Viscous Dynamics of Lyme Disease and Syphilis Spirochetes Reveal Flagellar Torque and Drag

Abstract

The spirochetes that cause Lyme disease (Borrelia burgdorferi) and syphilis (Treponema pallidum) swim through viscous fluids, such as blood and interstitial fluid, by undulating their bodies as traveling, planar waves. These undulations are driven by rotation of the flagella within the periplasmic space, the narrow (∼20-40 nm in width) compartment between the inner and outer membranes. We show here that the swimming speeds of B. burgdorferi and T. pallidum decrease with increases in viscosity of the external aqueous milieu, even though the flagella are entirely intracellular. We then use mathematical modeling to show that the measured changes in speed are consistent with the exertion of constant torque by the spirochetal flagellar motors. Comparison of simulations, experiments, and a simple model for power dissipation allows us to estimate the torque and resistive drag that act on the flagella of these major spirochetal pathogens.

Vancomycin Reduces Cell Wall Stiffness and Slows Swim Speed of the Lyme Disease Bacterium

“…Rotation of the flagella within the periplasm causes the waveform to propagate, leading to a traveling wave undulation of the entire body (10). Mathematical modeling has shown that the elastic interaction between the flagella and the cell body is sufficient to generate the planar waveform of the bacteria (11) and that rotation of the flagella will lead to traveling wave deformations, similar to what is observed experimentally (12,13). This mathematical modeling suggests that a key factor in determining the shape and motility of B. burgdorferi is the ratio of the flagellar stiffness to that of the cell body.…”

“…Interestingly, these bacteria have similar morphologies and motility mechanisms, which suggests that the shape of these bacteria may be extremely important to their ability to invade host tissue. A mathematical model has been developed that can explain the shape and movements of both of these pathogens (11,13,29). Although the model agrees well with the changes in velocity that accompany alterations in the external environment (13), it remains to be shown whether it accurately represents how speed and morphology are affected when the biophysical parameters of the organism are altered.…”

“…A mathematical model has been developed that can explain the shape and movements of both of these pathogens (11,13,29). Although the model agrees well with the changes in velocity that accompany alterations in the external environment (13), it remains to be shown whether it accurately represents how speed and morphology are affected when the biophysical parameters of the organism are altered. This question is important, since many antibiotics directly affect the cell wall in bacteria and motility is essential for the pathogenesis of Lyme disease (6-8) (and, by inference, is likely essential for syphilis pathogenesis, as well (13)).…”

“…Previous modeling developed a small-amplitude model for the swimming of B. burgdorferi (12,13). For the simulations reported here, we have further developed this model to account for large deformations.…”

“…An in-house tracking algorithm coded in MATLAB (The MathWorks, Natick, MA) was utilized to extract the center-of-mass position, cell orientation, and amplitude and wavelength of the flat-wave shape from the time-lapse images, as previously described by Harman et al (13,25). Velocity for spirochetes that remained in the field of view for at least 30 frames was determined using the difference between the center-of-mass positions between subsequent frames.…”