Biophysics: Electrobiology – Nervous System, Action Potentials, and Axon Circuits

Electrobiology

Nervous System

The nervous system is a complex network of neurons that receives, processes, and transmits information throughout the body. Neurons are specialized cells responsible for the conduction of electrical impulses, enabling communication between different body parts.

• Neurons form intricate networks to facilitate information transfer.

• Each neuron consists of a cell body, dendrites (input ends), and a long axon (output end).

• The axon propagates electrical signals away from the cell body.

Example: Sensory neurons in the skin detect pressure and transmit signals to the brain for processing.

Types of Neurons

Neurons are classified into three main types based on their function:

• Sensory neurons: Receive stimuli from sensory organs and monitor the body's internal and external environment. They convey information about heat, light, pressure, muscle tension, and odor.

• Motor neurons: Carry messages that control muscle cells, based on information from sensory neurons and the central nervous system.

• Interneurons: Transmit information between neurons, facilitating complex reflexes and neural circuits.

Example: A simple neural circuit involves a sensory neuron detecting a stimulus, an interneuron processing the signal, and a motor neuron triggering a muscle response.

Action Potential

Properties and Generation of Action Potentials

An action potential is a rapid, transient change in the electrical potential across a neuron's membrane, enabling the transmission of nerve impulses.

• Action potentials are produced when a neuron receives an appropriate stimulus (chemical, mechanical, or electrical).

• The electrical pulse is propagated along the axon, maintaining constant magnitude and duration regardless of stimulus intensity.

• To study nerve impulses, a probe can be inserted into the axon to measure voltage changes relative to the surrounding fluid.

Example: In laboratory experiments, an externally applied voltage is often used to elicit action potentials.

Threshold and Propagation

The generation and propagation of action potentials follow specific biophysical principles:

• A nerve impulse occurs only if the stimulus exceeds a certain threshold value.

• The impulse is generated at the point of stimulation and travels down the axon.

• The action potential involves a sudden rise in membrane potential (to about $+30\,\text{mV}$), followed by a rapid decrease (to about $-90\,\text{mV}$), and a slow return to the resting state.

• The entire pulse passes a given point in a few milliseconds.

• Fast-acting axons can propagate pulses at speeds up to $100\,\text{m/s}$.

Equation:

• Resting potential: typically around $-70\,\text{mV}$

• Action potential peak: $+30\,\text{mV}$

• Hyperpolarization: $-90\,\text{mV}$

Axon as an Electric Cable

Electrical Model of the Axon

The axon can be modeled as an electrical cable, with current flowing both inside and outside the axon membrane. This analogy allows the use of circuit theory to analyze nerve impulse propagation.

• The axon is represented by a series of resistors and capacitors, modeling its electrical properties.

• Current flows through the axon and across the membrane, similar to an electric cable.

Example: The cable model helps explain how voltage changes propagate along the axon.

Properties of Sample Axons

The following table compares the electrical properties of nonmyelinated and myelinated axons:

Property	Nonmyelinated Axon	Myelinated Axon
Axon radius	$5 \times 10^{-6}\,\text{m}$	$8 \times 10^{-6}\,\text{m}$
Resistance per unit length of fluid (both inside and outside axon)	$5.37 \times 10^{6}\,\Omega/\text{m}$	$4.37 \times 10^{6}\,\Omega/\text{m}$
Conductivity per unit length of axon membrane	$1.25 \times 10^{-7}\,\text{mho}/\text{m}$	$3.87 \times 10^{-7}\,\text{mho}/\text{m}$
Capacitance per unit length of axon	$3 \times 10^{-11}\,\text{F}/\text{m}$	$8 \times 10^{-11}\,\text{F}/\text{m}$

Analysis of Axon Circuit

The axon circuit can be simplified using electrical circuit models. When a steady voltage $V_0$ is applied at one point in the axon membrane, the voltage decreases exponentially along the axon:

• Voltage decay equation:

$V(x) = V_0 e^{-x/\lambda}$

• Where $\lambda$ is the length constant (about $0.8\,\text{mm}$ for typical axons).

• At a distance $0.8\,\text{mm}$ from the point of application, the voltage decreases to 37% of its initial value.

Synaptic Transmission

Transmission of Nerve Impulses

Action potentials are transmitted from axons to other neurons or muscle cells via synaptic transmission. This process can be electrical or chemical, depending on the type of synapse.

• In some cases, transmission occurs by direct electrical conduction.

• In vertebrates, transmission is usually chemical, involving neurotransmitter release.

• There is a gap (synapse) of about $1\,\text{nm} = 10^{-9}\,\text{m}$ between the nerve ending and the adjacent cell.

• When the impulse reaches the synapse, a chemical substance is released, diffuses across the gap, and stimulates the adjacent cell.

Example: Acetylcholine is a neurotransmitter released at neuromuscular junctions to stimulate muscle contraction.

Action Potentials in Muscles

Muscle Fiber Electrical Activity

Muscle fibers generate and propagate electrical impulses in a manner similar to neurons. The action potential in muscle fibers has the same shape as in neurons but typically lasts longer (about 20 milliseconds).

• Electrical impulses in muscle fibers initiate contraction and movement.

• Duration of muscle action potentials is usually longer than neuronal action potentials.

Example: Cardiac muscle cells produce action potentials that regulate heartbeats.

Additional info: The cable theory and circuit models are essential for understanding the biophysical basis of nerve impulse propagation and are widely used in biophysics and neurophysiology.