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

From Noskov, Berneshe and Roux, Nature,2004

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

Upward motion of voltage-sensor helices (S4)

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?

-70

+30

Na+Na+

K+

K+

R

C

V1V2

Charging time: = RC(delay)

time

V1

V2

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

Invertebrates Vertebrates

0.8 mm in diameter

2-5 micrometers

Po – intermembrane adhesion protein (immunoglobulin-like)PMP22 – helps compacting the membranesMBP – basic protein remaining in the cytosolGap junction proteins perforate membranes to allow nutrients

From

Hill

e, 2

00

1

Saltatory excitation in myelinated fibersFig. 8-17

Myelin coat reducesCAPACITANCE

Velocity is proportional to the internodal distance

Fig. 8-13