinesis) and reorient the swimming path by slowing flagellar rotation. The flagellar motor is energized by proton motive force, and torque is generated by electrostatic interactions at the rotor/stator (FliG/MotA-MotB) interface. Like the Escherichia coli flagellar motor that switches between counterclockwise and clockwise rotation, the S. meliloti rotary motor depends on electrostatic interactions between conserved charged residues, namely, Arg294 and Glu302 (FliG) and Arg90, Glu98 and Glu150 (MotA). Unlike in E. coli, however, Glu150 is essential for torque generation, whereas residues Arg90 and Glu98 are crucial for the chemotaxis-controlled variation of rotary speed. Substitutions of either Arg90 or Glu98 by charge-neutralizing residues or even by their smaller, charge-maintaining isologues, lysine and aspartate, resulted in top-speed flagellar rotation and decreased potential to slow down in response to tactic signalling (chemokinesis-defective mutants). The data infer a novel mechanism of flagellar speed control by electrostatic forces acting at the rotor/stator interface. These features have been integrated into a working model of the speed-modulating rotary motor.     

Structure of the DNA of the adenovirus 7-simian virus 40 hybrid, e46, by electron microscopy

The DNA molecule of the adenovirus 7-simian virus (SV) 40 hybrid, E46⁺, contains a single substitution of SV40 DNA located about 0.05 adenovirus 7 lengths from one end (arbitrarily designated the left end). The left to right direction in the SV40 DNA segment of the hybrid corresponds to the clockwise direction in the SV40 physical map. The left end point of the segment maps at about SV40 map position 0.50 ± 0.01 and the right end point at about SV40 map position 0.66 ± 0.01. The region between SV40 map positions 0.71 and 0.11 (clockwise) is deleted. Thus, the region between SV40 map position 0.50 and 0.66 (clockwise) is repeated in tandem.     

Torque and switching in the bacterial flagellar motor. An electrostatic model.

A model is presented for the rotary motor that drives bacterial flagella, using the electrochemical gradient of protons across the cytoplasmic membrane. The model unifies several concepts present in previous models. Torque is generated by proton-conducting particles around the perimeter of the rotor at the base of the flagellum. Protons in channels formed by these particles interact electrostatically with tilted lines of charges on the rotor, providing "loose coupling" between proton flux and rotation of the flagellum. Computer simulations of the model correctly predict the experimentally observed dynamic properties of the motor. Unlike previous models, the motor presented here may rotate either way for a given direction of the protonmotive force. The direction of rotation only depends on the level of occupancy of the proton channels. This suggests a novel and simple mechanism for the switching between clockwise and counterclockwise rotation that is the basis of bacterial chemotaxis.     

The QRS Vectorcardiogram of the Normal Newborn Human

A four-electrode resistance-combined network system was used to record the vector-cardiograms of 15 full-term infants, from birth to 96 hours of life. In the horizontal plane the QRS loop was described in a clockwise manner anterior to the point of origin. Initially it was directed anteriorly to the left and, terminally, posteriorly to the right. In the sagittal plane the loop described a figure-of-eight, with minimal superior and inferior displacement of the anterior and posterior components. In the frontal plane the QRS vector loop was described in either a clockwise direction inferior to the point of origin or a clockwise direction superior to the point of origin. Alterations in the appearance of the QRS vectorcardiogram result from changes in spatial orientation.     

A two-phase finite element model of the diastolic left ventricle

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.     

Cell envelopes of chemotaxis mutants of Escherichia coli rotate their flagella counterclockwise.

Flagella rotated exclusively counterclockwise in Escherichia coli cell envelopes prepared from wild-type cells, whose flagella rotated both clockwise and counterclockwise, from mutants rotating their flagella counterclockwise only, and even from mutants rotating their flagella primarily clockwise. Some factor needed for clockwise flagellar rotation appeared to be missing or defective in the cell envelopes.     

Swimming in circles: motion of bacteria near solid boundaries

Near a solid boundary, Escherichia coli swims in clockwise circular motion. We provide a hydrodynamic model for this behavior. We show that circular trajectories are natural consequences of force-free and torque-free swimming and the hydrodynamic interactions with the boundary, which also leads to a hydrodynamic trapping of the cells close to the surface. We compare the results of the model with experimental data and obtain reasonable agreement. In particular, the radius of curvature of the trajectory is observed to increase with the length of the bacterium body.     

Specific inactivator of flagellar reversal in Salmonella typhimurium.

Specific inhibition of flagellar rotation reversal was observed after exposure of chemotactic Salmonella typhimurium to citrate autoclaved at neutral pH. The presence of a rotation reversal inactivator was established in autoclaved citrate-containing media and nutrient broth. Since modulation of flagellar rotation by attractants and repellents is the basis of chemotactic behavior, a specific inhibitor of rotation reversal, which is essential for tumble generation, provides a useful probe into the molecular mechanism of bacterial chemotaxis. The inactivator inhibits clockwise rotation without affecting counterclockwise rotation, speed of rotation, or the capacity of the cells to grow and divide. Inactivation of clockwise rotation is gradual and irreversible, differing from the transient inhibition of clockwise rotation by attractants, which is characterized by an immediate suppression followed by a return to normal rotation patterns. The rotation reversal inactivator is stable to acidification, rotary evaporation, lyophilization, and rehydration.     

Around the Mediterranean: an extreme example of loop migration in a long‐distance migratory passerine

An important issue in migration research is how small‐bodied passerines pass over vast geographical barriers; in European–African avian migration, these are represented by the Mediterranean Sea and the Sahara Desert. Eastern (passing eastern Mediterranean), central (passing Apennine Peninsula) and western (via western Mediterranean) major migration flyways are distinguished for European migratory birds. The autumn and spring migration routes may differ (loop migration) and there could be a certain level of individual flexibility in how individuals navigate themselves during a single migration cycle. We used light‐level loggers to map migration routes of barn swallows Hirundo rustica breeding in the centre of a wide putative contact zone between the northeastern and southernwestern European populations that differ in migration flyways utilised and wintering grounds. Our data documented high variation in migration patterns and wintering sites of tracked birds (n = 19 individuals) from a single breeding colony, with evidence for loop migration in all but one of the tracked swallows. In general, two migratory strategies were distinguished. In the first, birds wintering in a belt stretching from southcentral to southern Africa that used an eastern route for both the spring and autumn migration, then shifted their spring migration eastwards (anti‐clockwise loops, n = 12). In the second, birds used an eastern or central route to their wintering grounds in central Africa, shifting the spring migration route westward (clockwise loops, n = 7). In addition, we observed an extremely wide clockwise loop migration encompassing the entire Mediterranean, with one individual utilising both the eastern (autumn) and western (spring) migratory flyway during a single annual migration cycle. Further investigation is needed to ascertain whether clockwise migratory loops encircling the entire Mediterranean also occur other small long‐distance passerine species.