Rotation of bacterial flagella as driven by cytomembrane streaming

Theoretical estimates are given to check the possibility that flagellar rotation of bacteria is driven by viscous forces exerted from a streaming cytomembrane matrix to the basal structure of the flagellum.For different regimes of cytomembrane streaming, i.e. for circular, shearing and uniform linear motion of the membrane matrix past the basal ring of the flagellum, the velocity of streaming is computed that will yield the necessary mechanical torque for rotation of a helical flagellum in a watery medium.It is shown that in the range of surface viscosities determined for phospholipid monolayers the required velocities of cytomembrane streaming may be expected in the range of 3 μm/s to 60 μm/s. Since streaming velocities of the latter order of magnitude have been observed in protozoan membrane, efforts appear warranted to demonstrate experimentally the existence of cytomembrane streaming in bacteria and to characterize the surface viscosity of their cytomembrane.     

Swimming of spermatozoa in a linear viscoelastic fluid.

A modified resistive force theory is developed for a spermatozoon swimming in a general linear viscoelastic fluid. The theory is based on a Fourier decomposition of the flagellar velocity, which leads to solving the Stokes flow equations with a complex viscosity. We use a model spermatozoon with a spherical head which propagates small amplitude sinusoidal waves along its flagellum. Results are obtained for the velocity of propulsion and the rate of working for a free swimming spermatozoon and the thrust on a fixed spermatozoon. There is no change in propulsive velocity for a viscoelastic fluid compared to a Newtonian fluid. The rate of working does change however, decreasing with increasing elasticity of the fluid, for a Maxwell fluid. Thus the theory predicts that a spermatozoon can swim faster in a Maxwell fluid with the same expenditure of energy for a Newtonian fluid.     

Electroviscosity of polyelectrolyte solutions

A theoretical expression for the electroviscous effect in polyelectrolyte solutions, caused by the distortion of counterion-distribution and counterion flow around a polyion under a velocity gradient of solvent flow, was obtained to elucidate the characteristic behaviour of the viscosity of highly charged polyelectrolyte solutions observed at low salt concentration. The derivation of the theory was performed on the basis of the Navier-Stokes-Onsager equation, Poisson equation, and diffusion equations for low molecular ions by the use of a cell model (free-volume model) for a polyion. Energy dissipation was obtained without directly solving these equations. It was found that the derived expression of viscosity explained the experimental results satisfactorily, and that the streaming potential effect caused by the counterion flow played an essential role in the increase in viscosity of polyelectrolyte solutions at finite polymer concentration and low salt concentration ranges.     

The physics of flagellar motion of E. coli during chemotaxis

Flagellar motion has been an active area of study right from the discovery of bacterial chemotaxis in 1882. During chemotaxis, E. coli moves with the help of helical flagella in an aquatic environment. Helical flagella are rotated in clockwise or counterclockwise direction using reversible flagellar motors situated at the base of each flagellum. The swimming of E. coli is characterized by a low Reynolds number that is unique and time reversible. The random motion of E. coli is influenced by the viscosity of the fluid and the Brownian motion of molecules of fluid, chemoattractants, and chemorepellants. This paper reviews the literature about the physics involved in the propulsion mechanism of E. coli. Starting from the resistive-force theory, various theories on flagellar hydrodynamics are critically reviewed. Expressions for drag force, elastic force and velocity of flagellar elements are derived. By taking the elastic nature of flagella into account, linear and nonlinear equations of motions are derived and their solutions are presented.     

Cytoplasmic streaming inParamecium

Summary Certain species ofParamecium demonstrate rotational cytoplasmic streaming, in which most cytoplasmic particles and organelles flow along permanent route, in a constant direction. By means of novel methods of immobilization, observation and recording, some dynamic properties of cytoplasmic streaming have been described. It was found that the velocity profiles of coaxial layers of cytoplasm have a (parabolic) paraboidal shape and the mean output of cytoplasm flow in different examined zones of streaming is constant. As the consequence of randomly distributed elementary propulsion units within the cytoplasm, particles, which serve as markers of movement, exhibit movements of a saltatory nature; this form of movement is seen inParamecium streaming only in cases of error due to polarization of the saltating particles. Interaction of actin filaments and myosin is likely to occur under specific conditions in microcompartments of cytoplasm where local solations are generated eventually leading to contractions which might propagate on gelated neighbouring areas. Places of elementary contractions are scattered. Therefore the motile effect appears as streaming. Rotational cytoplasmic streaming inParamecium may serve as a convenient model for the study of the dynamics and function of cytoplasmic motility.     

A mathematical explanation of an increase in bacterial swimming speed with viscosity in linear-polymer solutions

Bacterial swimming speed is sometimes known to increase with viscosity. This phenomenon is peculiar to bacterial motion. Berg and Turner (Nature. 278:349-351, 1979) indicated that the phenomenon was caused by a loose, quasi-rigid network formed by polymer molecules that were added to increase viscosity. We mathematically developed their concept by introducing two apparent viscosities and obtained results similar to the experimental data reported before. Addition of polymer improved the propulsion efficiency, which surpasses the decline in flagellar rotation rate, and the swimming speed increased with viscosity.     

The Effect of ATP (Disodium Salt) upon Rotational Streaming

Through the continuous treatment with various solutions of ATP disodium salt the rotational streaming of the cytoplasma in barley root hairs has been stimulated about 1.2–1.7 times. With the concentrations employed the stimulation of the streaming did not depend on the external ATP supply, but on the initial rate of streaming. It is assumed that the main source of energy supporting the protoplasmic streaming is ATP. Therefore, the results obtained may be interpreted on the basis of variations in ATP content and its degradation products. The differences between initial rates of streaming are supposed to be due to variations of the endogenous ATP level. The ATP taken up probably stimulates the rotational streaming both through the supply of delivered energy and by lowering the cytoplasm viscosity. On the contrary, products of ATP hydrolysis increase the cytoplasm viscosity and induce a lowering or even cessation of the streaming.     

Swimming Using Surface Acoustic Waves

Microactuation of free standing objects in fluids is currently dominated by the rotary propeller, giving rise to a range of potential applications in the military, aeronautic and biomedical fields. Previously, surface acoustic waves (SAWs) have been shown to be of increasing interest in the field of microfluidics, where the refraction of a SAW into a drop of fluid creates a convective flow, a phenomenon generally known as SAW streaming. We now show how SAWs, generated at microelectronic devices, can be used as an efficient method of propulsion actuated by localised fluid streaming. The direction of the force arising from such streaming is optimal when the devices are maintained at the Rayleigh angle. The technique provides propulsion without any moving parts, and, due to the inherent design of the SAW transducer, enables simple control of the direction of travel.     

Cytoplasmic streaming inChara rhizoids

Summary In-vivo videomicroscopy ofChara rhizoids under 10^–4g demonstrated that gravity affected the velocities of cytoplasmic streaming. Both, the acropetal and basipetal streaming velocities increased on the change to microgravity. The endogenous difference in the velocities of the oppositely directed cytoplasmic streams was maintained under microgravity, yet the difference was diminished as the basipetal streaming velocity increased more than the acropetal streaming velocity. Direction and structure of microfilaments labeled by rhodamine-phalloidin had not changed after 6 min of microgravity.Abbreviations g gravitational acceleration - Nizemi slow rotating centrifuge microscope - Texus technological experiments under reduced gravity     

Contribution of NK(2) tachykinin receptors to propulsion in the rabbit distal colon

The role of the tachykinin neurokinin (NK)(2) receptors on rabbit distal colon propulsion was investigated by using two selective NK(2)-receptor antagonists, MEN-10627 and SR-48968. Experiments on colonic circular muscle strips showed that contractile responses to [beta-Ala(8)]NKA-(4-10) (1 nM-1 microM), a selective NK(2)-receptor agonist, were competitively antagonized by MEN-10627 (1-100 nM), whereas SR-48968 (0.1-10 nM) caused an insurmountable antagonism, thus confirming the difference in the mode of action of the two compounds. Colonic propulsion was elicited by distending a mobile rubber balloon with 0.3 ml (submaximal stimulus) or 1.0 ml (maximal stimulus) of water. The velocity of anal displacement of the balloon (mm/s) was considered the main propulsion parameter. At low concentrations (1.0-100 nM and 0.1-10 nM, respectively), MEN-10627 and SR-48968 facilitated the velocity of propulsion, whereas at high concentrations (100 nM and 1 microM, respectively) they decelerated propulsion. The excitatory and inhibitory effects of both antagonists were observed only with submaximal stimulus. We focused on the hypothesis that the facilitatory effect on propulsion may result from blockade of neuronal NK(2) receptors and the inhibitory effect from suppression of the excitatory transmission mediated by NK(2) receptors on smooth muscle cells. In the presence of N(G)-nitro-L-arginine (300 microM), a nitric oxide synthase inhibitor, MEN-10627, at a concentration (10 nM) that was found to accelerate propulsion in control experiments inhibited the velocity of propulsion. In the presence of threshold (1-10 nM) or full (1 microM) concentration of atropine, which inhibited to a great extent the velocity of propulsion, the inhibitory effect of MEN-10627 (1 microM) was markedly increased. In conclusion, in the rabbit distal colon NK(2) receptors may decelerate propulsion by activating a nitric oxide-dependent neuronal mechanism and may accelerate it by a postjunctional synergistic interaction with cholinergic muscarinic receptors.     

Structural basis of cytoplasmic streaming in Characean internodal cells. A hydrodynamic analysis

Summary Hydrodynamic equations were derived which relate the velocity profile of endoplasmic streaming with the motive force generated by active sliding of endoplasmic organelles in Characean internodal cells, under two implicit assumptions that (1) the sliding velocity of putative organelles is comparable to the streaming velocity of endoplasm, and (2) subcortical endoplasm is far less viscous than bulk endoplasm.The equations were extended so as to calculate the velocity profile in flattened or perfused internodal cells. Calculated profiles were basically consistent with reported patterns of streaming under these conditions.Utilizing published data, we deduce some hydrodynamic parameters of streaming, and predict the dimensions of putative organelles expected to drive entire cytoplasm. A revision for published values of the motive force of streaming is proposed.Hydrodynamic analyses made earlier on the spherical organelles are repeated. The results show that the organelles may generate streaming, depending on the configurationin vivo of fine filaments protruding from the body of the organelles.     

The ultrasonic degradation of biological macromolecules under conditions of stable cavitation. I. Theory,methods, and application to deoxyribonucleic acid

Solutions of calf thymus DNA have been degraded in the presence of vibrating air bubbles in ultrasonic fields of low power which would not normally induce ultrasonic cavitation. The DNA was degraded to a limiting intrinsic viscosity, after which further irradiation by ultrasound had little or no effect. This limiting intrinsic viscosity decreased with increase in the ultrasonic intensity. Previously developed theories have-been adapted to calculate the maximum velocity gradient associated with the streaming of the solution around such vibrating air bubbles. The tensile force which is induced and which acts on the DNA has been calculated on the basis of current theories of degradation by hydrodynamic shear. These calculations indicate that the degradation of the DNA by ultrasound under conditions of “stable cavitation” is mainly the result of the shearing forces engendered in the solution around the oscillating bubbles.     

Endoplasmic filaments generate the motive force for rotational streaming in Nitella

The streaming endoplasm of characean cells has been shown to contain previously unreported endoplasmic filaments along which bending waves are observed under the light microscope using special techniques. The bending waves are similar to those propagated along sperm tails causing propulsion of sperm. In Nitella there is reason to believe that nearly all of the filaments are anchored in the cortex and that their beating propels the endoplasm in which they are suspended. This hypothesis is supported by calculations in which typical and average wave parameters have been inserted into the classical hydrodynamic equations derived for sperm tail bending waves. These calculations come within an order of magnitude of predicting the velocity of streaming and they show that waves of the character described, propagated along an estimated 52 m of endoplasmic filaments per cell, must generate a total motive force per cell within less than an order of magnitude of the forces measured experimentally by others. If we assume that undulating filaments produce the force driving the endoplasm, then the method described for measuring the motive force could lead to a lower than actual value for the motive force, since both centrifugation and vacuolar perfusion would reverse the orientation of some filaments. Observations of the initiation of particle translation in association with the filaments suggest that particle transport and wave propagation, which occur at the same velocity, may both be dependent on the same process. The possibility that some form of contractility provides the motive force for filament flection and particle transport is discussed.     

The pattern of acropetal and basipetal cytoplasmic streaming velocities in Chara rhizoids and protonemata, and gravity effect on the pattern as measured by laser-Doppler-velocimetry

 The spatial pattern of acropetal and basipetal cytoplasmic streaming velocities has been studied by laser-Doppler-velocimetry (LDV) in the positively gravitropic (downward growing) rhizoids of Chara globularis Thuill. and for the first time in the negatively gravitropic (upward growing) protonemata. The LDV method proved to be precise and yielded reproducible results even when tiny differences in velocities were measured. In the apical parts of the streaming regions of both cell types, acropetal streaming was faster than basipetal streaming. Starting at the apical reversal point of streaming, the velocity increased basipetally with the distance from that point and became fairly constant close to the basal reversal point; subsequently, the velocity decreased slightly acropetally as the apical reversal point was again approached. There was no change in velocity at the basal reversal point. However, at the apical reversal point there was an abrupt decrease in velocity. The pattern of the ratio of acropetal to basipetal streaming velocity (VR) was a function of the relative distance of the site of measurement from the apical reversal point rather than a function of the absolute distance. Upon inversion of the rhizoids, the VR decreased on average by 3.8% (±0.4%), indicating that the effect of gravity on the streaming velocity was merely physical and without a physiological amplification. Rhizoids that had developed on the slowly rotating horizontal axis of a clinostat, and had never experienced a constant gravity vector, were similar to normally grown rhizoids with respect to VR pattern. In protonemata, the VR pattern was not significantly different from that in rhizoids although the direction of growth was inverse. In rhizoids, oryzalin caused the polar organization of the cell to disappear and nullified the differences in streaming velocities, and cytochalasin D decreased the velocity of basipetal streaming slightly more than that of acropetal streaming. Cyclopiazonic acid, known as an inhibitor of the Ca²⁺-ATPase of the endoplasmic reticulum, also reduced the streaming velocities in rhizoids, but had slightly more effect on the acropetal stream. It is possible that the endogenous difference in streaming velocities in both rhizoids and protonemata is caused by differences in the cytoskeletal organization of the opposing streams and/or loading of inhibitors (like Ca²⁺) from the apical/subapical zone into the basipetally streaming endoplasm. Received: 4 October 1999 / Accepted: 4 November 1999     

Optico-hydrodynamic properties of high molecular weight DNA from steady-state flow birefringence and viscosity at extremely low velocity gradients

The flow birefringence, extinction angles, and shear-dependent viscosity over a velocity gradient range of approximately 0.1–3 sec^?1 have been obtained for T2 bacteriophage DNA at low concentration in neutral aqueous buffer. The data are found to be interpretable and self-consistent in terms of subchain dynamical theory, including hydrodynamic, interactions and excluded volume, and the parameters characterizing these phenomena are in good agreement with the results of other hydrodynamic experiments and theoretical calculations. No necessity for modification of the subchain model in terms of limited extensibility or internal viscosity is found for high molecular weight DNA at the velocity gradients studied, although the latter cannot be ruled out on the basis of the present data. The Kuhn statistical segment length is determined from the intrinsic optical anisotropy and is estimated as 930 Å. Implications of these findings and their relation to appropriate dynamical models for DNA are discussed.     

Time-series analysis of measurements on living cells illustrated by analysis of particle movement in the cytoplasm of tomato root hairs

Summary Within a given root hair, the velocity of particle movement, here equated with cytoplasmic streaming, is usually very variable, making it difficult to distinguish experimentally-induced changes in velocity from those due to natural variability. Time-series analysis has been combined with piece-wise linear regression to provide an objective means of assessing the results of experiments in which the rate of streaming was recorded repeatedly from the same root hair. Ordinarily, regression and analysis of variance assume that the values in a data set are not strongly autocorrelated. These methods are applicable to sets of single observations (thus, they cannot be used with data obtained by repeated sampling of the same cell). By contrast, time-series analysis can take account of autocorrelations within the data and allows trends in the noise structure to be separated from treatment effects. The statistical methods described in the present paper are illustrated using the results from experiments in which the effect of -naphthalene acetic acid on streaming velocity in tomato root hairs was recorded. The conclusions reached are in accord with published accounts of variation in protoplasmic streaming and the known behaviour of cells in response to auxins. Our results also provide an explanation for the failure of some workers to observe any consistent changes in streaming velocity in response to exogenous auxin. The method described makes use of well documented statistical techniques and could be applied to other investigations in which sequential measurements of quantifiable parameters, such as fluorometric determination of intracellular pH or concentrations of calcium, are made on intact living cells.Abbreviations NAA -naphthalene acetic acid - ARMA auto-regressive moving average models - AIC akaike information criterion - d.f. degrees of freedom     

A study of protoplasmic streaming inPhysarum by laser Doppler spectroscopy

Summary Protoplasmic streaming in the slime moldPhysarum polycephalum has been characterized using laser Doppler spectroscopy. Measurement of the spectrum of scattered laser light permits simultaneous determination of the velocities of all particles in the laser beam, with the relative intensity from each particle proportional to its light scattering cross-section. Simple experimental modifications allow the tracking of the oscillations of the streaming velocities. Rhythmic wall contractions can be monitored simultaneously with the flow velocities. Interpretation of the Doppler spectra shows that a small fraction of the particles in the flowing protoplasm are moving with velocities two to four times greater than the characteristic velocities reported by optical microscopy. Transverse velocities in the tubes are nearly as great as the longitudinal velocities. The shape of the Doppler spectrum at the maximum of the oscillation cycle is consistent with a spatial velocity profile which is sharper than parabolic, presumably because of a viscosity gradient from the center to the walls of the plasmodial tubes. The shape of the Doppler spectrum of depolarized scattered light is of approximately the same form. The response of the plasmodium to increased temperature is an increase in the frequency of the velocity oscillations with little change in the magnitude of the velocities. The response of the plasmodium to very high intensities of laser light is to gel at the point of incidence.     

Actin-mediated bacterial propulsion: comet profile, velocity pulsations

The propulsion of bacteria under the action of an actin gel network is examined in terms of gel concentration dynamics. The model includes the elasticity of the network, the gel-bacterium interaction, the bulk and interface polymerization. A formula for the cruise velocity is obtained where the contributions to bacterial motility arising from elasticity and polymerization are made explicit. Higher velocities correspond to lower concentration peaks and longer tails, in agreement with experimental results. The condition for the onset of motion is explicitly given. The behavior of the system is explored by varying the growth rates and the gel elasticity. At steady state two regimes are found, respectively, of constant and pulsating velocity; in the latter case, the velocity undergoes sudden accelerations and subsequent recoveries. The transition to the pulsating regime is obtained by increasing the elastic response of the gel.     

A study of protoplasmic streaming in Nitella by laser Doppler spectroscopy.

Laser light scattered from particles in the streaming protoplasm of a living cell is shifted in frequency by the Doppler effect. The spectrum of the scattered light can be measured and interpreted to infer details of the velocity distribution in the protoplasm. We have developed this approach to study the protoplasmic streaming in the fresh-water alga Nitella. Our results indicate a characteristic flow pattern to which diffusion makes a negligible contribution. No difference in the velocity of particles of different size is indicated. The streaming velocity linearly with temperature with a supraoptimal temperature of 34 degrees C, and the velocity distribution becomes narrower at high temperatures. The protoplasmic streaming can be inhibited by laser light, and this effect has been used to study the photoresponse of the algae. Using beam diameters of about 50 mum, we have shown that the inhibition is very local, becoming minimal at a displacement of about 200 mum in the upstream direction and 400 mum in the downstream direction. Prolonged exposure produces a bleached area free of chloroplasts, which is three orders of magnitude less sensitive to photoinhibition.     

Variation in velocity of cytoplasmic streaming and gravity effect in characean internodal cells measured by laser-Doppler-velocimetry

Summary Velocities of cytoplasmic streaming were measured in internodal cells ofNitella flexilis L. andChara corallina Klein ex Willd. by laser-Doppler-velocimetry to investigate the possibility of non-statolith-based perception of gravity. This was recently proposed, based on a report of gravity-dependent polarity of cytoplasmic streaming. Our measurements revealed large spatial and temporal variation in streaming velocity within a cell, independent of the position of the cell with respect to the direction of gravity. In 58% of the horizontally positioned cells the velocities of acropetal and basipetal streaming, measured at opposite locations in the cell, differed significantly. In 45% of these, basipetal streaming was faster than acropetal streaming. In 60% of the vertically positioned cells however the difference was significant, downward streaming was faster in only 61% of these. When cell positions were changed from vertical to horizontal and vice versa the cells reacted variably. A significant difference between velocities in one direction, before and after the change, was observed in approx. 70% of the measurements, but the velocity was faster in the downward direction, as the second position, in only 70% of the significantly different. The ratio of basipetal to acropetal streaming velocities at opposite locations of a cell was quite variable within groups of cells with a particular orientation (horizontal, normal vertical, inverted vertical). On average, however, the ratio was close to 1.00 in the horizontal position and approx. 1.03 in the normal vertical position (basipetal streaming directed downwards), which indicates a small direct effect of gravity on streaming velocity. Individual cells, however, showed an increased, as well as a decreased, ratio when moved from the horizontal to the vertical position. No discernible effect of media (either Ca^{2 +}-buffered medium or 1.2% agar in distilled water) on the streaming velocities was observed. The above mentioned phenomenon of graviperception is not supported by our data.Abbreviations g gravitational acceleration (9.81 m/s²) - LDV laser-Doppler-velocimetry - VR velocity ratio Dedicated to Professor Peter Sitte on the occasion of his 65th birthday