# Bioelectricity: A Quantitative Approach

## Dr. Roger Barr, Duke University

Nerves, the heart, and the brain are electrical. How do these things work? This course presents fundamental principles, described quantitatively.

### Electricity in Solutions

This week's theme focuses on the foundations of bioelectricity including electricity in solutions.

The learning objectives for this week are:

• Explain the conflict between Galvani and Volta

• Interpret the polarity of Vm in terms of voltages inside as compared to outside cells

• Interpret the polarity of Im in terms of current flow into or out of a cell.

• Determine the energy in Joules of an ordinary battery, given its specifications.

• State the “big 5” electrical field variables (potentials, field, force, current, sources) and be able to compute potentials from sources (the basis of extracellular bioelectric measurements such as the electrocardiogram) or find sources from potentials.

### Energy into Voltage

This week we will examine energy, by which pumps and channels allow membranes to "charge their batteries" and thereby have a non-zero voltage across their membranes at rest.

The learning objectives for this week are:

• Describe the function of the sodium-potassium pump
• State from memory an approximate value for RT/F
• Be able to find the equilibrium potential from ionic concentrations and relative permeabilities
• Explain the mechanism by which membranes use salt water to create negative or positive trans-membrane voltages

### Passive and Active Resonses, Channels

This week we'll be discussing channels and the remarkable experimental findings on how membranes allow ions to pass through specialized pores in the membrane wall.

The learning objectives for this week are:

• Describe the passive as compared to active responses to stimulation
• Describe the opening and closing of a channel in terms of probabilities
• Given the rate constants alpha and beta at a fixed Vm, determine the channel probabilities
• Compute how the channel probabilities change when voltage Vm changes.

### Hodgkin-Huxley Membrane Models

This week we will examine the Hodgkin-Huxley model, the Nobel-prize winning set of ideas describing how membranes generate action potentials by sequentially allowing ions of sodium and potassium to flow.

The learning objectives for this week are:

• Describe the purpose of each of the 4 model levels (1) alpha/beta (2)probabilities (3) ionic currents (4) trans-membrane voltage
• Estimate changes in each probability over a small interval \$\$\Delta t\$\$
• Compute the ionic current of potassium, sodium, and chloride from the state variables
• Estimate the change in trans-membrane potential over a short interval \$\$\Delta t\$\$
• State which ionic current is dominant during different phases of the action potential -- excitation, plateau, recovery

### Axial and Membrane Current in the Core-Conductor Model

This week we will examine axial and transmembrane currents within and around the tissue structure: including how these currents are determined by transmembrane voltages from site to site within the tissue, at each moment.

The learning objectives for this week are:

• Select the characteristics that distinguish core-conductor from other models.
• Identify the differences between axial and trans-membrane currents
• Given a list of trans-membrane potentials, decide where axial andtrans-menbrane currents can be found.
• Compute axial currents in multiple fiber sigments from trans-membrane potentials and fiber parameters
• Compute membrane currents at multiple sites from trans-mebrane potentials

### Propagation

this week we will examine how action potentials in one region normally produce action potentials in adjacent regions, so that there is a sequence of action potentials, an excitation wave. the learning objectives for this week are:

• Identify the differences between the propagation pattern following sub-threshold versus threshold stimuli
• Compute the changes in transmembrane potentials and currents from one time to a short time laterIdentify the outcome of stimulating a fiber at both ends
• Quantify the interval after propagation following one stimulus to the time when there will be another excitation wave following a 2nd stimulus
• Explain why "propagation" is different from "movement"

### Course Conclusion and Final Exam

In Week 7, we will briefly review the course, take a quick look at the next course at the second course in the series and complete the final exam. Good luck and thank you for joining me in the course. rcb.

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