Question

You have used "optical tweezers" to study the mechanics of myosin movement in a newly discovered member of the myosin II subfamily. Your results indicate that each myosin exerts a force of about 3 pN along the length of the actin filament, and displaces the filament by about 10 nm in each cycle of ATP hydrolysis. Assuming that the free-energy change for ATP hydrolysis is -50 kJ/mol under your experimental conditions, what is the efficiency of the myosin motor in converting the free energy to mechanical work? Remember that under a constant force F (in newtons), work (W; in joules) is calculated as W = F × d, where d is displacement (in meters) in the direction of the force. Avogadro's number is approximately 6 × 1023 molecules/mole. Write down your answer as a percentage with no decimals, e.g. 99%.

Answer 1

The efficiency of the myosin motor in converting free energy to mechanical work is 1%.

Step-by-step explanation:

To calculate the efficiency of the myosin motor in converting free energy to mechanical work, we can use the formula W = F × d, where W is work, F is force, and d is displacement. In this case, the force exerted by each myosin is about 3 pN and the displacement is about 10 nm. Converting the force to Newtons (1 pN = 1 × 10^-12 N) and the displacement to meters (1 nm = 1 × 10^-9 m), we have F = 3 × 10^-12 N and d = 10 × 10^-9 m.

Using the values of F and d, we can calculate the work done by each myosin in each cycle of ATP hydrolysis: W = F × d = (3 × 10^-12 N) × (10 × 10^-9 m) = 3 × 10^-20 J.

The free-energy change for ATP hydrolysis is given as -50 kJ/mol. To convert this to Joules, we use the conversion factor: 1 kJ = 1000 J and Avogadro's number: 1 mole = 6 × 10^23 molecules. Therefore, the free-energy change for ATP hydrolysis is -50 × 1000 J/mol / (6 × 10^23 molecules).

To calculate the efficiency, we divide the work done by the myosin motor in each cycle by the free-energy change for ATP hydrolysis: Efficiency = (3 × 10^-20 J) / (-50 × 1000 J/mol / (6 × 10^23 molecules)) = 3 × 10^3 / 50 × 1000 × 6 = 3 × 10^3 / 3 × 10^5 = 1 / 10^2 = 1%.