Torque generated by the bacterial flagellar motor close to stall.

Biophysical journal 71:6 (1996) 3501-3510

Authors:

RM Berry, HC Berg

Abstract:

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 69:1 (1995) 280-286

Authors:

RM Berry, L Turner, HC Berg

Abstract:

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 171:4 (1994) 387-395

Authors:

RM Berry, MA Nowak

Abstract:

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 133:1 (1993) 77-84

Authors:

RM Berry, DT Edmonds

Abstract:

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 64:4 (1993) 961-973

Abstract:

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.