Chapter 6

Probability and the First Proteins

  Even the simplest of these substances [proteins] represent
extremely complex compounds, containing many thousands
of atoms of carbon, hydrogen, oxygen, and nitrogen ar-
ranged in absolutely definite patterns, which are specific
for each separate substance.  To the student of protein
structure the spontaneous formation of such an atomic
arrangement in the protein molecule would seem as im-
probable as would the accidental origin of the text of
Virgil’s “Aeneid” from scattered letter type.¹
– A. I. Oparin

THE QUESTION MAY have occurred to the reader: If evolution is so improbable, why do many scientists and other intelligent people accept it?  This naturally is a central issue, and chapter 11 will be devoted to it.
   It should be mentioned now, however, that even the most intelligent people may not get around to concentrating their intelligence on some specific issues.  It is customary to accept without question many conclusions that are supposed to be “common knowledge” among scientists.  No one has time to look into every subject.  It is easy for even a scientist to take for granted that certain principles or axioms have actually been proved.
   It is currently the conventional attitude among scientists never

to question the notion that Darwin really proved the main idea of evolution.  An avowed communist like Oparin can freely admit, as in the quotation above, that it is futile to expect chance to put together anything so highly ordered.  He resorts instead to his philosophy of dialectical materialism.
   “Rationally,” Oparin writes, “life can be materialistically comprehended only as a special form of the motion of matter, arising in a regular manner at a certain stage in the development of matter.”²
   For the noncommunist materialist, this makes a great difficulty.  Many evolutionists have followed Oparin’s careful step-by-step plan of evolving life from nonliving chemicals.  They see no reason, however, to accept his communist philosophy.  This leaves one in an intolerable position, as it turns out.  The customary procedure seems to be to hope that nobody will notice the predicament, and to glide cheerfully over the problem.
   The difficulty is that there is nothing left but chance to do the whole job of creating life from nonlife.  Even to consider the thought of an intelligent Creator is completely out of the question, “an idea which of course has been long exploded.”  As seen in the previous chapter, natural selection would have no way to come to the rescue at that stage, for lack of an accurate duplicating process.

Wrong Ideas About Probability

   Probability theory does not deal with absolutes.  It never says that a thing is “impossible” unless it is completely outside the realm of subjects which involve uncertainty.  Charles-Eugène Guye, who was the eminent Professor of Physics at the University of Geneva, delineated this truth (using the word “evolution” in the general sense of any process of change, rather than as we are defining it):

   The evolution of a phenomenon tends to take place according to the greatest probability, and it follows that physico-chemical laws are viewed as statistical laws, very exact it is true on account of the law of large numbers, but no longer possessing that character of absolute determination which it has been customary to attribute to them.³

educated person supposes that surely someone has investigated these commonly believed scientific dogmas carefully.  With the information now at hand, you will find it possible to check firsthand for yourself the probability of certain popularly held conclusions.

Some Proteins Described

   We now come to the exciting application of the laws of chance to this major question: What is the probability that a protein molecule might have been aligned by chance?
   All known life on the earth consists largely of these giant molecules.  “The chemical basis of all life,” says the Encyclopaedia Britannica, “is protein in a watery medium.” 
   To learn the secrets of the composition of such an entity as a protein molecule was no simple undertaking.  Biologists spent years in painstaking, patient study.  One of the first molecules to be mapped was insulin, which is the smallest molecule qualifying as a protein.  It has fifty-one amino acid “links,” in two chains – one with twenty-one and the other with thirty amino acids.  The two chains are joined together by “sulfur bridges.”
   A method was discovered whereby an X-ray beam could be projected through a crystallized protein molecule.  The individual atoms of the molecule scattered the beam as it passed through.  From the pattern of this diffraction or deflection, it was possible to figure out the position of the various atoms.
   John C. Kendrew completed mapping the myoglobin molecule in 1959.  Then, by 1967, Max Perutz and others at Cambridge succeeded in solving the structure of the hemoglobin molecule, the most important protein in blood.  Larger than myoglobin, it consists of four chains fastened together and folded in a complex pattern.  In all, hemoglobin has 574 amino acid links.  The molecule has 10,000 atoms!⁶
   Hemoglobin is just one of the multitudinous kinds of proteins.

The length of the average protein in the smallest known living thing is at least 400 amino acid links, containing more than 7,000 atoms.

Protein Links Must Be in Correct Order

   Most proteins include all of the usual twenty kinds of amino acids.  Each protein has a specific exact sequence of these units.⁷  Of the hemoglobin molecule, John C. Kendrew wrote (using British spelling):

   Thus, practically everyone reading this book contains identically the same kind of haemoglobin molecules in his or her blood, identical down to the last amino acid and the last atom.  Anyone having a different haemoglobin would be seriously ill or dead, because only the very slightest changes can be tolerated by the organism.⁸

are astronomical against random production of a set of usable proteins for minimal life.  There’s no way without design.
   We may assume from present experimental knowledge that many places in a protein chain might allow substitution.  It appears probable, however, that only about one such substitution may be tolerated in an entire chain.⁹  Moreover, any substitute may have to be similar to the one it replaces.¹⁰  There can be absolutely no substitution in positions in the chain which comprise what is known as the “active site.”  Any substitution

anywhere is likely to be harmful if not lethal.  All twenty of the amino acids are listed in Figure 3.
   The present goal will be to find the probability that amino acids might happen to be in the right order by chance if natural forces were able to line them up.  It will be considered a success if the resulting chain is any usable protein molecule.  Also to be determined are the odds that the amino acids might be aligned correctly for a group of 239 proteins needed for the minimal living entity described by Morowitz.¹¹
   Every effort will be made to avoid getting overtechnical, so that the nonbiologist reader may follow the calculations and know for himself that the outcome is sound.  That is important in the attainment of certainty.  Even if one finds the figuring itself uninteresting or difficult, it is helpful to his progress toward certainty just to know the evidence is there if he ever needs to dig into it further.  The next chapter will be easier to read.

   Before figuring for average size proteins, just for practice we may calculate the odds for the random alignment of the amino acid units for insulin, since insulin is usually considered the smallest protein, with 51 amino acids.  Even insulin, it turns out, is not as simple as it first appears.
   The insulin molecule is composed of two strands that must be linked together in an exact manner by sulfur bridges.  To bring this about, the cell first constructs a longer chain of more than 80 amino acids called proinsulin.  It ranges in length from around 81 to 86 in various animals.  We will consider an insulin molecule of length 84 amino acids (of which an example is the pig).  This extended sequence of 84 units causes the chain to fold and cross-bond correctly, and then a particular section of 33 units is cut out by special enzymes, leaving the final 51 amino acids in two chains properly oriented with cross links between them.
   Chance will therefore need to align 84 amino acids in correct order to form proinsulin, as the precursor for insulin.
   Since each of the 84 positions in the chain could be occupied by anyone of the 20 kinds, the total possible arrangements is 20⁸⁴, which, after conversion to base 10, is roughly 10¹⁰⁹.  The different arrangements are considered equally probable; so the probability of anyone molecule being in the correct order for insulin is 1 in 10¹⁰⁹.  Allowing for one substitution (to be tolerated) makes it a bit easier for chance, and brings the probability down to 1 in 10¹⁰⁶ approximately.¹²
   Going back to Dr. Eden’s statement that the total number of protein molecules that ever existed on earth might be 10⁵² as a liberal estimate, we will give chance another big boost by assuming that the 10⁵² are all different and are all the proper length for insulin.  We can now figure the probability that any one of those would by chance be in correct order for insulin. 
   Émile Borel, French mathematician, tells the rule for such cases: “If an event can occur in several different ways which are

mutually exclusive, its probability equals the sum of the probabilities corresponding to the different alternatives.”¹³  Anyone of those 10⁵² is a different way that might fulfill the event of a chain being in the order for insulin.  Therefore, the sum of the different ways is 10⁵².  The probability that anyone of all that ever existed on earth would be insulin is therefore 10⁵² / 10¹⁰⁶. Dividing in order to simplify the fraction, the probability is 1 in 10^54.
   Therefore, the odds are a million trillion trillion trillion trillion to one that not a single protein molecule of all that ever existed on earth would by chance be in the correct order for an insulin molecule!  (Adjusting for different kinds of insulin would have little effect on a figure this size.)

Usable Proteins and Nonsense Chains of Amino Acids

   In this test, chance is supposed to come up with any usable protein.  How many of the total number of possible arrangements could be considered usable proteins? There is obviously no way on earth that anyone could say for sure.  One way to get a tentative idea is by comparison with other systems which have a number of parts that work only when in specific orders.  The best analogy is our alphabet with its 26 letters.  By putting them in various sequences, we can make multitudes of messages. 
   The letters are mere nonsense, however, unless they are in a meaningful order.  What percentage of the possible orders of the alphabet letters are meaningful?
   To answer that question, an experiment was conducted at the Center for Probability Research in Biology.  Thirty thousand letters were drawn at random, and then all meaningful sequences were listed – words, phrases, or messages that would carry a meaning to the average American.  The results are given below.

   In 30,000 letters drawn at random, the longest meaningful sequence contained only 7 letters.  The letters ABC appeared in order only once in the entire experiment.  AB occurred 41 times.
   It is quite clear that chance arrangements are predominantly nonsense arrangements.  Even many of the sequences that could be said to be meaningful require a stretch of the imagination. For example, the six-letter sequences were: RUINPA, WEETED, and AGMCAP.
   A working hypothesis derived from the experiment is that there is between 1/4 and 1/5 as good a chance of getting a meaningful sequence for each added letter of length, on the average.  The probability of getting a 400-letter sequence that would be meaningful would then be between 1 in 4⁴⁰⁰ and 1 in 5⁴⁰⁰.  (If one considers different languages using the same alphabet, not many such languages would be possible without changing the value of the letters, so it would not affect the calculations more than a few orders of magnitude.  Perhaps only one language should be considered, since the information value for the various letters is different in different languages, and amino acids only have to fit the one “protein language.”)
   For lack of any other way to estimate the proportion of meaningful amino acid sequences, let it be assumed that a similar probability exists as in the alphabet.  We will, however, use the figure of 1 in 4⁴⁰⁰, because the amino acids are fewer than the alphabet letters, there being only 20.
   On that basis, for an amino acid chain 400 long, the probability of getting a usable protein would be 1 in 4⁴⁰⁰, which is 1 in 10²⁴⁰.
   In using this formula based merely on the alphabet analogy, there is, of course, an uncertainty factor.  There are many similarities, however, between the alphabet and the 20 amino acids.  Some letters are much more “reactive” than others, like amino acids, and some are used sparingly.  This uncertainty affects only the first stage of our study, namely, the first protein molecule to be produced by chance.  There must be at least 239 matching protein molecules for a set, in order to provide the minimum number for the smallest theoretically possible living entity.  The second of these and

all the ones following would not involve this alphabet formula, and hence the uncertainty factor would be eliminated.¹⁴

Allowing Concessions to Make Things Easier for Chance¹⁵

   It has already become apparent that chance is very backward when it comes to producing an ordered result.  There clearly will be no hope at all of arranging a protein by chance unless some extreme advantages are allowed. 
   Two approaches will be used.  First, we will allow some exceedingly helpful concessions, for the present, to assist chance in arranging an average length protein, and to obtain one minimum set of such proteins for the theoretical smallest living thing.  Afterward, we will check on the probability of much simpler protein chains resulting from such random alignment.  In the latter case, the concessions will be reduced a bit, but chance will still be given numerous advantages that would not have actually existed at the time of the presumed evolution of the first living thing.
   It can be seen at a glance that most of the following fourteen concessions could not have actually been true, but chance will have enough of a task even when offered all this help.  If chance fails under such extreme conditions, it should indicate clearly that perhaps it is unreasonable to rely on it at all in the quest for the way life began.  Here are the fourteen assumptions for this purpose.  Some of these are extreme, and some are not.
   1.  Assume that the primitive atmosphere was as evolutionists claim.
   2.  Suppose that all of the twenty amino acids did form naturally and in the right proportions, by the action of ultraviolet rays, lightning, and heat.
   3.  Presume that the amino acids were formed in only the left-handed configuration.
   4.  In calculations that follow, consider that the average protein molecule is 400 units in length,¹⁶ which is shorter than the

445 average length computed earlier for the smallest theoretical cell from Morowitz’ data.
   5.  Postulate that all the atoms on earth have been used to form amino acids.  That is, all the carbon, nitrogen, oxygen, hydrogen, and sulfur atoms in air, water, and crust of the earth have been made up into amino acids for this all-out effort to get proteins by random alignment.
   6.  Consider that all of these amino acids are grouped in sets.  Each set contains one of each kind available at each position of the forming chain.  These groupings may be pictured as being in the form of coacervate droplets described by Oparin, or any other way so that they are together.
   7.  Let it be granted that these groupings are permanently protected in some manner from the destructive effect of ultraviolet rays.  It is widely recognized that ultraviolet rays would be lethal to the life being formed unless protected in some way.  These rays, particularly those in the wavelength range near 2600 Å, are “highly toxic (absorbed by protein and nucleic acids),”¹⁷ with lethal chemical changes resulting.

   8.  Concede also that the amino acids would automatically unite, even though this would require going against an “energy-gradient,” and the complex system which unites them in all known living things would be absent.¹⁸
   9.  Suppose that one substitution is allowable in each chain.  In this concession, it will not be required that the active site be exempt from substitution, and it will be considered permissible for any amino acid to substitute for any other at any point.  (See discussion of substitution earlier in this chapter.)  If future discoveries ever widen the viable limits of substitution, the extreme concessions we are allowing, such as in number ten below, would take up the slack.  In some cases a protein with substitutions may be partially functional.
   10.  Assume that the rate of chain formation is fantastically rapid, such that an entire chain requires only one-third of a ten-million-billionth of a second!  This is around 150 thousand trillion times the normal speed in living things which itself is quite fleet.¹⁹

   11.  For each set of amino acids, let it be figured that every unusable chain is immediately dismantled and another one made at the same rate of around 30 million billion per second, which is a trillion trillion (10²⁴) per year in each set.
   12.  Assume that nothing will interfere, so that chance will have an ideal opportunity,²⁰ and that if a usable sequence is ever obtained, the action will stop so that it may be preserved.  (In the matter of trying for a set of 239 proteins, regardless of the speed of trials, it would of course be necessary for 239 contiguous sets to obtain right sequences at the same time.  However, even if there were a way to arrange for a long time of overlapping existence of each sequence that occurred, with staggered timing of different sets; it would not make enough difference to affect the outcome.)
   13.  Consider further that if 239 proteins in contiguous sets are ever obtained, they will be able to merge into one group of proteins ready for working together in a living system.
   14.  For our present purpose, assume that the age of the earth is five billion years, and that the age of the universe is fifteen billion years.  From an evolutionary standpoint, these rounded figures are more or less standard at the present time.  (As we will see, evidence is growing for a much younger age.)
   With the extreme concessions listed above it might be thought that chance should easily arrange many protein chains in the course of earth’s history.  On the contrary, we will find it otherwise. The reader will recognize that many of these concessions are either definitely impossible or else have a probability that is “vanishingly small,” to put it mildly.  They are made merely to offer chance such a favorable opportunity that its failure to produce should be conclusive.

Using All the Atoms on Earth for Making Proteins by Chance

   In the list of concessions, it was assumed that all of the appropriate atoms on earth’s surface, including air, water, and crust of the earth, were made into amino acids and arranged conveniently in sets to make it easier for chance to come up

with a usable protein.  It can be estimated that there would be about 10⁴¹ such sets available.²¹
   With each of these sets making a total of 10²⁴ different chains per year as assumed in concession 11, that gives a total of 10²⁴ x 10⁴¹ chains produced on earth in a year’s time, which is 10⁶⁵. Under concession 14, the total chains made since the earth began would be 5 x 10⁷⁴, which we will round off to 10⁷⁵.

The Odds Against an Average Protein
by Chance Since the Earth Began

   We have just seen that chance could have made 10⁷⁵ different protein-length chains at the speed assumed during the entire time the earth has existed.  Using the formula from the alphabet, we can now estimate how many of those might be considered usable protein molecules.²²  First, we should allow for one substitution per chain.  This would have the effect of changing that 1/10²⁴⁰ formula to around 1/10²³⁶.  The probability, then, for usable protein molecules in this total of 10⁷⁵ produced since the world began is 10⁷⁵ / 10²³⁶.  Simplifying the fraction, we get 1 in 10¹⁶¹ as the probability that even one would be usable, on the average.
   Therefore, the odds are 10¹⁶¹ to 1 that not one usable protein would have been produced by chance in all the history of the earth, using all the appropriate atoms on earth at the fantastic rate described.  This is a figure containing 161 zeroes.
   It might be well to recall that even if one molecule were obtained, it would not help at all in arranging the second protein molecule unless there existed an accurate duplication process.  Even if there were such a process, there are many other kinds of proteins needed before there can be a living organism.

In Morowitz’ minimal cell, the 239 protein molecules required include at least 124 different protein species.²³

To Obtain a Set of Protein Molecules for Minimal Life

   It has just been calculated that the probability of a single protein molecule being arranged by chance is 1 in 10¹⁶¹, using all atoms on earth and allowing all the time since the world began.  What is the probability of getting an entire set of proteins for the smallest theoretical living entity?
   The second protein molecule will be far more difficult than the first, because it has to be part of a matching set.  The protein molecules of a cell are quite specifically adapted to work together as a team.  We assumed that the first protein could be any usable protein that might be good somewhere.  Once that first one is specified, the rest of the set has to match it exactly.  It is like assembling a car from a crate of automobile parts.  Once the kind of automobile is determined by the first component used, then all the other items must be of that same matching group.  Nothing else on earth will fit, in most cases, except the part made for that particular purpose.
   After the first protein molecule is obtained by chance (if it ever happens), then the others must be quite specific in the same way as the automobile components.

The Second Protein Molecule Is More Difficult

   The probability of getting the first protein molecule was influenced by the formula taken from the alphabet analogy.  The second one is more difficult to obtain, we have just seen, because it has to be more exact to match the first one, instead of being just any protein.
   The total number of possible orders in a chain of 400 amino acids of 20 kinds is 20⁴⁰⁰.  (The formula is: the number of kinds to the power of the number of units in the chain.)  As stated above, 20⁴⁰⁰ is the same as 10⁵²⁰.
   Considering the first one as already obtained, we need 238 more.  The second one could be any one of those 238.  The probability is therefore 238/10⁵²⁰.  The third one could be any of the 237 still needed, so its probability would be 237 /10⁵²⁰.  Calculating all of these, and allowing for one substitution per chain,

we arrive at a probability of 1 in 10¹²²⁴⁷⁰.  (See note 24 below.)  Even if almost a trillion different sequences might work in each protein, the probability resulting is 1 in 10¹¹⁹⁶¹⁴.  (See note 25 below.)
   This figure represents the second through the 239th protein molecules.  Multiplying in the first one, which was at a probability of 1 / 10²³⁶, we arrive at the final figure for the minimum set needed for the simplest theoretical living entity, namely. 1 chance in 10¹¹⁹⁸⁵⁰.
   Earlier, we obtained the figure of 10⁷⁵ which was the total number of chains made since the earth began.  In order to allow for overlapping sets of 239 each, we will use that same figure to represent the total protein sets formed.  Dividing into the big figure just calculated, we learn that the odds against one minimum set of proteins happening in the entire history of the earth are 10¹¹⁹⁷⁷⁵ to 1.  (See note 26 below.)
   Even if such a set could be obtained, we would not have life.  It would simply be a helpless group of nonliving molecules alone in a sterile world, uncaring and uncared for, the end of the line.  In chapter 10 we will see that even if unlimited substitution is allowed in 9/10 of all the positions, the odds against one minimum set of proteins are still beyond comprehension.

No Conceivable Chance of Success

   The odds against such a correctly ordered set of proteins for the smallest conceivable living entity are thus hopelessly large beyond understanding.  The next chapter will make it easier to realize the gigantic size of even the smaller figures with which we have been dealing.
   Chance was given every possible concession in this investigation.  Its failure was miserable beyond power to describe.  Yet chance is the only natural way that the first proteins could have been arranged.  In all of the careful efforts of Oparin and his

followers in their attempts to get life from nonlife, no real way has been found to get away from chance.  It is the only possible source of the sequence, in the absence of planning, in spite of the millions of words and the valiant efforts expended in the attempts that have been made.
   There is no real reason at present to believe that any living thing has ever existed that is simpler than the Mycoplasma hominis H39, which is the smallest living entity known.²⁷  Although some viruses may be smaller, they do not qualify as autonomous self-replicating systems.  A virus cannot duplicate itself without the help of a host cell whose machinery it must use to manufacture its proteins and nucleic acids.  Instead of being an earlier step on the ladder of evolution, viruses are now thought by some scientists to be just the opposite, a deterioration or setback rather than part of the line of progress. Could it be that they are intimately involved with the curse that the Bible describes as having come upon the earth as a result of man’s sin?
   Both the Mycoplasma hominis H39 and the theoretical smallest living thing have proteins averaging at least 400 amino acids of the 20 common varieties.²⁸  Dr. Morowitz’ eminent work on the lower limits of size and complexity for living things was done, in part, for the National Aeronautics and Space Administration.  Obviously the reason was to enable space missions to recognize any possible forms of life that might be simpler or different from our own.  There seems to be no actual scientific evidence that would indicate a more primitive, simpler method of duplication than the one in use in existing living things.
   Neither is there any adequate reason to think that there was ever a lesser number of amino acid types used in proteins.  Many vital functions require proteins with all the twenty kinds included. Even viruses use all twenty.  The same twenty are part of the theoretical minimal cell.
   It is significant that the Yale team working on this subject has revised its figures upward at least twice.  As research has progressed, it has become clear that the minimal living thing requires more parts than was at first thought.  From 45 different proteins estimated as the lowest minimum in 1967, the number

needed has risen to at least 124 different protein species.  The average molecular weight per protein has also been revised upward slightly.²⁹
   If words are adequate, the situation appears utterly hopeless for a random linkup in a usable order.  Even the hormones which the modern Lamarckian theory requires are likewise outside the realm of reasonable probability, as we saw in the case of insulin.  Some hormones are complex proteins much larger than insulin.

Another Extreme Concession to Help Chance, but All in Vain

   Just suppose that there are only ten kinds of amino acids, all left-handed.  Imagine further that the average protein requires only twelve units per chain,³⁰ and that one substitution is allowed in any of ten of those twelve positions.  Let it be granted that a living cell requires only ten proteins.  Assume a speed of polymerization of one chain in three seconds, or 10,000,000 per year per set.  Let all the other extreme concessions listed earlier remain in effect (use of all atoms on earth, automatic joining, the initial chain qualifying as “usable” under the formula developed on page 104, etc.).
   Even with these preposterous assumptions, the probability of one set being produced during the history of the earth is only 1 in 10³².  The odds, therefore, are 100 million trillion trillion to 1 that not one set of even this simple kind of “proteins” would have been obtained by chance since the earth was born.  So chance fails again.
   This section should be remembered in connection with any further research, if, for example, it is ever discovered that more substitution in regular-length proteins is allowable.  The margin by which chance fails is so vast that no conceivable amount of new discovery along this line could change the basic conclusion that complicated working systems do not arise by chance.  In order to obtain and continue to have certainty, one must remember and apply this key principle whenever new challenges are met.

A More Realistic Calculation

   Those extreme concessions we listed on page 105 and following were used to show that it is useless to expect a protein to result from random linkups even under such artificially ideal conditions.  Before leaving this subject, it may prove helpful if we now cut some of those concessions down to a more realistic picture (while remaining generous to chance so that there will still be no doubt about its failure). 
   When refigured thus, these conclusions can be reached:
   The probability of a protein molecule resulting from a chance arrangement of amino acids is 1 in 10²⁸⁷.  A single protein molecule would not be expected to happen by chance more often than once in 10²⁶² years on the average, and the probability that one protein might occur by random action during the entire history of the earth is less than 1 in 10²⁵². 
   For a minimum set of the required 239 protein molecules for the smallest theoretical life, the probability is 1 in 10¹¹⁹⁸⁷⁹.  It would take 10¹¹⁹⁸⁴¹ years on the average to get a set of such proteins.  That is 10¹¹⁹⁸³¹ times the assumed age of the earth and is a figure with 119,831 zeroes, enough to fill sixty pages of a book this size.³¹

   We are again prompted by the evidence to realize that Someone bigger surely had to be on the scene.  Even one small protein molecule the size of insulin cannot be accounted for otherwise.  In the following chapter, the implications of these odds will be considered.  Understanding the gigantic size of these numbers (of even the smallest figures we’ve discovered) is vital to the certainty toward which we are moving.