Table 2 Description of module discovery tools

CisModule

CisModule models the structure of sequences with a two-level hierarchical mixture-model and uses a Bayesian approach with Gibbs sampling to simultaneously infer the modules, TFBSs and PWMs based on their joint posterior distribution, which is the probability of a model given the input sequence set. At the first level, sequences are viewed as a mixture of module instances and background. At the second level, modules are modelled as a mixture of motifs and inter-module background. Parameters of the model include the widths and representations (PWMs) of single motifs and parameters related to distances between modules and between TFBS within modules. From a random initialization, CisModule iteratively cycles through steps of parameter update and module-motif detection. New parameter values are sampled from their conditional posterior distributions based on the currently predicted modules and motifs, and new predictions of modules and TFBSs are then sampled based on these updated parameter values. Positions in the sequences where the marginal posterior probability of being sampled within modules was greater than 0.5 were output as module predictions.

Cister

Given a set of PWMs and parameters specifying the expected number of motifs in modules, the expected distances between motifs in modules and the expected distance between modules, Cister builds a Hidden Markov Model (HMM) with three basic states: motif, intra-module background and inter-module background. Transition probabilities between these states follow geometric distributions according to the expected values input by the user. In the motif state, one of the PWMs is chosen uniformly at random and used to decide the probabilities of outputting nucleotides. Background-state emission probabilities are estimated from a sliding window centered on the current base in the query sequence. From this HMM, the posterior probability that each base in the input sequence was generated from a module state as opposed to the inter-module state can be calculated. Predicted modules are defined to occur at local maxima of this posterior probability curve where the value is at least 0.5 and no larger value is observed within 1200 bp.

Cluster-Buster

Cluster-Buster is developed by the same group that made Cister and is designed to search for clusters of pre-specified motifs in nucleotide sequences. Like Cister, Cluster-Buster constructs a HMM-model based on the user-supplied PWMs, an expected distance between motifs in clusters and background distributions estimated from the input sequence over sliding windows. Log likelihood ratios are used to determine whether a sequence is more likely to be generated by a "cluster-model" or a "background-model". Cluster-Buster uses a linear time heuristic to rapidly estimate log likelihood ratios for all subsequences of the input sequence and outputs those subsequences with ratios above a specified threshold that do not overlap with other higher scoring subsequences.

Composite Module Analyst (CMA)

The promoter model in CMA is expressed as a Boolean combination of one or more composite modules (CM), each of which consist of a set of single, independent motifs as well as pairs of motifs that must obey certain constraints on distance and orientation. Given a candidate promoter model, the method searches for potential matches to the CMs in the sequences, and a final promoter score is calculated after the presence or absence of each CM is established. CMA employs a Genetic Algorithm to search for the promoter model which best discriminates between a set of positive (co-regulated) and a set of negative sequences. The fitness function is based on a linear combination of several properties of the distribution of the promoter scores and of the individual CM scores in the two sequence sets.

MCAST

MCAST builds a HMM-model consisting of an intra-module state, an inter-module state and motif-states based on the supplied PWMs. The score for a motif-state is called a p-score and is the negative logarithm of the p-value of a log-odds score based on the probability of a segment in the target sequence being generated either by the PWM or a fixed, user-specified zero-order Markov background model. MCAST forbids transitions into motif-states that result in p-scores lower than some chosen threshold. Some state transitions are associated with certain costs. For instance, entering the inter-module state from a motif-state incurs a large one-time penalty while cycling through the intra-module state incurs smaller penalties for each nucleotide emitted. The Viterbi algorithm is used to find the highest scoring path through the HMM with respect to the input sequence, classifying each position in the sequence as either belonging to a module or to the background. Potential module segments are scored according to the number of motifs in the module and the p-scores of these motifs and are penalized by the number of intra-module background bases. Finally, modules are ranked according to the estimated E-values of these scores.

ModuleSearcher

Given a list of PWM hits with match scores for putative TFBSs in a sequence set, ModuleSearcher finds the module model (set of k PWMs) that best fits the sequences. The score of a module model is calculated as the sum of scores over all sequences, and the score function for a single sequence is based on the best scoring set of TFBSs in the sequence that corresponds to the PWMs in the module model. To be considered a valid TFBS set the binding sites must all lie within a short window, and the user can choose to ignore TFBS sets with overlapping binding sites or penalize sets that lack sites for some PWMs. An A*-algorithm (or alternatively a Genetic Algorithm) is employed to search the space of possible subsets of k motifs from the full PWM library in order to find the highest scoring module model.

MSCAN

MSCAN discovers modules by evaluating the combined statistical significance of sets of potential non-overlapping TF binding sites in a sliding window along the input sequence. PWMs are compared against each position within the window to obtain match scores, and p-values are calculated as the probability of obtaining similar or higher scores at a specific position in a random sequence with nucleotide distribution similar to the distribution in the window. MSCAN proceeds by calculating significance scores for all combinations of up to k binding sites in the window and then selects the optimal combination (the one with the lowest score). A prediction is output if a final p-value computed from this score is less than some user-specified threshold.

Stubb

The HMM used by Stubb consists of motif states based on supplied PWMs and a single background state based on a k th-order Markov model with probability distribution estimated from a sliding window. The scoring function is the log likelihood ratio that the sequence within a limited window was more likely generated by the full model than with a HMM consisting of only the background state. Unlike the other HMM methods presented here, the transition probabilities between states in Stubb are not based on user-input expectancies, but are estimated from the sequence using the Baum-Welch algorithm. This procedure finds the set of transition probabilities that maximizes the scoring function. If Stubb finds that some motifs are highly correlated with respect to order, it can make use of correlated transition probabilities. This means that the probability of entering a specific motif state will dependent on which previous motif was output. Stubb can also utilize phylogenetic comparisons between sequences from multiple species to highlight potentially regulatory modules.