Introduction to the Mathematics of Evolution

 

Chapter 9

 

DNA and RNA

 

 

Introduction

 

The rest of this book will get increasingly involved with DNA.  This chapter will introduce the reader to the molecule called: DNA.

 

Subsequent chapters will get more and more involved with DNA, so it is important to have a sold basis for understanding DNA.

 

It would also be wise to look at outside resources which discuss DNA.  It is far beyond the scope of this book to discuss many issues related to DNA.  This book will focus on very specific issues.  A broader understanding of DNA would be very helpful to the reader as this book progresses.

 

 

DNA (Deoxyribonucleic Acid)

 

DNA is a very large, very complex molecule made up of several different kinds of small molecules.

 

"Nucleotides" are a type of molecule found in DNA.  There are only 4 different kinds "nucleotides."  Nucleotides are the key to what DNA is able to do.  The sequence (i.e. order) of nucleotides is what provides the "information" that is needed for the cells to function.

 

To understand DNA, consider a large encyclopedia of 100 volumes.  Even though a large set of encyclopedia volumes is a huge set of books, and would be very, very heavy to lift, the encyclopedia only consists of 26 letters of the English alphabet.  A person could say that an encyclopedia consists of only 26 different letters; however, all of the letters are repeated many, many times in an encyclopedia.

 

Yes, an encyclopedia will also have numbers (e.g. 0,1,2,3,...,9), special characters (e.g. space, %, $, @, &, etc.), but still an encyclopedia, no matter how many volumes, still has only 26 letters of the alphabet, plus a few other characters.

 

For example, consider that a word in the English language, such as the word: "tergiversation" (which is the act of being deliberately ambiguous) is nothing but a permutation (i.e. a unique way of ordering the letters) of the 26 possible letters of the English alphabet which happens to have 14 consecutive letters in it.

 

An encyclopedia has a lot of words and thus a lot of individual letters, if we ignored the words and only looked at the letters.  In fact, when we look at DNA we may look at the letters (i.e. the nucleotides) and forget to look at DNA as "words" or "segments" which have meaning as a group of letters.

 

DNA only has 4 letters in its alphabet but the "words" in DNA are far more complex than the words in an Encyclopedia.  Human DNA consists of a chain of 3 billion nucleotides or 3 billion "letters"!!  Thus, DNA is really nothing but a long string of 4 nucleotides.  Actually the nucleotides are paired together, thus there are technically 3 billion "pairs" of nucleotides in human DNA, meaning 6 billion individual nucleotides.

 

 

More About DNA

 

Visually, DNA can be imagined to be like a very long ladder.  A ladder has two sides (i.e. two long side-rails).  These two sides are joined together by the steps, which, in a real ladder; people step on to climb the ladder.  When a person is climbing a ladder, their hands usually grab onto the two side-rails of the ladder, and their feet step on the rungs.

 

When comparing a ladder to DNA, the side-rails of the ladder can be compared to a long sequence of alternating types of molecules.  A sugar molecule and a phosphate molecule alternate many times to create each side-rail of the ladder.

 

In other words, many "sugar-phosphate" molecule pairs make up each side-rail of the DNA ladder to create two "sugar-phosphate backbones," one on each side of the DNA molecule.

 

For example, human DNA has 3,000,000,000 alternating pairs of the sugar-phosphate backbone in one long row.  This is just one side-rail of the ladder.  The other side-rail also has 3 billion alternating pairs of the sugar-phosphate backbone.

 

The two side-rails of DNA are designed such that the sugar molecules are across from each other.  Each of the sugar molecules (dioxyribose) attaches to a "nucleotide" molecule on the "step."  Each sugar molecule (on each side-rail) has a nucleotide attached to it.  Because each of the side-rails attach to a nucleotide, the "steps" of the ladder are a pair of nucleotides because each of the two nucleotides attach to an opposite side-rail.

 

Thus, when there is a rung on the DNA ladder, there are four consecutive molecules.  A sugar molecule on each side-rail and a nucleotide attached to each side-rail.  The two nucleotides are bound together by hydrogen bonds.

 

On each side-rail, and between each sugar molecule (which is where the rungs are), is a phosphate molecule holding the sugar molecules together on the side-rails.

 

DNA can be drawn like this (the hydrogen bond is not a physical object, but a type of attraction between two molecules):

(S=sugar, P=phosphate, N=nulceotide, H=hydrogen bond)

 

P       P

S-N-H-N-S

P       P

S-N-H-N-S

P       P

S-N-H-N-S

P       P

S-N-H-N-S

P       P

S-N-H-N-S

P       P

...

 

The two alternating P and S molecules are the two side-rails of the DNA ladder.  The S-N-H-N-S combination constitute a rung.

 

There are four different kinds of nucleotides (which are also referred to as "bases"):

'A' is for Adenine

'T' is for Thymine

'C' is for Cytosine

'G' is for Guanine

 

Substituting one of these nucleotide bases for each 'N' in the above chart, we might see this sequence:

 

P       P

S-A-H-T-S

P       P

S-T-H-A-S

P       P

S-C-H-G-S

P       P

S-G-H-C-S

P       P

S-C-H-G-S

P       P

...

 

Note in the above graph that if an 'A' attaches to one sugar molecule, on one side-rail of the DNA, a 'T' is supposed to attach to the opposite sugar molecule, on the other side-rail of the ladder.  These two molecules are bound together by hydrogen bonds.

 

Likewise, if a 'T' attaches to one sugar molecule, on one side of the DNA, an 'A' attaches to the opposite sugar molecule, on the other side of the ladder.

 

In other words, an 'A' and a 'T' should always be joined together on the same rung.

 

Likewise, a 'C' and a 'G' should always be joined together to form a single rung of the ladder.

 

Adenine actually forms two hydrogen bonds with thymine.  Guanine forms three hydrogen bonds with cytosine.  These hydrogen bonds, along with the two nucleotides, are referred to as "base-pairing."

 

Now we can take the above chart and improve on it ('2H' means two hydrogen bonds and '3H' means three hydrogen bonds):

 

P        P

S-A-2H-T-S

P        P

S-T-2H-A-S

P        P

S-C-3H-G-S

P        P

S-G-3H-C-S

P        P

S-C-3H-G-S

P        P

...

 

Because if we see an 'A' on one side of the rung, we know that there is a 'T' on the other side of the rung, generally scientists only talk about one side of the "ladder," and thus when the reader sees an 'A' in a chart, they are supposed to mentally supply the 'T' on the other side.  Or if the reader sees a 'T" they are supposed to understand that an 'A' is on the other side.  Ditto for 'G' and 'C'.

 

Thus, the entire chart above would normally be designated as simply:

ATCGC

 

 

"Unzipping DNA"

 

In the process of protein synthesis, which will be discussed in the next chapter, DNA is "unzipped."  What does that mean?  What it means is that all of the hydrogen bonds are broken and the DNA, instead of being one ladder with two sides, becomes two ladders with one side.  For example, the above diagram would look like this:

 

P               P

S-A           T-S

P               P

S-T           A-S

P               P

S-C           G-S

P               P

S-G           C-S

P               P

S-C           G-S

P               P

...

 

Once "zipped apart," the two half-sides of DNA can be built by new nucleotides either to make two complete DNA strands (which is how one DNA molecule is converted into two DNA molecules) or a side can be used to make RNA, which will be discussed later.

 

 

More Terminology

 

As mentioned above, when describing the sequence of nucleotides in a DNA strand, scientists generally only talk about the nucleotides which are connected to one side-rail of the ladder.

 

Thus, when you see something like this (the space is simply to make it easier to view):

ATCGCATCTG GGAAGCTACC

these "letters" represents the consecutive nucleotides on one side of the ladder.  The reader is expected to fill in the other side, if needed.

 

The above DNA section can be represented without showing the hydrogen bonds, and it can be shown like this (a '-' represents a phosphate molecule and a '=' represents a sugar molecule on the side of the ladder):

 

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

 A T C G C A T C T G G G A A G C T A C C

 T A G C G T A G A C C C T T C G A T G G

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

 

A DNA molecule is a double-helix (a 'helix' means a spiral shape), meaning it is looks like a very, very long ladder that has been twisted like a spiral staircase.

 

When "counting" how many nucleotides there are in a DNA strand, generally only one side is counted, as mentioned above.  Thus, when it is said that human DNA has about 3,000,000,000 nucleotides, they are really talking about 3,000,000,000 nucleotide pairs, meaning they are really talking about 6,000,000,000 nucleotides in a single human DNA.

 

The human body has about 100 trillion cells.  Each cell has a complete DNA strand inside its cell nucleus.  Exceptions to this rule are eggs, sperm and red blood cells.  Thus, your body contains about 100 trillion DNA molecules, each of which has 6,000,000,000 nucleotides (counting the nucleotides on both sides of the DNA).

 

"If the chromosomes in one of your cells were uncoiled and placed end to end, the DNA would be about 6 feet long. If all the DNA in your body were connected in this way, it would stretch approximately 67 billion miles! That's nearly 150,000 round trips to the Moon."

The New Genetics Chapter 1

 

But the most amazing thing about human DNA is not its shape or size, but what it does.

 

The sophistication of what human DNA accomplishes is literally beyond the ability of the human mind to comprehend.

 

As if that weren't enough, every cell in our body also has multiple mitochondria.  Mitochondria have their own DNA, though the DNA in mitochondria is very short compared to the very, very long main DNA of the cell.

 

But mitochondria are not the only organelle in the human cell that has its own short DNA.

 

This discussion of DNA is very primitive.  It is like describing the space shuttle as a "big grey tube with wings."  People get PhDs and Nobel Prizes for discovering things about DNA.

 

 

RNA

 

An RNA molecule has only a single side-rail.  RNA is much like one of the unzipped DNA molecules above.  Each sugar on this one side-rail has a nucleotide attached to it.  The sugar in the side-rail of RNA is a different combination of sugars than that found in DNA.

 

In RNA, the four nucleotides are:

'A' is for Adenine

'U' is for Uracil (replaces Thymine)

'C' is for Cytosine

'G' is for Guanine

 

Thus, an RNA strand might include this segment:

 

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

 A A U G C A U C U G G G A A G C U A C C

 

RNA can also be looped.

 

RNA has many functions, and thus there are many different kinds of RNA.

 

 

DNA Replication

 

Due to the way that DNA is designed, it is easy (from a visual perspective) to understand how DNA is replicated (i.e. how one DNA strand is converted into two DNA strands).

 

Now instead of looking at DNA as a ladder, let us think of it as a very long zipper.

 

In DNA replication, the DNA is "unzipped," as shown above, and the DNA is broken into two half-DNA strands, which look like RNA, but have a different set of nucleotides.

 

Each half-strand consists of one side-rail and the nucleotide that is associated with the sugar molecule on that side-rail.

 

A process essentially takes each of the two half-DNA strands, and builds a new, complete DNA strand by combining new nucleotides with each half; by matching an A with a T, a T with an A, etc.

 

So if we follow a single rung, after unzipping the DNA, suppose there is an A on one rung.  Attached to the A will be a T (which will be on the new rung).

 

The other side of the unzipped DNA will have a T on that rung.  Thus, an A will added to the new rung.

 

This results in a single DNA molecule becoming two identical copies of the original DNA strand.

 

Using the above unzipped DNA section, this is what it would look like:

 

 

P     P      P     P

S-A-T-S      S-A-T-S

P     P      P     P

S-T-A-S      S-T-A-S

P     P      P     P

S-C-G-S      S-C-G-S

P     P      P     P

S-G-C-S      S-G-C-S

P     P      P     P

S-C-G-S      S-C-G-S

P     P      P     P

...

 

Note that the two DNA sequences are identical.

 

If the reader has any problems understanding this chapter they are encouraged to look at a biology book to get more of a graphical understanding of what is going on.