9. 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?
a. 3.75 x 10+12 N
b. 6.25 x 10+12 N
c. 3.75 x 10-12 N
d. 6.25 x 10-12 N

Motor Protein Force Calculation: 8 nm Step, 30 kJ/mol ATP Energy

Motor proteins like kinesin exert force during 8 nm steps along microtubules using ATP hydrolysis energy of
30 kJ·mol⁻¹.
The correct answer is option d. (6.25 × 10⁻¹² N), calculated from the relation
Work = Force × Distance,
assuming all ATP energy converts to mechanical work per step.

Calculation Method

The work done equals energy input:

W = F × d   ⇒   F = W / d

Convert 30 kJ·mol⁻¹ to joules per molecule using Avogadro’s number
(N_A = 6.022 × 10²³ mol⁻¹):

Energy per molecule = (30 × 10³ J·mol⁻¹) / (6.022 × 10²³ mol⁻¹) = 4.98 × 10⁻²⁰ J

Step distance: d = 8 nm = 8 × 10⁻⁹ m

Thus,

F = (4.98 × 10⁻²⁰ J) / (8 × 10⁻⁹ m) ≈ 6.23 × 10⁻¹² N

This matches option d (6.25 × 10⁻¹² N) within rounding limits.

Option Analysis

• a. 3.75 × 10⁺¹² N: Incorrect; uses total molar energy without dividing per molecule, leading to an unrealistically large force.
• b. 6.25 × 10⁺¹² N: Wrong; same error as (a), treating 30 kJ/mol directly as macroscopic work.
• c. 3.75 × 10⁻¹² N: Slightly off; likely uses half the energy (15 kJ/mol) or double step size (16 nm).
• d. 6.25 × 10⁻¹² N: Correct; matches precise calculation considering molecular conversion.

Motor proteins generate force during 8nm steps along microtubules powered by ATP hydrolysis at 30 kJ/mol, crucial for CSIR NET Life Sciences. Kinesin takes one 8-nm step per ATP, converting chemical energy to mechanical work efficiently.​