NEU 330 Lecture 6

• Modification of membrane voltage causes current flow through two primary mechanisms:

  • Through resistors via open channels, where specific ions can pass through, affecting cellular excitability and signaling.

  • To the capacitor, which involves charging or discharging the membrane as ions shift in response to voltage changes, influencing overall cell function.

• Identified equations in membrane physics are crucial for understanding the dynamics of electrical signals:

  • $I<em>m = \frac{V</em>m}{R<em>m} + C</em>m \frac{dV_m}{dt}$, where the interplay of these variables elucidates how membrane currents and voltage interact over time.

  • Meaning of variables:

    • $I_m$: Membrane current, representing the flow of electric charge across the membrane.

    • $V_m$: Membrane voltage, indicating the electric potential difference across the membrane.

    • $R_m$: Membrane resistance, which quantifies how much the membrane opposes the current flow.

    • $C_m$: Membrane capacitance, reflecting the membrane's ability to store charge.

• As resistance ($R$) increases, current flow ($I$) decreases, leading to longer voltage change times due to the reduction in the rate at which voltage can respond to changes in current.

Time Constant

• Right after current is injected, the rate of voltage change is significantly determined by:

  • Resistance ($R$), which impacts how easily current flows through the membrane.

  • Capacitance ($C$), which impacts how quickly the membrane can charge and discharge in response to current.

Definition of Time Constant

• The time constant ($au$) is critical in understanding neuronal dynamics:

  • It is defined as the time it takes for the voltage change to reach $\frac{1}{e}$ or approximately 63% of its maximum value, an essential measure for analyzing signal transmission in neurons.

• The relationship for time constant is:

  • $\tau = R \cdot C$, signifying a direct product of the resistance and capacitance, which tells us how charge behavior varies in different membranes.

Cellular Capacitance

• Cell size and membrane structure profoundly influence cellular capacitance ($C$):

  • $C = \epsilon_0 \cdot \frac{A}{d}$ where the parameters define the electric properties of the cell membrane:

    • $\epsilon_0$: permittivity of free space, indicating how much electric field is supported in a vacuum.

    • $A$: area of the membranes, larger areas contribute to higher capacitance.

    • $d$: distance between membranes, where closer membranes result in higher capacitance.

• Specific capacitance for biological membranes is approximately 1 µF/cm², highlighting the efficiency of biological membranes in charge storage.

• As the membrane area increases, the capacity to hold charge also increases, impacting how cells communicate electrical signals.

Effect of Membrane Properties

• Capacitance remains relatively constant in most cells, making it a steady value while resistance dynamically changes based on the number and the type of ion channels that are open, crucially affecting cellular excitability.

• Larger cells exhibit higher capacitance and lower resistance, enhancing their ability to conduct electrical signals efficiently:

  • Example relationship: $C \propto \text{Membrane area}$ and $R_a \propto \frac{1}{\text{Membrane area}}$.

Properties of Biological Membranes

• Biological membranes possess two passive electrical properties:

  • Capacitance ($C$) which allows them to store electrostatic energy.

  • Resistance ($R$), which is critical in determining how quickly a neuron can respond to stimuli.

• Both properties are crucial in determining the speed of voltage change, reinforcing the fundamental relationship expressed in $\tau = R \cdot C$ and indicating the voltage change response detailed by $\Delta V = I \cdot R$.

Significance of Time Constants

• The functional relevance of time constants in neuronal activity cannot be understated:

  • It influences the integration windows of neurons, affecting how they process synaptic inputs over time:

    • Temporal summation vs. spatial summation both depend on these time constants.

• As conductance ($G$) increases (and hence resistance $R$ decreases), the size of excitatory postsynaptic potentials (EPSPs) diminishes, altering the response characteristics of neurons, essential for understanding synaptic transmission and plasticity.

Cell Physiology as an Electrical Circuit

• The biophysical model of cells can be understood as an electrical circuit comprising components that mimic physical elements:

  • Capacitor (lipid bilayer) that allows for the storage of charge and maintenance of membrane potential.

  • Resistor/conductor (ion channels) with variable conductance due to opening and closing in response to changes in voltage.

  • Current source (ion pumps/transporters) that maintain concentrations of ions across membranes serving to generate action potential.

  • Battery/electromotive force (ionic electrochemical gradient) enabling the driving force behind the movement of ions.

Electrophysiology

Electrical Recording Methods

• Multiple techniques for measuring neuronal signals have been developed, enhancing our understanding of nerve function:

  • Intracellular: Direct measurement within a neuron, allowing for high fidelity data concerning ionic currents.

  • Extracellular: Measurement outside the cell, often via electrodes, helping to assess general neuronal activity in networks.

  • This includes EEG and local field potentials which provide data on overall brain activity.

  • Patch Clamp: A sophisticated method used to study single neurons and ion channels, enabling the recording of:

    • Cell-attached mode: Access to the inside of a cell without causing major disruption.

    • Whole-cell mode: Provides comprehensive access to the entire cell after breaking the membrane, allowing detailed study of ionic currents.

    • Inside-out / Outside-out configurations for studying specific ion channel properties under controlled environments.

Electrode Mechanics

• Importance of proper electrode placement cannot be overstated:

  • Intracellular recording involves complex methods to achieve precise placement inside a neuron to avoid damage.

  • Techniques:

    • Sharp electrodes allow access, but pose a risk of damaging the cellular structures.

    • The use of patch clamp techniques provides high fidelity recordings with minimal leakage, crucial for capturing rapid changes in ionic currents.

Analysis of Action Potentials

Current Measurements

• Measuring unitary currents reveals the behavior of ion channels:

  • An example of Na⁺ current recorded during action potentials can illustrate the flow of ions during depolarization.

  • Calculated using:

    • $\text{Number of Na}^+ \text{ ions} = \frac{1.6 \times 10^{-12}}{1.6 \times 10^{-19} \times 10^3} = 10,000$, providing insights into channel activity.

• Comparison of ion currents analyzed with respect to voltage changes sheds light on how electrical signals propagate.

Single-channel Recording

• Allows detailed assessment of individual ion channels and their critical roles in action potentials:

  • Typically yield small current measurements with controlled conditions, essential for studying channel kinetics.

• Understanding Na⁺ and K⁺ channels helps clarify the complex phases of depolarization and repolarization during action potentials, enhancing our grasp of neuronal firing dynamics.

Methods and Protocols of Electrophysiological Studies

• Selecting appropriate configurations such as:

  • Current clamp: Control current while measuring voltage, crucial for observing passive properties like resistance and time constant.

  • Voltage clamp: Allows isolation of specific currents by maintaining a preset voltage, enabling targeted studies of channel behavior.

• Experimental Application Plan:

  • Consideration of behavioral testing and physiological responses using various recording methods is necessary for comprehensive understanding of neuronal circuits and their functions.

Lecture Wrap-Up and Questions

• Final thought questions on key learning objectives addressed in the lecture, including:

  1. Comparison of cellular capacitance and time constant relationships, which are foundational to neurophysiology.

  2. Implications of compounds that influence time constants in medication or neuronal diseases.

  3. Relationship between neuron passive properties and their voltage response to synaptic inputs, crucial for synaptic plasticity and learning.