LECTURE 5: More Complex Potentials.

Question 1

One Ion Problem:

• which equation

Answer 1

SLIDE 4

• Can use Nernst equation to predict potential if only one ion is permeable.
• For example if only permeable to K+ potential would be:
• -61/1 x log 140/5 = -88 mV

Question 2

Divalent Example

Answer 2

1. Concentration gradient would move Calcium in.
2. Cell would get positive charge.

Ve= -61/z x log[Ca]in/[Ca]out

Ve = -61/2 x log 0.0005/2.5

Ve= 113 mV e

Question 3

What About Several Ions

Answer 3

• Real cells are permeable to many ions.
• Resting membrane potential depends on the net effect of many different ions
• Nernst equation cannot predict membrane potential
• Goldman-Hodgkin-Katz solved the problem
• Different method to Nernst
• Calculated current from all ions
• Solved complex equation of voltage

Question 4

Goldman Voltage Equation

Answer 4

• Only dealing with monovalent ions.
• Negative ions change out for in in the concentrations

SLIDE 7

Question 5

Goldman Voltage Equation

Answer 5

• Inside concentrations; Na+ 10mM, Cl- 6mM, K+ 140mM
• Outside; Na+ 145mM, Cl- 106mM, K+ 5mM
• Permeability; Na+ 0.02, Cl- 0.5, K+ 1

Question 6

Goldman Voltage Equation PURPOSE = 4

Answer 6

1 * Only relative permeability is needed

2 * That is permeability of sodium and chloride as a
fraction of potassium.

3 * As permeability to one ion increases, the membrane potential moves closer to the Nernst equilibrium for that ion.

4 * Permeability to K+ high so close to K+ V . e

Question 7

Some rules for Goldman Voltage Equation

Answer 7

• Keep the ion concentrations constant
• Increase Na+
  permeability 250 times
• Permeability; Na+ 5, Cl- 0.5, K+ 1

Question 8

Goldman Voltage Equation
PURPOSE AND RULES…

Answer 8

1 * Opening ion channels changes permeability

2 * Increasing permeability moves membrane potential toward equilibrium potential for that ion.

3 * At rest most cells much more permeable to potassium than sodium.

4 * Opening sodium channels can make the cell flip from negative to positive charge.

5 * That is the basis of the nerve and skeletal muscle action potential.

6 * (Action potentials in cardiac and smooth muscle use calcium as well)

Question 9

Nerve Action Potential = 4

Answer 9

1 * Action potential carry nerve signals

2 * Membrane goes from -70mV to positive 30mV in ~1msec.

3 * Caused by opening Na+ channels.

4 * Na+ entry brings in positive charge.

Question 10

Nerve Action Potential – 4
IN DETAIL PROPERTIES

ON A GRAPH

Answer 10

1. • At rest cell is POLARIZED
     i.e. has a charge.

2 * Move towards 0mV is DEPOLARISATION or HYPOPOLARISATION

3 * Opening of more potassium channels moves cell more negative.

4 *HYPERPOLARISED is more negative than rest.

Question 11

understanding the FLOW OF IONS = 7

Answer 11

1 * Ions move under chemical and electrical gradients.

2 * -90 mV is equilibrium.

3 * At-70mV not at
equilibrium.

4 * Constant flow of ions must occur.

5 * How much flow?

6 * In or out?

7. *Current, flux, flow?

Question 12

Flow of ions Equation? SLIDE 15

Answer 12

• Flow (f) is movement of ions (or anything else) f=n/t
• Flux is flow/area (j)
• Often get lazy and call flux flow j=f/A
• Current is flow of charge i=q/t
• Faradays constant (F) relates charge to moles q=zFn
• That is n=q/zF
• So flow f=n/t = q/zFt = q/tzF but q/t=i
• Flow = i/zF
• Change from current to flow divide by zF.

Question 13

Flow of Ions-Qualitative….

Is there a flow in or out? = 3

Answer 13

1 * For Na+ both chemical and electrical gradients point in.

2 * If cell is permeable to Na+ it will flow in. An inward current.

3 * For potassium gradients are opposite.

4 * Remember Nernst equation.

5 * At equilibrium voltage V no current flows

6 * V for K+ -90mV e

7 * Actual V -70 mV

8 * Chemical gradient wins and K+ current flows out

Question 14

UNDERSTANDING CURRENT FLOW = 7

Answer 14

1 * At Ve no current flows.

2 * Between Zero and Ve chemical gradient wins.

3* Ve also called reversal potential because current reverses at that point.

4 * For potassium, Vm more negative than Ve current flows in m.

5 * Less negative than Ve current flows out.

6 * For sodium Vm less than 70 mV current flows in, above 70 mV sodium flows out.

7* Current given as flow of positive charge, i.e. Cl- flowing into cell is a outward current.

Question 15

Current Flow SLIDE 19

Answer 15

1. Ohms Law
2. Conductance is the inverse of resistance

Question 16

slide 19

Answer 16

• Conductance is to charge like permeability is to flow
• If only voltage moves ion expect
  i+=G+V

Question 17

resistance vs Conductance:

Answer 17

• Resistance (R) is how hard it is to move charge, unit ohms
• Conductance (G) is how easy to move charge, unit Siemens (S)

Question 18

IV Curves

Answer 18

1. Current (i) =0 A at V for that ion
2. Expect x (voltage axis) intercept at V
3. Reversal Potential
4. *DRIVING POTENTIAL depends on difference between membrane potential and equilibrium potential i.e. V -V

• For single ion channels follows simple ohms law
• If the channel stays open
• Outward current is positive

EQUATION I = G(Vm-Ve)

Question 19

understanding Ion Channels: 4

Answer 19

1 * Opening or closing ion channels changes permeability/ conductance

2 * Channels typically have three states.

3 * Closed, Open & Inactive (or refractory)

4 * Conductance of cell depends on conductance of individual ion channels and the number of open channels

Question 20

the properties of ION CHANNELS = 7

Answer 20

1 * Channels can be opened by stretch, ligands or voltage change.

2 * Many channels have open, closed and inactive states.

3 * Channels chatter open and closed

4 * A given type of channel has a characteristic conductance theUNITARY CONDUCTANCE (g)

5 * Permeability of the membrane to an ion is dependent on

6 * Unitary conductance of each channel, the number of channels in the membrane and the proportion open (opening probability).

7 * Channels are never half open its all of none

Question 21

how does a channel OPEN? = 3

Answer 21

1 * For many ion channels number of open channels depends on voltage

2 * Voltage changes cell conductance by opening ion channels

3 * Unitary conductance of an ion channel is its open conductance

Question 22

what are IV curves and what do they show? = 5

Answer 22

1 * IV (current voltage) curves give a quantitative view of ion movement

2 * Intercept is at equilibrium potential

3 * Driving potential is Vm-Ve

4 * Ohms law explains ion movement when channels open

5 * But voltage changes which channels and how many are open

Question 23

Summary = 6

Answer 23

1 *Goldman equation describes the membrane potential

2 * Increasing permeability to an ion move the membrane potential toward V for that ion

3 * If more than one ion is permeable membrane not at equilibrium for any of them.

4 * At V current for that ion is zero and direction of current e
reverses at V . e

5 * Ion channels opening or closing control permeability and hence potential.

6 * If Na+ can move in and K+ can move out what stops them?