Question

Fast Axonal Transport Neurons have long thin processes called axons, structures specialized for conducting signals throughout the organism's nervous system. The axons that originate in a person's spinal cord and terminate in the muscles of the toes can be as long as \(2 \mathrm{~m}\). Small membrane- enclosed vesicles carrying materials essential to axonal function move along microtubules of the cytoskeleton, from the cell body to the tips of the axons. If the average velocity of a vesicle is \(1 \mu \mathrm{m} / \mathrm{s}\), how long does it take a vesicle to move from a cell body in the spinal cord to the axonal tip in the toes?

Short answer

It takes approximately 555.56 hours for a vesicle to move from the spinal cord to the toes.

Step-by-step solution

Convert Distance to Micrometers

First, convert the distance from meters to micrometers because the velocity is given in micrometers per second. The given axon length is \(2\) meters. Since \(1\) meter is \(1,000,000\) micrometers, the axon is \(2,000,000\) micrometers long.

Determine Time Using the Velocity Formula

Use the formula for time, \( t = \frac{d}{v} \), where \( t \) is time, \( d \) is distance, and \( v \) is velocity. Substitute the known values: \( d = 2,000,000 \, \mu \mathrm{m} \) and \( v = 1 \, \mu \mathrm{m/s} \). This gives \( t = \frac{2,000,000 \, \mu \mathrm{m}}{1 \, \mu \mathrm{m/s}} = 2,000,000 \, \mathrm{s} \).

Convert Time to More Convenient Units

Convert the time from seconds to hours to get a more intuitive understanding. There are \(3600\) seconds in an hour, so divide the time by \(3600\): \( \frac{2,000,000 \mathrm{s}}{3600 \, \mathrm{s/h}} \approx 555.56 \, \mathrm{hours} \).

Key concepts

Neuronal Function

Neurons are the fundamental units of the brain and nervous system. They are responsible for receiving sensory input from the external world, processing this information, and sending commands to our muscles. Neuronal function involves the transfer of signals through long thin fibers called axons, which connect with other neurons or tissues.
Axons extend from the neuron's cell body and can be impressively long, especially in humans. They conduct electrical impulses with the help of chemical signals.
This precise function is essential for maintaining the normal operation of the nervous system, encompassing everything from reflex actions to complex cognitive processes.

Microtubules

Microtubules are a crucial component of a cell's cytoskeleton. They are tube-like structures that provide shape and support to the cell. Importantly, within neurons, they serve as the tracks along which materials are transported.
These microscopic tubular structures help in the movement of vesicles and organelles using specialized motor proteins like kinesin and dynein. This process is vital for maintaining cellular functions and supporting the axon's extensive reach within the nervous system.
The dynamic nature of microtubules allows them to assemble and disassemble according to cellular needs, facilitating fast axonal transport and ensuring the neuron's health and functionality.

Axon Length

Axons can vary significantly in length, depending on their location and function. In humans, some axons span from the base of the spine to the toes, measuring up to 2 meters. This impressive length allows for extensive communication across the body.
Despite their size, axons maintain their functionality through the efficient transport of molecules and cellular components, essential for their operation.
The long length of axons highlights the importance of efficient transport mechanisms within neurons to relay signals over vast distances, maintaining coordinated functioning across different parts of the body.

Velocity Calculation

Understanding the velocity of vesicle movement along axons is a fundamental part of studying axonal transport. Velocity (\( v \)) is simply the rate of change of the position of an object, determined here as being 1 micrometer per second for vesicles in axonal transport.
This concept involves calculating the time (\( t \)) it would take for a distance (\( d \)) to be covered at a given velocity. Using the formula \( t = \frac{d}{v} \), we can ascertain that a vesicle traveling the full 2 meters, or 2,000,000 micrometers, of an axon at a velocity of 1 micrometer per second, would take approximately 555.56 hours to reach the end.
This example highlights the importance of velocity calculation in determining the efficiency and capacity of neuronal communication over long distances, a key element in understanding how our nervous system operates.