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Mathematical Modeling of Bacterial Motility


Bacterial motility is an interesting field of biophysics with many open mysteries. Mathematical models integrate experimental observations into a conceptual framework that elucidates the underlying mechanisms. They also provide physical insight into the general principles that govern the motion, energy conversion, and signal transduction. This thesis summarizes models for two gliding bacteria: mycoplasma and myxobacteria.

The model for mycoplasma motility sheds light on how temperature affects the gliding speed of the cell by influencing the rupture dynamics of motor-substrate adhesion. Mycoplasmas exhibit a novel, substrate-dependent gliding motility that is driven by about 400 “leg” proteins. The legs interact with the substrate and transmit the forces generated by an assembly of ATPase motors. The velocity of the cell increases linearly by nearly 10 fold over a narrow temperature range of 10 – 40°C. This corresponds to an Arrhenius factor that decreases from ~ 45 kBT at 10°C to ~ 10 kBT at 40°C. On the other hand, load-velocity curves at different temperatures extrapolate to nearly the same stall force, suggesting a temperature-insensitive force generation mechanism near stall. The model proposes a leg-substrate interaction mechanism that explains the intriguing temperature sensitivity of this motility. The large Arrhenius factor at low temperatures comes about from the additive effect of many smaller energy barriers arising from many substrate binding sites at the distal end of the leg protein. The Arrhenius dependence attenuates at high temperature due to two factors: (1) the reduced effective multiplicity of energy barriers intrinsic to the multiple-site binding mechanism, and (2) the temperature-sensitive weakly facilitated leg release that curtails the power stroke. The model suggests an explanation for the similar steep, sub-Arrhenius temperature-velocity curves observed in many molecular motors, such as kinesin and myosin, wherein the temperature behavior is dominated not by the catalytic biochemistry, but by the motor-substrate interaction.

The model for myxobacteria explains the mechanism of the so-called Adventurous, or A-motility system. A-motility in myxobacteria recruits the bacterial cytoskeleton protein MreB along with proton-driven motors homologous to the stators of the bacterial flagellar motor. This is the first known prokaryotic example where the bacterial cytoskeleton mediates cell motility. The mechanism may be widespread in bacteria, since both MreB homologs and MotA-MotB homologs are common across a variety of bacterial species. The model introduces cargo-mediated force generation as a key assumption. There are two types of cargo, one causing high drag and the other low drag. They are unequally distributed along the two strands of the double helical track, thereby creating an unbalanced force that drives cell motion. The unequal distribution results from the unequal cargo exchange rates at the cell poles. And these rates are controlled by biochemical oscillators. Besides reproducing the cell velocity and the rotational speed of the track, the model also explains many other experimental observations on myxobacteria motility, including periodic reversals of the cell motion, short pauses before cell reversals, and a whole series of experiments showing the dynamics of motility-related protein clusters at the cell poles and periodically along the substrate interface.

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