Over half of the American population requires some degree of vision correction.[1] Eyeglasses and contact lenses remain the most common tools to restore proper eyesight but they are sometimes inconvenient. Not surprisingly, laser refractive surgery is becoming a popular option in vision correction for many people. Each year over a million Americans have a trained professional shine a high-powered laser in their eyes at a cost of $1500 to $2500 per eye.[1-3] The procedure is quick and almost painless, the recovery time is surprisingly short, and the results are nothing short of a miracle; however, nothing comes without a price. Laser eye surgery is relatively new and we are still in the process of determining the short- and long-term effects of this technology.

The three most common causes of vision loss are myopia (nearsightedness), hyperopia (farsightedness) and astigmatism. These conditions are caused by irregular formation of the cornea. The cornea is located on the surface of the eye and is responsible for focusing incoming light onto the retina at the back of the eye. If the cornea is too curved (myopia) light is focused in front of the retina. When this happens, nearby objects are in focus but distant objects appear blurred. A shallow curve in the cornea (hyperopia) causes the light to be focused beyond the retina, which makes it difficult to focus on objects close to the eye. If the cornea is not circular but is instead more oval-shaped, this is called astigmatism. It may be present alone or along with myopia or hyperopia. Astigmatism causes a distortion of the light as it passes through the cornea making it nearly impossible to focus at all.[2, 4-9]

Laser refractive surgery was made possible through the development of the excimer laser. This laser produces a beam of light that is capable of vaporizing thin layers of the cornea, effectively sculpting it into a more appropriate curvature for the eye. Slices measuring 0.25 microns thick (approximately 1/200th the thickness of a human hair) can be vaporized one layer at a time to create the proper curvature of the cornea without damaging the surrounding tissue.[3, 4, 9-12] A computer controls the length and number of pulses required to obtain the desired result. Correction of myopia requires flattening the curvature of the cornea by removing tissue from the center. Conversely, hyperopia is corrected by partially removing the outer edge of the cornea such that its curve is enhanced. Astigmatism is adjusted by removing tissue from the steepest areas of the cornea and making it circular again. The ultimate goal is to adjust the curvature of the cornea so that it more properly focuses light onto the retina. [3, 9]

The excimer laser first received FDA approval for use in the Photorefractive Keratectomy (PRK) procedure in 1995. It later received approval for use in the Laser Assisted In-Situ Keratomileusis (LASIK) procedure in 1998. [13] While both of these procedures use the excimer laser to reshape the cornea, they differ in how they manipulate the thin layer of protective cells that cover the cornea. In the PRK procedure, these cells are removed completely by the surgeon to expose the cornea before the laser is activated. The cells regenerate a few days after the surgery. [3, 6, 7, 9, 14, 15] The LASIK procedure uses a surgical tool called a microtome to create a partial slice of cells that is still connected to the eye by a thin piece of tissue. This ‘flap’ is held to the side while the laser sculpts the cornea; after the surgery it is carefully put back into place. Since the cells do not have to regenerate entirely the overall recovery time is reduced. [3, 6, 7, 9, 11, 15] The whole procedure takes approximately 30 minutes, of which the laser is only active for about 1 minute per eye.[9, 10]

A second system called the Holmium-Yttrium Aluminum Garnet laser console (YAG) was approved for use in the Laser Thermokeratoplasty (LTK) procedure in 2000. LTK is unique in that the laser does not remove tissue from the cornea. The laser creates heat spots in 8 points on the perimeter of the cornea and then repeats the pattern once more just a little further outwards for a total 16 spots. The whole process takes less than 4 seconds. The heat spots cause the cornea to shrink around the edges making it more steeply curved; the amount of shrinkage is directly related to the amount of heat created and the position of the spots. This treatment can only increase the corneal curvature and is therefore useful only in treating hyperopia. [16]

Not everyone is a good candidate for laser refractive surgery. Patients must be over 18 years of age and their eyes have to be in good health. There are a number of conditions that can be aggravated by laser treatment; for example it is not advisable for people with glaucoma or corneal scarring to undergo the treatment. These details are discussed on a pre-treatment consultation with the doctor. He/She will ensure that your vision is stable and that your eyes are fit to undergo the surgery. This involves making a map of the cornea to determine exactly what needs to be corrected and to ensure that the cornea is thick enough to endure the surgery. During the consultation the doctor will review the procedure and discuss the expectations of the patient and the risks involved. [2, 9, 12]

The goal is of laser surgery is 20/20 vision; however, the major determining factor is how the cornea heals after the treatment. Interestingly, statistics show that the most accurate predictions are made when moderate correction is required. When very mild or severe corrections are required the degree of predictability decreases and a second treatment is occasionally required to enhance the results. An improvement in visual quality is usually noticed a few weeks after treatment (the time it takes eyes to heal sufficiently). Over the course of a few months the cornea continues to heal and the quality of vision gradually improves. When it comes to obtaining perfect vision, the LASIK technique has a slightly better record than PRK, with studies showing that approximately 75% of patients achieve 20/20 vision and 95% at least 20/40. The minimum requirement to operate a vehicle in most regions is 20/40 and is considered acceptable by most people. Approximately 18% of patients undergo an additional ‘enhancement’ operation to obtain the results they desire. In LTK the goal is still 20/20 vision but it is more difficult to achieve because the initial adjustment relaxes significantly in the first few days post-treatment and continues to relax over the course of several years. To accommodate the relaxation of the cornea post-treatment a small degree of over correction is introduced during treatment. Due to the continual regression, the LTK procedure is considered non-permanent by the FDA even though 93.5% of patients see 20/20 or better 18 months after the operation. [1, 2, 7, 9, 10]

Complications that may arise after PRK and LASIK surgeries include: infection, scarring, dry eye, halos or starbursts of light, light sensitivity, reduction in night or fog vision, decrease in contrast sensitivity , decrease in best corrected vision (i.e., the patient cannot see as well after the surgery even with glasses/ contact lenses), irregular astigmatism and over- or under-correction. PRK operations are more prone to dry eye, scarring, halos and loss of contrast sensitivity, while LASIK surgeries have a tendency towards flap issues including infection and dislodging or improper placement of the flap. Fortunately, complications occur in less than one percent of operations and minor complications such as dry eye and halos usually resolve themselves in a few months as the cornea fully heals.[11] Over- or under-correction is the number one complaint among patients; however, when interviewing patients, these complaints were usually the result of expecting too much from the surgery. Occasionally the surgery can induce mild astigmatism due to suboptimal positioning of the laser; in this circumstance, a second surgery can be performed to enhance the visual quality. Very few patients experience infection-related difficulties which are usually due to improper sterilizing techniques in the clinic; overall, infections make up less than 1 percent of complications. Even though both techniques are very similar, patients are usually more satisfied with LASIK than PRK at 90 and 52 percent respectively. [9]

There are very few risks associated with LTK because no incision or tissue removal occurs. Again, the most common complaint is over- or under-correction. Additional treatment can increase the amount of correction but little can be done to reduce the degree of correction. LTK is designed for patients with low to moderate hyperopia so over correction is quite minor and usually regresses to acceptable levels shortly after the treatment. [15]

All three laser refractive surgery techniques appear to obtain satisfactory results with a very low number of complications. However, this does not mean that the operation is to be taken lightly. It is important to note that the FDA only approves the use of a laser for a particular application; they do not monitor the techniques used. Many of the complaints can be attributed to errors within individual clinics. Concern has been expressed over the “bargain basement” clinics that guarantee 20/20 vision for low, low prices. To make up the cost these clinics may cut corners which could involve using older equipment and sterilization techniques. [2, 17] These techniques are relatively new and improvements to the methods and equipment are being developed regularly.[18] Efforts are being made to reduce the amount of human error. The system is already largely computer driven and, with the introduction of eye tracking technology and wavefront-guided LASIK, it has become more so. The eye tracking technology allows the computer to check the position of the eye thousands of times per second and repositions the laser accordingly to ensure proper alignment during treatment. Wavefront-guided LASIK uses a second laser to help guide tissue removal and create a cleaner curve in the cornea. By keeping up-to-date, a clinic instills confidence that satisfactory results can be obtained while minimizing complications. [2, 9, 13, 18, 19]

With the outstanding success of laser refractive surgery millions of people are ‘going under the beam’ but they may be doing so with half the information they need. There is a lack of long-term studies focused on the performance and potential risks of refractive surgery. One study reported stability in PRK-treated eyes 12 years after treatment. [10] A more recent study however, has shown that the age degeneration of eyesight over 5 years was greater than normally expected in LASIK treated patients. While patients in this study still maintained vision that was better than their uncorrected state, this study suggests that the stability of the cornea may be compromised during the surgery. Stability of the cornea is of particular importance when the cornea is thin to begin with, possibly allowing for age-related degeneration to progress much more rapidly.[10] Genetic factors can contribute to this degeneration as well. One trait in particular, though rare (1 in 5000), can cause thinning of the cornea after surgery and premature vision loss that can only be corrected with transplants. One in five thousand sounds rare but when almost 2 million surgeries a year are performed the number of people suffering permanent vision loss due to this genetic variable alone is about 400. [4] It is important to remember that although PRK and LASIK are permanent, there are no guarantees that eye glasses will not be required in the future as age related degeneration occurs. [10]

Cataract and cancer formation after surgery are also theoretical concerns. Cataracts are a clouding of the natural lens of the eye that often occurs with age. [2] The laser is tuned so that very little damage occurs to the surrounding tissue but there is a potential for long-term complications. [3] Thus far, there are no studies that have investigated the relationship between laser refractive surgery and cataract formation. It is possible that insufficient time has passed since the first surgeries for an accurate study correlating cataract formation after laser refractive surgery. It may also be too early to correlate any potential increase in cancer in post-operative patients. The laser itself is deemed to be non-carcinogenic, but as our knowledge of factors contributing to cancer formation increases, this status may change.

As with most new techniques, improvements in refractive surgical methods and post operative treatment are still changing from year to year. [18] For example, the use of bandage soft contact lenses after LASIK surgery has been found to cause discomfort in a large percentage of patients and did not appear to contribute significantly to the overall healing process.[20] Small changes in methodology may seem minor but they suggest that further research is required to fully understand the nuances of refractive surgery.

Studies have shown that laser refractive surgery has an excellent track record of being safe and delivering the desired results. Consultation with a professional is essential to understanding the risks and the expected results of these procedures. Complications during and after these procedures are surprisingly rare and most are issues of minor discomfort that can be corrected with eye drops and further healing; the more serious complications such as over-correction and induced astigmatism can usually be corrected with enhancement surgery. One should keep in mind, however, that this data is based on surgeries performed within the last 5 years for LASIK and 12 years for PRK. The long-term effects of these procedures are still undetermined. Accelerated age-related degeneration may be a small price to pay for a mature patient but it may have a more pronounced effect on a 20-year old patient. As with any elective procedure, the patient must weigh the short term benefits versus the long term risks before undergoing laser refractive surgery.

References
1. Cia, J., Eyeing Perfection Dropping the Blindfold on LASIK eye Surgery. Harvard Science Review, 2004(winter): p. 52-55.

2. Murray, L.W. Photorefractive keratectomy and laser-assisted in-situ keratomileusis. 2002 [cited 21 Nov 2005].

3. Hersh, P., Carr, JD., Excimer Laser Photorefractive Keratectomy. Opthalmic Practice, 1995(13): p. 126-133.

4. Wikipedia. LASIK. 14 Nov 2005 [cited 14 Nov 2005].

5. Kim, H., Choun Ki Joo, C.K. , Visual Quality after Wavefront-Guided LASIK for Myopia. The Korean Journal of Medical Science 2005. 20(5): p. 860- 865

6. Laser Eye Surgery. [cited 21 Nov 2005].

7. Eyemdlink.com. Refractive Surgery-An Introduction. [cited 2005 14 Nov 2005].

8. Eyemdlink.com. Eye Anatomy – Refractive. [cited 14 Nov 2005].

9. Bower, K.S., Weichel, E.D., Kim,T.J. , Overview of Refractive Surgery. American Family Physician, 2001. 64(7): p. 1183-1190.

10. Jaycock, P.D., et al., 5-year follow-up of LASIK for hyperopia. Ophthalmology, 2005. 112(2): p. 191-199.

11. Eyemdlink.com. LASIK (Laser Assisted In-Situ Keratomileusis). [cited 14 Nov 2005].

12. Eyemdlink.com. Excimer laser. [cited 14 Nov 2005].

13. FDA. FDA-Approved lasers for LASIK. 2005 9 March 2005 [cited 2005 14 Nov 2005].

14. Eyemdlink.com. PRK (Photorefractive Keratectomy). [cited 14 Nov 2005].

15. Eyemdlink.com. Laser Thermokeratoplasty (LTK). [cited 14 Nov 2005].

16. Aker, A.B.M.D.F.A.C.S.F.S.E.E. and D.C.M.D.F.A.C.S.F.S.E.E. Brown, Hyperion Laser Thermokeratoplasty for Hyperopia. [Article]. International Ophthalmology Clinics Summer, 2000. 40(3): p. 165-181.

17. Stephen Colucciello, M. A Close Look at Eye Surgery. 2005 [cited 21 Nov 2005].

18. H. Sandoval, L.d.C., D. Vroman, K. Solomo, Refractive Surgery Survey. Journal of Cataract & Refractive Surgery, 2004. 31(1): p. 221-233.

19. Wikipedia. Wavefront. 14 Nov 2005 [cited 14 Nov 2005].

20. Sekundo W, D.H., Meyer CH., Benefits and Side Effects of Bandage Soft Contact Lens Application after LASIK A Prospective Randomized Study. Ophthalmology, 2005. Epub Ahead of Print: p. 1-5.

This is a knitted model of DNA, complete with GC/TA base pairs represented by orange-green bars with a pointed join and blue-yellow bars with a stepped join (because there weren’t enough stitches to make a wave or curve), replicating the standard simplified DNA model. As you can see from the picture, it also makes a good toy insofar as it holds its shape while squished or stretched, because it is stuffed firmly with cotton balls.

It was made with two equal black twisted tubes on size US 3 double-pointed needles (see the double-pointed needle tutorial and/or the tutorial on twisted tubes for more on how to make these). The stitch count for those was 18, or 6 per needle. The full stretched-out length of a black tube is about 13in/33cm, the natural relaxed coiled length is about 8in/20cm. The holes from dropping/adding stitches were woven through with more black yarn, as were any holes from increasing/decreasing at the ends.

The base pairs were 9 stitches around, or 3 per needle. The blue-yellow ones were one cast-on row of blue, then 5 rows of all blue, then as follows:

6th row: 2 yellow, 3 blue, 2 yellow, 2 blue
7th row: 3 yellow, 2 blue, 3 yellow, 1 blue
8th row: 4 yellow, 1 blue, 4 yellow

Then the 9th through 13th rows were all yellow, then a binding off row of yellow.

The orange-green ones were one cast-on row of orange, then 5 rows of orange, then as follows:

6th row: 1 green, 3 orange, 1 green, 3 orange, 1 green
7th row: 2 green, 1 orange, 3 green, 1 orange, 2 green

Then the 8th through 13th rows were all green, then a binding off row of green.

To put it all together, I held the two black coils side by side in a rough double-helix formation, then used three double-pointed needles jammed through at the middle and each end to hold the proper shape and distance. I pinned the first base pair just below the mid-point, then sewed it strongly into place using doubled-over black thread. Then I added the base pairs down that side to the end, then went up the other side, at each point ensuring that they were about the same distance apart and at roughly the same point on each black coil relative to where the coil’s woven lines were. As with real DNA, I varied the pattern of the base pairs, including reversing some of them.

Note that this model reflects a left handed helix, whereas DNA actually comes with a right-handed twist. The author is having a go at correcting this, and will hopefully one day have her solution available.

eyed with atlantic possibilities
far beyond our sensibilities
a depth so indigo
starfalls time in a recycled surge and flow
to obfuscate be wilder wisdom
from such limited dimension
(an inconceivable expanse of sea)
by our gracefoolish linearity

(onward ever we cycle
persisting because a
system can be ordered at
the expense of disordering
its surroundings)

so much randomness rearranged
we can never reach from this narrow frame
equilibrium (enlightenment)
through mere scientific disestablishment
destined to be continously reborn
into joy reversed, forlorn

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(REPRINTED FROM ISSUE ONE, JUNE 6th, 2005)

From the time of Charles Darwin, it has been the dream of many biologists to reconstruct the evolutionary history of all organisms on Earth and express it in the form of a phylogenetic tree. Phylogeny uses evolutionary distance, or evolutionary relationship, as a way of classifying organisms (taxonomy).

Phylogenetic relationship between organisms is given by the degree and kind of evolutionary distance. To understand this concept better, let us define taxonomy. Taxonomy is the science of naming, classifying and describing organisms. Taxonomists arrange the different organisms in taxa (groups). These are then further grouped together depending on biological similarities. This grouping of taxa reflects the degree of biological similarity.

Systematics takes taxonomy one step further by elucidating new methods and theories that can be used to classify species. This classification is based on similarity traits and possible mechanisms of evolution. In the 1950s, William Hennig, a German biologist, proposed that systematics should reflect the known evolutionary history of lineages, an approach he called phylogenetic systematics. Therefore, phylogenetic systematics is the field that deals with identifying and understanding the evolutionary relationships among many different kinds of organisms

Phylogenic relationships have been traditionally studied based on morphological data. Scientists used to examine different traits or characteristics and tried to establish the degree of relatedness between organisms. Then scientists realized that not all shared characteristics are useful in studying relationships between organisms. This discovery led to a study of systematics called cladistics. Cladistics is the study of phylogenetic relationships based on shared, derived characteristics. There are two types of characteristics, primitive traits and derived traits, which are described below.

Primitive traits are characteristics of organisms that were present in the ancestor of the group that is under study. They do not indicate anything about the relationships of species within a group because they are inherited from the ancestor to all of the members of the group. Derived traits are characteristics of organisms that have evolved within the group under study. These characteristics were not present in the ancestor. They are useful because they can help explain why some species have common traits. The most likely explanation for the presence of a trait that was not present in the ancestor of the whole group is that it evolved from a more recent ancestor.

Two extensive groups of analyses exist to examine phylogenetic relationships: Phenetic methods and cladistic methods. Phenetic methods, or numerical taxonomy, use various measures of overall similarity for the ranking of species. They can use any number or type of characters, but the data has to be converted into a numerical value. The organisms are compared to each other for all of the characters and then the similarities are calculated. After this, the organisms are clustered based on the similarities. These clusters are called phenograms. They do not necessarily reflect evolutionary relatedness. The cladistic method is based on the idea that members of a group share a common evolutionary history and are more closely related to members of the same group than to any other organisms. The shared derived characteristics are called synapomorphies.

The introduction of two important tools has dramatically improved the study of phylogenetics. The first tool is the development of computer algorithms capable of constructing phylogenetic trees. The second tool is the use of molecular sequence data for phylogenetic studies.

Phylogenetics can use both molecular and morphological data in order to classify organisms. Molecular methods are based on studies of gene sequences. The assumption of this methodology is that the similarities between genomes of organisms will help to develop an understanding of the taxonomic relationship among these species. Morphological methods use the phenotype as the base of phylogeny. These two methods are related since the genome strongly contributes to the phenotype of the organisms. In general, organisms with more similar genes are more closely related. The advantage of molecular methods is that it makes possible the study of genes without a morphological expression.

As previously mentioned, closely related species share a more recent common ancestor than distantly related species. The relationships between species can be represented by a phylogenetic tree. This is a graphical representation that has nodes and branches. The nodes represent taxonomic units. Branches reflect the relationships of these nodes in terms of descendants. The branch length usually indicates some form of evolutionary distance. The actual existing species called the operational taxonomic units (OTUs) are at the tip of the branches on the external nodes.

Tree construction methods
Some methods have been proposed for the construction of phylogenetic trees. They can be classified into two groups, the cladistic methods (maximum parsimony and maximum likelihood) and the phenetic method (distance matrix method).

Maximum parsimony trees imply that simple hypotheses are more preferable than complicated ones. This means that the construction of the tree using this method requires the smallest number of evolutionary changes in order to explain the phylogeny of the species under study. In the procedure, this method compares different parsimonious trees and chooses the tree that has the least number of evolutionary steps (substitutions of nucleotides in the context of DNA sequence).

Maximum likelihood This method evaluates the topologies of different trees and chooses the best based on a specified model. This model is based on the evolutionary process that can account for the conversion of one sequence into another. The parameter considered in the topology is the branch length.

Distance matrix is a phenetic approach preferred by many molecular biologists for DNA and protein work. This method estimates the mean number of changes (per site in sequence) in two taxa that have descended from a common ancestor. There is much information in the gene sequences that must be simplified in order to compare only two species at a time. The relevant measure is the number of differences in these two sequences, a measure that can be interpreted as the distance between the species in terms of relatedness.

Molecular phylogeny was first suggested in 1962 by Pauling and Zuckerkandl. They noted that the rates of amino acid substitution in animal hemoglobin were roughly constant over time. They described the molecules as documents of evolutionary history. The molecular method has many advantages. Genotypes can be read directly, organisms can be compared even if they are morphologically very different and this method does not depend on phenotype.

Phylogeny is currently used in many fields such as molecular biology, genetics, evolution, development, behaviour, epidemiology, ecology, systematics, conservation biology, and forensics. Biologists can infer hypotheses from the structure of phylogenetic trees and establish models of different events in evolutionary history. Phylogeny is an exceptional way to organize evolutionary information. Through these methods, scientists can analyse and elucidate different processes of life on Earth.

Today, biologists calculate that there are about 5 to 10 million species of organisms. Different lines of evidence, including gene sequencing, suggest that all organisms are genetically related and may descend from a common ancestor. This relationship can be represented by an evolutionary tree, like the Tree of Life. The Tree of Life is a project that is focused on understanding the origin of diversity among species using phylogeny.

References:
1) Whelan S., Lio P., Goldman N., (2001)Molecular phylogenetics: state-of-the-art methods for looking into the past Trends in Genetics, Volume 17, Issue 5, 1, Pages 262-272

2) Berger J. Introduction to Molecular Phylogeny Construction. BIOL 334.

3) Wen-Hsiung Li. Molecular Evolution. Sinauer Associates, 1997.

4) Pagel, M. (1999) Inferring historical patterns of biological evolution. Nature 401, 877–884

5) Zuckerlandl, E. and Pauling, L. (1962) Molecular disease, evolution, and genetic heterogeneity. In Horizons in Biochemistry (Kasha,M. and Pullman, B., eds), pp. 189–225, Academic Press 1921–1930

6) Felsenstein, J. (1981), Evolutionary trees from DNA sequences: a maximum likelihood approach, Journal of Molecular Evolution 17:368-376

7) Endo T., Ogishima S., Tanaka H. (2003) Standardized phylogenetic tree: a reference to discover functional evolution J Mol Evol; 57 Suppl 1:S174-81. Plant Species Biology

Murren C. (2002) Phenotypic integration in plants. Plant Species Biology. Volume 17 Issue 2-3 Page 89

9) Tree of life web project. What is phylogeny?

10) National Center of Biotechnology Information. Systematics and Molecular Phylogenetics.

11) Embley M. Molecular Systematics and evolution of microorganisms.

* * *

(REPRINTED FROM ISSUE ONE, MAY 23rd, 2005)

The biochemical potential of a cell to carry out specific chemical reactions is nothing short of enormous. Even the simplest of cells have the ability to catalyze over a thousand reactions, only a subset of which is required at any given time.

In order to save energy and resources, the cell needs to regulate these reactions such that only those that are necessary are carried out. In simplest terms, this involves a two-component system: one for sensing environmental conditions and thus metabolic needs, the other for translating these needs into a regulatory mechanism that can induce or suppress pathways according to the requirements of the cell.

Until very recently, these two functions were thought to be carried out exclusively by proteins. One common prototype for protein-mediated regula-tion is the E. coli trp operon, which regulates the cell’s ability to synthesize the amino acid tryptophan when it is not available from the environment. It involves direct binding of a repressor protein, TrpR, to DNA at the trp promoter site, physically occluding RNA polymerase from initiating transcription at that site (Fig 1a).

Figure 1. – Comparison of protein-mediated metabolic regulation and the riboswitch mechanism. a. In the trp operon, DNA is available for transcription of mRNA when only low levels of tryptophan are available. Presence of tryptophan from the environment causes a conformational change in the repressor protein that allows it to bind DNA at the promoter and repress transcription of the operon. b. The GlmS protein is an important enzyme of the glucosamine-6-phosphate (GlcN6P) synthesis pathway. A regulatory region of mRNA is found downstream of the coding region for GlmS. When no GlcN6P is present in the medium, the mRNA is translated and the GlmS synthesizes GlcN6P. Higher levels of GlcN6P lead to increased binding of the product to the regulatory region. The conformational change caused by binding induces auto-cleavage of the glmS mRNA, rendering it non-functional. Although the coding region for the protein is not affected, loss of the upstream region seems to prevent initiation of translation (From 7).

Recently, however, the unchallenged supremacy of proteins in metabolic regulation has been called into question through the discovery of riboswitches. These specialized stretches of non-coding mRNA can specifically bind their cognate metabolites, inducing conformational changes and/or ribozyme activity that lead to physical occlusion of the ribosome, transcription attenuation, or self-cleavage of the mRNA (Fig 1b). In this way, mRNAs can directly regulate the biosynthesis of protein products associated with the metabolites that bind them.

Suspiciously Elegant
The discovery of riboswitches was nearly as exceptional as the mechanism itself. In 1999, Ron Breaker of Yale University and his team were working on a class of synthetic RNAs, called aptamers, which bind to small molecules. It occurred to Breaker that the genetic methods that his group was exploiting to create these biosensors were so elegant and effective that it was surprising they hadn’t been observed in vivo (14). This speculation led to a search for natural riboswitch mechanisms.

The first natural riboswitches were found in genes involved in vitamin biosynthesis. These pathways had been somewhat perplexing to biologists, since no regulatory proteins had yet been associated with them (39). Investigations by Winkler et al and Nahvi et al found riboswitch regulation in B₁ (46) and B₁₂ (26) biosynthesis, respectively.

Intriguingly, Harold White III had suggested twenty-five years earlier that this type of binding between nucleic acids and coenzymes could be an artefact of a pre-protein world (44).

Relics of the Past?
Indeed, the discovery of riboswitches has been an exciting and confirming revelation for those biologists who believe early life was based on an RNA genome. This world is thought to have pre-dated DNA and protein and may have existed as many as four billion years ago (12).

The functional diversity of RNA has been appreciated for years; scientists have known of its roles as a carrier of genetic information and nucleic acid, amino acid adapter in translation, a primer for DNA replication, and a structural component in the ribosome. This ability of RNA to carry out so many essential cell functions, and particularly its pervasiveness in protein synthesis, is suggestive that current biological systems have their origins in an ‘RNA world.’ In addition to the afore-mentioned repertoire, catalytic activity was attributed to RNA in the early 1980’s with the discovery of ribozymes (16). Thus, it is plausible that RNA could have supported many of the essential roles presently represented by DNA and protein.

Although the discovery of ribozymes bolstered the theory of an ancient biological system based on RNA, some critical questions remained unanswered. Among them was how gene expression had been regulated according to signals from the environment if proteins had not yet evolved. Riboswitches seem to have answered this question.

The presence of riboswitches across the domains further supports the theory that they were involved in early forms of gene regulation. Although at this point, most known riboswitches have been identified in bacteria, there is emerging evidence of these systems in archaea and eukaryotes as well, particularly in the case of the THI-box riboswitch (17, 37, 43). Known riboswitches and their hosts are detailed in Table 1. Note that many of the organisms known to contain riboswitches are those that are well- studied (Bacillus) and have been subject to searches. Essentially, riboswitches can only be found where they are sought, and there is great promise that the host range for this unique genetic control system will expand with the appreciation of its significance in the scientific community.

Table 1 – Overview of known riboswitches and their mechanisms (integrated from 18, 29, 37, 40, 43 and 49)

Methods of Action
Despite the as yet still limited study of natural riboswitches, these mRNAs have proven themselves to be quite variable in their methods of action. Known methods include formation of stem-loops that lead to transcription attenuation (occlusion of RNA polymerase), inhibition of translation initiation (exclusion of ribosome at Shine-Dalgarno site, or RBS), or, as more recently seen in the glmS riboswitch, cleavage of mRNA (49).

It appears that organisms use different mechanisms in the functioning of the same riboswitch (35). As in traditional protein regulation, the trend seems to be that Gram-positive bacteria tend towards transcriptional regulation and Gram-negatives towards translational regulation (4, 41). However, this is merely a trend and not a rule, and the regulatory mechanisms may be seen in any bacterium, regardless of Gram stain characteristics. Indeed, two mechanisms may even act to regulate the same riboswitch element in the same cell. This appears to be the case in the B. subtilis RFN element, in which binding of flavin mononucleotide (FMN) acts on the rib operon mRNA via transcription termination but acts on the ypaA transcript via sequestration of the RBS (45).

In all cases, specific, high affinity binding of a metabolite effector to a highly conserved non-coding region of its cognate mRNA initializes a conformational change in the mRNA that leads to the formation of a stem-loop structure. Where this stem-loop forms, the characteristics of the region involved determine the overall effect of the binding. Figure 2 illustrates the known possibilities, which will be discussed below.

Figure 2. – Three known mechanisms of riboswitch action upon binding of metabolite (M): a) Transcription termination. b) Inhibition of translation initiation. c) Auto-cleavage. (From 35.)

Transcription termination
In conditions of low effector concentrations, these transcripts have an anti-terminator in their secondary structure that prevents the formation of a terminator loop. Binding of a metabolite to a nearby riboswitch element in the mRNA induces a change in secondary structure that destabilizes the hairpin anti-terminator in the mRNA. As the anti-terminator dissociates, the sequence formerly part of the stem is revealed and allowed to pair with a terminator sequence (Fig. 2a). The resultant terminator loop is usually located in the 5’ UTR and is often followed by a downstream polyuridine tract (18). The terminator loop thus reduces the stability of either the mRNA:RNA polymerase interaction and/or of the DNA:RNA hybrid in a rho-independent manner (27). This causes the RNA polymerase to dissociate, terminating transcription prematurely.

Inhibition of Translation Initiation
Alternatively, riboswitches may act at the level of translational control through the sequestration of the ribosome binding sequence in the mRNA. When no metabolite is bound, the Shine-Dalgarno (SD) site is exposed and the ribosome can bind and initiate translation. Binding of the metabolite to the 5’ leader region of the mRNA induces the formation of an SD:anti-SD stem-loop structure that masks the ribosome binding site such that initial step of translation, binding of the ribosome to the mRNA, is not achieved (Fig. 2b).

Auto-cleavage
Auto-cleavage is the most recently-discovered and possibly the most remarkable riboswitch mechanism known thus far. Whereas the previous two mechanisms have each been observed in multiple riboswitches and in a variety of bacterial systems, the only riboswitch with ribozyme action known to date is the glmS-box discovered by Winkler and his group as recently as 2004 (49).

Located in the 5’ untranslated region of the glmS gene, this riboswitch is astonishingly specific to its ligand, glucosamine-6-phosphte, whose binding increases the rate of cleavage 1,000 fold (49). The precise mechanism of cleavage remains unknown, but Winkler has proposed that it is accomplished through internal phosphoester transfer, which he noted has been studied in other known riboswitches (49). In short, it seems that the conformational change induced by the binding of the ligand to the riboswitch brings adjacent nucleotides in line with each other in an orientation that favours cleavage (Fig. 2c).

Other Methods of Action
All of the riboswitch effects described above have related to repression of gene function upon binding of a specific metabolite involved somehow in that gene’s function. It has, however, also been suggested that the same mechanisms could be involved in positive gene regulation as well (18, 29). In these cases, binding of a metabolite would release the terminator hairpin or liberate the SD-site, permitting full transcription or translation, respectively. Although this type of control has not yet been observed in natural systems, there is no reason to rule it out.

There is also speculation that eukaryotic riboswitches have the potential for more complex methods of regulation. For example, it has been suggested the riboswitches could also potentially play a role in the processing and transport of mRNA in eukaryotes (29). Again, this has not yet been observed, but bearing in mind how recent is the discovery of riboswitches, it may just be a matter of time. Our understanding of these elegant control systems is only just beginning to develop.

Identifying a Riboswitch
Several techniques are available to geneticists to detect, confirm, and investigate the presence of new riboswitches. Some of the most popular experiments include sequence analysis, lacZ fusions, and in-line probing and equilibrium dialysis, respectively, and will be discussed below.

Sequence analysis
As mentioned above, known riboswitch elements are well-conserved across genera (9). This makes sequence analysis a particularly useful tool in searching for new riboswitches. At present, at least two databases are available to investigate the sequences of putative riboswitches: Breaker Lab Intergenic Sequence Server (BLISS) and the Riboswitch Finder.

These databases are based on known riboswitch sequences and scan entries for related motifs. They are also able to predict the structure of the putative riboswitches, can evaluate the statistical probability of a positive identification, and have a low false-positive rate (3). The success of these search engines has been attributed to the pervasiveness of riboswitches throughout prokaryotic regulation of metabolism (3).

LacZ fusions
Once an RNA sequence has been singled out as a candidate for a new riboswitch, tests must still be carried out to substantiate the hypothesis. A simple and popular test is the lacZ fusion (20, 46).

The upstream region of the gene of interest is amplified by PCR. The product, which contains the proposed riboswitch region, is ligated into a plasmid upstream of and in-frame with the lacZ gene. ß-galactosidase expression should now be under control of the putative riboswitch.

Cells are transformed with the vector and successful transformants are found using a selectable marker present on the plasmid (for example, ampicillin resistance). Inducers can then be added that are known to be involved in the regulation of the original gene, and the effect can be measured with ß-galactosidase enzyme assays to detect the levels of LacZ in the cell. Sequencing should also be performed to confirm the identity of the regulatory region – this is done to test the integrity of the ligation reaction.

This type of assay is particularly useful in determining the specificity of a riboswitch for its ligand by using various analogs and comparing their effects. Many riboswitches are so specific that they will distinguish between something as small as an amino group exchanged for a hydroxyl group (49).

In-line Probing
This is a method to more accurately identify the 5’ and 3’ ends of the riboswitch region and calculate the size and apparent dissociation constant, K_D, of the ligand for its binding site. The K_D of riboswitches is completely analogous to the K_D of protein regulation systems, and represents the concentration of ligand that leads to a state of half-saturation of the binding site.

In-line probing relies on the fact that there is a natural rate of spontaneous cleavage within RNA. Cleavage occurs when a phosphodiester linkage is subjected to internal nucleophilic attack by the 2’ oxygen adjacent to and in-line with it (34). Structured regions of RNA, such as those in the base-paired stems of riboswitch stem-loops, are less susceptible to spontaneous cleavage than non-structured regions (25).

Therefore, assessing the cleavage products of a given riboswitch sequence in the absence of its cognate ligand can yield helpful information about the size, structure and precise location of the riboswitch. Such analyses are accomplished by amplifying the riboswitch region by PCR, making RNA copies of the PCR product, subjecting the products to cleavage, separating the resultant fragments with polyacrylamide gel electrophoresis (PAGE), and sequencing them (20, 25). An extension of this technique involves calculating the relative amounts of cleavage products in varying concentrations of metabolite ligand to calculate the K_D of the ligand:riboswitch complex (25, 34).

Equilibrium Dialysis
This is another popular technique used to identify which ligand binds a particular riboswitch, and what the K_D for that ligand is. The experimental setup consists of two chambers separated by a membrane: One chamber contains a solution of the riboswitch element, the other contains a radiolabelled form of the metabolite of interest (20). If the metabolite has binding affinity for the riboswitch, its concentration will shift towards the chamber with the riboswitch solution. If not, there will be no change in concentration. Higher binding affinities attract higher concentrations of metabolite towards the chamber with the riboswitch solution.

This, along with the lacZ fusion method, is a simple and convenient way to test the specificity of a riboswitch for its ligand.

Putting it all together: the RFN-box
The riboflavin (RFN) riboswitch was one of the first to be discovered and also appears to be one of the most common in natural systems (21). It serves as a good example of the steps involved in discovering and investigating a new riboswitch, as well as the mechanism of action in vivo.

At the beginning of the 1990’s, riboflavin, or vitamin B₂, was part of the perplexing puzzle of vitamin biosynthesis regulation. Although it was clear that negative regulation of genes involved in synthesis of vitamins was occurring, there was no “smoking gun”(18); no repressor proteins had yet been identified for these pathways.

However, what had been recognized was that the 5’ UTR of the rib operon was well conserved throughout Gram positive bacteria (9), and that mutations in this region led to the loss of negative control and over-production of riboflavin in the cell (11, 15). It was also known to have extensive secondary structure, folding into five hairpins with well-conserved sequences in the base pairs of the stems (9) (Fig. 3).

Figure 3 – The structure of the RFN element showing invariant bases (capitalized), well-conserved bases (lower case), and variable bases (R, Y, K, B, V, N or X) (From 41)

Taking a cue from studies of synthetic aptamers that bound RFN in vitro (1, 19, 31), Mikhail Gelfand was the first to suggest that this region may directly bind a metabolite regulator.

Shortly thereafter, Vitreschak et al published their results of an extensive sequence comparison study done on RFN elements (41). They found that these elements were present both in Gram positive and Gram negative bacteria, but their location and the arrangement of the rfn genes were somewhat different in each case.

In Gram positive organisms such as Bacillus, the rfn genes were arranged in operons, which contained genes coding for both metabolic and transport-related proteins. In most cases, each operon was preceded by an RFN element followed by a run of thymidines, indicating a potential transcription terminator.

By contrast, Gram negatives tended to have rfn genes distributed singly throughout the genome. These were more often preceded by an RFN element that overlapped the RBS, suggesting the presence of a sequestor for inhibition of translation initiation.

Though this study provided more insight into the pervasiveness of RFN elements across genera, as well as the regulation of rfn genes, it did nothing to confirm or deny the direct binding of metabolites to the RFN box. This was confirmed a few months later in a study by Winkler’s group (45).

This study took advantage of in-line probing to show that the structure of the RFN element was altered by addition of flavin mononucleotide (FMN, a riboflavin analog and derivative) to a solution in the absence of protein. Furthermore, the dissociation constants for FMN, riboflavin, and flavin adenine dinucleotide (FAD) were measured and were found to be quite different, at K_D = 5 nM, 3 µM, and 300 nM respectively. Amazingly, the phosphate group that differentiates FMN from riboflavin seems to make a 1,000 fold difference to the binding affinity of the ligand for the RFN element. This element was clearly very specific for its ligand.

Sequence analyses revealed yet another interesting twist to this element. While the majority of the rfn genes in B. subtilis were under riboswitch-mediated transcriptional control on the rfn operon, a lone gene, ypaA, believed to code for a transporter involved in riboflavin biosynthesis, was under control of a different riboswitch. The location of this riboswitch indicated a role in the sequestration of the RBS, that is, in translational control. This may be evidence of horizontal gene transfer of riboswitches between organisms.

Thus, Winkler’s study was the first to conclusively show that genes for riboflavin biosynthesis and transport were under control of direct metabolite-binding to mRNA, and that the region where this occurred corresponded to the well-conserved 5’ leader sequence known as the rfn element. This group’s findings were confirmed later in the same year by a similar study conducted by Alexander Mironov (24).

Implications and Applications
Since the discovery of riboswitches only a few years ago, at least seven different riboswitches have been found to exist in dozens of organisms spanning the kingdoms. It has been estimated that at least 68 genes in B. subtilis (2% of the genome) are under the control of these mRNA regulatory sequences (36). When one considers the elegance in the simplicity of the system, the potential for rapid response times, and the economics of not having to make a protein, it may be surprising that these elements are not more widespread. But the fact is that proteins did evolve, and thus there must have been a motivation for them. One advantage of proteins is that they provide more variation and flexibility than their polynucleotide cousins: there are 20 amino acids compared to just four ribonucleotides. Furthermore, their ability to act in trans allows for the biological cross-talk and intricate signalling pathways that are so important to regulatory networks. Clearly, riboswitches do not contain all the answers, but they have been overlooked for years and are now receiving the recognition they deserve.

What kind of future lies ahead for these unique mRNAs? Antibiotic potential has been suggested as one possibility (6, 48). Given the central role of riboswitches in essential cell metabolism, it is conceivable that they could be exploited to the detriment of their host. Synthetic analogs of riboswitch ligands could be engineered to shut off central metabolic pathways, arresting the growth of the bacteria. There is a hope that this type of antimicrobial treatment would be less toxic than the alternatives, since RNA is targeted instead of protein (18).

They could also be used for the same purposes as the synthetic aptamers that led to their discovery: as molecular chemosensors for measuring chemical composition or biochemical secretions (5). Given that the affinity for ligand in the natural systems is so much higher than their synthetic counterparts (29), this could develop into a sensitive new branch of biotechnology with applications in research and medicine, among other fields.

A further possibility is that of using riboswitch fusions to trans-genes as a means to regulate gene inserts through small molecule inducers (18). This could have widespread applications in genetic research, and even in medicine and gene therapy.
Yet another possible application is the use of riboswitches in taxonomic studies. Though regions of riboswitches are well-conserved, there are distinct variable regions that have been indicated as being dependant on taxonomy (41).

A better understanding of this relationship could lead to the use of riboswitches as another tool in determining the evolutionary relationships between organisms.

Probably the biggest task in current riboswitch research is getting a grip on just how widespread this mechanism is. If these elements are indeed relics of an ancient RNA world, then they have been under our noses all along, waiting to be discovered. It is humbling to think that RNA has surprised us yet again in its spectrum of capabilities. It leads one to wonder how much we have missed. There is a sense that the seven known riboswitches are just the tip of the iceberg.

It is difficult to say what time and research will reveal about the scope of riboswitch control in prokaryotes and eukaryotes alike, but one thing is certain – riboswitches have finally earned their spot in the repertoire of metabolic regulation mechanisms.

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Inspired by:

Cavalcanti, S.M.C. and Knowlton F.F., 1998. Evaluation of physical and behavioral traits of llamas associated with aggressiveness toward sheep-threatening canids. Applied Animal Behaviour Science, 61(2): 143-158

Franklin, W.L. and Powell, K., 1993. Guard llamas. Iowa State University—University Extension Publication, Ames, IA, 12 pp.

Markham, D., 1990. Llamas Are the Ultimate: Training, Feeding, Packing, Hunting, Fishing, and Care. Snake River Llamas, Idaho Falls, ID, pp. 8–14.

Markham, D., 1993. Warning to coyotes; this sheep ranch is guarded by llamas. Rocky Mountain Livestock Journal, Dec.-Jan., 29–33.

Meadows, L.E. and Knowlton, F.F., 2000. Efficacy of guard llamas to reduce canine predation on domestic sheep. Wildlife Society Bulletin 28(3): 614-622

- – - – -

Make no mistake about it: your life is in danger. Whether it be from the crazed smack addict willing to do anything for his next hit, a rival eager to revenge a perceived slight or an urbanized harpy eagle, your survival is constantly being threatened. The only way to ensure the safety of you and your family is to take your protection into your own hands: you, my friend, need a llama.

There are a few issues to consider when purchasing a llama. Firstly one must find a suitable llama supplier. There are many sources of high quality guard llamas including your local llama farm, llama brokers, the classifieds, the internet or any llama events that you might be attending including Llama Jamboree 2006 being held in Bute, Montana. Wherever you purchase your llama it will be wise to ensure that the animal is registered with the International Federation of Guard Llamas (IFGL). This will indicate that the llama has undergone the proper training in a variety of disciplines ranging from the basic predator guarding up to the more advanced hostage negotiation. You should decide beforehand what skill set you would like your llama to possess. There is nothing worse than an overqualified llama. For instance a llama, trained in the delicate arts of diplomacy, will become depressed and distant if it is only given the task of guarding your ’86 Chevy Cavalier from any would-be vandal. Consequently, it will probably let its guard down and you will be left with a llama with very low self-esteem and an antennae-less ’86 Chevy Cavalier with the words “Wash me” scrawled onto the dirt caked rear windshield.

When selecting an appropriate llama you should be looking for alertness, leadership ability and weight. Even the strongest llama won’t be able to defend you if they can’t first perceive the threat. Therefore, steer clear of any animals that show a tendency towards myopia or a fondness for drink. Also, the larger the animal the more aggressive, so go big. But don’t go too big, an obese llama is an ineffective llama. Most importantly though, you want a llama that shows initiative when it comes to scaring off coyotes, aggressive panhandlers and other predators, but that is not overly dominant. Remember, you are the boss, if you want to watch “Gilmore Girls” you should not have to endure a shower of llama-spit to do so.

Once you have purchased your llama you will now have to care for it. Luckily llamas are great scavengers and adapt quickly to an urban setting. It will probably be enough to simply give the llama a few hours of free time a day and it will be able to feed itself whether it be by grazing in local playing fields or surgical strikes on the grocers around the corner. If your llama begins to stay out for longer and longer periods of time be wary. Recently there has been a marked increase in llama gangs. These no-goodniks prey on young llamas that are new to the city and you do not want your new guard animal falling in with a disreputable crowd. I think we can all agree that the elderly made this country what it is today and should not, in their twilight years, have to suffer the indignity of being harassed by groups of idle llamas in ill-fitting leather jackets.

It is important to remember that llama disasters can occur, particularly through heat stress and improper training. Llamas are not equipped to handle high heat and humidity. If your llama starts to drool, breathe with its mouth, stumble and/or become depressed it is most likely suffering from heat stress. There are many ways to avoid this problem most of which are common sense: provide plenty of shade and drinking water/sports drinks, do not allow the llama to consume any fescue grass, dress the animal in only those novelty sweaters that are weather-appropriate etc. There is also a danger of Berzerk Llama Syndrome, which arises when baby llamas are over-socialized. You will know a berserk llama when you see one so it is unlikely that you will purchase a llama only to find out about its incessant head butting when you get it home. However, if you are raising your llama from birth you should remember that it is not a replacement for the children you can’t have but rather a wild animal that should be treated as such.

Llamas are not only great guard animals they are also great friends. Do not be afraid to confide in your llama for they are renowned in the animal kingdom for their discretion and tact unlike the talkative moose. They are also fiercely loyal and have a keen sense of irony. As long as you treat your llama with the care and respect it deserves your life together will surely be a long and rewarding one.

(This paper was designed by a group of students for a class project, and as such is completely fabricated)

TITLE:
Stoners eat your broccoli: Folic acid enhances the effects of cannabinoids at behavioral, cellular, and transcriptional levels

ABSTRACT:
Recent interest in cannabinoid receptors as therapeutic targets has spurred the investigation into the physiochemical responses to their activation. The cannabinoid pathways in mammalian systems of adult male CD1 mice were investigated using a combinatorial approach based on folic acid mediated response. Various tests of cannabimimetic activity of folic acid showed that the combination of folic acid with either AEA (N-arachidonoylethanolamine, ananamide) or THC (∆9- tetrahydrocannabinol) amplified the effects of the cannabinoid. Levels of cyclic AMP (cAMP) in brain tissue also show a marked reduction after the addition of folic acid to either AEA or THC at both 1 and 2.5 µM dose levels in comparison to the cannabinoid alone. Genetic studies using CB1 -/- knockout mice suggest the existence of a CB3 receptor localized in the brain tissue of mice that has yet to be cloned or characterized. In the CB1 knockout mice, addition of folic acid and THC resulted in a 129% increase of [3H]THC binding in the cortex and significant increases in all other areas of the brain when compared to THC alone. This indicates that folic acid is indeed affecting the neurotransmitter pathways of the cannabinoids by potentially acting with a third cannabinoid receptor. Using serial analysis of gene expression, it was found that transcription levels of genes shown to be up-regulated by cannabinoids were further increased upon addition of folic acid. ©2002 Elsevier Science B.V. All rights reserved.

(download pdf of paper here)

ABSTRACT:
Recent political efforts to broaden the scope of science education and bring science into the mainstream have generated a great deal of controversy. One of the things that has been sorely missing is the relationship between mathematics and religion. Here we attempt to inject a greater mathematical essence into religion as well as explore one immediate implication, the Immaculate Induction Hypothesis.

1. INTRODUCTION: We focus on the injection of a greater mathematical sensibility within the religious community and examine the resulting implications. In doing so we agree that intelligent design is a valid viewpoint, but ask what this implies. We find that this implies a countable sequence of all-powerful and all-knowing entities going back through all time. The basic argument is that the complexity of the known universe implies the existence of a creator. The union of the creator and creation is a set that is more complex than just the universe and thus implies a creator of the larger set. An induction hypothesis follows readily from this approach.

The motivation for this work comes from recent efforts to inject the ideas of intelligent design into the science curriculum which have generated enormous attention of the main stream media. Unfortunately, both sides accuse the other of being close minded. In a game of “tug of war” both sides must be recalcitrant in order for the game to continue.

The current situation comes as little surprise to those of us in the mathematics community. We have been well aware of the proclivities of both sides. We have been long time observers of both sides and have noted these tendencies for many millennia. The mathematics community itself is also composed of people who share most of the traits of both sides, dogmatic, religious fervor combined with supreme arrogance, and we watch this terrible conflict with an awful understanding of the pain felt on both sides.

It is for this very reason that the mathematics community can no longer sit on the sideline. In particular we address the need of a greater mathematical ethic within the religious community through a preliminary investigation of intelligent design. This may seem one sided, but the close relationship that has developed between the mathematics and science communities (with the exceptions of chemistry, biology, geology, and psychology) is already well documented and subject to intense scrutiny.

2. THE GENESIS STORY: There have always been some tension between science and religion. Ironically, this tension has been focused on seemingly minor issues. The trial over Galileo’s assertion that the earth revolves around the sun relies on a single, ambiguous statement within the Hebrew bible. Men of great intellect and passion clashed over a trivial statement that has since been all but forgotten.

We now find ourselves with a similar clash. We are focused on the story of our origin. Again the clash centers on a relatively minor aspect of a broad tale. This time it is the Genesis story that is at the center of the conflict. One might think that the Genesis story is really about the gift given to us by the Creator. This is the gift of creation but more importantly the gift of free will. We were given creation and allowed the freedom to experience it on our own terms with all of the associated responsibilities.

It is easy to think that the story of Genesis comes down to the simple message that it is immoral to force particular beliefs onto others. Such a simple interpretation ignores the powerful draw of the story of our origin. It is the story of our origin that has become the focal point of conflict. The primordial draw of the question of our origin drives us in a way that is beyond reason or explanation.

The sacred texts of Christianity, Judaism, Islam and all other religions provide numerous examples about the relationships between the weak and powerful, the rich and poor, and provide explicit guidance on how we should treat one another. Rather than focus on such simple ideals which are already clearly articulated within each of the sacred texts we instead focus on the much more difficult and important story of our origin.

3. THE MATHEMATICS OF THE CREATOR: Our only way of studying the creator is to examine creation. The universe is a collection of simple objects that when brought together represent a staggering set of interactions. We are capable of studying and generating a basic understanding of small parts but are incapable of understanding the whole. For example, while sitting within this goldfish bowl we call “earth,” light seemingly strikes us that appears to have been generated millions of years ago from events taking place on spatial scales beyond our understanding. At the same time the molecular kinetics of proteins within our own cells exhibit nonlinear, chaotic oscillations that taken together create the reliable, stable clockwork that makes life possible. This complexity implies the existence of a creator.

All things around us has been created, and we denote creation as the “universe” or more formally as U₀. That which initiated the creation of U₀ has the full power and understanding of all that is within U₀. All that is within us and beyond us is contained in U₀ and thus is a part of the understanding and abilities of the creator. At the same time the creator, denoted C₀ is an integral part of creation. The two do not stand apart rather are part of the unity of the “Grand Design.” Taken together we denote the union of C₀ and U₀ as G₀.

From where did G₀ arise? The subtle interactions found within U₀ imply the existence of C₀. The cardinality of G₀ is greater than or equal to the cardinality of U₀, since:

We find that a creator, denoted C₁, must exist that can explain the intricacies of G₀. From the existence of C₁ we find that G₀ must be contained within another universe composed of all that created by C₁ which we denote U₁.

It is possible that U₁ be equal to G₀ but it is not necessary. Hence we have that:

We now have the basis for our induction hypothesis: C₁ initiated U₁. We denote the union of these two sets,

Since the cardinality of G₁ is greater than or equal to the cardinality of U₁ which was created by C₁ there must exist a C₂ that can explain the intricacies and complexities of G₁.

Proceeding in this way we must conclude in the existence of G₂. Applying the same reasoning implies the existence of a countable set, G_i, where

We leave the formal statement and proof of the Immaculate Induction Hypothesis as an exercise for the reader.

Finally, this construction of G_i leads to a fascinating array of corollaries such as

which we do not explore here. We leave these as work to be completed with hopes that they will provide an enormous draw to this new and fascinating field of study.

4. CONCLUSION: In this paper we examine the mathematics of creation and uncover just one implication, the Immaculate Induction Hypothesis. The availability of the power of mathematical analysis helps make clear the connections between the sacred and the profane. In this one example we examine the implication of just one simple religious truth, the complexity and beauty of the world around us imply the existence of a creator, C₀.

Through this one example we readily see that the power of mathematical analysis is a necessary component of any complete religious education and makes the case that greater mathematical content be added to the religion curriculum. This is necessary because the practice of religious study requires the communication of complex ideals with intricate interactions. Religious dialogue requires that we discuss and share the nature of infinite love and the infinite universe. In doing so it simply is not possible to share the full spectrum of the sacred without the language of mathematics.

Put simply, it is self-evident that the nature of religious dialogue has all the hallmarks of a hidden grand design. The intense and complicated interactions of nearly all human thought hide an underlying intelligence that can only be explained by the presence of an intrinsic, hidden mathematical structure.

A crab might compete with a lobster for grotesqueness
rolling back carpets or just have one claw
feeding upsidedown in an underwater whirlwind
or wearing fancy stripes with plaid
but the lobster will just sit there
letting the tomfoolery tumble over her backside
she’ll do nothing but let her whiskers be taken
in time-honored ribbons by the swift dark sea
not moving an inch and win by a mile

GMO. Wait. Slow.
Are there enough tests on you
I just don’t know. Yo

(Haiku by Azar)

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