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Just tell me in clearly understood scientific terms the molecular basis for the THEORY of evolution. You can't.

Let me try.

Darwin thought that inheritance was a matter of fractions, continuously variable characters (traits) that would mix freely in the offspring of the parents. I.e., an orange cat might mate with a black cat to product a brown cat. Darwin was also something of a Lamarckian, in that he believed that acquired characters would be inherited by offspring. So a giraffe that stretched its neck a bit further than its parents would have offspring with longer necks.

This turns out to be wrong. Mendel discovered that characters are controlled by "genes" that are like little light switches that are either on or off. Unless a character is controlled by many genes (as sometimes happens), you either have the character or you don't. You have blue eyes or brown eyes but not some shade in between (well, hazel maybe). If you cross a black cat and a tabby orange cat, you don't get a brown cat, you might get a calico.

This was a big problem for the theory of evolution. You don't have a smooth blending of characters that Darwin supposed would happen. You don't have acquired characteristics being inherited. Instead, scientists realized, you have random mutations that appear, and if they are beneficial (usually they're neutral, neither good or bad), they spread throughout the population over hundreds of generations. The theory of this was worked out in the early to mid 20th century (the details are very mathematical; read something on "population genetics" and you'll see).

All of this happened before the fateful year of 1953 (or was it 1954?) when the structure of DNA was discovered. Now scientists were in a position to understand the exact molecular details of genetics, of inheritance, of mutations and of evolution itself. This was developed through the 1960s. The result is known as the "neo-Darwinian synthesis". That is, the synthesis of molecular biology (genetics) with evolutionary theory.

A very brief summary: most processes in an animal (or plant) body and cells are controlled by proteins. Proteins are chains of amino acids (peptides) glued together. There are 20 amino acids to choose from. DNA is a chemical code for proteins. A "gene" is a stretch of DNA that codes for a single protein. (We now know that it isn't always that simple, but never mind.) Now DNA resembles a spiral staircase, where each step ("base pair") is a mated pair of "nucleotides" whose names are abbreviated A C G or T. So we think of DNA as a chain of these four letters that occur in seemly random orders. Now it turns out that every three letters codes for one amino acid. A triple is called a "codon". There are 64 codons possible. Given that there are only 20 amino acids, it turns out some codons code for the same amino acid, but there are codons that code for no amino acid at all. These are "stop" codes on the DNA: they stop the synthesis of the protein. The protein, as I said above, is a chain of amino acids. These are assembled by an elaborate set of molecular machines which read the DNA, but they stop reading when the get to the stop code. The DNA controls other things, in particular when proteins are to be made ("gene regulation").

One spectacular discovery was made sometime in the 1980s (my knowledge here is a bit fuzzy): homeobox genes. These are the sets of genes that control how animal body plans develop. Apparently, we inherited these from the earliest segmented worms 600 million years ago or longer. All animals have these. A small change in these can result in a dramatic change in an animal's body plan. So small mutations in the right place can hasten the development of a new species in a population. I would guess this is what's going on when you see a kitten with an unusual number of toes. (A friend of mine had a cat with extra toes: he named the animal Bigfoot.) Anyone who sees a cat with extra toes shouldn't have much trouble understanding how mutations can cause harmless changes to an animal that might even prove beneficial.

I would be grateful if anyone who actually knows the molecular biology or genetics would correct or clarify what I've written (I'm only a mathematician).

"Let me try."

And I'll give your request a try too. Let me say that I am a microbiologist, so my knowledge of molecular biology of animals is somewhat less deep.

"Darwin thought that inheritance was a matter of fractions, continuously variable characters (traits) that would mix freely in the offspring of the parents. I.e., an orange cat might mate with a black cat to product a brown cat. Darwin was also something of a Lamarckian, in that he believed that acquired characters would be inherited by offspring. So a giraffe that stretched its neck a bit further than its parents would have offspring with longer necks."

Other than the reference to Lamarck, this appears to be OK.

"This turns out to be wrong. Mendel discovered that characters are controlled by "genes" [Mendel discovered the laws of genetics, but he had absolutely no idea what a gene was] that are like little light switches that are either on or off. Unless a character is controlled by many genes (as sometimes happens), you either have the character or you don't. You have blue eyes or brown eyes but not some shade in between (well, hazel maybe). If you cross a black cat and a tabby orange cat, you don't get a brown cat, you might get a calico."

OK, eye color is controlled by multiple genes and people with one blue eye and one brown one (like a particular breed of cats) are not rare. I have blue eyes, but one is about 1/3 brown. There is a "smear" on some traits. Some genes show dominance/recessivity some show partial dominance (say white/pink/red flowers).

"This was a big problem for the theory of evolution. You don't have a smooth blending of characters that Darwin supposed would happen. You don't have acquired characteristics being inherited. Instead, scientists realized, you have random mutations that appear, and if they are beneficial (usually they're neutral, neither good or bad), they spread throughout the population over hundreds of generations. The theory of this was worked out in the early to mid 20th century (the details are very mathematical; read something on "population genetics" and you'll see)."

This looks good, but I don't think genes were a problem for evolution, they explained so much. However, they did require adjustment to the theory.

"All of this happened before the fateful year of 1953 (or was it 1954?) when the structure of DNA was discovered. Now scientists were in a position to understand the exact molecular details of genetics, of inheritance, of mutations and of evolution itself. This was developed through the 1960s. The result is known as the "neo-Darwinian synthesis". That is, the synthesis of molecular biology (genetics) with evolutionary theory."

OK

"A very brief summary: most processes in an animal (or plant) body and cells are controlled by proteins. Proteins are chains of amino acids (peptides)[scratch this word - it doesn't fit] glued together. There are 20 amino acids to choose from. DNA is a chemical code for proteins. A "gene" is a stretch of DNA [doesn't have to be contiguous] that codes for a single protein. (We now know that it isn't always that simple, but never mind.) Now DNA resembles a spiral staircase, where each step ("base pair") is a mated pair of "nucleotides" whose names are abbreviated A C G or T. So we think of DNA as a chain of these four letters that occur in seemly random orders. Now it turns out that every three letters codes for one amino acid. A triple is called a "codon". There are 64 codons possible. Given that there are only 20 amino acids, it turns out some codons code for the same amino acid, but there are codons [3] that code for no amino acid at all. These are "stop" codes on the DNA: they stop the synthesis of the protein. The protein, as I said above, is a chain of amino acids. These are assembled by an elaborate set of molecular machines which read the DNA, but they stop reading when the get to the stop code. The DNA controls other things, in particular when proteins are to be made ("gene regulation"). [although most gene regulation happens at the level of DNA, it is mediated by small(er) molecules]"

"One spectacular discovery was made sometime in the 1980s (my knowledge here is a bit fuzzy): homeobox genes. These are the sets of genes that control how animal body plans develop. Apparently, we inherited these from the earliest segmented worms 600 million years ago or longer. All animals have these. A small change in these can result in a dramatic change in an animal's body plan. So small mutations in the right place can hasten the development of a new species in a population. I would guess this is what's going on when you see a kitten with an unusual number of toes. (A friend of mine had a cat with extra toes: he named the animal Bigfoot.) [this is a trait called polydactyly and is controlled by a single recessive gene in humans. I think this is also the case in most mammals.] Anyone who sees a cat with extra toes shouldn't have much trouble understanding how mutations can cause harmless changes to an animal that might even prove beneficial. "

"I would be grateful if anyone who actually knows the molecular biology or genetics would correct or clarify what I've written (I'm only a mathematician)."

You did pretty good, mega. Related to Bacillus megatherium?

However, the creationoid will not be satisfied with your answer.