Is the probability of Evolution by random/chemical mutations large enough to consider as a means of our existence ?

    In 1953, two important scientific discoveries were reported. In England James Watson and Francis Crick published their results on the structure of DNA, deoxyribose nucleic acid, the genetic code of life. In Chicago the same year, Stanley Miller and Harold Urey published results of their “origin of life” experiments in which they were able to produce amino acids from electrical energy and inorganic matter, i.e., chemicals. These two discoveries have subsequently been shown to be related through the theory of chemical evolution.
    Chemical evolution is the evolution of first life from inorganic chemicals. In the scenario of chemical evolution, the first living cells are thought to have evolved from chemicals in a series of steps. The first step was the creation of the basic molecules needed to form proteins, DNA, RNA, and membranes. The first experiments of Miller and Urey were concerned with the formation of amino acids, the “building blocks” for proteins. These basic molecules are thought to have occurred in a “primordial soup” and, through repeated independent trials, to have formed into long chains to produce proteins, DNA, RNA, and other organic compounds needed by the first living cell. These organic molecules then combined to form a proto cell and, finally, the first living cell.
        In this example, we shall consider one aspect of chemical evolution, the chance formation of proteins from the amino acids that make up proteins in living cells. Thus we shall assume that all of the 20 different amino acids needed in protein synthesis were available as building blocks. Nineteen of the 20 amino acids needed in living cells occur in two forms, which we shall denote as left-handed and right-handed. They occur in approximately equal numbers. But only left-handed forms appear in living cells. Thus there are effectively 39 possible choices of amino acids - 19 left-handed forms, 19-right handed forms, and one amino acid that is neither.
    An hypothesized mechanism by which these amino acids join together is “random,” i.e., the independent concatenation of amino acids, a reasonable mechanism for the appearance of first life? Let’s calculate the probability of forming one protein made up of 400 amino acids. A length of 400 is not, in fact, a large protein, but it is somewhat average.
    To begin the calculations, let’s assume that the 20 different kinds of amino acids occur in equal numbers, i.e., 400 ÷ 20 = 20 of each kind in our hypothetical protein. Let’s perform the calculation in two steps. Suppose we assume that the correct kind of amino acid is selected for each of the 400 locations in our protein. “Chance” is required to select only left-handed (versus right-handed) forms. That is, what is the probability of selecting 380 left-handed forms from 50/50 mixture of left- and right-handed forms? (We use 380 because one of the 20 kinds of amino acids occurs as neither left- or right handed) This probability is the same as the probability of 380 heads in 380 throws of a fair coin.

    Let N be the number of amino acids that independently concatenate per set of 400 amino acids in
1010 years per millisecond. You might think of this as randomly  adding one amino acid to the end of our 400-acid long sequence and  simultaneously removing one from the beginning of that sequence every millisecond for 1010 years. A sample space of possible amino acid sequences in an independent concatenation for each string of 400 is:

where X is the set of 20 forms of amino acids excluding right handed forms. Now define "s" as a particular sequence that is "m" amino acids long:

Let Ak be the event that "s" appears at the kth index in a sequence of amino acids of length N:

In other words, Ak is the event that a particular sequence, "s" , which is "m" amino acids long, appears in the one set's sequence and ends on index k (sm occurs on index k).  The event of interest is A, given by

In our case m =400, and N is the total number of amino acids that concatenate to our strand in 10
10 years per millisecond. Thus by Boole’s Inequality,

    Now the probability of the event Ak is the number of outcomes of event Ak divided by the total number of outcomes. The total number of outcomes for any chain of 400 amino acids with an equal number of 20 of each desired amino acid is 20N and the number of outcomes that produce event Ak is 20N-400. The exponent N-400 is because there are 400 positions specified in Ak. The remaining N-400 are arbitrary. Now suppose both the sequence of amino acids and left-handedness are selected by "chance." What is the probability of forming a single protein, 400 amino acids long, that is:

And so

Since N >> m. Thus P[A] is bounded above by N
÷10635, where N is the number of trials produced by a single set of 400 amino acids. This is the probability bound for one set of a 400 amino acid chine.

    To create a large number of trials, let's assume that every molecule in all the oceans on earth is an amino acid equally divided among the 39 forms. Assume that these amino acids link up in sets of 400 every millisecond for 10 billion years, we can think of forming one long sequence by concatenating all the sequences of all the sets of 400 in all the oceans so that N becomes the number of trials produced by all the sets in all the oceans.

Hence P[A] , on earth is bounded above by:

    Therefore any attempt to build a probabilistic model for protein formation, based on independent concatenation of amino acids, would assign probability zero to this event and discard independent trials as a plausible mechanism. “Chance” is not a reasonable mechanism to form a single average length protein, much less all the other proteins, DNA, RNA, and membrane molecules needed to produce a living cell.
    Some may argue that the entire 400-acid-long protein need not form in one simultaneous connection of 400 amino acids. Rather, the formation might occur with smaller units hooked up and then coming together in several steps. If the events of the amino acids coming together were independent, then it makes no difference how they are formed-whether in small chains or in one connection of 400. The probability of formation is the same. [Richard A. Roberts, An Introduction to Applied Probability, Page 89, Example 3.5.3 Copyright © 1992 by Addison-Wesley Publishing Company, Inc.]

    It should be noted that most theories of Evolution are constrained by Random/Chemical mutation. Random/Chemical mutation is born by the accidental occurrences in the formation of a chain of amino acids necessary to form an exact copy of itself. These accidents may replace, add, or  remove  a particular amino acid from its intended location, thus creating a better, worse, or similar protein. Because of this, few plausible theories have been devised, allowing them to circumvent calculations similar to this calculation. This calculation is, in fact, very generous in allowing for an enormous amount of simultaneous trials.

    Some may argue that there are many variations of the same protein, thus increasing its chances. Let us assume that there are 10
100 different variations of the same 400-acid-long protein. Moreover let us assume that there are only left-handed amino acids to choose from in all the oceans along with the one which is neither left nor right-handed. We get:

and so


Using the same N as above we get:


    Suppose we now allow every atom in the entire universe to represent a pool of all 19 left-handed amino acids along with the one amino acid which is neither right-handed nor left-handed. Suppose also, that we allow all the same conditions as on the earth in our very first calculation. Moreover, suppose there are  10
100  variations of the same 400-acid-long protein. The number of trials N is:

Thus we get N = 10100


Some known accepted facts:
Known Age of the universe is about 10 billion years.
Known Age of our solar system is about  4.6 billion years.
Our Sun has 5 billion years of energy before it burns out.
The Electron mass is 9.11*10
The Proton mass is 1.67*10
Mass of the sun is 99% of solar system = 2*10
Mass of some of the largest stars are 100 times our sun.
Mass of some of the smallest stars are 1/20
th times the mass of our sun.
There are about  100 billion stars in the Milky Way galaxy.
There are about 100 billion galaxies in the observable universe.
The matter in the Universe is made up of about 75% Hydrogen and about 24% Helium.

    Now that we have exhausted all possible time and all possible elements in the entire universe and replaced them with only left-handed amino acids and allowed for an enormous number of variations, let us look at the probability of the chance formation of n=1,2,3,... 400-acid-long proteins. The new formation of multiple proteins is analogous to a fair coin toss of  n multiple coins simultaneously tossed.  This is because, just as each coin is independent of the other, so too is the chance formation of each protein independent from any other, whether on one planet or on multiple planets. Because of  independence, the probabilities multiply as follows:

    There are about 2,000 proteins serving as enzymes for a cell’s activity and we shall assume that all 2,000 proteins are a length of about 400  amino acids. The probability of getting all 2,000 400-acid long proteins would be approximately :



    The reader may wonder what random/chemical mutation has to do with this calculation. Many people conclude that we are clearly decedents of ape's and/or monkeys. If this is so, then one can conclude that monkeys are decedents of small mammals such as rats. One can then conclude that rats are decedents of fish, which are decedents of worms, which are descendants of amebas, which are decedents of bacteria, which are decedents of self-replicating proteins.

    What are self-replicating proteins?  These are small acid-long proteins, supposedly able to reproduce themselves with the use of other material necessary for life. Self-replicating proteins are small enough to allow for probabilities large enough to merit a chance existence (perhaps a 20-30 acid long chain might make one??), given the age of the universe, and all other necessary conditions. However, random/chemical mutation is the accepted means by which anything alive, including self-replicating life improves. If this is so then the probabilities given above are completely valid, all the way up the evolutionary ladder. 

    Another interesting paradox is the right-handed Vs left-handed amino acid issue. Left-handed amino acids (the mirror image of Right-handed acids) are what make up all proteins known to man. One must ask the following question: Where are the right handed amino acid proteins? If there is, supposedly, a large probability for left-handed proteins to occur, then there's an equally large probability for right-handed acid life.      


Some interesting Quotes from the experts:

Francis Crick:

Carl Sagan:

The World Book Encyclopedia


Paleontologist Steven Stanley:

Robert Jastrow:

John Gliedman:

British zoologist Colin Patterson:

Encyclopedia Americana:

Poe Koller:

Encyclopedia Britannica

G. Ledyard Stebbins:

Isaac Asimov:

Richard Goldschmidt:

On Call (English medical journal):

Science magazine:

Molecules to Living Cells:

Symbiosis in Cell Evolution:

Scientific American:

C. H. Waddington:

Professor John Moore:

Fred Hoyle and Chandra Wickramasinghe:

Evolutionist Loren Eiseley:

Biologist Joseph Henry Woodger:

Physicist H. S. Lipson:

Mathematician Blaise Pascal