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B,*-~.L1yf-.J ~C-.. f

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J A. TuszvNsKI ET AL

125 nm1 15 nm--1

8nm

FIGURE 1. A section of a typical microtubule demonstrating thehelical nature of its construction and the hollow interior which isfillpd with l,vtoplasm. Each vertical column is known as a protofil-ament and the typi(;al MT has 13 protofilaments.

rolcs in alt~rnating protofilaments. This change results in the development of astructural discontinuity in the B lattice known as the seam [2].

Each tubulin monomer is comprised of approximately 450 amino acids andin thc neighbourhood of 7000 atoms. A detailed examination shows that eachmonomer is formf'ct by a core of two (j-sheets that are surrounded by a-helices.The monomer structure is very compact, but can be divided into three functionaldomains: an amino-terminal domain containing the nucleotide-binding region. an

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intermediate domain containing the taxol-binding site and a carboxy-terminal do-main (C-terminus), which probably constitutes the binding surface for motor pro-teins [8]. This is the one portion of the tubulin dimmerwhich was not imaged due toit.~ freedom to move following formation of the tubulin sheet in the crystallographicsamples. This tail of the molecule has been described by Sackett [11].

2. Thbulin's Charge Distributionlising the atomic resolution strurturc of tubulin fr'oli the Protein Dat,a Bank

(PDB) [4] provided by the electron diffraction crystallography of Nogales et al. [9],we have attempted to determine the electronic charge and the dipole moment.Calculations of the potential energy were done with the aid of a molecular

dynamics package, TINKER [6]. This computer program serves as a platform formolecular dynamics simulations and includes the facility to use several force-fieldparameter sets, some of which are protein specific. The most common of theseparameter sets for proteins are AMBER [10] and CHARMM [5]. AMBER was selectedover CHARMM on the rational that it is a more up-to-date parameter set. The overallperformance of the program gave us confidence that the results it provided for tubu-lin were meaningful. It was determined using TINKER that tubulin is quite highlynegatively charged at physiological pH and that much of the charge is concentratedon the C-terminus. (Perhaps as much as 40% of the overall charge.)In Table 1 we have summarized the results of our calculations for tubulin dimmerswithout the C-terminal tails.

Fig. 2 shqws a titration curve for the net charge on the tubulin a(:J heterodimer(with the C-termini) as a function of pH.

We have also been able to obtain a detailed map of the electric charge dis-tribution on the surface of the tubulin dimmer (see Fig.3). It is clear that theC-termini which extend outward carry a significant electric charge. At neutralpH, the negative charge on the carboxy-terminus causes it to remain extended dueto the electrostatic repulsion within the tail. Under more acidic conditions, thenegative charge of the carboxy-terminal region is reduced by associated hydrogenions. The effect is to allow the tail to acquire a more compact form by folding (seeFig.4). Although this is probably the largest structural change which occurs dueto changes in the cell's pH, we expect that other structural changes, perhaps theresult of post-translational modification in the process of microtubule assembly, cansimilarly affect the electrostatics of the tubulin dimmer

TABLE 1. Tubulin's Electrostatic Properties ( ail region excluded)

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TUSZYNSKI ET AL

~bJ)~..I:= .u~z

5 7 86pH

FIGURE 2. Tubulin titration curve for the tubulin 0(3 heterodimeras a function of pH; obtained with no salt and no intra-molecularcharge compensation. Figure courtesy of Dr. D. Sackett [12].

FIGURE 3. A map of the electric charge distribution on the surfaceof a tubulin dimmerwith C-t.ermini tails present.. Figure preparedusing MOLMoL [7].

50

-5-10-15-20-25-30

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ELECTROSTATIC' PROPERTIES OF TUBULIN AND MICROTUBULES

-+

-

+Low pH (acidic)

+

+

FIGURE 4. Cross-section of a MT including the carboxy-terminiof the tubulin subunits. The folding shown of the carboxy-terminiof the tubulin dimmerdemonstrates the change in the geometry ofthe molecule with pH. Neutral pH is shown on top, the tail foldsat lower pH as the negative charges are screened.

3. The Dipole Moment of Tubulin and MicrotubulesIn Table 1 we listed the dipole moment of the dimmerwithout the tails (seeFig.5a). The story here, however, is more complicated. As shown in Fig.5, there

are several additional sources of dipoles when tubulin is present in an ionic solution.When two dimmers re bound within a protofilament, their positively and negatively

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6 J A. TuszvNsKI ET AL

+++

(a) (b) (c) (d)FIGURE 5. The various contributions to the dipole moment of atubulin dimer: (a) the intrinsic dipole moment of the globularprotein, (b) the double layer formed when two dimers are bound ina protofilament, (c) a possible internal dipole created by electronictransitions in the hydrophobic pocket and (d) a double layer formedby counter ions surrounding the C-termini tails.

charged ends form a double layer with a net dipole moment along the protofilamentaxis (Fig.5b). Beside each tubulinmonomer there is a hydrophobic pocket thatmay develop a double well structure. This can give rise to an internal (switch-able) dipole moment due to electronic transitions on this positive background (seeFig.5c). Finally, as is shown in Fig.5d the C-termini which are negatively chargedare surrounded by counter ions in solution leading to the formation of double layers.

The principal contribution to the dipole moment of a tubulin dimer comes, how-ever, from the location of partial charges on the constituent amino acids. When thisis brought to bear on the structure of the microtubule, we predict the emergence ofa very interesting anti-ferroelectric structure with permanent dipoles placed almostperpendicular to the surface of the MT cylinders and almost cancelling each otherdue to rotational symmetry (see Fig.6).

4. Discussion and ConclusionsIn this paper we have summarized our calculations regarding the net charges

alld dipole 1IIoments of tubulin and microtubules. These calculations were per-formed using an atomic resolution structure of tubulin in conjunction with molec-ular dynamics simulations. We found a large negative charge concentrated on theouter surface of the protein, almost half of which is located on flexible peptide tailsattached to the outer face. This charge is undoubtably instrumental in tubulin-tubulin interactions as well as the interactions of tubulin with motor proteins suchas kinesin. Fig. 7 shows the results of our force field calculations were two tubulindimmers re placed in each other's neighbourhood and allowed to interact electrostat-ically. The brush strokes represent the direction of the Coulomb force of attraction.

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r:I,~:{'THOSTATI(' PROPERTIES Of TUBULI1\1 AND MIC'ROTliBULES

FIGURE 6. The arrows indicate the orientation of the permanentdipole moments of individual tubulin dimmerswith respect to thesurface of a microtubule. Figure prepared using MOLMoL [7].

It is clear that a hexagonal lattice is likely to emerge in the process of tubulin as-sembly into a microtubule. We have performed detailed calculations of the tubulin-tubulill electrostatic potelltial along various directions and they strongly supportthe creation of the known lattice structures. These and related results obtained inour study will be published elsewhere [14].Finally, we should comment on the role of electrostatic screening due to ions inthe cytoplasm or a buffer solution in which tubulin and microtubules may be found.Beyond a certain distance, the so-called Debye length, we can ignore electrostaticeffects due to screening. This is the most important length scale as the Bjerrumlength that compares electrostatic effects with thermal effects is larger. In our case,we expect that beyond 2.0 nm, illteractions can be neglected; be they of a charge-(;hargp, charge-dipole, or van der Waal's nature. The potential is gradually switchedoff in the calculation so there are no discontinuities in the electrostatic potential, 4>.This is in fact close to the true situation since ions in the surrounding solution willscreen any surface charges. Some of the results presented in this paper represent"vacuum" results givell that the solvent is not explicitly taken into account. If thesurroUllding l1Iixturp of iolls is considered, then the potential due to a point chargerlo~'~ lOt f..ul off sillll)I~, as l/r, but illstead as

1(/)'X -r,. 1(where [(-1 i~ thl' Debyl' lpllgth, t.\'pi(;all.,. 0,6 nm ulldpr plly~iologi(;al (;ollditioll~,Since Wf' (;onsirler locatioll~ withill 1.0 nm of the MT surfa(;e, they are not screen by

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\ r\.-;Z\~SI,

FIGURE 7. A view of the attractive regions about a tubulin dimmeras would be experienced by another diller. The smallest princi-pal moment of inertia of the dimmerss perpendicular the page, themiddle one is aligned vertically, the largest principal moment hori-zont.ally. See ext for more details. Figure prepared using RASMoL[13].

the ions of the solution as there is not sufficient room for even water to be locatediI] thf' intl'r\'l'Iling spacE'.

5. AcknowledgmentsThis r('.~par(.h was supported by gral1t.~ from ~SERC and MITACS-Ml'vlPD

Discussions \\ith Dr. Dan Sa(;kett of NIH are gratefully acknowledged.

References1. Bruce Alberts, Dennis Bray, .1ulian Lewis, Martin Raff, Keith Roberts, and .1ames D. Watson,

Molecular biology of the cell, 3rd ed., Garland Publishing, London, 1993.2 Linda ..\. l\mo:;, Thc microtubule lattice -20 years 011., rerlds il! Cell Biology 5 {1995), no.2,

48-51.3. Lil!da A. Arnos arId W. Bradshaw Amos, Molecule.~ of the cytoskeleton, 1st ed., MacMillan

Press, London, 1991.J Hl'll'n \" Berrrlan, .1ohn V\'('stbrook, Zukal!g [.',~ng, (:ary Gillilal!d, Talapady N. Bhat, Helge

Wei:;:;ig, Ilya N. Shil!dyalov, ,lnd Phil E. Bourne, The p1'otei71 data bank, Nucleic Acids Re-:;earch 28 {2000), 1!0. 1, 2:35242

5. Berrlard R. Brook:;, [{obert E. Brurcoleri, Barr.y D. Olaf:;ol!, David .1 State:;, S. Swamil!athal!,and rvlartin Karplus, CHARMM~ A r1'ofJ1'am or rnacrornolecula1' energy, minimization, arIdd""amirs calculation.~, .1ollrllill of ('orll[Jutational Chemistry 4 ( 191;:3), no.2, 187217.

(j \,lil~l,a{~1 .1. !)Udl'k illld .Jav \\ ['olld~r, Ac,urat" rnodelirl9 of the iru1'amolecular electrostaticenf'rqy ()fp1'ou;in.~. .1 or ()lllrlllalional ('llcmi:;try 16 {1995). rlo. 7,791-816.

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E;LEC'TROSTATIC' PROPERTIES OF TUBULIN AND MIC'ROTUBULES 9

7. Ret,o Koradi, Martin Billet,er, and Kurt Wiithrich, MoiMoi: A program for display and arlal-ysis of 7nacrornolecular structures, J Mol Graphics 14 (1996),51-,55.

8. Eckhard Mandelkow a!ld Eva-Maria Ma!ldelkow, Microtubule,~ artd rnic7'otubule-associatedproteirts, Current Opinion in Cell Biology 7 (1995), !lO. 1, 72-81.

9. Eva Nogales, Sharon G, Wolf, and Kenneth H. Downing, Structure of the alpha-beta tubulindirner by electron crystalography, Nature 393 (1998), !lo. 6663, 199-203.

10. David A. Pearlman, David A. Case, James. W. Caldwell, Wilson S. Ross, Thomas E.Cheatham, Stephen E. DeEolt, David M. Ferguson, George L. Seibel, and Peter A. Koll-man, AMBER, a package of computer programs for applying molecular mechanics, normalmode analysis, molecular dynamics and free energy calculations to simulate the structuraland energetic properties of molecules, Computer Physics Communications 91 (1995), 1-41.

11. Dan L. Sackett, Subcellular biochemistry, Proteins: Structure, Function and Engineering,vol. 24, ch. Structure and Function in the Tubulin Dimmer and the Role of the Acidic CarboxylTerminus, Plenum Press, New York, 1995.

12. -, personal communication, 2000.13. Roger Sayle and E. James Milner-White, RasMol: Biomolecular graphics for all, Trends in

Biochemical Sciences (TIES) 20 (1995), no.9, 374.14. Jack A. Tuszyiiski, James A. Brown, Eric J. Carpenter, Ellen Crawford, and M. L. Alex Nip,

Electrostatics properties of tubulin and microtubules, submitted to Proc. Nat. Acad. Sci.

1 DEPARTMENT OF PHYSICS, UNIVERSITY OF ALBERTA, EDMONTON AB CANADA, T6G 2Jl

2DI;:P,\RTMENT OF PHYSIC'S, UNIVERSITY OF ALBERTA, EDMONTON AB CANADA, T6C; 2J 1Current addr'ess: Faculty of Medicine, Department of Biochemistry, University of Montreal,rvlontreal, QC Canada, H3C 3J7