Cell and membrane volume physics

In summary, the typical human cell has a diameter of 10 μm and a membrane thickness of 4.2 nm. To find the volume of the cell, it can be modeled as a sphere with a radius of 5 μm, giving a volume of 523.60 μm^3. To find the volume of the cell membrane, it can be modeled as a shell with a radius of 5 μm and a thickness of 4.2 nm, giving a volume of 7.06 μm^3. This means that the cell membrane occupies approximately 1.3% of the total cell volume.
  • #1
Akewal
2
1

Homework Statement


A typical human cell is approximately 10 μm in diameter and enclosed by a membrane that is 4.2 nm thick. To simplify the calculations, model the cell as a sphere.
1) What is the volume of cell? (in μm^3)
2) What is the volume of cell membrane? (in μm^3)
3) Percent cell volume the membrane occupies

Homework Equations


V= 4/3*pi*r^3

The Attempt at a Solution


I knew the volume of sphere, so I could easily solve for number 1 Because 10 was the diameter, I divided it by 2 which gave me a radius of 5.
1) 4/3*pi*125= 523.60μm^3
2) This is where I got stuck. I converted 4.2 nm to μm (multiplying 4.2 with 0.001), and used the volume formula, with .0042 μm as my r. The answer is wrong!

What I am doing wrong?
 
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  • #2
Hello Akewal, ##\qquad##:welcome:##\qquad##!

The way you describe it, you calculated the volume of a sphere with a radius of 4.2 nm ...

If you make a coarse sketch, you see that you are after the volume of a shell with radius 5 ##\mu##m and a thickness of 4.2 nm ... A different beast !
 

1. What is the importance of cell and membrane volume physics in biological systems?

Cell and membrane volume physics is crucial for maintaining the structural integrity and proper functioning of cells in biological systems. It helps regulate cellular processes, such as osmosis, cell division, and cell signaling, which are essential for the survival of organisms.

2. How does the size and shape of a cell affect its volume and membrane physics?

The size and shape of a cell can significantly impact its volume and membrane physics. Larger cells have a higher volume and require a more efficient transport system for nutrients and waste products. The shape of a cell can also affect its surface-to-volume ratio, which influences the efficiency of membrane transport processes.

3. What factors influence the movement of molecules across cell membranes?

The movement of molecules across cell membranes is influenced by several factors, including molecular size, charge, and concentration gradient. The properties of the membrane, such as its composition and permeability, also play a role in determining the movement of molecules.

4. How do cells maintain their volume and osmotic balance?

Cells use various mechanisms to maintain their volume and osmotic balance. These include active transport, where cells actively pump ions and molecules in and out of the cell to maintain the proper balance, and passive transport, such as osmosis, where water moves across the cell membrane to equalize solute concentrations.

5. What are the implications of membrane volume changes in diseases?

Changes in membrane volume have been linked to several diseases, including hypertension, diabetes, and cancer. Alterations in membrane volume can affect the transport of essential molecules and disrupt cellular processes, leading to disease progression. Understanding the role of membrane volume physics in diseases can help develop targeted treatments.

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