Biophysics: Electrobiology of the Nervous System, Action Potentials, and Axon Circuits

Biophysics: Electrobiology

Nervous System

The nervous system is a complex network of specialized cells called neurons that receive, process, and transmit information throughout the body. This system is fundamental for sensing environmental changes, coordinating responses, and maintaining homeostasis.

• Neurons are the primary cells of the nervous system, forming intricate networks for communication.

• Neurons transmit information via electrical pulses generated in response to stimuli.

• These pulses travel along the neuron's cable-like structure, known as the axon.

• The electrical pulses are constant in magnitude and duration, regardless of stimulus intensity (all-or-none principle).

Classes of Neurons

• Sensory neurons: Receive stimuli from sensory organs and monitor both external and internal environments. They convey information about factors such as heat, light, pressure, muscle tension, and odor.

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

• Interneurons: Transmit information between neurons, facilitating communication within the nervous system.

Structure of a Neuron

• A typical neuron consists of a cell body (soma), dendrites (input ends), and a long axon (output tail).

• Dendrites receive incoming signals, while the axon conducts electrical impulses away from the cell body.

Example: The reflex arc is a simple neural circuit involving sensory neurons, interneurons, and motor neurons to produce a rapid response to a stimulus.

Action Potential

An action potential is a rapid, transient change in the electrical potential across the membrane of a neuron, enabling the transmission of signals along the axon. This phenomenon is central to neural communication and muscle contraction.

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

• A nerve impulse is triggered by a stimulus (chemical, mechanical, or electrical) applied to the neuron or axon.

• Most experiments use an externally applied voltage as the stimulus.

• An action potential occurs only if the stimulus exceeds a threshold value.

• The action potential is characterized by 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 tens of meters per second.

Key Terms:

• Resting potential: The stable, negative charge of a neuron when inactive (typically around $-70\,\text{mV}$).

• Threshold: The minimum stimulus required to trigger an action potential.

• Depolarization: The phase where the membrane potential becomes more positive.

• Repolarization: The phase where the membrane potential returns to a negative value.

Example: The classic action potential graph shows a sharp spike (depolarization), followed by a dip (repolarization), and a return to baseline (resting potential).

Action Potential Equation

The change in membrane potential during an action potential can be described by the Hodgkin-Huxley model (simplified):

$\frac{dV}{dt} = \frac{1}{C_m}(I_{\text{stim}} - I_{\text{ion}})$

where $V$ is the membrane potential, $C_m$ is the membrane capacitance, $I_{\text{stim}}$ is the stimulus current, and $I_{\text{ion}}$ is the ionic current.

Axon Circuit

The axon can be modeled as an electrical cable, allowing the study of how electrical signals propagate along its length. This approach uses principles from physics and electrical engineering to understand biological signal transmission.

• If a steady voltage $V_0$ is applied at one point on the axon membrane, the voltage decreases exponentially with distance along the axon.

• The voltage at a distance $x$ from the point of application is given by:

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

• Here, $\lambda$ (the length constant) is typically about $0.8\,\text{mm}$, meaning that at $0.8\,\text{mm}$ from the stimulus, the voltage is about $37\%$ of its initial value.

• The axon circuit can be simplified as a series of resistors and capacitors, representing the membrane's electrical properties.

Properties of the Axon Circuit

Property	Description
Resistance per unit length	Determines how easily current flows along the axon
Capacitance per unit length	Determines how much charge the membrane can store
Length constant ($\lambda$)	Distance over which voltage drops to 37% of its original value

Example: In myelinated axons, the length constant is increased, allowing faster and more efficient signal transmission.

Synaptic Transmission

Signals are transmitted from one neuron to another or to muscle cells at specialized junctions called synapses. This process can be electrical or chemical, depending on the type of synapse.

• In vertebrates, synaptic transmission is usually chemical.

• A small gap (synaptic cleft, about $10^{-7}\,\text{m}$) separates the nerve ending from the target cell.

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

Example: Acetylcholine is a neurotransmitter that transmits signals from motor neurons to muscle fibers, triggering contraction.

Muscle Fiber Action Potentials

Muscle fibers also produce and propagate action potentials, similar to neurons. However, the duration of the muscle action potential is typically longer (about 20 milliseconds).

• The shape of the action potential in muscle fibers is similar to that in neurons, but with a longer duration.

Example: The action potential in cardiac muscle cells is prolonged, allowing for sustained contraction necessary for pumping blood.

Additional info: Some equations and terms (e.g., Hodgkin-Huxley model, length constant) were inferred and expanded for academic completeness.