Group theory and biomolecular conformation: I. Mathematical and computational models

Journal of Physics Condensed Matter

Volumn 22, Issue 32, 2010, Pages

  Chirikjian, Gregory S ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL MACROMOLECULE; BIOMOLECULAR CONFORMATIONS; CHEMICAL MODEL; COMPUTATIONAL MODEL; CONTINUUM MODEL; GEOMETRIC SYMMETRY; GRAINED MODELS; GROUP THEORY; QUANTUM MECHANICAL; SECONDARY STRUCTURES; STRUCTURAL BIOLOGY;

ALGEBRA; CONTINUUM MECHANICS; ELECTRORHEOLOGICAL FLUIDS; MACROMOLECULES; QUANTUM THEORY;

CONFORMATIONS;

BIOLOGY; CHEMISTRY; COMPUTER SIMULATION; CONFORMATION; MACROMOLECULE; METHODOLOGY; REVIEW; THEORETICAL MODEL;

COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; MACROMOLECULAR SUBSTANCES; MODELS, THEORETICAL; MOLECULAR CONFORMATION;

EID: 77956893119     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/22/32/323103     Document Type: Review

References (172)

1. Abraham R and Marsden J E 1978 Foundations of Mechanics 2nd edn (San Mateo, CA: Benjamin-Cummings)
2. Antman S S 1995 Nonlinear Problems of Elasticity (New York: Springer)
3. Arnol'd V I 1978 Mathematical Methods of Classical Mechanics (New York: Springer)
4. Atilgan A R, Durell S R, Jernigan R L, Demirel M C, Keskin O and Bahar I 2001 Anisotropy of fluctuation dynamics of proteins with an elastic network model Biophys. J. 80 505-15
5. Bahar I and Jernigan R L 1998 Vibrational dynamics of transfer RNAs: comparison of the free and synthetase-bound forms J. Mol. Biol. 281 871-84
6. Balaeff A, Mahadevan L and Schulten K 2003 Modeling DNA loops using the theory of elasticity arXiv.org (http://arxiv.org/abs/physics/0301006)
7. Balaeff A, Mahadevan L and Schulten K 2004 Structural basis for cooperative DNA binding by CAP and Lac repressor Structure 12 123-32
8. Banavar J R and Maritan A 2003 Colloquium: geometrical approach to protein folding: a tube picture Rev. Mod. Phys. 75 23-34
9. Barut A O and Raczka R 1986 Theory of Group Representations and Applications (Singapore: World Scientific)
10. Baumann C G, Smith S B, Bloomfield V A and Bustamante C 1997 Ionic effects on the elasticity of single DNA molecules Proc. Natl Acad. Sci. USA 94 6185-90
11. Bawendi M G and Karl F F 1985 A wiener integral model for stiff polymer chains J. Chem. Phys. 83 2491-6
12. Benham C J 1979 Elastic model of the large-scale structure of duplex DNA Biopolymers 18 609-23
13. Benham C J and Mielke S P 2005 DNA mechanics Annu. Rev. Biomed. Eng. 7 21-53
14. Berman H M, Westbrook J, Feng Z, Gilliland G, Bhat T N, Weissig H, Shindyalov I N and Bourne P E 2000 The protein data bank Nucl. Acids Res. 28 235-42
15. Bhattacharjee S M and Muthukumar M 1987 Statistical mechanics of solutions of semiflexible chains: a path integral formulation J. Chem. Phys. 86 411-8
16. Bowie J U 1997 Helix packing angle preferences Nat. Struct. Biol. 4 915-7
17. Brockett R W 1972 System theory on group manifolds and coset spaces SIAM J. Control 10 265-84
18. Brooks B and Karplus M 1983 Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic typsin inhibitor Proc. Natl Acad. Sci. USA 80 6571-5
19. Brooks B and Karplus M 1985 Normal modes for specific motions of macromolecules: application to the hinge-bending mode of lysozyme Proc. Natl Acad. Sci. USA 82 4995-9
20. Brooks B R, Bruccoleri R E, Olafson B D, States D J, Swaminathan S and Karplus M 1983 CHARMM - a program for macromolecular energy, minimization, and dynamics calculations J. Comput. Chem. 4 187-217
21. Buchiat C, Wang M D, Allemand J F, Strick T, Block S M and Croquette V 1999 Estimating the persistence length of a worm-like chain molecule from force-extension measurements Biophys. J. 76 409-13
22. Chirikjian G S and Wang Y F 2000 Conformational statistics of stiff macromolecules as solutions to PDEs on the rotation and motion groups Phys. Rev. E 62 880-92
23. Chirikjian G S and Kyatkin A B 2000 An operational calculus for the Euclidean motion group with applications in robotics and polymer science J. Fourier Anal. Appl. 6 583-606
24. Chirikjian G S and Kyatkin A B 2001 Engineering Applications of Noncommutative Harmonic Analysis (Boca Raton, FL: CRC Press)
25. Chirikjian G S 2001 Conformational statistics of macromolecules using generalized convolution Comput. Theor. Polym. Sci. 11 143-53
26. Chirikjian G S 2003 A methodology for determining mechanical properties of macromolecules from ensemble motion data Trends Anal. Chem. 22 549-53
27. Chirikjian G S 2008 The stochastic elastica and excluded-volume perturbations of DNA conformational ensembles Int. J. Non-Linear Mech. 43 1108-20
28. Chirikjian G S 2009 Stochastic Models, Information Theory, and Lie Groups (Basle: Birkhäuser)
29. Chothia C, Levitt M and Richardson D 1981 Helix to helix packing in proteins J. Mol. Biol. 145 215-50
30. Cieplak M, Hoang T X and Robbins M O 2004 Stretching of proteins in the entropic limit Phys. Rev. E 69 011912
31. Cluzel P, Lebrun A, Christoph H, Lavery R, Viovy J L, Chatenay D and Caron F 1996 DNA: an extensible molecule Science 271 792
32. Coleman B D, Dill E H, Lembo M, Lu Z and Tobias I 1993 On the dynamics of rods in the theory of Kirchhoff and Clebsch Arch. Ration. Mech. Anal. 121 339-59
33. Coleman B D, Tobias I and Swigon D 1995 Theory of the influence of end conditions on self-contact in DNA loops J. Chem. Phys. 103 9101-9
34. Coleman B D, Swigon D and Tobias I 2000 Elastic stability of DNA configurations. II: supercoiled plasmides with self-contact Phys. Rev. E 61 759-70
35. Coleman B D, Olson W K and Swigon D 2003 Theory of sequence-dependent DNA elasticity J. Chem. Phys. 118 7127-40
36. Crick F 1953 The packing of α-helices: simple coiled coils Acta Crystallogr. 6 689-97
37. Daniels H E 1952 The statistical theory of stiff chains Proc. R. Soc. A 63 290-311
38. de Gennes P G 1979 Scaling Concepts in Polymer Physics (Ithaca, NY: Cornell University Press)
39. de Gennes P G and Prost J 1998 The Physics of Liquid Crystals 2nd edn (Oxford: Clarendon)
40. des Cloizeaux J and Jannink G 1990 Polymers in Solution: Their Modelling and Structure (Oxford: Clarendon)
41. Dichmann D J, Li Y and Maddocks J H 1995 Hamiltonian formulations and symmetries in rod mechanics Mathematical Approaches to Biomolecular Structure and Dynamics ed J P Mesirov, K Schulten and D Summers (New York: Springer) pp 71-113
42. Dixit S B, Beveridge D L, Case D A, Cheatham T E, Giudice E, Lankas F, Lavery R, Maddocks J H, Osman R, Sklenar H, Thayer K M and Varnai P 2005 Molecular dynamics simulations of the 136 unique tetranucleotide sequences of DNA oligonucleotides. II: sequence context effects on the dynamical structures of the 10 unique dinucleotide steps Biophys. J. 89 3721-40
43. Doi M and Edwards S F 1986 The Theory of Polymer Dynamics (Oxford: Clarendon Press)
44. Dyson F 1996 Selected Papers of Freeman Dyson with Commentary (Providence, RI: American Mathematical Society)
45. Fain B and Rudnick J 1999 Conformations of closed DNA Phys. Rev. E 60 7239-52
46. Fain B, Rudnick J and Ostlund S 1997 Conformations of linear DNA Phys. Rev. E 55 7364-8
47. Flory P J 1969 Statistical Mechanics of Chain Molecules (New York: Wiley-Interscience)
48. Fuller F B 1978 Decomposition of the linking number of a closed ribbon: a problem from molecular biology Proc. Natl Acad. Sci. USA 75 3557
49. Fuller F B 1971 The writhing number of a space curve Proc. Natl Acad. Sci. USA 68 815
50. Gel'fand I M, Minlos R A and Shapiro Z Ya 1963 Representations ofthe Rotation and Lorentz Groups and Their Applications (New York: Macmillan)
51. Gell-Mann M and Ne'eman Y 2000 The Eightfold Way (Boulder, CO: Westview Press)
52. Gobush W, Yamakawa H, Stockmayer W H and Magee W S 1972 Statistical mechanics of wormlike chains. I. Asymptotic behavior J. Chem. Phys. 57 2839-43
53. Gonzalez O and Maddocks J H 2001 Extracting parameters for base-pair level models of DNA from molecular dynamics simulations Theor. Chem. Acc. 106 76-82
54. Goyal S, Perkins N C and Lee C L 2005 Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables J. Comput. Phys. 209 371-89
55. Grosberg A Yu and Khokhlov A R 1994 Statistical Physics of Macromolecules (New York: American Institute of Physics)
56. Ha B Y and Thirumalai D 1997 Semiflexible chains under tension J. Chem. Phys. 106 4243-7
57. Hagerman P J 1985 Analysis of the ring-closure probabilities of isotropic wormlike chains: application to duplex DNA Biopolymers 24 1881-97
58. Hermans J J and Ullman R 1952 The statistics of stiff chains, with applications to light scattering Physica 18 951-71
59. Hinsen K 1998 Analysis of domain motions by approximate normal mode calculations Protein Struct. Function Genet. 33 417-29
60. Holm D D, Marsden J E and Ratiu T S 1998 The Euler-Poincare equations and semidirect products with applications to continuum theories Adv. Math. 137 1
61. Horowitz D S and Wang J C 1984 Torsional rigidity of DNA and length dependence of the free energy of DNA supercoiling J. Mol. Biol. 173 75-91
62. Inui T, Tanabe Y and Onodera Y 1996 Group Theory and its Applications in Physics 2nd edn (Berlin: Springer)
63. Kalmykov Y P and Coffey W T 1998 Analytical solutions for rotational diffusion in the mean field potential: application to the theory of dielectric relaxation in nematic liquid crystals Liq. Cryst. 25 329-39
64. Kamein R D, Lubensky T C, Nelson P and O'Hern C S 1997 Direct determination of DNA twist-stretch coupling Europhys. Lett. 28 237-42
65. Kholodenko A L 1995 Statistical mechanics of semiflexible polymers: yesterday, today and tomorrow J. Chem. Soc. Farady Trans. 91 2473-82
66. Kim J-S and Chirikjian G S 2006 Conformational analysis of stiff chiral polymers with end-constraints Mol. Simul. 32 1139-54
67. Kim M K, Jernigan R L and Chirikjian G S 2002 Efficient generation of feasible pathways for protein conformational transitions Biophys. J. 83 1620-30
68. Kim M K, Chirikjian G S and Jernigan R L 2002 Elastic models of conformational transitions in macromolecules J. Mol. Graph. Modeling 21 151-60
69. Kim M K, Jernigan R L and Chirikjian G S 2003 An elastic network model of HK97 capsid maturation J. Struct. Biol. 143 107-17
70. Kim M K, Jernigan R L and Chirikjian G S 2005 Rigid-cluster models of conformational transitions in macromolecular machines and assemblies Biophys. J. 89 43-55
71. Kleinert H 1995 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics 2nd edn (Singapore: World Scientific)
72. Klenin K, Merlitz H and Langowski J 1998 A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes Biophys. J. 74 780-8
73. Kostelec P J and Rockmore D N 2003 FFTs on the Rotation Group (Santa Fe Institute Working Papers Series) Paper #03-11-060
74. Kovacs J A and Wriggers W 2002 Fast rotational matching Acta Crystallogr. D 58 1282-6
75. Kratky O and Porod G 1949 Rontgenuntersuchung Geloster Fadenmolekule Recueil des Travaux Chimiques des Pays-Bas 68 1106-22
76. Kroy K and Frey E 1996 Force-extension relation and plateau modulus for wormlike chains Phys. Rev. Lett. 77 306-9
77. Lagowski J B, Noolandi J and Nickel B 1991 Stiff chain model - functional integral approach J. Chem. Phys. 95 1266-9
78. Lavery R, Moakher M, Maddocks J H, Petkeviciute D and Zakrzewska K 2009 Conformational analysis of nucleic acids revisited: curves+ Nucl. Acids Res. 37 5917-29
79. Leach A R 2001 Molecular Modelling: Principles and Applications 2nd edn (Harlow: Longman)
80. Lee S and Chirikjian G S 2004 Inter-helical angle and distance preferences in globular proteins Biophys. J. 86 1105-17
81. Lee S and Chirikjian G S 2005 Pose analysis of alpha-carbons in proteins Int. J. Robot. Res. 24 183-210
82. Levene S D and Crothers D M 1986 Ring closure probabilities for DNA fragments by Monte Carlo simulation J. Mol. Biol. 189 61-72
83. Lesk A M 2001 Introduction to Protein Architecture (Oxford: Oxford University Press)
84. Liverpool T B and Edwards S F 1995 Probability distribution of wormlike polymer loops J. Chem. Phys. 103 6716-9
85. Liverpool T B, Golestanian R and Kremer K 1998 Statistical mechanics of double-stranded semiflexible polymers Phys. Rev. Lett. 80 405-8
86. Love A E H 1944 A Treatise on the Mathematical Theory of Elasticity (New York: Dover)
87. Luckhurst G R, Zannoni C, Nordio P L and Segre U 1975 A molecular field theory for uniaxial nematic liquid crystals formed by non-cylindrically symmetric molecules Mol. Phys. 30 1345-58
88. Ma J P 2004 New advances in normal mode analysis of supermolecular complexes and applications to structural refinement Curr. Protein Peptide Sci. 5 119-23
89. Marko J F and Siggia E D 1994 Bending and twisting elasticity of DNA Macromolecules 27 981-8
90. Marko J F 1998 DNA under high tension: overstretching, undertwisting, and relaxation dynamics Phys. Rev. E 57 2134-49
91. Maroun R C and Olson W K 1988 Base sequence effects in double-helical DNA. 2. Configurational statistics of rodlike chains Biopolymers 27 561-84
92. Maslen D K 1993 (May) Fast transforms and sampling for compact groups PhD Dissertation Department of Mathematics, Harvard University
93. Maslen D K and Rockmore D N 1997 Generalized FFTs - a survey of some recent results DIMACS Series in Discrete Mathematics and Theoretical Computer Science vol 28, pp 183-237
94. Maslen D K 1998 Efficient computation of Fourier transforms on compact groups J. Fourier Anal. Appl. 4 19-52
95. Matsutani S 1999 Statistical mechanics of no-stretching elastica in three-dimensional space J. Geom. Phys. 29 243-59
96. McConnell J 1980 Rotational Brownian Motion and Dielectric Theory (New York: Academic)
97. Mehraeen S, Sudhanshu B, Koslover E F and Spakowitz A J 2008 End-to-end distribution for a wormlike chain in arbitrary dimensions Phys. Rev. E 77 061803
98. Miller W 1964 Some applications of the representation theory of the Euclidean group in three-space Commun. Pure Appl. Math. 17 527-40
99. Ming D, Kong Y F, Lambert M A, Huang Z and Ma J P 2002 How to describe protein motion without amino acid sequence and atomic coordinates Proc. Natl Acad. Sci. 99 8620-5
100. Ming D, Kong Y F, Wu Y H and Ma J P 2003 Substructure synthesis method for simulating large molecular complexes Proc. Natl Acad. Sci. 100 104-9
101. Miyake A 1981 Stiff-chain statistics in relation to the Brownian process J. Phys. Soc. Japan 50 1676-82
102. Miyazawa S and Jernigan R L 1985 Estimation of effective interresidue contact energies from protein crystal-structures-quasi-chemical approximation Macromolecules 18 534-52
103. Moroz J D and Nelson P 1997 Torsional directed walks, entropic elasticity, and DNA twist stiffness Proc. Natl Acad. Sci. USA 94 14418-22
104. Moroz J D and Nelson P 1998 Entropic elasticity of twist-storing polymers Macromolecules 31 6333-47
105. Nelson P 1998 Sequence-disorder effects on DNA entropic elasticity Phys. Rev. Lett. 80 5810
106. Nelson P 1998 New measurements of DNA twist elasticity Biophys. J. 74 2501
107. Niewierczerzam S and Cieplak M 2009 Stretching and twisting of the DNA duplexes in coarse grained dynamical models arXiv:0901.0082v1
108. Norisuye T, Tsuboi A and Teramoto A 1996 Remarks on excluded-volume effects in semiflexible polymer solutions Polym. J. 28 357-61
109. Odijk T 1995 Stiff chains and filaments under tension Macromolecules 28 7016-8
110. Perrin F 1928 Étude Mathématique du Mouvement Brownien de Rotation Ann. Sci. L' École Normale Supérieure 45 1-51
111. Peter F and Weyl H 1927 Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe Math. Ann. 97 735-55
112. Podtelezhnikov A A, Cozzarelli N R and Vologodskii A V 1999 Equilibrium distributions of topological states in circular DNA: interplay of supercoling and knotting Proc. Natl Acad. Sci. USA 96 12974
113. Pohl W F 1968 The self-linking number of a closed space curve J. Math. Mech. 17 975
114. Riccardi D, Schaefer P, Yang Y, Yu H, Ghosh N, Prat-Resina X, Köinig P, Li G, Xu D, Guo H, Elstner M and Cui Q 2006 Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biophysical processes J. Phys. Chem. B 110 6458-69
115. Risbo T 1996 Fourier transform summation of Legendre series and D -functions J. Geodesy 70 383-96
116. Sattinger D H and Weaver O L 1986 Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics (New York: Springer)
117. Schiessel H, Rudnick J, Bruinsma R and Gelbart W M 2000 Organized condensation of worm-like chains Europhys. Lett. 51 237-43
118. Schmidt M and Stockmayer W H 1984 Quasi-elastic light scattering by semiflexible chains Macromolecules 17 509-14
119. Schuyler A D and Chirikjian G S 2004 Normal mode analysis of proteins: a comparison of rigid cluster modes and Cα coarse graining J. Mol. Graph. Modelling 22 183-93
120. Schuyler A D and Chirikjian G S 2005 Efficient determination of low-frequency normal modes of large protein structures by cluster-NMA J. Mol. Graph. Modelling 24 46-58
121. Schuyler A D, Jernigan R L, Qasba P K, Ramakrishnan B and Chirikjian G S 2009 Iterative cluster-NMA (icNMA): a tool for generating conformational transitions in proteins Prote. Struct. Function Bioinform. 74 760-76
122. Shafer L 1999 Excluded Volume Effects in Polymer Solutions, as Explained by the Renormalization Group (New York: Springer)
123. Shi Y, He S and Hearst J E 1996 Statistical mechanics of the extensible and shearable elastic rod and of DNA J. Chem. Phys. 105 714-31
124. Shimada J and Yamakawa H 1985 Statistical mechanics of DNA topoisomers J. Mol. Biol. 184 319-29
125. Shore D and Baldwin R L 1983 Energetics of DNA twisting J. Mol. Biol. 170 957-81
126. Simo J C and Vu-Quoc L 1986 A three-dimensional finite-strain rod model. Part II: computational aspects Comput. Methods Appl. Mech. Eng. 58 79-116
127. Sippl M J 1995 Knowledge-based potentials for proteins Curr. Opin. Struct. Biol. 5 229-35
128. Smith S B, Finzi L and Busmante C 1992 Direct mechanical measurements of the elasticity of single DNA-molecules by using magnetic beads Science 258 1122-6
129. Spakowitz A J and Wang Z-G 2005 End-to-end distance vector distribution with fixed end orientations for the wormlike chain model Phys. Rev. E 72 041802
130. Steigmann D J and Faulkner M G 1993 Variational theory for spatial rods Arch. Ration. Mech. Anal. 133 1-26
131. Stepanow S 1996 Kramer equation as a model for semiflexible polymers Phys. Rev. E 54 R2209-11
132. Sternberg S 1994 Group Theory and Physics (New York: Cambridge University Press)
133. Strick T R, Allemand J F, Bensimon D, Bensimon A and Croquette V 1996 The elasticity of a single supercoiled DNA molecule Science 271 1835-7
134. Sulkowska J I and Cieplak M 2007 Mechanical stretching of proteins a theoretical survey of the protein data bank J. Phys.: Condens. Matter 19 283201
135. Swigon D, Coleman B D and Tobias I 1998 The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes Biophys. J. 74 2515-30
136. Tama F, Gadea F X, Marques O and Sanejouand Y H 2000 Building-block approach for determining low-frequency normal modes of macromolecules Protein Struct. Function Genet. 41 1-7
137. Tama F and Sanejouand Y H 2001 Conformational change of proteins arising from normal mode calculations Protein Eng. 14 1-6
138. Tama F, Wriggers W and Brooks C L 2002 Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory J. Mol. Biol. 321 297-305
139. Thirumalai D and Ha B-Y 1998 Statistical mechanics of semiflexible chains: a mean field variational approach Theoretical and Mathematical Models in Polymer Research ed A Grosberg (New York: Academic) pp 1-35
140. Tirion M M 1996 Large amplitude elastic motions in proteins from a single-parameter, atomic analysis Phys. Rev. Lett. 77 1905-8
141. Tirion M M and Ben-Avraham D 1993 Normal mode analysis of G-actin J. Mol. Biol. 230 186-95
142. Tirion M M and Ben-Avraham D 1998 Normal modes analyses of macromolecules Physica A 249 415-23
143. Tobias I, Swigon D and Coleman B D 2000 Elastic stability of DNA configurations. I: general theory Phys. Rev. E 61 747-58
144. Trovato A and Seno F 2003 A new perspective on the analysis of helix-helix packing preferences in globular proteins arXiv:cond-mat/0304429 v1
145. Varshalovich D A, Moskalev A N and Khersonskii V K 1998 Quantum Theory of Angular Momentum (Singapore: World Scientific)
146. Vilenkin N J, Akim E L and Levin A A 1957 The matrix elements of irreducible unitary representations of the group of Euclidean three-dimensional space motions and their properties Dokl. Akad. Nauk SSSR 112 987-89 (in Russian)
147. Vilenkin N J and Klimyk A U 1991 Representation of Lie Groups and Special Functions vol 1-3 (Dordrecht: Kluwer Academic)
148. Vologodskii A V, Anshelevich V V, Lukashin A V and Frank-Kamenetskii M D 1979 Statistical mechanics of supercoils and the torsional stiffness of the DNA double helix Nature 280 294-8
149. Vologodskii A 1992 Topology and Physics of Circular DNA (Boca Raton, FL: CRC Press)
150. von Neumann J 1955 Mathematical Foundations of Quantum Mechanics (Princeton, NJ: Princeton University Press)
151. Walther D, Springer C and Cohen F E 1998 Helix-helix packing angle preferences for finite helix axes Protein Struct. Funct. Genet. 33 457-9
152. Wang M D, Yin H, Landick R, Gelles J and Block S M 1997 Stretching DNA with optical tweezers Biophys. J. 72 1335-46
153. Wang Y and Chirikjian G S 2006 Error propagation on the Euclidean group with applications to manipulator kinematics IEEE Trans. Robot. 22 591-602
154. Wang Y and Chirikjian G S 2008 Nonparametric second-order theory of error propagation on the Euclidean group Int. J. Robot. Res. 27 1258-73
155. Weiner P K and Kollman P A 1981 AMBER: assisted model building with energy refinement. A general program for modeling molecules and their interactions J. Comput. Chem. 2 287-303
156. Weyl H 1950 The Theory of Groups and Quantum Mechanics (New York: Dover)
157. White J H and Bauer W R 1986 Calculation of the twist and the writhe for representative models of DNA J. Mol. Biol. 189 329
158. Wiggins P A, Phillips R and Nelson P C 2004 Exact theory of kinkable elastic polymers arXiv:cond-mat/0409003 v1
159. Wigner E P 1939 On unitary representations of the inhomogeneous Lorentz group Ann. Math. 40 149-204
160. Wigner E P 1931 Gruppentheorie und ihre Anwendungen auf die Quantenmechanik der Atomspektren (Braunschweig: Vieweg Verlag)
161. Griffin J J 1959 Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (New York: Academic) (Engl. Transl.)
162. Wilhelm J and Frey E 1996 Radial distribution function of semiflexible polymers Phys.Rev. Lett. 77 2581-4
163. Winkler R G, Harnau L and Reineker P 1997 Distribution functions and dynamical properties of stiff macromolecules Macromol. Theory Simul. 6 1007-35 (Pubitemid 127500059)
164. Winkler R G 1999 Analytical calculation of the relaxation dynamics of partially stretched flexible chain molecules: necessity of a wormlike chain descrption Phys. Rev. Lett. 82 1843-6
165. Wyllie G 1980 Random motion and Brownian rotation Phys. Rep. 61 327-76
166. Yamakawa H and Stockmayer W H 1972 Statistical mechanics of wormlike chains. II. Excluded volume effects J. Chem. Phys. 57 2843-54
167. Yamakawa H 1997 Helical Wormlike Chains in Polymer Solutions (Berlin: Springer)
168. Zandi R and Rudnick J 2001 Constraints, histones, and 30-nm spiral Phys. Rev. E 64 051918
169. Zhao S R, Sun C P and Zhang W X 1997 Statistics of wormlike chains. I. Properties of a single chain J. Chem. Phys. 106 2520-9
170. Želobenko D P 1973 Compact Lie Groups and their Representations (Translations of Mathematical Monographs) (Providence, RI: American Mathematical Society)
171. Zhou Y and Chirikjian G S 2003 Conformational statistics of bent semiflexible polymers J. Chem. Phys. 119 4962-70
172. Zhou Y and Chirikjian G S 2006 Conformational statistics of semi-flexible macromolecular chains with internal joints Macromolecules 39 1950-60