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Solvent-accessible surfaces of proteins and nucleic acids
Chapter 9
Solvent-accessible surfaces of proteins and nucleic acids Computer graphics has made the results of X-ray crystallographic studies of proteins and nucleic acids more accessible to biochemists and molecular biologists. Traditionally, computer-generated images of molecular structures have consisted of lines for chemical bonds [1–3] or spheres [4–7] and ellipsoids [8] for atoms. This chapter presents a method that can be used to analytically calculate a smooth, three-dimensional contour about a molecule. A molecular surface envelope may be drawn on either color raster computer displays or real-time vector computer graphics systems. Molecular areas and volumes may be computed analytically from this surface representation. Unlike most previous computer graphic representations of molecules, which imitate wire models or space-filling plastic spheres, this surface shows only those atoms that are accessible to solvent. This analytical method extends the earlier dot surface numerical algorithm, which has been applied in enzymology, rational drug design, immunology, and understanding DNA base sequence recognition. Applications of this surface representation include enzymology, rational drug design, the elucidation of molecular diseases such as sickle cell anemia, the recognition of specific DNA base sequences by proteins and drugs, and the location of possible antigenic determinants on viruses. The historical basis for the smooth surface envelope method is the work of Richards [9] and colleagues on solvent-accessible area. Their emphasis was on chemical calculations measuring the sizes of hydrophobic and hydrophilic areas, while the methods described below were developed primarily for visualizing molecular structure and interactions. Nevertheless, these new methods also permit the measurement of area and volume during graphical display.
9.1 Solvent-accessible area A solvent-accessible area was originally defined and computed by Lee and Richards [10] as the area traced out by the center of a probe sphere representing a solvent molecule as it is rolled over the surface of the molecule of interest. Such computational methods were invented as tools that can be used to attack the protein-folding problem [9]. The problem is predicting the threedimensional structure of a protein given only its primary sequence of amino acids. Simply measuring the size of an area is insufficient for the study of many aspects of protein and nucleic acid function, such as substrate binding Nucleic Acids as Gene Anticancer Drug Delivery Therapy. https://doi.org/10.1016/B978-0-12-819777-6.00009-3 © 2019 Elsevier Inc. All rights reserved.
125
126 Nucleic acids as gene anticancer drug delivery therapy
and catalysis, drug-nucleic acid interaction, and recognition by the immune system. A method for visualizing solvent-accessible surreentrant surfaces was developed by Shrake and Rupley [11]. To calculate the size of solvent- accessible area they developed a numerical computer algorithm for placing dots over the solvent-accessible molecular surface of a protein [12, 13]. In what follows we briefly review the dot surface algorithm and present some analytical surface methods. For each probe position that does not experience van der Waals overlap with the atoms of a protein, points lying on the inward-facing surface of the probe sphere become part of the protein’s solvent-accessible surface. The probe may be placed tangent to (i) single atoms creating a dot at the point of tangency, (ii) pairs of atoms creating a concave arc of dots connecting the two points of tangency, and (iii) triples of atoms creating a concave triangle of dots between the three points of tangency. For each surface point generated the numerical algorithm calculates not only its coordinates but also an approximate solventaccessible area associated with the point and an outward-pointing unit vector perpendicular to the surface at that point. The pancreatic trypsin-trypsin inhibitor complex [14] is shown in Fig. 9.1 with a dot surface for the enzyme only. This method has proved useful in enzymology [15–19], immunology [20, 21], virology [22], molecular pathology [23], and the study of protein-ligand [24] and protein-protein [25–27] interactions. Despite the many applications of the dot surface numerical algorithm it was necessary to invent an analytical surface algorithm to generate high-resolution color raster display images and to compute more accurate molecular areas and volumes. A continuous molecular
FIG. 9.1 Stereo pair of the pancreatic trypsin-trypsin inhibitor complex. The enzyme is represented by a dot surface. Bonds represent residues of the inhibitor that are in contact with the enzyme. The part of the trypsin surface that is kept from contacting the solvent by the presence of the inhibitor is colored red (dark gray in print version).
Solvent-accessible surfaces of proteins and nucleic acids Chapter | 9 127
FIG. 9.2 Heme molecule drawn on a color raster graphics system. Surface pieces join at circular arcs. Green (gray in print version), convex surface; red (light gray in print version), saddle surface; blue(dark gray in print version), concave surface.
surface contour is defined as the union of pieces of spheres and tori joining smoothly at circular arcs. There are three kinds of pieces: concave spherical triangles, saddle-shaped rectangles, and convex spherical regions (Fig. 9.2). To start with each concave triangle is given three concave arcs as edges. In the next step connecting adjacent concave arcs along the inner surfaces of tori (Fig. 9.3) are grouped to form the saddle rectangles. The edges of each saddle rectangle consist of a pair of concave arcs and a pair of convex arcs. In the final
FIG. 9.3 (Left) Trajectory of probe rolling over a molecular surface. Trajectory arcs (red—gray in print version) connect positions where the probe is simultaneously tangent to three atoms. In a corresponding manner saddle rectangles connect concave triangles. These reentrant surfaces (green—dark gray in print version) then define the boundaries of convex surfaces (magenta—light gray in print version). (Right) Yeast phenylalanyl transfer of an RNA anticodon (GAA). Contact surfaces of the three-anticodon bases is shown. Contact areas in square angstroms are displayed next to the atom labels.
128 Nucleic acids as gene anticancer drug delivery therapy
step the convex arcs on each atom are grouped to form closed circuits, or cycles, and zero defines the boundary of each convex face of one or more cycles.
References [1] R. Diamond, in: D. Sayre (Ed.), Computational Crystallography, Oxford Univ. Press, Oxford, 1982, pp. 318. T.A. Jones, in ibid., p. 303. [2] F.P. Brooks Jr., in: B. Gilchrist (Ed.), Proceedings of the 1977 International Federation of Information Processing, North-Holland, Amsterdam, 1977, pp. 625. [3] C.D. Barry, C.E. Molnar, F.U. Rosenberger, Technical Memo 229, Computer Systems Laboratory, Washington University, St. Louis, MO, 1976. C.D. Barry, H.E. Bosshard, R.A. Ellis, G.R. Marshall, in: W. Siler, D.A.B. Lindberg (Eds.), Computers in Life Science Research, Plenum, New York1975, pp. 137. [4] T.K. Porter, Spherical shading, ACM SIGGRAPH Comp. Graph. 12 (3) (1978) 282– 285, https://doi.org/10.1145/965139.639789; T.K. Porter, The shaded surface display of large molecules, ACM SIGGRAPH Comp. Graph. 13 (2) (1979) 234–236, https://doi. org/10.1145/965103.807449. [5] R.J. Feldmann, et al., Progress in immunology VI: sixth international congress of immunology, Proc. Natl. Acad. Sci. U. S. A. 75 (1978) 5409. [6] K. Knowlton, L. Cherry, ATOMS, a three-D opaque molecule system, Comput. Chem. 1 (3) (1977) 161–166. [7] N.L. Max, Computational methods for biological systems, in: Theoretical Chemistry of Computer Graphics, vol. 13, 1979, pp. 165. Available from: https://books.google.com.eg/ books?isbn=9401132623. [8] C.K. Johnson, Fortran thermal-ellipsoid plot program for crystal structure illustration, ORTEPII Report ORNL-5138, Oak Ridge National Laboratory, Tennessee, 1976. [9] F.M. Richards, Areas, volumes, packing and protein structure, Annu. Rev. Biophys. Bioeng. 6 (1977) 151–176. [10] B. Lee, F.M. Richards, The interpretation of protein structures: estimation of static accessibility, J. Mol. Biol. 55 (3) (1971) 379–400. [11] A. Shrake, J.A. Rupley, Environment and exposure to solvent of protein atoms. Lysozyme and insulin, J. Mol. Biol. 79 (2) (1973) 351–371. [12] M. L. Connolly, Thesis, University of California, Berkeley (1981). [13] R.S. Pearlman, QCPE Bull. 1 (1981) 75. The dot molecular surface program (MS) is written in Fortran and may be obtained by writing to Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington 47405. [14] R. Huber, D. Kukla, W. Bode, P. Schwager, K. Bartels, J. Deisenhofer, W. Steigemann, Regulatory proteolytic enzymes and their inhibitors: 11th meeting, J. Mol. Biol. 89 (1974) 73. [15] R.N. Smith, C. Hansch, F.H. Kim, B. Omiya, G. Fukumura, C.D. Selassie, P.Y.C. Jow, J.M. Blaney, R. Langridge, Applications of interactive computer graphics in analyses of biomolecular structures, Arch. Biochem. Biophys. 215 (1982) 319. [16] C. Hansch, R. Li, J.M. Blaney, R. Langridge, Comparison of the inhibition of Escherichia coli and Lactobacillus casei dihydrofolate reductase by 2,4-diamino-5-(substituted-benzyl) pyrimidines: quantitative structure-activity relationships, X-ray crystallography, and computer graphics in structure-activity analysis, J. Med. Chem. 25 (7) (1982) 777–784. [17] S. Sprang, R. Fletterick, M. Stern, D. Yang, N. Madsen, J. Sturtevant, Analysis of an allosteric binding site: the nucleoside inhibitor site of phosphorylase alpha, Biochemistry 21 (9) (1982) 2036–2048.
Solvent-accessible surfaces of proteins and nucleic acids Chapter | 9 129 [18] E. Goldsmith, S. Sprang, R. Fletterick, Structure of maltoheptaose by difference Fourier methods and a model for glycogen, J. Mol. Biol. 156 (2) (1982) 411–427. [19] S.R. Sprang, E.J. Goldsmith, R.J. Fletterick, S.G. Withers, N.B. Madsen, Catalytic site of glycogen phosphorylase: structure of the T state and specificity for alpha-D-glucose, Biochemistry 21 (21) (1982) 5364–5371. [20] R.A. Lerner, Biotechnology and biological frontiers—in practice, peptides are synthesized according to the high repetitive yield methods developed by Merrifield, Nature (London) 299 (1982) 592. [21] A. J. Olson, G. Cohen, D. Davies, Antibody Structure, Film Available from Byron Motion Pictures, 65 K Street, NE, Washington, D.C. 20002. [22] A.J. Olson, Virus Wars, computer-generated film presented at the International School of Crystallography, in: Conference on Crystallography in Molecular Biology, Italy, June, 1982. [23] R.E. Dickerson, I. Geis, Hemoglobin: Structure, Function, Evolution, and Pathology, Benjamin/Cummings, Menlo Park, CA, 1983136. [24] I.D. Kuntz, J.M. Blaney, S.J. Oatley, R. Langridge, T.E. Ferrin, A geometric approach to macromolecule-ligand interactions, J. Mol. Biol. 161 (2) (1982) 269–288. [25] R. Langridge, T.E. Ferrin, I.D. Kuntz, M.L. Connolly, Real-time color graphics in studies of molecular interactions, Science 211 (4483) (1981) 661–666. [26] R.O. Fox Jr., F.M. Richards, A voltage-gated ion channel model inferred from the crystal structure of alamethicin at 1.5-A resolution, Nature 300 (5890) (1982) 325–330. [27] M.L. Connolly, Solvent-accessible surfaces of proteins and nucleic acids, Science 221 (4612) (1983).
Solvent-accessible surfaces of proteins and nucleic acids Computer graphics has made the results of X-ray crystallographic studies of proteins and nucleic acids more accessible to biochemists and molecular biologists. Traditionally, computer-generated images of molecular structures have consisted of lines for chemical bonds [1–3] or spheres [4–7] and ellipsoids [8] for atoms. This chapter presents a method that can be used to analytically calculate a smooth, three-dimensional contour about a molecule. A molecular surface envelope may be drawn on either color raster computer displays or real-time vector computer graphics systems. Molecular areas and volumes may be computed analytically from this surface representation. Unlike most previous computer graphic representations of molecules, which imitate wire models or space-filling plastic spheres, this surface shows only those atoms that are accessible to solvent. This analytical method extends the earlier dot surface numerical algorithm, which has been applied in enzymology, rational drug design, immunology, and understanding DNA base sequence recognition. Applications of this surface representation include enzymology, rational drug design, the elucidation of molecular diseases such as sickle cell anemia, the recognition of specific DNA base sequences by proteins and drugs, and the location of possible antigenic determinants on viruses. The historical basis for the smooth surface envelope method is the work of Richards [9] and colleagues on solvent-accessible area. Their emphasis was on chemical calculations measuring the sizes of hydrophobic and hydrophilic areas, while the methods described below were developed primarily for visualizing molecular structure and interactions. Nevertheless, these new methods also permit the measurement of area and volume during graphical display.
9.1 Solvent-accessible area A solvent-accessible area was originally defined and computed by Lee and Richards [10] as the area traced out by the center of a probe sphere representing a solvent molecule as it is rolled over the surface of the molecule of interest. Such computational methods were invented as tools that can be used to attack the protein-folding problem [9]. The problem is predicting the threedimensional structure of a protein given only its primary sequence of amino acids. Simply measuring the size of an area is insufficient for the study of many aspects of protein and nucleic acid function, such as substrate binding Nucleic Acids as Gene Anticancer Drug Delivery Therapy. https://doi.org/10.1016/B978-0-12-819777-6.00009-3 © 2019 Elsevier Inc. All rights reserved.
125
126 Nucleic acids as gene anticancer drug delivery therapy
and catalysis, drug-nucleic acid interaction, and recognition by the immune system. A method for visualizing solvent-accessible surreentrant surfaces was developed by Shrake and Rupley [11]. To calculate the size of solvent- accessible area they developed a numerical computer algorithm for placing dots over the solvent-accessible molecular surface of a protein [12, 13]. In what follows we briefly review the dot surface algorithm and present some analytical surface methods. For each probe position that does not experience van der Waals overlap with the atoms of a protein, points lying on the inward-facing surface of the probe sphere become part of the protein’s solvent-accessible surface. The probe may be placed tangent to (i) single atoms creating a dot at the point of tangency, (ii) pairs of atoms creating a concave arc of dots connecting the two points of tangency, and (iii) triples of atoms creating a concave triangle of dots between the three points of tangency. For each surface point generated the numerical algorithm calculates not only its coordinates but also an approximate solventaccessible area associated with the point and an outward-pointing unit vector perpendicular to the surface at that point. The pancreatic trypsin-trypsin inhibitor complex [14] is shown in Fig. 9.1 with a dot surface for the enzyme only. This method has proved useful in enzymology [15–19], immunology [20, 21], virology [22], molecular pathology [23], and the study of protein-ligand [24] and protein-protein [25–27] interactions. Despite the many applications of the dot surface numerical algorithm it was necessary to invent an analytical surface algorithm to generate high-resolution color raster display images and to compute more accurate molecular areas and volumes. A continuous molecular
FIG. 9.1 Stereo pair of the pancreatic trypsin-trypsin inhibitor complex. The enzyme is represented by a dot surface. Bonds represent residues of the inhibitor that are in contact with the enzyme. The part of the trypsin surface that is kept from contacting the solvent by the presence of the inhibitor is colored red (dark gray in print version).
Solvent-accessible surfaces of proteins and nucleic acids Chapter | 9 127
FIG. 9.2 Heme molecule drawn on a color raster graphics system. Surface pieces join at circular arcs. Green (gray in print version), convex surface; red (light gray in print version), saddle surface; blue(dark gray in print version), concave surface.
surface contour is defined as the union of pieces of spheres and tori joining smoothly at circular arcs. There are three kinds of pieces: concave spherical triangles, saddle-shaped rectangles, and convex spherical regions (Fig. 9.2). To start with each concave triangle is given three concave arcs as edges. In the next step connecting adjacent concave arcs along the inner surfaces of tori (Fig. 9.3) are grouped to form the saddle rectangles. The edges of each saddle rectangle consist of a pair of concave arcs and a pair of convex arcs. In the final
FIG. 9.3 (Left) Trajectory of probe rolling over a molecular surface. Trajectory arcs (red—gray in print version) connect positions where the probe is simultaneously tangent to three atoms. In a corresponding manner saddle rectangles connect concave triangles. These reentrant surfaces (green—dark gray in print version) then define the boundaries of convex surfaces (magenta—light gray in print version). (Right) Yeast phenylalanyl transfer of an RNA anticodon (GAA). Contact surfaces of the three-anticodon bases is shown. Contact areas in square angstroms are displayed next to the atom labels.
128 Nucleic acids as gene anticancer drug delivery therapy
step the convex arcs on each atom are grouped to form closed circuits, or cycles, and zero defines the boundary of each convex face of one or more cycles.
References [1] R. Diamond, in: D. Sayre (Ed.), Computational Crystallography, Oxford Univ. Press, Oxford, 1982, pp. 318. T.A. Jones, in ibid., p. 303. [2] F.P. Brooks Jr., in: B. Gilchrist (Ed.), Proceedings of the 1977 International Federation of Information Processing, North-Holland, Amsterdam, 1977, pp. 625. [3] C.D. Barry, C.E. Molnar, F.U. Rosenberger, Technical Memo 229, Computer Systems Laboratory, Washington University, St. Louis, MO, 1976. C.D. Barry, H.E. Bosshard, R.A. Ellis, G.R. Marshall, in: W. Siler, D.A.B. Lindberg (Eds.), Computers in Life Science Research, Plenum, New York1975, pp. 137. [4] T.K. Porter, Spherical shading, ACM SIGGRAPH Comp. Graph. 12 (3) (1978) 282– 285, https://doi.org/10.1145/965139.639789; T.K. Porter, The shaded surface display of large molecules, ACM SIGGRAPH Comp. Graph. 13 (2) (1979) 234–236, https://doi. org/10.1145/965103.807449. [5] R.J. Feldmann, et al., Progress in immunology VI: sixth international congress of immunology, Proc. Natl. Acad. Sci. U. S. A. 75 (1978) 5409. [6] K. Knowlton, L. Cherry, ATOMS, a three-D opaque molecule system, Comput. Chem. 1 (3) (1977) 161–166. [7] N.L. Max, Computational methods for biological systems, in: Theoretical Chemistry of Computer Graphics, vol. 13, 1979, pp. 165. Available from: https://books.google.com.eg/ books?isbn=9401132623. [8] C.K. Johnson, Fortran thermal-ellipsoid plot program for crystal structure illustration, ORTEPII Report ORNL-5138, Oak Ridge National Laboratory, Tennessee, 1976. [9] F.M. Richards, Areas, volumes, packing and protein structure, Annu. Rev. Biophys. Bioeng. 6 (1977) 151–176. [10] B. Lee, F.M. Richards, The interpretation of protein structures: estimation of static accessibility, J. Mol. Biol. 55 (3) (1971) 379–400. [11] A. Shrake, J.A. Rupley, Environment and exposure to solvent of protein atoms. Lysozyme and insulin, J. Mol. Biol. 79 (2) (1973) 351–371. [12] M. L. Connolly, Thesis, University of California, Berkeley (1981). [13] R.S. Pearlman, QCPE Bull. 1 (1981) 75. The dot molecular surface program (MS) is written in Fortran and may be obtained by writing to Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington 47405. [14] R. Huber, D. Kukla, W. Bode, P. Schwager, K. Bartels, J. Deisenhofer, W. Steigemann, Regulatory proteolytic enzymes and their inhibitors: 11th meeting, J. Mol. Biol. 89 (1974) 73. [15] R.N. Smith, C. Hansch, F.H. Kim, B. Omiya, G. Fukumura, C.D. Selassie, P.Y.C. Jow, J.M. Blaney, R. Langridge, Applications of interactive computer graphics in analyses of biomolecular structures, Arch. Biochem. Biophys. 215 (1982) 319. [16] C. Hansch, R. Li, J.M. Blaney, R. Langridge, Comparison of the inhibition of Escherichia coli and Lactobacillus casei dihydrofolate reductase by 2,4-diamino-5-(substituted-benzyl) pyrimidines: quantitative structure-activity relationships, X-ray crystallography, and computer graphics in structure-activity analysis, J. Med. Chem. 25 (7) (1982) 777–784. [17] S. Sprang, R. Fletterick, M. Stern, D. Yang, N. Madsen, J. Sturtevant, Analysis of an allosteric binding site: the nucleoside inhibitor site of phosphorylase alpha, Biochemistry 21 (9) (1982) 2036–2048.
Solvent-accessible surfaces of proteins and nucleic acids Chapter | 9 129 [18] E. Goldsmith, S. Sprang, R. Fletterick, Structure of maltoheptaose by difference Fourier methods and a model for glycogen, J. Mol. Biol. 156 (2) (1982) 411–427. [19] S.R. Sprang, E.J. Goldsmith, R.J. Fletterick, S.G. Withers, N.B. Madsen, Catalytic site of glycogen phosphorylase: structure of the T state and specificity for alpha-D-glucose, Biochemistry 21 (21) (1982) 5364–5371. [20] R.A. Lerner, Biotechnology and biological frontiers—in practice, peptides are synthesized according to the high repetitive yield methods developed by Merrifield, Nature (London) 299 (1982) 592. [21] A. J. Olson, G. Cohen, D. Davies, Antibody Structure, Film Available from Byron Motion Pictures, 65 K Street, NE, Washington, D.C. 20002. [22] A.J. Olson, Virus Wars, computer-generated film presented at the International School of Crystallography, in: Conference on Crystallography in Molecular Biology, Italy, June, 1982. [23] R.E. Dickerson, I. Geis, Hemoglobin: Structure, Function, Evolution, and Pathology, Benjamin/Cummings, Menlo Park, CA, 1983136. [24] I.D. Kuntz, J.M. Blaney, S.J. Oatley, R. Langridge, T.E. Ferrin, A geometric approach to macromolecule-ligand interactions, J. Mol. Biol. 161 (2) (1982) 269–288. [25] R. Langridge, T.E. Ferrin, I.D. Kuntz, M.L. Connolly, Real-time color graphics in studies of molecular interactions, Science 211 (4483) (1981) 661–666. [26] R.O. Fox Jr., F.M. Richards, A voltage-gated ion channel model inferred from the crystal structure of alamethicin at 1.5-A resolution, Nature 300 (5890) (1982) 325–330. [27] M.L. Connolly, Solvent-accessible surfaces of proteins and nucleic acids, Science 221 (4612) (1983).