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Molecular Dynamics Calculations of the Electrostatic Properties of Tubulin andTheir Consequences for Microtubules

J. A. Tuszynski,* E. J. Carpenter,* E. Crawford,* J. A. Brown,* W. Malinski,* and J. M. Dixont*Department of Physics, University of Alberta, Edmonton AB Canada, T6G 2Jl.fphysics Department, University of Warwick, Coventry, U K" CV4 TAL

jtus@phys, ualberta. ca

Abstract crystallographic results were made available through theProtein Data Bank (PDB) (entries: ITUB and IJFF)which allowed us to view the 3D atomic resolutionstructure oftubulin. (see Fig. I) Each tubulin monomer iscomposed of more than 400 amino acids and, in spite oftheir similarity, slight folding differences can be seen. Itis worth stressing that several different versions of boththe {X- and 13-monomers xist and are called isotypes. [3].The biophysical properties of these variants have beenexamined and are discussed below in this paper.

Fig. 1 is diagram of the tubulin molecule producedfrom the Nogales et al. [2] crystallographic data (fileIJFF) shows the similarity between the {X-subunit (lefthalt) and the 13-subunit right halt). The white spheresindicate the location of GTP , GDP and taxol when bound.

We present the results of molecular dynamicscomputations based on the atomic resolution structures oftubulin published as lTUB and IJFF in the Protein DataBank. Values of net charge, spatial charge distributionand Cartesian dipole moment components are obtainedfor the tubulin alpha-beta heterodimer. Physicalconsequences of these results and subsequentcomputations are discussed or microtubules in terms ofthe effects on test charges, test dipoles, and neighboringmicrotubules. Our calculations indicate typical distancesover which electrostatic effects can be felt bybiomolecules, ions, and other microtubules. We alsodemonstrate the importance of electrostatics in theformation of the microtubule lattice and the tubulin-kinesin binding strength.Keywords: tubulin, kinesin, molecular dynamics,microtubules, electrostatics1. Introduction

Figure 1. Tubulin dimer, prepared using MolMol. [4]2. Electrostatic modelling of tubulin

Fig. 2 shows the results of our molecular dynamicssimulations for the electric charge distribution on thesurface of a tubulin dimer tha includes the two carboxy-termini that are very flexible and which have not beenresolved crystallographically.2.1. C-termini

The C-termini of tubulin are strongly electro-negative(having up to 10 net negative charges) and interact

Microtubules (MTs) are protein filaments of thecytoskeleton with lengths that vary but commonly reach5-10 ~m. Theyare composed of 12 to 17 protofilamentswhen self-assembled in vitro and almost exclusively of 13protofilaments in vivo. These protofilaments are stronglybound internally and are connected via weaker lateralbonds to form a sheet that is wrapped up into a tube in thenucleation process. The general structure of MTs has beenwe.l established experimentally. A small differencebetween the (X- and 13-monomersof tubulin allows theexistence of at least two lattice types. Moving around theMT in a left-handed sense, protofilaments of the A latticehave a vertical shift of 4.92 nm upwards relative to theirneighbors. In the B lattice this offset is only 0.92 nmbecause the (X- and 13-monomershave switched positionsin alternating filaments. This change results in thedevelopment of a structural discontinuity in the B latticeknown as a seam.In 1998 Nogales et al. reported crystallization oftubulin in the presence of zinc ions. [1, 2] Their

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Bearing in mind that tubulin is both highly charged andpossessesa pennanent dipole moment we have attemptedto estimate the strength of electrostatic effects on: a) a testcharge, b) a test dipole, c) another microtubule in thevicinity, and d) the dipole-dipole interaction between twomicrotubules. Below we summarize our calculations.

First of all, we have perfonned calculations of thedimer-dimer interaction that arises due to the charge anddipole moment present on each independent protein insolution. The result of these calculations is shown inFig. 5 in tenns of force lines of attraction between twoneighboring dimers. It is interesting to note that the linesof attraction appear consistent with the presence of ahexagonal lattice structure on the surface of amicrotubule.

~

It is worth noting that there is a significant diversity inthe values of dipole moments and an even greatervariation in the net charge per monomer. We arecurrently pursuing a larger scale study intended to provideconclusive evidence for the correlation between thestructure and function of this very important protein.

Fig. 4 is a reconstruction of the electric polarization ofa microtubule that takes into account the dipole momentsof the individual dipoles and their orientation with respectto the microtubule axis. It is interesting to note that whilethe net dipole moment of tubulin is very large, itssymmetrical ordering around the MT axis gives rise to anet cancellation effect such that a minimal amount oftorque is expected to arise from the application of anexternal electric field to a microtubule in solution.

Figure 5. A view of the attractive regions about atubulin dimer as would be experienced by anotherdimer. The smallest principal moment of inertia ofthe dimers is perpendicular to the page, the middleone is aligned vertically, the largest principal momenthorizontally. See text for more details. Figureprepared using Rasmol. [7]3.1. Microtubule-Charge interaction

As an example, we considered a microtubule of length5 ~m, outer radius 12.5 nm, and surface charge densitya = 0.5e/nm2. With a test charge of +5 e located at adistance 5 nm from the surface of a microtubule we obtaina force of electrostatic attraction of 6 pN in water, whichis reduced to only 0.5 pN in standard ionic solutions withDebye lengths between 0.6 and 1.5 nm depending on theionic strength. This would indicate that the maximumdistance over which a microtubule can exert an influenceon a charged particle is on the order of 5 nm from itssurface.

Figure 4. The arrows indicate the orientation of thepermanent dipole moments of individual tubulindimers with respect to the surface of a microtubule.Figure prepared using MolMol. [4]

microtubule. Electrostaticstructure

effects of

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[I] E. Nogales, S.G. Wolf, and K.H. Downing, "Structure of thea13- ubulin Dirner by Electron Crystallography", Nature, NaturePublishing Group, London, Jan. 08, 1998, pp. 199-203.

5. Conclusions

[2] J. Lowe, H. Li, K.H. Downing, and E. Nogales, "RefinedStructure of ~- Tubulin at 3.5 A Resolution", Journal ofMolecular Biology, Academic Press-Elsevier, London, Feb. 26,2002, pp. 1045-1057.[3] Q. Lu, G.D. Moore, C. Walss, and R.F. Luduena, "Structuraland Functional Properties of Tubulin Isotypes", Advances inStructural Biology, Jai Press, Stanford U.S.A., 1998, pp. 203-227.[4] R. Koradi, M. Billeter, and K. Wuthrich, "MOLMOL: AProgram for Display and Analysis of MacromolecularStructures", Journal of Molecular Graphics, Elsevier, London,Feb. 1996, pp. 51-55.[5] B. Boeckmann, A. Bairoch, R. Apweiler, M.-C. Blatter, A.Estreicher, E. Gasteiger, M.J. Martin, K. Michoud, C.O'Oonovan, I. Phan, S. Pilbout, and M. Schneider, "TheSWISS-PROT Protein Knowledgebase and its SupplementTrEMBL in 2003", Nucleic Acids Research, 2003, OxfordUniversity Press, Oxford, Jan. 1,2003, pp. 365-370.[6] M.A. Marti-Renom, A. Stuart, A. Fiser, R. Sanchez, F.Melo, A. Sali, "Comparative Protein Structure Modeling ofGenes and Genomes", Annual Review of Biophysics andBiomolecular Structrue, Annual Reviews, Palo Alto, USA,2000, pp. 291-325.[7] R. Sayle and E.J. Milner-White, "RASMOL: BiomolecularGraphics for All", Trends in Biochemical Sciences (TIBS),Elsevier Science Ltd., London, Sep. 1995, pp. 374-376.

In this paper we have considered the role ofelectrostatics in the interactions between tubulin,microtubules and other charged or polarized molecules.In particular, we have shown that in spite of Debyescreening, a microtubule can exert a Coulomb force on acharged particle that is up to 5 nm away from its surface.The dipole-dipole forces that have been calculated arenegligible for the most part. However, they can be felt bydipoles that are perpendicular to the microtubule surfaceand removed from the equatorial plane. When twomicrotubules are found in the same vicinity, they can exertsignificant forces of repulsion even in the presence ofionic screening. Since the negatively charged C-terminiprotrude perpendicularly to the microtubule surface thiseffect is additionally increased and explains the existenceof the so-called 'zone of exclusion' [10] known to cellbiologists for many years.

We have shown that the microtubule structure, inparticular the lateral binding between protofilaments, isconsistent with the location of positive and negativesegments of the electrostatic potential for optimal binding.It is worth mentioning that a recent paper [11] showed theelectrostatic surface of the whole microtubule followingcomputations involving the Poisson-Boltzmann equation.From these calculations a dramatic difference between theplus and minus ends of a microtubule has been revealed.It is very likely that this difference leads to the well-known difference in polymerization kinetics involvingthese two ends.We hope that the new insights gained by performingthese computations will be useful in our understanding ofthe cellular machinery as well as in the efforts to constructnanomachinery that uses biomolecular components orhybrid structures mimicking the effects observed in livingcells.

[8] W. Wriggers and K. Schulten, "Nucleotide-DependentMovements of the Kinesin Motor Domain Predicted bySimulated Annealing", Biophysics Journal, Biophysical Society,Bethesda. U.S.A., Aug. 1998, pp. 646--{)61.[9] M. Kikkawa, E.P. Sablin, Y. Okada, H. Yajima, R.J.Fletterick, and N. Hirokawa, "Switch-Based Mechanism ofKinesin Motors", Nature, Macmillan Publishers Ltd., England,May 24,2001, pp. 439-445.

6. AcknowledgmentsThis research was supported by grants from NSERCand MITACS-MMPD. Discussions with Dr. Dan SackettofNIH are gratefullyacknowledged. I. M. D. would like

to thank the staff of the Theoretical Physics Institute of theUniversity of Alberta for all their kindness during hisvisit.

[10] Dustin, p ., Microtubules, Springer- V erlag, Berlin, 1984.[11] N.A. Baker, D. Sept, S. Joseph, M.J. HoIst, and J.A.McCammon, "Electrostatics of Nanosystems: Application toMicrotubules and the Ribosome", Proceedings of the NationalAcademy of Sciences, National Academy of Sciences,Washington U.S.A., Aug. 21,2001, pp. 10037-10041.7. References