Today’s New Reason To Believe

Keith McPherson

Keith McPherson received his Master of Science in Electrical Engineering from Georgia Institute of Technology in 1993, and currently works as an electrical engineer in Melbourne, FL, in the fields of communications and signal processing.

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Parts 1 and 2 of this series observed that biological genetic systems function as information-processing systems, and a case was made for coding techniques that protect the genetic data. As a specific example, the genetic code appears designed to minimize the effects of errors in a way that is directly analogous to Gray codes. Gray codes are commonly used by engineers to protect data processed by many modern digital communications systems.

We now turn our attention to another analogy.

Analogy: Complementary Base Pairing Parity Code

A useful concept to have in mind to better appreciate this analogy is Hamming distance.¹ Good codes reduce the probability of error by increasing the minimum Hamming distance between codewords relative to the distance that would have been obtained if no code (or a less powerful code) was used. This minimum distance of a code is like the weakest link in a chain and, therefore, characterizes the code’s strength.

As the code’s minimum distance is increased, it is easier for a recipient to detect a message with no errors. Consider a scavenger hunt game where you “hide” something for a toddler to find, for example, a large blue ball among a pile of smaller white balls. The intent is to make the target blue ball stand out among the others. This exercise is roughly analogous to high Hamming distance. The large blue ball (the intended message) among a number of smaller white balls (errors) exhibits a relatively large dissimilarity, and so the blue ball is easily visible and detectable.

On the other hand, as the code’s minimum distance is decreased the recipient is more likely to make errors in message detection. Now consider an adult scavenger hunt where objects are “hidden” in plain sight because they blend in so nicely in their surroundings. It is difficult to “see” an object you are looking for, even if you are staring straight at it. The intent here is to make the object blend in with the objects around it. This is roughly analogous to low Hamming distance. The target object (the intended message) is hidden among very similar objects (errors) and exhibits a relatively large similarity. Thus, the desired object is not easily visible and detectable.

In digital communications perhaps one of the simplest examples of an error-detecting code (see here and here) is an even parity code. This code is used on a binary message frame (i.e., a sequence of binary digits, 1’s and 0’s). In this code, one parity bit is added to a message frame and its value is chosen to “round” the frame “value” out, to make the message stand out more among the possibilities by increasing the code’s minimum distance (like the example with the blue ball). This allows the recipient to more easily detect that an error has occurred if it detects a “non-round value” (i.e., a white ball). Values that are “round” or “non-round” have precise mathematical definitions in coding theory. The main point is that all parity codes, and the even parity code in particular, impart a precise mathematical structure to the protected (coded) data. This mathematical structure increases the minimum distance between valid codewords and allows for more robust error detection. (See here for more information on parity codes used in engineering.)

Recall that the DNA is a double-strand structure, specifically a double helix. And the four nucleotide bases in the DNA chemical alphabet are A, C, G, and T. Nucleotides A and T are complementary, as are G and C, and these pairings are the basis for the double-stranded structure, where each strand carries the same information as the other strand. Research into the chemical bonds at work between these complementary base pairs reveals that the natural nucleotide alphabet has been chosen to minimize the probability that a given nucleotide on one strand will be incorrectly paired with a partner on the opposite strand. More specifically, a researcher found that the nucleotides used for the DNA chemical alphabet actually form an even parity code. (See research work here and here.)

A convention was used to consistently assign binary values (i.e., 1 or 0) to certain features associated with the four nucleotides that comprise the chemical alphabet in DNA. The relevant features are the relative size of the nucleotide, and its donor-acceptor pattern. The donor-acceptor pattern is relevant for hydrogen bonding. Hydrogen bonds are formed between a nucleotide and its partner on the opposite strand. Careful observation of the resulting binary values reveals that they form an even bit parity code. To be more precise, the relative size of a nucleotide is related to its hydrogen donor-acceptor (D/A) pattern as a parity bit.²

In nature, there are actually 16 nucleotides. Why did nature settle on these specific four, and why only four? At first glance, one may impugn a designer’s inefficiency because there are more nucleotides that could have been used to increase the size of the alphabet, leading to a more efficient genetic code and protein synthesis mechanism. In fact, there has been speculation along these lines. The researcher used the same binary convention to determine the binary representation for the other 12 nucleotides. Upon close inspection, he found that the 16 total nucleotides can be arranged using this framework as eight belonging to the even parity set, and eight belonging to the odd parity set, where the natural alphabet uses a subset of the even parity nucleotides. “Nucleotide Hamming distance” is maximized as a result, as is typical for parity codes, leading to a robust mechanism for error minimization.

The resulting specific four nucleotides emerge as optimal. From this perspective, the genetic machinery is directly analogous to a 1-bit, even-parity code decoder as used routinely in engineering applications. Such a decoder is the optimal way to recover the intended message when a parity code has been used.

The parity code model is an interpretation that readily flows from the relevant chemical bonds that bind the complementary nucleotide pairs. It is a way to mathematically represent or express what is happening at a chemical level. The researcher comments that:

The purine-pyrimidine and hydrogen donor-acceptor patterns governing nucleotide recognition are shown to correspond formally to a digital error-detecting (parity) code, suggesting that factors other than physiochemical issues alone shaped the natural nucleotide alphabet…When this error-coding approach is coupled with chemical constraints, the natural alphabet of A, C, G, and T emerges as the optimal solution for nucleotides.³

In summary, we have seen that an error-detecting code (a parity code) is at work to minimize incorrect bonding between nucleotide pairs on the complementary strands of DNA. For DNA replication to be accurate it is critical that the strands be the true complement of each other. We furthermore note that the specific code used by DNA, an even parity code, is a mainstay in modern communications systems.

The next article in this series will examine another coding analogy between modern digital communications systems and the genetic information-processing system.

Notes/References:

1. See here and here for more information on Hamming distance.

2. Refer to Figure 1 here. A and G are larger nucleotides called purines, C and T are smaller nucleotides called pyrimidines. Lone pairs are rich in electrons and participate in weak bonding with hydrogen atoms to form hydrogen bonds between complementary pairs. Hydrogen atoms are also referred to as hydrogen donors, and lone pairs as hydrogen acceptors. A binary “1” was assigned for hydrogen (i.e., hydrogen donors, D). A binary “0” was assigned to “lone pairs” (i.e., hydrogen acceptors, A). A binary “1” was assigned to the smaller nucleotides (i.e., pyrimidines). A binary “0” was assigned to the larger nucleotides (i.e., purines).

3. Dónall A. Mac Dónaill, “A Parity Code interpretation of Nucleotide Alphabet Composition,” ChemComm 18 (2002): 2062-63.

God’s Instructions to “Subdue” and “Rule” Imply the World Was Harsh Before the Fall

by Daniel J. Dyke, M.Div., M.Th., and Hugh Henry, Ph.D.

Our last article reviewed uses of the words kabash (“subdue”) and radah (“rule”) in the Old Testament beyond Genesis 1. In all cases, they imply strong control exerted in the face of fierce resistance—or potential resistance. This helps us understand the true meaning of God’s instructions to man after his creation:

“Be fruitful and multiply, and fill the earth, and subdue it; and rule over … every living thing”(emphasis added).

Such commands cannot refer to the benign stewardship characteristic of the popular “blissful Nirvana” interpretation of the world before the fall. A command to subdue the earth and to rule over other living things implies conquest and subjugation of creation, as in: defeating and/or brutally ruling a strong enemy; subjugating another into slavery and/or bending slaves to a master’s will; fighting humanity’s sinful nature, and so on. By comparison, these are not the instructions given to a new CEO of a smoothly running company. These are the kind of instructions given to a CEO who must shake up an inefficient but potentially profitable company. God is commanding humans to confront and control a “very good” creation that needs organization and management.

The implication of violence and brutality in kabash and radah does not suggest humans should destroy creation—as some new CEOs will destroy a company to “save” it. The point is that creation will resist humanity’s management like a strong army or like a free man resisting enslavement. Humans are to carry out God’s goal of improving a creation that is already “very good” (tob meod). Creation can only realize its full potential through management by humankind.

Therefore, a logical interpretation of Genesis 1:28 is that men and women are formed in the image of God to continue God’s work of bringing order out of chaos. God gives them the power and ability to complete His work by channeling and directing creation toward maximum productivity. In this way, humans fulfill their destiny as God’s image-bearers. Yet, the task is not easy. God challenges men and women, as a father challenges his children, in order to mature them.

God’s instructions to “be fruitful and multiply, and fill the earth” do not only mean to reproduce. Humans are to make God’s creation more fruitful by cultivating the soil, domesticating animals, etc.

It is indisputable that fallen humanity has abused its role as steward of God’s creation; that is called sin. But human sinfulness does not detract from the central responsibility of completing creation by making it more productive. Edible fruits and berries grow on their own, but do so in much greater quantity and quality when they are cultivated. Anything cultivated and harvested becomes plentiful; and this includes both plants and creatures.

What changed with the fall? What was different after God “cursed” the ground with “thorns and thistles,” and man was doomed to procure food “by the sweat of your face”?¹ The options are:

1. A radical system change, including the death of vertebrate animals for the first time (necessitating the transformation of certain creatures into carnivores, which includes modifications to their mouths, digestive systems, and instincts). This is the view taken by many young-earth creationists, as represented by Dr. Jonathan Sarfati in part one of this series.
2. A minor system change, something less than a radical modification of certain creatures into carnivores, but perhaps a hardening of the soil and allowing “thorns and thistles” to grow.
3. A change of venue by removing Adam from a garden with perfect growing conditions to something more typical of the world today.
4. An internal change in man, such that work which was fun or easy before becomes arduous or difficult. This could be a physical and/or mental modification.
5. A combination of two or more of the above.

By using the words kabash and radah in Genesis 1:28, Moses, the likely author, strongly implies that creation was harsh in the beginning. Conditions before the fall did not reflect the popular perception of the “blissful Nirvana.” Hence, the radical system change suggested in the first option seems unlikely.

It is much more likely that the change in conditions after the fall principally represented a change in degree, as suggested by options 2-5. There is substantial evidence for this position. For example, God’s curse on Eve after the fall was “I will greatly multiply your pain in childbirth, in pain you shall bring forth children” (emphasis added). A simplistic translation of the Hebrew even reads: “in pain I shall increase your pain.” God does not introduce pain after the fall. Pain existed before the fall; God merely increases it!

The same holds true for God’s warning to Adam about the forbidden fruit: “in the day that you eat from it you shall surely die.” The Hebrew mot tamut reads “to die you will die,” which implies that Adam is probably familiar with the concept of death.

What is the degree of change after the fall? Which of the options 2-5 is more likely? An important clue is found in the work God tells man to perform before and after the fall. Before the fall, man is to “cultivate the ground”; after the fall, his task is still to “cultivate the ground”. The same Hebrew word, abad, is used in both cases. However, the instruction from before the fall is subtly different from after the fall. (The implications of this difference will be addressed in a subsequent paper.)

Nevertheless, Adam and Eve before the fall were not lounging about eating grapes and drinking nectar like Greek deities, as the “blissful Nirvana” view suggests. Adam had to put out effort for his food. Without humans, the world could be an overgrown jungle, where fast-growing, unfruitful vines crowd out food-producing plants (as the kudzu vine does in the American southeast if not aggressively controlled).

At the very least, the world could not fulfill its potential without human beings. This point is emphasized by the unambiguous statement in Genesis 2 that before humanity, there was “no shrub of the [cultivated] field” and “no plant of the [cultivated] field” (also using abad). One of the reasons for this was the absence of humans to do the cultivating. Without humans, herds of sheep provided easy prey to “a lion or a bear” and other predators. By contrast, with people in control, fruitful vineyards are carefully pruned to maximize production and herds of sheep are led “beside still waters” by shepherds prepared to kill their predators.

Humans sinned at the fall and, therefore, “creation groans” due to mismanagement. But the fall did not usher in a radical system change to God’s creation, introducing conditions such as decay and the death of vertebrate animals where there were none before. Harsh conditions were part of creation in the beginning. Indeed, men and women were created to manage and control those conditions.

Endnotes:

1. Genesis 3:17-19 (NASB)

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Mr. Daniel J. Dyke received his Master of Theology from Princeton Theological Seminary 1981 and currently serves as Professor of Old Testament at Cincinnati Christian University in Cincinnati, OH.

Dr. Hugh Henry received his Ph.D. in Physics from the University of Virginia in 1971, retired after 26 years at Varian Medical Systems, and currently serves as Lecturer in Physics at Northern Kentucky University in Highland Heights, KY.

Keith McPherson

Keith McPherson received his Master of Science in Electrical Engineering from Georgia Institute of Technology in 1993, and currently works as an electrical engineer in Melbourne, FL, in the fields of communications and signal processing.

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In part 1 of this series we learned how the genetic system is an information-processing system, and outlined several reasons why we could expect to find coding techniques in play to protect the genetic data. Such coding techniques are known and used by engineers to protect the data processed by many modern digital communications systems.

We now turn our attention to a few analogies of such coding techniques.

Analogy: Optimality of the Genetic Code and Gray Mapping

The first analogy will show from a qualitative and quantitative perspective that the genetic code is in fact an optimal (or near optimal) mapping from codons to amino acids. (See here for a table describing the genetic code.)

The genetic code seems optimized to the specific nucleotide error probabilities quite well, as is the case for a good code from an engineering perspective. For example, the first and third nucleotides of a codon (see here) are more likely to be misread during translation, and this error appears to be taken into account in the genetic code mapping. These most common errors, or mutations, translate the desired codon into a codon that codes either for the same amino acid, or for an amino acid that has very similar physicochemical properties, thus minimizing function loss. This is similar to Gray codes used in digital communications.

More specifically, the genetic code seems to be specifically designed to code for the same or very similar amino acids for the most common types of substitution mutations (errors), thereby minimizing protein function loss. In like fashion, Gray codes used in engineering are specifically designed to code for the most similar bit patterns for the most common types of symbol errors, thereby minimizing information loss.

I noticed the similarity to Gray coding after reading a paper by Dr. Fazale Rana in 2002. The Gray code interpretation was highlighted by Manish Gupta in a paper published in 2006. Gupta plotted the 64 codons used in the genetic code in terms of nucleotide distance (see Figure 3 here), and remarked on the correspondence to Gray codes used in engineering. The concept of nucleotide distance and the illustrated plot establishes the validity of the Gray map interpretation.

Recall from part 1 that many genetic code mappings are possible due to the high level of redundancy. Therefore, from a qualitative perspective, and from an engineering perspective, the genetic code is superb, perhaps much better than one may expect from a naturalistic perspective.

Recent work shows just how remarkable the natural code is. (See here and here.) Researchers studying the error-minimizing properties of the genetic code noticed that prior work concluded that the natural code ranked in the top 0.02 percent for efficiency, but that the prior work overlooked bias in mutations.¹ When this bias is taken into account, the natural code makes a radical leap forward from the top 0.02 percent to literally one in a million.

Dr. Fazale Rana comments further on the error-minimizing properties of the genetic code:

The genetic code’s error-minimization properties are actually more dramatic than these results indicate. When researchers calculated the error-minimization capacity of one million randomly generated genetic codes, they discovered that the error-minimization values formed a distribution where the naturally occurring genetic code’s capacity occurred outside the distribution. Researchers estimate the existence of 10¹⁸ possible genetic codes possessing the same type and degree of redundancy as the universal genetic code. All of these codes fall within the error-minimization distribution. This finding means that of 10¹⁸ possible genetic codes, few, if any, have an error-minimization capacity that approaches the code found universally in nature. ²

In summary, qualitative and quantitative evidence suggests that the natural genetic code is highly optimized and, in fact, tuned to the most common type of errors (mutations). In addition, this work highlights an underlying analogy between the genetic system and modern communications systems—the so-called Gray code.

The next article in this series will look at another coding analogy between modern digital communications systems and the genetic information-processing system.

Notes/References:

1. Bias includes the fact that not all codons are equally mistranslated to other codons, and that certain nucleotide positions within the codon are more prone to error. Purine/purine and pyrimidine/pyrimidine errors (transition mutations) are more common than purine/pyrimidine errors (transversion mutations), and the ranking of the positions is 3rd, 1st, and 2nd in terms of being more error prone.

2. Fazale Rana, “FYI: I.D. in DNA; Deciphering Design in the Genetic Code,” Facts for Faith, Quarter 1, 2002, 14-23.