Our Scientific Publication on Gene Regulatory Networks for the John Templeton Foundation Grant

As part of our work for the John Templeton Grant #57657  “A New Biology of Spiritual Information” awarded to the Natural Philosophy Institute for the period from Sept 2015 through August 2017, my wife Aniko Albert and I published a paper in the Journal of Theoretical and Computational Science on the theory of gene regulatory networks. This is a peer reviewed, technical paper, and it describes most of the work we did to understand how the complexity of these networks could be understood.

We plan to put the scientific work described in this paper into a more theological or spiritual context in future publications, online posts, or other methods of public dissemination. While the official period of the grant is almost over, we intend to continue to work on several other aspects of the project (including this blog) for some time to come.

The paper is freely available online at this link

The complete citation for the paper is:

Garte S, Albert A (2017) The Role of Genotype in the Predictability of Dynamical Behavior in Complex Model Gene Regulatory Networks. J Theor Comput Sci 4: 155. doi:10.4172/2376-130X.1000155

I have posted below 1) the abstract from the paper, and 2) a description of the what the paper says in less technical language, including a summary of what we found. This also includes two figures from the paper. I will be happy to answer any questions about this research in the comments section of this post.

Abstract

Models of gene regulatory networks (GRN) have proven useful for understanding many aspects of the highly complex behavior of biological control networks. Randomly generated non-Boolean networks were used in experimental simulations to generate data on dynamic phenotypes as a function of several genotypic parameters. We hypothesized that the topological component of network genotype could be an obstacle to the discovery of mathematical formulas that can predict certain phenotypic parameters. Our data support that hypothesis. We quantitated the effect of topological genotype (TGE) and determined its influence on a number of dynamical phenotypes in simple and complex multi-gene networks. For situations where the TGE was low, it was possible to infer formulas to predict some phenotypes with good accuracy based on number of network genes, interaction density, and initial conditions. In addition to formulation of these mathematical relationships, we found a number of dynamic properties, including complex oscillation behaviors, that were largely dependent on genotype topology, and for which no such formulas were determinable. For integrated measures of gene expression state, we observed a variety of oscillation patterns, including stable, periodic cycling with a wide variety of period length, aperiodic cycling, and apparent chaotic dynamics. It remains to be determined if these results are applicable to biological gene regulatory networks.

Summary

Gene regulatory networks are some of the most important and most complex functional structures in biology. Such networks or circuits control which genes are active (actually being translated into proteins), and which are silent at different times, and in different cells. We have recently learned that the systems for control of gene expression are far more elaborate and convoluted than anyone could have imagined.

For a typical network, some genes become active (turned on) because they are the target of molecular switches made by other genes. At the same time, genes can also be silenced (turned off) by the action of other genes in the network.

The result of all of these interactions between genes is an incredibly complex web of control that is challenging to analyze in any detail.

A number of researchers have tackled the complexity of GRNs by using model networks and then analyzing their behavior by mathematical and algorhythmic methods. The idea is to try to come up with some general principles that might be applicable to actual real-world biological gene networks.

That is exactly the approach we took in our research. First we designed a system of gene regulatory networks, where (for example) there are 5 genes, each of which can have many different patterns of interactions with the other genes in the network. An example is shown in Figure 1.

One

FIGURE 1. Five-gene model regulatory network. A) Matrix array showing numerical values for each interaction between all genes. The effect of genes in the rows on genes in the columns is given by 0 (no interaction), +1, or -1. Self-regulation is not included. B) A diagram of the interactive network shown in A, with green arrows showing activating interactions, and red blunted arrows showing suppressive interactions. Green double arrows (between Genes 1 and 5 and between Genes 4 and 5) indicate reciprocal activation, and bicolor arrows (between genes 3 and 4, Genes 2 and 3, and Genes 2 and 5) indicate inverse reciprocal interaction, where one gene activates another gene that suppresses it. For example, Gene 2 suppresses Gene 3, activates Genes 1 and 5, is activated by Gene 3, and suppressed by Gene 5.

To construct these networks using a random number generator. Each network we made can be described by several characteristics. These include the number of genes that activate other genes, the number of genes that suppress other genes, and the exact pattern of how all the genes interact with each other, which can be described as the “topology” of the network. All these parameters together are called the genotype of the particular network. For 5 genes, there are more than 3 billion possible genotypes.

In some kinds of networks, the effect of the topological component of the genotype is very strong, while for others, it’s weaker. We found that when the topological component (the map of the network) was not as important as the quantitative parameters of the genotype (the number of activating and suppressing genes and the total density of gene interactions), it was possible to derive very accurate formulas that could predict the behavior of the networks as a function of time and other variables. But when the topological component was dominant, such equations only gave very approximate results.

An additional finding of our experiments using these models was that the time-related behavior of some very dense networks was extremely complex. We found that many of these networks showed an oscillatory pattern, as had been seen previously. But we also found that the details of the cycling oscillations were not very predictable, and at times became so complex as to resemble chaotic dynamic behavior. Figure 2 shows examples of oscillating patterns of gene expression with time produced in some of these networks.

Ten

FIGURE 2. The complex oscillatory patterns of three Compound networks.  A) Oscillatory period = 42 iterations.  B) An example of a commonly seen period of 60 iterations (present in about 13% of Compound networks). C) An aperiodic network, with an appearance of chaotic dynamics.

We don’t know yet if any of these results will be applicable to actual biological gene regulatory networks. But we do believe that the discovery of quantitative laws that govern the dynamic behavior of certain networks and the finding of the importance of network topology in determining how accurately these laws can predict the detailed behavior will have important implications for understanding how gene regulatory networks function to allow for some of the complexity that we know is everywhere in living creatures.

 

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The American Scientific Affiliation Annual Meeting

From July 26 to July 31, my wife, teenage stepson and I were in Colorado, first to visit an old friend in Boulder, and then to participate in the 76th annual meeting of the ASA in Golden (outside of Denver).

We started things off with a geology tour of the Front Range, including the Red Rocks, and Dinosaur Ridge. Knowing almost nothing about geology, I learned a lot, and was as impressed as everyone said I would be at the magnificent views and scenery of the Rocky Mountains. I have spent a lot of time in the Alps, and the Rockies are at least as grand.

The actual conference began the next day (Saturday the 28th). After a wonderful plenary lecture by climate scientist Katharine Hayhoe, I moderated the first Biological Sciences section of the meeting. Then after lunch, I went to the second Biology session, where I presented my talk on The Biochemical Teleology of Evolution. As I expected, there were some questions and comments, but not as much resistance to the idea of bringing teleology back into biology as I had anticipated. Parts of the talk included some of the material I have posted here recently about the Non-Conservation Principle in biology.

In the same session, Josh Swamidass, whom I have come to know from the Biologos blog, presented a fascinating idea about human genealogy (as opposed to genetics), in which he stated (correctly, in my view) that there is nothing contrary to science in believing that a single couple (Adam and Eve) are the progenitors of the entire human race, assuming that there were also other people alive outside of the Garden of Eden. That talk was very controversial, and there were many arguments and discussions about the idea, even after the session.

In the third and final Biological Sciences session, I was very happy to hear two talks focusing on the Extended Evolutionary Synthesis as a new and exciting development in evolutionary theory. Perry Marshall and Emily Ruppel Herrington (both friends of mine) presented these two talks, and again, a good deal of discussion was stimulated.

As in every conference, the best part is meeting old friends and making new ones. I was fortunate enough to meet several people whom I had come to know online from the Facebook group Celebrating Creation by Natural Selection (CCNS) and from my Twitter feed. Jeff Greenberg, John Pohl, Dana Oleskiewicz, and Kurt Wood were among those.

I was also thrilled to meet Leslie Wickman, the new Executive Director of ASA, and to catch up with lots of old pals in the science and Christianity movement, especially the previous Executive Director and old friend, Randy Isaac, who has guest posted on this blog (and hopefully will do so again).

One of the high points of the conference for me was the daily worship service, reminding all of us that science is derived from God’s creative majesty. On Sunday morning, Pastor Peter Hiett delivered one of the most powerful sermons I have ever experienced, bringing almost everyone to tears. His theme was “Daddy Love” and he talked about God’s love for His children in analogy with our love for our own kids. Not a novel theme, but the content and delivery were both stunning and overpowering.

On Monday morning, after an excellent plenary talk by Jim Peterson (the editor of the ASA journal Perspectives on Science and Christian Faith) about the ethical and religious implications of the new gene-editing technique called CRISPR, we drove our rented car back to Denver airport and flew home to Maryland, getting home about 11 PM.

I always get very tired after a conference, mostly from the intensity of the discussions, and the degree of thinking required. This one was no exception, but we were not able to take much rest. The next day we got up at 6 AM and went to our Church, where we had made a commitment to teach a science class at Vacation Bible School for the rest of the week. In addition, I had meetings to attend every night of the week after getting home.

So today, Friday, I am finally able to catch a breath, write and post this blog, and prepare for what comes next. But I am not complaining. Instead I thank God for the blessings of my life, which include the ability to remain active in the three things I love the most: science, my Christian faith, and the love of my wife (not necessarily in that order).

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Biological Non-Conservation and Natural Selection (Part 3)

The non-conservation principle (NCP) of life is directly responsible for the process of natural selection. We know that groups of organisms differ in their birth and death rates due to differences in the function of various forms of genes called alleles. This is generally what is meant by fitness. If Yp is the number of organisms with the p allele of a particular gene, and Yq is the number of organisms in a population with the q allele, then we have Eq 1:

EQ3.1

EQ3.1B

where dBp/dT is the birth rate for those with the p allele, and dDp/dT is the corresponding death rate. If we assume that either birth or death rates for both populations with different alleles are different, then

EQ3.2                                Eq 2

or vice versa. That is the definition of natural selection, where the strength of selection, S, is a function of the difference in population numbers containing the two alleles. This also stands for one definition of relative fitness, W (see next post for more discussion of fitness).  Eq 3:

EQ3.3

This follows the standard neo-Darwinian approach of assuming all evolutionary change is directly related to allele frequency differences in populations. However, to stay in keeping with more recent concepts in evolutionary theory, one could easily substitute any inheritable characteristic, such as epigenetic marks or alterations in gene expression regulation.

Note that if biological organisms obeyed a conservation law, such that

EQ3.4

as is true for matter and energy (see previous post), then

EQ3.5                        Eq 4

and S would always be 0. The conclusion is that the NCP allows for and gives rise to evolution by natural selection.

There are other physical and chemical entities that can be said to be created (born) and destroyed, such as reaction products of a spontaneous chemical reaction, meteorological events like a hurricane or storm,  geological events like volcanic eruption and island formation and loss, and all the cosmological events related to the birth and death of stars and planets. All these phenomena follow the law of conservation for matter and energy, (as does life)  and for all of them there are rates of birth and death that determine the rate of change of the higher level of organization, whether that is a spiraling storm, the life of a star, or the half-life of an organic compound in an aqueous solution.

And yet, biology is different, and one of the most important differences is found in the nature of the alleles we called, p and q. The existence of alleles implies a system of inheritance of characteristics that is not found in any other physical or chemical system. And it is the existence of genetic variation (alleles, or any other form of inherited genetic information) that makes natural selection (Eq 3) possible.

In the next post we will explore the relationship of biological variation to the teleology in biology.

 

 

 

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Some Personal Updates

I thought I might take an opportunity to update readers on some recent and planned activities that are keeping me busy.

I have been working under the aegis of my John Templeton Grant on an analysis of the dynamics of model gene regulatory networks. The goal of this work was to see if it might be possible to formulate new laws that could be applied to how real biological gene circuits work. The answer (as is often the case in biology) is: yes, and no, depending. I have written a manuscript describing my findings, which was recently accepted for publication in the Journal of Theoretical and Computational Science, a peer-reviewed, online journal. I will post a link to the paper when its available along with the abstract, here.

In two weeks, we will be traveling to Golden Colorado for the annual meeting of the American Scientific Affiliation. I will be speaking on “The Biochemical Teleology of Evolution” and chairing a session on Biological Sciences. I expect to meet up with lots of friends, including some I haven’t met in person before.

A couple of nights ago, my wife and I went to a dinner and conversation at a Washington DC restaurant sponsored by the Trinity Forum. The topic was “What does it mean to be human?”. It was a follow-up of a lecture we went to in June by Praveen Sethupathy in Washington, also sponsored by the Trinity Forum, and Biologos. Praveen gave a fantastic talk, and the follow-up discussions at the restaurant were exciting, with a great group of people. I was asked to put on my geneticist hat, and had fun being my old pedantic professorial self.

Speaking of genetics, on August 17 at 4 PM, I will be speaking at the Smithsonian Museum of Natural History, Hall of Human Origins about “The Biology and Theology of Race and Diversity in Modern Humans”. If you will be in the Washington DC area at that time, I would love to see you. Here is a link to the event.

I also have some church based activities planned for August, including delivering the sermon while our pastor is away on vacation. Please pray for me on that one.

So, not a dull moment in sight, as I just celebrated the second anniversary of my retirement, and the third anniversary of my marriage to my wonderful bride, Aniko. I am truly blessed. Peace to all, and thanks for your indulgence in reading this unusually personal post.

 

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Non Conservation, Evolution and Teleology in Biology (Part 2)

We have seen in the last post (Part 1) that life is not conserved, while matter and energy are. We know that life is an emergent phenomenon from complex chemical interactions. As discussed in the last post, there are a multitude of complex systems that also emerge from physical and chemical interactions that are not alive. A storm emerges from a particular set of circumstances involving temperature, humidity, pressure and wind, and some of these (like wind) are themselves emergent phenomena of more basic components (such as temperature gradients in the atmosphere). A storm, as a complex system, can be said to be born as a result of accidental configurations that occur together in the right place at the right time. The storm will last for some period (its “lifetime”), and then “die” as the factors that keep it in homeostasis either dissipate or change due to other random, accidental events. If conditions of temperature and other factors are right, a random collision between two molecules in the atmosphere or the ocean may lead to a chemical reaction, producing the “birth” of a new compound. That compound will also remain in existence until it is in turn degraded by further chemical interactions, hydrolysis, or decomposition.

Furthermore, it appears that the processes by which complex systems are terminated or destroyed have much in common, whether those systems are alive or not. In each case, it isn’t matter or energy that is lost, but the complexity and regularity of the system itself. In each case, the homeostasis or maintenance of the system breaks down. A storm travels over land and dissipates its energy; the wind dies down, the rain clouds scatter. An organism runs out of food, and the energy required to maintain its cellular integrity is not available. A star runs out of nuclear fuel. Sometimes such death events are accidental, and sometimes they are inevitable, predictable part of the process of the system.

However these systems, while they share the features of complexity, emergence, and decomposition with life, do not undergo natural selection, because (as we saw in the last post), they lack inheritance: they have no inherent informational content that is passed to progeny.

But there is another major difference between life and nonlife that cannot be accounted for by physical laws. And that is teleology. Life operates with purpose – it is goal oriented. That is a remarkable and highly controversial statement, but it is demonstrably true. Most people will agree that nonbiological natural events are dysteleological: they occur with no purpose, no agency guiding them other than relevant physical laws and natural conditions. There are no agents that decide when a volcano will erupt except the accumulation of forces – forces that follow no plan and are not organized toward any purpose. The same is true for star birth, supernovas, storms, or spontaneous chemical reactions. Many will hold that the same is true for biological systems, but that is easily disproven, at least for modern systems (meaning all life since LUCA).

For almost the whole history of our planet, new living forms have been created from other living forms. Furthermore, this process, which we call reproduction, is planned, purposeful, and directed by specific biochemical processes. Every living entity on the earth today is the result of a teleological process built into the normal functioning of all living creatures by billions of years of evolution by natural selection. The critical biochemical pathways that make life purposeful are replication of the genetic information, reproduction of the organism, and translation of the genetic information into biological characteristics (the linkage between genotype and phenotype).

Each of these biochemical processes are highly purposeful. They do not occur at random, depending on accidental appearances of forces or material, but are well controlled and very specific in timing and outcome. The agent of these processes (as well as of all the other processes required for life, such as energy conversion, biochemical synthesis, and homeostatis) is the living organism itself. While this might appear to be a circular statement, it follows directly from the uniquely biological law of natural selection.

Any allele p that is preserved and inherited, and leads to an increase in dY/dT, will increase in the population according to the population genetics law of selection:

EQ2.1                                                    where S is the selection coefficient related to fitness. Therefore, strong selection pressure for alleles (or new genes) that increase the ability of organisms to engage in the activities (such as reproduction or translation) that will maintain their existence results in an ever increasing dY/dT (meaning that the second derivative is positive).

Cells do not decide to improve themselves, but evolutionary processes do. And this is unique to biology. No storm system cares if it dies out or does not give rise to another storm. But bacteria, oak trees, and dolphins do care. Not consciously, of course, but as life becomes more and more complex, we can begin to see an actual will to survive (also part of evolutionary development) so that animals will flee predators, and parents will protect offspring.

This is not what Aristotle had in mind with his Telos. It is an automatic, non-conscious form of purpose (sometimes called internal teleology or teleonomy), but it is still purpose, and to deny its existence in life forms is to completely deny one of the most fundamental principles of biology, a principle that follows directly from the NCP and from evolution by natural selection.

 

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The Non-Conservation Principle in Biology (Part 1)

There is no denying that biology is a form of chemistry. Biology is derived from and depends on all the rules of chemistry, including equilibrium, reaction kinetics, catalysis, organic synthesis, hydrolysis, entropy, etc. However, biology is a form of chemistry not seen elsewhere in the universe. Biology has emergent properties that do not allow the chemical rules we know from simple chemistry to fully (or even partially) explain the behavior of biological systems.

At first glance, the most important distinguishing feature of biological chemistry from non-biological chemistry is the degree of complexity found in living organisms. Several hundred growth factors, cyclins, kinases, molecular switches, cascade systems, recognition signals, signal transducers, receptors, and assorted other protein factors have been identified in just the related fields of transcriptional regulation and cell growth control. All of these chemical entities interact in complex concentration-dependent ways with each other and with other factors. The same is true for energy conversion, homeostasis, reproduction, and all the other functional attributes of living cells. Add a higher level of physiological complexity for multicellular organisms, and we have further emergent properties that we can see in the life all around us.

But it isn’t only the enormous degree of complexity per se that makes biology fundamentally different from the chemistry and physics from which it emerged. The distinguishing factor of biological entities is that there is no conservation law for life. Life may be created and destroyed. Living entities are formed from other living entities, and the destruction of life (defined as death) is irreversible.

The biological non-conservation principle does not violate the physical laws of conservation, because when a biological entity dies, only its biological attributes are destroyed. Matter and energy of the organism are neither created nor destroyed but are conserved or transformed as required by the laws of physics.

The physical law of energy and matter conservation can be expressed by the simple equation:

EQ1.1

where X is the sum of energy and matter in a system, and T is time. There is no change in the total energy and matter content in the system as time goes by. Therefore  X = K, a constant.

If Y is the sum of biological entities, a simple analog of the first equation is

EQ1.2

where the rate of change in Y can be anything from negative to 0 to positive, depending on the relative values of the rates of birth (dB/dT) and death (dD/dT). The value for Y at any time can range from 0 (extinction) to C, the maximum carrying capacity of the system for life. This indicates that life is not conserved – it can be created or destroyed.

The non-conservation principle (NCP) distinguishes life from all other forms of energy and matter and leads directly to some of the important laws and attributes of biological systems. Physical and chemical rules can be used to describe the action of an enzyme or the flow of energy in a cell, but at higher levels of biological organization, physical laws are not of much use, and uniquely biological laws that take the NCP into account are required. The most important of these is evolution by natural selection, which is utterly dependent on the NCP. Without biological death, natural selection could not function. It is the requirement for death, as well as the requirement for inheritance of characteristics, that make evolution a biological construct, not directly applicable (except in very general analogies) to nonbiological systems.

Organisms die when the complex chemical interactions between hundreds to thousands of molecules no longer function in a way to maintain chemical homeostasis. The death of organisms is not equally probable, and that fact allows for natural selection to occur. Because natural selection must favor survival (by definition), biological creatures evolve with a teleonomic (Mayr’s term for programmed teleology in biology) drive toward increased fitness. Thus, creatures become better adapted to their environments, and new features arise. This is not at all proof or even indication of external design, but it is evidence for an internal design.  I might mention that Daniel Dennett is a proponent of biological teleology, so the idea is clearly not theistic in and of itself.

The reductionist temptation to dismiss the existence of purely biological laws in the study of biology is a philosophical mistake that has likely been a barrier to progress in our understanding of life. Many modern biologists have rejected this view, and devoted themselves to an exciting exploration of the way complexity and emergence can lead to major insights in biological theory. I believe that a recognition of the non conservation principle in biology should be an important part of that exploration. .

 

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About the Bible.

“You guys are kidding, right?”

“What do you mean?”

“What do I mean? You are collaborating on a book. One of you writes the first chapter, the other writes the second. And so on”

“Right. That’s what we did.”

“Great. But tell me something. Did either of you read what the other one wrote?”

The two authors looked at each other, and then back at the editor.

“Um, well, I mean… Not in, you know, detail,” said the first author (we will call him P). “But I thought he did a fine job.”

“Really? Interesting. You thought he did a fine job. You (pointing at P) talk about man being created “male and female, He created them” on Day 6, and your friend here (pointing at Mr. J) talks about some guy made of dust and a woman made from his rib. Did you happen to notice that the two of you wrote two chapters for one book (and a very important book, because the plan was to put it in the beginning of the whole anthology) that not only are inconsistent but  contradict each other?” The editor was raising his voice.

After a brief silence, J spoke up. “I cannot change a word or a jot of what I wrote” (I don’t know what a jot is, but that’s what he said). “Everything I wrote was inspired directly from God.”

“Me too,” said P.

The editor threw his pencil down on the desk in exasperation. “Look, we all work for the same team here. If you insist I will send these two chapters upstairs, but I am sure you are both facing some major rewrites.”

A short time later, God called the editor for an audience.

“Yes, Lord?”

“Great job on the Genesis book. I love those first two chapters.”

“Um, thank you, Lord, but…. I mean, are you sure? Don’t they strike you as… Oh, I don’t know, a bit discordant with each other?”

“Well, they were written by two fellas, each with different styles, so yeah, they are diverse all right. That’s exactly what I was going for when I assigned those guys to do this.”

“But, Lord, I am sorry to say this, and I mean no offence, but, well, they contradict each other. I mean there are two completely different versions of the creation of man.”

The Lord smiled.

“I think you are a great editor. But there is something you need to learn about this whole project. I have chosen some wonderful writers with great faith and passion. I have chosen some other writers who are not that wonderful, but whose faith and passion are even deeper. Every word they write is inspired by me, but written by them. If I think they got it wrong, I have them change it. So you never have to worry that I don’t approve of what they hand in to you. You can consider all of it to be preapproved.”

“Now, I will also tell you that I don’t care about having a book that is an easy read. It is not going to be something you can read in two weeks at the beach, and then forget the plot and the names of the characters. It is not going to have a single cliché in it. Many times it will not make sense at all. It will have violence, and poetry, love and anger; it will be exciting, and more boring than a cookbook. It will appear to contradict itself, like in those two chapters, but it won’t really. It will contain enigmas, puzzles, challenges, clues, mysteries, allegories, history, and lots of characters. Sometime the heroes will seem to be villains, and even I will come off as unpleasant at times.”

“But Lord, I thought you wanted this Book, or this series of books, to stand the test of time, to inspire generations of people, to be translated into hundreds of languages and spread throughout the word – to give comfort, advice, and inspiration to your people. Why would you want this book to be so hard to figure out?”

“Because that is exactly how it will stand the test of time and be spread around the world. This Book, My Book, will be read and not understood, until someone works hard enough to get it. It will be discussed and debated. And so people will think and learn. Believe me, I know what I’m doing. I am God, after all.”

“Oh, and by the way. Those first two chapters of Genesis that you are worried about?”

“Yes, Lord?”

“Don’t worry, they don’t contradict each other at all. There is a hidden message in there, that might be a bit obscure, but my people will find all kinds of new ways to understand the world, and when they do, they will figure everything out, including my book. They are good at figuring things out – it’s what they like to do. That’s one of the reasons I love them. They will think and argue and do experiments…

“Do what, Lord?” the editor interrupted.

“Never mind, you will find out. Anyway, eventually they will get it all, and then when they praise Me and the glory of My creation, they will really mean it, for its glorious splendor will amaze and delight them.”

The editor sighed. Sometimes he wished God was not such a micromanager, but then He wouldn’t be God, would he?

“OK Lord, I understand. I will let it all go as I get it.”

“Good. I’m glad to hear it. Because if you think Genesis is tough, wait until you see what D hands in”

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