Graphical representation of proteins

Chemical Reviews

Volumn 111, Issue 2, 2011, Pages 790-862

  Randić, Milan ^a,b   Zupan, Jure ^a   Balaban, Alexandru T ^c   Vikić Topić, Dražen ^b   Plavšić, Dejan ^b  

^a NATIONAL INSTITUTE OF CHEMISTRY   (Slovenia)

^b RUDER BO KOVI INSTITUTE   (Croatia)

^c TEXAS A AND M UNIVERSITY AT GALVESTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHICAL REPRESENTATIONS; NUMERICAL CHARACTERIZATION; VISUAL INSPECTION;

DNA; GRAPHIC METHODS; NUCLEIC ACIDS;

DNA SEQUENCES;

DNA; PROTEIN; RNA;

ARTICLE; CHEMISTRY; CONFORMATION; GENETIC CODE; PROTEOMICS;

DNA; GENETIC CODE; NUCLEIC ACID CONFORMATION; PROTEINS; PROTEOMICS; RNA;

EID: 79951633245     PISSN: 00092665     EISSN: 15206890     Source Type: Journal    
DOI: 10.1021/cr800198j     Document Type: Article

References (321)

1. Wilson, E. B. Introduction to Scientific Research; McGraw-Hill: New York, 1952.
2. Kolbe's criticism of van't Hoff: http://www.chem.yale.edu/-chem.125/125/ history99/6Stereochemistry/Kolbe.html.
3. From a letter of R. G. Parr to M. Randić: .....In the very early 1930s the leading young American physical chemists got very upset by the disdain for quantum mechanics, molecular spectroscopy, and the like, shown toward such subjects by the editor of the then Journal of Physical and Colloid Chemistry (later JPC), a chap named Bancroft, and the fact that the chemical leadership in the country would not force a change. They {Harold Urey, Joe Mayer, John Kirkwood, Robert Mulliken, others} went to the American Physical. Society, and there soon followed the founding of JCP. Take a look at issue 1, volume 1, of JCP, and you will [be] amazed by the high quality. It took forty years or so for JPC to recover (perhaps one should say "be born again )....."
4. Boys, S. F. Proc. R. Soc. [London] 1950, A200, 542.
5. Boys, S. F. Proc. R. Soc. [London] 1950, A201, 125.
6. Boys, S. F. Proc. R Soc. [London] 1951, A206, 489.
7. Boys, S. F. Proc. R. Soc. [London] 1951, A207, 181.
8. Boys, S. F. Proc. R. Soc. [London] 1951, A207, 197.
9. Boys, S. F. Philos. Trans. R. Soc. 1952, A245, 95.
10. Hohenberg, P.; Kohn, W. Phys. Rev. 1964, B136, 864.
11. Kohn, W.; Sham, L. J. Phys. Rev. 1965, A140, 1133.
12. Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785.
13. German alchemist and physician Theophrastus Bombastus von Hohenheim (1493-1541), known as Paracelsus, has recognized medical use of small amounts of toxic chemicals. For more on the history of hormesis, see: Stebbing, A. R. D. BELLE Newsletter 1997, 6; No. 2, September.
14. Randić, M.; Estrada, E. J. Proteome Res. 2005, 4, 2133.
15. Randić, M. MATCH Commun. Math. Comput. Chem. 2008, 59, 5.
16. Randić, M, Indian J. Math. Teach. 2000, 26, 11 (Unfortunately, galley proofs were not sent to the author, leaving the text with several confusing printing errors left uncorrected).
17. Calabrese, E. J.; Baldwin, L. A. Annu. Rev. Pharmacol. Toxicol. 2003, 43, 175.
18. Calabrese, E. J. Cell Mol. Biol. 2005, 51, 643.
19. Calabrese, E. J.; Baldwin, L. A. Nature 2003, 421, 691.
20. As cited in John Horgan's End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age; Addison Wesley: New York, 1996.
21. Gernert, D. J. Sci. Explor. 2008, 22, 233.
22. Planck, M. Survey of Physical. Theory; Dover Publications: New York, 1993.
23. Lipman, D. J.; Pearson, W. R. Science 1985, 227, 1435.
24. Altschul, S. F.; Gish, W.; Miller, W.; Myers, E. W.; Lipman, D. J. J. Mol. Biol. 1990, 215, 403.
25. Bartlett, F. C. Remembering: A Study in Experimental and Social Psychology; Cambridge University Press: England, 1932; p 168.
26. See Randić, M. MATCH Commun. Math. Comput. Chem. 2008, 59, 46.
27. After being rejected by J. Chem. Phys. the "childish" paper: "Symmetry properties of chemical graphs. VI. Isomerization of octahedral complexes" was published in collaboration with M. I. Davis in Int. J. Quantum Chem 1984, 26, 69.
28. Part of the foreword in Chemical Applications of Graph Theory; Balaban, A. T., Ed.; Academic Press: London, 1976.
29. Randić, M. Indian J. Chem. 2003, 42A, 1207.
30. Veltman, M. Diagrammatica: The Path to Feynman Diagrams (Cambridge Lecture Notes in Physics); Cambridge University Press: Cambridge, U.K., 1995.
31. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: New York, 1972.
32. Lecointre, G.; Le Guyader, H. The Tree of Life: A Phylogenetic Classification; Harvard University Press Reference Library: Cambridge, MA, 2006.
33. Goldstine, H. H. The Computer from Pascal to von Neuman; Princeton University Press: Princeton, NJ, 1993; pp 266-267.
34. König, D. Theorie der endlichen und unendlichen Graphen; Akademische Verlagsgesellschaft: Leipzig, 1936. English translation with, commentary by W. T. Tutte, Birkhäuser: Basel, Switzerland, 1990.
35. Harary, F. Graph Theory; Addison-Wesley: Reading, MA, 1969.
36. Wilson, R. J. Introduction to Graph Theory; Oliver & Boyd: Edinburgh, U.K., 1972.
37. Bondy, J. A.; Murty, U. S. R. Graph Theory with Applications; American Elsevier: New York, 1976.
38. Pisanski, T.; Randić, M. In Geometry at Work, Papers in Applied Geometry; Gorini, C. A., Ed.; Math. Assoc. America No. 53: Washington, DC, 2000; pp 174-194.
39. Chemical Applications of Graph Theory; Balaban, A. T., Ed.; Academic Press: London, 1976.
40. Trinajstić, N. Chemical Graph Theory, 2nd ed.; CRC Press: Boca Raton, FL, 1992.
41. Nandy, A.; Harle, M.; Basak, S. C. ARKIVOC 2006, 9, 211.
42. Hamori, E.; Ruskin, J. J. Biol. Chem. 1983, 258, 1318.
43. Hamori, E. Nature 1985, 574, 585.
44. Hamori, E. Biotechniques 1989, 7, 710.
45. Hamori, E.; Varga, G.; LaGuardia, J. J. Comput. Appl. Biosci. 1989, 5, 263.
46. Hamori, E. In Frontiers of Scientific Visualization; Pickover, C. A., Tewksbury, S. K., Eds.; Wiley-Interscience: New York, 1994; pp 90-121.
47. Randić, M. SAR QSAR Environ. Res. 2004, 15, 147.
48. Gates, M. A. J. Theor. Biol. 1986, 119, 319.
49. Leong, P. M.; Morgenthaler, S. Comput. Appl. Biosci. 1995, 11, 503.
50. Nandy, A. Curr. Sci. 1994, 66, 309.
51. Guo, X.; Randić, M.; Basak, S. C. Chem. Phys. Lett. 2001, 350, 106.
52. Guo, X.; Nandy, A. Chem. Phys. Lett. 2003, 369, 361.
53. Zhang, C.-T.; Zhang, R.; Ou, H.-Y. Bioinformatics 2003, 19, 593.
54. Randić, M. Chem. Phys. Lett. 2004, 386, 468.
55. Liao, B.; Tan, M.; Ding, K. Chem. Phys. Lett. 2005, 402, 380.
56. Yau, S. S-T.; Wang, J.; Niknejad, A.; Lu, C.; Jin, N.; Ho, Y.-K. Nucleic Acids Res. 2003, 31, 3078.
57. Randić, M.; Vračko, M.; Nandy, A.; Basak, S. C. J. Chem. Inf. Comput. Sci. 2000, 40, 1235.
58. Randić, M.; Kleiner, A. F.; De Alba, L. M. J. Chem. Inf. Comput. Sci. 1994, 34, 277.
59. Randić, M. Int. J. Quantum Chem. 1980, 18 (S7), 187.
60. From Chemical Topology to Three-Dimensional Geometry; Balaban, A. T., Ed.; Plenum Press: New York, 1997.
61. Balaban, A. T.; Harary, F. Tetrahedron 1968, 24, 2505.
62. Balaban, A. T. Tetrahedron 1969, 25, 2949.
63. Anderson, P. G. In Fibonacci Numbers and Their Applications; Philippou, A. N., Bergum, P. G., Horadam, A. F., Eds.; D. Reidel Publishing Company: Dordrecht, The Netherlands, 1986; p 2.
64. See p 3553 in Randić, M. Chem. Rev. 2003, 103, 3449.
65. Balaban, A. T. MATCH Commun. Math. Comput. Chem. 1989, 24, 29.
66. Zhu, H.; Klein, D. J. J. Chem. Inf. Comput. Sci. 1996, 36, 1067.
67. Ivanciuc, O.; Ivanciuc, T.; Klein, D. J. MATCH Commun. Math. Comput. Chem. 2001, 44, 251.
68. Spencer, J.; Szemerédy, E.; Trotter, W. T., Jr. In Graph Theory and Combinatorics 1983: Cambridge Combinatorial Proceedings in Honour of Paul Erdos; Bollobás, B., Ed.; Academic Press: London, 1984; pp 293-303.
69. Erdös, P. Am. Math. Mon. 1946, 53, 248.
70. Randić, M.; Zupan, J.; Vikić-Topić, D. J. Mol. Graphics Model. 2007, 26, 290.
71. Randić, M.; Razinger, M. In From Chemical Topology to ThreeDimensional Geometry; Balaban, A. T., Ed.; Plenum. Press: New York, 1996; pp 159-236.
72. Randić, M.; Vračko, M.; Novič, M.; Basak, S. C. MATCH Commun. Math. Comput. Chem. 2000, 42, 181.
73. Bytautas, L.; Klein, D. J.; Randić, M.; Pisanski, T. DIMACS Series Discovery Math. Theor. Comput. Sci. 2000, 51, 39.
74. Randić, M. Int. J. Quantum Chem. 1995, 56 (S22), 61.
75. Randić, M.; Krilov, G. Int. J. Quantum Chem. 1996, 60 (S23), 1851.
76. Randić, M.; Krilov, G. Int. J. Quantum Chem. 1997, 65, 1065.
77. Randić, M.; Krilov, G. Chem. Phys. Lett. 1997, 272, 115.
78. Randić, M.; Krilov, G. Int. J. Quantum Chem. 1999, 75, 1017.
79. Krilov, G.; Randić, M. New J. Chem. 2004, 28, 1608.
80. Randić, M.; Zupan, J.; Novič, M. J. Chem. Inf. Comput. Sci 2001, 41, 1339.
81. Randić, M.; Witzmann, F.; Vračko, M.; Basak, S. C. Med. Chem. Res. 2001, 10, 456.
82. Randić, M. In Handbook of Proteomic Methods; Conn, P. M., Ed.; Humana Press: Totowa, NJ, 2003; pp 429-450.
83. Jeffrey, H. J. Nucleic Acids Res. 1990, 18, 2163.
84. Jeffrey, H. J. Comput. Graph. 1992, 16, 25.
85. Barnsley, M. F.; Rising, H. Fractals Everywhere, 2nd ed.; Academic Press: Boston, MA, 1993.
86. Zupan, J.; Randić, M. J. Chem. Inf. Model. 2005, 45, 309.
87. Randić, M. Acta Chim. Slov. 2006, 53, 477.
88. Randić, M.; Zupan, J. SAR QSAR Environ. Res. 2004, 15, 191.
89. Randić, M. J. Math. Chem. 2008, 43, 756.
90. Randić, M.; Vračko, M.; Plavšić, D. Int. J. Chem. Model 2008, 7, 305.
91. Randić, M. J. Chem. Inf. Comput. Sci. 2001, 41, 1330.
92. Randić, M.; Lerš, N.; Plavšić, D.; Basak, S. C. Croat. Chem. Acta 2004, 77, 345.
93. Randić, M.; Lerš, N.; Plavšić, D.; Basak, S. C. J. Proteome Res. 2004, 3, 778.
94. Randić, M.; Nović, M.; Vračko, M. J. Chem. Inf. Model. 2005, 45, 1205.
95. Zupan, J.; Randić, M. J. Chem. Inf. Model. 2005, 45, 309.
96. Fiser, A.; Tusnady, G. E.; Simon, I. J. Mol. Graph. 1994, 12, 302.
97. Yu, Z.-G.; Anh, V.; Lau, K.-S. J. Theor. Biol. 2004, 226, 341.
98. Basu, S.; Pan, A.; Dutta, C.; Das, J. J. Mol. Graphics Modell. 1997, 15, 279.
99. Solovyev, V. V. Biosystems 1993, 30, 137.
100. Joseph, J.; Sasikumar, R. BMC Bioinformatics 2006, 7, 243.
101. Parthasarathy, S. In Book of Abstracts of Fifth International Conference on Dynamic Systems and Applications, Atlanta, GA, May 30June 2, 2007.
102. Mandelbrot, B. B. Fractals and Chaos. The Mandelbrot Set and Beyond; Springer Verlag: New York, 2004.
103. Mandelbrot, B. B. The Fractal Geometry of Nature; W. H. Freeman: New York, 1983.
104. Sierpinski, W. Compt Rend. Acad. Sci. Paris 1915, 160, 302.
105. http://mathworid.wolfram.com/SierpinskiSieve.html.
106. For history, see Pascal's triangle in Wikipedia (a free, web-based, collaborative, multilingual encyclopedia project supported by the nonprofit Wikimedia Foundation), http://en.wikipedia.org/wiki/Pascal's-triangle.
107. Sloane, N. J. A. The On-line Encyclopedia of Integer Sequences; http://www.research.att.com/-njas/sequences/Seis.html.
108. See: Sloane, N. J. A. Home Page, http://www.research.att.com/-njas/.
109. Gardner, M. Mathematical Carnival; Vintage Books: New York, 1977; pp 194-207.
110. Applications of Discrete Mathematics, updated ed.; Michaels, J. G., Rosen, K. H., Eds.; McGraw-Hill: New York, 2007.
111. Bondarenko, B. A. Fibonacci Triangles and Pyramids, Their Fractals, Graphs, and Applications; The Fibonacci Association: Santa Clara, CA, 1993.
112. Gordon, M.; Davison, W. H. T. J. Chem. Phys. 1952, 20, 428.
113. Balaban, A. T.; Tomescu, I. Croat. Chem. Acta 1984, 57, 391.
114. Balaban, A. T.; Tomescu, I. MATCH Commun. Math. Comput. Chem. 1985, 17, 91.
115. See p 3481 and Fig. 31 in Randić, M. Chem. Rev 2003, 103, 3449.
116. Randić, M.; Morales, D. A.; Araujo, O. J. Math. Chem. 1996, 20, 79.
117. Randić, M.; Vračko, M.; Lerš, N.; Plavšić, D. Chem. Phys. Lett. 2003, 368, 1.
118. Randić, M.; Vračko, M.; Lerš, N.; Plavšić, D. Chem. Phys. Lett. 2003, 371, 202.
119. Randić, M.; Zupan, J.; Vikić-Topić, D.; Plavšić, D. Chem. Phys. Lett. 2006, 431, 375.
120. Graphical alignment is not confined only to spectral representations of proteins. It can be extended to chaos-game representations of DNA and proteins, as will be clarified in the section on representation of proteins via the "magic circle". The paper on graphical alignment of proteins was submitted, revised, and accepted for publication in 2006 by J. Proteome Res. At the stage of typsetting, objections were raised to citing a question raised by one of the reviewers, with request that this reference to anonymous reviewer be deleted. However, even before responding, an additional report (for an already accepted paper) came with request by the same reviewer who insisted on the removal of the figure showing 20 amino acids uniformly placed on the circumference of a unit circle because it was already published before. In addition, the anonymous reviewer wanted to continue the dialogue! Since the author did not want to remove the figure nor was he interested in private dialogue with an anonymous scientist, the manuscript was withrawn and resubmitted to J. Math. Chem., where it appeared in J. Math. Chem. 2008, 43, 756 (unchanged as accepted by J. Proteome Res.).
121. http://www.bioweb.uwlax.edu/GenWeb/Molecular/Seq-Anal/Alignment/ alignment.htm.
122. Liao, B.; Chen, W.; Sun, X.; Zhu, W. J. Comput. Chem. 2009, 30, 2205.
123. Liao, B.; Wang, T.-M. J. Biomol. Struct. Dyn. 2004, 21, 827.
124. Zhan, J.; Liao, B.; Zhang, Y. Internet Electronic Conference of Molecular Design 2003, November 23-December 6, 2003, http://biochempress.com/Files/IECMD- 2004/IECMD-2004-018.pdf.
125. Bai, F.; Zhu, W.; Wang, T. Chem. Phys. Lett. 2005, 408, 258.
126. Feng, J.; Wang, T.-M. Chem. Phys. Lett. 2008, 454, 355.
127. Liu, L.; Wang, T. J. Math. Chem. 2007, 42, 595.
128. Yao, Y.-H.; Nan, X.-Y.; Wang, T.-M. J. Comput. Chem. 2005, 26, 1339.
129. Yao, Y.-R; Liao, B.; Wang, T.-M. J. Mol. Struct: THEOCHEM 2005, 755, 131.
130. Li, C.; Xing, L.; Wang, X. Chem. Phys. Lett. 2008, 458, 249.
131. Zhu, W.; Liao, B.; Ding, K. J. Mol. Struct: THEOCHEM 2005, 757, 193.
132. Zhang, Y.; Qui, J. Q.; Su, L. Q. Chem. Phys. Lett. 2008, 458, 180.
133. Randić, M.; Vračko, M.; Novič, M.; Plavšić, D. Int. J. Quantum Chem. 2009, 109, 2982.
134. Reusken, C. B. E. M.; Bol, J. F. Nucleic Acids Res. 1996, 24, 2660.
135. Koper-Zwaithoff, E. C.; Bol., J. F. Nucleic Acids Res. 1980, 8, 3307.
136. Cornelissen, B. J. C.; Janssen, H.; Zuidema, D.; Bol., J. F. Nucleic Acids Res. 1984, 12, 2427.
137. Houser-Scott, F.; Bear, M. L.; Liem, K. F.; Cai, J. M.; Gehrke, L. N. J. Virol. 1994, 68, 2194.
138. Scott, S. W.; Ge, X. J. Gen. Virol. 1995, 76, 957.
139. Scott, S. W.; Ge, X. J. Gen. Virol. 1995, 76, 1801.
140. Balaban, A. T.; Plavšić, D.; Randić, M. Chem. Phys. Lett. 2003, 379, 147.
141. Randić, M. Chem. Phys. Lett. 2000, 317, 29.
142. Randić, M.; Novič, M.; Vračko, M. SAR QSAR Environ. Res. 2008, 19, 339.
143. These matrices are in general nonsymmetric. Nevertheless, one can construct additional 8-component vectors as supplementary characterization of RNA by using amplitudes of complex numbers as vector entries.
144. Shu, W.; Bo, X.; Zheng, Z.; Wang, S. BMCBioinformatics 2008, 9, 188
145. Yao, Y.-H.; Nan, X.-Y.; Wang, T.-M. J. Comput. Chem. 2005, 26, 1339.
146. Liu, L.; Wang, T. J. Math. Chem. 2007, 42, 595.
147. Randić, M.; Balaban, A. T. J. Chem. Inf. Comput. Sci. 2003, 43, 532.
148. Randić, M.; Plavšić, D. Chem. Phys. Lett. 2009, 476, 277.
149. Randić, M.; Vračko, M.; Novič, M.; Plavšić, D. Uniform representation of proteins by distance matrix. In Quantuim Frontiers of Atoms and Molecules; Putz, M. V., Ed.; Nova Publishers: New York, 2009.
150. Randić, M.; Lerš, N.; Plavšić, D.; Basak, S. C.; Balaban, A. T. Chem. Phys. Lett. 2005, 407, 205.
151. Randić, M.; Mehulić, K.; Vukičević, D.; Pisanski, T.; Vikić-Topić, D.; Plavšić, D. J. Mol. Graphics Modell. 2009, 27, 637.
152. Randić, M. Chem. Phys. Lett. 2004, 386, 468.
153. Randić, M. Chem. Phys. Lett. 2007, 444, 176.
154. Crick, F. H. C.; Barnett, L.; Brenner, S.; Watts-Tobin, R. J. Nature 1961, 192, 1227.
155. Fickett, J. W. Nucleic Acids Res. 1982, 10, 5303.
156. Balaban, A. T.; Randić, M. In Proceedings of the International Conference on Biocomputation, Bioinformatics, and Biomedical Technologies, June 29-July 5, 2008, Bucharest, Romania; pp 76-82. IEEE Trans.
157. Randić, M. In Encyclopedia of Computational Chemistry; Schleyer, P. v. R., Allinger, N. L., Clark, T., Gasteiger, J., Kollman, P. A., Schaefer, H. F., III, Schreiner, P. R., Eds.; John Wiley & Sons: Chichester, U.K., 1998; pp 3018-3032.
158. Balaban, A. T. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon and Breach: Amsterdam, The Netherlands, 1999; pp 403-453.
159. Basak, S. C.; Grunwald, G. D.; Niemi, G. J. In From Chemical Topology to Three-Dimensional Geometry; Plenum Press: New York, 1977; pp 73-116.
160. Estrada, E. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon and Breach: Amsterdam, The Netherlands, 1999; pp 403-453.
161. Randić, M.; Zupan, J. In Topology in Chemistry: Discrete Mathematics of Molecules; Rouvray, D. H., King, R. B., Eds.; Horwood Publ. Ltd.: Chichester, U.K., 2002; pp 249-291.
162. Randić, M. J. Mol. Graphics Modell. 2001, 20, 19.
163. Randić, M. J. Chem. Inf. Comput. Sci. 2001, 41, 607.
164. Randić, M. New J. Chem. 1997, 21, 1078.
165. Hardy, G. H. A. Course of Pure Mathematics, 10th ed.; Cambridge University Press: Cambridge, U.K., 2002.
166. Randić, M.; Zupan, J.; Balaban, A. T. Chem. Phys. Lett. 2004, 397, 247.
167. Randić, M.; Vikić-Topić, D.; Graovac, A.; Lerš, N.; Plavšić, D. Period. Biol. 2005, 107, 437.
168. Randić, M.; Balaban, A. T.; Novič, M.; Založnik, A.; Pisanski, T. Period. Biol. 2005, 107, 403.
169. Randić, M.; Butina, D.; Zupan, J. Chem. Phys. Lett. 2006, 419, 528.
170. Randić, M.; Zupan, J.; Novič, M.; Gute, B. D.; Basak, S. C. SAR QSAR Environ. Res. 2002, 13, 689.
171. Randić, M.; DeAlba, L. M. J. Chem. Inf. Comput. Sci. 1997, 37, 1078.
172. Randić, M. Chem. Phys. Lett. 2008, 456, 84.
173. Read, R. C.; Corneil, D. G. J. Graph Theory 1977, 1, 339.
174. Gatti, G. J. Graph Theory 1979, 3, 95.
175. Randić, M. J. Chem. Phys. 1974, 60, 3920.
176. addendum J. Chem. Phys. 1975, 62, 309.
177. Randić, M. J. Chem. Inf. Comput. Sci. 1975, 15, 105.
178. Balaban, A. T.; Liu, X.; Klein, D. J.; Babić, D.; Schmalz, T. G.; Seitz, W. A.; Randić, M. J. Chem. Inf. Comput. Sci. 1995, 35, 396.
179. Balaban, A. T.; Farcasiu, D.; Bǎnicǎ, R. Rev. Roum. Chim. 1966, 11, 1205.
180. Julius Petersen (1839-1910), Danish mathematician.
181. Petersen, J. L'Intermédiaire des Mathématidens 1898, 5, 225.
182. Holton, D. A.; Sheehan, J. The Petersen Graph, Australian Math. Soc. Lecture Series No.7; Cambridge University Press: Cambridge, U.K., 1993.
183. Dunitz, J. D.; Prelog, V. Angew. Chem. 1968, 80, 700.
184. Randić, M. Croat. Chem. Acta 1977, 49, 643.
185. Prelog, V. In Chemical Applications of Graph Theory; Balaban, A. T., Ed.; Academic Press: London, 1976.
186. Zaretskij, K. A. Usp. Mat. Nauk 1965, 20, 90.
187. 191
188. Platt, J. R. J. Chem. Phys. 1947, 15, 419.
189. Platt, J. R. J. Phys. Chem. 1952, 56, 328.
190. Randić, M. J. Chem. Inf. Comput. Sci. 1992, 32, 57.
191. Randić, M. J. Am. Chem. Soc 1975, 97, 6609.
192. Kier, L. B.; Murray, W. J.; Randić, M.; Hall, L. H. J. Pharm. Sci. 1976, 65, 1226.
193. Kier, L. B.; Hall, H. L. J. Pharm. Sci. 1976, 65, 1806.
194. Hall, H. L.; Kier, L. B.; Murray, W. J. J. Pharm. Sci. 1975, 64, 1974.
195. Murray, W. J.; Hall, L. H.; Kier, L. B. J. Pharm. Sci. 1975, 64, 1978.
196. Kier, L. B.; Hall, L. H. Molecular Connectivity in Chemistry and Drug Research; Academic Press: New York, 1976.
197. Randić, M.; Razinger, M. J. Chem. Inf. Comput. Sci. 1995, 35, 594.
198. Randić, M. J. Chem. Inf. Comput. Sci. 1995, 35, 373.
199. Randić, M. New J. Chem. 1995, 19, 781.
200. Randić, M. J. Math. Chem. 1996, 19, 375.
201. Randić, M.; Razinger, M. In From Chemical Topology to ThreeDimensional Geometry; Balaban, A. T., Ed.; Plenum. Press: New York, 1977; pp 159-236.
202. Jacques Hadamard (1865-1963), French mathematician.
203. Issai Schur (1875-1941), German/Jewish mathematician.
204. Leopold Kronecker (1823-1891), German mathematician.
205. Gilat, A. MATLAB: An Introduction with Applications, 3rd ed.; Wiley & Sons: New York, 2008. MATLAB is the acronym for "matrix laboratory". It was invented by Cleve Moler at the Computer Science Department of the University of New Mexico in the late 1970s. For more information, consult Wikipedia.
206. Funk & Wagnalls Standard Desk Dictionary; Harper & Row Publishers: New York, 1984.
207. Orengo, C. A.; Brown, N. P.; Taylor, W. T. Proteins 1992, 14, 139.
208. Holm, L.; Sander, C. J. Mol. Biol. 1993, 233, 123.
209. Notredame, C.; Holm, L.; Higgins, D. G. Bioinformatics 1998, 14, 407.
210. Vriend, G.; Sander, C. Proteins 1991, 11, 52.
211. Fisher, D.; Bachar, O.; Nussinov, R.; Wolfson, H. J. Biomol. Struct. Dyn. 1992, 9, 769.
212. Shindyalov, I. N.; Bourne, P. E. Protein Eng. Des. Sel. 1998, 11, 739.
213. Alexandrov, N. N. Protein Eng. Des. Sel. 1996, 9, 727.
214. Alexandrov, N. N.; Fisher, D. Proteins 1996, 25, 354.
215. Levenshtein, V. I. Sov. Phys. Dokl. 1966, 10, 707.
216. Handbook of Chemoinformatics-From Data to Knowledge in 4 Volumes; Gasteiger, J., Ed.; Wiley-VCH: Weinheim, Germany, 2003; Vol. 3.
217. Altschul, S. F.; Madden, T. L.; Schaffer, A. A.; Zhang, J.; Zhang, Z.; Miller, W.; Lipman, D. J. Nucleic Acids Res. 1997, 25, 3389.
218. Pearson, W. R.; Lipman, D. J. Proc. Natl. Acad. Sci. 1988, 85, 2444.
219. Martin, T. C. The Inventions, Researches and Writings of Nikola Tesla; Barnes & Noble Books: New York, 1995.
220. Comment by an anonymous reviewer.
221. Novič, M.; Randić, M. SAR QSAR Environ. Res. 2008, 19, 317.
222. Hashimoto, Y.; Niikura, T.; Tajima, H.; Yasukawa, T.; Sudo, H.; Ito, Y.; Kita, Y.; Kawasumi, M.; Kouyama, K.; Doyu, M.; Sobue, G.; Koide, T.; Tsuji, S.; Lang, J.; Kurokawa, K.; Nishimoto, I. Proc. Natl. Acad. Sci. 2001, 98, 6336.
223. Jaklič, G.; Pisanski, T.; Randić, M. J. Comput. Biol. 2006, 13, 1558.
224. Jaklič, G.; Pisanski, T.; Randić, M. MATCH Commun. Math. Comput. Chem. 2007, 58, 301.
225. Randić, M.; Zupan, J.; Pisanski, T. J. Math. Chem. 2008, 43, 674.
226. Otto Topliz (1881-1940), German mathematician.
227. Hermann Hankel (1839-1873), German mathematician.
228. Brookes, M. The Matrix Reference Manual, http://www.ee.ic.ac.uk/hp/staff/ dmb/matrix/intro.html.
229. Hladnik, M.; Marušič, D.; Pisanski, T. Discrete Math. 2002, 244, 137.
230. Hladnik, M. Linear Algebra Appl. 1999, 286, 261.
231. Davis, P. J. Circulant Matrices; Wiley: New York, 1979.
232. Putnam, C. R. Pac J. Math. 1964, 14, 651.
233. The form of the matrix will depend on ordering of amino acids, but because we are interested in matrix invariants, any ordering is acceptable. We will continue to order amino acids alphabetically based on three-letter amino acid codes.
234. Randić, M.; Novič, M.; Vračko, M. SAR QSAR Environ. Res. 2008, 12, 339.
235. Chou, K.-C. J. Protein Chem. 1999, 18, 473.
236. Liu, W.-m.; Chou, K.-C. Protein Eng. Des. Sel. 1999, 12, 1041.
237. Tsai, H.-H; Gunasekaran, K.; Nussinov, R. Structure 2006, 14, 1059.
238. Dill, K. A. Biochemistry 1985, 24, 1501.
239. Chan, H. S.; Dill, K. A. Macromolecules 1989, 22, 4559.
240. Lau, K. F.; Dill, K. A. Macromolecules 1989, 22, 3986.
241. Shih, C. T.; Su, Z. Y.; Gwan, J. F.; Hao, B. L.; Hsieh, C. H.; Lee, H. C. Phys. Rev. Lett. 2000, 84, 386.
242. Li, H.; Helling, R.; Tang, C.; Wingreen, N. S. Science 1996, 273, 666.
243. Wang, B.; Yu, Z.-G. J. Chem. Phys. 2000, 112, 6084.
244. Wolynes, P. G. Nat. Struct. Biol. 1997, 4, 871.
245. Li, H.; Tang, C.; Wingreen, N. S. Phys. Rev. Lett. 1997, 79, 765.
246. Shakhnovich, E.; Gutin, A. J. Chem. Phys. 1990, 93, 5967.
247. Klimov, D. K.; Thiramalai, D. Phys. Rev. Lett. 1996, 76, 4070.
248. Sali, A.; Shahknovich, E.; Karplus, M. Nature 1994, 569, 248.
249. Hückel, E. Z. Phys. 1930, 60, 423.
250. Hückel, E. Z. Phys. 1931, 70, 204.
251. Hückel, E. Z. Phys. 1932, 76, 628.
252. Bloch, F. Z. Phys. 1928, 52, 555.
253. It is not widely known that E. Hückel was a theoretical physicist and his seminal work on HMO applied to benzene was part of his Magister thesis.
254. Riddle, D. S.; Santiago, J. V.; Bray-Hall, S.; Doshi, N.; Grantcharova, V. P.; Yi, Q.; Baker, D. Nat. Struct. Biol. 1997, 4, 805.
255. Wang, J.; Wang, W. Nat. Struct. Biol. 1999, 6, 1033.
256. Randić, M.; Vračko, M.; Novič, M.; Plavšić, D. SAR QSAR Environ. Res. 2009, 20, 415.
257. According to Wikipedia, 'Tree of life (science), a metaphor used first by Charles Darwin and subsequently to describe the interrelatedness of all living things through evolution."
258. Yu, Z.-G.; Anh, V.; Lau, K.-S. Physica A 2004, 337, 171.
259. Yang, J.-Y.; Yu, Z.-G.; Anh, V. Chaos Solitons Fractals 2009, 40, 607.
260. Li, T.; Fan, K.; Wang, J.; Wang, W. Protein Eng. Des. Sel. 2003, 16, 323.
261. Wang, J.; Wang, W. Phys. Rev. E. 2000, 61, 6981.
262. Dokholyan, N. V. Proteins 2004, 54, 622.
263. The characterization of such work as "academic exercise" originates with an anonymous referee of one of our manuscripts.
264. Janin, J. Nature 1979, 277, 491.
265. Wolfenden, R.; Andersson, L.; Cullis, P. M.; Southgate, C. C. B. Biochemistry 1981, 20, 849.
266. Kyte, J.; Doolite, R. F. J. Mol. Biol. 1982, 157, 105.
267. Rose, G.; Geselowitz, A.; Lesser, G.; Lee, R.; Zehfus, M. Science 1985, 229, 834.
268. http://cds.unina.it/petrilli/aminoac/amiac.htm?htm.
269. Nandy, A.; Gosh, A.; Nandy, P. In Silico Biol. 2009, 9, 0008.
270. Liu, N.; Wang, T. Chem. Phys. Lett. 2007, 435, 127.
271. Yu, Z.-G.; Anh, V.; Lau, K.-S. J. Theor. Biol. 2004, 226, 341.
272. Brown, T. A. Genetics, A Molecular Approach, 3rd ed.; Chapman, and Hall: London, 1998.
273. Bai, F.; Wang, T. Chem. Phys. Lett. 2005, 413, 458.
274. Bai, F.; Wang, T. J. Biomol. Struct. Dyn. 2006, 23, 537.
275. Yang Y. Wang, T. Private communication.
276. Guo, Y.; Wang, T.-m, J. Biomol. Struct. Dyn. 2008, 26, 367.
277. Sternberg, M. J. E.; Thornton, J. M. J. Mol. Biol. 1977, 110, 269.
278. Yuan, C.; Liao, B.; Wang, T.-M. Chem. Phys. Lett. 2003, 379, 412.
279. Chew, L. P.; Kedem, K. Algorithmic 2003, 38, 115.
280. González-Díaz, H.; Vilar, S.; Santana, L.; Uriarte, E. Curr. Top. Med. Chem. 2007, 7, 1015.
281. González-Díaz, H.; González-Díaz, Y.; Santana, L.; Ubeira, F. M.; Utiarte, E. Proteomics 2008, 8, 750.
282. González-Díaz, H.; Prado-Prado, F. J. J. Comput. Chem. 2008, 29, 656.
283. González-Díaz, H.; Agüero-Chapin, G.; Varona, J.; Molina, R.; Delogu, G.; Santana, L.; Uriarte, E.; Podda, G. J. Comput. Chem. 2007, 28, 1049.
284. González-Díaz, H.; Saíz-Urra, L.; Molina, R.; González-Díaz, Y.; Sánchez-González, A. J. Comput. Chem. 2007, 28, 1042.
285. González-Díaz, H.; Saíz-Urra, L.; Molina, R.; Santana, L.; Uriarte, E. J. Proteome Res. 2007, 6, 904.
286. González-Díaz, H.; Peréz-Castillo, Y.; Podda, G.; Uriarte, E. J. Comput. Chem. 2007, 28, 1990.
287. González-Díaz, H.; Prado-Prado, F.; Ubeira, F. M. Curr. Top. Med. Chem. 2008, 8, 1676.
288. Randić, M. J. Chem. Inf. Comput. Sci. 2001, 47, 1330.
289. Randić, M.; Zupan, J.; Novič, M. J. Chem. Inf. Comput. Sci. 2001, 41, 1339.
290. Randić, M.; Witzmann, F.; Vračko, M.; Basak, S. C. Med. Chem. Res. 2001, 10, 456.
291. Randić, M.; Vračko, M.; Novič, M. J. Proteome Res. 2002, 1, 217.
292. Randić, M. Int. J. Quantum Chem. 2002, 90, 848.
293. Randić, M.; Basak, S. C. J. Chem. Inf. Comput. Sci. 2002, 42, 983.
294. Randić, M.; Novič, M.; Vračko, M.; Plavšić., D. J. Theor. Biol. 2010, 266, 21.
295. Bajzer, Ž.; Randić, M.; Plavšić, D.; Basak, S. C. J. Mol. Graphics Modell. 2003, 22, 1.
296. Randić, M.; Lerš, N.; Plavšić, D.; Basak, S. C. J. Proteome Res. 2004, 3, 778.
297. Randić, M.; Novič, M.; Vračko, M. J. Chem. Inf. Model. 2005, 45, 1205.
298. The approaches based on Voronoi regions can be further generalized by considering boundaries that will reflect the relative weights (amplitudes) of the protein spots.
299. Randić, M.; Pompe, M.; Mills, D.; Basak, S. C. Molecules 2004, 9, 1177.
300. Balaban, A. T. In QSPR/QSAR Studies by Molecular Descriptors; Diudea, M. V., Ed.; Nova Sci. Publ.: Huntington, NY, 2001; pp 1-30.
301. Randić, M. J. Math. Chem. 1992, 9, 97.
302. Balaban, A. T. In Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J., Balaban, A. T., Eds.; Gordon, and Breach: Amsterdam, The Netherlands, 1999; pp 403-453.
303. Katritzky, A. R.; Lobanov, V.; Karelson, M. CODESSA (Comprehensive Descriptors for Structural and Statistical Analysis); University of Florida: Gainesville, FL, 1994.
304. Karelson, M. Molecular Descriptors; Wiley: New York, 2000.
305. Todeschini, R.; Consonni, V. Molecular Descriptors for Chemoinformatics, Vol. I Alphabetical Listing/Vol II Appendices, References (Methods and Principles in Medicinal Chemistry; Mannhold, R., Kubinyi, H., Folkers, G., Eds.; Wiley-VCH: Weinheim, Germany, 2009; Vol. 41.
306. Randić, M.; DeAlba, L. M. J. Chem. Inf. Comput. Sci. 1997, 37, 1078.
307. Dijkstra, E. W. Numer. Math. 1959, 1, 269.
308. With, courtesy of Witzmann, F. Molecular Anatomy Laboratory, Department of Biology; Indiana University & Purdue University: Columbus, IN 47203.
309. Anderson, N. L.; Esquer-Blasco, R.; Richardson, F.; Foxworthy, P.; Eacho, P. Toxicol. Appl Pharmacol. 1996, 137, 75.
310. MATLAB (abbreviation for Matrix Laboratory) is a product of The Math Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098.
311. Georgy Voronoi (1868-1908), Russian mathematician. His first paper (on factorization of polynomials) appeared while he was in high school.
312. Voronoi, G. J. Reine Angew. Math. 1907, 133, 97.
313. Boris Delaunay (1890-1980), Russian mathematician, a student of G. Voronoi. The Delaunay triangulation was introduced in 1934.
314. Delaunay, B. Izvestia Akad. Nauk SSSR, Otdel. Mat. Estest. Nauk 1934, 7, 793.
315. Kowalski, B. R.; Bender, C. F. J. Am. Chem. Soc. 1972, 94, 5632.
316. Brualdi, R. C.; Cvetkovié, D. A Combinatorial Approach to Matrix Theory and Its Applications; Chapman & Hall/CRC Press: Boca Raton, FL, 2009.
317. Babić, D.; Klein, D. J.; Lukovits, I.; Nikolić, S.; Trinajstić, N. Int. J. Quantum Chem. 2002, 90, 166.
318. Chan, O.; Lam, T. K.; Mereis, R. J. Chem. Inf. Comput. Sci. 1997, 37, 762.
319. Lovász, L.; Pelikán, J. Period. Math. Hung. 1973, 3, 175.
320. Randić, M.; Guo, X. F.; Bobst, S. DIMACS Series Disc. Math. Theor. Comput. Sci. 2000, 51, 305.
321. Župerl, Š.; Pristovšek, P.; Menart, V.; Gaberc-Porekar, V.; Novič, M. J. Chem. Inf. Model. 2007, 47, 737.