Twilight zone of protein sequence alignments

Burkhard Rost

European Molecular Biology Laboratory

EMBL, 69 012 Heidelberg, Germany; rost@columbia.edu;http://www.columbia.edu/~rost/

contact e-mail:rost@columbia.edu


Table of Contents


Explanation



When are two naturally evolved proteins likely to have similar structures?

Originally, Sander & Schneider defined a length-dependent cut-off for significant pairwise sequence identity. I refined their analysis on a much larger data set, and re-defined thresholds for pairwise sequence idenity and pairwise sequence similarity (unpublished).

Here I give a table for the old and the new thresholds.

Significant sequence identity (Sander & Schneidder, 1991):

The HSSP-curve was originally defined by (Sander & Schneider, 1991):

(1)

where L gave the number of residues aligned between two proteins; pI the cut-off percentage of identical residues over the L aligned residues; and n described the distance in percentage points from the curve (n = 0 corresponds to the original HSSP-curve; n = 5 to the official HSSP database releases (Schneider et al., 1997)).

Significant sequence identity (refined Rost, unpublished):

Although the absolute value for the threshold of the HSSP-curve was questioned, the functional shape proved basically correct. However, the larger data set analysed here revealed several problems in detail. First, a threshold of 25% was not reasonable for alignment length lower than about 150-200. Second, above alignment length of 100, the derivative of the curve separating true and false positives should be lower than at lengths below 80. I attempted to solve these problems by defining the following curve for the separation true and false positives:

(2)

where L gave the number of residues aligned between two proteins; pI the cut-off percentage of identical residues over the L aligned residues; and n described the distance in percentage points from the curve. The particular functional form guaranteed an approximate saturation for long alignments. For alignments shorter than 13 residues eq. 2 yielded values above 100%. This was acceptable as 100% identical residues for poly-peptides of 10-11 residues does NOT imply structural similarity between these peptides (Cohen et al., 1993; Cerpa et al., 1996; Minor & Kim, 1996; Muñoz & Serrano, 1996).

Significant sequence similarity (refined Rost, unpublished):

Compiling sequence identity neglects the physico-chemical nature of amino acids. Any multiple sequence alignment illustrates that, e.g., the feature hydrophobicity is more conserved than is the residue type. For the million protein pairs investigated, here, this was reflected in a shift of the scatter plot towards lower percentages. The original HSSP-curve was derived for sequence identity, not for sequence similarity (Sander & Schneider, 1991). Nevertheless, the curve was clearly more conservative in terms of excluding false positives for similarity than for identity. The major problem was the saturation at levels of 25% sequence identity. Indeed, for longer alignments false positives fall below about 15% pairwise sequence similarity. The principle functional dependence between similarity and length appeared similar to the one between identity and length. This prompted a similar definition for the separation between true and false positives based on similarity:

(3)

where L gave the number of residues aligned between two proteins; pS defined cut-off for the percentage of residue similarity over the L aligned residues; and n described the distance in percentage points from the curve.

Cumulative percentage of correct hits at 'significant levels'

The cumulative number of protein pairs with similar structure detected at the level of significant sequence identity is:

To obtain levels of 99% true positives you have to add N percentage points to the values given below, with N being:






Table

Number of residues alignedSignificant sequence identity (eq. 1)Significant sequence identity (eq. 2)Significant sequence similarity (eq. 3)
1 100.0 100.0 100.0
2 100.0 100.0 100.0
3 100.0 100.0 100.0
4 100.0 100.0 100.0
5 100.0 100.0 100.0
6 100.0 100.0 100.0
7 97.2 100.0 100.0
8 90.2 100.0 100.0
9 84.4 100.0 96.7
10 79.5 100.0 90.1
11 75.4 100.0 84.6
12 71.8 98.8 79.9
13 68.6 94.0 75.7
14 65.8 89.7 72.1
15 63.3 85.9 68.9
16 61.1 82.6 66.0
17 59.0 79.5 63.4
18 57.2 76.7 61.1
19 55.5 74.2 59.0
20 53.9 71.9 57.0
21 52.4 69.8 55.2
22 51.1 67.8 53.5
23 49.8 66.0 52.0
24 48.6 64.3 50.6
25 47.5 62.7 49.3
26 46.5 61.3 48.0
27 45.5 59.9 46.8
28 44.6 58.6 45.8
29 43.7 57.4 44.7
30 42.9 56.2 43.7
31 42.1 55.1 42.8
32 41.4 54.1 42.0
33 40.7 53.1 41.1
34 40.0 52.2 40.3
35 39.3 51.3 39.6
36 38.7 50.4 38.9
37 38.1 49.6 38.2
38 37.6 48.9 37.6
39 37.0 48.1 36.9
40 36.5 47.4 36.3
41 36.0 46.8 35.8
42 35.5 46.1 35.2
43 35.0 45.5 34.7
44 34.6 44.9 34.2
45 34.2 44.3 33.7
46 33.7 43.8 33.3
47 33.3 43.2 32.8
48 32.9 42.7 32.4
49 32.6 42.2 32.0
50 32.2 41.7 31.5
51 31.8 41.3 31.2
52 31.5 40.8 30.8
53 31.2 40.4 30.4
54 30.8 40.0 30.1
55 30.5 39.6 29.7
56 30.2 39.2 29.4
57 29.9 38.8 29.1
58 29.6 38.4 28.8
59 29.3 38.1 28.4
60 29.1 37.7 28.2
61 28.8 37.4 27.9
62 28.5 37.0 27.6
63 28.3 36.7 27.3
64 28.0 36.4 27.0
65 27.8 36.1 26.8
66 27.5 35.8 26.5
67 27.3 35.5 26.3
68 27.1 35.2 26.1
69 26.9 35.0 25.8
70 26.6 34.7 25.6
71 26.4 34.4 25.4
72 26.2 34.2 25.2
73 26.0 33.9 25.0
74 25.8 33.7 24.8
75 25.6 33.5 24.6
76 25.4 33.2 24.4
77 25.3 33.0 24.2
78 25.1 32.8 24.0
79 24.9 32.6 23.8
80 24.7 32.4 23.6
81 25.0 32.2 23.4
82 25.0 32.0 23.3
83 25.0 31.8 23.1
84 25.0 31.6 22.9
85 25.0 31.4 22.8
86 25.0 31.2 22.6
87 25.0 31.0 22.5
88 25.0 30.8 22.3
89 25.0 30.7 22.2
90 25.0 30.5 22.0
91 25.0 30.3 21.9
92 25.0 30.2 21.7
93 25.0 30.0 21.6
94 25.0 29.9 21.5
95 25.0 29.7 21.3
96 25.0 29.6 21.2
97 25.0 29.4 21.1
98 25.0 29.3 20.9
99 25.0 29.1 20.8
100 25.0 29.0 20.7
101 25.0 28.8 20.6
102 25.0 28.7 20.5
103 25.0 28.6 20.3
104 25.0 28.5 20.2
105 25.0 28.3 20.1
106 25.0 28.2 20.0
107 25.0 28.1 19.9
108 25.0 28.0 19.8
109 25.0 27.8 19.7
110 25.0 27.7 19.6
111 25.0 27.6 19.5
112 25.0 27.5 19.4
113 25.0 27.4 19.3
114 25.0 27.3 19.2
115 25.0 27.2 19.1
116 25.0 27.1 19.0
117 25.0 27.0 18.9
118 25.0 26.9 18.8
119 25.0 26.8 18.7
120 25.0 26.7 18.7
121 25.0 26.6 18.6
122 25.0 26.5 18.5
123 25.0 26.4 18.4
124 25.0 26.3 18.3
125 25.0 26.2 18.2
126 25.0 26.1 18.2
127 25.0 26.0 18.1
128 25.0 25.9 18.0
129 25.0 25.8 17.9
130 25.0 25.8 17.8
131 25.0 25.7 17.8
132 25.0 25.6 17.7
133 25.0 25.5 17.6
134 25.0 25.4 17.5
135 25.0 25.3 17.5
136 25.0 25.3 17.4
137 25.0 25.2 17.3
138 25.0 25.1 17.3
139 25.0 25.0 17.2
140 25.0 25.0 17.1
141 25.0 24.9 17.1
142 25.0 24.8 17.0
143 25.0 24.8 16.9
144 25.0 24.7 16.9
145 25.0 24.6 16.8
146 25.0 24.6 16.8
147 25.0 24.5 16.7
148 25.0 24.4 16.6
149 25.0 24.4 16.6
150 25.0 24.3 16.5
151 25.0 24.2 16.5
152 25.0 24.2 16.4
153 25.0 24.1 16.3
154 25.0 24.1 16.3
155 25.0 24.0 16.2
156 25.0 23.9 16.2
157 25.0 23.9 16.1
158 25.0 23.8 16.1
159 25.0 23.8 16.0
160 25.0 23.7 16.0
161 25.0 23.7 15.9
162 25.0 23.6 15.9
163 25.0 23.5 15.8
164 25.0 23.5 15.8
165 25.0 23.4 15.7
166 25.0 23.4 15.7
167 25.0 23.3 15.6
168 25.0 23.3 15.6
169 25.0 23.2 15.5
170 25.0 23.2 15.5
171 25.0 23.1 15.4
172 25.0 23.1 15.4
173 25.0 23.0 15.3
174 25.0 23.0 15.3
175 25.0 23.0 15.3
176 25.0 22.9 15.2
177 25.0 22.9 15.2
178 25.0 22.8 15.1
179 25.0 22.8 15.1
180 25.0 22.7 15.0
181 25.0 22.7 15.0
182 25.0 22.7 15.0
183 25.0 22.6 14.9
184 25.0 22.6 14.9
185 25.0 22.5 14.8
186 25.0 22.5 14.8
187 25.0 22.5 14.8
188 25.0 22.4 14.7
189 25.0 22.4 14.7
190 25.0 22.3 14.6
191 25.0 22.3 14.6
192 25.0 22.3 14.6
193 25.0 22.2 14.5
194 25.0 22.2 14.5
195 25.0 22.2 14.5
196 25.0 22.1 14.4
197 25.0 22.1 14.4
198 25.0 22.0 14.4
199 25.0 22.0 14.3
200 25.0 22.0 14.3
201 25.0 21.9 14.3
202 25.0 21.9 14.2
203 25.0 21.9 14.2
204 25.0 21.9 14.2
205 25.0 21.8 14.1
206 25.0 21.8 14.1
207 25.0 21.8 14.1
208 25.0 21.7 14.0
209 25.0 21.7 14.0
210 25.0 21.7 14.0
211 25.0 21.6 13.9
212 25.0 21.6 13.9
213 25.0 21.6 13.9
214 25.0 21.5 13.8
215 25.0 21.5 13.8
216 25.0 21.5 13.8
217 25.0 21.5 13.7
218 25.0 21.4 13.7
219 25.0 21.4 13.7
220 25.0 21.4 13.7
221 25.0 21.4 13.6
222 25.0 21.3 13.6
223 25.0 21.3 13.6
224 25.0 21.3 13.6
225 25.0 21.3 13.5
226 25.0 21.2 13.5
227 25.0 21.2 13.5
228 25.0 21.2 13.4
229 25.0 21.2 13.4
230 25.0 21.1 13.4
231 25.0 21.1 13.4
232 25.0 21.1 13.3
233 25.0 21.1 13.3
234 25.0 21.0 13.3
235 25.0 21.0 13.3
236 25.0 21.0 13.2
237 25.0 21.0 13.2
238 25.0 21.0 13.2
239 25.0 20.9 13.2
240 25.0 20.9 13.1
241 25.0 20.9 13.1
242 25.0 20.9 13.1
243 25.0 20.9 13.1
244 25.0 20.8 13.0
245 25.0 20.8 13.0
246 25.0 20.8 13.0
247 25.0 20.8 13.0
248 25.0 20.8 13.0
249 25.0 20.7 12.9
250 25.0 20.7 12.9
251 25.0 20.7 12.9
252 25.0 20.7 12.9
253 25.0 20.7 12.8
254 25.0 20.6 12.8
255 25.0 20.6 12.8
256 25.0 20.6 12.8
257 25.0 20.6 12.8
258 25.0 20.6 12.7
259 25.0 20.6 12.7
260 25.0 20.5 12.7
261 25.0 20.5 12.7
262 25.0 20.5 12.7
263 25.0 20.5 12.6
264 25.0 20.5 12.6
265 25.0 20.5 12.6
266 25.0 20.4 12.6
267 25.0 20.4 12.6
268 25.0 20.4 12.5
269 25.0 20.4 12.5
270 25.0 20.4 12.5
271 25.0 20.4 12.5
272 25.0 20.4 12.5
273 25.0 20.3 12.4
274 25.0 20.3 12.4
275 25.0 20.3 12.4
276 25.0 20.3 12.4
277 25.0 20.3 12.4
278 25.0 20.3 12.4
279 25.0 20.3 12.3
280 25.0 20.2 12.3
281 25.0 20.2 12.3
282 25.0 20.2 12.3
283 25.0 20.2 12.3
284 25.0 20.2 12.3
285 25.0 20.2 12.2
286 25.0 20.2 12.2
287 25.0 20.2 12.2
288 25.0 20.1 12.2
289 25.0 20.1 12.2
290 25.0 20.1 12.2
291 25.0 20.1 12.1
292 25.0 20.1 12.1
293 25.0 20.1 12.1
294 25.0 20.1 12.1
295 25.0 20.1 12.1
296 25.0 20.1 12.1
297 25.0 20.0 12.0
298 25.0 20.0 12.0
299 25.0 20.0 12.0
300 25.0 20.0 12.0
301 25.0 20.0 12.0
302 25.0 20.0 12.0
303 25.0 20.0 12.0
304 25.0 20.0 11.9
305 25.0 20.0 11.9
306 25.0 20.0 11.9
307 25.0 19.9 11.9
308 25.0 19.9 11.9
309 25.0 19.9 11.9
310 25.0 19.9 11.9
311 25.0 19.9 11.8
312 25.0 19.9 11.8
313 25.0 19.9 11.8
314 25.0 19.9 11.8
315 25.0 19.9 11.8
316 25.0 19.9 11.8
317 25.0 19.9 11.8
318 25.0 19.9 11.7
319 25.0 19.8 11.7
320 25.0 19.8 11.7
321 25.0 19.8 11.7
322 25.0 19.8 11.7
323 25.0 19.8 11.7
324 25.0 19.8 11.7
325 25.0 19.8 11.7
326 25.0 19.8 11.6
327 25.0 19.8 11.6
328 25.0 19.8 11.6
329 25.0 19.8 11.6
330 25.0 19.8 11.6
331 25.0 19.8 11.6
332 25.0 19.8 11.6
333 25.0 19.7 11.6
334 25.0 19.7 11.5
335 25.0 19.7 11.5
336 25.0 19.7 11.5
337 25.0 19.7 11.5
338 25.0 19.7 11.5
339 25.0 19.7 11.5
340 25.0 19.7 11.5
341 25.0 19.7 11.5
342 25.0 19.7 11.5
343 25.0 19.7 11.4
344 25.0 19.7 11.4
345 25.0 19.7 11.4
346 25.0 19.7 11.4
347 25.0 19.7 11.4
348 25.0 19.7 11.4
349 25.0 19.7 11.4
350 25.0 19.7 11.4
351 25.0 19.6 11.4
352 25.0 19.6 11.3
353 25.0 19.6 11.3
354 25.0 19.6 11.3
355 25.0 19.6 11.3
356 25.0 19.6 11.3
357 25.0 19.6 11.3
358 25.0 19.6 11.3
359 25.0 19.6 11.3
360 25.0 19.6 11.3
361 25.0 19.6 11.3
362 25.0 19.6 11.2
363 25.0 19.6 11.2
364 25.0 19.6 11.2
365 25.0 19.6 11.2
366 25.0 19.6 11.2
367 25.0 19.6 11.2
368 25.0 19.6 11.2
369 25.0 19.6 11.2
370 25.0 19.6 11.2
371 25.0 19.6 11.2
372 25.0 19.6 11.1
373 25.0 19.6 11.1
374 25.0 19.6 11.1
375 25.0 19.6 11.1
376 25.0 19.6 11.1
377 25.0 19.6 11.1
378 25.0 19.6 11.1
379 25.0 19.6 11.1
380 25.0 19.6 11.1
381 25.0 19.5 11.1
382 25.0 19.5 11.1
383 25.0 19.5 11.0
384 25.0 19.5 11.0
385 25.0 19.5 11.0
386 25.0 19.5 11.0
387 25.0 19.5 11.0
388 25.0 19.5 11.0
389 25.0 19.5 11.0
390 25.0 19.5 11.0
391 25.0 19.5 11.0
392 25.0 19.5 11.0
393 25.0 19.5 11.0
394 25.0 19.5 11.0
395 25.0 19.5 11.0
396 25.0 19.5 10.9
397 25.0 19.5 10.9
398 25.0 19.5 10.9
399 25.0 19.5 10.9
400 25.0 19.5 10.9
401 25.0 19.5 10.9
402 25.0 19.5 10.9
403 25.0 19.5 10.9
404 25.0 19.5 10.9
405 25.0 19.5 10.9
406 25.0 19.5 10.9
407 25.0 19.5 10.9
408 25.0 19.5 10.9
409 25.0 19.5 10.8
410 25.0 19.5 10.8
411 25.0 19.5 10.8
412 25.0 19.5 10.8
413 25.0 19.5 10.8
414 25.0 19.5 10.8
415 25.0 19.5 10.8
416 25.0 19.5 10.8
417 25.0 19.5 10.8
418 25.0 19.5 10.8
419 25.0 19.5 10.8
420 25.0 19.5 10.8
421 25.0 19.5 10.8
422 25.0 19.5 10.8
423 25.0 19.5 10.7
424 25.0 19.5 10.7
425 25.0 19.5 10.7
426 25.0 19.5 10.7
427 25.0 19.5 10.7
428 25.0 19.5 10.7
429 25.0 19.5 10.7
430 25.0 19.5 10.7
431 25.0 19.5 10.7
432 25.0 19.5 10.7
433 25.0 19.5 10.7
434 25.0 19.5 10.7
435 25.0 19.5 10.7
436 25.0 19.5 10.7
437 25.0 19.5 10.7
438 25.0 19.5 10.7
439 25.0 19.5 10.6
440 25.0 19.5 10.6
441 25.0 19.5 10.6
442 25.0 19.5 10.6
443 25.0 19.5 10.6
444 25.0 19.5 10.6
445 25.0 19.5 10.6
446 25.0 19.5 10.6
447 25.0 19.5 10.6
448 25.0 19.5 10.6
449 25.0 19.5 10.6
450 25.0 19.5 10.6
451 25.0 19.5 10.6
452 25.0 19.5 10.6
453 25.0 19.5 10.6
454 25.0 19.5 10.6
455 25.0 19.5 10.6
456 25.0 19.5 10.6
457 25.0 19.5 10.5
458 25.0 19.5 10.5
459 25.0 19.5 10.5
460 25.0 19.5 10.5
461 25.0 19.5 10.5
462 25.0 19.5 10.5
463 25.0 19.5 10.5
464 25.0 19.5 10.5
465 25.0 19.5 10.5
466 25.0 19.5 10.5
467 25.0 19.5 10.5
468 25.0 19.5 10.5
469 25.0 19.5 10.5
470 25.0 19.5 10.5
471 25.0 19.5 10.5
472 25.0 19.5 10.5
473 25.0 19.5 10.5
474 25.0 19.5 10.5
475 25.0 19.5 10.5
476 25.0 19.5 10.5
477 25.0 19.5 10.4
478 25.0 19.5 10.4
479 25.0 19.5 10.4
480 25.0 19.5 10.4
481 25.0 19.5 10.4
482 25.0 19.5 10.4
483 25.0 19.5 10.4
484 25.0 19.5 10.4
485 25.0 19.5 10.4
486 25.0 19.5 10.4
487 25.0 19.5 10.4
488 25.0 19.5 10.4
489 25.0 19.5 10.4
490 25.0 19.5 10.4
491 25.0 19.5 10.4
492 25.0 19.5 10.4
493 25.0 19.5 10.4
494 25.0 19.5 10.4
495 25.0 19.5 10.4
496 25.0 19.5 10.4
497 25.0 19.5 10.4
498 25.0 19.5 10.4
499 25.0 19.5 10.4
500 25.0 19.5 10.3
501 25.0 19.5 10.3
502 25.0 19.5 10.3
503 25.0 19.5 10.3
504 25.0 19.5 10.3
505 25.0 19.5 10.3
506 25.0 19.5 10.3
507 25.0 19.5 10.3
508 25.0 19.5 10.3
509 25.0 19.5 10.3
510 25.0 19.5 10.3
511 25.0 19.5 10.3
512 25.0 19.5 10.3
513 25.0 19.5 10.3
514 25.0 19.5 10.3
515 25.0 19.5 10.3
516 25.0 19.5 10.3
517 25.0 19.5 10.3
518 25.0 19.5 10.3
519 25.0 19.5 10.3
520 25.0 19.5 10.3
521 25.0 19.5 10.3
522 25.0 19.5 10.3
523 25.0 19.5 10.3
524 25.0 19.5 10.3
525 25.0 19.5 10.3
526 25.0 19.5 10.3
527 25.0 19.5 10.3
528 25.0 19.5 10.2
529 25.0 19.5 10.2
530 25.0 19.5 10.2
531 25.0 19.5 10.2
532 25.0 19.5 10.2
533 25.0 19.5 10.2
534 25.0 19.5 10.2
535 25.0 19.5 10.2
536 25.0 19.5 10.2
537 25.0 19.5 10.2
538 25.0 19.5 10.2
539 25.0 19.5 10.2
540 25.0 19.5 10.2
541 25.0 19.5 10.2
542 25.0 19.5 10.2
543 25.0 19.5 10.2
544 25.0 19.5 10.2
545 25.0 19.5 10.2
546 25.0 19.5 10.2
547 25.0 19.5 10.2
548 25.0 19.5 10.2
549 25.0 19.5 10.2
550 25.0 19.5 10.2
551 25.0 19.5 10.2
552 25.0 19.5 10.2
553 25.0 19.5 10.2
554 25.0 19.5 10.2
555 25.0 19.5 10.2
556 25.0 19.5 10.2
557 25.0 19.5 10.2
558 25.0 19.5 10.2
559 25.0 19.5 10.2
560 25.0 19.5 10.2
561 25.0 19.5 10.2
562 25.0 19.5 10.2
563 25.0 19.5 10.2
564 25.0 19.5 10.1
565 25.0 19.5 10.1
566 25.0 19.5 10.1
567 25.0 19.5 10.1
568 25.0 19.5 10.1
569 25.0 19.5 10.1
570 25.0 19.5 10.1
571 25.0 19.5 10.1
572 25.0 19.5 10.1
573 25.0 19.5 10.1
574 25.0 19.5 10.1
575 25.0 19.5 10.1
576 25.0 19.5 10.1
577 25.0 19.5 10.1
578 25.0 19.5 10.1
579 25.0 19.5 10.1
580 25.0 19.5 10.1
581 25.0 19.5 10.1
582 25.0 19.5 10.1
583 25.0 19.5 10.1
584 25.0 19.5 10.1
585 25.0 19.5 10.1
586 25.0 19.5 10.1
587 25.0 19.5 10.1
588 25.0 19.5 10.1
589 25.0 19.5 10.1
590 25.0 19.5 10.1
591 25.0 19.5 10.1
592 25.0 19.5 10.1
593 25.0 19.5 10.1
594 25.0 19.5 10.1
595 25.0 19.5 10.1
596 25.0 19.5 10.1
597 25.0 19.5 10.1
598 25.0 19.5 10.1
599 25.0 19.5 10.1
600 25.0 19.5 10.1
601 25.0 19.5 10.1
602 25.0 19.5 10.1
603 25.0 19.5 10.1
604 25.0 19.5 10.1
605 25.0 19.5 10.1
606 25.0 19.5 10.1
607 25.0 19.5 10.1
608 25.0 19.5 10.1
609 25.0 19.5 10.1
610 25.0 19.5 10.1
611 25.0 19.5 10.1
612 25.0 19.5 10.1
613 25.0 19.5 10.0
614 25.0 19.5 10.0
615 25.0 19.5 10.0
616 25.0 19.5 10.0
617 25.0 19.5 10.0
618 25.0 19.5 10.0
619 25.0 19.5 10.0
620 25.0 19.5 10.0
621 25.0 19.5 10.0
622 25.0 19.5 10.0
623 25.0 19.5 10.0
624 25.0 19.5 10.0
625 25.0 19.5 10.0
626 25.0 19.5 10.0
627 25.0 19.5 10.0
628 25.0 19.5 10.0
629 25.0 19.5 10.0
630 25.0 19.5 10.0
631 25.0 19.5 10.0
632 25.0 19.5 10.0
633 25.0 19.5 10.0
634 25.0 19.5 10.0
635 25.0 19.5 10.0
636 25.0 19.5 10.0
637 25.0 19.5 10.0
638 25.0 19.5 10.0
639 25.0 19.5 10.0
640 25.0 19.5 10.0
641 25.0 19.5 10.0
642 25.0 19.5 10.0
643 25.0 19.5 10.0
644 25.0 19.5 10.0
645 25.0 19.5 10.0
646 25.0 19.5 10.0
647 25.0 19.5 10.0
648 25.0 19.5 10.0
649 25.0 19.5 10.0
650 25.0 19.5 10.0
651 25.0 19.5 10.0
652 25.0 19.5 10.0
653 25.0 19.5 10.0
654 25.0 19.5 10.0
655 25.0 19.5 10.0
656 25.0 19.5 10.0
657 25.0 19.5 10.0
658 25.0 19.5 10.0
659 25.0 19.5 10.0
660 25.0 19.5 10.0
661 25.0 19.5 10.0
662 25.0 19.5 10.0
663 25.0 19.5 10.0
664 25.0 19.5 10.0
665 25.0 19.5 10.0
666 25.0 19.5 10.0







REFERENCES




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