Lecture 18 Selectivity Electrophysiology continued Vgating The speed

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Lecture 18 Selectivity Electrophysiology continued: V-gating The speed of spike propagation and the geometry

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

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 m. V) to evoke excitation. High selectivity for K+ is required specifically to repolarize the cell to its resting state (-70 m. V) and keep it there.

Potassium channel Kcs. A (from Streptomyces lividans) Selectivity filter carbonyl oxygens (red) substitute for

Potassium channel Kcs. A (from Streptomyces lividans) Selectivity filter carbonyl oxygens (red) substitute for water and provide high selectivity for potassium

In the selectivity filter of Kcs. A the K+ ion is overcoordinated relative to

In the selectivity filter of Kcs. A 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

K+ ion can be coordinated by water (Hydroxyls), formamide (Carbonyls) and by di-glycine (Bidentate

K+ ion can be coordinated by water (Hydroxyls), formamide (Carbonyls) and by di-glycine (Bidentate carbonyl ligands). The latter mimics the Kcs. A 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. from Varma and Rempe, BJ 2007

Carbonyl oxygens cannot ‘come in touch’ with the smaller Na+ because they start repelling

Carbonyl oxygens cannot ‘come in touch’ with the smaller Na+ because they start repelling each other (partial charge ~-0. 7 e on each)

According to Molecular Dynamics, the selectivity filter of Ksc. A is not rigid, but

According to Molecular Dynamics, the selectivity filter of Ksc. A 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

From Noskov, Berneshe and Roux, Nature, 2004

From Noskov, Berneshe and Roux, Nature, 2004

The selectivity filter of L type Ca Channel consists of four Glutamic acid sidechains

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 Crowded with Charge + ++ Selectivity Filter O ½ “E Side Chains” Wolfgang Nonner, Robert Eisenberg

Selective Binding Curve: at approximately 10 -6 M Ca 2+ displaces Na+ in the

Selective Binding Curve: at approximately 10 -6 M Ca 2+ displaces Na+ in the selectivity filter L type Ca channel L type Ca Channel Wolfgang Nonner

Radial Crowding is Severe In order to convert the channel from Ca to Na-selective,

Radial Crowding is Severe 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 Ion Diameters ‘Pauling’ Diameters 6Å Snap Shots of Contents 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 ‘Side Chains’ are Spheres Free to move inside channel Parameters are Fixed in all calculations in all solutions for all mutants Experiments and Calculations done at p. H 8 Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie 13

The Voltage Sensor + voltage-gated channel o + + electrometer c helices S 1

The Voltage Sensor + voltage-gated channel o + + electrometer c helices S 1 -S 6 Voltage dependence of open probability Charged transmembrane helix = voltage sensor

Upward motion of voltage-sensor helices (S 4)

Upward motion of voltage-sensor helices (S 4)

intrinsic bias o c 1 0. 8 Po 1( x) 0. 6 Po 2(

intrinsic bias o c 1 0. 8 Po 1( x) 0. 6 Po 2( x) Po 3( x) 0. 4 0. 2 Variations of the charge in the sensor change both the midpoint and the slope of activation curves 0 0. 05 0. 1 Df, V 0. 15

1 0. 1 Po 1( x) 0. 01 Po 2( x) Po 3( x)1.

1 0. 1 Po 1( x) 0. 01 Po 2( x) Po 3( x)1. 10 3 1. 10 4 1. 10 5 0 0. 05 0. 15 Df, V A semi-log plot provides limiting slope for Po at low potentials, which is proportional to z

Typical z values for ion channels: Shaker (delayed rectifier) z ~ 13 (3. 25/subunit)

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

VDAC = voltage dependent anion channel, conducts ATP and ADP Scheme of VDAC gating

VDAC = voltage dependent anion channel, conducts ATP and ADP Scheme of VDAC gating under positive or negative membrane potentials positive ‘lip’

Modification of the gate by polyelectrolytes (dextran sulfate) dramatically changes apparent z in VDAC

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

Properties of different fibers (axons) in the peripheral NS Fiber type Myelination Function Diameter μm Conduction velocity m/s Aa + motoneurons 12 -20 70 -120 Ab + Touch sensation 5 -12 30 -70 Ag + muscle spindle 3 -6 15 -30 Ad no pain, temperature 2 -5 12 -30 B + visceral afferents, 1 -3 auton. preganglion. 3 -15 C no pain, temperature, 0. 3 -1. 3 auton. postganglion. 0. 7 -2. 5

What defines the speed of spike propagation? unmyelinated fiber =regular wire myelinated fiber =High-frequency

What defines the speed of spike propagation? unmyelinated fiber =regular wire myelinated fiber =High-frequency cable

K+ Na+

K+ Na+

V 1 V 2 Charging time: t = RC (delay) V 1 t time

V 1 V 2 Charging time: t = RC (delay) V 1 t time

r Na+ L Internal conductance is proportional to the cross-section: G ~ pr 2

r Na+ L Internal conductance is proportional to the cross-section: G ~ pr 2 R = 1/G, therefore R ~ 1/r 2 Capacitance is proportional to the surface area of the cylinder A ~ 2 pr L therefore C~r Delay t=RC is proportional to 1/r, therefore velocity V ~ r

Invertebrates 0. 8 mm in diameter 2 -5 micrometers Vertebrates

Invertebrates 0. 8 mm in diameter 2 -5 micrometers Vertebrates

Po – intermembrane adhesion protein (immunoglobulin-like) PMP 22 – helps compacting the membranes MBP

Po – intermembrane adhesion protein (immunoglobulin-like) PMP 22 – helps compacting the membranes MBP – basic protein remaining in the cytosol Gap junction proteins perforate membranes to allow nutrients

From Hille, 2001

From Hille, 2001

Saltatory excitation in myelinated fibers Fig. 8 -17 Myelin coat reduces CAPACITANCE Velocity is

Saltatory excitation in myelinated fibers Fig. 8 -17 Myelin coat reduces CAPACITANCE Velocity is proportional to the internodal distance

Fig. 8 -13

Fig. 8 -13