J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

THE NEED FOR A QUANTIFIABLE MODEL OF

Elizabeth A Siewert*1 and Thomas A Siewert2

1Retired from University of Colorado & 2Retired from NIST

(Received on Date: 6th August 2017 Date of Acceptance: 18th September 2017)

ABSTRACT

When Charles Darwin first published his book, the origin of the species, he explained his theory by appealing to analogy. He observed that man can develop desirable traits in domestic plants and animals by selectively breeding for these traits. In a similar way, nature can develop desirable traits in plants and animals – not by intention, but by an undirected process of natural selection acting on random variation. Unfortunately, much of evolutionary theory today is still explained using only descriptive arguments. There have been few attempts to develop a quantitative model of this undirected process. We describe two attempts at a quantitative model – one by Sir Fred Hoyle and the other by Dr. Richard Dawkins. While most models modify a previously-existing, functional, complex structure, both of these models are attempts to quantify the ability of evolution to innovate rather than modify. We critique these two models, and present our quantitative model. Specifically, we hypothesize a primitive version of Chlamydomonas reinhardtii, a simple single-celled green alga, which does not yet have a functional eyespot. We then calculate the probability of developing an eyespot that is functional enough to confer an evolutionary benefit assuming all components are pre-existing, except a few proteins. We conclude by encouraging others to become involved in developing quantitative evolutionary models Keywords: evolution, quantitative model, eyespot, Chlamydomonas

No: of References: 8

2017 September Edition |www.jbino.com | Innovative Association

J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

INTRODUCTION

In his book, The Origin of the Species, (e.g., being able to run faster if you‟re a Charles Darwin speculated that the wide wolf or, for that matter, a deer) might be variety of beaks seen on of the inherited by some unknown mechanism – Galápagos Islands developed their thus allowing a continuous gradual different shapes and sizes (depending change from one generation to the next. upon the type of food available to them Darwin praised Lamarck in his Origin of the on each island) through a series of Species, saying “Lamarck was the first man incremental changes in much the same whose conclusions on the subject excited way that desirable traits of domesticated much attention” and calling him a “justly plants and animals are developed through celebrated naturalist.” (Darwin, 1859) husbandry. He proposed that while man So, considering the state of scientific breeds and selects for traits that he desires knowledge at that time, Darwin could only in his plants and animals, the variation of argue intuitively from what he knew. He traits seen in nature is due to an undirected saw the adaptations in organisms that process of natural selection acting on favored survival (eg., green leaf-eating random variation. He further extended this insects, mottled-grey bark-feeding insects), undirected process of developing variation he observed the obvious relationships within a species to the development of the among the species based on gross various species, themselves – thus the title anatomies, and he understood the of his book, The Origin of the Species. In his practice of selective breeding to obtain concluding remarks, he states, “Thus the desirable characteristics in domestic plants small differences distinguishing varieties of and animals. On these observations, he the same species steadily tend to increase, proposed his theory of the origin of the till they equal the greater differences species through an undirected process of between species of the same genus, or natural selection acting on random, even of distinct genera.” (Darwin, 1859) incremental (and at that time, not It‟s important to understand that in 1859 understood) variation among individuals. when Darwin published his theory, the cell Today, we know much more about the was thought to be a fairly simple bag of complex structure of the cell, the source of protoplasm; its internal structure was not variation among individuals, and the discovered until the advent of the electron genetic relationship among the species. microscope in the 20th century. The However, Darwin‟s theory is still mostly mechanism for inheritance was also presented using only descriptive unknown until the structure of DNA was arguments. Although this gives some discovered in 1953. In the early 1800s, intuitive understanding of his theory, it lacks Lamarck had proposed that acquired traits

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J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

rigor. What is needed is a quantifiable Hoyle‟s model dramatically illustrates the model to provide mathematical precision “outrageously small” probability of the to his theory. There have been multiple “origin of life by chance” problem. attempts to quantify the probability that However, evolutionary theory states that complex structures can develop via a complexity is built up slowly step by gradual process of random variation and incremental step–not all at once and selection. We provide two of these suddenly. This model, although attempts – a very large-scale one from the quantifiable, is too complex to represent a astronomer, Sir Fred Hoyle, and a small- single, incremental evolutionary step. scale one from evolutionary biologist, Dr. Richard Dawkins, on the other hand, has Richard Dawkins. While most models presented a much simpler model. In his modify a previously-existing, functional, book, The Blind Watchmaker, he proposed complex structure, both of these models a model of developing the phrase, are attempts to quantify the ability of “METHINKS IT IS LIKE A WEASEL” in evolution to innovate rather than modify. incremental steps. (Dawkins, 2006) In this Fred Hoyle, along with many scientists of case, at each iteration he randomly the mid 1900s, was a proponent of the generated letters and spaces for each of Steady State Theory, proposed by Sir Isaac the 28 positions, kept the letters and Newton in 1687, which postulated an spaces that matched the target phrase, infinite age of the universe. He is credited and regenerated the letters and spaces with giving the Big Bang theory its name as that did not match the desired phrase until a pejorative because he objected to the all matched. He calculated that if he had implication that a finite universe put too tried to generate this phrase in a single much restriction on the ability of life to step, the probability would be one chance occur by chance. In his book, Evolution in 2728 or 1040 – an extremely low from Space, he states, “Life cannot have probability. However, by keeping any had a random beginning … The trouble is letters and/or spaces that agreed with the that there are about two thousand target phrase, “METHINKS IT IS LIKE A enzymes, and the chance of obtaining WEASEL” at each step, he showed that he them all in a random trial is only one part in could reach the 100% match in only a 1040,000, an outrageously small probability small number of iterations. that could not be faced even if the whole universe consisted of organic soup.” (Hoyle and Wickramasinghe , 1981)

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J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

Generation 01: WDLTMNLT DTJBKWIRZREZLMQCO P Generation 02: WDLTMNLT DTJBSWIRZREZLMQCO P Generation 10: MDLDMNLS ITJISWHRZREZ MECS P Generation 20: MELDINLS IT ISWPRKE Z WECSEL Generation 30: METHINGS IT ISWLIKE B WECSEL Generation 40: METHINKS IT IS LIKE I WEASEL Generation 43: METHINKS IT IS LIKE A WEASEL

While this example illustrates the process of goal. For example, one approach might achieving complexity via random, be to define success as matching any incremental steps, it does not correctly word in the dictionary, and possibly model an undirected process. Dawkins including grammar and syntax rules to had a predefined goal and retained letters determine whether a coherent sentence until they all matched that defined goal. or phrase could be formed. He knew, as the programmer, what phrase A. Proposed Quantifiable Model of he wanted to reach and defined each Darwin’s Theory incremental “success” with respect to that predefined goal. In other words, in this With today‟s knowledge of molecular model, Dawkin‟s blind watchmaker had , and the development of the resulting phrase firmly in sight. mathematical modeling of biological systems, it is no longer justifiable to present Methods and Results Darwin‟s theory using only descriptive Neither of the two previous models fairly arguments. This is an important issue and represents Darwin‟s theory of evolution. should be modeled quantitatively. In this While Hoyle‟s model is much too complex paper, we propose a biological model for and thus fails to be an incremental step in one incremental, undirected, random step evolution, Dawkins‟s model pre-defines the in evolution that is quantifiable. final goal, and thus fails to be undirected. Specifically, we propose to quantify the We need an example that is simple occurrence of one small component of a enough to depict the small incremental primitive eyespot assuming all other steps of evolution, and undefined enough components already exist. We chose the to model an undirected process of , as it seems to be a popular example evolution. One possibility would be to by both the critics and the proponents of improve Dawkin‟s “METHINKS IT IS LIKE A Darwin‟s theory. In fact, Darwin, himself, WEASEL” program by restricting each presented the eye as a testable example success to be independent of the final

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J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

of his theory. He stated, “If numerous green alga. This organism is a facultative gradations from a simple and imperfect heterotroph meaning that it can make its eye to one complex and perfect can be own food (glucose) using its chloroplast shown to exist … then the difficulty of and sunlight as an energy source, or it can believing that a perfect and complex eye use acetate as a food, if it‟s in the dark. could be formed by natural selection, So, evolutionarily, it can survive while a though insuperable by our imagination, functional eyespot develops, which would should not be considered as subversive of furnish a survival benefit over those that do the theory.”(Darwin, 1859) not have an eyespot. The modern eyespot of Chlamydomonas is located in the Critics of Darwin cite the as an chloroplast membrane and consists of lipid example of a complex structure to illustrate (fat-like) globules and proteins arranged in the falsehood of Darwin‟s theory. However, highly ordered layers which can initiate a these critics make the same mistake that signaling cascade in response to light. This Hoyle made in that the fully developed signal is transmitted to the flagella (the human eye is too complex. In contrast, means of motility for the organism) so that proponents of Darwin respond by stating it can maintain the proper light that the human eye didn‟t happen all at environment for the organism. once. It developed slowly over a great many years, one incremental step at a The question we asked is, “How difficult time, with each step giving the organism a would it be for a Chlamydomonas without slight survival advantage. They hypothesize a functional eyespot to develop a primitive that the earliest eye might have been just eyespot that is functional enough to confer a patch of light-sensitive cells on the skin. an evolutionary benefit? ”The organism Then, through random mutations, a would need to solve several problems to depression in the light-sensitive spot gain this minimum functionality. It would developed and slowly evolved into a need to be able to detect the presence of retina, and over more time, perhaps a lens light (the eyespot), the ability to swim developed. (Nilsson and Pelger, 1994) toward that light (the flagella), and a These, however, are still only descriptive signaling system from the primitive eyespot rather than quantitative models. to the flagella. Otherwise, given that it could swim, and could detect where it B. Proposal of the Eyespot as an wanted to swim, if there are no means of Incremental Step in Evolution communication between the eyespot and We propose to use this hypothesized patch the flagella, there is not a functional of light-sensitive cells as our model. advantage. Specifically, we propose a primitive version C. Assumptions for Calculation of the eyespot of Chlamydomonas reinhardtii which is a motile, single-celled

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J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

In order to model an incremental step, we (basic, acidic, neutral and will make some simplifying assumptions in hydrophobic, neutral and calculating the difficulty of developing a hydrophilic). At times, one amino minimally functional eyespot. acid might be able to substitute for another amino acid without  The Chlamydomonas already has affecting the folding properties or the ability to swim toward the light (if other characteristics of the protein. it could detect that light) and the In our model, we make the signaling system from the (yet non- assumption that this is always true. In functioning) eyespot to the flagella. other words, rather than building the  All other components for the patch proteins out of the 20 amino acids of light-sensitive cells exist. Only 10 common in today‟s proteins, we will more proteins are needed for the assume that we only need to choose eyespot to be functional. from 4 generic amino acids. (Proteomic analysis identified 202  Each of the 10 proteins is 100 amino different proteins from the modern acids long. (The photoreceptor day eyespot of Chlamydomonas proteins in the modern day (Schmidt, et al ., 2006), so this is a Chlamydomonas eyespot are ~700 reasonable assumption to model an amino acids long (Sineshchekov, et incremental step.) al.,2002), so this, also, is a reasonable  The chloroplast is already functioning assumption.) – presumably being used when the „blind‟ Chlamydomonas happens to D. Probability Calculations be in sunlight. It is important to remember that we are not  All the amino acids are available for calculating the number of ways to make a use and are of the same optical patch of light-sensitive cells. Our isomerization (the „left-handed‟ assumptions allow for already existing type). Since proteins made out of a components and capabilities for the mixture of optical isomerizations may eyespot to be functional enough to not fold properly, we assume we provide some survival advantage – if only it only have the “correct” type of had these 10 more proteins. We are also isomer. not calculating the number of ways to  A mechanism for building proteins make 10 specific proteins. Our only out of the amino acids is available, requirement is that these proteins have a i.e., gathering the amino acids and more or less similar conformation as the forming the peptide bonds. specific (larger) proteins so that it can  The amino acids are completely have some minimal light-detecting interchangeable within each of the capability. Our assumptions also allow for four broad types of amino acids

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J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

substitutions of amino acids as long as they mole (18 ml of water = 1 mole) to give 4.3 × are within one of the four general types of 1046 molecules of water in the ocean. We amino acids. Therefore, we submit that will assume that 10% of these molecules in these assumptions model an undirected, the oceans are amino acids instead of incremental step in evolution. water which results in 4.3 × 1045 (~1046) amino acids. There are 4100 ways to make one 100-unit- long protein using 4 types of amino acids. Next, we assume each amino acid and/or But, this one protein has no value by itself, polypeptide can interact with every other as we need all 10 proteins to make this one at the molecular vibration rate of 1014 primitive eyespot functional. Therefore, we Hz – the highest vibration frequency for a need to determine how many ways we diatomic molecule – that of the hydrogen can make 10 proteins. To do this we raise molecule. This gives 1046×1014 = 1060 the number of ways to make one protein attempts to form the functional proteins to the 10th power. Thus, there are (4100)10 or every second. We can also give these 10602 possible ways to make these 10 reactions more time to occur, by proteins. So, the probability to make 10 incorporating the age of the earth into our proteins that have some light-detecting resources. Although most would say that capability is 10-602. the water on the early earth was present as steam, we will assume that it was in a E. Resources liquid state since the earth was formed 4.5 This calculation, however, is too billion years (~1017 seconds) ago. This gives conservative because it doesn‟t take into a total of 1046 × 1014 × 1017 = 1077 possible account the probabilistic resources. It is attempts. Given these resources, we can only the probability to make the 10 proteins calculate the probability of making 10 given one chance. But, evolution offers proteins that have some light-detecting lots of chances for this to occur. How capability somewhere in the oceans since many chances could there be if many the formation of the earth. reactions were occurring in parallel? 1 – (1 – 10-602) 10^77 Since the Chlamydomonas lives in water, it ~ 10-602 × 1077 is logical to calculate the probability of this eyespot developing by chance = 10-525 somewhere in the oceans of the world. This extremely low probability of forming The earth contains about 1.3 billion cubic the appropriate proteins should cause us kilometers of water. We can convert this to re-evaluate our assumptions. One volume of water to molecules of water by possibility proposed by some is that using Avogadro‟s number (6.022 × 1023 proteins within an already functioning molecules/mole) and the definition of one

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organelle in our primitive Chlamydomonas This is still an extremely small probability to could be “recycled” to create a set of produce one piece of a primitive eyespot photosensitive proteins for the eyespot. somewhere in the universe during the life of However, this just transfers the probability the universe – assuming all the other of making the proteins to the probability of components are available and can be making the previously existing proteins, with assembled correctly to produce a the additional problem of modifying those sufficiently-functioning organelle to confer existing proteins to give the capability of a survival benefit upon which natural detecting light. So, that model would selection can operate. We submit this result in an even smaller probability than quantitative model as one incremental, we already have. undirected, random step of evolution.

There is a better way to increase the Discussion probability of the primitive eyespot. We Evolution is the theory that the don‟t need to limit the origin of life to development of the species is best earth. It could have originated in any explained by a series of many incremental number of likely planets throughout the steps – each step an undirected process of universe. Rather than calculate the natural selection acting on random probability using the number of molecules variation. This is a useful theory in many, in the ocean and the age of the earth, we wide-ranging areas of biological research. will substitute the number of particles in the Examples range from utilizing the universe and the age of the universe since evolutionary distances among the species the Big Bang. The universe contains about to extract genomic information using 1080 particles and the age of the universe sequence and expression data (Siewert gives us an additional 10 billion years of and Kechris, 2013) to studying alcohol time (for a total of 1018 sec) to randomly susceptibility in fruit flies to understand the generate the 10 light-sensitive proteins. genetics of alcoholism in humans. (Rodan With these additional resources, we have and Rotherfluh, 2010) 1080 × 1014 × 1018 = 10112 chances to produce the amino acid combinations. Darwin explained his theory by appealing The probability in this case is only slightly to the obvious relationship among the better. species and the common practice of selective breeding in domestic plant and 1 – (1 – 10-602) 10^112 animal husbandry. Today, most ~ 10-602 × 10112 evolutionary models still are only descriptive in nature. Some use genetic = 10-490 sequences in much the same way that Darwin used gross anatomies to show that the species are related. Others propose a

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J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

sequence of events to describe how an than modifying a previously existing organism could co-opt another already function, it was not an undirected search. functioning organelle or proteins from Ours, on the other hand, is an undirected other functioning organelles to acquire a search because our simplifying novel function, but again, these are only assumptions 1) do not require specific descriptive models – not quantitative. proteins and 2) require only a minimal Since our knowledge of molecular biology length of the proteins. It is also incremental has dramatically increased, it is no longer because we have assumed all necessary justifiable to present evolutionary models components to make a minimally- using only descriptive arguments. This is an functioning eyespot, except for a few important issue and should be modeled proteins. quantitatively. There are a few quantitative Although we used a primitive eyespot evolutionary models, but so far most have based on Chlamydomonas structure, been limited to methods for determining nothing in our calculations requires this. the best topology of evolutionary trees and Our calculations are applicable to any the lengths of their branches (to show the novel proteins; and, even making relationship among the species), reasonable assumptions, it would seem simulations of speciation assuming an that the event of even a few small proteins original species, and calculations for the occurring by chance somewhere in the time it takes one functioning structure to universe at some time during the life of the evolve into another functioning structure. universe is nearly impossible. These results Rather than modeling the modification of are rather unsatisfying and we can a previously functioning organelle to make empathize with Fred Hoyle‟s rejection of a better functioning organelle, we the Big Bang Theory because of the attempted to quantitate how likely it is for “outrageously small probability.” evolution to innovate rather than modify a Nonetheless, this is our attempt to develop previously-existing, functional, complex a quantifiable, biological model of an structure where only a few more proteins undirected, random, incremental step in are required. We proposed a model evolution. Note that this is not a model of assuming all components, except one, evolution in general, but a model for were pre-existing, which needed to occur evolution to innovate rather than to to obtain a minimally functioning modify. Our hope is that this paper would organelle. Both Hoyle and Dawkins encourage others to become involved in attempted to answer this question. either modifying this model or developing However, Hoyle‟s model was not an other quantitative models of an incremental step. And while Dawkins‟s incremental, undirected, random model shows the power of an incremental evolutionary step. There obviously needs process to innovate a novel function rather to be more work done in this area.

2017 September Edition |www.jbino.com | Innovative Association

J.Bio.Innov6 (5), pp: 685-694, 2017 |ISSN 2277-8330 (Electronic) Elizabeth & Thomas

REFERENCES

Darwin, C. (1859): The Origin of the Species Sineshchekov, O.A., Jung, K-H., and by means of Natural Selection or, The Spudich, J. L. (2002): Two rhodopsins Preservation of Favoured Races in the mediate phototaxis to low- and high- Struggle for Life; 6th ed. Project Gutenburg. intensity light in Chlamydomonas reinhardtii. PNAS, 99(13):pp. 8689-8694. Dawkins, R. (2006): The Blind Watchmaker. 5thed. UK: Penguin.

Hoyle, F. and Wickramasinghe, N. C. (1981): Evolution from Space; London: J.M. Dent & Sons.

Nilsson, D-E. and Pelger, S. (1994): A pessimistic estimate of the time required for an eye to evolve. Proceedings: Biological Sciences, 256:pp. 53-58.

Rodan, A. R., and Rotherfluh, A. (2010): The genetics of behavioral alcohol responses in . Int Rev Neurobiol, 91:pp. 25-51.

Schmidt, M., Geßner, G., Luff, M., Heiland, I., Wagner, V., Kaminski, M., Geimer, S., Eitzinger, N., Reißenweber, T., Voytsekh, O., Fiedler, M., Mittag, M., and Kreimer, G. (2006): Proteomic analysis of the eyespot of Chlamydomonas reinhardtii provides novel insights into its component and tactic movements. The Plant Cell, 18:pp. 1908- 1930.

Siewert, E. and Kechris, K. J. (2013): Modeling considerations for using expression data from multiple species. Statist Med, 32:pp. 4057-4070.

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