Chapter 10

Could Chance Arrange the Code for One Gene?

At the present time, there is no satisfactory hypothesis to explain the evolution of the protein-synthesizing mechanism.¹

—from Biology and the Future of Man (1970)

The DNA System Excites Admiration

The main job done by DNA is to give the instructions for synthesizing proteins.  In the preceding chapter, we saw that the mechanism by which these instructions are carried out is in some ways even more astounding than the code itself.
    Almost two hundred of America’s best biologists cooperated in writing the outstanding volume quoted at top of this page.  Their purpose was to give a complete account of the status of knowledge in the entire field up to the time of writing, and to point out areas where more research was most needed.
    The wonderment and admiration of scientists for the DNA system is frequently expressed in that book.  “Although we can see the basic design in the process, a chemical understanding of certain remarkable features has thus far eluded us.”²  They praise “the high fidelity we know exists in the overall process.”³  Considering the system, it is natural to agree with a sentiment expressed by missile expert Wernher von Braun.  He said he found it as difficult “to understand a scientist who does

not accept the presence of a superior rationality behind the existence of the universe as it is to comprehend a theologian who would deny the advances of science.”⁴
    It is strangely true that a number of scientists and many other people do try to explain everything without reference to any intellect back of what exists.  Without a Designer, however, the materialist is left with only one source, namely chance, to do it all.
    In spite of desperate attempts by some to introduce natural selection long before actual life existed, it has become quite evident that such a control was utterly impossible without an accurate duplication system for all the essential parts.

The Only Duplication System

    There has been no indication found of any system for such duplication other than the precise DNA-mRNA-ribosome-enzymes-tRNA-twenty amino acid plan described in the preceding chapter.  For this reason, Morowitz postulates it as part of the minimal theoretical living entity.⁵  Could such a system come about by random association of molecules?
    The all-important central component would have to be DNA (or possibly RNA) with a coded message.  The message would give instructions for making the necessary parts for the living system, including the enzymes that govern the duplication of the code molecule itself.⁶

    In addition to the coded message, there would have to exist at the start the minimum machinery to produce what the code specified.  One or more copies of each component of the system would have to exist, or else the code message would be absolutely powerless to get life moving.  Among those items required at the beginning would be ribosomes, amino acids, RNA polymerase, ATP for energy, and all the other enzymes and vital factors recently discovered that are necessary for any protein production whatever.
    Let’s now apply the laws of chance to just one facet of the operation—the probability that code letters might ever become arranged in any usable order fortuitously (if, of course, code letters were already existing).  In other words, could chance conceivably account for a correct sequence for just one set of genes for minimal life, or even for a single gene?  Any arrangement at the start would have been random, if creative design is ruled out.  First, we need to understand exactly what a gene is.

A Gene Is a “Paragraph” of the DNA Message

We have seen that DNA carries the instructions of heredity in the form of bases or letters strung along the middle of a double spiral molecule.  This message can be thought of as divided into sections or paragraphs which are called genes.  Usually, a single gene will code for a single protein chain.  The average gene in the smallest theoretical living thing would have over 1,200 letters or nucleotide pairs.⁷
    A gene may contain from a few hundred to a few thousand base pairs or nucleotide pairs.  The smallest known cell has about 600 genes.⁸  A set of human chromosomes, containing the

cell’s DNA, consists of over two million genes.⁹  If a chain could link up, what is the probability that the code letters might by chance be in some order which would be a usable gene, usable somewhere—anywhere—in some potentially living thing?

Using All the Atoms in the Universe

    From the calculations in previous chapters, it could be guessed that to obtain a gene would be at least as difficult as to obtain a protein molecule.  Instead of using all the atoms on earth, therefore, this time let us assume that all the atoms of the entire cosmos have been made into sets of nucleotides, and that these are activated, ready for linkup.  (Nucleotides are made of atoms of carbon, nitrogen, hydrogen, oxygen, and phosphorus.)
    It will be presumed that each chain will polymerize or link up at the swiftest speed of atomic processes (of which the limit is said to be around 10¹⁶ per second as noted earlier).¹⁰  With each nucleotide being added at such a speed, the number of complete chains (genes) per second is 8.3 x 10¹² in any one set.  In a year, a set of nucleotides would produce 2.6 x 10²⁰ genes, which we will round off to 10²¹.
    Chance is trying for the first gene in the universe, so there is no pattern strand of DNA or RNA existing.  The four different nucleotides will occur only in random order in the chain.  If just one side of the ladder or double helix is obtained, it will be considered sufficient, in the thought that if one is obtained, the other side might form by base pairing.
    From standard estimates of the cosmic abundance of the elements,¹¹ it can be found that phosphorus is the limiting element in forming activated nucleotides.  There are estimated to be 1.5 x 10⁷² phosphorus atoms in the universe.¹²  Three atoms of phosphorus are needed for each activated nucleotide.  This

will make 10⁶⁸ sets, so that one copy of each of the four kinds of nucleotides is present at each point of the 1,200-unit chain being formed.
    If each set is producing 10²¹ sequences per year, that will be a total of 10⁸⁹ different chains annually, using all of the appropriate atoms of the universe.  As in the case of proteins, it is assumed that each chain will be dismantled immediately and another one built until there is a usable gene.  This is done at the prodigious speed of eight trillion chains per second.¹³

The Number of Possible Orders in a Gene

    There are three different ways to determine the number of possible sequences in a DNA chain.  The general formula, it may be recalled, is: the number of kinds to the power of the number of units in the chain.  If each order is equally likely, the probability of a particular sequence will then be one in the total of possible orders.
    With four kinds of nucleotides, and a chain 1,200 long, the total of possible arrangements would be 4¹²⁰⁰, which is approximately 10⁷²².  The letters of a gene, however, are read in triplet codons (comprising sixty-four kinds of triplets) of which there are 400 in this size chain.  If computed in this way, there would be a total of 64⁴⁰⁰ possible orders, and this turns out to be the same as when figured by individual letters, namely 10⁷²².
    The reader may recall, however, that many of the twenty amino acids are coded by more than one triplet.  The duplicate codons are thought by some to be “a historical accident,” Others believe they may be “perhaps a regulatory factor in some cases,”¹⁴ since nature is “seldom redundant” for very long.¹⁵  As mentioned in the preceding chapter, evidence is accumulating that these seeming duplicates may serve the vital purpose of regulating¹⁶

the synthesis of proteins.  If that turns out to be true, then there would be no useless duplicates among the 64 codons,¹⁷ and the total real sequences would be the 10⁷²² figure.
    Since research is not yet final on that point, however, let’s again give chance the benefit of the doubt and figure it as if all the duplicates were useless extras.
    There are only twenty-one different possible primary outcomes for each codon position.  Those potential outcomes which are signalled by codons are the twenty amino acids plus “end of chain.”  We will therefore figure on the basis of twenty-one kinds, for a chain 400 amino acids long.  The figure 21⁴⁰⁰ is approximately 10⁵²⁸.  If we allow one substitution per chain¹⁸ (without limiting it to the active site—another boost for chance), then the equivalent total of different sequences is 10⁵²⁴.

Chances of One Gene in the Entire Universe

    Using again the formula obtained from the alphabet analogy, it can be assumed that 1/10²⁴⁰ is the proportion of orders that might be usable somewhere.  Since 10²⁴⁰ is less than 10⁵²⁴, the probability of getting a usable gene on any one try is 1/10²⁴⁰ for the first gene.  Allowing for one substitution has the effect of reducing the figure to 1/10²³⁶.
    The total orders produced in a year by all the nucleotide sets from the entire cosmos was 10⁸⁹, as seen on page 159.  The probability of getting a usable gene in a year is therefore 10⁸⁹/10²³⁶, which is 1/10¹⁴⁷.  With all the concessions given, one could expect a usable gene in 10¹⁴⁷ years, from the tremendously rapid efforts of all the nucleotide sets of all the atoms of the universe.
    Professor Warren Weaver in his book on probability states the rule we are using in these words: “If two events are independent, the probability that they both will occur is the product of their respective probabilities.”¹⁹  This is that same central principle, the multiplication rule.  By “independent” is meant

that they do not interfere with each other.  In nucleotide linkups, apparently there is equal probability and no interference.
    In this model experiment, the entire chain is formed by the random action at each position in sequence independently.  The rule therefore is to multiply the probabilities of all the positions.  In this way, one obtains the “product of their respective probabilities.”  This is the method we have used.

How Long Is 10¹⁴⁷ Years?

Dr. Weaver told this interesting story which may be used for comparison with our time of “once in 10¹⁴⁷ years”:

In the lore of India there is a tale about a stone, a cubic mile in size, a million times harder than a diamond.  Every million years a holy man visits the stone to give it the lightest possible touch. . . .  Removing one [atom] every 10⁶ years then indicates that 10⁵¹ years would perhaps be required.²⁰

Random Occurrences Governed by Rules

    Irving Adler in his book Probability and Statistics said, ”Random occurrences, like fully determined events, are governed by certain rules.”²¹  Those carefully researched rules, which are depended upon so widely in science and industry today, are the ones being followed in our calculations.  The results should be as trustworthy as the Golden Gate Bridge or the Eiffel Tower, both built in dependence on the principles of probability theory.  (In such construction, not every piece of steel and not every rivet is tested, nor is every act by every workman.  By the use of sampling tests, however, the probability is calculated that

any particular component would be defective or inadequate as to allowable limits of stress.  By the multiplication rule, the chance of failure of, say, two components which augment each other can be known.  The overall probability of the structure can likewise be calculated as to stability.)
    Our “margin of safety” is exceedingly greater than engineers ever would consider necessary for complete assurance.²²

The Fallacy That Time Can Produce the Extremely Improbable

    Those intent on getting life from nonlife sometimes put their hope in life forming on distant worlds by chance, throughout the vast galaxies of the universe during several billions of years.  Surely in all that time and all that amount of matter, they suppose life would happen many times.
    French paleontologist André de Cayeux quoted a Russian scientist, Kostitzin, as saying that in the totality of the universe, “the development of an improbable condition is not impossible, and the nondevelopment of such a condition is not very probable.”²³  Another example of this sort of assumption is expressed in noted medical researcher George Wald’s epic article ”The Origin of Life” when he wrote:

The important point is that since the origin of life belongs in the category of at-least-once phenomena, time is on its side.

However improbable we regard this event, or any of the steps which it involves, given enough time it will almost certainly happen at least once. . . .
    Time is in fact the hero of the plot.  The time with which we have to deal is of the order of two billion years.  What we regard as impossible on the basis of human experience is meaningless here.  Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain.  One has only to wait: time itself performs the miracles.²⁴

    When one looks at it mathematically, he might suspect that Dr. Wald, like Kostitzin, just didn’t get around to extensive calculating on this problem.  Also, we should remember, knowledge about the DNA system (and proteins) was quite limited at the time he wrote, compared to the present.  Note that he referred to a time of about 2 x 10⁹ years, in which he supposed that the entire present milieu of living things evolved from nonliving chemicals.

    By contrast, compare the figure arrived at by calculations in the preceding pages, namely, 1 chance in 10¹⁴⁷ years of trials under conditions that were so extremely advantageous to chance.  One chance of what?  Getting just ONE usable gene.  It takes, however, a minimum of at least 124 genes to code for the different kinds of proteins for Morowitz’ minimal living entity described earlier.  With all 124 genes required, it will never be a case, then, of merely obtaining a complex molecule “at least once.”

    It would be discouraging to wait those 10¹⁴⁷ years for one gene, since 10¹⁴⁷ is a thousand billion billion. . . (till the word billion is used sixteen times).  Even if it could happen “just once,” we would not be out of the woods at all.  It would be just one of the many complex parts that must all be in position before the smallest living thing could live.  To get the probability of all of these parts, the chances of each one would have to be computed together.

Wasting “Cerebral Horsepower”

Trying to get complex order out of random arrangements is

to waste time.  Sooner or later, logic calls reasonable minds to realize that there are here too many virtual impossibilities.  Dr. Joseph L. Henson, biologist, says that to believe in evolution, one has to have “faith to believe that the statistically improbable is going to happen again and again and again.”²⁵  When the statistically improbable is as improbable as 1/10²³⁶ for just the first gene,²⁶ consider what kind of unfounded faith would be required!
    Kenneth K. Landes, in an article entitled “Illogical Geology” in Geotimes, used an interesting phraseology on another subject which might correctly be appropriated here.  He spoke of “the cerebral horsepower now being wasted on futile attempts to explain away the truth. . . . ”²⁷
    Surely it is wasted intellectual effort to try to coax chance into producing precise and intricate order.²⁸

Slowing the Ameba to One Angstrom Unit in Fifteen Billion Years!

How long is this time that it will take for one gene to occur by chance, on the average?  With a probability of once in 10¹⁴⁷ years, the ameba described in an earlier chapter could transport many complete universes the entire distance of the diameter of the cosmos while chance is still working on one random gene that will be usable.
    It is interesting to contemplate the slowest speeds our minds can grasp.  The diameter of a hydrogen atom is about one Angstrom unit.  Suppose our ameba from chapter 7 has travelled only that distance since the universe began, using the assumed fifteen-billion-year figure again.  If the tiny traveller continues to move at that snail’s pace of all snail’s paces, it will take 3,810,000,000,000,000,000 years to span the distance of ONE INCH!
    Traveling that slowly, the ameba would complete the task

of carrying the entire universe across in about 4 x 10¹²⁵ years.  In this leisurely fashion, the little space crawler would have time to convey 2 x 10²¹ complete universes, one atom at a time, all the way across the thirty billion light years of the assumed diameter of the cosmos, during the time that chance could be expected to arrange one gene in any usable order, trying at the unbelievable speed noted earlier, using all the atoms in the universe!
    If all the people living on earth—men, women, and children of all ages—were put to work counting rapidly day and night, it would take them five thousand years just to count the number of complete universes that this ameba could transport during the average time that chance could produce one lonesome gene!  Remember that chance was using all the atoms in the universe in this test.

The Second Gene Would Take Interminably Longer

As with proteins, if the first gene was on hand, all the others for a minimum set would have to match, like the parts of a particular kind of watch.  The second gene, therefore, would be much harder to get than the first, because it would have to match.  After obtaining the first gene, the aim would then be to get anyone of the other 123 genes needed to complete the set.  For that second gene, this would mean that we would have to overcome odds of 10⁵²⁴ to 123.
    Even if the most fantastic advantages were given to chance, the situation would still be hopeless.  Suppose, for example, that it is allowed that for each gene, as many different sequences would be acceptable as there are atoms in the universe.  With such an extreme concession, the ameba could still transport more than 10⁵⁷⁸⁰⁰ complete universes across that thirty-billion-light-year distance, traveling at the rate of one Angstrom unit in fifteen billion years, during the time that chance could be expected to get the sequence in correct order for a minimum set of genes for the smallest theoretical living thing.
    Just to print the figure for the number of those universes carried by the ameba would require around twenty-eight pages.
    Looking at it another way, let us suppose that substitution is freely allowed in nine-tenths of the loci or positions in the chain.  That is, such a tremendous degree of variation is permissible that in a chain of 400, only 40 need be correct and the others can be anything.  This would be a similar situation

whether one considers a protein chain, or a gene of 400 codons.  It is like an exam where all that matters is that you get 40 out of 400 right.
    With this extreme amount of variability, the odds against success in a chance arrival at a usable set of either genes or proteins are still fantastic.  This is true even at the speed postulated and using all the atoms of the universe in the attempt.  Let’s consider the length of time in which just one-half of the required set of genes (or of proteins) might occur by random alignment.  We will again measure that time by the number of complete universes the ameba can transport across the diameter of the universe one atom at a time at the unbelievably slow speed described a bit earlier.  That number of universes is so large that if all the atoms of the universe were people counting steadily, it would take them 5,000 years just to count those universes which the ameba could carry during the average waiting time for one-half of a minimum gene or protein set to align in usable sequence.
      The formula for probability with multiple substitutions allowed, just in case you happen to be curious, is:

The Single Law of Chance

Émile Borel, a distinguished French expert on probability, stated what he called “the single law of chance,” or merely “the law of chance,” in these words: “Events whose probability is extremely small never occur”²⁹  He calculated that probabilities smaller than 1/10¹⁵ were negligible on the terrestrial scale, and, he said:

    We may be led to set at 10^-50 the value of negligible probabilities on the cosmic scale.  When the probability of an event is below this limit, the opposite event may be expected to occur with certainty, whatever the number of occasions presenting themselves in the entire universe.³⁰

Logic Requires Belief in a Designer

    This old analogy is as reasonable now as ever: We intuitively know that a watch requires a watchmaker.  It has many parts that must be precision-adapted to match other parts that are useless alone.  Why would anyone attempt to circumvent this principle in science?  We will look into the reasons for this in the next chapter.
    The conflict is basically between chance, disorder, and chaos on the one hand, and God, order, and organization on the other.  Of him it is said that he “sustains the universe by his word of power.”³¹  Nothing else gives any adequate explanation of what we ourselves can observe.
    There is a type of evidence which may be far more convincing to an individual than the mathematical proof we have been considering, as weighty as we have found that to be.  It is the assurance which God has promised to all who will take him up on the following offer:
    He said, through Christ, “Whoever has the will to do the will

of God shall know whether my teaching comes from him. . . .”³²  Such a person will be given inner assurance that Christ was who he claimed to be: the Son of God by whom the worlds were made.³³