A. Priel, J.A. Tuszynski and N. Woolf: Transitions in Microtubule C-termini Conformations as a...

8/3/2019 A. Priel, J.A. Tuszynski and N. Woolf: Transitions in Microtubule C-termini Conformations as a Possible Dendritic Signaling Phenomenon

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Transitions in Microtubule C-termini Conformatio

Signaling Phenomenon

Running Title: MT C-termini Transitions

Avner Priel,* Jack A. Tuszynski* and Nanc

*Department of Physics, University of Alberta Edmonto# Behavioral Neuroscience, Department of Psychology, Universit90095-1563, USA

(Dated: November 25, 2004)


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(Dated: November 25, 2004)

I. INTRODUCTION

Microtubules (MTs) have long been known to play key role

cells. Cell division, for example, is accomplished by the dynamic re

and the segregation of the chromosomes by mitotic spindles that ar

2002). Whereas all living cells contain MTs, in neurons they facilit

extend over large (even macroscopic) distances. Elongated structur

dendrites of large pyramidal cells of cerebral cortex, provide an env

are electromagnetic in nature may propagate along the long axis of


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When Nogales et al. (1998) determined a 3D-structure of tubu

resolved because the C-terminus region is highly flexible and lies o

tubulin. However, one can model conformation dynamics of the C-

sequences in conjunction with the available crystallographic structu

relevant results in the next section.

The C-termini of tubulin are located on the outside of the M

with other proteins, such as MAP2 and kinesin (Sackett, 1995). Ind

12 near the C termini of tubulin in MTs (Al Bassam et al 2002)


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is a phenomenological property of the ions ability to compensate f

on temperature and the solvent. In 1926, Bjerrum developed a mod

formation theory provided that the ions are small, of high valence,

the solvent is small. The Bjerrum length is the distance at which the

charges equals kB

T, the thermal energy, creating an equilibrium fro

preferentially move. The cylindrical volume of ionic depletion outs

polymer serves as an electrical shield. Thus, the wire-like behavio


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II. STRUCTURAL AND ELECTROSTATIC PROPE

INCLUDING C-TERMINI

In humans tubulin exists in dozens of homologous isoforms, s

expressed in the human brain (Lu et al., 1998). A 3D structure of tu

et al. (1998) and later refined by Lwe et al. (2001) but several ami

termini of the protein were not resolved, and hence these amino aci


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not be interpreted as corresponding to any real conformation. The

were in part produced using MolMol (Koradi et al., 1996).

The C-termini of tubulin are strongly negatively charged (h

electrons each) and interact electrostatically with several other char

namely: (a) the surface of the tubulin dimer (which is generally neg

16 negative charges per tubulin monomer, but which has a positive

surface that can bind a C-terminus), (b) with neighboring C-termin

as kinesin or MAP2


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e.g. wave propagation. As will be elaborated in the discussion, such

switched on and off; this might be of significance to dendritic infor

trafficking. However, due to the complexity and computational de

faced with a need to simplify the modeling effort.

III. MODELING THE C-TERMINI AS CHARGED R

Based on the assumption that C-termini dynamics plays an im


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between the two metastable states is relatively small, on the order o

allowing for transitions between the two main conformational state

elaborate on this below.

In this preliminary analysis we map the interaction energy of

neighbors to investigate its static properties; dynamic properties wi

simplicity, we model the C-terminus as a charged rod (of negligible

to the surface of the tubulin dimer and can move otherwise above t


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180), and D is the Debye screening length that depends on the

surrounding solution.

The tubulin dimer has a complex surface both geometrically a

we model it as a 2D rectangular area with a certain average charge

positively charged regions whose locations are based on calculation

Considering the dimer and one of its C-termini, with center of the d

surface contribution to the interaction energy is given by:


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>

+=

nmd

nmdd

d

r 7.1

7.1

80

1)( 7.1

79

Further effects of the ionic solution are taken into account o

Huckel factors (Daune, 1999).

The governing equations were evaluated on a grid defining the

5 depicts the simulation setup where a test C-terminus is rotating w

base is fixed), (, ) denoting the azimuth and elevation, respective

is frozen i e neighboring C termini and the dimers surface a neg


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here is that, at least under the assumptions of the model, there are tw

moderate energy barrier separating them. The insert in Fig. 7 shows

IV. DESCRIPTION OF A FLEXIBLE C-TERM

In this section we extend our model in order to simulate the d

To enable exhaustive simulations, we model the C-terminus as a se

connections, instead of the rigid rod, in what is known as the bead-

f i l i l Th i l i i j


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B. The Bead-Spring Model

A C-terminus has a molecular weight of ~2 kDa and is arrang

of trying to model its entire secondary structure, we use an approxi

modeled by a bead with an equivalent mass while the charge is dist

To maintain the chain we use the following interactions:

Coulomb interactions between the electric charges; The Lennard-Jones potential: short range forces

distance is shorter than a cut-off. This force is respo


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The harmonic dihedral potential:

Udihedral = K d(1+cos(n - 0))

where for the quartet (ijkl) we define

= (ijk) (jkl), the angle be

(ijk) and the plane spanned by (jkl).

The other two contributions to the equation of motion are:

Friction forcesFf= -m v,

where v is the velocity vector and

is the friction coeffi


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shown in Fig. 10 describe the minimal energy positions of beads repr

residues of a C-terminus ranging from 3 to the end for each run after

minimized value can come from each of the beads at positions from 3

permanently connected to the surface and hence has no freedom to m

be at the vertical coordinatez = 0.45 nm for technical reasons. Fig. 1

of the probabilities corresponding to the data shown in Fig. 10. It is s

the down position which includes all cases of full or partial attachme

V. MODEL OF AN IONIC WAVE PROPAGATION A


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domain is composed of roughly the first 418 amino acids so we tak

of MAP2b to constitute the projecting domain. Assigning a single p

residue, and a negative ones to Asp and Glu with His being given a

isoelectric point and leaving the remaining residues neutral, we tak

projecting domain to be 150 e and its charge distribution to be ve

We are now able extend our model to include MAP2 as a su

which counter ions are attached We are aware of the still unresolv


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viscous force due to temperature fluctuations and a perturbation ex

changing its state (details given below). An additional constraint is

located approximately 0.2 nm from the MAP2 (representing a repel

Our main focus in the following investigation is the charact

perturbation along the MAP2. The results reported below were obta

model. The model Hamiltonian can be written as follows:

|(|21

)|(|21

2 12

02

rrbrr KbKM

Hi

iic

iii

b

ii ++= &


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assumption about the average distance between binding sites. As d

of the residues of MAP2 we infer that there are approximately 150

MAP2 is a 50 nm rod-like structure, we obtain a charge distribution

the MAP2 axis (length estimation is obtained from average measur

model actually represents a two-dimensional structure perpendicula

the average charge separation to be l0= 1 nm. The bond length for t

is 2.5-4 ; in our simulations we, therefore, used b0=3.5 . The rep

chosen here is an average between sodium and calcium ions M 30


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Three figures show several properties of the wave propagati

counter-ions. Figure 13 depicts the counterion displacement paralle

the ith counter-ion. The counter-ions near the MAP2-base are attrac

displacement is effectively negative. The wave propagates along th

from the other end; this process may re-occur a few times. The amp

attenuated and depends on the value of the damping factor . The a

mainly an artifact of the experimental setup in which the C-terminu

th th d h f t i t d hibit fl t ti


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vph 2 nmps-1. Finally, it is worth mentioning that the velocity sc

More details of this analysis will be published separately.

V. SUMMARY AND DISCUSSION

In this paper we have modeled static and dynamic properties of the

comprise neuronal microtubules. We have used various computatio


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state. In other words, the system tends to be mostly in the 'up-state'

surface binding sites where the probability of attraction increases.

Finally, we studied the properties of ionic wave propagation from o

MAP2. The trigger for this wave may be a near by C-terminus chan

an adjacent ion-channel. Under the non-condensed counter-ions ass

motion for a one-dimensional chain of counter-ions along the MAP

properties of such a wave It has been found that the wave may pro


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states of C-termini affect this binding (Al-Bassam et al., 2002; Tho

conformational states of the C-termini must at some point be taken neural processing that depends on transport of synaptic proteins ins

connection, Kim and Lisman (2001) have shown that inhibition of

AMPA receptor-mediated response in hippocampal slice. This mea

receptors depends on MT dynamics, and MT motors determine the

postsynaptic currents (EPSC).

Furthermore a walking kinesin carries with it a protein or a


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REFERENCES

Al-Bassam, J., R.S. Ozer, D. Safer, S. Halpain, and R.A. Mill

bind longitudinally along the outer ridges of microtub

Biol. 157:1187-1196

Alberts, B., A. Johnson, J. Lewis, M. Raff, K. Roberts, and P

Biology of the Cell. Garland Science Publishing, New

Brooks, B.R., R.E. Bruccoleri, B.D. Olafson, D.J. States, S. S


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Koradi R., M. Billeter, and K. Wuthrich. 1996. MolMol: A Pr

Analysis of Macromolecular Structures. J. Mol. GrapLwe, J., H. Li, K.H. Downing, and E. Nogales. 2001. Refine

3.5 . J. Mol. Biol. 313:1083-1095

Lu, Q., G.D. Moore, C. Walss, and R.F. Luduena. 1998. Struc

Properties of Tubulin Isotypes. Adv. Structural Biol. 5

Makrides, V., T.E. Shen, R. Bhatia, B.L. Smith, J. Thimm, R.

2003 Microtubule dependent oligomerization of tau:


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engineering. B.B. Biswas, and S. Roy, editors. Kluwe

Dordrecht. 24:255-302.Steward, O., and E.M. Schuman. 2001. Protein synthesis at sy

Annu. Rev. Neurosci. 24:299325

Stracke, R., K.J. Bohm, L. Wollweber, J.A. Tuszynski, and E

the migration behaviour of single microtubules in elec

Biophys. Res. Commun.293:602-609

Swope W C H C Andersen P H Berens and K R Wilson


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APPENDIX A

The choice of model parameters

The basic units in our simulation were selected as follow

o Mass: 1 amu = 1 Dalton = 1.661027 kg

o Time: 1 ps (11012 s)

o Charge: 1 e (1.61019 C)

o Length: 1 nm (hence, velocity is 1 nm/ps)

E kJ/ l


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o K

d = 4 (the force constant)

o 0 = 0

0 (or

)

o n=2 multiplication factor

The friction coefficient used:

=0.03

The noise was taken from a (3D) uniform distribution [-

External force representation:

The external force is simulated as a traveling localized wave w

F(z(i), t) = amp sech (b(z(i) vt))2 wherez(i) is thez-coordinate o


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Figure Captions

Fig. 1. Diagram of C-termini on the tubulin dimers of microtubules

synapses. Axon terminals typically input to spines, many of which

glutamate receptors. Kinesin motors transport cargo along microtub

transport of kinesin along microtubules and this affects transport of

Fig 2 A map of the electric charge distribution on the surface of a


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Fig. 6. Evaluation of Eq. 1 for the interaction energy between a testvs. the azimuthal angle; each line in the figure describes an elevatio

Fig. 7. Energy surface of the interaction between the test C-terminu

colorbar is in [eV]. The insert shows a zoom of a saddle point on th

Fig 8 Plot of the function F(z(i) t)= amp sech(b(z(i) vt))2 where


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Fig. 12. A schematic model of the MAP2 interacting with positive

two dimers at both ends of the MAP2 and a slanted C-terminus. Thmodel used to describe the interactions between the MAP2 and the

Fig. 13. Results of the MAP2 model simulation describing the coun

axis denotes the discrete indices of the counter-ions). The color bar

Fig 14 Time derivative of the counterions displacement evaluated

D d it S


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Dendrite S

Spine

Axon

Terminal

Micro

tubu

les


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C-termini


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tubulin

dimer

C-termini


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I t ti E t V


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0.4

0.5

0.6

nEnergy(eV)

Interaction Energy at Va


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1

1.2

rgy

ev

20

300.3

0.4

0.5

6


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3

4

5

6

C terminal Conformations (A


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4 2

0

2

4

1

3

4 2 0

2 4

0

2

4

50

5

1

3

55

C-terminal Conformations (Ax

Bead Position Probabil


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10

9

8

7

65

bead 3

bead 4bead 5

ans,unnormalized) Bead Position Probabil

Bead Position Cumu


40/460 50.6

0.7

0.8

0.9

1.0

bead 3

bead 4bead 5

a

t

y

Bead Position Cumu


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l0 = 1 nm

inm


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Propagation Velocity


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50

45

4035

30

25tion(nm)

Propagation Velocity


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kinesin detach where

C-termini lie flat

C-terminal stto adja

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