243:
479:
275:
772:
values throughout the protein's sequence agreed with all of the simulated transition state but one helix which folded semi-independently and made native-like contacts with the rest of the protein only once the transition state had formed fully. Such variation in the folding rate in one protein makes
726:
to numbers greater than zero is the same as assuming the mutation increases the stability and lowers the energy of neither the native nor the transition state. It is in the same line assumed that interactions that stabilize a folding transition state are like those of the native structure, though
973:
depend strongly on how many data point are available. A study of 78 mutants of WW domain with up to four mutations per residue has quantified what types of mutations avoid interference from native state flexibility, solvation, and other effects, and statistical analysis shows that reliable
642:
is relatively unfolded or unstructured in the transition state, and values near one suggest the transition state's local structure near the mutation site is similar to the native state's. Conservative substitutions on the protein's surface often give phi values near one. When
751:
simulations, he found that the transition state between folding and unfolding looks like the native state and is the same no matter the reaction direction. Phi varied with the mutation location as some regions gave values near zero and others near one. The distribution of
474:{\displaystyle \phi ={\frac {(\Delta G_{W}^{TS\rightarrow D}-\Delta G_{M}^{TS\rightarrow D})}{(\Delta G_{W}^{N\rightarrow D}-\Delta G_{M}^{N\rightarrow D})}}={\frac {\Delta \Delta G^{TS\rightarrow D}}{\Delta \Delta G^{N\rightarrow D}}}}
637:
doesn't affect the structure of the folding pathway's rate-limiting transition state, and a value of one suggests the mutation destabilizes the transition state as much as the folded state; values near zero suggest the
688:, which states that energy and chemical structure are correlated. Though the relationship between the folding intermediate and native state's structures may correlate that between their energies when the
572:
524:
610:
bits are the differences in energy between the native and denatured state. The phi value is interpreted as how much the mutation destabilizes the transition state versus the folded state.
703:
may be. As nonconservative mutations may not bear this out, conservative substitutions, though they may give smaller energetic destabilizations which are harder to detect, are preferred.
608:
136:
The protein's residues are mutated one by one to identify residue clusters that are well-ordered in the folded transition state. These residues' interactions can be checked by
692:
has a well-defined, deep global minimum, free energy destabilizations may not give useful structural information when the energy landscape is flatter or has many local minima.
897:-value analysis to measure the response of mutants as a function of temperature to separate enthalpic and entropic contributions to the transition state free energy.
162:, in which the single-site mutants' effects are compared to the double mutants'. Most mutations are conservative and replace the original residue with a smaller one (
1603:
Miguel; Los Rios, A. De; Muraidhara, B.K.; Wildes, David; Sosnick, Tobin R.; Marqusee, Susan; Wittung-Stafshede, Pernilla; Plaxco, Kevin W.; Ruczinski, Ingo (2006).
1424:
1404:
1304:
1235:
1215:
971:
951:
923:
895:
875:
851:
819:
791:
770:
724:
661:
631:
264:
232:
156:
107:
61:
37:
1028:
Rios, MA; Daneshi, M; Plaxco, KW (2005). "Experimental investigation of the frequency and substitution dependence of negative phi-values in two-state proteins".
1160:
Fersht, AR; Matouschek, A; Serrano, L (1992). "The folding of an enzyme I. Theory of protein engineering analysis of stability and pathway of protein folding".
1476:
1286:
Krantz, BA; Dothager, RS; Sosnick, TR (March 2004). "Discerning the structure and energy of multiple transition states in protein folding using
1117:
Matouschek, A; Kellis, JT; Serrano, L; Fersht, AR (1989). "Mapping the transition state and pathway of protein folding by protein engineering".
793:
values as the transition state structure must otherwise be compared to folding-unfolding simulations which are computationally expensive.
933:
that are nearly pure or the stability difference between the native and mutant protein is 'low', or less than 7 kJ/mol. This may cause
266:= 0 (left) or 1 (right). D is the energy of the denatured state, dagger, that of the transition state, and N, that of the native state.
1568:
Sanchez, IE; Kiefhaber, T (2003). "Origin of unusual phi-values in protein folding: evidence against specific nucleation sites".
801:
Other 'kinetic perturbation' techniques for studying the folding transition state have appeared recently. Best known is the psi (
1341:
Krantz, BA; Sosnick, TR (2001). "Engineered metal binding sites map the heterogeneous folding landscape of a coiled coil".
125:. These measure the mutant residue's energetic contribution to the folding transition state, which reveals the degree of
1716:
926:
727:
some protein folding studies found that stabilizing non-native interactions in a transition state facilitates folding.
1065:"Theoretical and Experimental Demonstration of the Importance of Specific Nonnative Interactions in Protein Folding"
533:
485:
1706:
130:
1721:
1711:
577:
81:
in a two-state manner. The structure of the folding transition state is hard to find using methods such as
685:
905:
The error in equilibrium stability and aqueous (un)folding rate measurements may be large when values of
133:
of the unfolded state, the folded state, and the transition state for the wild-type and mutant proteins.
993:
988:
671:
633:
may have been meant to range from zero to one, negative values can appear. A value of zero suggests the
86:
853:-value was used to study segment association in a folding transition state as covalent crosslinks like
66:
1366:
1142:
748:
126:
663:
is well between zero and one, it is less informative as it doesn't tell us which is the case:
1683:
1634:
1585:
1550:
1501:
1457:
1358:
1323:
1268:
1177:
1134:
1099:
1045:
674:
of near-equal numbers, one kind which is mostly-unfolded and the other which is mostly-folded.
1673:
1665:
1624:
1616:
1577:
1540:
1532:
1491:
1447:
1437:
1350:
1315:
1258:
1248:
1169:
1126:
1089:
1079:
1037:
930:
829:
as a function of metal ion concentration, though Fersht thought this approach difficult. A '
689:
527:
70:
1409:
1389:
1289:
1220:
1200:
974:
information about transition state perturbation can be obtained from large mutant screens.
956:
936:
908:
880:
860:
836:
804:
776:
755:
709:
646:
616:
249:
217:
141:
92:
46:
22:
1011:
826:
110:
78:
89:
because folding transitions states are mobile and partly unstructured by definition. In
1678:
1653:
1629:
1604:
1545:
1520:
1094:
854:
242:
118:
74:
1452:
1385:
1263:
1196:
1700:
1173:
175:
1605:"On the precision of experimentally determined protein folding rates and phi-values"
1146:
1064:
983:
195:
129:
around the mutated residue in the transition state, by accounting for the relative
1370:
821:) value which is found by engineering two metal-binding amino acid residues like
736:
82:
1072:
Proceedings of the
National Academy of Sciences of the United States of America
1669:
1581:
1536:
1319:
830:
199:
179:
1442:
1253:
1084:
822:
207:
203:
187:
114:
1687:
1638:
1589:
1554:
1505:
1461:
1362:
1327:
1272:
1103:
1049:
1181:
1138:
1620:
740:
171:
1654:"High-Resolution Mapping of the Folding Transition State of a WW Domain"
1197:"Differences in the folding transition state of ubiquitin indicated by
744:
211:
167:
1496:
1041:
1130:
191:
183:
1354:
574:
is the same energy difference but for the mutant protein, and the
241:
1475:
Wedemeyer, WJ; Welker, E; Narayan, M; Scheraga, HA (June 2000).
1014:, Fersht AR. (2000). Transition states in protein folding. In
1652:
Dave, K; Jäger, M; Nguyen, H; Kelly, JW; Gruebele, M (2016).
526:
is the difference in energy between the wild-type protein's
1521:"Quantifying protein folding transition states with phi-T"
739:
pioneered phi value analysis in his study of the small
1063:
Zarrine-Asfar, Arash; Wallin, Stefan (July 22, 2008).
1412:
1392:
1292:
1223:
1203:
959:
953:
to fall beyond the zero-one range. Calculated values
939:
911:
883:
863:
839:
807:
779:
758:
712:
649:
619:
580:
536:
488:
278:
252:
220:
144:
95:
49:
25:
667:
The transition state itself is partly structured; or
69:
technique for studying the structure of the folding
877:-T value analysis has been used as an extension of
1418:
1398:
1298:
1229:
1209:
965:
945:
917:
889:
869:
845:
813:
785:
764:
718:
655:
625:
602:
566:
518:
473:
258:
226:
150:
101:
55:
31:
1018:2nd ed, editor RH Pain. Oxford University Press.
699:isn't significantly altered, though the folding
1078:(29). Natural Academy of Sciences: 9999–10004.
1195:Sosnick, TR; Dothager, RS; Krantz, BA (2004).
567:{\displaystyle \Delta G_{M}^{TS\rightarrow D}}
519:{\displaystyle \Delta G_{W}^{TS\rightarrow D}}
8:
113:and conformational folding stability of the
206:, individual domains of proteins L and G,
1677:
1628:
1544:
1495:
1451:
1441:
1411:
1391:
1291:
1262:
1252:
1222:
1202:
1093:
1083:
958:
938:
910:
882:
862:
838:
806:
778:
757:
711:
648:
618:
603:{\displaystyle \Delta G^{N\rightarrow D}}
588:
579:
549:
544:
535:
501:
496:
487:
456:
429:
416:
395:
390:
368:
363:
333:
328:
303:
298:
285:
277:
251:
219:
143:
94:
48:
24:
1004:
695:Phi value analysis assumes the folding
825:into a protein and then recording the
1477:"Disulfide bonds and protein folding"
7:
117:protein are compared with those of
1393:
581:
537:
489:
449:
446:
422:
419:
383:
356:
321:
291:
14:
1519:Ervin, J; Gruebele, M (2002).
592:
556:
508:
460:
436:
407:
399:
372:
353:
348:
340:
310:
288:
1:
1525:Journal of Biological Physics
1016:Mechanisms of Protein Folding
1658:Journal of Molecular Biology
1174:10.1016/0022-2836(92)90561-W
684:Phi value analysis assumes
1738:
1430:Proc. Natl. Acad. Sci. USA
1241:Proc. Natl. Acad. Sci. USA
1670:10.1016/j.jmb.2016.02.008
1582:10.1016/j.jmb.2003.10.016
1320:10.1016/j.jmb.2004.01.018
214:have all been studied by
194:mutants can be used too.
164:cavity-creating mutations
929:must be extrapolated to
640:area around the mutation
1537:10.1023/A:1019930203777
1443:10.1073/pnas.0407863101
1254:10.1073/pnas.0407683101
1085:10.1073/pnas.0801874105
1420:
1400:
1300:
1231:
1211:
967:
947:
919:
891:
871:
847:
815:
787:
766:
720:
657:
627:
604:
568:
520:
475:
267:
260:
228:
152:
103:
57:
33:
1421:
1419:{\displaystyle \psi }
1401:
1399:{\displaystyle \Phi }
1301:
1299:{\displaystyle \psi }
1232:
1230:{\displaystyle \psi }
1212:
1210:{\displaystyle \phi }
994:Equilibrium unfolding
989:Denaturation midpoint
968:
966:{\displaystyle \phi }
948:
946:{\displaystyle \phi }
920:
918:{\displaystyle \phi }
892:
890:{\displaystyle \phi }
872:
870:{\displaystyle \phi }
848:
846:{\displaystyle \phi }
816:
814:{\displaystyle \psi }
788:
786:{\displaystyle \phi }
773:it hard to interpret
767:
765:{\displaystyle \phi }
721:
719:{\displaystyle \phi }
658:
656:{\displaystyle \phi }
628:
626:{\displaystyle \phi }
605:
569:
530:and denatured state,
521:
476:
270:Phi is defined thus:
261:
259:{\displaystyle \phi }
245:
238:Mathematical approach
229:
227:{\displaystyle \phi }
153:
151:{\displaystyle \phi }
109:-value analysis, the
104:
102:{\displaystyle \phi }
87:X-ray crystallography
58:
56:{\displaystyle \phi }
34:
32:{\displaystyle \phi }
1621:10.1110/ps.051870506
1410:
1390:
1290:
1221:
1201:
957:
937:
909:
881:
861:
837:
805:
777:
756:
710:
647:
617:
578:
534:
486:
276:
250:
246:Energy diagrams for
218:
142:
138:double-mutant-cycle
93:
47:
23:
1717:Protein engineering
1436:(50): 17327–17328.
1384:Fersht, AR (2004).
1247:(50): 17377–17382.
925:for solutions with
686:Hammond's postulate
672:protein populations
563:
515:
406:
379:
347:
317:
67:protein engineering
65:is an experimental
1416:
1396:
1296:
1227:
1207:
963:
943:
915:
887:
867:
843:
811:
783:
762:
749:molecular dynamics
716:
653:
623:
600:
564:
540:
516:
492:
471:
386:
359:
324:
294:
268:
256:
224:
148:
99:
53:
29:
17:Phi value analysis
1707:Protein structure
1497:10.1021/bi005111p
1349:(12): 1042–1047.
1343:Nat. Struct. Biol
1042:10.1021/bi0505621
931:aqueous solutions
857:were introduced.
833:' variant of the
469:
411:
1729:
1692:
1691:
1681:
1649:
1643:
1642:
1632:
1600:
1594:
1593:
1576:(5): 1077–1085.
1565:
1559:
1558:
1548:
1516:
1510:
1509:
1499:
1481:
1472:
1466:
1465:
1455:
1445:
1425:
1423:
1422:
1417:
1405:
1403:
1402:
1397:
1381:
1375:
1374:
1338:
1332:
1331:
1305:
1303:
1302:
1297:
1283:
1277:
1276:
1266:
1256:
1236:
1234:
1233:
1228:
1216:
1214:
1213:
1208:
1192:
1186:
1185:
1157:
1151:
1150:
1131:10.1038/340122a0
1114:
1108:
1107:
1097:
1087:
1069:
1060:
1054:
1053:
1025:
1019:
1009:
972:
970:
969:
964:
952:
950:
949:
944:
924:
922:
921:
916:
896:
894:
893:
888:
876:
874:
873:
868:
852:
850:
849:
844:
827:folding kinetics
820:
818:
817:
812:
792:
790:
789:
784:
771:
769:
768:
763:
732:Example: barnase
725:
723:
722:
717:
690:energy landscape
662:
660:
659:
654:
632:
630:
629:
624:
609:
607:
606:
601:
599:
598:
573:
571:
570:
565:
562:
548:
525:
523:
522:
517:
514:
500:
480:
478:
477:
472:
470:
468:
467:
466:
444:
443:
442:
417:
412:
410:
405:
394:
378:
367:
351:
346:
332:
316:
302:
286:
265:
263:
262:
257:
233:
231:
230:
225:
157:
155:
154:
149:
127:native structure
111:folding kinetics
108:
106:
105:
100:
71:transition state
62:
60:
59:
54:
38:
36:
35:
30:
1737:
1736:
1732:
1731:
1730:
1728:
1727:
1726:
1722:Protein methods
1712:Protein folding
1697:
1696:
1695:
1651:
1650:
1646:
1609:Protein Science
1602:
1601:
1597:
1567:
1566:
1562:
1531:(23): 115–128.
1518:
1517:
1513:
1479:
1474:
1473:
1469:
1408:
1407:
1388:
1387:
1383:
1382:
1378:
1340:
1339:
1335:
1288:
1287:
1285:
1284:
1280:
1219:
1218:
1199:
1198:
1194:
1193:
1189:
1159:
1158:
1154:
1125:(6229): 122–6.
1116:
1115:
1111:
1067:
1062:
1061:
1057:
1036:(36): 12160–7.
1027:
1026:
1022:
1010:
1006:
1002:
980:
955:
954:
935:
934:
907:
906:
903:
879:
878:
859:
858:
855:disulfide bonds
835:
834:
803:
802:
799:
775:
774:
754:
753:
734:
708:
707:
681:
679:Key assumptions
645:
644:
615:
614:
584:
576:
575:
532:
531:
484:
483:
452:
445:
425:
418:
352:
287:
274:
273:
248:
247:
240:
216:
215:
140:
139:
91:
90:
75:protein domains
63:-value analysis
45:
44:
21:
20:
12:
11:
5:
1735:
1733:
1725:
1724:
1719:
1714:
1709:
1699:
1698:
1694:
1693:
1664:(8): 115–128.
1644:
1615:(3): 553–563.
1595:
1560:
1511:
1467:
1415:
1395:
1376:
1355:10.1038/nsb723
1333:
1295:
1278:
1226:
1206:
1187:
1152:
1109:
1055:
1020:
1003:
1001:
998:
997:
996:
991:
986:
979:
976:
962:
942:
914:
902:
899:
886:
866:
842:
810:
798:
795:
782:
761:
733:
730:
729:
728:
715:
704:
693:
680:
677:
676:
675:
670:There are two
668:
652:
622:
597:
594:
591:
587:
583:
561:
558:
555:
552:
547:
543:
539:
513:
510:
507:
504:
499:
495:
491:
465:
462:
459:
455:
451:
448:
441:
438:
435:
432:
428:
424:
421:
415:
409:
404:
401:
398:
393:
389:
385:
382:
377:
374:
371:
366:
362:
358:
355:
350:
345:
342:
339:
336:
331:
327:
323:
320:
315:
312:
309:
306:
301:
297:
293:
290:
284:
281:
255:
239:
236:
223:
147:
98:
52:
28:
13:
10:
9:
6:
4:
3:
2:
1734:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1704:
1702:
1689:
1685:
1680:
1675:
1671:
1667:
1663:
1659:
1655:
1648:
1645:
1640:
1636:
1631:
1626:
1622:
1618:
1614:
1610:
1606:
1599:
1596:
1591:
1587:
1583:
1579:
1575:
1571:
1564:
1561:
1556:
1552:
1547:
1542:
1538:
1534:
1530:
1526:
1522:
1515:
1512:
1507:
1503:
1498:
1493:
1489:
1485:
1478:
1471:
1468:
1463:
1459:
1454:
1449:
1444:
1439:
1435:
1431:
1427:
1413:
1406:value versus
1380:
1377:
1372:
1368:
1364:
1360:
1356:
1352:
1348:
1344:
1337:
1334:
1329:
1325:
1321:
1317:
1314:(2): 463–75.
1313:
1309:
1293:
1282:
1279:
1274:
1270:
1265:
1260:
1255:
1250:
1246:
1242:
1238:
1224:
1204:
1191:
1188:
1183:
1179:
1175:
1171:
1168:(3): 771–82.
1167:
1163:
1156:
1153:
1148:
1144:
1140:
1136:
1132:
1128:
1124:
1120:
1113:
1110:
1105:
1101:
1096:
1091:
1086:
1081:
1077:
1073:
1066:
1059:
1056:
1051:
1047:
1043:
1039:
1035:
1031:
1024:
1021:
1017:
1013:
1008:
1005:
999:
995:
992:
990:
987:
985:
982:
981:
977:
975:
960:
940:
932:
928:
912:
900:
898:
884:
864:
856:
840:
832:
831:cross-linking
828:
824:
808:
796:
794:
780:
759:
750:
746:
742:
738:
731:
713:
705:
702:
698:
694:
691:
687:
683:
682:
678:
673:
669:
666:
665:
664:
650:
641:
636:
620:
611:
595:
589:
585:
559:
553:
550:
545:
541:
529:
511:
505:
502:
497:
493:
481:
463:
457:
453:
439:
433:
430:
426:
413:
402:
396:
391:
387:
380:
375:
369:
364:
360:
343:
337:
334:
329:
325:
318:
313:
307:
304:
299:
295:
282:
279:
271:
253:
244:
237:
235:
221:
213:
209:
205:
201:
197:
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1000:References
528:transition
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180:isoleucine
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