Computational Details
Conductances: The conductance of the luminal core region was calculated as:

ax
lumen
G
2
K0 cbulk rlumen
,

l
(S1)
where l is the length of one tubulin monomer, taken as 40.5Å, cbulk is the bulk
concentration assumed to be 150 mM throughout this study, and rlumen is the radius of
the inner lumen.
The conductances along the ionic atmospheres adjacent to the inner and outer
surfaces of the microtubule were determined by first solving the Poisson-Boltzmann
(PB) equation for an electrostatic potential grid (r), and then determining a total
number N of positive charges as:
N
 rdr =  
e
bulk

q r 
kB T
dr 

 q r 
1
dr ,
 kB T 
bulk
(S2)
where (r) represents the density of ions with charge q. The Poisson-Boltzmann solver

implemented
in the 3d PB-PNP program was used to determine maps of electrostatic
potential[1--4], as will be described below. These conductances are then given by,

G
ax
surface

K NA 13K0 N monomer
,
 0

Vl
l2
(S3)
where Nmonomer is the ion count within the condensed counterion atmosphere extending
the length of one monomer along the microtubule.
To approximate the conductances determining the flow of cations in the radial
direction between the outer ionic atmosphere and the bulk, and between the inner ionic
atmosphere and the inner lumen respectively, integration of resistive elements
corresponding to cylindrical shells with differential widths dL was performed over
radial positions L ranging from the radial position of the ion, L*, in the counterion
sheath, to the boundary of the outer or inner atmosphere of condensed counterions with
width w, and an average was taken over values of L* ranging from the microtubule
surface at radial position s to s ± w (where the plus sign should be taken for the outer
surface and the minus sign for the inner surface):
R
rad


dL
sw
L*
K0 cL A( L)

L*s , s  w 
1

13

dL2
sw
L*
K0 N monomer dL 
,

(S4)
L *s , s  w 
where c(L) and A(L) are, respectively, the concentration and cross-sectional area at
radial position L, and Nmonomer(dL) is the ion count within a differential cylindrical shell
extending the length of one monomer along the microtubule.
Brownian dynamics: Brownian dynamic calculations were performed on microtubule
nanopores of types 1 and 2, created from atomic level models of tubulin isotypes αIV
and βI, as described elsewhere [5]. These models were constructed using an in-house
VMD [6] script and are representative of microtubules composed of the canonical 13
protofilaments [7]. AMBER format files were obtained from pdb files using the LEAP
module of AMBER9 [8], and the system was then centered at the origin using the ptraj
module of AMBER9. After writing effective Born radii and partial atomic charges of
all atoms from the AMBER03 force field, file formats were then converted to
CHARMM-style [9] input files. The protein was placed in an orthorhombic box with
dimensions 140.5Å by 110.5Å by 54.5Å. A KCl salt buffer at a bulk concentration of
150mM was implemented. The dielectric constant was set to 2 for the protein and 80
for the surrounding solvent. The electrostatic potential grid around the protein mapping
the static field contribution to the multi-ion potential of mean force was created using
the PB-PNP program [1,2], first on a coarse grid with 2503 points and a spacing of 1.5
Å, and then on a finer grid using 2503 points and a spacing of 0.75 Å. The accessible
surface area based on exclusion radii (Stern radius) was also created using the PB-PNP
program to incorporate the repulsive contribution to PMF, and finally Brownian
dynamics trajectories were run with the GCMC/BD program [3].
In the GCMC/BD method, random walks of ions are generated with creation and
destruction of ions occurring in two outer buffer regions, one on each side of the
channel, according to a fixed chemical potential, taken to be -0.187 kcal/mol for K+ and
-0.190 kcal/mol for Cl- according to solution of the Ornstein-Zernike equation [1].
These outer regions were placed at from 25.25 to 27.25Å and from -27.25 to -25.25Å,
respectively, along the z-axis, which is directed radially through the pore. K+ and Clions were assigned diffusion constants of 0.196 and 0.203 Å2/ps, respectively, in
accordance with theoretical and experimental data [1,2]. For each data point
corresponding to a different value of the electric field V, 5 independent simulation runs
were generated using different values of the random number seed and used to determine
average values for currents. Each of these simulations corresponded to a length of 0.3
s and a time step of 15 fs, and followed 3 ns of equilibration using the same time step.
C-terminal tails: Atomic level representations of nanopores were used. One molecule
of GTP was included on the -tubulin, and one GDP on -tubulin, as well as one Mg2+
ion on each monomer with positions taken from the pdb-listed crystal structures 1TVK
[10] or in the case of the non-exchangeable Mg2+, from 1JFF [11]. Protonation states of
protein residues were assigned using the PROPKA program [12,13]. A slight
modification of the PB-PNP code was introduced to count ions in a box with lateral and
longitudinal dimensions equal to those of a monomer, centered on an axis directed
through the middle of the nanopore.
Literature Cited
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Figure Headings.
Figure S1: (a) Two kinds of pores in the microtubule lattice, viewed from above,
visualized using the VMD program (6) (type 1 on the right and type 2 on the left). The
two  protofilament sequences are oriented with plus ends to the right. (b) Cut
through microtubule pore type 2, viewed down the microtubule axis from the plus end
with the luminal side on the bottom using the DINO program [14]. Cl- ions are depicted
in red and K+ ions in green. The surface is colored by electrostatic potential, using a
grid created with the APBS program [15].
Figure S2: Cationic charge within condensed outer counterion atmosphere versus
voltage between ionic atmosphere and bulk, plotted for a one monomer-sized area
centered about a pore of type 1 (a), and type 2 (b).
Figure S3: (a) Current-voltage relation from GCMC/BD simulation for conductance of
anions through the type 1 pore. Conductances of cations and anions through the type 2
pore are shown in parts (b) and (c) respectively. Error bars represent standard deviations
over 5 independent data subsets.
Figure S4: Time-integrated current (nC) for asymmetric pore conductance plotted
against time (ns), with an external voltage of 1mV, and a stochastic voltage of 0mV.
The four panels, are from top to bottom, time-integrated current through (a) the bulk
solution outside the microtubule, (b) the outer ionic atmosphere of the microtubule, (c)
the inner ionic atmosphere of the microtubule, and (d) the rest of the lumen.
Figure S5: Time-integrated current (nC) for symmetric pore conductance plotted against
time (ns), with an external voltage of 1 mV, and a stochastic voltage of 28mV. Parts (a)
- (d) correspond to the same 4 cylindrical regions as in Figure S4.
Figure S6: Color plot showing integrated current (nC) as a function of time (ns) and
tubulin unit through (a) the bulk solution outside the microtubule, (b) the outer ionic
atmosphere of the microtubule, (c) the inner ionic atmosphere of the microtubule, and
(d) the rest of the lumen. A stochastic voltage of 28 mV was used, and an external
voltage of 1 mV.
Figure S7: Current-voltage relations calculated using the circuit model for conductance
of cations through the microtubule lumen. The dotted and dashed lines correspond to
stochastic voltages of 14mV and 28mV, respectively, with a microtubule length of 30
monomers; the solid and dash-dotted lines correspond to stochastic voltages of 14mV
and 28mV, respectively, with a microtubule length of 10 monomers.
Fig. S1 (a)
Fig S1 (b)
Fig. S2 (a)
Fig. S2 (b)
Fig. S3 (a)
Fig. S3 (b)
Fig. S3 (c)
Fig. S4
Fig. S5
Fig. S6
Fig. S7