Edges

A component of a tree. Those which connect nodes have an evolutionary divergence associated with them, generally denoted as t_i. The sum of edge distance is an estimate of genetic distance.

Monophyletic group

All the individuals that are derived from a common ancestor. All ancestral taxa from a given node. Considered to reflect true genealogies. Infamous for instability, with many names for groups.

Uses a matrix to represent sequence alignments. Starting with sequence alignments, records the frequency of nucleotide matches in a matrix.

F_xy = (nAA/N nAC/N nAG/N nAT/N nCA/N nCC/N nCG/N nCT/N nGA/N nGC/N nGG/n nGT/N nTA/N nTC/N nTG/N nTT/N)

F_xy = (a b c d e f g h i j k l m n o p)

Corrections for evolutionary distance.

1. Correction for different substitution rates in the genome. Some domains are more conserved than others, in order to remain functional. Changes occur equally, but natural selection takes out individuals with mutations in crucial domains. 

2. Correct for nucleotide frequency in the genome. Baterial genomes are high in CG. Substitutions between nucleotides do not occur at equal frequency.

3. Correct for analysis of protein-coding sequences. Genetic code is redundant. Calculate distance with non-synonymous and synonymous substitutions separately; the former produces a distance five times greater!

Database for Annotation, Visualization, and Integrated Discovery

An online gene annotation investigation website. Contains functions of genes and gene ontology.

Holds the best scores for sequence alignments between one sequence (x) ending at position i, and another sequence (y) ending at position j. A common gap penalty is -8. There are three possible transitions to move from one state to another. Optimal score of an alignment, F(i,j), is the highest possible value of a previous optimum score, and the transition probability to the new state at (i,j). Uses BLOSUM 50 tables and penalties to obtain scores. The best alignment of sequences ending in x_i and y_j is a previous alignment score, plus the transition score to a new alignment. To obtain the best alignment, start at the best score, and follow the traceback through the matrix. The number of columns and rows is n + 2. A very error-prone process.

F(i,j) = max {F_{(i - 1,j - 1)} + S (x_i,y_j); F_{(i - 1,j)} - 8; F_{(i,j - 1)} - 8}

1. F(0,0) = 0. Adding both x1 and y1 residues together from a previous point.

2. F(1,0) = -8. Point back to the originating cell. Adding residue from x1 only to a previous alignment.

3. F(0,1) = -8. Point back to the originating cell. Adding residue from y1 only to a previous alignment.

A simple correction for hidden substitutions (back and multiple). Assumes all nucleotides have equal frequency, and equal rates of substitution betwen them. The deviation of d_xy from D decreases as D approaches 0.75, where d_xy is the corrected distance, and D is the population of nucleotides that have a difference.

D = 1 - (a + f + k + p)

d_xy = - (3/4) ln (1 - (4/3)D)

A parameter model that corrects for different transition and tranversion rates. Assumes equal nucleotide frequencies. If transitions and transversions occur at the expected ratio of 1:2, it produces the same calculation as Jukes and Cantor.

d_xy = (1/2) ln (1 / (1 - 2P - Q)) + (1/4) ln (1 / (1 - 2Q))

P = frequency of transitions = c + h + i + n

P = frequency of transversions = b + d + e + g + j + l + m + o

"An ancestral miRNA-1304 allele present in Neanderthals regulates genes involved in enamel formation and could explain dental differences with modern humans."

Noted that the miR-1304 seed region is the site important for identifying transcript targets, and it differs between Neanderthals and humans. Which species has the derived allele? What are target genes of the human and Neanderthal miRNAs? Are genes targeted by human miRNA associated with a specific process? Examined known DNA and a new sequence from a 49,000 year old sample, to ensure that amelotin and enamelin genes have miRNA target sites in Neanderthals.

A model which uses transition proabilities. Assumes probability of a residue depends on previous residues. Not intrinsically obvious how to use it. Helps obtain optimal alignments. The number of possible alignments can be astronomically high. It is impossible to evaluate them all for the best using a BLOSM matrix and gap penalties. Instead, captures the best alignment with fewer calculations. Calculates transition probabilities between different sequence residues. Works in logs, and sum of log P values.

P(x) = q_xi Π_{(i = 2)} r_x(i-1),xi

log (P(x)) = log (q_xi) + Σ^N_{(i = 2)} log (r_{x(i -1),xi})

x = sequence

q_xi = initial probability of some residue or sequence

r_{x(i - 1),xi} = transition probability between x_i and x_{(i - 1)}. Depends on previous states

N = length of alignment x.

MArkov TRAnsition of protein Structure evolution

A program designed to compare 3D protein structures. Unique because of its structural similarity score and various structure comparison methods. Allows researchers to infer functional properties of recently discovered proteins, classify protein structures, and view if certain protein structures were considered in evolution.

A criteria used in the optimization method of tree-making. The tree with the higest likelihood of probability is favoured. Assumes that substitutions are rare. Counts each change based on its probability. The goal is to obtain the phylogenetic tree, out of all possible trees, that would be the most likely to produce the observed sequences. Likelihood of a tree corresponds to the probability that a proposed evolutionary process and hypothesized history would give rise to the observed data.

P(data | model)

"Molecular evidence of HIV-1 transmission in a criminal case"

Richard Schmidt was accused of infecting his ex-girlfriend with HIV that had been drawn from a patient under his care. He had a sample of HIV-positive blood in his fridge. The ex-girlfriend later died of HIV. The HIV reverse transcriptase of the victim as well as Schmidt's patients were sequenced. A phylogenetic tree of the sequence showed that patients formed a paraphyletic group. The patient and victim's sequences were both monophyletic. Patient's sequences were closer to the victim's than other Louisiana HIV sequences. This supports the conclusion that Schmidt is guilty of murder.

Homo neanderthalensis

Diverged from humans 100,000 years ago. Became extinct 30,000 years ago. Had larger skulls than humans, but thinner tooth enamel.

Assumes independence of each site

P(X | M) = Πⁿ_{(i = 1)} {x_i}

log (P(x)) = Σⁿ_{(i = 1)} q_xi

x = sequence

x_i = probability of each nucleotide

Identifies the optimal local alignment between two sequences. Gives the best subsequence alignments. Aligns local motifs that are shared. Can identify shared domains between otherwise divergent proteins. Traceback begins from any point in the matrix, not just in the cell within the final row and final column. Ends when a 0 is encountered. Doesn't align the whole protein together. Similar to the Needleman-Wunsch algorithm, except there is a fourth possibility, 0.

F(i,j) = max {F_{(i - 1,j - 1)} + S(x_i,y_j); F_{(i - 1,j)} - 8; F_{(i,j - 1)} - 8; 0}

Tree-based Consistency Objective Function For alignment Evaluation

A multiple alignment software that uses global and local alignment software inputs to output an alignment and a phylogenetic tree. Algorithm involves weighting two libraries by building a primary library, then building an extended library where alignments in the primary library are compared to other sequences. Extended alignment is the stop that contributes the most to accuracy. Very accurate, but requires a lot of computational time to run the program. Can be used to discover novel proteins via homology, and align known proteins and genomes to create phylogenetic trees.

Leaf

Terminal taxa

A component of a tree. Represents sequences or organisms for which there are data. There is one possible tree with three terminal nodes, three possible trees with four, 15 possible with five, 10 million possible with 10, and 2.2 x 10²⁰ possible with 20. The number of possible trees with n nodes is:

B(n) = Πⁿ_{(i = 3)} (2i - 5)

A global multiple sequence alignment software. Can be customized by assigning penalties for gaps and mismatched nucleotides. Capable of multiple sequence alignments, phylogenies, alignment visualizations, and more.

1. Pairwise alignments done between sequences

2. Similarity matrix used for building guide trees to organize alignments

3. Combines and aligns sequences following branch order in the similarity tree