Question

A dimeric kinesin-1 molecule has 8-nm steps and can move at rates of about 1 µm/sec. Olympic 100-meter sprinters typically run at about 180 steps per minute and can reach speeds of about 42 km/h. With the same step size, if the Olympic runner had a step frequency of a kinesin-1 molecule, how fast could she run? Write down your answer in km/h, e.g. 52 km/h.

Answer 1

With the same step size as a dimeric kinesin-1 molecule, an Olympic sprinter running at the kinesin-1 step frequency could reach a speed of approximately 4.32 km/h.

Step-by-step explanation:

In order to determine the speed of the Olympic sprinter with the kinesin-1 step frequency, we need to calculate the step frequency of the kinesin-1 molecule. Given that the kinesin-1 molecule has 8-nm steps and moves at 1 µm/sec, we can calculate the step frequency using the formula:

`\[ \text{Step frequency} = \frac{\text{Speed}}{\text{Step size}} \]`

Substituting the given values, we get:

`\[ \text{Step frequency} = \frac{1 \, \mu \text{m/sec}}{8 \, \text{nm}} \]`

After obtaining the step frequency, we can then calculate the speed of the Olympic sprinter by multiplying her step frequency (steps per minute) with her step size:

`\[ \text{Speed} = \text{Step frequency} * \text{Step size} * 60 \]`

Substituting the known values:

`\[ \text{Speed} = \text{Step frequency} * 8 \, \text{nm} * 60 \]`

Converting the result from nanometers per minute to kilometers per hour gives the final speed of the Olympic sprinter with the kinesin-1 step frequency.

This calculation illustrates that even with the same step size, the inherent biological differences between molecular and human-scale movements result in a significantly lower speed for the Olympic sprinter.