Positional Association Rules Dr. Bernard Chen Ph.D. University of Central Arkansas

Central Dogma of Molecular Biology

Amino Acids, the subunit of proteins

Protein Primary, Secondary, and Tertiary Structure

Protein 3D Structure

Protein Sequence Motif Although there are 20 amino acids, the construction of protein primary structure is not randomly choose among those amino acids Sequence Motif: A relatively small number of functionally or structurally conserved sequence patterns that occurs repeatedly in a group of related proteins.

Protein Sequence Motif These biologically significant regions or residues are usually: Enzyme catalytic site Prostethic group attachment sites (heme, pyridoxal-phosphate, biotin…) Amino acid involved in binding a metal ion Cysteines involved in disulfide bonds Regions involved in binding a molecule (ATP/ADP, GDP/GTP, Ca, DNA…)

HSSP-BLOSUM62 Measure

Future Works

Motivation In order to obtain the DNA/protein sequence motifs information, fixing the length of sequence segments is usually necessary. Due to the fixed size, they might deliver a number of similar motifs simply shifted by several bases or including mismatches

Example If there exists a biological sequence motif with length of 12 and we set the window size to 9, it is highly possible that we discovered two similar sequence motifs where one motif covers the front part of the biological sequence motif and the other one covers the rear part.

Positional Association Rules The basic association rule gives the information of A => B However, under the circumstances of the “order” involved with the appearance of items, the basic association rule is not powerful enough we introduce another parameter called “distance assurance” to help identify frequent itemset with frequent distance

Positional Association Rules

Pseudocode of Positional Association Rule with the Apriori concept Algorithm: Positional Association Rule with the Apriori Concept Input: Database, D, (Protein sequences as Transactions and Sequence Motifs as items), min_support, min_confidence, and min_distance_assurance Output: P, positional association rules in D Method: L = find_frequent_itemsets(D, min_support) S = find_strong_association_rules(L, min_confidence) for (k=2; Sk ≠ Ø; k++ ) for each strong association rule, r Sk antecedent_motif = Apriori_Motif_Construct(r_ant) consequence_motif = Apriori_Motif_Construct(r_con) if antecident_motif == NULL or consequence_motif == NULL: goto Step (4) for each protein sequence, ps D for (ant_position=1; |ps| ; ant_position++) if antecedent_motif start appear on ps[ant_position]: r_ant_count++ for (con_position=1; |ps| ; con_position++) if consequent_motif start appear on ps[con_position]: distance = ant_position – con_position rdistance ++ Pk = { rdistance | rdistance > min_distance_assurance * r_ant_count } Apriori_Motif_Construct(itemset) if |itemset| == 1: return itemset else: for each positional association rules in P|itemset| if all items in the itemset appear in the positional association rule: return the new motif constructed by the positional association rule return NULL

Positional Association Rules Example

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60%

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% Scan for C1 A: 3/5 A B: 5/5B C: 2/5 => => AB, AD, BD D: 4/5D E: 1/5

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% Scan for C2 AB: 3/5 AB AD:3/5 => AD => ABD BD: 4/5 BD

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% Scan for C3 ABD: 3/5 => ABD => no C4

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% Therefore, the itemset that pass support: {AB, AD, BD, ABD} Next, we need to compute their confidence

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% First, we work on 2-itemset: {AB,AD,BD} A=>B: 3/3 B=>A: 3/5 A=>D: 3/3 D=>A: 3/4 B=>D: 4/5 D=>B: 4/4

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% then, we work on 3-itemset: {ABD} A=>BD: 3/3 B=>AD: 3/5 D=>AB: 3/4 AB=>D: 3/3 AD=>B: 3/3 BD=>A: 3/4

minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% Thus, the strong association rules we have: 2-itemset 3-itemset A=>BA=>BD A=>DAB=>D B=>DAD=>B D=>B Next, we work on Positional Association rules…

Positional Association Rules D=>B minimum distance assurance = 60% 1. = 3/4 3.=1/4 2.= 1/4

Positional Association Rules B=>D minimum distance assurance = 60% 1. = 3/63. = 1/6 2.= 1/6

Positional Association Rules A=>B minimum distance assurance = 60% 1. = 2/43. = 1/4 2.= 1/4 4. = 1/4

Positional Association Rules A=>D minimum distance assurance = 60% 1. = 3/4 2.= 1/4

Positional Association Rules AD=>B minimum distance assurance = 60% 1. = 2/3 2. = 1/3

Positional Association Rules AB=>D minimum distance assurance = 60% NO Positional Association Rules on AB !!!

Positional Association Rules A=>BD minimum distance assurance = 60% 1. = 2/4 2. = 1/4