Setting the Odds of Life
You want equations? We got 'em! Check out this paper by Dermott J. Mullan.
(Remember, the upper limit on a statistical probability is 1 over 10^30 to perhaps 10^50. Statisticians do agree that any probability less than 1 over 10^50 is a statistical impossibility.)
It begins, "We evaluate the probability Pr that the RNA of the first cell was
assembled randomly in the time available (1.11 billion years
[b.y.]). To do this calculation, we first set a strict upper limit
on the number of chemical reactions nr which could have occurred
before the first cell appeared."
What follows is well explained and the math is presented completely along the way. 47 pages but note that the presenter is a member of The International Society for Complexity, Information, and Design and not a YEC creation scientist per se. Mullan presents standard Darwinist time scales within the context of his work. Yet, he still comes to the same conclusion that I share:
"23. Conclusion
We have numerically evaluated the probability Pr that, in the first
1.11 billion years of Earth's existence, random processes were
successful in putting together the RNA for the first cell. In
estimating Pr, we initially assumed that the first cell follows the
rules which guide modern life-forms. That is, we assume there are
Naa = 20 distinct amino acids in proteins, and triplet codons in
the genetic code.
In calculating Pr, we consider only the random assembly of RNA: we
assume that once the RNA is present, it will generate the proteins
for the cell. (Thus, we are not requiring that the proteins be
assembled randomly: if we were to impose such a requirement, the
probabilities of random assembly of the first cell would be even
smaller than the results we obtain here.) Furthermore, we consider
a cell which is much smaller than those which exist in the modern
world. The latter contain at least 250 proteins. By contrast, we
have reduced the requirements of the first living cell to a bare
minimum: we assume that that cell was able to function with only
12 proteins. Compared to the smallest known living cell, our
choice of 12 proteins seems almost absurdly reductionist. Our
"cell" looks more like a modern virus (which cannot reproduce
itself) than a bona fide cell. But we proceed anyway.
Moreover we also assume that each protein consists of a chain of
no more than 14 amino acids. We refer to this as a (12-14) cell.
Again, a chain with only 14 amino acids is considerably shorter
than the smallest known protein in the modern world (which
contains a few dozen amino acids). It is not clear that a protein
with only 14 acids would be subject to the 3-dimensional folding
which is essential to protein functioning. Nevertheless, we make
these reductionist assumptions about a cell with the aim of
optimizing the probability of assembling the first cell.
In this spirit, we start with the assumption that the only amino
acids which existed in the primitive Earth were the 20 (or so)
distinct types of amino acids which occur in the proteins of
modern living cells. Also in the spirit of optimization, we assume
that the entire pre-biomass of the Earth was in the form of
proteinous amino acids. We specifically exclude the non-biological
amino acids (numbering more than one hundred) which may have been
produced in the primitive Earth. Moreover, we also assume that all
20 of the proteinous amino acids were present solely in the Lisomer
form so that the growth of a protein chain is not ended
prematurely by unintentional inclusion of a D-isomer. Furthermore,
we assume that the initial cell occurred in the physical
conditions which are most commonly cited in textbooks, i.e. in a
"primeval soup". This allows us to obtain a firm (and generous)
upper limit on the number of chemical reactions which could have
occurred before the first cell appeared on Earth.
With all of these assumptions, we find that the probability of
assembling the RNA required for even the most primitive (12-14)
cell by random processes in the time available is no more than one
in 10^79.
In order to improve on the probability that random processes
assembled the RNA for the first cell, we make the (unproven but
likely) assumption that proteins in the earliest cells were
constructed from a smaller set of distinct amino acids than those
which occur in modern cells. In order to ensure that the primitive
life forms had a similar level of error protection in theirgenetic code as that which exists in the modern world, we consider
a case in which the early proteins consisted of only Naa = 5
distinct amino acids. For these, the genetic code can operate with
doublet codons. In such a world, the probability of randomly
assembling the RNA for the first cell in the time available is
certainly larger than in our modern (triplet codon) world. But the
probability is still small, no more than one part in about 10^63.
We have identified a region in parameter space where, once the
genetic code exists, the probability of random assembly of the
first cell could have reached formally large values in optimal
conditions. These conditions include the following: (i) the first
cell contained 12 proteins; (ii) each protein in the cell
contained 14 amino acids; (iii) there were 4 bases in DNA; (iv)
the protein specificity index was no larger than 2.5 (far below
its average value); and (v) conditions in the primitive prebiosphere
were such that chemical reactions occurred at their
maximum possible rates. (The last of these conditions almost
certainly involves an optimization which is unrealistic by as much
as 10 orders of magnitude.)
(Note that we have said nothing about how the genetic code came
into existence. We merely assume that it is already in operation.
The origin of the code is a more formidable problem than the one
we have addressed here.)
If mathematics were the only consideration, our conclusions would
suggest that the RNA for the first cell could have been assembled
randomly in the primeval soup in 1.11 b.y. once there was a code
and abundant supplies of between 11 and 14 distinct proteinous
amino acids. However, when we take into account considerations of
coding theory (especially the necessity to protect the proteins
from errors of transcription), it appears that this region of
parameter space is hostile to protein production. And the genetic
code has to pass through a "bottleneck" in order to enter into the
modern world, with its 20 proteinous amino acids. As a result, the
first cell might have had serious difficulties surviving as an
autonomous biological system.
Finally, the extreme nature of our assumptions regarding the first
cell (12 proteins, each containing 14 amino acids) can hardly be
overstated. If a cell is to fulfil even the minimum requirements
of a Von Neumann self-replicating machine, it probably needs at
least 250 proteins. Even with multiple optimizations in our
assumptions about the primeval soup, the window of opportunity for
creating such a cell in 1.11 b.y. narrows down to a very
restricted region in phase space: (I) there must have been exactly 14 distinct amino acids in the cell proteins, (II) the protein
specificity index must have been between 1.0 and 1.17, and (III)
at least 10^58 chemical reactions must have occurred between the
bases (or amino acids) in 1.11 b.y. The "fine tuning" of such
conditions presents a problem. However, there are more serious
problems than fine tuning: error protection in the genetic code
fails altogether in these conditions. Even the Central Dogma of
biology breaks down. A cell formed under these conditions would
truly be subject to serious uncertainties not only during day-today
existence but especially during replication. The cell could
hardly be considered robust.
Nevertheless, as Yockey (p. 203) points out, the possibility that
an organism from the doublet-codon world might have survived the
"bottleneck" may have some empirical support. According to the
endosymbiotic theory (L. Margulis 1970, Origin of Eukaryotic
Cells, Yale Univ. Press, New Haven CT), mitochondria might have
been at one time free-living bacteria which now survive in a
symbiotic relationship with the cytoplasma of other cells. In
mitochondria, the genetic code differs somewhat from the code in
other cells. Perhaps mitochondria are representative of organisms
which originated in the doublet-codon world, but which could not
survive on their own because of the difficulties associated with
the hostile zone of parameter space where they originated.
In summary, if the first cell actually originated by random
processes, the genetic code must already have existed, and
conditions must have been "finely tuned" in order to trace a path
through a narrow (and hostile) region of parameter space. The idea
that some of the constants of the physical world have been subject
to "fine tuning" in order to allow life to emerge, has been widely
discussed in recent years (e.g. in the book by J. D. Barrow and F.
J. Tipler, The Anthropic Cosmological Principle, Oxford University
Press, 1994, 706 pp). If we are correct in concluding that "fine
tuning" is also required in order to assemble the first cell, we
might regard this conclusion as a biological example of the
Anthropic Principle."
In a side note, you will notice that no Darwinist has been able to claim The Origin-of-Life Prize ® as posted on the internet.
""The Origin-of-Life Prize" ® (hereafter called "the Prize") will be awarded for proposing a highly plausible mechanism for the spontaneous rise of genetic instructions in nature sufficient to give rise to life. To win, the explanation must be consistent with empirical biochemical, kinetic, and thermodynamic concepts as further delineated herein, and be published in a well-respected, peer-reviewed science journal(s).
The one-time Prize will be paid to the winner(s) as a twenty-year annuity in hopes of discouraging theorists' immediate retirement from productive careers. The annuity consists of $50,000.00 (U.S.) per year for twenty consecutive years, totalling one million dollars in payments."
(Remember, the upper limit on a statistical probability is 1 over 10^30 to perhaps 10^50. Statisticians do agree that any probability less than 1 over 10^50 is a statistical impossibility.)
It begins, "We evaluate the probability Pr that the RNA of the first cell was
assembled randomly in the time available (1.11 billion years
[b.y.]). To do this calculation, we first set a strict upper limit
on the number of chemical reactions nr which could have occurred
before the first cell appeared."
What follows is well explained and the math is presented completely along the way. 47 pages but note that the presenter is a member of The International Society for Complexity, Information, and Design and not a YEC creation scientist per se. Mullan presents standard Darwinist time scales within the context of his work. Yet, he still comes to the same conclusion that I share:
"23. Conclusion
We have numerically evaluated the probability Pr that, in the first
1.11 billion years of Earth's existence, random processes were
successful in putting together the RNA for the first cell. In
estimating Pr, we initially assumed that the first cell follows the
rules which guide modern life-forms. That is, we assume there are
Naa = 20 distinct amino acids in proteins, and triplet codons in
the genetic code.
In calculating Pr, we consider only the random assembly of RNA: we
assume that once the RNA is present, it will generate the proteins
for the cell. (Thus, we are not requiring that the proteins be
assembled randomly: if we were to impose such a requirement, the
probabilities of random assembly of the first cell would be even
smaller than the results we obtain here.) Furthermore, we consider
a cell which is much smaller than those which exist in the modern
world. The latter contain at least 250 proteins. By contrast, we
have reduced the requirements of the first living cell to a bare
minimum: we assume that that cell was able to function with only
12 proteins. Compared to the smallest known living cell, our
choice of 12 proteins seems almost absurdly reductionist. Our
"cell" looks more like a modern virus (which cannot reproduce
itself) than a bona fide cell. But we proceed anyway.
Moreover we also assume that each protein consists of a chain of
no more than 14 amino acids. We refer to this as a (12-14) cell.
Again, a chain with only 14 amino acids is considerably shorter
than the smallest known protein in the modern world (which
contains a few dozen amino acids). It is not clear that a protein
with only 14 acids would be subject to the 3-dimensional folding
which is essential to protein functioning. Nevertheless, we make
these reductionist assumptions about a cell with the aim of
optimizing the probability of assembling the first cell.
In this spirit, we start with the assumption that the only amino
acids which existed in the primitive Earth were the 20 (or so)
distinct types of amino acids which occur in the proteins of
modern living cells. Also in the spirit of optimization, we assume
that the entire pre-biomass of the Earth was in the form of
proteinous amino acids. We specifically exclude the non-biological
amino acids (numbering more than one hundred) which may have been
produced in the primitive Earth. Moreover, we also assume that all
20 of the proteinous amino acids were present solely in the Lisomer
form so that the growth of a protein chain is not ended
prematurely by unintentional inclusion of a D-isomer. Furthermore,
we assume that the initial cell occurred in the physical
conditions which are most commonly cited in textbooks, i.e. in a
"primeval soup". This allows us to obtain a firm (and generous)
upper limit on the number of chemical reactions which could have
occurred before the first cell appeared on Earth.
With all of these assumptions, we find that the probability of
assembling the RNA required for even the most primitive (12-14)
cell by random processes in the time available is no more than one
in 10^79.
In order to improve on the probability that random processes
assembled the RNA for the first cell, we make the (unproven but
likely) assumption that proteins in the earliest cells were
constructed from a smaller set of distinct amino acids than those
which occur in modern cells. In order to ensure that the primitive
life forms had a similar level of error protection in theirgenetic code as that which exists in the modern world, we consider
a case in which the early proteins consisted of only Naa = 5
distinct amino acids. For these, the genetic code can operate with
doublet codons. In such a world, the probability of randomly
assembling the RNA for the first cell in the time available is
certainly larger than in our modern (triplet codon) world. But the
probability is still small, no more than one part in about 10^63.
We have identified a region in parameter space where, once the
genetic code exists, the probability of random assembly of the
first cell could have reached formally large values in optimal
conditions. These conditions include the following: (i) the first
cell contained 12 proteins; (ii) each protein in the cell
contained 14 amino acids; (iii) there were 4 bases in DNA; (iv)
the protein specificity index was no larger than 2.5 (far below
its average value); and (v) conditions in the primitive prebiosphere
were such that chemical reactions occurred at their
maximum possible rates. (The last of these conditions almost
certainly involves an optimization which is unrealistic by as much
as 10 orders of magnitude.)
(Note that we have said nothing about how the genetic code came
into existence. We merely assume that it is already in operation.
The origin of the code is a more formidable problem than the one
we have addressed here.)
If mathematics were the only consideration, our conclusions would
suggest that the RNA for the first cell could have been assembled
randomly in the primeval soup in 1.11 b.y. once there was a code
and abundant supplies of between 11 and 14 distinct proteinous
amino acids. However, when we take into account considerations of
coding theory (especially the necessity to protect the proteins
from errors of transcription), it appears that this region of
parameter space is hostile to protein production. And the genetic
code has to pass through a "bottleneck" in order to enter into the
modern world, with its 20 proteinous amino acids. As a result, the
first cell might have had serious difficulties surviving as an
autonomous biological system.
Finally, the extreme nature of our assumptions regarding the first
cell (12 proteins, each containing 14 amino acids) can hardly be
overstated. If a cell is to fulfil even the minimum requirements
of a Von Neumann self-replicating machine, it probably needs at
least 250 proteins. Even with multiple optimizations in our
assumptions about the primeval soup, the window of opportunity for
creating such a cell in 1.11 b.y. narrows down to a very
restricted region in phase space: (I) there must have been exactly 14 distinct amino acids in the cell proteins, (II) the protein
specificity index must have been between 1.0 and 1.17, and (III)
at least 10^58 chemical reactions must have occurred between the
bases (or amino acids) in 1.11 b.y. The "fine tuning" of such
conditions presents a problem. However, there are more serious
problems than fine tuning: error protection in the genetic code
fails altogether in these conditions. Even the Central Dogma of
biology breaks down. A cell formed under these conditions would
truly be subject to serious uncertainties not only during day-today
existence but especially during replication. The cell could
hardly be considered robust.
Nevertheless, as Yockey (p. 203) points out, the possibility that
an organism from the doublet-codon world might have survived the
"bottleneck" may have some empirical support. According to the
endosymbiotic theory (L. Margulis 1970, Origin of Eukaryotic
Cells, Yale Univ. Press, New Haven CT), mitochondria might have
been at one time free-living bacteria which now survive in a
symbiotic relationship with the cytoplasma of other cells. In
mitochondria, the genetic code differs somewhat from the code in
other cells. Perhaps mitochondria are representative of organisms
which originated in the doublet-codon world, but which could not
survive on their own because of the difficulties associated with
the hostile zone of parameter space where they originated.
In summary, if the first cell actually originated by random
processes, the genetic code must already have existed, and
conditions must have been "finely tuned" in order to trace a path
through a narrow (and hostile) region of parameter space. The idea
that some of the constants of the physical world have been subject
to "fine tuning" in order to allow life to emerge, has been widely
discussed in recent years (e.g. in the book by J. D. Barrow and F.
J. Tipler, The Anthropic Cosmological Principle, Oxford University
Press, 1994, 706 pp). If we are correct in concluding that "fine
tuning" is also required in order to assemble the first cell, we
might regard this conclusion as a biological example of the
Anthropic Principle."
In a side note, you will notice that no Darwinist has been able to claim The Origin-of-Life Prize ® as posted on the internet.
""The Origin-of-Life Prize" ® (hereafter called "the Prize") will be awarded for proposing a highly plausible mechanism for the spontaneous rise of genetic instructions in nature sufficient to give rise to life. To win, the explanation must be consistent with empirical biochemical, kinetic, and thermodynamic concepts as further delineated herein, and be published in a well-respected, peer-reviewed science journal(s).
The one-time Prize will be paid to the winner(s) as a twenty-year annuity in hopes of discouraging theorists' immediate retirement from productive careers. The annuity consists of $50,000.00 (U.S.) per year for twenty consecutive years, totalling one million dollars in payments."