Surface Area to Volume Ratio

So who cares right? - Why should we care about a cell's surface area to volume ratio? Think about it, our cell is TINY that we have to use a microscope to see INTO it.

Surface Area to Volume Ratio

Life requires three things according to a documentary on scientists aspiring to artificially create life - i forgot the name... ASIDE Surface Area to Volume Ratio

• 1-needs a membrane
• 2-needs DNA or information storage to divide
• 3-needs metabolism

Ok before I lose you.

Something as simple as surface area to volume ratio has a significant impact in our life. Our cell is a sphere that obiously lives and therefore has all the three mentioned above BUT remember the fact that it is TINY!

So in terms of just ONE organelle: Nucleus and DNA

Focus on DNA

Take for example my prof's (Dr Turos) premise of trying to bring this back to the basics of DNA and biology while incorporating math:
"I have told you that the typical DNA molecule is a double helix of polynucleotides, and that its molecule weight is about 50 billion atomic mass units (that's "50 times ten to the ninth power"). It is a big organic molecule. Now, assuming that DNA is made up of a 1:1.56 ratio of (guanine + cytosine) : (adenine + thymidine), and the average distance between each base pair is 3.4 angstroms (or 34 angstroms for every 10 base pair units), calculate the linear length of DNA. In other words, how big would the nucleus of your cell have to be to contain even one molecule of DNA? How big would it be if the ratio of base pairs above drops to 1:1? I am hoping that this should be a fun exercise to consider, and not beyond the average math skills of an advanced organic chemistry student."

Calculating Length

• Long story short, and some calculations, the length of a theoretical cell's DNA taking into account the weight of phosphodiester bonds and the deoxysugar, it would be 2.56 centimeters = 1 inch
  • Calculation DNA Length

Calculating Volume

• So it can be packed rather efficiently in a small cell (assuming this is DNA form B). So what is the most efficient way of packing something? In any case, we will attempt to pack DNA into a simple sphere, (because thinking of luggage is becomming out of my league for math) so we are going to assume that the volume of a strand of DNA lenghtwise will roughly equal the volume of a spherical ball of the lengthwise DNA.
• Converting a grossly long strand of DNA (in terms of the typical cell size) into a small compact sphere.
  • Yields a diameter of a sphere that is 5.34E-7 while the size of typical cell is 1E-6 in diameter.
  • The diameter would take up 53.4% of a typical cell
• Meaning that HALF of the cell would have to be DNA! That is if there was no such thing as topoisomerases.
  • Calculation DNA Volume

Meaning

• For one we just did some math that took Watson and Crick spent their career elicidating. The diameter and length per base pair of DNA.
• Secondly, it shows the importance of enzymes with supercoiling to make life even possible by reducing the volume for other vital functions of a cell's life.

Concepts:

• AMU to grams/mole - CHEM
  • Ask A Scientist
    • AMU=grams/mole
• Surface Area British Columbia

Additional Information:

• Wikipedia
• National Institute of General Medical Sciences
• TIME Magazine
• BBC Venter
• Michigan State Univ