In some phototrophic bacteria the reaction centre's pmf drives the flagellar motor…
PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics
Forces, Machines and Signals, Ch Proton gradients, ATP synthesis and photosynthesis
Problem
In some phototrophic bacteria the reaction centre's pmf drives the flagellar motor directly, with no ATP intermediate; mechanically the motor is the same rotary class of machine as the F0 rotor met with the F1 motor, run in the same sense (protons flowing inward down the gradient drive rotation).
((a)) The antenna has N=200 bacteriochlorophylls, each absorbing on average 0.4 photons per second in dim light. If the reaction centre can turn over at most 50s−1, calculate the ratio of the antenna's total delivery rate to this turnover rate, and state whether the centre is under-supplied, just supplied, or saturated.
((b)) Each successful turnover pumps one proton net across the membrane. At the steady turnover rate of 50s−1, calculate the proton current in amperes.
((c)) The bacterium's pmf is Δp=150mV. Using P=IΔp, calculate the power delivered to the flagellar motor, and then, taking the motor's rotational drag coefficient in water as ζr=4×10−21Nms (so that P=ζrΩ2 at steady rotation, as for any rotor at low Reynolds number), estimate the angular velocity Ω this single reaction centre's proton current could sustain. Compare it with a typical flagellar rotation rate of order 630rads−1 (100Hz).