Efficiency of interacting molecular motors
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Efficiency of interacting molecular motors František Slanina [email protected] www.fzu.cz/~slanina. Brownian motion. Maxwell d e mon. Heats hot. Cools cold. Smoluchows ki r atchet. Granular r atchet. Feynman r atchet. On-off ratchet. Thermal ratchet. Pump: rocking ratchet.

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Efficiency of interacting molecular motorsFrantišek Slanina

[email protected]

www.fzu.cz/~slanina



Maxwell demon

Heats

hot

Cools

cold


Smoluchowski ratchet


Granular ratchet


Feynman ratchet








cytoskeletal traffic



myosin

dynein

kinesin




Ribosomes

ASEP (B.Derrida)


RNA polymerase

„traffic jams“

„Christmass tree“


Membrane tubes

„traffic jam“


“reversible” ratchet

Spatial

periodicity

Temporal

periodicity


Potential

Hopping probabilities

Measured:

expedited

absorbed



(full)

(empty)







Mean-field approximation

Step I: “stroboscopic trick”

Time within period

which period

Position within period

Many hops per unit time

Time-independent rates

Time-independent master equation


Mean-field

Step II: effective potential

MF1

MF2

or: effective hopping probability

Poisson distribution parameter


Mean-field

or: effective hopping probability

MF3


Recursion: first step

For calculation of

On condition particle at x

On condition two particles at x


Recursion: second step

For calculation of

On condition particles at x and y

Recursion: and so on…



Comparison of MF schemes

MF2

MF1

simulation

MF3


Phase diagram

Non-optimizable phase

MF1

MF1

simulation

optimizable phase


Work distribution

g = 0.12

g = 0


Energy balance

current

efficiency

energy input


Large deviations

Fluctuation theorem?

l.d.f.


Conclusions

  • Efficiency increased by not too strong interaction

  • Current reversals when interaction and/or density increases

  • Energetic, rather than entropic effect

  • Complex behavior of response

  • Large deviations: non-Gaussian

Outlook

  • Realistic model of myosin V

  • Clarify fluctuation symmetries

Thanks: GAČR No. 202/07/0404


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