USING SAS/GRAPH R SOFTWARE FOR THREE-DIMENSIONAL ILLUSTRATIONS... if} OF AMINO ACID DIVERSITY -ct->,-t- 0

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1 <Q<V~~~ USING SAS/GRAPH R SOFTWARE FOR THREE-DIMENSIONAL ILLUSTRATIONS... if} OF AMINO ACID DIVERSITY -ct->,-t- Perry Watts, Fox Chase Cancer Center Samuel Litwin, Fox Chase Cancer Center ABSTRACT: Antibodies have a pattern of amino acid sequence diversity that is intrinsically related to their physical structure. Highly specialized equipment such as the Evans & Sutherland PS39 graphics system provides a realistic threedimensional display of an antibody's backbone. Amino acid residues are represented as colored spheres where hue is an indicator of diversity. However, the system is expensive, and the color displayed is influenced by a point's depth coordinate. 1bis means that there is a discrepancy between an explanatory legend positioned in the foreground and the antibody that is being rendered. Reproduction of hard-copy results for journal publication requires photography instead of the more convenient color laser printing. Given these problems, there is a role for PROC G3D. This procedure is used to draw a molecular disc and stick model with hues representing varying degrees of diversity among the residues. Depth is heightened by diminishing the disc size and width of connecting lines for more distant residues. A numbered legend attached to eight hues clearly demarcates cut-off points for the diversity measure. Care must be taken to allow for hidden lines and discs, but connecting to a PostScript R driver makes this task manageable. 1bis particular display shows that PROC G3D can be used for other applications besides needle, scatter or surface plots. ORIGIN AND DESCRIPTION OF THE DATA: The input data set for the graphic is a table of x-y-z coordinates and the Shannon (H) measure of diversity for each amino acid residue (locus) of a selected antibody. The coordinates come from a data base that is in the public domain (ref. I ), and the diversity measure is the product of FORTRAN programs that use files of amino acid sequences (refs. 2-5) as their input. In the amino acid files the rows are sequences and the columns are loci (fig. I). H is calculated using frequency counts of the 2 different amino acids (figs.2,3). While there is information on 11 different loci, graphics coordinates are available for only 95 of them. TWO DIMENSIONAL HISTOGRAMS: Initially, a modified type of histogram (fig.4) is used to display H with 95% confidence bounds. This graphic is created using PROC GPLOT with the areas option and a SYMBOL statement containing INTERPOL=STEPCJ to show that the data is discrete rather than continuous. Nevertheless, immunologists complain that the graphic is still difficult to read. Even when the one plot is broken down to three (fig.5), there appears to be no connection between locus number and the measure of diversity. To determine the signficance of the measure, an effort is made to link it to the convoluted physical structure of the antibody. The placement of the locus onto the antibody requires three-dimensional representation. INITIAL EFFORTS AT 3-D: PROC G3D with the SCATTER statement and noneedle option is used to create an unadorned first version of the graphic (fig.6). The balloons are colored to reflect eight ranges of equal length for the value of H. Unfortunately, the yellow ones are almost invisible. What is needed is a solid disc to replace the bollow balloon. Also, there is no automatic way to add connecting lines to the graphic. 1249

2 With these limitations, the ANNOTATE facility is required for rendering a more visible graphic. Along with the greater control provided by ANNOTA1E, however, comes the requirement for calculating the distance of a given point from the viewer. Knowing distance (d) allows one to take advantage of the PostScript R feature where anything drawn will cover what was previously there. Therefore, to partially overlap a more distant locus with a closer one, all that has to be done is to draw the more distant one first. The same method works for lines, showing that hidden shapes are soley dependent on the proper timing managed by d. Without ANNOTATE, this timing is controlled by PROC G3D itself maldng the balloon graphic a reliable check for the accuracy of hidden discs in the enhanced graphs. GETTINGd: Vectors are needed for calculating the scalar, d. The SYMPUT function is used for obtaining minimum and maximum values of the coordinates that define given vectors. Figure 7 illustrates the geometry needed to obtain the distance, d, for a plotted point, P, whereas the following shows how the vectors are actually calculated: data vectors (keep::::d, x, Y I Z J locus /H) i retain ax ay az nx ny nz; set fig3dat; if _n_ = 1 then do; ax=&xmini ay=&ymini bx=&xmaxi by=&ymin; cx=&xmini cy=&ymaxi dx=&xmin; dy=&ymaxi ex=ax-cx; ey=ay-cyi fx=ax-bxi fy=ay-by; gx=dx-cxi gy=dy-cy; end; nx=2*ax+ex+fx+gx; ny=2*ay+ey+fy+gyi nz=2*az+ez+fz+9zi dx=x-axi dy=y-ay; dz=z-az; d=(dx*nx)+(dy*ny)+{dz*nz}; run; az=&zmini bz=&zmini cz=&zmini dz=&zmaxi ez=az-czi fz=az-bzi gz=dz-cz i *A; *B; *c; *; *Ei *Fi *Gi *n; *P-A; The lag function is used on the figure 3 data set to record coordinates for connecting lines between loci. Then the data set is duplicated and sorted in d order so that loci will be drawn before lines when values for d are equal (fig.8). When the graph is plotted on the screen, lines and discs arise in d order with the most distant loci being drawn first. The operation almost looks random, but it most definitely is not Distance is enhanced in the graphic by maldng line thickness and disc size a function of d. CONCLUSIONS: Figure 9 shows the complete graph which is more visible in color. While there is not an ironclad association between structure and diversity, loci tend to be grouped by hue, and a higher measure of di versity is seen at the periphery of the structure where there is greater exposure to the host environment. Because of the antibody's convoluted structure, it is still difficult if not impossible to identify a locus by number (fig. I ). This problem require~ further study. REFERENCES: 1. Lascombe, M.B., et.a!. Three-dimensional structure of Fab RI9.9, a monoclonal murine antibody specific for the p azobenzenearsonate group. Proc. Nail. Acad. Sci. 86: Jores, Rita, et.a!. Resolution of hypervariable regions in T-cell receptor P chains by a modified Wu-Kabat index of amino acid diversity. Proc. Natl. Acad. Sci. 87: Kabat, E.A., et.a!. Sequences of Proteins of Immunological Interest (U.S. Public Health Service, National Institutes of Health, Bethesda, MD). 4. George, D.G., et.a!. (1988) in The National Biomedical Research Foundation Protein Sequence Database, ed. Lesk, A.M., (Oxford Univ. Press, Oxford), pp Bilofsky, H.S. & Burks, C. (1988) Nucleic Acids Res. 16, SASR Language: Reference, Version 6 Edition. Cary, NC: SAS Institute Inc., SASIGRAPH R Software, Volumes I and 2. Reference, Version 6, First Edition. Cary, NC: SAS Institute Inc.,

3 LOCI SEQ N VLTQSPAS ATYYCQQNNEDP 2 VLTQSPAS ATYYCQQSNEDP 3 VLTQSPAS ATYYCQHSRELP 4 VLTQSPAS ATYYCQHSWEIP 5 VLTQSPAS ATYYCQQSIEDP VMTCSCKF AVYFCaCYNSYP 16 VMTQSHKF AVYYCQQHYSTP 17 VMTQSHKF AVYYCQQHYSTP 18 N VMTQSPKS ADYHCGQGYSYP 19 N VMTQSPKS ADYFCGQSYSYP Figure 1. Input Data Set of Amino Acid Sequences.,.,_I Calculate pq for lhe ith AmIno Acid ai lhe jth Locus such thai pq - nq/"1 and "1-I: nq Eg: POl - 57/ LOCI,,,.. ".. " 1 11 ~:~~-~::~ A,..., 1 c...,.., " 1,.., 1 " " K,...,,... ",,....., N,,..,, " ".. Q, " ",,.. T... " " ", v,, "...,, w,... T, " ".., " '",oa,oa '" '" '" '" '" '" E " " G H,,... ",...,, Figure 4. Modified Histogram of H plus 95% Confidence Bounds. H ; 1 IIGJO 4OtiOtOl'II to to 1 H H Figure 2. Frequency Counts for the 2 Amino Acids. Figure 5. Three Histograms of H plus 95 % Confidence Bounds.,. x,y,z coordinates from the Fab R19.9 data base H = - 1: P, 1Sh PI where P, are the multinomial parameters for the 2 different! nino acids z LOCUS X Y Z H std - H S O : 15 2:593 : : O ' _ O Figure 3. The Data Set used for Graphics Displays. Figure 6. Balloon Graph of the H Measure of Amino Acid Diversity. 1251

4 d is the projection of P on n that points to an eye. Loci are sorted and plotted in d order. n=2a+e+f+g P is a given locus on the plot d = (P - A). n p A+G D o I a II CI c A+F Figure 7. Vector Geometry for Plotting Overlapping Loci. 1252

5 7: d 4 (Locus) - Processed - Not Yet Processed d = 2 (Locus) 5: d = 2 (Une) 6: d = 3 (Locus) d = 1 (locus) 2: d = 1 (Une) 3: d = 1 (Une) /./ o.. /(2) Figure 8. Hidden Line Algorithm showing how each locus and line is added to the plot. 1253

6 z {: H Diversity Scale..-<.3..3-<.6..8-< < < < x Figure 9. The Fi1aJ, Enhanced Graph. X Enlarged ldcua Scale (Ineo/orrowa) ' ' ' 1.8 ' Contact: Perry Watts Address: BIOSTAT. C-283 Fox Chase Cancer Center 771 Burholme Avenue Phi ladelphia, PA Telephone: FAX: Figure 1. Arrows Depict the ConvoluIBd Structure of the AntIbody. INTERNET: watts&castor.rm.fccc.edu 1254