Informatics describes the study and practice of creating, storing, finding, manipulating and sharing information. There are many other neologisms and phrases derived from this: bioinformatics, chemoinformatics, health informatics, nursing informatics, poli-informatics, for example.
Bioinformatics is a largely but not exclusively computational subject. In the biological sciences, bioinformatics is so central to understsanding the enormous data sets that characterise modern biology that it is arguably not a separate discipline. Nevertheless the theory of information is extremely important and a comprehensive book can be read on the Web thanks to David J C MacKay at Cambridge.
The following is the only survivor from the original Web site (this revision August 2015). These notes accompanied a set of lectures on the chemical and biological background to bioiformatics for students who had studied neither chemistry nor biology.

1: Biological chemistry in time and space

Time scales

Here is a summary of history from the big bang to today.

The units on the abscissa are 10^-12 years. The scale is approximate and, arguably, contentious. Also the cartoons might be misleading: the old world continents were formed quite recently and we do not know what the first form of life might have looked like. This form of life was probably some kind of "bacterium" but the cartoon is realistic in the sense that the organism was certainly not green. The point we make is that life on earth occupies a significant proportion of the "history of everything" on a linear scale on the abscissa. Although we look at this in more detail in

Size scales

Complexity

Molecular shapes

We cannot cover all organic chemistry but there is no shortage of references.
We need to recall the valencies ("combining power") of some of the elements of importance in biological chemistry.

Chirality

Conventions

A "rule" (more exactly a mnemonic) used by biochemists for describing the absolute configuration of an L-amino acid is "CORN".

Properties

Dissociation of acids and bases: The group -CO₂H is the "carboxylic acid" group. Our carboxylic acid is acetic acid and in water it forms an equilibrium mixture with the -vely charged cognate anion (acetate) and a hydrated hydrogen ion (correctly the "oxonion ion") H₃O⁺ as shown in (a). (b) emphasises that the two C-O bonds in the acetate ion are not different as (a) implies: the π electrons are delocalised so each O atom carries half a -ve charge. Note it is this delocalisation and the consequent spreading of the load of carrying a negative charge between 2 O atoms that means that acetic acid can dissociate and "is an acid" unlike (for example), ethanol Et-OH. (c) shows the conventional way of writing the equilibrium: we take it as read that water has reacted and that H⁺ is in reality H₃O⁺ and not a proton (sub-atomic particle).
Ammonia is a weak base, i.e. it reacts with water and in the equilibrium mixture OH^- (hydroxide ions) are formed.

Oxidation and reduction: In the illustration (acetaldehyde and acetic acid) "oxidation" is the addition of O (or the abstraction of 2H) and "reduction" is the addition of 2H (or the abstraction of O).

Addition: A simple reaction of the form:
    A + B → C
is an addition. The example shown would seem to be obscure to a reader of elementary chemistry texts but is important in carbohydrate chemistry. The red O is to clarify which parts of the addition product come from where.
Condensation: A simple reaction of the form:
    A + B → C + D
where D is a simple molecule such as water is a condensation. Again red atoms are coloured to clarify the reactions:
(a) is the reaction of an acid and an alcohol to form an ester
(b) is the reaction of an acid and an amine to form an amide.
both of these reactions could, in principle, be reversed by the reaction of the ester or amide with water and these reactions would be examples of hydrolysis.
(c) is another method of forming an amide (it is the method used in protein bioisynthesis) and in this an alcohol not water is removed.

Delocalisation and tautomerism: we saw that the π electrons in the acetate ion are delocalised. Other examples are benzene (a) and its derivatives. The two structures are referred to as the canonical forms of benzene.
(b) phenol, hydroxybenzene. Phenol is a weak acid because the negative charge is delocalised: two canonical forms of the phenate anion are shown in (c).
(d) is pyridine, i.e. it is similar to benzene except one of the CH groups in the ring has been repalced by N.
(e) What are these?... "hydroxy-pyridine" or something else (it would be called "pyridone")? Answer: yes !. These are not "canonical forms" because we have moved, not just π electrons but an H atom as well but the fact remains that the two structures in (e) are in equilibrium, they cannot be separated and are referred to as tautomers.
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References

Equilibrium

From the table, we can see that for a reaction such as:
    X ↔ Y + Z
in which substance X dissociates to form Y and Z, theres will be an equilibrium constant, K:     K = [X]/([Y].[Z])
and, as K is a constant (at a given temperature etc.), the equation can be used for calculating the value of two of the concentrations, given a knowledge of the other one.
The dissociation of acetic acid in water is an example of such an equilibrium. If we call acetic acid, AcOH, the equation becomes:
    K_A = ([H⁺].[AcO^-)/[AcOH]
(K_A is the acid dissociation constant). Likewise the solution of ammonia in water can be represented as
    NH₃ + H₂O ↔ NH₄⁺ + OH^-
    K_B = ([NH₄⁺].[OH^-])/[NH₃]
Don't worry about the seeming loss of [H₂O] .... water has an effective unit acitivity in this reaction... in other words, "if an H₂O molecule is needed, there'll be one on hand".
Acetic acid is a "weak acid" and ammonia is a "weak base" which is another way of saying that the two constants K_A and K_B are very small. We take as examples a strong acid, HCl and a strong base NaOH. In solution these are effectivley completely dissociated:
      HCl   → H⁺ + Cl^-
    NaOH → Na⁺ + OH^-
Thus in 1mM HCl [H⁺] is 10^-3 and the pH is 3.
What about 1mM NaOH? For this we need to know K for the dissociation of water itself... it is 10^-7 and thus the pH of pure water is 7 (referred to as neutrality) so the pH of 1mM NaOH is 10.

Now we'll have another look at the equation
    K_A = ([H⁺].[AcO^-]/[AcOH]
Rearrange and take logs to the base 10 (remembering what we mean by "p") and you should end up with:
    pH = pK_A + log₁₀([OAc^-]/[HOAC])
Now we look at what happens if we have a mixture of HOAC and a salt such as sodium acetate (NaOAc) both in solution. To first, approximations, [AcO^-] is the same as [NaOAc] because it is a salt and dissociated and [HOAc] is the conentration of acetic acid we put in the solution (provided, as is the case with acetic acid, K_A is very small. So for such solutions containing a weak acid and a salt of that acid, the equation is one beloved of biochemists who call it the Henderson-Hasselbalch equation:
    pH = pK + log₁₀([salt]/[acid])
Clearly this has some applications, given the pK of acetic acid (it's around 4.0) and we are asked to go into a chemistry lab and make up a solution of, say, pH 5.1, we can use the equation to work out how much HOAc and NaOAC to weigh out and dissolve in water. However the importance of this equation is that the solution is an example of a buffer. This refers to the fact that the pH is relatively insensitive to addition of small amounts of acid and alkali. It is left as an exercise for the reader to convince herself(himself) of the justification for this claim. The important point is that biolological fluids whether within cells, in fluids such as blood or in a solution for experiments in a biochemistry are all buffered with mixtures (not typically the acetic acid/acetate system though).

Equlibrium

Symbol	Meaning	Equation/explanation
T R	Absolute temperature Universal Gas Constant
H	Enthalpy or "Heat Content"	H = U + pV where U is internal energy; p, V are pressure and volume.
S	Entropy	A measure of disorder in a system
F (or A)	Helmholz Free Energy	F = U - TS
G	Gibbs Free Energy	G = H - TS
a	Activity	a thermodynamic function that describes the effective concentration of a substance; for many cases in solution, for substance X, aX  is approximately [X].
Go	Standard free energy	G at unit activity; it appears as a constant in equations such as the following which describes G for the ith component of a system: Gi = Gio + RTlnai
	Standard free energy change	Take the reaction W + X ↔ Y + Z i.e. RTlnK  IFF we accept the "a is [ ]" approximation.
ΔG	Free energy change	For the reaction W + X → Y + Z

1. A + B → C + D
2. C + E → F + G
3. F → H + J

• pumping of nutrient molecules up a concentration gradient
• formation of bonds in the synthesis of complex compounds from simple ones
• biosynthesis of nucleic acids and proteins^*

Reaction rates

Rate constants
A rate constant, k appears in differential equations that describe the rate of reaction. For example in a simple reaction
A→B
let a be [A] at time 0 and at time t, [A]=(a-x) then
rate of reaction = dx/dt = k(a-x)
If we integrate this, evaluate the constant of integration by noting x=0 when t=0 we have:
   kt = ln(a/(a-x))
For a slightly more complicated case, A + B→C
and using the same conventions,   dx/dt = k(a-x)(b-x) which can also be integrated.
What about "really complicated reactions"? .... in fact reactions of the sort written down as "balanced equations" in school chemistry texts are all broken down into simple reactions with one reactant (unimolecular) or two reactants (bimolecular). Genuine trimolecular reactions are chemical curiosities.
What does k mean? Let us take the simple reaction molecules X and YZ. The reaction is bimolecular and the products are going to be XY and Z.

Amino acids peptides and proteins

Carbohydrates, nucleotides, polynucleotides

Protein structure

DNA structure

6: Genomes, gene regulation and protein biosynthesis

Genes and gene expression

• gene a sequence of DNA (RNA in some viruses) which is responsible for an inherited character. In many cases the gene product is a protein
• chromosome a DNA sequence that exists as a continuous molecule and contains several genes. Bacteria contain one chromosome; other forms of life contain several (or many in the case of ferns)
• genome all the chromosomes
• genetic system In animals and fungi, the mitochondria have their own chromosomes the phrase "mitochondrial genetic system", in contrast to the nuclear-cytoplamic genetic system, is used to describe this. This is true also of plants and they also have a chloroplast genetic system. Mitochonrial and chloroplast genes are inherited maternally (also called "non-Mendelian inheritance").
• haploid and diploid A cell that contains one set of chromosome is haploid; one that contains two sets is diploid. Bacteria are haploid. The somatic cells in tissues such as fingers, heart, root, leaves... are diploid but germ cells are haploid. Some fungi have haploid somatic cells. The word ploidy is useful to describe organisms whose somatic cells contain other than one or two sets of chromosomes (wheat is an example).
• allele a version of a gene. Although this is somewhat over-simplified, human eye colour, at least in European races, can be regarded as having blue and brown alleles. This introduces the idea that brown is dominant in this case as a person with both alleles will have brown eyes. The same idea can be expressed by saying that blue eyes are a recessive character.

• Not all enzymes are proteins: some, the ribozymes, are RNA molecules
• Errors that occur during DNA replication are corrected
• There are mechanisms (quite complicated in some cases) for regulating macromolecular biosynthesis
• Macromolecules are not merely sysnthesised: RNA and protein are turned over
• Many of the processes are thermodynamically highly unfavourable
• There is an important difference between the eukaryotic system and that in bacteria, mitochondria and chloroplasts. Most DNA in eukaryotes is in a separate cell compartment, the nucleus, and RNA is transported to the cytoplasm for translation. In bacteria etc. there is no nuclear membrane and not only do transcription and translation occur in the same cell compartment but they can be coupled, i.e. translation occurs while transcription is taking place.

Sequence relationships; the Genetic Code

The relationship between the 2 DNA strands and between the transcribing strand obey the rules of complementarity. The relationship between the sequence of mRNA (or the + strand of DNA) and the protein is the Genetic Code, which is a 3-letter non-overlapping code: 3 nucleotides (usually referred to as "bases") constitute a codon and, for example, the 2nd amino acid in pCro is E, the codon is GAA.
For a "biochemist's view" and "a modest suggestion for a better view" click here.

Well, that seems fairly straightforward because "we knew" how to relate the cro and pCro sequences. If we had known that and merely had a piece of DNA sequence, there would be two problems: (1) are we dealing with a plus or minus strand? and (2) where do we start looking up the codons?
The example below is part of the cro gene.

The complexities of the components of the gene expression system ensure that that cells can solve the problem. One task in bioinformatics is to enable us to do that.

Metabolism: some principles (i) Enzymes

Enzyme kinetics

The rates of simple enzyme catalysed reactions of the form S → P1 + P2... (we use S to stand for Substrate) follow the Michaelis-Menten equation: v = Vmax.[S]/([S]+KM) where KM is the Michaelis constant and Vmax is the maximum velocity. The equation represents a hyperbola: -KM and Vmax are asymptotes.

Implications of the Michaelis-Menten equation:

• K_M is charactersitic of the enzyme and has the dimensions of concentration (typical values would be of the order of 1 mM)
• K_M is determined by the amount of enzyme in the preparation used for the measurement
• A small K_M results in a steeper dependence of velocity on [S] and this can be expressed that enzymes with low K_Ms have high affinity for their substrate.

Limitations of this treatment:

• We have not considered reactions of the type
  S1 +S2 → P1 + P2...
  However there are such equations but they depend the mechanism of the enzyme catalysed reactions
• More complicated kinetics are involved in allosteric enzymes in whcih the binding of compound (which may or may not be a substrate) affects the activity of the enzyme.
• Equally we have left unexplored the properties of enzyme inhibitors but note here that competitive inhibitors reduce K_M but leave V_max unchanged.
• The major limitation to this type of equation is that K_M values are derived from rate constants describing the association and dissociation of substrate(s) with enzyme and the dissocation of product(s). Biochemists express this by stating that these are steady state kinetics and note gloomily that many enzyme catalysed reactions in vivo are not at the steady state.

Nevertheless we can learn:

• Enzyme catalysed reactions are saturable which gives us in principle a simple chemical mechanism for recognising thresholds and performing a switch.
• Kinetics of the Michaelis-Menten type apply equally to transport processes. To take two examples:
  • the reason why plants can scavange incredibly low concentrations of soluble phosphate from soil is that their roots (or in some cases symbioitic fungi) have phosphate uptake systems with very low apparent K_Ms
  • imagine you are resting after a meal of fish and chips, cream cakes and sweet tea. Your blood glucose will be very high and glucose will enter your red blood cells but not in a great rush. Glucose transport in this case is thermodynamically favourable but it does not diffuse into your blood by simple dialysis. It enters through a process of facilitated diffusion whose rate is determined by a red-cell glucose transport protein.

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Metabolism: some principles (ii) triphosphates and REDOX

Now come to my promised examples of the use of ATP and other triphosphates in the thermodynamically difficult jobs of making polynucleotides and polypeptides.
For the polynucleotides we shall consider the chain extension reactions and use a slightly expanded version of the abbreviated sequence. We shall draw the 3'-terminus of a polynucleotide as
....NpNpNpNOH
, i.e. N for nucleosides and a small OH as the 3'-terminal OH. Further we draw the template strand (always DNA) in black, the growing strand in blue and the next residue in red. The enzymes (RNA- or DNA- polymerases) are only parts of the machinery of DNA replication and transcription.
3'...ApApCpTpGpGpCpApApCpTpApApGpGp...5'
5'...TpTpGpApCpCOH + pppGOH →
3'...ApApCpTpGpGpCpApApCpTpApApGpGp...5'
5'...TpTpGpApCpCpGOH + pp

      pp → p + p

These two favourable reactions allow the unfavourable formation of a new phosphodiester link and the unfavourable entropy change involved in selecting just one (G in this case) out of a possible of 4 nucleoside triphosphates.

With protein synthesis there are two separate steps: activation of amino acids and peptide bond formation. An essential component of the system is transfer RNA (tRNA) and we shall represent its C-terminus as above. Each amino acid has its own small family of tRNAs. The activation step takes place in two stages. We represent an amino acid thus H₂NaaCO₂H and ATP as pppA:

1. there is a growing chain of polypeptidyl-tRNA attached to a suitable site and an aminoacyl-tRNA is selected by nucleic acid complementarity between the codon (in mRNA) and a sequence, the anticodon in the aminoacyl-tRNA. This process involves proteins called elongation factors and one GTP molecule is concommitantly hydrolysed to GTP + P_i.
2. The polypeptidyl tRNA and aminoacyl tRNA react:
   (N)....aa^X-tRNA^X + H₂Naa^Y-tRNA^Y → (N)....aa^Xaa^Y-tRNA^Y + tRNA^X
   This reaction is catalysed by a ribozyme, peptidyl transferase, a component of the ribosome and does not require hydrolysis of ATP or GTP.
3. The mRNA "tape" has to be threaded through the ribosome and, following conformational changes, a new site for aminoacyl-tRNA is brought into register over the next codon. This process is translocation and requires hydrolysis of GTP.

Metabolic networks

1. Biochemical pathways are actually components of networks
2. Thermodynamic considerations dominate the subject
3. There are 2 useful nouns
   • catabolism (adjective catabolic) metabolism that results in the breakdown of more to less complex substances, i.e. -ve free energy changes
   • anabolism (adjective anabolic) metabolism that results in the biosynthesis of more complex substances, i.e. +ve free energy changes
4. The networks are described as "metabolic maps"^* and there are several resources on the Web, e.g.
   • in Japan,
   • Switzerlan and
   • Germany
   ^*They are graphs rather than maps but the metaphor might have been be derived from "maps" such as that of the London Underground.

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   Regulatory networks

   Regulation can involve several chemical interactions:
   1. Rearrangment of DNA sequences
   2. Alternative splicing of mRNA precursors
   3. Interaction of transcription factors and DNA
      1. the transciption factors can repress transcription
         1. this can require binding of a co-repressor to the repressor
         2. this can be inhibited by the binding of an inducer to the repressor
         3. very "simple" mechanism: is the repressor present or absent?
      2. the transciption factors can activate transcription
   4. Translational control
      1. Attenuation
      2. masking of translational iniation
         1. by antisense RNA
         2. by RNA-protein interactions
   5. Enzyme regulation
      1. substrate availability, saturation kinetics etc.
      2. allosteric mechanisms
      This list is by no means comprehensive: very approximately we can regard the list from 1 to 5 as representing coarse to fine control. Not all mechanisms apply to all cells and all circumstances and it must be emphasised that these mechanisms apply to components of what are typically extensive regulatory networks. These are just a few generalisations and examples.
      Examples of 1 and 2 can be found in the immune system and some of the methods used by invading micro-organisms to evade it. Another example of 1 is the ability of yeasts to undergo a "sex change", correctly a switch in mating type. We return shortly to 3 but note here that we have left a lot out of 3.2 and examples of this include many processes controlled by hormones. 4.1 involves the optional recognition or non-recognition of transcriptional terminators: the mechanism relies on the fact that RNA polymerase, recognises a terminator sequence in its transcript, not in its template. 4.2.1 is perhaps worth considering briefly: the method is used in the genetic engineering of certain crop plants and as an approach to treatment of genetic diseases but it does occur naturally, for example in E. coli. Again, a gross over-generalisation: 5 is very characteristic of cells in animals, plants and fungi but bacteria tend to rely on 3.1, 3.2, 4.1 and 4.2 for regulating the activities of enzymes because they are designed to respond to changes in their ecoment but there is simply not enough room in (for example) an E. coli cell for biochemically significant amounts of every enzyme that might come in useful.

      I shall not consider these regulatory networks in detail but rather shall just show one example of how a protein considered previously can effect a switch: an irreversible one in this case. cro is a gene in lambdoid phages. Phages (short for bacteriophages) are bacterial viruses. Some, including the lambdoid phages, are said to be temperate which means that, following infection, the phage can either be reproduced with (in the case of these phages) lysis of the cell or can establish a state known as lysogeny in which the phage DNA is incorporated into the host's genome as a prophage. (This use of the affix pro is used more generally: e.g. HIV forms a provirus in infected cells.) The sketch below shows part of a lambdoid prophage.
      
      In a lysogen, the only prophage gene to be expressed is cI but if pCI is inactivated, pCro appears in the cells and, following this, the first stage in induction, cI is never expressed again: the E. coli cell is doomed and lysis and release of more phage particles is sure to occur after about 3/4 of an hour. The system is designed to allow prophage to be propagated as part of the E. coli genome until the cell is at risk: a system, not described here, ensures that pCI is destroyed if the cell is exposed to UV or ionising radiation or to genotoxic chemicals. Given that, the phage make use of their 50 genes to construct new phage particles, to traverse the environment and find a new host.
      Two final points about the cI-and cro (also known as immunity) system.

      1. It is vastly over-simplified in the sketch: there are 3 binding sites for pCI and pCro in the regions of (i) P_L and (ii) the overlapping P_R and P_M sites and pCI and pCro actually compete with each other bu titrating out the more favourable sites.
      2. The sites these proteins bind to are operators and are palindromes. The binding of pCro to one of its palindromic sites in DNA (such regulatory DNA sequences for -vely acting regulatory proteins are, in bacteria, referred to as operators. Two pCro molecules and the operator form a ternary complex.
      
      

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      Neural networks

      This section is included to give computer scientists interersted in artificial neural nets (ANNs) access to intructory material on real neural nets. One type of simple ANN devised for machine learning might rely on a sigmoidal or logisitic activation function:
      
      ... and might be used in a "feed-forward" ANN for machine learning;

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      Of course there are many different designs for ANNs and in particular we refer to the completely connected Hopfield networks but my task here is to draw attention to differences between neurons in vivo and the artificial neurons, perceptrons... ("units" in the diagram).
      First there are more neurons (10¹¹ in a human brain).
      Secondly, they do not look much like computer hardware or software:
      
      Thirdly the anatomy of the brain involves the very precise organisation of neurons, e.g. in layers achieved by having axons of different lengths (the axons are electrical conductors and the myelin is an insulator).
      The diagram highlights them. Here is another more anaimated) diagram and one from a more psychological perspective. Link 1 and Link 2 to tutorials on computational aspects.
      Oct. 2009 replacement of defunct links.

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      8: Classification and ontologies in biological sciences

      Contents	Speciation Enzymes and Molecules
      Abstract	Biological classification or taxonomy was originally based on the scoring of characters in specimens. The systematic method of doing this was an early example of computer aided linkage analysis. Modern taxonomies rely on macromolecular sequences. Enzymes are classified in a system of "EC numbers". The heirarchy in this case is less easy to parse.
      Objectives	At the end of this topic, the student should have a working knowledge of the principles and practice of biological taxonomy and to be familar with resources to relate EC numbers and enzyme activities.
      Why is this topic important?	Classification is important in relating current research studies to older literature descriptions.
      Why is it interesting?	Biological taxonomy is an example of an ontology.

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      Speciation

      The biological description and classification of organisms dates from a period of natural history. Most people are familiar with the idea that humans belong to the species Homo sapiens and therefore to the genus Homo of which H. sapiens is the only surviving species. We also have a sense that there are larger groupings: e.g. H. sapiens and monkeys are part of a tighter grouping than, for example, H. sapiens and rabbits and all of these are more "related" to one another than they are to fish, mushrooms, cauliflowers, seaweed, bacteria. The general name for categories such as species, genera, families... is taxon. The first systematic approach to defining taxa was made by Adanson in the XVIII century. The idea recognised that there are variations in populations of, e.g. H. sapiens but if we were to score characters (true or false) for enough specimens, the specimens could be put into taxa. A simple, not to say rather ridiculous, example follows.
      

      ↓ Character | Specimen →	1	2	3	4	5	6	7	8	9
      has 4 legs, 1 at each corner	1	1	1	1	0	1	1	1	1
      has a tail	1	1	1	1	0	1	1	0	1
      has course hair	0	0	1	0	0	1	0	0	1
      has soft fur	1	1	0	0	0	0	1	1	0
      makes miaowing sound when stroked	1	0	0	0	0	0	1	1	0
      is coloured black	0	1	0	0	0	0	0	1	1
      makes barking noise when needs feeding	0	0	1	0	0	1	0	0	0

      From this we may deduce that specimens 1, 2, 7 and 8 may be cats (although 2 may have a sore throat and 8 presumably comes from the Isle of Man) and 3, 6, 7 and 9 may be dogs (of which 7 and 9 are laudably quiet). We note that being black is a variable character in both groups and that we cannot say much about specimen 5. Nevertheless Adanson was well ahead of his time: this is an objective method and, given hundreds or thousands of specimens and characters there is a system of classification which worked very effectively for many years, notably in the characterisation of bacteria. Of course it awaited advances in statistics and the advent of computers to construct the clusters and to produce hierarchic taxa. Today the clustering might well be done by K-means but computational methods of linkage analysis were pioneered by Sneath and Sokal for Adansonian analysis. In theory at least the grouping of organisms into larger and larger clusters, e.g. species, genus, family, order, class... can be achieved by such methods. Modern taxonomies are based on clustering of macromolecular sequence data rather than characters such as colour etc. but, rather remarkably, the fit between classical and such "molecular" taxonomies is quite good provided we do not rely on "classical" methods to investigate relationships between deeply divided taxa.
      There are several problems surrounding these taxa of which here are a few.

      	Question	Possible answer	Problem
      1	What is a species?	defined by saying (i) 2 members of a species can interbreed but (ii) members of different species cannot	Any gardener or keeper of pet fish can tell you (ii) is not true and (i) fails for organisms that do not reproduce sexually.
      2	How are members of a taxon related?	They had a common ancestor	Among the bacteria (possibly higher organisms) genes or clusters of genes can be transferred between very unrelated organisms.
      3	How do we decide how the boundaries of a taxon might be defined?	let's say that a certain degree of similarity, sequence homology etc. defines a species etc.: S% for a species, G% for a genus, F% for a family... where S<G<F ...	Well that's not going to work too well! Using the criteria of bacterial taxonomy, humans, chimpanzees and gorillas would all be minor variations within the same species and yet they are not even in the same genus.

      Molecular biology and bioinformatics have resolved some of the problems of biological taxonomy. Sequence analysis has enabled the objective classification of organisms and consequently the familiar phylogenetic trees of biology text books can be extended considerably. The nature of the macromolecule to sequence depends on the nature of the problem we set ourselves. In the sketch I show 3 phylogenetic trees. Although the scales are not given, the qualitative conclusions are reasonably acceptable.
      
      If we are prepared for a root node, these are binary trees. In the case of 4 great apes, the root could be an animal believed to be an ancestor (e.g. a monkey as suggested in the sketch) or a fish. Such a root is referred to as and outgroup. With the three major divisions of life (b), we do not know what the ancestor might be as there is neither fossil record nor an extant intermediate form to help us but the word urkaryote has been coined to describe some eukaryotic antecedent with mitochondrial or chloroplast genetic systems. Part (c) describes to the current version of the history of life. Here we can estimate the time axis: some 4x10⁹ years. The Archaea resemble Eubacteria in that they have no nuclear envelope and are hence prokaryotes. Examples of archaea include the purple bacteria that grow in saturated saline solution and in several other extreme environments. Such trees can be constructed by macromolecular sequence comparison. In order to construct a tree such as (c), we need macromolecules which are present in forms of life, fulfil the same role in all of these and evolve slowly: rRNAs are the molecules of choice and it was analysis of the sequences of these that led to the recognition of the archaea (formerly "archaebacteria") by Carl Woese. Subsequenctly several other features link the archaea and the eukaryotes, notably the presence of introns. For (b), rRNA sequence data are reinforced by RNA polymerase sequence comparisons and certain metabolic similarities. The great ape classification relies on several points such as the sequence relatiobships of a a characteristic and variable region of mitochondrial DNA (mtDNA): the short sequence is not required for any known mitochondrial function and thus there is no (or at least little) selection against mutation. Moreover, the role of mitochondria in respiration results on a relatively high concentration of DNA-reactive reactive oxygen species (ROSs: examples include the superoxide ion ^-O₂ and its breakdown products).

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      Enzymes and molecules

      Biochemists established several years ago a classification for enzyme-catalysed reactions. The classification is in the hands of a committee, the Enzyme Commission, EC, which is perhaps a bioichemical counterpart of IEEE or ISO. In considering the EC systme it is important to recognise that it is not a classification of enzymes as proteins but rather of the reactions classified so, for example two enzymes might be structurally similar but catalyse different reactions. EC classifications are known as "EC numbers" and take the form EC N1.N2.N3.N4. There are plenty of W3 sites that summarise EC numbers but this is an official one. In summary there are six values of N1 from 1-6 and these plus a few extra examples are listed in the table below.

      N1	Description	number of N2's	examples
      1	Oxidoreductases	19+"97"
      2	Transferases	9
      3	Hydrolases	13
      4	Lyases	6+"99"	4.1 carbon-carbon lyases 4.2 carbon-oxygen lyases
      5	Isomerases	5+"99"
      6	Ligases	5	6.1 forming carbon-oxygen bonds 6.4 forming carbon-carbon bonds

      A full EC number would be, for example, EC 1.1.1.1 (alcohol dehydrogenase). Three points deserve making as they are important in any software that might be used in parsing EC numbers.
      1. as a tree it is very unbalanced
      2. large numbers are used to refer to reactions awaiting classification (e.g. the EC 1.97 enzymes)
      3. there are no rules for determining the nodes. For example, the EC 4.1 enzymes break C-C bonds but EC 6.4 enzymes form them.
      The EC system and biological taxonomy raise problems in bioinformatics because they are, to some extent rigid, and do not respond readily to advances in the molecular sciences. However they fulfill a separate role. They are useful in defining organisms or enzymes that are described in the literature before the current molecular understanding. Accepting this caveat, analysis of biological phylogenetic trees and the EC system are different problems. The fact that the EC system is a general tree (or possibly a forest of 6 such trees) is trivial as any general tree can be transformed into a binary tree. However, analysis of biological classification is a tree traversal problem whereas the EC system, despite its reliance on heirarchies, is essantially a look-up table.
      
      One of the successes of bioinformatics has been the developoment of methods for classifying macromolecules on the basis of sequence and structure. An important generalisation is that structure is more highly conserved than sequence. GOTO top
      

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      9 Recombination, repair, rearrangment and evolution

      Contents	Recombination (1) Recombination (2) DNA repair Evolution
      Abstract	Reciprocal recombination, not be confused with chromosome inheritance occurs during meiosis. Site-specific recombination is important in several events notably transposition of genes. Enzymes monitor DNA for evidence of damage or erroneous replication and effect repair frequently by re-synthesis. DNA biochemistry provides a mechanism for biological evolution and site-specific recombination and allied processes provide a mechanism for lateral gene transfer between bacteria.
      Objectives	At the end of this topic, the student should be familar with DNA rearrangements in genetic recombination, the response of cells to damaged DNA and should have an understanding of the role of molecular biology in providing plausible mechanisms for biological evolution.
      Why is this topic important?	Bioinformatics relies extensively on principles of change and evolution.
      Why is it interesting?	This topic has generated one of the most powerful heuristics in computer science: the genetic algorithm.

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      Recombination: part 1

      Below we look at the result of "reciprocal recombination". Blue and red parental double stranded DNA molecules have crossed over at the points marked X so that the sequences are changed. The sketch omits both biological and biochemical details but we can point out that the event occurs during the process of meiosis (or its equivalent) and that intermdiates not shown here involve a heteroduplex intermediate, i.e. a DNA molecule with one blue and one red strand. The numbers 1-9 represent genetic markers (let's just oversimplify and say "genes") and if the blue and red alleles are phenotypically different we find a new assortment of genes, e.g. the upper product of the cross is
      1 2 3 4 5 6 7 8 9
      The phenotype is the property. For example let us imagine that the cross occurs in some kind of fish with coloured spots and fins, that gene 2 determines the spot colour (blue or red) and that gene 4 determines the fin colour. The parental phenotypes are blue fins, blue spots and red fins, red spots. We have below the genotype of an offspring that has red fins (4) and blue spots(2).

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      Before we proceed, it is imortant not to confuse recombination of this sort with the assortment of chromosomes first described by Mendel in peas. The next cartoon shows some fish and we introduce a new character. Their eyes can be either dark or yellow:
      
      In (a) each parent has identical alleles for the eye colour gene (Ey or Ed for yellow or dark eyes. Each offspring inherits half of its chromosomes from each parent and the result in this fictitious case is that 3/4 will have the dark eyed phenotype because the Ed allele is dominant. In (b) we are looking at the assortment of characters involving also fin-and-spot colour. Note from the appearence of the right hand parent, the red "allele" (Cr) is seemingly dominant. It is possible to follow Mendel and calculate the expected frequencies of phenotypes in the offspring. Fish (c) can only arise from crosses such as that in (b) if recombination arises. Thus the C gene is actually 2 genes (we have called them 2 and 4) and offspring such as (c) will arise rarely. The genes 1 to 9 are said to be linked and chromosomes are thus examples of linkage groups.

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      Recombination: part 2

      The integration of the DNA of a lambdoid temperate phage into a bacterial chromosome is shown in the next sketch. Note that the DNA is circularised, the integration involves a single cross-over and, importantly, the gene order in the phage and prophage DNAs are different.

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      As the integration occurs at one of a very limited number of sites (only one in the case of the E. coli chromosome and the lambdoid phages) and a specific sequence in the phage DNA, this is an example of site-specific recombination. Finally we look at other examples (both taken from bacterial genetics) of comparable processes. To simplify the diagrams, double stranded DNA is drawn as a single line.
      
      The left hand panel shows that the integration of prophage DNA has its counterpart with certain plasmids ("episomes;") that can integrate into the bacterial chromosome. In these cases the "specific sites" are insertion sequences (ISs) and as these are mobile genetic elements, episomes can integrate at a wide variety of sites. The right hand side of the picture illustrates one type of transposition in which a transposable genetic element is copied from one site to another. The cartoon is meant to show such an element being copied from a plasmid to a bacterial chromosome but this is not the only circumstance under which this can happen. The events we have just covered have great implications for evolution but here we just tidy up a few points of nomenclature and other implications.
      1. Transposable genetic elements that carry genes for functions other than their own transposition are transposons
      2. ISs are examples of transposable genetic elements
      3. Transposons are not unique to bacteria: they cause genetic instability in several organisms and were first discovered as a cause for this in maize.
      4. Certain bacterial transposons include genes for resistance to anitbiotics, drugs and disinfectants.
      5. Certain bacterial plasmids are conjugative which means they can be "transferred" (actually they are copied as DNA replciation is involved) from donor to recipient cell and these cells to not need to belong to the same or even a related species.
      6. Conjugative plasmids are not the vehicles for gene transfer between bacteria: certain phages can do this and phage-mediated gene transfer from cell to cell is called transduction.
      7. The importance of points 4-6 to the clinical management of infectious diseases can hardly be overestimated. New arrangements of drug-resistance genes are constructed by these mechanisms.
      

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      DNA repair

      There is a lecture on this subject under Mol. Biol. An important consequence of DNA repair is that it can result in errors and hence in mutation.

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      Evolution

      The basis of Darwinism^* is that variations arise in populations and certain of these variants survive because they are in some sense fit. Darwin was unaware of Mendel's pioneering study of genetics and of course neither had any knowledge of molecular biology.
      ^* I have avoided referring to this as a "theory of evolution" because as a theory or hypothesis it is ill formed: as far as we know it has only happened once and cannot be tested. Perhaps Darwinism should be described as a diagnosis. A more formal account would be to observe that evolution is an example of emergent properties which takes us back to where we began.
      The cartoon below illustrates a present day view of Darwinism as it applies to 10 species (numbered in hexadecimal!).
      
      (a) Organisms 1-4 have a common ancestor A1234; we show one example of variant that became extinct between A1234 and A12/A34.
      (b) The fate of the lineage from A5678 is more complicated and we conclude that one extinction was due to some kind of catastrophe.
      (c) Some of A5678's decendents had a more successful history. (d) Natural extinctions occurred early in the lineage from the antecedents of A9A.
      Evolution has proceeded at an uneven pace. One factor is that large evolutionary change has a pre-requisite for DNA amplification and the selective advantage may not increase fitness. DNA rearrangement can result in big changes occurring over a short period of time and changes in a very small number of genes can affect the phenotype. For example, in recent human evolution, in which the species Homo erectus was displaced more-or-less successively by the H. sapiens types, Neanderthal, Cro-Magnon and Modern, one of events may have been neoteny, the retention of juvenile characteristics into adulthood and few mutations and/or recombinations might in principle achieve this.

      Lateral gene transfer mediated by mechanisms described earlier result in a more complicated pattern of inheritance. Drug resistance and the migration of genes been organelles are ex\mples of this.
      
      We have noted already the importance of the potentially very short time scale involved in such rearrangements.
      

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