Visualizing Biological Information

The following sections are included:

• Preface

• List of Contributors

• Contents

• References

• Glossary

Proteins and nucleic acids are linear biological polymers of 20 and 4 building blocks respectively. The sequence of building blocks along the polymer determines the properties of the protein or nucleic acid. By convention, letters of the Roman alphabet represent such sequences. This representation consumes more space than necessary and hampers the visual recognition of interesting and important features of the sequences. The Puppy representation of sequences of nucleotides overcomes these problems for nucleic acids. We designed two representations for the sequences of amino acid residues in proteins. In a minimal representation, each residue type is depicted by a different series of vertically aligned marks. In the second representation, "Kitty", the characters reflect chemical structures of the residues. Comparison of the two representations for the amino acid sequences of three proteins suggested that the "Kitty" method may be more useful in displays of sequences.

The 3-D (physical) structure of a protein is complicated and hard to remember in detail, but it is coarsely described by a ribbon or rope making a tortuous path through space. The "ribbon" describes the path in space of a linear polymer of amino acids. Thus, an alternative linear representation of the protein is simply the "text" giving its amino acid sequence. The two descriptions give the viewer very different and independent pieces of information, and one cannot be inferred from the other. Both kinds of information are needed in a correlated form. A diagram is presented which combines the two kinds of information in a schematic 2-D (plane) projection of the 3-D structure with the amino acid sequence written along the trace of the projection. Such a diagram provides a compact, easy-to-use summary of the approximate relative positions of the amino acids in space. Knowledge of the space positions of amino acids in a protein is important for understanding its biochemical function, for modifying it by genetic engineering, and for developing an understanding of how a 1-D amino acid sequence dictates the 3-D structure of a protein.

By comparing corresponding gene sequences from three or more organisms, we can deduce relationships which can be used for biological classification. Portions of a gene with the greatest number of differences (polymorphisms) generally produce the largest amount of useful data for classification of new specimens. In order to identify highly polymorphic regions, we displayed the 28S ribosomal RNA gene as a sequence logo.¹⁵ In this representation, the height of letters measures the degree of sequence conservation among several species. We then picked a region which has two conserved motifs surrounding a highly variable domain. The conserved portions are the same in many organisms, so we were able to use the polymerase chain reaction (PCR) technique to amplify the variable portion in the middle. When sequenced and compared, these amplified pieces of DNA will allow taxonomic classifications to be made.

Computer calculations on sequences provide specific answers to specific questions. On the other hand, graphical representations of sequences are perhaps better suited for drawing one's attention towards unsuspected features. Three types of graphical coding of nucleic acid sequences, in which the four nucleotides G, C, A, T (or U) are replaced with graphical symbols, are presented. A vectorial representation, transforming the sequence into a planar trajectory, reveals the long-range statistical properties of the sequences. Intron-exon junctions or boundaries between secondary structure domains often coincide with changes in direction of the representative curve.

Two-dimensional polyacrylamide gel electrophoresis is a technique for separating hundreds to thousands of polypeptides by two distinct characteristics: Isoelectric point and apparent molecular mass. One goal in analyzing a group of gels is to find interesting sets of polypeptides which appear as spots. A second goal is to make sense of this data when large numbers of spots, gels, and experimental conditions are involved. As part of the GELLAB-II system, we can present this data in different ways or "views". We suggest that these tools may be used to help find co-regulated genes.

The power of today's graphics workstations has made visual presentation of scientific results commonplace. Often the results presented do not require complicated analysis, and consequently, the use of complex software packages is not necessary. Thus, simple and easy-to-use programs are desirable. This paper reports on a simple program, VisiCoor, which can be used for the visualization of protein structures.

We proposed a tonal assignment (solmization) of four DNA bases, i.e., guanine = D(re), cytosine = E(mi), thymine = T(sol), and adenine = A(la), in a previous note.¹ To extend the assignment to amino acids, we ordered the amino acids primarily by hydropathy index with minor adjustments to preserve groupings of similar amino acids. The scale used for the bases was expanded by repeating it up and down to encompass twenty notes. The assignment in six parenthesized groups was (Arg = D1#, Lys = F1, His = G1) (Asp = A1#, Glu = C2) (Asn = D2, Gln = F2, Ser = G2, Thr = A2) (Gly = C3, Pro = D3, Ala = E3, Cys = G3) (Tyr = A3, Trp = B3, Phe = D4) (Met = E4, Leu = F4#, Val = A4, Ile = B4) (middle C = C3). To perform sequence comparison, each sequence melody of DNA or protein is assigned to a different instrument with distinct sonority, and several sequences are played polyphonically in tutti or in canon. This work is facilit0ated by MIDI-sequencers and synthesizers, and our preliminary explorations are sketched.

In this paper we review and develop the "diagrammatic representation" of base composition in DNA sequences and discuss its applications. The main idea of the diagrammatic representation is that the occurrence frequencies of bases A, C, G, and T in a DNA sequence are associated with the four distances to four faces from a point within a regular tetrahedron, whose edge is equal to . This point is regarded as a representation or a mapping of the frequencies of bases. The mapping points are projected to some coordinate planes for convenience. The projection of the points constitutes a diagrammatic representation of the frequencies of bases. We have shown that the distribution of projection points for 1490 human protein coding sequences, obtained from the Gen-Bank Genetic Sequences Data Bank (Release 62.0, Dec, 1989), constitutes a particular pattern in such diagrams, which is different from those of other species. We suggest that diagrams like these may be regarded as a characteristic representation for each species. These diagrams should be very useful in the study of the molecular evolution of organisms. The application of the "tetrahedron lattices" is also discussed.

Nucleic sequences are conveniently represented as arrays of four symbols corresponding to the four nucleotides most prevalent in nature. This representation is essentially qualitative and not easily amenable to mathematical analysis. For several reasons, some of which are discussed below, it is of interest to represent nucleotide sequences as quantitative functions. A quantitative mathematical representation of such arrays has to take into account the qualitative, discrete essence of nucleotide sequences. The method proposed in this report is based on the assessment of the coordinates for the center of mass of a 3-D mechanical analog. Each of the four vertices in a tetrahedron is assigned one of the four bases in a nucleotide sequence. The entire mass of the system is assumed to be applied only in these vertices, and the mass of every new base is assumed to be proportional to the entire mass already in the system. Then, for every nucleotide position, it is possible to compute the coordinates of the center of mass. The relationship between the angular coordinates of this center and the base position corresponds to a function with fractal properties.

The DRAW algorithm is presented which permits the visualization of open reading frames (ORFs, RNA sequences that can be translated into protein) in messenger RNAs folded into low energy secondary structures. The ORFs are color-coded for easy localization, and the initiating AUG codons are color-coded to indicate the theoretical strength of their ability to initiate protein synthesis. The DRAW program allows display and plotting in either color or in different fonts and character sizes. The easy visualization of ORFs in folded mRNAs provides insight into potential sites of regulation of gene expression at the translational level.

This paper describes a method for displaying protein sequences in the form of 2-D graphics, known as the "HCA method" (HCA). This technique, essentially visual, makes it possible to compare and align reliably protein sequences that exhibit less than 20% similarities. HCA may also be of interest in predicting secondary structures from amino acid sequences. The usefulness of the method is demonstrated through a series of examples extracted from the most recent literature. A discussion of the superiority of helical nets over other 2-D plots is included.

A system for diagnosing complex patterns within protein sequences is described. The method uses composite pattern-recognition discriminators to scan individual query sequences, and displays the results graphically, giving an instant evaluation of diagnostic performance in that sequence. The graphs yield separate profiles for each element of the composite discriminator, each with a statistical breakdown of the result, thereby providing both qualitative and quantitative assessments of discriminating power. The method is useful for the purpose of confirmation, in sequences whose family membership is already known, or of profile verification, in sequences whose family membership is only suspected. Since each element of the discriminator is treated independently, the graphs may also indicate whether a sequence is characterised by only part of a particular pattern, or indeed by none of it. Examples are provided to illustrate the characteristic signature of the superfamily of G-protein-coupled receptors, and those of kringle domains, zinc fingers and complement-binding domains.

Existing genes are compared with random nucleotide sequences of the same base composition for their ability to form stem-loop structures. RNA viral sequences are more "folded" than the random sequences, while the prokaryotic transcripts are more "extended". In the eukaryotic transcripts, the coding regions are more "neutral" in folding than the non-coding regions.

The 3-D folded structure of RNA has evolved throughout time and affects various functions of mRNA, tRNA, snRNA or rRNA. This property of RNA must have evolved as other biological parameters have.

We previously devised a computer algorithm predicting the folding structure of a single stranded RNA. The predicted structures of tRNA, snRNA and viroids agreed well with the experimentally confirmed ones.^1–3

To express the degree of global folding of RNA, we therefore derived a value called information mass volume (IMV).² IMV is defined as the sum total of the information values^1,4 reflecting the degree of the folding of a given sequence. Generally, if a sequence contains more regions of possible intra-strand annealing, the IMV value is higher.

In the past decade, researchers such as Hamori,^2–4 Gates,⁵ and Pickover⁶ have mapped genetic letter-series sequences using arbitrary vector-codes. These codes are based on vectors in either Cartesian 2- or 3-space. Recently several papers were published on the development of point geometry which is not based on the Cartesian system of coordinates but on the multidimensional Hgram system of coordinates.^1,9–16 Using the Hgram graph as a reference, a method of classifying graphs is described. A list of desirable design criteria for vector-codes is given. The design procedure of Huen's vector-code for protein sequences is outlined. Included is the outline of the specifications for writing software for the visual representation of protein sequences on microcomputers. The new code has some advantages over previous codes in that there are no overlaps of individual vectors and no requirement for spatial rotational viewing. Each basic symbol can embody a large amount of information, and only 2-D graphical software is needed for its implementation. It is suggested that letter-series sequences should be viewed as points in n-dimensional space. Visual analyses using the new code is advantageous since the mapping can be done without any loss of information from the IUB standard symbol table.

Index