Resting Membrane Potential (L4-5)

Predict the direction of ion movement by considering both the concentration gradient and the electrical gradient acting on an ion.

1. Ion flux across the membrane is influenced by both electric field and concentration gradients

2. This is due to:

   1. Different concentrations of ions inside and outside the cell (caused by active transport and passive distribution). Ions will diffuse from high to low concentrations

   2. The non-zero electric field within the membrane due to the separation of ions. A negative charge will move to an area with excessive positive charge (and vice versa)

3. Ion flux is thus the combination of diffusion and drift flux

Use the Nernst equation to calculate an ion’s equilibrium potential and explain what that potential represents physiologically.

1. The current flow through the membrane is driven by electrochemical potentials (concentration gradient and electric field).

2. The membrane potential at which the net cross-membrane current is zero is described by the Nernst equation:

   1. R= gas constant

   2. T= absolute temperature

   3. z= ion charge 

   4. F= faraday’s constant

   5. [C]= ion concentration 

3. This relationship can be simplified (RT/F treated as a constant)

example of Nernst equation

in this example: Increased temperature → voltage is higher due to temp and to cancel out concentration gradient

Equilibrium Potential

1. When the net cross membrane current is 0 (membrane is at rest) the two forces that drive the current (the chemical gradient and electrical field) are equal and opposite in magnitude

2. The corresponding voltage is the Equilibrium Potential

3. Unit to use is E:

EX: Equilibrium potential with K+

Membrane Potential:

1. Is the voltage difference between the inside and outside of a cell (Vinside - Voutside) and represented by VM

2. expressed /units in millivolts (mV)

3. The result of charge separation by active and passive transport

4. All neurons have a resting membrane potential

5. There is a steady state electrical potential across the cell membrane that can range from -30 mV to -100 mV depending on the cell types

6. Changes to the membrane potential can be depolarizing (making the inside of the cell less negative) or hyperpolarizing (making the inside of the cell more negative).

7. Movement of ions is controlled by the opening and closing of ion channels. Ions are charged particles that cannot pass through the hydrophobic lipid bilayer of the cell membrane

depolarization

making inside of cell less negative

hyperpolarization

making inside of cell more negative

Remember Ion Channels…

1. Are transmembrane proteins with a central pore that is open to both the cell cytoplasm and the extracellular fluid.

2. Are gated and selective, only certain ions pass through 

3. Can change their conformation from open to closed or closed to open and almost instantaneously

4. Fluctuate around a mean open time specific to the channel 

5. When activated or deactivated by a stimulus (eg, neurotransmitter binding, physical stimulation) the mean open time will increase or decrease

6. Can be inactivated (if a voltage-sensitive channels) or desensitized (if sensitive to chemical signals) meaning that they cannot be opened

7. Can be open but blocked, the channel pore is open but no ions can flow due to a molecule physically blocking the pore

Explain why the resting membrane potential is normally closer to the potassium equilibrium potential than to the sodium equilibrium potential.

A neuron at rest has a steady electrical potential across its membrane, with the inside of the cell being negative with respect to the outside

For a cell membrane to remain in steady state, a number of conditions need to be met:

1. Both the intracellular and extracellular solutions must be electrically neutral: 

   1. Outside the cell, the positive charges (K+ and Na+) are balanced by negative charges, Cl-

   2. Inside the cell: little Cl- to balance the positive charges, but high concentration of large organic anions (along with a small amount of Cl-) balances the Na+ and K+

2. The total concentrations of ions must be equal inside and outside to maintain osmotic balance. More ions inside the cell will cause swelling

3. There must be no net movement of any particular ion into/out of the cell. If there are no open channels the resting membrane potential (VM) is 0 because there is no charge separation across the membrane

first condition of cell membrane to remain in steady state

1. Both the intracellular and extracellular solutions must be electrically neutral: 

   1. Outside the cell, the positive charges (K+ and Na+) are balanced by negative charges, Cl-

   2. Inside the cell: little Cl- to balance the positive charges, but high concentration of large organic anions (along with a small amount of Cl-) balances the Na+ and K+

second condition of cell membrane to remain in steady state

The total concentrations of ions must be equal inside and outside to maintain osmotic balance. More ions inside the cell will cause swelling

third condition of cell membrane to remain in steady state

There must be no net movement of any particular ion into/out of the cell. If there are no open channe;s the resting membrane potential (VM) is 0 because there is no charge separation across the membrane

Resting membrane potential example 1: 

1. In a real neuron at rest, many K+ channels are open in the membrane. How will opening K+ channels affect the VM?

2. Here, we are going to start with resting membrane potential, VM at 0:

a. When we first open the 𝐾+channels, will there be an electrical force on 𝐾+?

b. Will there be a concentration force on 𝐾+ions?

c. Which direction will 𝐾+ions move?

d. Will 𝐾+ions continue to move out of the cell until there is an equal concentration of 𝐾+inside and outside?

e. When will 𝐾+ ions stop moving?

f. If the cell membrane is permeable only to 𝐾+ ions, what will be the resting membrane potential of the cell?

a. No because no electrical charge to move K+

b. Yes, because the concentrations of K+ on each side of the membrane are different

c. Which direction will 𝐾+ions move?

d. No, potential across the membrane (thus, an electrical force) will be created after K+ ions. This electrical force will eventually be enough to stop the flow of ions.

e. When the electrical force is equal to concentration force 

Ek = 58 mV/ 1 * log (3/90) = -85 mV

f. -85 mV because only channel open and has influence over cell potential

Resting VM is due to many different ions:

1. We can measure the VM of a cell using an electrode, and see whether changing the intra- and extra-cellular K+ concentrations produces the change in VM predicted by the Nernst Equation:

   1. When the intracellular and extracellular K+ concentrations are controlled by replacing the axoplasm with a solution of known K+ concentration, the measured resting VM is always somewhat less negative than that predicted by the Nernst equation

   2. If the extracellular K+ concentration is varied systematically, the Nernst equation should predict that concentration by a factor of 10 should change the VM by 58 mV at room temperature

   3. This would result in a straight line of slope 58 mV if one plots membrane potential against external K+ concentration

   4. In fact, again, the membrane potential in this experiment is constantly more positive than the Nernst equation

Resting 𝑉𝑀 is due to many different ions:

What can explain the difference between the Nernst potential predictions and the actual membrane potential? What happens when we open Na+ channels are open

Remember, with only K+ channels open, the membrane potential is at -85 mV

a. When we first open the 𝑁𝑎+channels, will there be an electrical force on 𝑁𝑎+ ions?

b. Will there be a concentration force on 𝑁𝑎+ ions

c. Which direction will sodium ions move?

d. What will happen to the membrane potential?

e. Now what will be the driving force on 𝐾+ ions?

f. When will the cell reach a constant membrane potential?

g. The resting membrane potential of the neuron now will be somewhere between what two potentials?

a. Yes, F(electrical)= zV= 85 mV, into the cell. Na+ ions are moving towards cell due to negative charges inside cell

b. F(concentration) = E(Na+) = 58 mV/1 * log(117/30) = 34 mV into the cell

c. into the cell

d. Less negative → depolarization

e. K+ no longer in equilibrium

f. The influx of the sodium is exactly balanced by the efflux of potassium

g. Between E(K+) and E (Na+) E= equilibrium potential

Resting 𝑉𝑀 is due to many different ions:

1. The membrane potential of a real neuron tends to be somewhere around -70 mV, close to the E(K+)

   1. This is because the cell at rest is much more permeable to K+ than to Na+ (typically the Na+ conductase is 1 to 10% of the K+ conductase)

   2. Cl- channels are open in cells at rest. Intracellular Cl- concentrations are not well regulated, so Cl- concentrations are not well regulated, so Cl- ions move freely into.out of the cell until the Cl- concentrations are such that the E(Cl-) is equal to the resting VM. In some cells, however, Cl- is regulated by transporters, so it can also influence the VM

Use the Goldman-Hodgkin-Katz equation conceptually to predict how changes in ion concentrations or relative permeabilities affect membrane potential.

1. In reality many charged molecules contribute to the overall electrical properties of the cell membrane

2. For a given concentration gradient, the greater the membrane permeability to an ion, the greater the contribution that ion will make to the membrane potential

3. The GHK equation is an expansion of the Nernst Equation that gives the resting membrane potential in terms of ion permeabilities and concentration inside and outside the cell

4. Note that Cl- concentrations are reversed because Cl- is an anion and its movement has the opposite effect on membrane potential.

5. Take into account the relative permeabilities of the main 3 ions contributing to the resting potential and also their concentrations to obtain a more accurate estimate

Goldman-Hodgkin-Kat (GHK) equation describe ionic flow across the membrane makes several assumptions:

1. Ion movement within the membrane obeys the Nernst Equation

2. Ions move across the membrane independently (without interacting with each other)

3. The electric field across the membrane is constant

Thus, this model falls short in describing membrane current when these assumptions are not valid.

structure of a neurom

1. cell body/soma

2. dendrites

3. axon/nerve fiber

4. axon hillock

5. myelin sheath

6. nodes of Ranvier

cell body/soma

contains the nucleus and machinery for protein synthesis. Receives inputs from other neurons

dendrites

highly branched outgrowths of the cell body. Also, receives inputs from other neurons

axon/nerve fiber

process that extends from the cell body and carries output signal to target cells. length varies (micron to over a meter)

axon hillock

trigger zone where most electrical signals are generated

myelin sheath

concentric layers of cell membrane that enhance the speed of signal transmission

nodes of ranvier

space between adjacent sections of myelin

Diversity in neuron structure:

1. come in many different shapes and sizes depending on where they are in the nervous system and what their function is

2. Neurons can be classified by function into sensory neurons, motor neurons or interneurons, as well as other features

3. In general, however, they all have the same overall structure

4. They also can be classified according to different properties:

   1. Morphology (Unipolar/Pseudounipolar, bipolar, multipolar)

   2. Chemicals they use to communicate

   3. Location

   4. function/connection (sensory, motor, interneurons)

Neuronal classification:

three different functional groups

1. sensory neurons

2. motor neurons

3. interneurons

sensory neurons

• afferent neurons (sends info away from the stimulus site)

• provides information on external environment, position within environment and the activity of other organ systems

motor neurons

• efferent neurons (sends info/command to effector)

• target voluntary (skeletal) and involuntary (cardiac) muscles

interneurons

• located entirely within the CNS

• interconnect other neurons

• Responsible for the analysis of sensory inputs

Some properties of neurons:

1. Neurons produce electrical potentials across their cell membranes

2. Neurons can transmit electrical pulses quickly

3. Neurons have receptors which convert chemical messages to electrical

4. Neurons are differentiated cells; they are developmentally mature, and do not divide (non-mitotic)

5. Neurons are specialized for integration and transmission of info

6. Neurons form circuits; neuronal circuits constitute the structural basis for brain function

Biological electrical signals:

voltage gradients across cell membranes generated by the movement of ions like sodium, potassium, and calcium

two types:

action and graded potentials

action potentials

1. A brief (ms scale) all-or-none depolarization of the membrane

2. In a given neuron, does not vary in magnitude (identical)

3. Conducted without decrement

4. The principle way neurons communicate

5. Allows rapid signaling over long distances

graded potentials

1. Change in membrane potential whose magnitude is proportional to the stimulus intensity (vary in size)

2. Decays with distance along the axon

3. Change in membrane potential (magnitude proportional to stimulus intensity) that decays (due to current leakage and internal resistance) along the cell

4. Occur in dendrites and cell body, occasionally near axon terminals

5. Can be a hyperpolarizing (inhibitory) or depolarizing (excitatory) stimulus

   1. Change in membrane potential whose magnitude is proportional to the stimulus intensity (vary in size)

   2. Decays with distance along the axon

   3. Change in membrane potential (magnitude proportional to stimulus intensity) that decays (due to current leakage and internal resistance) along the cell

   4. Occur in dendrites and cell body, occasionally near axon terminals

   5. Can be a hyperpolarizing (inhibitory) or depolarizing (excitatory) stimulus

   6. Used for short distance- communication and to initiate action potentials (depolarization)

   7. They result from a brief injection of current, typically the result of synaptic transmission and the opening of ligand-gated ion channels. These are not the same as leak channels

   8. They can also result from an experimenter injecting current using an electrode

Membrane potential changes: Depolarization

1. Reduction in membrane potential

2. Inside of cell becomes less negative

3. Inside goes closer to zero and may move above zero to become positive

Membrane potential changes: hyperpolarization

1. Increase in membrane potential

2. Inside of cell becomes more negative

3. Reduces the probability of generating action potentials

excitatory Postsynaptic potential (EPSP)

1. Depolarizing events that bring VM closer to threshold, more likely to fire an action potential (excitatory neurotransmitters: glutamate and acetylcholine)

What is the ionic selectivity of the postsynaptic receptor for excitatory Postsynaptic potential (EPSP)?

non-specific cation channels that are permeable to multiple positive ions, allowing a net influx of sodium Na+ and often calcium Ca2+ into the cell.

Inhibitory Postsynaptic Potential (IPSP):

Hyperpolarizing events that bring VM away from threshold, less likely to fire an action potential. (inhibitory neurotransmitters include GABA and glycine)

What is the ionic selectivity of the postsynaptic receptor for Inhibitory Postsynaptic Potential (IPSP)?

selective for chloride ions Cl- via influx or potassium ions K+ via efflux

Temporal Summation:

One single presynaptic neuron fires repeatedly in rapid succession at a single location (synapse). The signals add up over time before the previous potential fades. ("Temporal" means time)

Spatial Summation:

Multiple different presynaptic neurons fire simultaneously at different locations on the postsynaptic neuron. Their combined signals add up at the same time. ("Spatial" means space or location).

EPSP ISPS Cancellation:

excitatory and inhibitory (opposite) come together have own refactor periods and cancel each other due to respective periods