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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, \(5.1 \times 10^{-20} \mathrm{J},\) to produce a displacement of \(10 \mathrm{nm}\) against a force of \(1.0 \mathrm{pN} .\) What is the efficiency?

Short Answer

Expert verified
The efficiency of the power stroke of the myosin protein is approximately 19.61 %.

Step by step solution

01

Calculation of Work Done

The work done is calculated as the product of the displacement and the force exerted during the displacement. Therefore, it would be \(1.0 \times 10^{-12}\) Newton (1.0 pN) times \(10 \times 10^{-9}\) meter (10 nm), which equals \(1.0 \times 10^{-20}\) Joule.
02

Calculation of Efficiency

The efficiency would then be calculated as the ratio of the work done over the total energy consumed (energy in one ATP molecule). Therefore, efficiency = \(\frac{1.0 \times 10^{-20}}{5.1 \times 10^{-20}}\) which yields approximately \(0.1961\). If we want the efficiency in percentage, we simply multiply by 100, which equals to 19.61 %.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

ATP energy conversion
Muscles need energy to contract and perform work. This energy comes from Adenosine Triphosphate (ATP), a molecule found in every living cell. ATP is the main source of energy for various cellular activities. During muscle contraction, ATP is converted into another molecule called ADP (Adenosine Diphosphate), releasing energy in the process. This released energy is crucial for the movement of the myosin protein within muscle fibers.

When ATP is used, it spans multiple cycles within the muscle cells. First, ATP binds to the myosin head (a part of the myosin protein), allowing it to detach from the actin filament. Then, ATP becomes ADP, and energy is released. This energy allows the myosin head to change shape and move forward, pulling the actin filament with it.
  • One ATP molecule has an energy of approximately 5.1 x 10^{-20} Joules.
  • The energy converted from ATP is utilized in the power stroke of muscle movement.
Understanding this energy conversion is critical to grasp how muscles effectively use ATP in contraction.
Work done calculation
In physics, work is defined as the force exerted on an object multiplied by the displacement of that object in the direction of the force. This is what happens during muscle contraction. Calculating the work done during a single cycle of muscle contraction involves understanding both the force applied and how far the muscle shortens.

In the exercise given, the force exerted is 1.0 piconewton (pN), which is equivalent to 1.0 x 10^{-12} Newton. The displacement or movement caused by this force is 10 nanometers (nm), equivalent to 10 x 10^{-9} meters.
  • The formula for work done: Work = Force x Displacement.
  • Using the exercise values: Work done = 1.0 x 10^{-12} N x 10 x 10^{-9} m = 1.0 x 10^{-20} Joules.
This calculation shows how efficiently muscles work during contractions, providing insights into energy usage during physical activity.
Myosin protein
The myosin protein is a vital component of muscle cells that plays a central role in muscle contraction. It works closely with actin filaments, creating the contractile units known as sarcomeres. Myosin proteins are like tiny motors. They cycle through attachment, movement, and detachment to facilitate muscle fiber contraction.

Each myosin molecule has a head and tail structure, with the head binding to the actin filament. This attachment occurs as the myosin head binds to ATP. When ATP is hydrolyzed to ADP, the head pivots, creating a motion known as the power stroke. This pulls the actin filament past the myosin, causing contraction and muscle shortening.
  • Myosin cross-bridges attach to actin filaments through ATP binding.
  • A single cycle involves the myosin heads moving from one position to another, requiring ATP hydrolysis.
  • Understanding myosin's functionality helps explain muscle contraction at a molecular level.
By examining the myosin protein, we learn about the efficiency and precision of our muscles during every movement.

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Most popular questions from this chapter

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