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Anatoly B. Kolomeisky

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

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  1. Anatoly B. Kolomeisky UNDERSTANDING MECHANOCHEMICAL COUPLING IN KINESINS USING FIRST-PASSAGE PROCESSES

  2. 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

  3. 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).

  4. 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

  5. Motor Proteins: myosin-II kinesin RNA-polymeraze F0F1-ATPase There are many types:linear, rotational, processive, non-processive

  6. 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% (!!!)

  7. Motor Proteins Main Problems: What mechanism of motility? How many mechanisms?

  8. THEORETICAL MODELING • Thermal Ratchet Models periodic spatially asymmetric potentials 2)Multi-State Chemical Kinetic (Stochastic) Models sequence of discrete biochemical states

  9. 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;

  10. Multi-State Chemical Kinetic (Stochastic) Models Assumption: themotor proteinmoleculesteps through a sequence ofdiscrete biochemical states

  11. 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

  12. Single-Molecules Experiments Optical Trap Experiment: laser bead kinesin microtubule Optical trap works like an electronic spring

  13. 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])

  14. 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 • …

  15. 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

  16. 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

  17. OUR THEORETICAL APPROACH Effect of an external loadF: load distribution factors activation barrier F >0 F=0 j j+1 j j+1

  18. RESULTS FOR KINESINS stall forcedepends on [ATP] Michaelis-Mentenplots N=2model F=3.59 pN F=1.05 pN

  19. RESULTS FOR KINESINS force-velocitycurves randomness

  20. 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)

  21. 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

  22. Mechanochemical Coupling Investigation of kinesin motor proteins motion using optical trapping nanometry system Nishiyama et al., Nature Cell Biology, 4, 790-797 (2002)

  23. 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)

  24. 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)

  25. 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)

  26. 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)

  27. 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

  28. 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

  29. Our Approach -splitting probability to go to site N, starting from the site 0, fraction of forward steps fraction of backward steps

  30. 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

  31. Our Approach Important observation: Dwell times for the forward and backward steps are the same, probabilities are different Drift velocity

  32. Our Approach With irreversible detachments j -probability to dissociate before reaching N or -N, starting from j - fractions of steps forward, backward and detachments

  33. Our Approach With irreversible detachments j Define new parameters: j – the solution of matrix equation -vector matrix elements

  34. Our Approach With irreversible detachments j Model with detachments Model without detachments N=1case:

  35. 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

  36. Comparison with Experiments Fractions of forward and backward steps, and detachments [ATP]=1mM [ATP]=10M

  37. Comparison with Experiments Dwell times before forward and backward steps, and before the detachments at different ATP concentrations

  38. APPLICATION FOR MYOSIN-V N=2model mean forward-step first-passage time Kolomeisky and Fisher, Biophys. J., 84, 1642 (2003)

  39. 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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