An algorithm for the display of nuddc add secondary structure

A simple algorithm is presented for the graphic display of nucleic acid secondary structure. Examples of secondary structure displays are given for tRNA, 5S RNA and part of the 16S RNA. Due to its speed, this algorithm could easily be used in conjunction with secondary structure programs which calculate various alternate structures. INTRODUCTION Ever since the first RNA was sequenced, considerable effort has been invested in Inferring the intramolecular base pairing (i.e. the secondary structure) of these molecules. Recently the comparison of secondary structures of ribosomal RNAs has been very useful In evaluating evolutionary relationships among diverse organisms, chloroplasts and even mitochondria [1-5]. It is clear In these works, that much time has been devoted not only in the determination of sequences but also in the graphic representation of these data. We present here a rapid, easily used algorithm for the automatic display of secondary structures of nucleic acids. THE DATA AND THE ALGORITHM The data for the algorithm consists of a string of letters (i.e. the primary structure) and a list of paired positions in this string (e.g. AACACCAUU / 1-9,2*8 is the input for a molecule which forms a "hairpin loop" with the first two A's paired to the last two U's). The input must obey a "no-knots" constraint: if "i«j" and "k»l" are two sets of base pairs then i) k and 1 are both between 1 and j 11) neither k nor 1 is between 1 and j © IRL Press Limited, Oxford, England. 8351 0305-1048/82/1024-835182.00/0 Nucleic Acids Research The strategy followed by the algorithm Is to first place (I.e. find the two dimensional coordinates) a base pair "i»j" where i and j are as far away as possible in the string (assuming i is less than j). This automaticaly determines the placement of (i+l)-(j-l), (i+2)-(j-2), up to (i+n)-(J-n) if i-j is the first in a series of exactly n+1 stacked base pairs in the secondary structure. Usually n is at least 1. When the procedure encounters a pair i*j for which (i+1) and (J-l) are not paired to each other, it must construct a loop. It does this by counting the number of bases in the loop as follows. The ith position count as one. If the i+lst base is not paired the count increases by one and the algorithm moves to the i+2nd position. If this is not paired it adds one, and so on. When a base is encountered which is at a paired position, e.g. position k, paired to position 1, it adds two and moves to the 1+lst position. This continues until we eventually arrive at position j. The n bases counted up to this point, including i and j are placed at the corners of a n-sided polygon for which the coordinates can be calculated based on the previous placement of the ith and jth bases. If all the bases in the molecule have now been placed, the algorithm stops as would be the case for the example which is depicted in Figure 1 . If some base pairs (e.g. k'l) have been encountered in counting n for the last loop however, there will remain some as yet unplaced bases (the (k+l)st to the (l-l)st bases). The algorithm then proceeds recursively, starting at each such base pair k*l in the loop, and so on, until all bases have been placed. The algorithm may be summarized as follows: while there remain unplaced bases ft J B I C H D G E F