7. What does a cell need in order to function?
To determine the probability that the first cell was assembled
randomly, we first need to answer the following general question:
what is required in order to make a functional living cell?
In other words, what is the bare minimum number of proteins for a
cell to function at all? If we can answer this, it should help us
determine what the very first cell might have looked like.
As a first step in answering this, it is worthwhile to consider
the simplest known cell that exists in the world today. This is an
organism called "Mycoplasma genitalium" (MG) whose genetic
information is many times smaller than the information in the
human genome: the number of genes required for the functioning of
MG in its natural state is only 517. (Humans have tens of
thousands of genes.)
Recently, researchers have raised the interesting issue: are all
517 of these genes really necessary for MG to function properly?
The answer is No. By removing genes one at a time, researchers
have been able to show that the cell continues to function with
fewer than the total complement of 517. By eliminating more and
more of the genes, it has emerged that MG continues to function
normally as long as there are between 265 and 350 protein-coding
genes (see Hutchison et al., Science vol. 286, p. 2165, 1999). An
earlier estimate of the minimum cell size in nature had suggested
that the minimum number of proteins for cell operation might
indeed be about 250 (J. Maniloff, Proc. Natl. Acad. Sci. USA Vol.
93, p, 10004, 1996).
It appears, then, that the simplest cell in the modern world
requires at least 250 proteins in order to survive in viable form.
Many of the 250 (or so) essential proteins in MG have identifiable
14
functions. Hutchison et al. list 13 categories of identified
functions in the MG genome: (1) cell envelope, (2) cellular
processes, (3) central intermediary metabolism, (4) co-factors and
carriers, (5) DNA metabolism, (6) energy metabolism, (7) fatty
acid metabolism, (8) nucleotides, (9) protein fate, (10) protein
synthesis, (11) regulatory functions, (12) transport/binding
proteins, and (13) transcription. Each of these 13 categories
contains multiple genes, so that (e.g.) protein synthesis does not
depend solely on a single protein for its operation: there are
backups and multiple redundancies in each category. For example,
some 19 proteins are used for membrane maintenance (category (1)).
About 150 of the MG proteins can be assigned with some confidence
to one of the 13 categories.
However, more than 100 of the MG genes perform functions that are
currently unidentified. Nevertheless, the cell certainly requires
them: without them, there is empirical proof that the cell fails
to function.
8. The first cells to appear on Earth: reducing the requirements
to an absolute minimum
It might be argued that the first cells to appear on Earth were
smaller than the simplest cells (such as MG) that exist in the
world today. Those primitive cells might have been able to operate
with many fewer proteins than the 265 needed by MG.
Although we will use this argument below, it is actually difficult
to substantiate. The mathematician John Von Neumann estimated the
bare necessities which are necessary in order to construct what he
referred to as “a self-replicating machine” (Theory of Self-
Reproducing Automata: Univ. of Illinois press, 1966). It has been
a popular exercise among science fiction writers to use this idea
in connection with how a civilization might colonize a galaxy by
sending out machines. Von Neumann concluded that the number of
parts in one such machine must be in the millions. Other authors
have reduced this estimate somewhat, but even according to the
most optimistic estimate, the numbers remain very large: the best
estimates suggest that there must be between 105 and 106 parts in a
self-replicating machine. This means that the genome needs at
least 105 bits in order to metabolize and replicate (Yockey, p.
334). Using the information content in a typical modern protein,
Yockey concludes that the original genome must have been able to
specify at least 267 proteins. The fact that this is close to the
minimum number required for a modern cell (such as MG) suggests
that one is not necessarily permitted to assume that the original
15
cell contained significantly fewer proteins than the smallest
modern cell.
Nevertheless, other authors have argued that the Von Neumann
approach is overly restrictive. E.g., Niesert (1987, origins of
Life 17, 155)) estimates that the first cell might have been able
to operate with as few as 300-400 amino acids.
Which of these various estimates of minimum requirements for the
first cell should we consider? There must be some absolute minimum
requirements for making even the simplest cell. For example, one
might argue that, among the 12 non-regulatory categories of gene
functions listed by Hutchison et al., one representative protein
should be present in the first cell. And each of these 12 proteins
should have an accompanying protein to serve in a regulatory role.
This line of reasoning would suggest that 24 proteins are a
minimum for cell operation.
Can we reduce this to an even barer minimum? Examples of minimum
cell requirements have been summarized by the paleontologist
George Gaylord Simpson. Of the 13 categories listed by Hutchison
et al, Simpson narrows down the bare minimum to the following: (i)
energy generation, (ii) storing information; (iii) replicating
information; (iv) an enclosure to prevent dispersal of the
interacting sub-structures; (v) digestion of food; (vi) waste
product ejection (Science vol. 143, p. 771, 1964).
In view of these bare-bones requirements, it is hard to imagine
how any cell could function without at least the following six
types of proteins: (i) those that help to digest food, (ii) those
that generate energy for cell operations, (iii) those that carry
away waste products, (iv) those that preserve and repair the cell
membrane, (v) those that determine when reproduction is to occur,
and (vi) those which actually catalyze the tasks of reproduction.
Corresponding to each of these six, there must be a regulatory
protein which ensures that the corresponding protein does not
“express itself” in the wrong location in the cell.
It is hard to imagine how a living cell would exist at all if it
failed to contain at least these 12 proteins.
The fact that the simplest cell in the modern world (MG) requires
265 proteins as a bare minimum in order to function makes our
estimate of 12 proteins look ridiculously small. But since it is
possible that the first living cells may have been much simpler
than those we find in the world today, let us make the (perhaps
16
absurdly reductionist) assumption that the first cells in fact
were able to operate on the basis of the bare minimum 12 proteins.
As an illustration of how reductionist our assumption is, we note
that in the first cell, we are assuming that a single protein is
responsible for ensuring proper functioning of the lipid membrane
of that cell. In contrast, the smallest known cell in the modern
world (MG) uses 19 genes to encode for lipoproteins (Hutchison et
al. Science vol. 286, p. 2166). The use of 19 genes in the modern
cell is an example of the large amount of redundancy that nature
uses to ensure that the membrane survives. But the first cell may
not have had the luxury of redundancy: it may have been forced to
survive using only one gene for its membrane. It would have been a
precarious existence.
We have argued that each protein must contain at least 14 amino
acids: thus our bare minimum cell, with 12 proteins and 14 amino
acids in each, contains 168 amino acids. This is even smaller than
the bare minimum of 300-400 amino acids described by Niesert
(1987, Origins of Life, 17, 155). The DNA of our minimal (12-14)
cell would contain only about 500 bases. This is 10 times shorter
than the genome of a certain virus (PHI-X 174) which transmits 9
proteins. It is widely believed that a virus cannot be regarded as
a “living cell” (it has no self-contained replication system), so
this again indicates the extreme nature of our assumption that the
first cell could have as few as 12 proteins. But let us proceed in
the spirit of optimizing the probability that the first cell
appeared by chance.
8.1. The first cell: putting the proteins together by chance
In the early Earth, the commonest concept of conditions back then
is that the primeval "soup" consisted of various chemicals that
were stirred up and forced into contact with one another as a
result of the forces of nature (including rain, ocean currents,
lightning). Simple chemical reactions in the soup were easily able
to create amino acids: these molecules are so small (containing no
more than 10-30 atoms each) that random processes can put them
together quickly from the abundant C, O, N, and H atoms in the
soup. As a result, we expect to find in the primeval soup, in
abundant supply, all of the 22 amino acids that occur in modern
life forms. (For the number 22, see Nature vol. 417, 478, 2002).
In fact, there are more than 100 amino acids in modern nature, but
only 22 are used in proteins. And of those 22, numbers 21 and 22
are rare. Most living material relies on only 20 of these amino
acids, and we will use that number here.
17
To be sure, the “primeval soup” hypothesis is not without its
opponents (e.g. Yockey, pp. 235-241). Laboratory experiments which
claim to replicate conditions in the primeval Earth generate not
only amino acids but also a tarry substance (as the principal
product). This substance should have survived as a non-biological
kerogen in ancient sedimentary rocks, but no evidence for this has
been found. It should not be surprising that, in the primeval
soup, other amino acids, not currently used in life forms, could
have been formed. (This would include the acids that are used in
nylon.) And each of the amino acids which are created randomly in
the primeval soup would be created in two forms: the D-variety and
the L-variety. (These varieties refer to the ability of the
molecule to rotate the polarization of light either right or left:
this ability depends on the chirality of the molecule, i.e. on the
handedness of its 3-dimensional structure.) For reasons that are
not yet obvious, only one of these varieties (the L-variety) is
actually used in present-day life forms. However, the basic
property of amino acids, that they polymerize, operates only
between L alone or D alone: when an L and a D amino acid combine,
their opposite chirality has the effect of locking out any
possibility of further polymerization.
Another difficulty of a very different nature has to do with
reactions in an aqueous solution. The very process of assembling
amino acids into a polypeptide chain (so as to make a protein)
requires the removal of H from the amino radical and the removal
of OH from the acid radical: it is not obvious how these
constituents of a water molecule can be removed in an aqueous
solution.
Despite these difficulties with the primeval soup hypothesis, the
idea of the soup is so widespread in textbooks that it is a
natural starting point for an optimized estimate of probabilities.
In the spirit of the present approach (where we do whatever we can
to optimize the chances of assembling the first cell randomly), we
will simply go along with the textbooks. We shall assume that the
formation of the first cell in the early Earth began in liquid
water where only 20 L-amino acids need to be taken into account.
Other simple chemical reactions in the soup also give rise more or
less quickly to the four bases (two purines and two pyrimidines)
that form the "rungs" of DNA. Why are these formed relatively
readily? Because each base consists on no more than 13-16 atoms,
random processes can also assemble these bases rapidly from the
abundant C, O, N, and H atoms. It was probably more difficult to
form pyrimidines than purines, but the principle is robust:
18
formation of small molecules is essentially inevitable in the
early Earth.
In order for the first cell to come into existence, at least 12
proteins, each with Na amino acids in a specific order, had to
emerge in the same patch of the "primeval soup". To be sure,
individual proteins were probably emerging at random at many
places around the world. But if our aim is to form a complete
living cell, it will not help if the membrane protein emerged (at
random) in China, the energy protein in Russia, and the
replication protein in South America. That will not do: the only
way to have the first cell develop is if all 12 proteins emerge in
close enough proximity to one another to be contained within a
single membrane.
How might this have happened in random processes? By way of
example, let us consider one particular protein, in which the
chain of amino acids happens to be denoted by the series of
letters ABCDEFGHIJKLMN. In order that this protein be made by
chance, amino acid E (say) (one of the 20 commonest in nature)
might have started off by entering into a chemical reaction with
amino acid F (another of the 20), such that the two found it
possible to become connected by a peptide bond. Then amino acid D
might have had a chemical reaction so as to join onto the EF pair
at the left end, forming DEF by means of a new peptide bond. Note
that it is important to form DEF rather than EFD, which would be a
very different protein. This process presumably continued until
the entire 14-unit protein chain ABCDEFGHIJKLMN was complete.
8.2. The first cell: putting the DNA/RNA together by chance
It is not enough to assemble 12 proteins to have a functional
living cell: the cell must be able to reproduce, and for that
the cell needs DNA (or at least RNA). In order to ensure
reproduction of the cell, there had to be (also in the same patch
of the primeval soup) at least 12 genes on an RNA strand, each
containing 3Na+6 bases in a specific order.
Thus, in the very same patch of "soup" where the protein
ABCDEFGHIJ formed by chance, a strand of RNA must have been formed
where the three bases that encode for amino acid A were joined in
a specific order along the RNA strip by a series of chemical
reactions. Then the three bases that encode for amino acid B had
to be added in a specific order to the sidepieces, right next to
the three bases that encode for A. This process must have
continued until the triplets of bases that encode for each of C,
D, E, F, G, H, I, J, K, L, M, and N respectively were assembled in
19
a specific order into a chain of 30 bases. There would also be one
triplet at each end of the 30-base sequence to serve as markers
for start and stop. This 36-base sequence would then form the gene
for the first protein in the first cell.
Now that we know how the first proteins and RNA/DNA were put
together, we are in a position to estimate the probability that
this will occur by random processes.
9. Probability of protein formation at random
In the example given above, we recall that amino acid (say) E is
only one of 20 amino acids that exist in living matter. Amino acid
F is also one of 20. Therefore, a process that successfully forms
the sequence EF at random out of a soup where all amino acids are
present in equal abundances, has a probability p2 which is roughly
equal to (1/20) times (1/20) = 1/400.
Actually, however, pre-living matter contains not only the Lvariety
of each amino acid, but also the D-variety. Therefore, a
better estimate of the probability p2 that the correct pair of Lamino
acids be formed is (1/40) times (1/40), i.e. p2 = 1/1600.
However, once an L-acid unites with a D-acid, the opposite nature
of their chiralities leads to a “lock-out”: no further
polymerization is possible. So we will optimize probability by
assuming that only the L-variety is present. We therefore take p2 =
1/400.
Another way to state this result is that if we wish to create the
combination EF (both L-variety) by chance, the number of chemical
reactions that must first occur between amino acids in the
primeval soup is about 1/p2, or about 400. That is, if we allow so
much time to elapse that 400 reactions can occur in the primeval
soup, then there is a high probability (close to a certainty) that
the combination EF will appear simply at random.
This argument assumes that the only amino acids in the primeval
soup are the 20 which occur in modern living organism. However,
there were certainly other non-biological amino acids available.
As a result, many more than 400 reactions was almost certainly
required before the combination EF appeared at random. However, we
will optimize the chances for random assembly of the first cell by
ignoring the non-biological amino acids.
After creating EF by random processes, the next step is to have
the next amino acid to join the chain be the L-variety of (say) G,
i.e. only 1 out of the 20 types available. Then the probability
20
that the three amino acids EFG will be assembled in the correct
order is about (1/20)3.
Continuing this all the way through a sequence of Na amino acids
in a protein, the chance f1 of correctly picking (at random) all
the necessary amino acids to create one particular protein is
roughly equal to (1/20) raised to the power Na. This corresponds to
f1 = (1/10)x where x = 1.3Na. Actually, to the extent that some
amino acids may be replaced by others without affecting the
functionality of the protein, the above expression for f1 is a
lower limit. (We will allow for this later in this section.)
Yockey (p. 73) shows that instead of 20N for the value of 1/f1, a
more accurate estimate is 2NH where H is the mean value of a
quantity known as the Shannon entropy of the 20-acid set (see
below). In the limit where all amino acids have equal probability
of being encoded, and are equally probable at all sites in the
protein, 2NH turns out (from the definition of H) to be equal to
20N . In all other cases, 2NH is less than 20N. This returns us to
the previous conclusion: the above expression for f1 is a lower
limit on the true value.
Suppose that the particular protein with probability f1 has been
formed in a particular patch of the primeval soup. Then in order
to form a single cell (with at least 12 proteins as a bare minimum
to function), eleven more proteins must also be formed in the same
patch of soup, in close enough proximity to one another to be
contained within a single membrane. Each of these proteins also
has a certain number of amino acids: for simplicity let us assume
that all have length Na.
The overall probability f12 that all twelve proteins arise as a
result of random processes is the product of the probability for
the twelve separate proteins. That is, f12 is roughly equal to f1
12,
i.e. f12 is roughly (1/10)y where y = 15.6Na.
We can now quantify the claim that the first cell was assembled by
random processes. If the first cell consisted of only the bare
minimum 12 proteins, and if each of these proteins was uniquely
suited to its own task, the probability that these particular 12
proteins will be formed by random processes in a given patch of
primeval soup is f12.
Now let us turn to the fact that a protein may remain functional
even if a certain amino acid is replaced with another one.
(Obviously, we are not referring to invariant sites here.) For
example, it may be that the protein which we have specified as the
one that is responsible for (say) energy generation in the cell is
21
not unique. There may exist other groupings of amino acids which
also have the shape and properties that enable the task of energy
production for the cell. Maybe the others are not as efficient as
the first one, but let us suppose that they have enough efficiency
to be considered as possible candidates for energy production in
the first cell. Then we need to ask: how many energy-producing
proteins might there be in the primeval soup?
It is difficult to tell: in principle, if Na has the value 14
(say), then one could examine the molecular structure of all 14-
amino acid proteins (of which there are some 2014 , i.e. 1018.2 if
all amino acids are equally probable) and identify which ones
would be suitable for performing the energy task. Presumably there
must be some specificity to the task of energy production:
otherwise, a protein which is supposed to perform the task of
(say) waste removal might suddenly start to perform the task of
(say) membrane production in the wrong part of the cell.
Therefore, it is essential for stable life-forms that not all
available proteins can perform all of the individual tasks.
Suppose the number of alternate energy-producers Q is written as
10q. In a world where all proteins have Na = 14, the absolute
maximum value that q can have is qmax = 18.2. This is the total
number of discrete locations in the “14-amino acid phase space”.
In the real world, a more realistic estimate of qmax would be
smaller than the above estimate. First, not all amino acids have
equal probability of being encoded: there are more codons in the
modern genetic code for some amino acids than for others. (E.g.,
Leu, Val, and Ser have 6 codons each, whereas 10 others have only
2 codons each.) When these are allowed for in the probability
distribution, it is found that the “effective number” of amino
acids in the modern world is not 20 but 17.621 (Yockey, p. 258).
Thus, with Na = 14, a more accurate estimate of qmax(eff) is 17.4
(rather than 18.2).
As a result, in the real world, qmax(eff) may be considerably
smaller than 18.2. However, in the spirit of optimizing
probabilities, let us continue to use the value 18.2.
The requirement that some specificity of task persists among
proteins requires that the value of q must certainly not exceed
qmax. At the other extreme, in a situation where each protein is
uniquely specified, q would have the value qmin = 0 (so that one
and only one protein could perform the task of energy production).
22
Now we can see that our estimate of f12 needs to be altered. We
were too pessimistic in estimating f12 above. Each factor f1 needs
to be multiplied by 10q. For simplicity, let us assume that q has
the same value for each of the 12 proteins in the cell. Then the
revised value of f12 is 1/10z where
z = 15.6Na - 12q . (eq. 1)
This result applies to a cell with 12 proteins, each composed of
amino acids chosen from a set of 20 distinct entries.
10. Random formation of DNA/RNA
The first cell could NOT have functioned if it consisted only of
proteins. In order to merit the description living, the cell must
also have had the ability to reproduce. That is, it must also have
had the correct DNA to allow all 12 proteins to be reproduced by
the cell.
In order to estimate the probability of assembling a piece of DNA
by random processes, we can follow the same argument as for
proteins, except that now we must pick from the available set of 4
bases.
Repeating the arguments given above, we see that for each protein
which contains Na amino acids in a certain sequence (plus one start
and one stop), there must exist in the DNA a strip of B = 3Na+6
bases in a corresponding sequence. If we pick bases at random from
a set of 4 possibilities, the probability of selecting the correct
sequence for a particular protein is (1/4)B. Therefore, the
probability of selecting the correct sequences for all twelve
proteins, if each protein is unique, is (1/4)D where D = 36Na + 72.
Writing this with the symbol fRNA, we see that fRNA is equal to
(1/10)E where
E = 21.7Na + 43.3. (eq. 2)
Again, however, if instead of unique proteins for each task, there
are 10q proteins available to perform each task in the cell, then
we must increase the above value of fRNA to 10-G where
G = 21.7Na + 43.3 - 12q.
