Lecture 18 Selectivity Electrophysiology continued: V-gating The speed of spike propagation and the...
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Transcript of Lecture 18 Selectivity Electrophysiology continued: V-gating The speed of spike propagation and the...
Lecture 18
Selectivity
Electrophysiology continued: V-gating
The speed of spike propagation and the geometry of the axon
Role of myelination
Why are K+ channels highly selective for K+ and Na+ channels are not always highly selective for Na+?
From the Goldman treatment we can see that a sufficient depolarization can be easily achieved with a non-selective cationic channel that passes both Na+ and K+. Indeed, we need to depolarize the membrane to the threshold (- 55 mV) to evoke excitation.
High selectivity for K+ is required specifically to re-polarize the cell to its resting state (-70 mV) and keep it there.
Potassium channel KcsA (from Streptomyces lividans)
carbonyl oxygens (red) substitute for water and provide high selectivity for potassium
Selectivity filter
In the selectivity filter of KcsA the K+ ion is overcoordinated relative to bulk water where only four molecules constitute the first hydration shell around the ion. It’s because water forms electrostatic H-bonds with the surrounding water which largely outcompete the ion. In contrast, there are no H-binding groups around the selectivity filter, which is dedicated to coordinate the ion only.
from Varma and Rempe, BJ 2007
from Varma and Rempe, BJ 2007
K+ ion can be coordinated by water (Hydroxyls), formamide (Carbonyls) and by di-glycine (Bidentate carbonyl ligands). The latter mimics the KcsA binding site and the computed free energy of transfer from water to this biding site is close to zero. This is the condition for the fastest transport in/out/across the channel.
Carbonyl oxygens cannot ‘come in touch’ with the smaller Na+ because they start repelling each other (partial charge ~-0.7e on each)
From Noskov, Berneshe and Roux, Nature,2004
According to Molecular Dynamics, the selectivity filter of KscA is not rigid, but can easily ‘collapse’ on a smaller Na+ ion. However, the resultant energy becomes higher due to repulsion between the carbonyl oxygens (see table on the next slide)
NMA = N-methylacetamide, a ligand that has carbonyls
O½
Selectivity Filter
Crowded with Charge
Wolfgang Nonner, Robert Eisenberg
+
++
The selectivity filter of L type Ca Channel consists of four Glutamic acid sidechains (EEEE) crowded in a narrow space. Ions are
attracted or excluded based on the charge/volume ratio
“E Side
Chains”
Selective Binding Curve: at approximately 10-6 M Ca2+ displaces Na+ in the selectivity filter L type Ca channel
Wolfgang Nonner
L type Ca Channel
13
Ion Diameters‘Pauling’ Diameters
Ca++ 1.98 Å
Na+ 2.00 Å
K+ 2.66 Å
‘Side Chain’ Diameter
Lysine K 3.00 Å
D or E 2.80 Å
Channel Diameter 6 Å
Parameters are Fixed in all calculations in all solutions for all mutants
Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie
‘Side Chains’ are Spheres Free to move inside channel
Snap Shots of Contents
In order to convert the channel from Ca to Na-selective, the EEEE motif can be changed to DEKA. All you need is to put the charges into a 6Ǻ confinement
6Å
Radial Crowding is Severe
Experiments and Calculations done at pH 8
The Voltage Sensor
++
+
electrometer
voltage-gated channel
kTzekTG
c
o eeP
P //
o
c
Charged transmembrane helix = voltage sensor
Voltage dependence of open probability
helices S1-S6
0 0.05 0.1 0.150
0.2
0.4
0.6
0.8
1
0
Po2 x( )
Po1 x( )
Po3 x( )
, V
kTzeGokTG
c
o eeP
P /)(/
oc PP 1
1
1
1 /)(/)(
/)(
kTzeGokTzeGo
kTzeGo
o ee
eP
10
4
2
310
/10381.1
106022.1
10
3
2
1
23
19
z
z
z
KT
KJk
Ce
kTG
Variations of the charge in the sensor change both the midpoint and the slope of activation curves
intrinsic bias
kTzeGo
o
o eP
P /)(
1
o
c
A semi-log plot provides limiting slope for Po at low potentials, which is proportional to z
, V
0 0.05 0.1 0.151 10 5
1 10 4
1 10 3
0.01
0.1
1
Po1 x( )
Po2 x( )
Po3 x( )
Typical z values for ion channels:
Shaker (delayed rectifier) z ~ 13 (3.25/subunit)
Various TRP channels z ~ 0.6-2
VDAC (mitochondrial anion channel) z~ 3-4
Scheme of VDAC gating under positive or negative membrane potentials
VDAC = voltage dependent anion channel, conducts ATP and ADP
positive ‘lip’
Modification of the gate by polyelectrolytes (dextran sulfate) dramatically changes apparent z in VDAC
Properties of different fibers (axons) in the peripheral NS
Fiber type Myelination Function Diameter Conduction velocity
μm m/s
A + motoneurons 12-20 70-120
A + Touch sensation 5-12 30-70
A + muscle spindle 3-6 15-30
A no pain, temperature 2-5 12-30
B + visceral afferents, 1-3 3-15auton. preganglion.
C no pain, temperature, 0.3-1.3 0.7-2.5auton. postganglion.
unmyelinated fiber myelinated fiber
=regular wire =High-frequency cable
What defines the speed of spike propagation?
R
Cr
Delay =RC is proportional to 1/r, therefore velocity V ~ r
R = 1/G, therefore R ~ 1/r2
Internal conductance is proportional to the cross-section: G ~ r2
Capacitance is proportional to the surface area of the cylinder A ~ 2r L
therefore C ~ r
Na+
L
Po – intermembrane adhesion protein (immunoglobulin-like)PMP22 – helps compacting the membranesMBP – basic protein remaining in the cytosolGap junction proteins perforate membranes to allow nutrients
Saltatory excitation in myelinated fibersFig. 8-17
Myelin coat reducesCAPACITANCE
Velocity is proportional to the internodal distance