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

Electrobiology

Introduction9

Electrobiology is the study of the electrical properties of biological cells and tissues. This section focuses on the physics underlying the nervous system, the generation and propagation of action potentials, and the modeling of axons as electrical circuits.

Nervous System

Structure and Function of Neurons

• Neurons form a complex network within the body that receives, processes, and transmits information from one part to another.

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

• The axon conducts electrical impulses away from the cell body.

Classes of Neurons:

• Sensory neurons: Receive stimuli from sensory organs and monitor the external and internal environment (e.g., heat, light, pressure).

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

• Interneurons: Transmit information between neurons.

Key Point: The nervous system relies on the rapid transmission of electrical signals for communication and control throughout the body.

Action Potential

Generation and Propagation of Action Potentials

• When a neuron receives an appropriate stimulus, it produces electrical pulses known as action potentials.

• The pulse is propagated along the axon's cable-like structure.

• Action potentials are constant in magnitude and duration, independent of the stimulus intensity (all-or-none law).

Stimulus Types:

• Injected chemical

• Mechanical pressure

• Applied voltage (most common in experiments)

Threshold and Action Potential Shape:

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

• The impulse is a sudden rise of the potential inside the axon to about +30 mV, followed by a rapid decrease to about -90 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 the pulse at speeds up to 100 m/s.

Graphical Representation: The action potential is typically shown as a sharp spike in membrane potential over time, with distinct phases: resting potential, depolarization, repolarization, and hyperpolarization.

Axon as an Electric Cable

Electrical Model of the Axon

• The axon can be modeled as an electrical cable with distributed resistance and capacitance.

• Current flows both inside and outside the axon, and the axon membrane acts as a capacitor.

Equivalent Circuit: The axon is represented by a series of resistors (for cytoplasmic and membrane resistance) and capacitors (for membrane capacitance).

Property	Nonmyelinated Axon	Myelinated Axon
Axon radius	5 × 10-6 m	5 × 10-6 m
Resistance per unit length of fluid (both inside and outside axon)	5.37 × 106 Ω/m	5.37 × 106 Ω/m
Conductivity per unit length of axon membrane (gm)	1.25 × 10-7 mho/m	3 × 10-9 mho/m
Capacitance per unit length of axon (cm)	3 × 10-9 F/m	8 × 10-11 F/m

Voltage Decay Along the Axon

• If a steady voltage $V_0$ is applied at one point in the axon membrane, the voltage decreases exponentially down the axon:

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

• Where $\lambda$ (the length constant) is about 0.8 mm. At a distance of 0.8 mm from the point of application, the voltage decreases to 37% of its value.

Synaptic Transmission

Transmission of the Action Potential

• The action potential is transmitted from the axon to other neurons or muscle cells via synaptic transmission.

• In some cases, transmission is by direct electrical conduction; in vertebrates, it is usually by a chemical substance (neurotransmitter).

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

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

Action Potentials in Muscles

Electrical Activity in Muscle Fibers

• Muscle fibers produce and propagate electrical impulses in the same way as neurons.

• The shape of the action potential is similar to that in neurons, but its duration is usually longer (about 20 ms).

Summary Table: Key Properties of Axons

Feature	Neuron	Muscle Fiber
Action potential duration	~1 ms	~20 ms
Propagation speed	Up to 100 m/s	Varies (slower than neuron)

Additional info: The cable model of the axon is fundamental in understanding how electrical signals attenuate and propagate in biological tissues, and forms the basis for quantitative analysis in neurophysics and biophysics.