Anatoly b kolomeisky
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Anatoly B. Kolomeisky. UNDERSTANDING MECHANOCHEMICAL COUPLING IN KINESINS USING FIRST-PASSAGE PROCESSES. Collaboration: Alex Popov, Evgeny Stukalin – Rice University Prof. Michael E. Fisher - University of Maryland Prof. Ben Widom – Cornell University Financial Support:

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Anatoly b kolomeisky

Anatoly B. Kolomeisky

UNDERSTANDING MECHANOCHEMICAL COUPLING IN KINESINS USING FIRST-PASSAGE PROCESSES


Anatoly b kolomeisky

Collaboration:

Alex Popov, Evgeny Stukalin – Rice University

Prof. Michael E. Fisher -University of Maryland

Prof. Ben Widom – Cornell University

Financial Support:

National Science Foundation

Dreyfus Foundation

Welch Foundation

Rice University


Publications

PUBLICATIONS:

  • J. Stat. Phys., 93, 633 (1998).

  • PNAS USA, 96, 6597 (1999).

  • Physica A, 274, 241 (1999).

  • Physica A, 279, 1 (2000).

  • J. Chem. Phys., 113, 10867 (2000).

  • PNAS USA, 98, 7748 (2001).

  • J. Chem. Phys., 115, 7253 (2001).

  • PNAS USA, 98, 7748 (2001).

  • Biophys. J., 84, 1642 (2003).


Motor proteins

Motor Proteins

Enzymes that convert the chemical energy into mechanical work

Functions: cell motility, cellular transport, cell division and growth, muscles, …

Courtesy of Marie Curie Research Institute, Molecular Motor Group


Motor proteins1

Motor Proteins:

myosin-II

kinesin

RNA-polymeraze

F0F1-ATPase

There are many types:linear, rotational, processive, non-processive


Motor proteins2

Motor Proteins

Properties:

Non-equilibrium systems

Velocities: 0.01-100 mm/s

Step Sizes: 0.3-40 nm

Forces: 1-60 pN

Fuel: hydrolysis of ATP, or related compound,polymerization

Efficiency: 50-100% (!!!)


Motor proteins3

Motor Proteins

Main Problems:

What mechanism of motility? How many mechanisms?


Theoretical modeling

THEORETICAL MODELING

  • Thermal Ratchet Models

periodic spatially asymmetric potentials

2)Multi-State Chemical Kinetic (Stochastic) Models

sequence of discrete biochemical states


Ratchet models

Idea: motor proteins are particles that move in periodic but asymmetric potentials, stochastically switching between them

Ratchet Models

Advantages:

1) continuum description, well developed formalism;

2) convenient for numerical calculations and simulations;

3) small number of parameters;

  • Disadvantages:

  • mainly numerical or simulations results;

  • results depend on potentials used in calculations;

  • hard to make quantitative comparisons with experiments;

  • not flexible in description of complex biochemical networks;


Multi state chemical kinetic stochastic models

Multi-State Chemical Kinetic (Stochastic) Models

Assumption: themotor proteinmoleculesteps through a sequence ofdiscrete biochemical states


Multi state chemical kinetic stochastic models1

Multi-State Chemical Kinetic (Stochastic) Models

  • Advantages:

  • Exact results

  • Agreement with biochemical observations

  • Flexibility in description of complex biochemical systems

  • Agreement with experiments

  • Disadvantages:

  • Discreteness

  • Mathematical complexity

  • Large number of parameters


Single molecules experiments

Single-Molecules Experiments

Optical Trap Experiment:

laser

bead

kinesin

microtubule

Optical trap works like an electronic spring


Experiments on kinesin

EXPERIMENTS ON KINESIN

optical force clamp with a feedback-driven optical trap

Visscher,Schnitzer,Block (1999) Nature 400, 184-189

step-size d=8.2 nm

precise observations:

mean velocityV(F,[ATP])

stall force

dispersion D(F,[ATP])

mean run lengthL(F,[ATP])


Theoretical problems

Theoretical Problems:

  • Description of biophysical properties of motor proteins (velocities, dispersions, stall forces, …) as the functions of concentrations and external loads

  • Detailed mechanism of motor proteins motility

  • coupling between ATP hydrolysis and the protein motion

  • stepping mechanism – hand-over-hand versus inchworm

  • conformational changes during the motion


Our theoretical approach

OUR THEORETICAL APPROACH

N=4model

j=0,1,2,…,N-1 – intermediate biochemical states

kinesin/

microtubule/ADP

kinesin/

microtubule/ATP

kinesin/

microtubule/ADP/Pi

kinesin/

microtubule


Our theoretical approach1

OUR THEORETICAL APPROACH

our model

periodic hopping model on 1D lattice

exact and explicit expressions for asymptotic (long-time) for any N!

Derrida, J. Stat. Phys. 31 (1983) 433-450

drift velocity

dispersion

x(t) – spatial displacement along the motor track

randomness

bound!r >1/N

stall force


Our theoretical approach2

OUR THEORETICAL APPROACH

Effect of an external loadF:

load distribution factors

activation barrier

F >0

F=0

j

j+1

j

j+1


Results for kinesins

RESULTS FOR KINESINS

stall forcedepends on [ATP]

Michaelis-Mentenplots

N=2model

F=3.59 pN

F=1.05 pN


Results for kinesins1

RESULTS FOR KINESINS

force-velocitycurves

randomness


Mechanochemical coupling in kinesins

Mechanochemical Coupling in Kinesins

  • How many molecules of ATP are consumed per kinesin step?

  • Is ATP hydrolysis coupled to forward and/or backward steps?

Nature Cell Biology, 4, 790-797 (2002)


Mechanochemical coupling

Mechanochemical Coupling

  • Kinesin molecules hydrolyze a single ATP molecule per 8-nm advance

  • The hydrolysis of ATP molecule is coupled to either the forward or the backward movement (!!!!!!!!!!)

Schnitzer and Block, Nature, 388, 386-390 (1997)

Hua et al., Nature, 388, 390-394 (1997)

Coy et al., J. Biol. Chem., 274, 3667-3671 (1999)

Problem: back steps ignored in the analysis

Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)

Backward steps are taken into account


Mechanochemical coupling1

Mechanochemical Coupling

Investigation of kinesin motor proteins motion using optical trapping nanometry system

Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)


Mechanochemical coupling2

Mechanochemical Coupling

Fraction of 8-nmforward and backward steps, and detachments as a function of the force at different ATP concentrations

circles - forward steps;

triangles - backward steps;

squares – detachments

Stall force – when the ratio of forward to backward steps =1

Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)


Mechanochemical coupling3

Mechanochemical Coupling

Dwell times between the adjacent stepwise movements

Dwell times of the backward steps+detachments are the same as for the forward8-nm steps

Both forward and backward movements of kinesin molecules are coupled to ATP hydrolysis

Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)


Mechanochemical coupling4

Mechanochemical Coupling

Branched kinetic pathway modelwith asymmetricpotential of the activation energy

Idea: barrier to the forward motion is lower than for the backward motion

Conclusion:kinesin hydrolyses ATP at any forward or backward step

Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)


Mechanochemical coupling5

Mechanochemical Coupling

  • PROBLEMS:

  • Backward biochemical reactions are not taken into account

  • Asymmetric potential violates the periodic symmetry of the system and the principle of microscopic reversibility

  • Detachments are not explained

Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)


Our approach

Our Approach

The protein molecule moves from one binding site to another one through the sequence of discrete biochemical states, i.e., only forward motions are coupled with ATP hydrolysis

Random walker hopping on a periodic random infinite 1D lattice

Dwell times – mean first-passage times;Fractions – splitting probabilities


Our approach1

Our Approach

N,j– the probability that Nis reached before –N, starting from the site j

Boundary conditions:

N.G. van Kampen, Stochastic Processes in Physics and Chemistry, Elseiver, 1992


Our approach2

Our Approach

-splitting probability to go to site N, starting from the site 0,

fraction of forward steps

fraction of backward steps


Our approach3

Our Approach

TN,j – mean first-passage time to reach N, starting from j

TN,0 – dwell time for the forward motion;

T-N,0 – dwell time for the backward motion

with


Our approach4

Our Approach

Important observation:

Dwell times for the forward and backward steps are the same, probabilities are different

Drift velocity


Our approach5

Our Approach

With irreversible detachments

j

-probability to dissociate before reaching N or -N, starting from j

- fractions of steps forward, backward and detachments


Our approach6

Our Approach

With irreversible detachments

j

Define new parameters:

j – the solution of matrix equation

-vector

matrix elements


Our approach7

Our Approach

With irreversible detachments

j

Model with detachments

Model without detachments

N=1case:


Our approach8

Our Approach

With irreversible detachments

j

Description of experimental data using N=2 model; reasonable for kinesins

Fisher and Kolomeisky, PNAS USA, 98, 7748 (2001).

Load dependence of rates


Comparison with experiments

Comparison with Experiments

Fractions of forward and backward steps, and detachments

[ATP]=1mM

[ATP]=10M


Comparison with experiments1

Comparison with Experiments

Dwell times before forward and backward steps, and before the detachments at different ATP concentrations


Application for myosin v

APPLICATION FOR MYOSIN-V

N=2model

mean forward-step first-passage time

Kolomeisky and Fisher, Biophys. J., 84, 1642 (2003)


Conclusions

CONCLUSIONS

  • Analysis of motor protein motility using first-passage processes is presented

  • Effect of irreversible detachments is taken into account

  • Our analysis of experimental data suggests that 1 ATP molecule is hydrolyzed when the kinesin moves forward 1 step


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