Question

Cellular Energy. A typical eukaryotic cell, such as a cell in the human body, uses about \(2 \times 10^{-17}\) joule of energy each second. The breakdown of a single molecule of ATP (in which a phosphate separates from ATP to make ADP; see Figure 5.12 ) releases about \(5 \times 10^{-20}\) joule of energy. (a) About how many molecules of ATP must be broken down and reassembled each second to keep a eukaryotic cell alive? (b) How many times does this ATP recycling occur each day in a typical cell? (c) The human body has roughly \(10^{14}\) cells. Approximately how many cycles of the ATP reaction occur each day in your body?

Short answer

(a) About 400 ATP molecules per second. (b) Each cell recycles ATP ~34,560,000 times per day. (c) ~3.456 x 10^21 ATP cycles occur daily in the body.

Step-by-step solution

Understanding Energy Usage

We need to calculate how many ATP molecules must be broken down every second to provide the required energy for a cell, which is \(2 \times 10^{-17}\) joules per second.

Calculating ATP Requirement per Second

The energy released by one ATP molecule is \(5 \times 10^{-20}\) joules. To find the number of ATP molecules needed each second, we divide the energy required by the energy per ATP molecule: \[ \text{ATP molecules per second} = \frac{2 \times 10^{-17}}{5 \times 10^{-20}} = 400 \] This means 400 ATP molecules need to be broken down each second.

Determining ATP Recycling Per Day

There are 86400 seconds in a day (24 hours * 60 minutes * 60 seconds). Multiplying the number of ATP molecules used per second by the number of seconds per day gives the total ATP turnover: \[ 400 \times 86400 = 34,560,000 \] Thus, each cell recycles ATP about 34,560,000 times per day.

Calculating Total ATP Cycles in the Body

Given the human body has approximately \(10^{14}\) cells, multiplying the daily ATP cycles per cell by the number of cells gives: \[ 34,560,000 \times 10^{14} = 3.456 \times 10^{21} \] Therefore, approximately \(3.456 \times 10^{21}\) cycles of the ATP reaction occur each day in the human body.

Key concepts

ATP breakdown

The process of ATP breakdown is crucial for powering cells in your body. ATP, or adenosine triphosphate, is a molecule that acts like a battery for cellular functions. It stores energy which cells use to perform various tasks.
When a cell needs energy, it breaks down ATP starting with the detachment of a single phosphate group. This chemical reaction transforms ATP into ADP (adenosine diphosphate), releasing energy in the process.
This released energy, approximately \(5 \times 10^{-20}\) joules per ATP molecule, powers activities such as muscle contraction, nerve impulses, and synthesizing new compounds.
During this process, the specific breaking of the phosphate bond is what releases the stored energy, allowing cells to perform essential functions.

eukaryotic cell energy

Eukaryotic cells, like those in humans, require a constant energy supply to sustain life. These powerhouse cells have organelles such as mitochondria that play a critical role in energy production.
Inside every cell, energy processes must continually run to maintain essential operations, like growth, metabolism, and response to environmental changes.

• Mitochondria convert nutrients into energy through cellular respiration.
• Energy is primarily stored and transported in the form of ATP molecules.
• This energy supply is indispensable for both daily activities and long-term cellular health.

Without this consistent energy source from ATP and mitochondria, cells would stop functioning properly, which could lead to severe consequences for the organism.

ATP recycling

ATP recycling is an efficient process that ensures cells always have the energy they need. After ATP breakdown, cells don't discard ADP and phosphate groups. Instead, they recycle them back into ATP.

• Cells take ADP and phosphate and reconvert them into ATP via cellular respiration within the mitochondria.
• The process of recycling occurs thousands of times per day in each cell.
• This continuous cycle of breakdown and reassembly makes ATP a highly effective energy currency for cells.

This efficient recycling means that each ATP molecule is used repeatedly, aligning with the concept of resource sustainability within cells.

human body cells

The human body is composed of approximately \(10^{14}\) cells. Each of these cells needs ATP to function and survive. This massive number of cells continuously terminates and rebuilds trillions of ATP molecules every day.
These cells perform various critical functions, such as:

• Producing enzymes and proteins.
• Replicating DNA and dividing during growth and repair.
• Maintaining homeostasis in response to internal and external stimuli.

Given the staggering amount of ATP activity, it's awe-inspiring how the human body efficiently manages these energy processes, ensuring our survival and the performance of every single task necessary for life.