Question

The basis of muscle action is the power stroke of the myosin protein pulling on an actin filament. It takes the energy of one molecule of ATP, 5.1×10⁻²⁰ J, to produce a displacement of 30 nm against a force of 1.0 pN. What is the energy required to produce a displacement of 60 nm against the same force?

1) 2.55×10⁻²⁰ J
2) 5.1×10⁻²⁰ J
3) 1.02×10⁻¹⁹ J
4) 2.04×10⁻¹⁹ J

Answer 1

The energy required to produce a displacement of 60 nm against a force of 1.0 pN would be double the energy required for a 30 nm displacement. Since one molecule of ATP provides 5.1×10⁻²⁰ J for a 30 nm displacement, the energy required for a 60 nm displacement is 1.02×10⁻¹⁹ J.

Step-by-step explanation:

The energy required for muscle contraction comes from the hydrolysis of adenosine triphosphate (ATP). In a muscle contraction, myosin heads bind to actin, creating a cross-bridge and pulling the actin filaments toward the center of the sarcomere in what is known as a power stroke. During this process, the myosin heads use energy derived from ATP to perform mechanical work.

Calculate the energy required for a 60 nm displacement using the work-energy principle: Work = Force × Displacement. Given that it takes the energy of one molecule of ATP (5.1×10⁻²⁰ J) to produce a displacement of 30 nm against a force of 1.0 pN, we can deduce that the work done is directly proportional to the displacement when the force is constant. Therefore, to produce a displacement of 60 nm (double the original displacement), the energy required would also double.

The correct answer is:3) 1.02×10⁻¹⁹ J