Download Role of the Intracellular Cavity in Potassium Channel Conductivity

Role of the Intracellular Cavity in
Potassium Channel Conductivity
Simone Furini, Francesco Zerbetto, and
Silvio Cavalcanti.
J. Phys. Chem. B 111: 13993-14000, 2007
Department of Electronics, Computer Science and Systems, and Department of
Chemistry “G. Ciamician”, University of Bologna, Italy.
http://einstein.ciencias.uchile.cl
28 de mayo 2010
Role of the Intracellular Cavity in Potassium Channel Conductivity
Fig. 7. Two mechanisms by which the K1 channel stabilizes a cation in the middle of the
membrane. First, a large aqueous cavity stabilizes an ion (green) in the otherwise
hydrophobic membrane interior. Second, oriented helices point their partial negative
charge (carboxyl end, red) towards the cavity where a cation is located.
Doyle et al 1998. Science 289:69-77
Calculated free energy (in kilocalories per mole) for the transfer of a single K1 ion from
bulk water to the cavity center is shown for a variety of conditions. K 1 refers to the ion
being transferred into the cavity, whereas K2 and K3 refer to the ions in the selectivity
filter. The pore helix consists of residues Tyr62 to Thr74 in addition to the main-chain
atoms of Thr75, but excluding its carbonyl group. The side chain of Glu71 has been
modeled in its protonated state. “All protein” and “pore helices only” refer to the part of
the protein where charges have been turned on.
Roux and MacKinnon 1999 Science 285:100-103
Figure 1 Channel models and amino acid sequences. The crystallographic structure of KcsA is
shown, together with the structures of the KvAP- and MthK-based models. For the sake of
clarity, only two of the four channel subunits are shown (M1 helixes in blue, M2 in red and Ploop in green). The amino acid sequences of KcsA, KvAP, MthK, and mSlo1 (BK potassium
channel) are shown at the bottom. The amino acids A108 and T112 in the KcsA sequence are
highlighted in purple, as the negatively charged residues in the M2 helix of MthK and mSlo1.
Published in: Simone Furini; Francesco Zerbetto; Silvio Cavalcanti; J. Phys. Chem. B 2007, 111, 13993-14000.
DOI: 10.1021/jp0747813
Copyright © 2007 American Chemical Society
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Electrostática:
Una carga eléctrica, q, genera un campo eléctrico a su alrededor. Este
campo se manifiesta por el potencial eléctrico en la vecindad de la carga.
El potencial eléctrico,  de un punto en el espacio se define como el
trabajo (joule) necesario para traer una carga unitaria (coulomb) desde
el infinito a ese punto del espacio. Se mide en volt (joule/coulomb)
El potencial eléctrico depende de distancia entre el punto y la
carga que crea el campo. El gradiente de potencial eléctrico se
llama intensidad de campo E. Se mide en volt/metro es un
vector y su magnitud y tiene unidades de newton coulomb-1.
E   (r) NC-1
El flujo eléctrico  que emana de una superficie cerrada es la
integral de la intensidad de campo eléctrico sobre el toda el
área de la superficie cerrada.
   E  ds Nm C
2
A
-1
ds es un elemento,minfinitesimal de
área,
E
La ley de gauss:
El flujo eléctrico  que emana de una superficie cerrada es la
integral del campo eléctrico potencial eléctrico sobre el toda
el área de la superficie cerrada.
2 -1 ds es un elemento,infinitesimal de área.
   E  ds Nm C
A
La ley de Gauss dice que el flujo
proporcional a la carga Q encerrada en la
superficie cerrada.
   E  ds 
A
0
Nm2C-1
0  8.85421012 C2 N-1m-2
El factor de proporcionalidad es 1/0, y 0
es la permitividad eléctrica.
   E  ds     Edv 
Q
Q

Nm2C-1
Teorema de la divergencia
0
A
V
Supongamos que E representa un flujo de material por unidad de superficie. La
ecuación dice que la cantidad total de material que sale por toda la superficie es igual al
cambio en la cantidad total de materia en el recinto, que a su vez es la sumatoria de los
cambios de cantidad de material en cada uno de los elementos de volumen del recinto.
   E  ds     Edv 
A
V
     Edv 
V
E 
q(r)
0
1
0
Nm2C-1
2 -1
q
(
r
)
dv
Nm
C

0 V
-1
Q
-1
Nm C
Ley de Gauss, forma diferencial.
En un medio material
hay que considerar la
permitividad relativa o
constante dieléctrica 
q(r) es la densidad de carga en
cada elemento de volumen
coulomb m-3.
q(r)
-1 -1
E 
Nm C
 0 (r)
e(r) es la constante dieléctrica.
   0 (r)E  q(r) Cm
E   (r) NC-1
  0 (r)(r)  q(r) Cm-3
Poisson
ni (r)  n0ee0zi (r) / kT m-3
Los iones se mueven libremente y
se distribuyen según Boltzmann.
n = number density m-3
-3
   0 (r) (r)  q proteina(r)   e0 zi ni (r) Cm-3
n
i 1
Potencial químico 
Flujo J
 G 
i   
joule mol-1
 ni  P,T ,ni
Ji (r)  ci (r)uii (r)
i newtonmol-1
J = flujo, mol m-2s-1
c = concentración mol m-3
u = movilidad ms-1/Nmol-1
= fuerza Nmol-1
i  i0  RT ln ci (r)  zi F(r)
Ji (r)  ci (r)ui RT ln ci (r)  zi F(r)
 ci (r)

J i (r)  ci (r)ui RT
 zi F (r) Di  ui RT
ci (r)

 Einstein
F

 Mult. Por No
J i (r)  Di ci (r) 
zi ci (r) (r)
RT

 Avogadro
e0


Nernst-Plank
J i (r)  Di ni (r) 
zi ni (r) (r)
kT


Flujo en partículas m-2s-1
PNP Poisson-Nernst-Plank
   0 (r)(r)  q proteina(r)   e0 zi ni (r) Cm
n
-3
Poisson
i 1
e0


J i (r)  Di ni (r) 
zi ni (r) (r) m-2s-1
kT


  J i (r)  0
I  e0  zi Ji (r) amper m-2
Método de las diferencias finitas.
Definición de la grilla tridimensional en coordenadas cilíndricas:
z a lo largo del eje del poro, un nodo cada 0.05 nm ( 140 nodos).
r coordenada radial, un nodo cada 0.025 nm (150 nodos), 1.5 veces el
radio de la proteína)
 Coordenada angular , un nodo cada 0.087 radianes ( 73 nodos).
Usa dos iones K+ y Cl-. Concentración de la sal es 100 mM.
Coeficientes de difusión son los de difusión en agua menos un 10%
Nernst-Plank
Steady state
Figure 1 Channel models and amino acid sequences. The crystallographic structure of KcsA is
shown, together with the structures of the KvAP- and MthK-based models. For the sake of
clarity, only two of the four channel subunits are shown (M1 helixes in blue, M2 in red and Ploop in green). The amino acid sequences of KcsA, KvAP, MthK, and mSlo1 (BK potassium
channel) are shown at the bottom. The amino acids A108 and T112 in the KcsA sequence are
highlighted in purple, as the negatively charged residues in the M2 helix of MthK and mSlo1.
Published in: Simone Furini; Francesco Zerbetto; Silvio Cavalcanti; J. Phys. Chem. B 2007, 111, 13993-14000.
DOI: 10.1021/jp0747813
Copyright © 2007 American Chemical Society
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the
entrance cavity increases.
Figure 2 Channel conductance at different gate openings. The blue dashed line (circular points)
and the red dotted line (square points) show the channel conductance when the membrane
potential is set to 100 mV and 25 mV, respectively. The x axis ranges from the KcsA-based
model to the MthK-based model. Tics on the x axis highlight the location of the KcsA-, KvAPand MthK-based model. The mean radius of cavity in these structures is shown. Potassium and
chloride concentrations are set to 100 mM.
Published in: Simone Furini; Francesco Zerbetto; Silvio Cavalcanti; J. Phys. Chem. B 2007, 111, 13993-14000.
DOI: 10.1021/jp0747813
Copyright © 2007 American Chemical Society
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the
entrance cavity increases.
Widening of the vestibule, in fact, increases the volume accessible to water, which is the
volume with a high dielectric constant. In turn, water screens the attractive charges of the Ploop backbone.
Figure 3. Gate opening: electric potential and K+
concentration.
(Upper panels) Electric potential () and potassium
concentration ([K+]) inside the KcsA- and the KvAPbased model. The color maps show the electric
potential and the potassium concentration on a
longitudinal section of the channel. In order to focus
the color maps on the intracellular cavity, electric
potential and potassium concentrations in the
selectivity filter and in the extracellular compartment
are not shown.
(Bottom plots) Electric potential () and potassium
concentration ([K+]) along the channel axis. The z axis
extends from the intracellular to the extracellular
compartment. A logarithmic scale is used for the
potassium concentration. Different colors are used for
different intracellular gate openings: KcsA-based model
in red, color spectrum from red to purple for wider gate
openings. Continuous lines are used for the KvAP- and
MthK-based model, and dashed lines are used for the
other structures. Membrane potential is set to 100 mV,
and ion concentrations are set to 100 mM, both for the
data in the color maps and for the data in the
250
200
pS
150
100
4
5
6
7
Å
Figura 14. Gráfico de correlación entre las conductancias unitarias de los mutantes y los
radios ( del poro del canal BK) obtenidos. En el eje x están los radios ( del poro) obtenidos de
la medición teórica de los mutantes y el canal nativo (Å) y en el eje y las conductancias
unitarias obtenidas experimentalmente (pS). La regresión de los datos fue 0.86 y el ajuste
lineal representa al coeficiente de correlación (R2) de 0.734.
.
PAULA MANRÍQUEZ TESIS PARA OPTAR AL GRADO DE MAGÍSTER EN CIENCIAS MENCIÓN NEUROCIENCIA U.V.
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the
entrance cavity increases.
Widening of the vestibule, in fact, increases the volume accessible to water, which is the
volume with a high dielectric constant. In turn, water screens the attractive charges of the Ploop backbone.
Backbone charges of the M2 helixes instead oppose the entrance of potassium ions through a
complicated mechanism that can be separated in the activity of two interfering dipoles.
Figure 4. Protein charges neutralization:
electric potential and K+ concentration in
the MthK-based model. (Upper panels)
Changes in electric potential () and
potassium concentration ([K+]) induced
by the neutralization of the P-loop or M2
backbone charges in the MthK-based
model. As in Figure 3, a longitudinal
section of the channel is shown and the
color maps are focused on the intracellular
cavity. P-loop and M2 helixes, together
with dipole directions (from the negative
to the positive pole), are shown. (Bottom
plot) Potassium concentration ([K+]) along
the channel axis. The z axis extends from
the intracellular compartment to the
ottom of the selectivity filter.
Membrane potential is set to 100 mV, and
ion concentrations are set to 100 mM, for
the data both in the color maps and in the
plot.
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the
entrance cavity increases.
Widening of the vestibule, in fact, increases the volume accessible to water, which is the
volume with a high dielectric constant. In turn, water screens the attractive charges of the Ploop backbone.
Backbone charges of the M2 helixes instead oppose the entrance of potassium ions through a
complicated mechanism that can be separated in the activity of two interfering dipoles.
The conductance of the KcsA models increased when two neutral residues in M2 were
mutated to glutamic acid, in agreement with experimental results (Nimigean, and Miller.
Biochemistry 42: 9263-9268, 2003).(Brelidze, T. I.; Niu, X.; Magleby, K. L. PNAS 2003, 100, 90179022).
KcsA
MthK
Electrostatic Tuning of Ion Conductance in Potassium Channels. Nimigean, and
Miller. Biochemistry 42: 9263-9268, 2003.
Electrostatic Tuning of Ion Conductance in Potassium Channels. Nimigean, and
Miller. Biochemistry 42: 9263-9268, 2003.
A ring of eight conserved negatively charged amino acids doubles the conductance of BK
channels and prevents inward rectification. Brelidze, Niu, Magleby. PNAS 100: 90179022, 2003.
Figure 1 Channel models and amino acid sequences. The crystallographic structure of KcsA is
shown, together with the structures of the KvAP- and MthK-based models. For the sake of
clarity, only two of the four channel subunits are shown (M1 helixes in blue, M2 in red and Ploop in green). The amino acid sequences of KcsA, KvAP, MthK, and mSlo1 (BK potassium
channel) are shown at the bottom. The amino acids A108 and T112 in the KcsA sequence are
highlighted in purple, as the negatively charged residues in the M2 helix of MthK and mSlo1.
Published in: Simone Furini; Francesco Zerbetto; Silvio Cavalcanti; J. Phys. Chem. B 2007, 111, 13993-14000.
DOI: 10.1021/jp0747813
Copyright © 2007 American Chemical Society
Figure 5. Amino acid mutations: electric
potential and K+ concentration
in the MthK-based model. (Upper panels)
Electric potential () and potassium
concentration ([K+]) in the MthK-based
model, wildtype or with the A108E/T112E
mutations. As in Figure 3, a longitudinal
section of the channel is shown, and the
color maps are focused on the intracellular
cavity. (Bottom plot) Potassium
concentration ([K+]) along the channel axis.
The z axis extends from the intracellular
compartment to the bottom of the
selectivity filter. Membrane potential is set
to 100 mV, and ion concentrations are set
to 100 mM, for the data both in the
color maps and in the plot.
El efecto es
electrostático
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the
entrance cavity increases.
Widening of the vestibule, in fact, increases the volume accessible to water, which is the
volume with a high dielectric constant. In turn, water screens the attractive charges of the Ploop backbone.
Backbone charges of the M2 helixes instead oppose the entrance of potassium ions through a
complicated mechanism that can be separated in the activity of two interfering dipoles.
The conductance of the KcsA models increased when two neutral residues in M2 were
mutated to glutamic acid, in agreement with experimental results (Brelidze, T. I.; Niu, X.;
Magleby, K. L. PNAS 2003, 100, 9017-9022).
As a general conclusion, a relation between channel conductance and potassium concentration
in the intracellular cavity
Ji (r)  ci (r)uii (r)
Role of the Intracellular Cavity in Potassium Channel Conductivity
The role of several fragments of the potassium channel KcsA has been examined by the
Poisson-Nernst-Planck (PNP) theory.
Perhaps counter-intuitively, the calculated ion current decreases when the mean radius of the
entrance cavity increases.
Widening of the vestibule, in fact, increases the volume accessible to water, which is the
volume with a high dielectric constant. In turn, water screens the attractive charges of the Ploop backbone.
Backbone charges of the M2 helixes instead oppose the entrance of potassium ions through a
complicated mechanism that can be separated in the activity of two interfering dipoles.
The conductance of the KcsA models increased when two neutral residues in M2 were
mutated to glutamic acid, in agreement with experimental results (Brelidze, T. I.; Niu, X.;
Magleby, K. L. PNAS 2003, 100, 9017-9022).
As a general conclusion, a relation between channel conductance and potassium concentration
in the intracellular cavity
Although the ion transport is the result of the fine balance of a number of different effects,
the experimental results can be reproduced quantitatively only on the basis of electrostatic
forces, which are the only driving forces modeled by the PNP theory.