This text describes the score assigned to the entire corpus of
regulatory information associated with two genes: the guide-species
gene and one of its orthologs.  This score, called the
ConservedRegulationScore, will be generated for every potential
ortholog of a guide gene in every species.  Then, the supporting gene
in each non-guide species with the highest ConservedRegulationScore
among orthologs in that species will be selected.  Finally, the set of
selected orthologs will be sorted by ConservedRegulationScore and used
in best-rank fashion to rank all guide-species genes.


ConservedRegulationScore

Properties: 

1.  Expresses the expected # of pairs of conserved functional modules
as the sum of module-pair probabilities 
   P(M1 functional)P(M2 functional)P(M1 and M2 are orthologous)

2.  Assumes the approximation that the unique module-to-module mapping
(which may not involve all modules of each gene) that produces the
spatial arrangement of sequences with maximal conditional probability
of conservation is the actual mapping.

3.  Each module-pair probability of functionality and conservation is
in (a) log space, and (b) in fixed proportion to P(ortho|score)

4.  More-is-better.  All else being equal, a gene-pair with more conserved
functional modules will score higher.

5.  Only conserved functionality is honored.  All three factors in the
module-pair probability must be good in order for the overall score to
be good.  The approach is that, while any one module could look like
it likely regulates the gene in question, whether it is conserved is
an independent question.  Similarly, even in the face of high
conservation, one or both modules need not be viable in terms of
regulation.  The scoring procedures for both of these are independent.





GeneRegulonSimilarity

Seeing as how each gene may have multiple associated modules, there
are many ways in which the modules associated with two orthologous
genes can be matched up and pairwise compared.  The
GeneRegulonSimilirity, or weighted regulatory similarity score is a
measure of the overall similarity in how two different orthologous
genes are regulated.  The GeneRegulonSimilirity assumes that a subset
of modules belonging to each ortholog map one-to-one to each other.
Given this mapping, there are a set of pairs of regulatory relations,
which can be compared each by an RegulonSimilarity.  The weighted sum
of RegulonSimilarities is taken, with the weights being the product of
the RegulonFunctionalities of each of the two modules.  Since the
RegulonFunctionalities are probabilities, the product of
RegulonFunctionalities represents the probability that both Regulons
are functional, and the weighted sum then represents the expected
value of the sum of RegulonSimilarities that involve functional
modules.



WholeGeneScore

As provided, groups of genes comprise mixed orthology/paralogy
relationships.  CisOrtho makes the assumption that true orthology
relationships must be one-to-one between two species.  Implicitly, it
assumes that among all species analyzed, there is one which is the
organism of interest, and the rest are used as supporting species for
conservation analysis.  So, it proceeds as follows:

For each ortholog group OG,
  For each gene GG in guide species,
    For each support species SS,
     
      Find gene in SS with maximum GeneRegulonSimilirity with GG and
        add to the set of supporting species.


Thus, this produces one or more sets of { (gene1,
GeneRegulonSimilirity), (gene2, GeneRegulonSimilirity), ... (geneN,
GeneRegulonSimilirity) } for each guide gene GG in the guide species.
This list of supporting genes and their regulatory similarities may be
used in opportunistic rank fashion, taking the best-ranking score in
its coverage class (class from 1 to N supporting species).


Drawbacks: 

The set of one-to-one module relationships found between each pair of
genes (one guide-species gene and one supporting gene), called a
bijection, naturally defines an N-jection for a set of N-pairs
involving the same guide-species gene.  While each bijection is chosen
to optimize the GeneRegulonSimilirity for that gene pair, the implied
N-jection, though it optimizes the set of N GeneRegulonSimilirity
scores, it does not necessarily optimize the remaining
GeneRegulonSimilirity scores in all (N-1)(N-2)/2 gene pairings *not*
involving the guide species.

To calculate this optimal N-jection would require a very large search.

However, it should be noted that the RegulonSimilarity measure obeys
the triangle inequality because it is itself a weighted sum of three
components that also obey the triangle inequality.



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