# Supervised Dynamic Correlated Topic Model for Classifying Categorical Time Series
## 4 Application for Promoter Sequence Identification in _E. coli_ DNA Sub-Sequences  
Proteins are one of the most important classes of biological molecules, being the carriers of the message contained in the DNA. An important process involved in the synthesis of proteins is called transcription. During transcription, a single-stranded RNA molecule, called messenger RNA, is synthesized (using the complementarity of the bases) from one of the strands of DNA corresponding to a gene (a gene is a segment of the DNA that codes for a type of protein). This process begins with the binding of an enzyme called RNA polymerase to a certain location on the DNA molecule. This exact site, which determines which of the two strands of DNA will be a transcript and in which direction, is recognized by the RNA polymerase due to the existence of certain regions of DNA placed near the transcription start site of a gene, called promoters. Because determining the promoter region in the DNA is an important step in the process of detecting genes, the problem of promoter identification is of major importance within the field of bioinformatics. We considered a dataset of 106 _E. coli_ DNA sub-sequences that is publicly available at [[https://archive.ics.uci.edu/dataset/67/molecular+biology+promoter+gene+sequences](https://archive.ics.uci.edu/dataset/67/molecular+biology+promoter+gene+sequences)]([https://archive.ics.uci.edu/dataset/67/molecular+biology+promoter+gene+sequences](https://archive.ics.uci.edu/dataset/67/molecular+biology+promoter+gene+sequences)) (accessed on 12 March 2023), among which 53 DNA sub-sequences contain promoters and the remaining 53 DNA sub-sequences do not contain promoters. Each sub-sequence consists of 57 nucleotides, represented by the four nucleotide bases: adenine (\(a\)), guanine (\(g\)), cytosine (\(c\)), and thymine (\(t\)). Given the two sets of DNA sub-sequences, with and without the presence of promoter regions, we used sDCTM to uncover the hidden patterns or motifs that could serve as markers for promoter presence to classify the sub-sequences. A detailed data description is provided in [31]. We present the results of the sDCTM model applied to analyze the E. Coli DNA sub-sequences. We treated each DNA sub-sequence as a document and the presence/absence of promoter regions as the associated class label. Each word in the document was represented by the nucleotide observed at that position in the sub-sequence. We divided the data into an 80-20 train-test split in order to assess the model performance. We trained the model on data with \(M_{tr}=86\) (number of train DNA sub-sequences) and set \(T=57\) (length of each DNA sub-sequence), \(V=4\) (number of unique nucleotide levels), and \(C=2\) (indicating the levels of the response variable). To choose the number of topics \(J\), we ran the model for different values of J and chose \(J\) based on the highest test accuracy. We set the number of latent topics as \(J=3\). The confusion matrices obtained on the train and test data with \(M_{\text{Tsl}}=20\) (number of test DNA sub-sequences) using the sDCTM model are shown in Tables 5 and 6. We were able to achieve a training accuracy of 100% and a test accuracy of 90%. The distribution of nucleotides accross the three topics identified by the sDCTM model is shown in Figure 2. We observed that nucleotide levels \(a\), \(c\), and \(g\) were highly probable within Topic 1, nucleotide level \(t\) was highly probable within Topic 2, and nucleotide level \(a\) was highly probable within Topic 3. In addition, based on the model predictions, we also constructed a sequence logo plot [32] to identify the diversity of sequences between the two predicted groups. The sequence logo plot based on the train model predictions are shown in Figure 3. We can see that that the promoter presence plot demonstrated significantly higher conservation at various positions compared with the promoter absence plot. The higher bits values in the promoter presence plot highlight critical motifs essential for promoter activity.