The original OperonDB algorithm defined the concept of a gene pair, and estimated the probability that genes in a conserved gene pair belonged to the same operon (
4). A gene pair is defined as two adjacent genes (G1, G2) on the same strand, separated by at most 200 bp. A conserved gene pair is a gene pair that is found in two or more distinct genomes, where for pair (A, B) in genome G
1 and (C, D) in genome G
2, A and C are orthologs, and B and D are orthologs.
The probability that a conserved gene pair between two genomes belongs to an operon was estimated (in the original OperonDB algorithm) from the overall proportion of conserved gene pairs as:
where S and D are the sets of adjacent gene pairs on the same and different strands, respectively, SN is a subset of S that contains only pairs that do not belong to the same operon and P
chance is the probability that a conserved S pair has homologs in other genomes.
We recently re-designed the algorithm behind OperonDB to make it more efficient and to improve its accuracy. The new implementation has increased sensitivity due to a relaxation of the constraints required to assign a gene pair to an operon. For example, in the current implementation, we eliminate the adjacency requirement by requiring a gene pair to be co-linear, but allowing genes on the same strand to be separated by other genes with the same orientation. A threshold determines the maximum number of genes that are allowed to separate genes in any conserved gene pair. This relaxation allows for re-shufflings of gene order between species as well as genes inserted erroneously by misannotations. We also eliminated the 200-bp minimum separation between genes: while this limit works well for
E. coli, other species have different distributions of intergenic lengths, and genes within operons are likely to reflect this difference (
5).
By assuming that the conservation of a gene pair is independent of intergenic distance
l, we can rewrite
Equation 1 as:
where the two probabilities
P(
l|
S) and
P(
l|
D) define the probabilities for a given
S or
D pair to have length
l (estimated from the distributions of intergenic distances between same strand and opposite strand pairs, respectively).
Due to the enormous quantities of data involved when dealing with the numerous prokaryotic genomes available today, the most computationally intensive step in estimating the probabilities in
Equation 2 is the identification of conserved pairs. To speed-up this step, we identify all orthologs between all pairs of genomes with highly parallelized BLAST (
6) searches run on a grid-based system. We then find conserved gene clusters with a slightly modified version of the HomologyTeams (
7) software. The algorithm implemented by HomologyTeams is a fast way to identify sets of orthologous genes. Within the conserved clusters neither the order of the genes nor their orientation need to be conserved, but a fixed threshold limits the distance between adjacent genes. We modified the HomologyTeams program to allow conserved pairs to be separated by a fixed number of non-conserved genes as well. This modification allows us to estimate both
S and
D conserved pairs in the context of our relaxed definition of gene pair.
Although
Equation 2 is an attempt to compute the probability
P that two genes belong to the same operon, it incorporates several simplifying assumptions related to both the operon model (e.g. by assuming that
D pairs can never belong to operons) and the evolutionary reason for gene cluster conservation (e.g. by ignoring alternative causes such as lateral gene transfer). As shown previously (
4), these assumptions serve to make our estimate of
P more conservative; i.e. it is an underestimate. Therefore, for the remainder of this discussion we will use the term
confidence value instead of probability when we refer to the estimated value of
P.
The confidence value computed by
Equation 2 does not take into account the evolutionary distance between the species containing the conserved gene pairs. Intuitively, the probability that a conserved gene cluster is co-transcribed should be higher if a larger evolutionary distance separates the species. To reflect this fact, we first estimate the evolutionary distance between any two genomes
G1 and
G2 using the Jaccard distance (
8):
where
n(
Gi) is the number of genes in
Gi and
h(
Gi;
Gj) is the number of homologues from
Gj in
Gi. The previously computed confidence value for a conserved gene pair in two genomes
G1 and
G2 is then weighted with the ratio between
d(
G1,
G2) and the maximum genome distance observed in the database.
shows Receiver Operating Characteristic (ROC) curves of true positive versus false positive operon predictions for the new OperonDB database. The ROC curves are computed using a set of 602
E. coli operon pairs from RegulonDB (
9), all of which are supported by experimental evidence. In the figure, a true positive is defined as any prediction of a conserved gene pair that is contained in a documented operon, and a false positive is any predicted pair where only one of the two genes belongs to a confirmed operon from the
E. coli data set. Our new method shows substantial improvement over the previous implementation, especially for sensitivity levels >60%. Using , we can compute the accuracy (defined as the average of sensitivity and specificity) of the new OperonDB for all possible thresholds. The maximum accuracy achieved is 80%, which is comparable to accuracies obtained by other recent operon prediction methods (
10).
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