Mathematical modeling of evolution. Solved and open problems

Theory in Biosciences

Volumn 130, Issue 1, 2011, Pages 71-89

  Schuster, Peter ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Error threshold; Molecular evolution; Natural selection; Neutral evolution; Quasi species; RNA structures

Indexed keywords

BIOLOGICAL MODEL; CONFERENCE PAPER; GENETIC SELECTION; MOLECULAR EVOLUTION; MUTATION;

EVOLUTION, MOLECULAR; MODELS, GENETIC; MUTATION; SELECTION, GENETIC;

EID: 79952192799     PISSN: 14317613     EISSN: 16117530     Source Type: Journal    
DOI: 10.1007/s12064-010-0110-z     Document Type: Conference Paper

References (76)

1. β replicase EMBO J 11 13 5129 5135 (Pubitemid 23023457)
2. Biebricher C, Eigen M (1988) Kinetics of RNA replication by Qβ replicase. In: Domingo E, Holland J, Ahlquist P (eds) RNA genetics, vol I. CRC Press, Boca Raton, pp. 1-21
3. CK Biebricher M Eigen C William J Gardiner 1983 Kinetics of RNA replication Biochemistry 22 2544 2559 1:CAS:528:DyaL3sXhslCqtbo%3D 10.1021/bi00279a036 6860647
4. CK Biebricher M Eigen C William J Gardiner 1984 Kinetics of RNA replication: plus-minus asymmetry and double-strand formation Biochemistry 23 3186 3194 1:CAS:528:DyaL2cXktlCmu7g%3D 10.1021/bi00309a012 6205687
5. CK Biebricher M Eigen C William J Gardiner 1985 Kinetics of RNA replication: competition and selection among self-replicating RNA species Biochemistry 24 6550 6560 1:CAS:528:DyaL2MXlvFWmsbc%3D 10.1021/bi00344a037 2417621 (Pubitemid 16207130)
6. ZD Blount C Z RE Lenski 2008 Historical contingency an the evolution of a key innovation in an experimental population of Escherichia coli Proc Natl Acad Sci USA 105 7898 7906 10.1073/pnas.0803151105 (Pubitemid 351904703)
7. Blythe RA, McKane A (2007) Stochastic models of evolution in genetice, ecology and linguistics. J Stat Mech P07018:1-58
8. D Brown L Gold 1996 RNA replication by Qβ replicase: a working model Proc Natl Acad Sci USA 93 11558 11562 1:CAS:528:DyaK28Xmtlagt7Y%3D 10.1073/pnas.93.21.11558 8876174 (Pubitemid 26347160)
9. P Cahill K Foster DE Mahan 1991 Polymerase chain reaction and Qβ replicase amplification Clin Chem 37 1482 1485 1:CAS:528:DyaK3MXmtVahtrs%3D 1893572 (Pubitemid 21905201)
10. Darwin C (1859) On the origin of species by means of natural selection or the preservation of favoured races in the struggle for life. John Murray, London
11. L Demetrius P Schuster K Sigmund 1985 Polynucleotide evolution and branching processes Bull Math Biol 47 239 262 1:CAS:528:DyaL2MXltVSmsLg%3D 4027436
12. B Derrida L Peliti 1991 Evolution in a flat fittness landscape Bull Math Biol 53 355 382
13. RA Dimitrov M Zuker 2004 Prediction of hybridization and melting for double-stranded nucleic acids Biophys J 87 215 226 1:CAS:528: DC%2BD2cXmtVemu7o%3D 10.1529/biophysj.103.020743 15240459 (Pubitemid 38880079)
14. Dobzhansky T, Ayala FJ, Stebbins GL, Valentine JW (1977) Evolution. W. H. Freeman & Co., San Francisco
15. Domingo E (ed) (2005) Virus entry into error catastrophe as a new antiviral strategy. Virus Res 107(2):115-228
16. JW Drake 1993 Rates of spontaneous mutation among RNA viruses Proc Natl Acad Sci USA 90 4171 4175 1:CAS:528:DyaK3sXkt1aitb8%3D 10.1073/pnas.90.9.4171 8387212 (Pubitemid 23134188)
17. JW Drake B Charlesworth D Charlesworth JF Crow 1998 Rates of spontaneous mutation Genetics 148 1667 1686 1:CAS:528:DyaK1cXks1eiurg%3D 9560386 (Pubitemid 28180696)
18. AW Edwards 1994 The fundamental theroem of natural selection Biol Rev 69 443 474 1:STN:280:DyaK2M%2Fpt12ksQ%3D%3D 10.1111/j.1469-185X.1994.tb01247.x 7999947
19. M Eigen 1971 Selforganization of matter and the evolution of biological macromolecules Naturwissenschaften 58 465 523 1:CAS:528:DyaE38XjtFaksw%3D%3D 10.1007/BF00623322 4942363
20. Eigen M, Biebricher C (1988) Sequence space and quasispecies distribution. In: Domingo E, Holland J, Ahlquist P (eds) RNA Genetics, vol III, CRC Press, Boca Raton, pp 211-245
21. M Eigen J McCaskill P Schuster 1989 The molecular quasispecies Adv Chem Phys 75 149 263 1:CAS:528:DyaK3cXmtlOqtb0%3D 10.1002/9780470141243.ch4
22. Fisher RA (1930) The genetical theory of natural selection. Oxford University Press, Oxford
23. W Fontana P Schuster 1987 A computer model of evolutionary optimization Biophys Chem 26 123 147 1:CAS:528:DyaL2sXltFait70%3D 10.1016/0301-4622(87)80017- 0 3607225
24. W Fontana P Schuster 1998 Continuity in evolution: on the nature of transitions Science 280 1451 1455 1:CAS:528:DyaK1cXjtlars78%3D 10.1126/science.280.5368.1451 9603737 (Pubitemid 28264841)
25. W Fontana P Schuster 1998 Shaping space. The possible and the attainable in RNA genotype-phenotype mapping J Theor Biol 194 491 515 1:CAS:528: DyaK1cXnsVektrs%3D 10.1006/jtbi.1998.0771 9790826 (Pubitemid 28493247)
26. W Fontana W Schnabl P Schuster 1989 Physical aspects of evolutionary optimization and adaptation Phys Rev A 40 3301 3321 1:CAS:528:DyaL1MXmtFSltLg%3D 10.1103/PhysRevA.40.3301 9902537
27. W Fontana DAM Konings PF Stadler P Schuster 1993 Statistics of RNA secondary structures Biopolymers 33 1389 1404 1:CAS:528:DyaK3sXmtF2ku7s%3D 10.1002/bip.360330909 7691201 (Pubitemid 23249156)
28. DT Gillespie 1976 A general method for numerically simulating the stochastic time evolution of coupled chemical reactions J Comp Phys 22 403 434 1:CAS:528:DyaE2sXnvFCisw%3D%3D 10.1016/0021-9991(76)90041-3 (Pubitemid 8008311)
29. DT Gillespie 1977 Exact stochastic simulation of coupled chemical reactions J Phys Chem 81 2340 2361 1:CAS:528:DyaE1cXht1GntA%3D%3D 10.1021/j100540a008
30. DT Gillespie 2007 Stochastic simulation of chemical kinetics Annu Rev Phys Chem 58 35 55 1:CAS:528:DC%2BD2sXlslSisbY%3D 10.1146/annurev.physchem.58. 032806.104637 17037977 (Pubitemid 46877584)
31. Hamming RW (1986) Coding and information theory, 2nd edn. Prentice-Hall, Englewood Cliffs
32. DM Held ST Greathouse A Agrawal DH Burke 2003 Evolutionary landscapes for the acquisition of new ligand recognition by RNA aptamers J Mol Evol 57 299 308 1:CAS:528:DC%2BD3sXnvFGmuro%3D 10.1007/s00239-003-2481-y 14629040 (Pubitemid 37082936)
33. IL Hofacker W Fontana PF Stadler LS Bonhoeffer M Tacker P Schuster 1994 Fast folding and comparison of RNA secondary structures Monatshefte für Chemie 125 167 188 1:CAS:528:DyaK2cXivFaht7k%3D 10.1007/BF00818163
34. Hofacker IL, Fontana W, Stadler PF, Bonhoeffer LS, Tacker M, Schuster P (1994b) Vienna RNA package. Current Version 1.8.4. Institute for Theoretical Chemistry, University of Vienna, Vienna.
35. K Hosoda T Matsuura H Kita N Ichihashi K Tsukada T Yomo 2007 Kinetic analysis of the entire RNA amplification process by Qβ replicase J Biol Chem 282 15516 15527 1:CAS:528:DC%2BD2sXltl2gurc%3D 10.1074/jbc.M700307200 17412690 (Pubitemid 47093276)
36. Z Huang JW Szostak 2003 Evolution of aptamers with a new specificity and new secondary structures from an ATP aptamer RNA 9 1456 1463 1:CAS:528:DC%2BD3sXps1Oju7w%3D 10.1261/rna.5990203 14624002 (Pubitemid 37463472)
37. MA Huynen PF Stadler W Fontana 1996 Smoothness within ruggedness. The role of neutrality in adaptation Proc Natl Acad Sci USA 93 397 401 1:CAS:528:DyaK28Xjslymug%3D%3D 10.1073/pnas.93.1.397 8552647 (Pubitemid 26038166)
38. BL Jones HK Leung 1981 Stochastic analysis of a non-linear model for selection of biological macromolecules Bull Math Biol 43 665 680 1:CAS:528:DyaL38Xksl2ltw%3D%3D (Pubitemid 12218707)
39. BL Jones RH Enns SS Rangnekar 1976 On the theory of selection of coupled macromolecular systems Bull Math Biol 38 15 28
40. GF Joyce 2007 Forty years of in vitro evolution Angew Chem Int Ed 46 6420 6436 1:CAS:528:DC%2BD2sXhtVOhsL3O 10.1002/anie.200701369 (Pubitemid 47340165)
41. Judson H (1979) The eighth day of creation. The makers of the revolution in biology. Jonathan Cape, London
42. Kimura M (1983) The neutral theory of molecular evolution. Cambridge University Press, Cambridge
43. A Kupczok P Dittrich 2006 Determinants of simulated RNA evolution J Theor Biol 238 726 735 1:CAS:528:DC%2BD28XjvVyhtA%3D%3D 10.1016/j.jtbi.2005.06.019 16098538 (Pubitemid 43075585)
44. B Küppers M Sumper 1975 Minimal requirements for template recognition by bacteriophage Qβ replicase: approach to general RNA-dependent RNA synthesis Proc Natl Acad Sci USA 72 2640 2643 10.1073/pnas.72.7.2640 1058479
45. RE Lenski MR Rose SC Simpson SC Tadler 1991 Long-term experimental evolution in Escherichia coli. I. Adaptation and divergence during 2,000 generations Am Nat 38 1315 1341 10.1086/285289
46. NB Leontis A Lescoute E Westhof 2006 The building blocks and motifs of RNA architecture Curr Opin Struct Biol 16 279 287 1:CAS:528:DC%2BD28Xls1aks7w%3D 10.1016/j.sbi.2006.05.009 16713707 (Pubitemid 43831653)
47. TA Lincoln GF Joyce 2009 Self-sustained replication of an RNA enzyme Science 323 1229 1232 1:CAS:528:DC%2BD1MXit1elu74%3D 10.1126/science.1167856 19131595
48. Malthus TR (1798) An Essay of the principle of population as it affects the future improvement of society. J. Johnson, London
49. A Maxam W Gilbert 1977 A new method of sequencing DNA Proc Natl Acad Sci USA 74 560 564 1:CAS:528:DyaE2sXhtFOhsbw%3D 10.1073/pnas.74.2.560 265521 (Pubitemid 8038842)
50. JS McCaskill 1984 A localization threshold for macromolecular quasispecies from continuously distributed replication rates J Chem Phys 80 5194 5202 1:CAS:528:DyaL2cXktlCrsrY%3D 10.1063/1.446590
51. G Mendel 1866 Versuche über Pflanzen-Hybriden Verhandlungen des naturforschenden Vereins in Brünn 4 3 47
52. G Mendel 1870 Über einige aus künstlicher Befruchtung gewonnenen Hieracium-Bastarde Verhandlungen des naturforschenden Vereins in Brünn 8 26 31
53. DR Mills RL Peterson S Spiegelman 1967 An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule Proc Natl Acad Sci USA 58 217 224 1:CAS:528:DyaF2sXltFektL8%3D 10.1073/pnas.58.1.217 5231602
54. PB Moore 1999 Structural motifs in RNA Annu Rev Biochem 68 287 300 1:CAS:528:DyaK1MXlvFajsLk%3D 10.1146/annurev.biochem.68.1.287 10872451 (Pubitemid 29449194)
55. T Nakaishi K Iio K Yamamoto I Urabe T Yomo 2002 Kinetic properties of Qβ replicase, an RNA dependent RNA polymerase J Biosci Bioeng 93 322 327 1:CAS:528:DC%2BD38Xjs1Wgsbw%3D 10.1263/jbb.93.322 16233208 (Pubitemid 34539146)
56. S Okasha 2008 Fisher's fundamental theorem of natural selection-a philosophical analysis Br J Phil Sci 59 319 351 10.1093/bjps/axn010
57. Phillipson PE, Schuster P (2009) Modeling by nonlinear differential equations. Dissipative and conservative processes. World Scientific Series on Nonlinear Science A, vol 69. World Scientific, Singapore
58. GR Price 1972 Fisher's "fundamental theorem" made clear Annals Human Genetics 36 129 140 1:STN:280:DyaE3s7ktlWlsw%3D%3D 10.1111/j.1469-1809. 1972.tb00764.x
59. C Reidys PF Stadler P Schuster 1997 Generic properties of combinatory maps. Neutral networks of RNA secondary structure Bull Math Biol 59 339 397 1:CAS:528:DyaK2sXhvFCnsr4%3D 10.1007/BF02462007 9116604 (Pubitemid 27150355)
60. F Sanger S Nicklen A Coulson 1977 DNA sequencing with chain-terminating inhibitors Proc Natl Acad Sci USA 74 5463 5467 1:CAS:528:DyaE1cXhtlaru7Y%3D 10.1073/pnas.74.12.5463 271968
61. EA Schultes DP Bartel 2000 One sequence, two ribozymes: implications for the emergence of new ribozyme folds Science 289 448 452 1:CAS:528: DC%2BD3cXlsV2gtLg%3D 10.1126/science.289.5478.448 10903205 (Pubitemid 30490456)
62. Schuster P (2003) Molecular insight into the evolution of phenotypes. In: Crutchfield JP, Schuster P (eds) Evolutionary dynamics-exploring the interplay of accident, selection, neutrality, and function, Oxford University Press, New York, pp 163-215
63. P Schuster 2006 Prediction of RNA secondary structures: from theory to models and real molecules Reports on Progress in Physics 69 1419 1477 1:CAS:528:DC%2BD28XlsFKju7Y%3D 10.1088/0034-4885/69/5/R04 (Pubitemid 43862450)
64. P Schuster J Swetina 1988 Stationary mutant distribution and evolutionary optimization Bull Math Biol 50 635 660 1:STN:280:DyaL1M7hvVKktA%3D%3D 3219448 (Pubitemid 18268678)
65. P Schuster W Fontana PF Stadler IL Hofacker 1994 From sequences to shapes and back: a case study in RNA secondary structures Proc R Soc Lond B 255 279 284 1:CAS:528:DyaK2cXmslCmsL0%3D 10.1098/rspb.1994.0040 (Pubitemid 24102288)
66. Seneta E (1981) Non-negative matrices and Markov chains, 2nd edn. Springer-Verlag, New York
67. S Spiegelman 1971 An approach to the experimental analysis of precellular evolution Q Rev Biophys 4 213 253 1:CAS:528:DyaE38XhtV2htr4%3D 10.1017/S0033583500000639 5134462
68. BRM Stadler PF Stadler GP Wagner W Fontana 2001 The topology of the possible: formal spaces underlying patterns of evolutionary change J Theor Biol 213 241 274 1:CAS:528:DC%2BD3MXoslGhu7k%3D 10.1006/jtbi.2001.2423 11894994 (Pubitemid 33096020)
69. CJ Thompson JL McBride 1974 On Eigen's theory of the self-organization of matter and the evolution of biological macromolecules Math Biosci 21 127 142 10.1016/0025-5564(74)90110-2
70. P Verhulst 1838 Notice sur la loi que la population pursuit dans son accroisement Corresp Math Phys 10 113 121
71. C Weissmann 1974 The making of a phage FEBS Lett 40 S10 S18 10.1016/0014-5793(74)80684-8 4605288
72. T Wiehe 1997 Model dependency of error thresholds: the role of fitness functions and contrasts between the finite and infinite sites models Genet Res Camb 69 127 136 10.1017/S0016672397002619 (Pubitemid 27356696)
73. M Zuker 1989 On finding all suboptimal foldings of an RNA molecule Science 244 48 52 1:CAS:528:DyaL1MXkt1SnsbY%3D 10.1126/science.2468181 2468181 (Pubitemid 19130742)
74. Zuker M (1989b) The use of dynamic programming algorithms in RNA secondary structure prediction. In: Waterman MS (ed) Mathematical methods for DNA sequences, CRC Press, Boca Raton, pp 159-184
75. M Zuker P Stiegler 1981 Optimal computer folding of larger RNA sequences using thermodynamics and auxiliary information Nucl Acids Res 9 133 148 1:CAS:528:DyaL3MXhtFKqurc%3D 10.1093/nar/9.1.133 6163133
76. Zwillinger D (1998) Handbook of differential equations, 3rd edn. Academic Press, San Diego