Speed of the bacterial flagellar motor near zero load depends on the number of stator units

Proceedings of the National Academy of Sciences National Academy of Sciences (0)

RM Berry

Torque generated by the flagellar motor of Escherichia coli while driven backward.

Biophysical journal 76 (1999) 580-587

RM Berry, HC Berg

The technique of electrorotation was used to apply torque to cells of the bacterium Escherichia coli tethered to glass coverslips by single flagella. Cells were made to rotate backward, that is, in the direction opposite to the rotation driven by the flagellar motor itself. The torque generated by the motor under these conditions was estimated using an analysis that explicitly considers the angular dependence of both the viscous drag coefficient of the cell and the torque produced by electrorotation. Motor torque varied approximately linearly with speed up to over 100 Hz in either direction, placing constraints on mechanisms for torque generation in which rates of proton transfer for backward rotation are limiting. These results, interpreted in the context of a simple three-state kinetic model, suggest that the rate-limiting step in the torque-generating cycle is a powerstroke in which motor rotation and dissipation of the energy available from proton transit occur synchronously.

Absence of a barrier to backwards rotation of the bacterial flagellar motor demonstrated with optical tweezers.

Proceedings of the National Academy of Sciences of the United States of America 94 (1997) 14433-14437

RM Berry, HC Berg

A cell of the bacterium Escherichia coli was tethered covalently to a glass coverslip by a single flagellum, and its rotation was stopped by using optical tweezers. The tweezers acted directly on the cell body or indirectly, via a trapped polystyrene bead. The torque generated by the flagellar motor was determined by measuring the displacement of the laser beam on a quadrant photodiode. The coverslip was mounted on a computer-controlled piezo-electric stage that moved the tether point in a circle around the center of the trap so that the speed of rotation of the motor could be varied. The motor generated approximately 4500 pN nm of torque at all angles, regardless of whether it was stalled, allowed to rotate very slowly forwards, or driven very slowly backwards. This argues against models of motor function in which rotation is tightly coupled to proton transit and back-transport of protons is severely limited.

Torque generated by the bacterial flagellar motor close to stall.

Biophysical journal 71 (1996) 3501-3510

RM Berry, HC Berg

In earlier work in which electrorotation was used to apply external torque to tethered cells of the bacterium Escherichia coli, it was found that the torque required to force flagellar motors backward was considerably larger than the torque required to stop them. That is, there appeared to be substantial barrier to backward rotation. Here, we show that in most, possibly all, cases this barrier is an artifact due to angular variation of the torque applied by electrorotation, of the motor torque, or both; the motor torque appears to be independent to speed or to vary linearly with speed up to speeds of tens of Hertz, in either direction. However, motors often break catastrophically when driven backward, so backward rotation is not equivalent to forward rotation. Also, cells can rotate backward while stalled, either in randomly timed jumps of 180 degrees or very slowly and smoothly. When cells rotate slowly and smoothly backward, the motor takes several seconds to recover after electrorotation is stopped, suggesting that some form of reversible damage has occurred. These findings do not affect the interpretation of electrorotation experiments in which motors are driven rapidly forward.

Mechanical limits of bacterial flagellar motors probed by electrorotation.

Biophysical journal 69 (1995) 280-286

RM Berry, L Turner, HC Berg

We used the technique of electrorotation to apply steadily increasing external torque to tethered cells of the bacterium Escherichia coli while continuously recording the speed of cell rotation. We found that the bacterial flagellar motor generates constant torque when rotating forward at low speeds and constant but considerably higher torque when rotating backward. At intermediate torques, the motor stalls. The torque-speed relationship is the same in both directional modes of switching motors. Motors forced backward usually break, either suddenly and irreversibly or progressively. Motors broken progressively rotate predominantly at integral multiples of a unitary speed during the course of both breaking and subsequent recovery, as expected if progressive breaking affects individual torque-generating units. Torque is reduced by the same factor at all speeds in partially broken motors, implying that the torque-speed relationship is a property of the individual torque-generating units.

Defective escape mutants of HIV.

J Theor Biol 171 (1994) 387-395

RM Berry, MA Nowak

The virological literature presents two broad types of defective virus mutants that can alter the outcome of viral infection. In some infections, defective interfering particles reduce the replication of wild-type virus and lead to an attenuated or persistent infection. In other cases, very specific and highly pathogenic defective mutants lead to virulent disease in the presence of a much less pathogenic but replication-competent helper virus. Here, we outline the theoretical possibility that defective mutants of HIV, which escape from some of the immune responses directed at the wild-type virus, can have a positive effect on total virus growth in HIV infections. The high error rate of HIV may generate many mutants that have some altered epitope (escape mutants), but at the cost of greatly reduced or completely impaired reproductive abilities. If these mutants retain some ability to impair immune cell function, then the production of such "defective escape" mutants may enhance overall virus reproduction. This will be illustrated by a mathematical model.

Correlated ion flux through parallel pores: application to channel subconductance states.

J Membr Biol 133 (1993) 77-84

RM Berry, DT Edmonds

Many ion channels that normally gate fully open or shut have recently been observed occasionally to display well-defined subconductance states with conductances much less than those of the fully open channel. One model of this behavior is a channel consisting of several parallel pores with a strong correlation between the flux in each pore such that, normally, they all conduct together but, under special circumstances, the pores may transfer to a state in which only some of them conduct. This paper introduces a general technique for modeling correlated pores, and explores in detail by computer simulation a particular model based upon electric interaction between the pores. Correlation is obtained when the transient electric field of ions passing through the pores acts upon a common set of ionizable residues of the channel protein, causing transient changes in their effective pK and hence in their charged state. The computed properties of such a correlated parallel pore channel with single occupation of each pore are derived and compared to those predicted for a single pore that can contain more than one ion at a time and also to those predicted for a model pore with fluctuating barriers. Experiments that could distinguish between the present and previous models are listed.

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

Biophys J 64 (1993) 961-973

RM Berry

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.

Carrier-like behaviour from a static but electrically responsive model pore.

Journal of theoretical biology 154 (1992) 249-260

R Berry, DT Edmonds

Because of the low dielectric constant of most proteins and lipids, the electric field of an ion passing through a narrow pore is long range and will interact with neighbouring ionizable residues of the channel protein. The electrical structure of the channel may thus change transiently in response to an ion passing through the pore. Model calculations then reveal that the ratio of the unidirectional ion fluxes may approach 1 as expected for a carrier or shuttling ionophore rather than the Ussing ratio expected for a pore. Saturation behaviour also becomes carrier-like. Computer simulation is reported showing a continuous variation between pore-like and carrier-like behaviour as the parameters of the system are allowed to change smoothly.

The proton ladder, a static mechanism for ion/proton coports and counterports

European Biophysics Journal 20 (1991) 241-245

DT Edmonds, R Berry

An ion/proton counterport is formed simply by locating a chain of ionizable residues connected by a proton conducting path near a passive ion pore which spans the membrane. The electric coupling between the ion in transit through the pore and the residues can ensure that for each ion passing through the pore in one direction a proton is driven along the chain of ionizable residues (the proton ladder) in the same or in the opposite direction. The mechanism is symmetrical in that a trans-membrane ion gradient may drive protons against their electrochemical potential gradient or a proton gradient may drive ions against theirs. The mechanism is applicable to cation or anion channels and to coports or counterports. No mechanical motion is required other than the motion of the ions and the protons. Monte Carlo computer simulations are performed on the model and its predicted properties are listed. The new type of counterport model is compared with currently used models. © 1991 Springer-Verlag.