j.a. tuszynski, t. luchko, e.j. carpenter and e. crawford: results of molecular dynamics...

8/3/2019 J.A. Tuszynski, T. Luchko, E.J. Carpenter and E. Crawford: Results of Molecular Dynamics Computations of Structura

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Results of Molecular Dynamics Computations of

the Structural and Electrostatic Properties of

Tubulin and Their Consequences for Microtubules

J. A. Tuszynski, T. Luchko, E. J. Carpenter and E. Crawford

Department of Physics

University of Alberta

Edmonton, AB, Canada

T6G 2J1

[email protected]

April 13, 2004

Abstract

We present the results of molecular dynamics computations based on

the atomic resolution structures of tubulin published as 1TUB and 1JFF

in the Protein Data Bank. Values of net charge, spatial charge distri-

bution and Cartesian dipole moment components are obtained for the

tubulin alpha-beta heterodimer. Physical consequences of these results

and subsequent computations are discussed for microtubules in terms of

the effects on test charges, test dipoles, and neighboring microtubules.

Our calculations indicate typical distances over which electrostatic effects

can be felt by biomolecules, ions, and other microtubules. We also demon-

strate the importance of electrostatics in the formation of the microtubule

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lattice and the tubulin-kinesin binding strength.

Keywords: tubulin, kinesin, molecular dynamics, microtubules, elec-

trostatics

1 Introduction

Microtubules (MTs) are protein filaments of the cytoskeleton with lengths that

vary but commonly reach 5-10m. They are composed of 9 to 16 protofila-

ments when self-assembled in vitro and almost exclusively of 13 protofilaments

in vivo[1]. These protofilaments are strongly bound internally and are connected

via weaker lateral bonds to form a sheet that is wrapped up into a tube in the

nucleation process. These cylindrical protein organelles, found in all eukary-

otes, are critically involved in a variety of cellular processes including motility,

transport and mitosis[2]. Their component protein, tubulin, is composed of two

polypeptides of related sequence, designated and . In addition to - and

-tubulin, many microtubules in cells require the related -tubulin for nucle-

ation. Two other tubulins, designated and , are widespread, although their

roles are still uncertain. The general structure of MTs has been well established

experimentally. A small difference between the - and -monomers of tubulin

allows the existence of at least two lattice types. Moving around the MT in a

left-handed sense, protofilaments of the A lattice have a vertical shift of 4.92

nm upwards relative to their neighbors. In the B lattice this offset is only 0.92

nm because the - and -monomers have switched positions in alternating fila-

ments. This change results in the development of a structural discontinuity in

the B lattice known as a seam.

At the molecular level tubulins roles are highly complex. For example, mi-

crotubules undergo cycles of rapid growth and disassembly in a process known

as dynamic instability that appears to be critical for microtubule function, es-

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pecially in mitosis. The kinetics of hydrolysis of the GTP bound to -tubulin is

critical for this process by affecting the loss of the so-called lateral cap that stabi-

lizes the microtubule structure[3]. In addition to forming microtubules, tubulin

interacts with a large number of associated proteins. Some of these, such as

tektin, may play structural roles; others, the so-called microtubule-associated

proteins (MAPs) such as tau or MAP2, may stabilize the microtubules, stim-

ulate microtubule assembly and mediate interactions with other proteins. Still

others, such as kinesin and dynein, are motor proteins that move cargoes, e.g.

vesicles, along microtubules[4].

The precise molecular basis of the properties of tubulin is still not well under-

stood, in part because tubulins highly flexible conformation makes it difficult

to crystallize. In a major advance in the field, the three-dimensional structure

of bovine brain tubulin has been determined by electron crystallography by

Nogales et al. in the presence of zinc ions[5, 6]. Once the three-dimensional

structure of a protein has become known it is possible to use affinity modeling

to predict the structures of related forms of the protein with some degree of

accuracy. The crystallographic results were made available through the Protein

Data Bank (PDB) (entries: 1TUB and 1JFF) which allowed us to view the 3D

atomic resolution structure of tubulin. Each tubulin monomer is composed of

more than 400 amino acids and, in spite of their similarity, slight folding differ-

ences can be seen. It is worth stressing that several different versions of both the

- and -monomers exist and are called isotypes[7]. We have applied affinity

modeling techniques to a series of some 290 different tubulins, representing -

and -tubulins from animals, plants, fungi and protists, as well as several -, -

and -tubulins. A summary of this work will be published elsewhere.

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2 Conformational and electrostatic changes due

to GTP hydrolysis

Tubulin is believed to exist in two conformational states depending on whether

GTP or GDP is found in the E-site. Importantly, when GTP is found in the

E-site tubulins net charge is reduced by one. Furthermore, it is believed that

having GTP in the exchangeable site is necessary for polymerization while GDP

in the exchangeable site contributes to depolymerization[3].

To determine conformational changes due to GTP hydrolysis a series of sim-

ulations were carried out as described in Section 2.1. 10 coordinate sets per

ps where recorded and analyzed for the final 600ps and 300ps of the first and

second equilibrium runs of GTP and GDP tubulin. Common indicators of con-

formational change such as water accessible surface area, radius of gyration and

RMS fluctuations from the crystal structure showed little difference between

the four runs. Average structures were produced and root-mean-square (RMS)

deviations from the crystal structure as well as differences between the aver-

age structures were taken. Similar changes were found among runs with the

same nucleotide as with different nucleotides suggesting no significant confor-

mational changes were found. Though similar protocols have found conforma-

tional changes in proteins before, for example [8], we believe that these results

are likely because the annealing runs were too short to allow a sufficient con-

formational search to occur. Either several longer annealing runs or alternate

computational techniques are required to achieve this.

2.1 Computational methods

Molecular dynamics simulations with CHARMM[9] and the CHARMM27 force

field[10] were performed using the crystal structure file 1JFF as initial condi-

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tions for the protein structure. Simulated annealing was preformed on structures

containing GTP and GDP in the exchangeable (E) site. Following this, equi-

librium molecular dynamics was preformed to obtain average structures from

which properties were calculated.

In order to use 1JFF as the initial conditions for our simulations it was

necessary to remove the taxol molecule and zinc ion and add several parts of

the amino acid chains that were missing in the crystal structure. Except for the

C-termini, the locations of the missing residues were obtained from the 1TUB

structure. In addition, we have been able to predict with some confidence the

conformations of the C-termini of tubulin since the C-termini of- and -tubulin

were not resolved in the original electron crystallographic reconstruction of the

tubulin molecule due to their flexibility. Our results raise the possibility that the

movements of the C-termini of tubulin may play a major role in kinesin motility

and that they may have some novel, hitherto unsuspected, roles in ion transport

along microtubules especially in the axoplasm of neurons. The C-termini had

been previously added to 1TUB using MolMol[11] and were added to the 1JFF

structure in the same manner as the other missing residues. Residues 1A-2A,

27A-64A, 436A-451A, 1B-3B, and 435B-455B were added individually by root-

mean-square devitation (RMSD) fitting the backbone atoms of five residues

adjacent to the missing segments on either side and pasting the missing residues

into the new structure.

Besides the Mg2+ ion that was part of the crystal structure 4 Na+, 55

K+ and 6 Cl ions were added to the system to maintain electro-neutrality

and an ion concentration consistent with that of cytoplasm. An additional K+

was added for simulations with GTP in the E-site. These ions were placed

at random positions about the fixed protein in a box 105A X 65A X 125A

and equilibrated for 2ns using Langevin dynamics with a friction coefficient of

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62ps1 and periodic boundary conditions (PBC)[12]. The two systems were

then hydrated by tiling a box of 3000 pre-equilibrated water molecules and

minimized for 400 steps of steepest descent.

Simulated annealing was then performed based the protocol outlined in [8].

Our systems were heated to 500K in 40ps and held there for 10ps and then

cooled to 200K over 120ps using time steps of 2fs and utilizing SHAKE to

maintain rigid bond lengths. The resulting coordinate sets and their subsequent

simulations will be referred to as GTP1 and GDP1. A second coordinate set

for each system (GTP2 and GDP2) was produced by maintaining the system at

500K for an additional 15ps before cooling. All four coordinate sets were then

equilibrated at 300K for 150ps with 1fs time steps without SHAKE.

A total of 2.1ns of production simulation was performed between the four

systems. GTP1 and GDP1 each were simulated for 600ps while GTP2 and

GDP2 were both simulated for 300ps. Coordinate sets were recorded every

0.1ps.

2.2 Electrostatic properties

For self-assembly of MTs to occur individual tubulins must interact via long-

range forces (i.e. electrostatic forces) for attraction and alignment to occur.

Since tubulin is highly charged and, thus, naturally repulsive to other tubulins

the shape of the electric field and how it interacts with its ionic environment is

of great importance.

To estimate an upper bound for the maximum distance over which tubulin

electric fields may have some significant interaction we may look to the critical

concentration of Tu-GTP required for MT growth. While the concentration

depends on such factors as the use of nucleation seed, a minimal estimate of

5mM[13] may be used. Typically, the Tu-GTP critical concentration in vitro

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must be higher. This corresponds to an average separation between the centers

of mass of 150A or, between surfaces, of roughly 100A. We can consider this the

maximum distance at which tubulin dimers may interact.

For orientation-dependent measurements, such as the dipole moment, we

have RMSD fit the -helix and -sheet portions of the backbone of each co-

ordinate set to 1JFF. Prior to this we have rotated 1JFF structure 26 with

respect to the protofilament axis (x-axis) such that the y-axis is tangential and

the z-axis is inward and perpendicular to the MT surface[14].

Furthermore, unless otherwise noted, all electrostatics calculations have been

carried out with a dielectric constant of 1 corresponding to a vacuous environ-

ment. Since the force field parameters have been optimized for a dielectric con-

stant of 1 and the simulations performed under such conditions, this produces

the most realistic and relevant results for our simulations. Ions are included

where noted (Mg2+ at the N-site is considered part of the protein) and water

is generally included though explicit waters except where noted.

The porcine tubulin sequences of the - and -monomers used have a typ-

ical net charge of -24e each at pH 7.0. Including the two nucleotides and the

bound Mg2+ the net charge of the structure is -53e and -54e for GDP bound

and GTP bound tubulin, respectively. Although we have found no significant

conformational differences between any of our simulations we will report the

electrostatic properties of both GDP bound and GTP bound tubulin separately

due to the differences in net charge.

Although no obvious conformational differences were found between GTP1,2

and GDP1,2 there was a difference in ionic condensation around the exchange-

able site. In both GDP1 and GDP2 a positive ion is tightly bound to the surface

of the exchangeable nucleotide analogous to Mg2+ at the non-exchangeable site.

In GTP1,2 two positive ions are tightly bound to the surface of the nucleotide.

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Over the length of the runs these bound ions had an average root-mean-square

fluctuation (RMSF) of 0.79A for GTP1,2 and 0.53A for GDP1,2. Also observed

in all simulations was a single ion oscillating 5 to 8A from the exchangeable

nucleotides. Not strongly bound, these had an average RMSF value of 5.7A for

GTP1,2 and 4.3A for GDP1,2.

While several ions in all of the simulations became bound to the surface,

other than around the E-site, only one other site bound ions in all simulations.

A single sodium in GDP1,2 and a single potassium in the case of GTP1,2 was

found between residues 417 and 426 of the -monomer. This is a highly charged

area of the N-terminal end of the H12 helix. The sodium ions found in GDP1,2

were much more tightly bound with RMSF of 1.2A as compared to 5.1A for the

potassium ions in GTP1,2.

The distribution of the electrostatic potential on the surface of the protein

in the absence of water and ions is shown in Figure 1. Due to the large net

charge of tubulin the surface potential is completely negative. However, poten-

tial gradients can be seen across the surface along the lateral and longitudinal

directions that are important for binding within the MT. Laterally the almost

neutral side of the tubulin, Figure 1(f), will be in contact with its negative side,

Figure 1(e), of its neighbors. Similarly, the exposed end of the -monomer, Fig-

ure 1(d) is quite negative in comparison to the exposed end of the -monomer,

Figure 1(c), particularly around the E-site.

[Figure 1 about here.]

The shape of the electric field at large distances is typically discussed in terms

of the multipole expansion. Unfortunately, neither the dipole nor quadrupole

moment can be uniquely defined for a structure that has a non-zero net charge.

However, by using the center-of-mass as our origin we can attempt to quantify

the distribution of charge within the molecule and how this may affect long-range

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interactions. How this shape changes with the addition of ions and the multipole

approximation to it can be seen in Figure 2. Table I summarizes the results of

our calculations of the tubulins net charge, dipole moment from our simulations.

Note that the x-direction in Table 1 coincides with the protofilament axis. The

-monomer is in the direction of increasing x values relative to the -monomer.

The y-axis is oriented radially towards the MT center and the z-axis is tangential

to the MT surface.

[Table 1 about here.]


2.3 Dimer-dimer interactions

Protofilament and microtubule dynamics are a result of tubulin dimer-dimer

interactions. In order to quantify these interactions a potential energy map

was produced by moving one tubulin dimer relative to another (see Figure 3)

and calculating the electrostatic and Lennard-Jones interaction energy in the

absence of water and ions using CHARMM and a 30A cut-off.


The mapping of dimer-dimer interactions was done in a planar grid tangent

to the MT surface. The grid spacing used was 2 A with center-of-mass displace-

ments ranging from 0 to 120A longitudinally and -80A to 80A laterally. Due

to the symmetry created by using pairs of identical dimers (produced from the

average structures of GTP1 and GDP1) it was not necessary to perform calcu-

lations with a negative displacement in the longitudinal axis. Rotation of the

dimers was not varied with the lateral separation. As a result these calculations

may more closely represent protofilament sheets than MTs.

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steps of 1 fs.

Conformational changes that were found in tubulin have been seen to affect

both lateral and longitudinal contacts, providing some insight into the nature of

the dynamical instability of microtubules. We have also seen that the hydrolysis

state of kinesin affects its binding affinity for tubulin. Figure 4 shows the shape

of the binding potential whose depth is approximately 0.5 eV corresponding

closely to the ATP hydrolysis energy that drives the process of kinesins walk

along the filament. Figure 5 shows the electric charge distribution on the motor

domain of kinesin that appears complementary to the charges on tubulin. Fur-

thermore, the calculated kinesin binding site of MTs agrees with results from

crystallography. (see Figure 6)




4 Conclusions

The electrostatic charge of tubulin, although significantly screened by counter-

ions in solution, could affect microtubule assembly by influencing dimer-dimer

interactions on relatively short distances (approximately 5 nm) and the kinetics

of assembly. This has been recently demonstrated by Sept et al[16] who cal-

culated the electrostatic energy of protofilament-protofilament interactions and

concluded from their work that the two types of microtubule lattices (type A

and B) correspond to the local energy minima.

The dipole moment could play a role in microtubule assembly and other

processes also. This could be instrumental in the docking process of molecules to

tubulin and in the proper steric configuration of a tubulin dimer as it approaches

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a microtubule for binding. A tubulin dimer surrounded by water molecules and

counter-ions has a dominant dipolar contribution to the electrostatic energy as

shown in Figure 2. Once a microtubule has been formed, the greater the dipole of

each of its units is, the less stable the microtubule since dipole-dipole interactions

provide a positive energy disfavoring a microtubule structure. Note that the

strength of the interaction potential is proportional to the square of the dipole

moment hence microtubule structures formed from tubulin units with larger

dipole moments should be more prone to undergo disassembly catastrophes

compared to those microtubules that contain low dipole moment tubulins.

In work published elsewhere [17] we have also considered the role of elec-

trostatics in the interactions between tubulin, microtubules and other charged

or polarized molecules. In particular, we have shown that in spite of Debye

screening, a microtubule can exert a Coulomb force on a charged particle that

is up to 5 nm away from its surface. The dipole-dipole forces that have been

calculated are negligible for the most part. However, when two microtubules

are found in the same vicinity, they can exert significant forces of repulsion even

in the presence of ionic screening. This is increased by the negatively charged

C-termini protrude perpendicularly to the microtubule, explaining the existence

of the so-called zone of exclusion[2] known to cell biologists for many years.

We have shown that the microtubule structure, in particular the lateral

binding between protofilaments, is consistent with the location of positive and

negative segments of the electrostatic potential for optimal binding. It is worth

mentioning that a recent paper[18] showed the electrostatic surface of the whole

microtubule following computations involving the Poisson-Boltzmann equation.

From these calculations a dramatic difference between the plus 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 involving these two ends.

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Finally, the state of the C-termini could mediate how motor proteins such as

kinesin bind to and move on microtubules. Our simulations show that kinesin

binds preferentially to upright C-termini and not to C-termini lying on the

surface of the microtubule. Very minor changes in the local ionic environment

or the pH could halt the processive motion of a two-headed kinesin by collapsing

the C-termini. One can postulate that the proportion of C-termini that are in

the upright conformation in a given portion of the microtubule could determine

the actual rate of kinesin movement. It is likely that such arguments could

apply to other motor proteins as well.

We hope that the new insights gained by performing these computations

will be useful in our understanding of the cellular machinery as well as in the

efforts to construct nanomachinery that uses biomolecular components or hybrid

structures mimicking the effects observed in living cells.

Acknowledgments

This research was supported by grants from NSERC and MITACS-MMPD.

References

[1] D. Chretien and R. Wade, Biol. Cell 71, pp. 161174, (1991).

[2] P. Dustin, Microtubules, Springer-Verlag, Berlin, (1984).

[3] H. Flyvbjerg, T. Holy, and S. Leibler, Phys Rev. E. 54(5), pp. 55385560,

(1996).

[4] M. Kikkawa, E. Sablin, Y. Okada, H. Yajima, R. Fletterick, and N. Hi-

rokawa, Nature 411, pp. 439445, (2001).

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[5] E. Nogales, S. Wolf, and K. Dowling, Nature 391, pp. 199203, (1998).

PDB ID 1TUB.

[6] J. Lowe, H. Li, K. Dowling, and E. Nogales, J. Mol. Biol. 313, pp. 1045

1057, (2001). PDB ID 1JFF.

[7] Q. Lu, G. Moore, C. Walss, and R. Luduena, Structural and functional

properties of tubulin isotypes in Advances in Structural Biology, 5, pp. 203

227, Jai Press, Stanford U.S.A., (1998).

[8] W. Wriggers and K. Schulten, Biophysical Journal 75, pp. 646661, (1998).

[9] B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan,

and M. Karplus, J. Comp. Chem 4, pp. 187217, (1983).

[10] A. D. MacKerell, Jr., D. Bashford, M. Bellott, R. Dunbrack Jr.,

J. Evanseck, M. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-

McCarthy, L. Kuchnir, K. Kuczera, F. Lau, C. Mattos, S. Michnick, T. Ngo,

D. Nguyen, B. Prodhom, W. Reiher, III, B. Roux, M. Schlenkrich, J. Smith,

R. Stote, J. Straub, M. Watanabe, J. Wiorkiewicz-Kuczera, D. Yin, and

M. Karplus, J. Phys. Chem. B 102, pp. 35863616, (1998).

[11] R. Koradi, M. Billeter, and K. Wuthrich, J. Mol. Graphics 14, pp. 5155,

(1996).

[12] B. Roux, Personal communications (2002).

[13] M. Symmons, S. Martin, and P. Bayley, Journal of Cell Science 109,

pp. 27552766, (1996).

[14] H. Li, D. J. DeRosier, W. V. Nicholson, E. Nogales, and K. H. Downing,

Structure 10, pp. 13171328, (2002).

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[15] V. VanBuren, D. J. Odde, and L. Cassimeris, PNAS 99, pp. 60356040,

(2002).

[16] D. Sept, N. Baker, and J. A. McCammon, Protein Science 12, pp. 2257

2261, (2003).

[17] J. Tuszynski, J. Brown, E. Crawford, E. Carpenter, M. Nip, J. Dixon, and

M. Sataric, Mathematical and Computer Modelling , (accepted April 11

2003).

[18] N. Baker, D. Sept, S. Joseph, M. Holst, and J. McCammon, Proceedings

of the National Academy of Sciences 21, pp. 1003710041, (2001).

[19] W. Humphrey, A. Dalke, and K. Schulten, J. Molecular Graphics 14,

pp. 3338, (1996). http://www.ks.uiuc.edu/Research/vmd/.

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Results of Molecular Dynamics Computations of the Structural andElectrostatic Properties of Tubulin and Their Consequences for Microtubules

J. A. Tuszynski et al.

(a) (b)

(c) (d)

(e) (f)

Figure 1: Electrostatic potential at the water accessible surface. Blue is neg-ative, white is neutral and red (none shown) is positive. The views are facingradially out of (a) and into (b) the MT, the exposed -end (c) and the exposed-end (d) and tangential to the MT with the monomer on the right(e) andthe left (f). Images created with VMD [19].

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(a) (b) (c)

Figure 2: A tubulin dimer in vacuum (a) is seen principally as a monopole fromthe point of view of the electrostatic potential while it is mainly dipolar when

surrounded by counterions and water ((b) and (c)). Images created with VMD[19].

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(a) (b)

Figure 3: Potential energy tubulin-tubulin interaction map for the average struc-

tures of (a) GTP1 and (b) GDP1. The axes represent the center-of-mass dis-placement between the two dimers while the colour represents the potentialenergy in kcal/mole. Areas of high steric conflict have been colored blue.

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Potential

(eV)

Kinesin Position

Along Protofilament ()

Kinesin

Position

()

Figure 4: Map of the interaction energy between a kinesin head and a protofil-ament.

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Figure 5: Electrostatic potential at the water accessible surface of the kinesinhead domain (PDB ID: 1I6I)[4]. Figure prepared using MolMol[11].

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Figure 6: A kinesin head domain is shown bound to two tubulin monomers.Data from PDB file 1IA0[4]. Image created with VMD [19].

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Table I: The key electrostatic properties of the tubulin dimer withGTP or GDP in the exchangeable site.

Tubulin properties Tu-GTP RMSF Tu-GDP RMSF(w.r.t. center of mass)

charge (electrons) -54 -53dipole (Debye)

overall magnitude 4850 360 5090 140x-component 700 140 870 220y-component 200 180 370 410z-component 4800 341 4970 130

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