Efficiency of interacting molecular motors
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Efficiency of interacting molecular motors František Slanina [email protected] fzu.cz/~slanina PowerPoint PPT Presentation


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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 motors František Slanina [email protected] fzu.cz/~slanina

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Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Efficiency of interacting molecular motorsFrantišek Slanina

[email protected]

www.fzu.cz/~slanina


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Brownian motion


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Maxwell demon

Heats

hot

Cools

cold


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Smoluchowski ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Granular ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Feynman ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

On-off ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Thermal ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Pump: rocking ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Quantum ratchet


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Muscles


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

cytoskeleton


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

cytoskeletal traffic


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Cell division


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

myosin

dynein

kinesin


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Hand-over-hand mechanism


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Neurons


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Ribosomes

ASEP (B.Derrida)


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

RNA polymerase

„traffic jams“

„Christmass tree“


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Membrane tubes

„traffic jam“


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

“reversible” ratchet

Spatial

periodicity

Temporal

periodicity


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Potential

Hopping probabilities

Measured:

expedited

absorbed


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Without interaction


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

(full)

(empty)


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

With interaction


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Gained efficiency


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

At strong interaction


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Response


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Response


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

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


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Mean-field

Step II: effective potential

MF1

MF2

or: effective hopping probability

Poisson distribution parameter


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Mean-field

or: effective hopping probability

MF3


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Recursion: first step

For calculation of

On condition particle at x

On condition two particles at x


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Recursion: second step

For calculation of

On condition particles at x and y

Recursion: and so on…


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Mean-field MF1


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Comparison of MF schemes

MF2

MF1

simulation

MF3


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Phase diagram

Non-optimizable phase

MF1

MF1

simulation

optimizable phase


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Work distribution

g = 0.12

g = 0


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Energy balance

current

efficiency

energy input


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

Large deviations

Fluctuation theorem?

l.d.f.


Efficiency of interacting molecular motors franti ek slanina slanina fzu cz fzu cz slanina

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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