It is correct that the product of the conceptual translation of a nucleotide sequence into an amino acid sequence results in the loss of certain information present in the former. An obvious example is that the amino acid sequences of the same protein in two individuals may be identical, but there may be silent mutations in the DNA, and these can be useful in tracing ancestry. The one part of Crick’s Central Dogma about which there can be no argument is that you cannot go from protein to DNA because the information for the nucleotide sequence is not present in the protein, with or without the genetic code.
An amino acid sequence contains information that is not present in the gene from which it originates, if we just consider the sequence as mathematical sequence of symbols. And, with 20 letters instead of 4, this new information has a different (and greater) complexity. The mistake is an unspoken assumption that the information of the genetic code is inherent in the nucleotide sequence. It is not. Yes, if we have the information of the genetic code, then the nucleotide sequence also has the information of the amino acid sequence, but that is not the practical question at issue.
So (addressing the poster) in the majority of practical instances your school teacher is correct. I am not a mathematician, so I cannot be sure what is the flaw of your argument. Perhaps it is the fact that only a subsection of the information can be used in the sequence comparison, perhaps the fact that you are talking three symbols from a set of four in your non-injective function to produce one symbol from a set of 20, or perhaps it is the biology. That’s something for you to work out. But if your conclusions are wrong (which they are) there must be a flaw in your logic)
The Question at Issue
The practical question at issue is:
Which is more suitable for determining the evolutionary relatedness of
two organisms — a pairwise comparison of the amino acid sequences of a functionally
similar protein (e.g. cytochrome c) or of the nucleotide sequences of the corresponding gene?
The general answer is:
It depends on the relatedness of the organisms, but, except for very
close kinship (e.g. humans and neanderthals) or certain specialized
problems, the answer is likely to be the amino acid sequences.
How can this be?
In relationship to the evolutionary distance between organisms, it
is necessary to consider the different rates at which nucleotides and
amino acids mutate, and the constraints on what mutations are likely
to occur. If the rate of mutation is too fast there will be a time
difference after which it will be difficult or impossible to
calculate their evolutionary divergence accurately and ultimately even
to detect any relationship between them.
Nucleotides mutate more rapidly than amino acids, and in practice comparison of nucleotide sequences is less useful than comparison of amino acid sequences for longer timespans.
Because of the degeneracy of the genetic code (the fact that an amino acid can be encoded by more than one triplet of nucleotides) it is possible for one or even two nucleotides to mutate without affecting the amino acid sequence. (And the similarity between sequences is computed from a letter-by-letter comparison.)
Statistics is not my forté, but in a general sense, because there are only four bases, 25% identity between two nucleotide sequences would be expected to occur by chance, whereas two amino acid sequences that are 25% identical would be statistically significantly similar because there are 20 amino acids. (Only 5% identity would arise by chance.)
There is a further aspect of divergence of amino acid sequence that is useful for evolutionary comparison, and this is that the nature of the mutation of amino acids is far more constrained than that of nucleotides. Admittedly purine-to-purine or pyrimidine-to-pyrimidine mutations are more frequent than purine/pyrimidine mutations, but amino acid mutations are often constrained by the role the amino acid plays in a protein. However one can construct empirical matrices of the likelihood of different amino acid mutations to obtain a more subtle and accurate estimate of relatedness.
What this means in practice is that instead of having to use a scoring system for comparisons of amino acid sequences that is either 1 for identity or 0 for non-identity, one can use a scoring system that gives ‘half marks’ (as it were) for structural/functional similarity. Thus, two amino acid sequences having 5% identity in pairwise comparison could be shown to be related because of an overall higher ‘similarity’ score.
Appendix 1: Sequence Comparison
It is important to realize that however much information resides in nucleotide or amino acid sequences, only the information that is actually used in the practical methods of determining evolutionary differences is relevant. These methods involve computer programs that compare sequences according to mathematical algorithms to answer the question of how similar two (or more) sequences are. So, regardless of the fact that the amino acid sequence is generally computed from the gene sequence, the question is “should I imput nucleotide or amino acid sequences into the program to get the best comparison?”. It is in this context that the remarks above about rate of change and likelihood of interconversions should be taken.
To quote from an article by one of the pioneers in sequence comparison, W. R. Pearson:
“Protein (and translated-DNA) similarity searches are much more sensitive than DNA:DNA searches. DNA:DNA alignments have between 5–10-fold shorter evolutionary look-back time than protein:protein or translated DNA:protein alignments. DNA:DNA alignments rarely detect homology after more than 200–400 million years of divergence; protein:protein alignments routinely detect homology in sequences that last shared a common ancestor more than 2.5 billion years ago (e.g. humans to bacteria). Moreover, DNA:DNA alignment statistics are less accurate than protein:protein statistics; while protein:protein alignments with expectation values < 0.001 can reliably be used to infer homology, DNA:DNA expecation values < 10−6 often occur by chance, and 10−10 is a more widely accepted threshold for homology based on DNA:DNA searches.”
There are Wikipedia articles about sequence alignment, and about the use of BLOSUM and PAM matrices. The section on sequence alignment in Berg et al. online — which involves amino acid, rather than nucleotide sequences — may also be of interest.
Appendix 2: Terminology and Definitions
As the term, Genetic Code, was misused in the unedited version of the question — and is widely misused in the press — I thought that a glossary of terms might be helpful
DNA (from which the genome and its constituent genes are constructed) are linear polymers of 4 nucleotides. The order of these is called the nucleotide sequence, or, because the only the purine or pyrimidine base varies between nucleotides, the base sequence.
Proteins are linear polymers of 20* amino acids. The order of these is called the amino acid sequence.
The Genetic Code is a cipher — and can be represented as a table showing the correspondence between 64 triplets of three nucleotides and the 20 amino acids and three stop signals when these nucleotides are part of the translatable part of a gene. The genetic code is highly — but not absolutely — conserved between organisms (and differs for proteins encoded by mitochondrial DNA).
In NO circumstances can the word Genetic Code be used as a synonym of Genome, although this is abused by even the scientific press, and is difficult for computer programmers to come to terms with, working as they do in a field where the noun ‘code’ is used for the product of encoding instructions.
*The genetic code has a certain plasticity and two additional amino acids can be encoded by termination codons in certain circumstances.