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HURDLE NUMBER 29. THE INSUFICIENT MUTATIONS HURDLE.
WARNING! The material in this hurdle is of a slightly technical and mathematical nature, and requires basic numeracy. In that case, the “faint hearted” may wish to skip this hurdle, and go straight to HURDLE 30.
The total number of single separate point mutations (in germ cells) in the whole of Earth’s history would be absolutely insufficient to “find” by random search the correct configuration (of amino acids) for even one single (average sized) protein. Proteins are very highly specific in their structure. However, even if this were not so and there were a million possible amino acid configurations that would carry out the specific function of some one particular protein, there still would not be enough mutations in Earth’s history to create this single specific protein function. There is an INSUFFICIENT NUMBER OF MUTATIONS in Earth’s history to account for biological life forms. The following will (as I hope) convince the reader that the above statement is correct:-
Here is a quote from the paper Natural Selection And The Complexity of The Gene, by Frank B. Salisbury (of The Plant Sciences Department, Utah State University), published in (The Journal) Nature, volume 224, issue for October 25th, 1969, pages 342 to 343:-
“If life really depends on each gene being as unique as it appears to be, then it is too unique to come into being by chance mutation. - - - - - It is possible to ask the following question. In reasonable time intervals is mutation by random rearrangement of nucleotides likely to produce an enzyme - - - - - (?) - - - - - - - THE MUTATIONAL MECHANISM as presently imagined COULD FALL SHORT BY HUNDREDS OF ORDERS OF MAGNITUDE OF PRODUCING IN A MERE FOUR BILLION YEARS EVEN A SINGLE REQUIRED GENE.” (My capitals and highlighting.)
My comment:- Unfortunately he is right! I will now provide a simple mathematical demonstration of this fact:-
Neo-Darwinism tells us that all biological life-forms have come into being by a series of random mutations. However, THERE HAVE NOT BEEN ENOUGH SINGLE SEPARATE POINT MUTATIONS IN THE WHOLE OF EARTH’S HISTORY TO PRODUCE EVEN ONE AVERAGE SIZED PROTEIN. An average sized protein contains a chain of 200 amino acids in a very precise and specific sequence. DNA “codes” for proteins. You would need a length of DNA 600 nucleotides long (again in a very precise and specific sequence) to “code” for a particular specific protein 200 amino acids long. The number of possible permutations (ie:- possible ways of positioning) of 600 nucleotides is 10360 (ie:- 1 followed by 360 zeros. (I will explain all these above figures later in this article.)
The problem is that the maximum possible number of single separate point mutations that could have occurred during the whole of Earth’s history is only 1054
(ie:- 1 followed by 54 zeros). (I will explain how this figure is arrived at later in this article.)
In that case, the probability that all the mutations in Earth’s history could by a “random search process” “find” even one of the (supposedly) 100,000 different proteins in the human body is
ONE CHANCE IN (10360 ÷ 1054) which is equal to
ONE CHANCE IN (10360 – 54) which is equal to
ONE CHANCE IN 10306
ie:- 1 followed by 306 zeros!
In that case, the statistical odds against random mutations successfully “finding” any single specific protein are
ONE CHANCE IN 10306
ie:- 1 followed by 306 zeros!
The statistical odds against random mutations “finding” ALL of the (supposedly) 100,000 proteins in the human body are ONE CHANCE IN 1 followed by an absolutely enormous number of zeros! In other words, it cannot happen!
(I will further clarify these above calculations further on in this article.)
These are apparently impossible odds, making it clear that biological life-forms cannot have come about simply by a process of random mutations. The problem is that, according to The Neo-Darwinian Hypothesis, random mutation is the ONLY possible way for evolution to proceed. To substantiate this, let me provide a quote from C.H. Waddington (Professor of Animal Genetics at Edinburgh University) (This quote is taken from the book Scientific Creationism by Henry M. Morris Ph.D. published by Master Books, 21st printing, 1998, page 55.)
(Quoting C.H. Waddington) “We know of no way other than random mutations by which new hereditary variation comes into being.”
OBJECTIONS TO THE ABOVE ARGUMENT.
Let’s consider some possible objections to the above argument.
FIRST OBJECTION. “OPTIONAL” AMINO ACIDS:- For a particular protein with a specific function, many of the amino acids might be “optional”, so that exchanging (for example) the 27th amino acid in the “chain” for some different amino acid will not alter the function of the protein. In that case, the “random search process” is fairly unrestricted in its possible “goals”.
REBUTTAL TO THE FIRST OBJECTION:- Here is a quote from the book – Molecular Biology of The Cell by Alberts, Bray, Lewis, Raff, Roberts, and James D. Watson (co-discoverer of DNA structure), published by Garland Publishing Inc, NY and London, 1994, page 119.
“For a typical protein length of about 300 amino acids, more than 10390 different proteins can be made (ie:- 20300). We know, however, that only a very small fraction of these possible proteins would adopt a stable 3-dimensional conformation. The vast majority would have many different (possible) conformations - - - - - - - - Proteins with such variable properties would not be useful - - - - - - Present day proteins have - - - - - unique folding properties - - - - - a single conformation is extremely stable - - - - - has the precise chemical properties - - - - - to perform a specific catalytic or structural function in the cell. Proteins are so precisely built that the change of - - - - one amino acid can sometimes disrupt the structure and cause a catastrophic change in function”.
Here is another quote in a similar vein:- This quote is from the book What Darwin Got Wrong, by Jerry Fodor (He held the position of State of New Jersey of Professor of Philosophy, Emeritus, at Rutgers University.) and Massimo Piattelli-Palmarini (Professor of Cognitive Science at The University of Arizona), published by Profile Books, 2010, page 35:-
“The three-dimensional spatial configuration of each protein determines its biological function, AND HAS TO BE ATTAINED QUITE EXACTLY, OR ELSE- - - - - -” (My Capitals.)
I can provide many similar quotes from authoritative sources. The above quote quashes the “optional amino acids” objection. Most biological proteins have to be exactly the way they are, and their configurations are not “optional”.
There are two further possible objections which I will deal with later in this article: but first, I will clarify the figures presented above:-
In the book Life Itself by Francis Crick (co-discoverer of the structure of DNA, and Research Professor at The Salk Institute in San Diego), published by Futura, 1982, page 51 – Crick states “Suppose the chain (of amino acids in a protein) is 200 amino acids long. This if anything is rather less than the average protein of all types.”
Now if we take this (less-than-average-sized) protein of 200 amino acids, the DNA (chain) required to code for it must be 200 x 3 = 600 nucleotide bases long. The reason for this is that the genetic code involves “triplets” (or “codons”), ie:- groups of THREE nucleotide bases to code for one single amino acid. DNA contains only FOUR types of nucleotide base. In that case, the number of possible permutations of a length of DNA 600 nucleotide bases long is 4600, ie:- 10360 (ie:- 1 followed by 360 zeros.
Now I will explain how I arrived at the maximum possible figure of 1054 mutations in the whole history of The Earth.
(A). There are 1030 organisms on The Earth.
(B). A human has in each germ cell 6 x 109 nucleotide bases.
(C). A bacterium replicates some 50 times per day.
(D). The number of days in a year is 365
(E). The age of The Earth is 4550 x 106 years.
1030 x 6 x 109 x 50 x 365 x 4550 x 106 = 1054
Now I will provide references for the above figures A to E:-
(A). In the book The Copernicus Complex by Caleb Scharf (Director of The Astrobiology Centre at Columbia University), published by Allen Lane, 2014, page 127, Scharf states – “Our current estimates are that The Planet Earth harbors in excess of a million trillion trillion (1030) single celled organisms.” (Note:- My own calculations suggest that, if anything, this is an OVERestimate, which I will shortly demonstrate.)
(B). In the book – Genetic Entropy and the Mystery of The Genome (Classroom Edition), by Doctor J.C.Sanford (Cornell University Professor – Ph.D in plant genetics) Third edition, Published by FMS Publications, 2008, on page 69, Doctor Sanford tells us – “There are 3 billion nucleotide positions, each with 2 copies in the genome, and so there are 6 billion possible point mutations.”
A billion is a thousand million – so there are 6,000,000,000 possible point mutations (ie:- 6 x 109) for each organism.
(C). In the book – Undeniable. How Biology Confirms Our Intuition That Life is Designed by Douglas Axe Ph.D (who held a position of Research Scientist at Cambridge University), Axe tells us on page 105 that “Bacteria - - - - - can reproduce within half an hour of their birth”
(My comment:- This means that bacteria can replicate themselves approximately 50 times per day.)
I can provide many similar quotes from authoritative sources.
(D). It is well known that there are 365 days in a year.
(E). According to the Planetary Scientist’s Companion, by K. Lodders and Bruce Fegley (Professor of Planetary Sciences at Washington University, St Louis, Missouri), Published by Oxford University Press, 1998, page 132 (Table 6.7 Geologic Time Scale), the age of The Earth is 4550 million years, ie:- 4550 x 106 years.
(A).1030 x (B). 6 x 109 x (C). 50 x (D). 365 x (E). 4550 x 106 = 1054
THE PROBABILITY THEORY.
I will now clarify the probability theory:- If there are 1054
mutations, and they are required to “hit” a “target” of one particular specific arrangement of nucleotide bases out of a possible 10360 arrangements of these nucleotide bases, then the probability of success is
ONE CHANCE IN (10360 ÷ 1054) which is equal to
ONE CHANCE IN (10360 – 54) which is equal to
ONE CHANCE IN 10306
To clarify this, imagine a chess board of 64 squares. If you throw a dart blindfold, the odds against hitting a particular specific target square are 1 chance in 64. If you throw FOUR darts, the odds against hitting a particular specific target square are 1 chance in 16.38 – These odds are calculated by a complicated use of binomial probability theory. An alternative method – the simple method – is as follows:-
The odds are 1 chance in 1 ÷ (4 ÷ 64) = 16.
I chance in 16 instead of 1 chance in 16.38
Using this method give odds that are very slightly SHORTER than the ACTUAL odds. In other words, the “simple” method slightly UNDERestimates just how improbable a successful outcome really is.
Now imagine that the chessboard, instead of having 64 squares, has 10360 squares. Each square represents one of the possible permutations (ie:- arrangements) of nucleotide bases in a length of DNA that is 600 nucleotide bases long. Now imagine that you throw 1054
darts blindfold at this “chess board”. Each dart represents one mutation of a single nucleotide base. There is just one specific square on this vast “chess board” that represents the precise configuration of nucleotide bases in the DNA sequence that will “code” for a specific “target” protein (ie:- a protein containing a specific and precise arrangement of amino acids enabling a specific and precise function of the protein). What are the odds against hitting this particular square? The odds are:-
ONE CHANCE IN (10360 ÷ 1054) which is equal to
ONE CHANCE IN (10360 – 54) which is equal to
ONE CHANCE IN 10306
THE NUMBER OF BACTERIA ON THE EARTH.
There is still one slight question mark. Is Caleb Scharf’s estimate of 1030 bacteria on The Earth correct? Here are my own calculations:-
Quoting from the book – Brock Biology of Microorganisms by M.T.Madigan (Professor of Microbiology at Southern Illinois University) et al, published by Prentice Hall, 9th edition, 2000, page 4, caption to Figure 1.2
“Photomicrograph of rod-shaped bacterial cell - - - - a single cell is about 1 µm in diameter”
According to The New Penguin Dictionary of Science, ed M.J. Clugston, published by Penguin Books, 1998, page 832, the symbol µ stands for “micro”. On page 499 of this book we are told that the term “micro” (symbol µ) means one millionth of a base unit, eg:- 1 µg is one millionth of a gram. On this basis, 1 µm is one millionth of a meter.
If the average bacterium is one millionth of a meter in diameter, then, if the bacteria were packed very tightly together, there would be in one cubic meter a million x a million x a million, ie:- 1 x 1018 bacteria.
According to the Planetary Scientist’s Companion, by K. Lodders and Bruce Fegley (Professor of Planetary Sciences at Washington University, St Louis, Missouri), Published by Oxford University Press, 1998, page 87 (Table 2.4 the radius of The Earth is 6371.01 km.
One km is 1000 meters.
The surface area of a sphere is 4πr2.
ie:- 4 x π x (6371.01 x 1000)2
= 5 x 1014 square meters.
Suppose that the bacteria are not merely on the surface, but exist up to 10 km depth, ie:- 100,000 meters deep.
In that case, the volume of bacterial material will be 5 x 1014 x 100,000 = 519 cubic meters of bacteria.
The number of bacteria in this volume (ie:- on The Earth) will be
(1 x 1018) x 5 19 = (approximately) 2 x 1031
These above calculations assume that all the bacteria on The Earth would be packed together “shoulder to shoulder”. In fact, there would be areas of low bacterial density. In that case, the above result is an OVERestimate of the number of bacteria on The Earth.
FURTHER PROBABILITY THEORY ISSUES.
If you have a chess board of 64 squares, and you throw 3 darts at it blindfold, the odds against hitting one particular specific square on that chess board are calculated in the following manner:-
The number of darts = the number of trials = n = 3.
The number of (required) successful outcomes = r = 1.
The probability that any single specific trial will result in a successful outcome = p = (1 ÷ 64) = 0.015625
The probability that any single specific trial will result in an unsuccessful outcome = q = 1 – p = 1 – 0.015625 = 0.984375
Using these above four parameters, n, r, p, and q, we employ the following formula:-
p(r ≥ 1) = 3C1 x 0.9843752 x 0.0156251 = 0.0454187
+ 3C2 x 0.9843751 x 0.0156252 = 0.00072098 + 3C3 x 0.9843750 x 0.0156253 = 0.0000038
Sum = 0.046143
If 0.046143 is the probability, then the odds against chance occurrence is the reciprocal of this value, ie:- (1 ÷ 0.046143) = odds of 1 chance in 21.67
The “simple” formula for this calculation is simply 3 ÷ 64 = 0.046875, ie:- odds against chance occurrence of 1 chance in (1 ÷ 0.046875) = odds of 1 chance in 21.33
Using the “simple formula” always gives odd against chance occurrence that are a slight UNDERestimate. The “simple” formula always underestimates just how really improbable an event really is.
OBJECTIONS TO THE ABOVE ARGUMENT.
Let’s consider a further possible objection to the above argument.
SECOND OBJECTION. MULTIPLE TARGETS.
Suppose there were many possible amino acid sequences that would perform the same function as our “target” sequence. In that case, you are using a random search process to “find” – not just one – but perhaps 100, or 1000, or even 1,000,000 “target sequences”. “Hitting” any one of these “target sequences” would provide a protein that performed the same required function.
My retort to the above objection:-
Even if there were 1,000,000 amino acid sequences that could perform this same specific function, this would not appreciably decrease the astronomically long odds against “hitting” a protein that has this specific function. Let me demonstrate this.
Imagine a chess board with 64 squares, of which not just one square BUT FOUR SQUARES count as a successful “hit” with a dart (thrown blindfold). Here is a depiction of the chessboard:-
The darkened squares represent the four squares that count as “success” for a dart strike (although these “success” squares can be located ANYWHERE on the “chess board”. They are only grouped together to make a point.).
You have effectively created a new chess board that has SIXTEEN squares rather than SIXTY FOUR squares. The new chess board that you have created looks like this:-
The new chess board that you have created now has only sixteen squares, and the original FOUR “success” squares are now ONE SINGLE “success” square.
If you throw three darts blindfold, the probability of a successful “hit” (ie:- hitting the shaded square) is 3 ÷ 16 = 0.1875 – ie:- odds against chance occurrence of one chance in (1 ÷ 0.1875) = 1 chance in 5.333
(Note:- the “real” odds are actually one chance in 5.68, so the “simple” formula slightly UNDERestimates how improbable a successful “hit” actually is.)
Now suppose that a MILLION amino acid sequences could perform the same specific function as the “target” amino acid sequence. In that case, you have now created a new “chessboard”. You started off with a “chess board” that had 10360 squares, and you threw 1054 “darts”.
Your new “chess board” now has only
(10360 ÷ 1,000,000) squares.
Which is equal to 10360 – 6 = 10354 squares.
And you still have only 1054 “darts”.
Your odds against a success are still astronomically long, ie:- one chance in (10354 ÷ 1054)
which is equal to 10354 – 54 = 10300
You can suppose (if you like) suppose that a BILLION BILLION amino acid sequences could perform the same specific function as the “target” amino acid sequence. In that case, your “chess board” has
10360 – 18 = 10342 squares, and still only 1054 “darts”.
In that case, your odds against getting a successful “hit” are one chance
in (10342 ÷ 1054)
which is equal to 10324 – 54 = 10288
Also we need to bear in mind that the human body contains approximately 100,000 different proteins. To substantiate this statement, here is a quote from the book – Genetic Entropy and the Mystery of The Genome (Classroom Edition), by Doctor J.C.Sanford (Cornell University Professor – Ph.D in plant genetics) Third edition, Published by FMS Publications, 2008, On page 2, Doctor Sanford tells us that there are “roughly 100,000 different human proteins”
Here is a further quote from the book Biochemistry For Dummies by J.T. Moore (Master’s Degree in Chemistry) and Richard Laughley, Ph.D. (Bachelor’s Degree in Chemistry), published by Wiley, 2008, page 77.
“There are thousands of different proteins in each cell.”
If all the possible mutations in Earth’s history cannot “find” by random search even just ONE specific protein that has a specific function, then “finding” several thousand “target” proteins is even more impossible.
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