Detectable states, cycle fluxes, and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis

Abstract

The process by which a kinesin motor couples its ATPase activity with concerted mechanical handover-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.

Keywords

graph theory / molecular motor / state detection / cycle flux / motility scaling

References

[1] R. D.Vale and R. A.Milligan, The way things move: Looking under the hood of molecular motor proteins, Science288(5463), 88 (2000)

[2] S. M.Block, Kinesin motor mechanics: Binding, stepping, tracking, gating, and limping, Biophys. J. 92(9), 2986(2007)

[3] A.Gennerichand R. D.Vale, Walking the walk: How kinesin and dynein coordinate their steps, Curr. Opin. Cell Biol. 21(1), 59(2009)

[4] S. S.Rosenfeld, P. M.Fordyce, G. M.Jefferson, P. H.King, and S. M.Block, Stepping and Stretching: How kinesin uses internal strain to walk processively, J. Biol. Chem. 278(20), 18550(2003)

[5] L. M.Klumpp, A.Hoenger, and S. P.Gilbert, Kinesin’s second step, Proc. Natl. Acad. Sci. USA101(10), 3444(2004)

[6] N. R.Guydoshand S. M.Block, Backsteps induced by nucleotide analogs suggest the front head of kinesin is gated by strain, Proc. Natl. Acad. Sci. USA103(21), 8054(2006)

[7] D. D.Hackney, Evidence for alternating head catalysis by kinesin during microtubule-stimulated ATP hydrolysis, Proc. Natl. Acad. Sci. USA91(15), 6865(1994)

[8] Y. Z.Maand E. W.Taylor, Interacting head mechanism of microtubule-kinesin ATPase, J. Biol. Chem. 272(2), 724(1997)

[9] S.Uemuraand S.Ishiwata, Loading direction regulates the affinity of ADP for kinesin, Nat. Struct. Biol. 10(4), 308(2003)

[10] A. B.Asenjo,N.Krohn, and H.Sosa, Configuration of the two kinesin motor domains during ATP hydrolysis, Nat. Struct. Biol. 10(10), 836(2003)

[11] A.Yildiz, M.Tomishige, R. D.Vale, and P. R.Selvin, Kinesin walks hand-over-hand, Science303(5658), 676(2004)

[12] T.Mori, R. D.Vale, and M.Tomishige, How kinesin waits between steps, Nature450(7170), 750(2007)

[13] A. B.Asenjoand H.Sosa, A mobile kinesin-head intermediate during the ATP-waiting state, Proc. Natl. Acad. Sci. USA106(14), 5657(2009)

[14] K.Visscher, M. J.Schnitzer, and S. M.Block, Single kinesin molecules studied with a molecular force clamp, Nature400(6740), 184(1999)

[15] W. R.Schief, R. H.Clark, A. H.Crevenna, and J.Howard, Inhibition of kinesin motility by ADP and phosphate supports a hand-over-hand mechanism, Proc. Natl. Acad. Sci. USA101(5), 1183(2004)

[16] N. J.Carterand R. A.Cross, Mechanics of the kinesin step, Nature435(7040), 308(2005)

[17] M. J.Schnitzer, K.Visscher, andS. M.Block, Force production by single kinesin motors, Nat. Cell Biol.2(10), 718(2000)

[18] K. S.Thorn, J. A.Ubersax, and R. D.Vale, Engineering the processive run length of the kinesin motor, J. Cell Biol.151(5), 1093(2000)

[19] J.Yajima, M. C.Alonso, R. A.Cross, and Y. Y.Toyoshima, Direct long-term observation of kinesin processivity at low load, Curr. Biol.12(4), 301(2002)

[20] K.Kawaguchiand S.Ishiwata, Temperature dependence of force, velocity, and processivity of single kinesin molecules, Biochem. Biophys. Res. Commun.272(3), 895(2000)

[21] I.Naraand S.Ishiwata, Processivity of kinesin motility is enhanced on increasing temperature, Biophysics2, 13(2006)

[22] S.Uemura, K.Kawaguchi, J.Yajima, M.Edamatsu, Y. Y.Toyoshima, and S.Ishiwata, Kinesin-microtubule binding depends on both nucleotide state and loading direction, Proc. Natl. Acad. Sci. USA99(9), 5977(2002)

[23] N. R.Guydoshand S. M.Block, Direct observation of the binding state of the kinesin head to the microtubule, Nature461(7260), 125(2009)

[24] A.Yildiz, M.Tomishige, A.Gennerich, and R. D.Vale, Intramolecular strain coordinates kinesin stepping behavior along microtubules, Cell134(6), 1030(2008)

[25] Q.Shaoand Y. Q.Gao, On the hand-over-hand mechanism of kinesin, Proc. Natl. Acad. Sci. USA103(21), 8072(2006)

[26] W. W.Zheng, D.Fan, M.Feng, and Z. S.Wang, Loadresisting capacity of kinesin, Phys. Biol. 6(3), 036002(2009)

[27] Z. S.Wang, M.Feng, W. W.Zheng, and D. G.Fan, Kinesin is an evolutionarily fine-tuned molecular ratchetand- pawl device of decisively locked directionality, Biophys. J.93(10), 3363(2007)

[28] C.Hyeonand J. N.Onuchic, Internal strain regulates the nucleotide binding site of the kinesin leading head, Proc. Natl. Acad. Sci. USA104(7), 2175(2007)

[29] Y.Okadaand N.Hirokawa, Mechanism of the singleheaded processivity: Diffusional anchoring between the K-loop of kinesin and the C terminus of tubulin, Proc. Natl. Acad. Sci. USA97(2), 640(2000)

[30] S.Liepeltand R.Lipowsky,Kinesin’s network of chemomechanical motor cycles, Phys. Rev. Lett.98(25), 258102(2007)

[31] R. A.Cross, The kinetic mechanism of kinesin, Trends Biochem. Sci.29(6), 301(2004) (and references therein)

[32] D. G.Fan, W. W.Zheng, R.Hou, F.Li, and Z. S.Wang, Modelling motility of the kinesin dimer from molecular properties of individual monomers, Biochemistry47(16), 4733(2008)

[33] W. O.Hancockand J.Howard, Kinesin’s processivity results from mechanical and chemical coordination between the ATP hydrolysis cycles of the two motor domains, Proc. Natl. Acad. Sci. USA96(23), 13147(1999)

[34] S. D.Auerbachand K. A.Johnson, Alternating site ATPase pathway of rat conventional kinesin, J. Biol. Chem. 280(44), 37048(2005)

[35] T. L.Hill, Studies in irreversible thermodynamics (IV): Diagrammatic representation of steady-state fluxes for unimolecular systems, J. Theor. Biol. 10(3), 442(1966)

[36] T. L.Hilland Y. D.Chen, Stochatics of cycle completions (fluxes) in biochemical kinetic diagram, Proc. Natl. Acad. Sci. USA72(4), 1291(1975)

[37] H. H.Kohlerand E.Vollmerhaus, The frequency of cyclic processes in biological multistate systems, J. Math. Biol. 9(3), 275(1980)

[38] W. T.Tutter, Graph Theory, Cambridge: Cambridge University Press, 2001

[39] E. L.Kingand C.Altman, A schematic method of deriving the rate laws for enzyme-catalyzed reactions, J. Phys. Chem. 60(10), 1375(1956)

[40] S. M.Block, C. L.Asbury, J. W.Shaevitz, and M. J.Lang, Probing the kinesin reaction cycle with a 2D optical force clamp, Proc. Natl. Acad. Sci. USA100(5), 2351(2003)

[41] S.Rice, A. W.Lin, D.Safer, C. L.Hart, N.Naber, B. O.Carragher, S. M.Cain, E.Pechatnikova, E. M.Wilson-Kubalek, M.Whittaker, E.Pate, R.Cooke, E. W.Taylor, R. A.Milligan, and R. D.Vale, A structural change in the kinesin motor protein that drives motility, Nature402(6763), 778(1999)

[42] W.Hua, E. C.Young, M. L.Fleming, and J.Gelles, Coupling of kinesin steps to ATP hydrolysis, Nature388(6640), 390(1997)

[43] M. J.Schnitzerand S. M.Block, Kinesin hydrolyses one ATP per 8-nm step, Nature388(6640), 386(1997)

[44] A.Seitz, H.Kojima, K.Oiwa, E. M.Mandelkow, Y. H.Song, and E.Mandelkow, Single-molecule investigation of the interference between kinesin, tau and MAP2c, EMBO J. 21(18), 4896(2002)

[45] S.Lakämper, A.Kallipolitou, G.Woehlke, M.Schliwa, and E.Meyhofer, Single fungal kinesin motor molecules move processively along microtubules, Biophys. J. 84(3), 1833(2003)

[46] R. D.Vale, T.Funatsu, D. W.Pierce, L.Romberg, Y.Harada, and T.Yanagida, Direct observation of single kinesin molecules moving along microtubules, Nature380(6573), 451(1996)

[47] D. L.Coy, M.Wagenbach, and J.Howard, Kinesin takes one 8-nm step for each ATP that it hydrolyzes, J. Biol. Chem. 274(6), 3667(1999)

[48] S.Courty, C.Luccardini, Y.Bellaiche, G.Cappello, and M.Dahan, Tracking individual kinesin motors in living cells using single quantum-dot imaging, Nano Lett. 6(7), 1491(2006)

[49] D.Vale, Myosin V motor proteins, J. Cell Biol. 163, 445(2003)

[50] J.Ren, V. Y.Chernyak, andN. A.Sinitsyn, Duality and fluctuation relations for statistics of currents on cyclic graphs, J. Stat. Mech.: Theo. Exp. 05, 05011(2011)

[51] J.Renand N. A.Sinitsyn, Braid group and topological phase transitions in nonequilibrium stochastic dynamics, Phys. Rev. E87(5), 050101(2013) (R)

[52] R.Tarjan, Enumeration of the elementary circuits of a directed graph, SIAM J. Comput. 2(3), 211(1973)

[53] L.Onsagerand S.Machlup, Fluctuations and irreversible processes, Phys. Rev. 91(6), 1505(1953)

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