Question

a motor protein moves cargo in cells by taking forward steps along linear tracks called microtubules. assume each step has size 8nm and consumes 30 kj mol⁻¹ of energy by burning atp. if this energy is converted to work, what is the force exerted at each step?

Answer 1

A motor protein exerting force to move cargo along a microtubule does so by utilizing energy from ATP. With 8nm steps and 30kJ mol⁻¹ energy used per step, the force exerted is calculated to be approximately 6 piconewtons per step.

Step-by-step explanation:

The student asked how much force a motor protein exerts when it moves cargo along microtubules in a cell. To find this, we use the work-energy principle. Work done by the motor protein is the product of force exerted and the distance over which the force acts. Given that each step is 8 nm and that each step consumes 30 kJ mol⁻¹, we first convert the energy per mole into energy per step by dividing by Avogadro's number and then calculate the force using the work formula.

Energy consumed per mole: 30 kJ mol⁻¹

Energy per step in joules (J): 30 x 10³ J mol⁻¹ / (6.022 x 10²³ mol⁻¹) = 4.98 x 10⁻¹¹ J/step

Distance per step in meters (m): 8 nm = 8 x 10⁻¹ m

Force (F) = Work (W) / Distance (d), so F = 4.98 x 10⁻¹¹ J / 8 x 10⁻¹ m = 6.225 x 10⁻¹ pN

Therefore, the force exerted by the motor protein at each step is approximately 6 piconewtons.