Ion Channels Flashcards

January 30, 2024

• Sections start next week:
  • Sunday 4:00 PM
  • Monday 4:30 PM
  • Monday 7:30 PM
• Office Hours Today: 2:00 PM - 3:30 PM, SFH 464

Syllabus Information

• Details regarding sections and office hours are available in the syllabus.
• Relevant YouTube videos:
  • https://www.youtube.com/watch?v=f_3Utmj4RPU
  • https://www.youtube.com/watch?v=llmgLi_cJjA

Myotonia Congenita

• Reference: Imbrici, et al. Front. Cell. Neurosci., 27 April 2015 | https://doi.org/10.3389/fncel.2015.00156
• Myotonia congenita is a channelopathy.
• It results from a mutation in the CLC1 chloride channel gene.

Ion Channel Function and Measuring Ionic Currents

• Key topics:
  • What is a current?
  • Voltage clamp
  • Single-channel recording
  • Equal ion concentration scenarios
  • Concentration gradient scenarios
  • I/V plots (current-voltage)
  • Macroscopic currents
  • Probability of ion channel opening
  • I/V plots: ohmic and non-ohmic (rectifying channels)
  • Reversal potential of multi-ion permeable channels

Definition of Current

• Current is the net flow of charge.
• Convention: The direction of current flow is the direction of positive charge flow.

Conditions for Current Flow Across a Membrane

1. Charge Carriers: Ions must be present to carry the charge.
2. Passageway: Open channels are required for ions to pass through.
3. Driving Force: A concentration gradient or voltage difference must exist.

Hodgkin and Huxley

• Measured currents during an action potential in squid giant axons.
• Predicted the existence of ion channels carrying these currents.

Experimental Techniques

• Current Clamp
• Voltage Clamp
• Patch-clamp method:
  • Allows recording of current from single channels.
  • Can detect conformational changes of a single protein.

Patch Clamp Configurations

• Cell-attached recording: Mild suction.
• Whole-cell recording: Cytoplasm is continuous with pipette interior; tight contact between pipette and membrane.
• Inside-out recording: Expose to air; cytoplasmic domain accessible; strong pulse of suction.
• Outside-out recording: Extracellular domain accessible; ends of membrane anneal; retract pipette.

Voltage Clamp

• The current injected by the amplifier is equal in magnitude but opposite in sign to the current flowing through the cell.
• Vc = Command Voltage

Voltage Clamp on a Single K^+ Channel

• Outside-out patch
• Fluctuations between open and closed states
  • +20 mV: Current (I)
  • 0 mV

Case 1: No Concentration Gradient ([K^+]{out} = [K^+]{in})

• Ohm’s Law: I = gV
  • V = Voltage (volts - typically mV)
  • I = Current (amperes - typically pA)
  • R = Resistance (ohms - typically MΩ)
  • g = Conductance (siemens - typically pS)
  • R = \frac{1}{g}
• V=IR
• I = gV
• \Delta V \propto \Delta I

I/V Plot with No Concentration Gradient

• Current (I) vs. Membrane Potential (V)
• What determines the slope?
  • Conductance (g) is a combined measure of permeability and number of ions.
  • g \propto [ion]
• Ohmic relationship
• V = IR
• I \propto V
• V = \frac{1}{g} I
• V = g
• \Delta g \propto \Delta I

Case 2: Concentration Gradient ([K^+]{in} > [K^+]{out})

• Equilibrium: No net flow of K^+
• Nernst Equation: E{ion} = \frac{RT}{ZF} \ln \frac{[K^+]{out}}{[K^+]_{in}}
• Simplified Nernst Equation (at room temperature): E{ion} = 58 \log \frac{[K^+]{out}}{[K^+]_{in}}
• Equilibrium potential (E_{ion}) is the voltage at which the driving force due to the concentration gradient and the driving force due to voltage exactly balance one another.

Nernst Equation Example for Potassium

• EK = 58 \log \frac{[K^+]{out}}{[K^+]_{in}}
• Given:
  • [K^+]_{in} = 100 \text{mM}
  • [K^+]_{out} = 10 \text{mM}
• Calculation:
  • E_K = 58 \log \frac{10}{100}
  • E_K = 58 \log (\frac{1}{10})
  • E_K = 58 (-1) = -58 \text{mV}

I/V Plot with Concentration Gradient

• E_K = -58 \text{mV}

Neuro 102 Puzzler: Sodium Channel I/V Plot

• If the concentration of sodium (Na^+) outside the cell is 10 times greater than inside the cell, what will the IV plot of a single Na^+ channel look like?

Nernst Equation Example for Sodium

• E{Na} = 58 \log \frac{[Na^+]{out}}{[Na^+]_{in}}
• Given:
  • [Na^+]_{in} = 10 \text{mM}
  • [Na^+]_{out} = 100 \text{mM}
• Calculation:
  • E_{Na} = 58 \log \frac{100}{10}
  • E_{Na} = 58 \log 10
  • E_{Na} = 58 (1) = 58 \text{mV}

Reversal Potential (Eion)

• Relationship: V = IR or i = Vg
• Magnitude of the current depends on:
  • Ion concentration gradient
  • Membrane potential
  • Conductance
• Single-channel current equation:
  • i = (Vm - E{ion})g
  • V_m = membrane potential
  • E_{ion} = equilibrium potential
  • g = single channel conductance
• The driving force is not the absolute membrane potential but rather the difference between the membrane potential and the equilibrium potential.

Neuro 102 Puzzler: Chloride Channel I/V Plot

• What would a single channel I/V plot for Cl^- channel look like?

Macroscopic and Microscopic Membrane Currents

• Transmembrane ion currents
• Action potential generation
  • Sodium channels (Na^+ influx)
  • Potassium channels (K^+ efflux)
  • Total current flow across the membrane
• Inward vs. Outward currents

Macroscopic Current Equation and Channel Gating

• Macroscopic Current: I = i \cdot n \cdot P_o
  • I = macroscopic current
  • i = single channel current (microscopic)
  • n = number of channels
  • P_o = probability of open channel
• Single-channel currents build the whole-cell (macroscopic) current.
• Open probability (P_o) is dynamic and depends on gating and modulation.
• Channel Gating: Transition of channels between open and closed states.
  • Voltage
  • Ligand
  • Temperature
  • Light
  • Stretch

Gating of Ion Channels and Activation Curves

• Voltage dependence of ion channels affects macroscopic I/V relationship.
• Need to determine the probability of channel opening as a function of voltage.
• K^+ and Na^+ activation curves are very similar.
• Activation Curve: Probability of Channel Opening

Macroscopic Current I/V Plots

• Non-voltage-gated channel: Linear I/V plot.
• Voltage-gated channel: Exponential I/V plot.
• I = i \cdot n \cdot P_o
• n = 1000 \text{ channels}

Problem 2: Macroscopic I/V Curve for Na^+ Current

• Assume the activation curve for Na^+ channels is the same as for K^+ channels (in reality, they are very similar).

Rectification

• I = i \cdot n \cdot P_o
• i = (V_m - E)g
• I = (Vm - E{Na}) \cdot g \cdot n \cdot P_o
• Rectification: Non-ohmic I/V relationship.
• Current passes in one direction better than it does another.
  • Inward Rectifier
  • Outward Rectifier

Potassium Inward Rectifier (K_{ir})

• Open at rest, little outward current.
• Voltage-dependent block can be caused by intracellular cations (e.g., Mg^{++}).
• Some K_{ir} channels still rectify with no internal Mg^{++}; they are blocked by Polyamines (spermine).
• Lu and MacKinnon 1994

Multi-Ion Permeable Channels and Ligand-Gated Channels

• Nicotinic Acetylcholine Receptor (nAChR): Ligand-gated channel (receptor).
• nAChR: Permeable to both Na^+ and K^+ in the presence of ACh.
• Reversal Potential (V_{rev})

Ion Flow at Different Voltages in nAChR

• The current of individual ions depends on the driving force on that ion.
• At E_K the driving force on K is zero (no K current), but there is a large driving force on Na (inward Na current).
• At the nAChR reversal potential, I = 0, and the net flow of charges is zero; thus, I{K^+} = I{Na^+}.
• To calculate the reversal potential of the nAChR, one needs to take into account both E{Na^+} and E{K^+} and the relative permeability to the ions.

Goldman-Hodgkin-Katz Equation

• At Reversal Potential: I{K^+} = I{Na^+}
• V{rev} = \frac{(g{Na} \cdot E{Na^+}) + (gK \cdot E{K^+})}{g{Na} + g_K}

Summary

• V = IR
• Voltage clamp: Allows measuring currents at different voltages.
• Single-channel recordings.
• I/V plots.
• Reversal potential (for single ions = Nernst equilibrium).
• Driving force (difference between Vm and E{ion}).
• Macroscopic currents (I = i \cdot n \cdot P_O).
• I/V plots of multi-ion permeable channels.