Theory of helix-coil transitions in biopolymers: Statistical mechanical theory of order-disorder transitions in biological macromolecules
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Acad. Pr.
1970
|
| Schriftenreihe: | Molecular biology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 797 S. Ill., graph. Darst. |
| ISBN: | 0125595506 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804116370691981312 |
|---|---|
| adam_text | THEORY OF
HELIX-COIL TRANSITIONS
IN BIOPOLYMERS
STATISTICAL MECHANICAL THEORY OF
ORDER-DISORDER TRANSITIONS IN
BIOLOGICAL MACROMOLECULES
by DOUGLAS POLAND
and HAROLD A SCHERAGA
DEPARTMENT OF CHEMISTRY
CORNELL UNIVERSITY
ITHACA, NEW YORK
AC AD E MIC PRESS New York and London
Contents
Preface vii
1 Helical Structures in Biological Macromolecules
A The Notion of the Random Coil from Polymer Chemistry 1
B Helical Structures in the Solid State of Synthetic Polymers 2
C Hydrogen Bonds and Specific Interactions 2
D Helix and Random Coil in Solution 3
References 4
2 Theory for Short Chains
A Statement of the General Problem 5
B Independence of Sequences 7
C The a-Helix Model 8
D The Tendency to Long Sequences 11
E The Tendency to Short Sequences 12
F One-Sequence Approximation 13
G The Fraction of Hydrogen Bonds from the Partition Function 16
H Evaluation of Sums 17
I Application of One-Sequence Approximation 19
J Validity of One-Sequence Approximation 19
3 Theory for Infinite Chains
A The Simplification of Ignoring Ends 20
B Nearest-Neighbor Ising Model 20
XI
CONTENTS
C Peller’s Theory 22
D Incorrectly Treating Single h States 22
E The Balance between Long and Short Sequences 23
F The Generalized Ising Model of Hill 24
G The Method of Sequence Generating Functions 25
H The Case of Independent Units 27
I Comparison of Combinatorial Expressions 28
J The General Results 29
4 Theory for Chains of any Length: the Matrix Approach
A The Importance of Chain Length as an Experimental Variable 30
B The Partition Function Written as a Matrix Product 31
C Matrix Treatment of the Nearest-Neighbor Ising Model 32
D Evaluation of the Partition Function 33
E The Size of the Matrix Required 34
F Treatment of the a-Helix Model according to Miyake, and Lifson and
Roig 36
G Use of the Largest Eigenvalue for Long Chains 37
H The Model of Zimm and Bragg 38
I The Model of Nagai 39
J A Matrix Treatment of the Nearest-Neighbor Ising Model
Approximation for the a-Helix 40
K Reduction of Matrix Size 42
L Partition Function for General Chain Length for the Zimm-Bragg-Nagai
Model 47
M Illustration of Matrix Multiplication for the Various Models 49
N Periodic Boundary Conditions 52
O Matrix Treatment of the Generalized Ising Model 55
P Treatment of Complex Roots 61
Q Matrices for Any Number of States per Unit 64
R Matrices for Higher Dimensions 65
S The Partition Function for Finite Chain Length from the Grand
Partition Function 67
References 69
5 Unwinding from Ends in Chains of Any Length
A The Theory of Gibbs and DiMarzio for Infinite Chains 71
B The Effect of Ends and Chain Length 78
C Range of Validity of Approximate Theories 80
D Some Properties of the Infinite Chain 84
E Fraction of Unwinding from the Ends in Very Long Chains 85
F A General Formula for Unwinding from the Ends 87
G Unwinding from the Ends in Polyamino Acids, According to the
Lifson-Roig Theory 92
H Some Compact Relations and a “ Universal ” Function 94
I Generalization of the Short-Chain Combinatorial Approach 98
xii
CONTENTS
J Expansion of s in Power of (T— T,) 101
K Evaluation of Parameters from Experimental Data 104
References 105
6 Electrostatic Interactions
A The Importance and Difficulty of Treating Electrostatic Interactions 106
B The Theory of Zimm and Rice 107
C Illustration of the Electrostatic Interaction Matrix 109
Reference 111
7 Distribution Functions and Fluctuations
A Formal Relations 112
B The Polymer of Independent Units 113
C The Gaussian Form of P(Nh) for Long Chains 117
D The Polyamino Acid Model 121
E Comparison of Approximations to the Helix-Length Distribution 127
F Alternate Approach to the Moments of the Helix-Length Distribution 129
G The Helix-Length Distribution for the Finite Generalized Ising
Model 132
H The Use of Distribution Functions 134
I A General Interpretation of the Polyamino Acid Model 135
Reference 137
8 The Helix-Coil Transition in Heteropolymers
A The Partition Function for the Specific-Sequence
Heterogeneous Nearest-Neighbor Ising Model 140
B The Partition Function for a Distribution of Copolymer Sequences 142
C Simple Probability Distributions 145
D A Hybrid Method Based on the Work of Lifson and Allegra 149
E The Method of Allegra 154
F A Simple Copolymer Example 160
G Comparison of Approximate Treatments with the Exact Result 161
H The Arithmetic Mean from Sequence Generating Functions 166
I Physical Picture of the Helix-Coil Transition in Heteropolymers 167
J Coarse Graining 171
K Determination of Parameters 175
References 177
9 Nucleic Acids
A Background 178
B Model 181
C Particular Interpretation of the Model 184
D Entropy of Loops 188
xiii
CONTENTS
E Infinite Chains; Homogeneous Perfect-Matching Model 191
F Infinite Chains; Imperfect-Matching Model with Identical Chains 194
G Infinite Chains; Imperfect-Matching Model with Different
Homogeneous Chains 197
H Infinite Chains; Simple Hairpin Model 199
I Matrix Treatment for Finite Chains in the Simple Hairpin Model 202
J Matrix Treatment for Finite Chains in the Homogeneous Perfect-
Matching Model 203
K Combinatorial Treatment of Finite Chains 215
L Infinite Chains; Heterogenous, Random Perfect-Matching Model 220
M Evaluation of Sums 221
N Numerical Results; Properties of the Models 223
O Chain Dissociation 237
P Matrix Treatment of Finite, Specific-Sequence DNA 241
References 249
10 Relation to Other Topics in Physical Chemistry
A Ensembles and Partition Functions; Lattice Gas and Magnet 251
B One Dimensional Classical Fluid 265
C Thermodynamics of the Helix-Coil Transition 283
D Phase Transitions 289
References 301
11 Miscellaneous Topics 302
References 303
appendix A Computation of Eigenvectors and Eigenvalues 304
appendix B The Partition Function for a Cyclic Lattice 314
appendix C Computation of the Maximum Term by the Method
of Undetermined Multipliers 316
appendix D Truesdell’s Table 319
Reference 319
appendix E Calculation of Average Quantities as a Direct
Matrix Product 320
References 322
XIV
CONTENTS
Reprinted Papers
paper 1 L Pauling, R B Corey, and H R Branson The Structure of
Proteins: Two Hydrogen-Bonded Helical Configurations of the
Polypeptide Chain Proc Natl Acad Sei U S 37,205 (1951) 323
paper 2JD Watson and FHC Crick Molecular Structure of Nucleic
Acids Nature 171, 111 (1953) 330
paper 3MHF Wilkins, A R Stokes, and H R Wilson Molecular
Structure of Deoxypentose Nucleic Acids Nature 171, 738 (1953) 334
paper 4RE Franklin and R G Gosling Molecular Configuration in
Sodium Thymonucleate Nature 171, 740 (1953) 340
paper 5JD Watson and FHC Crick Genetical Implications of the
Structure of Deoxyribonucleic Acid Nature 171,964 (1953) 346
paper 6JA Schellman The Thermodynamics of Urea Solutions and the
Heat of Formation of the Peptide Hydrogen Bond Compt Rend
Trav Lab Carlsberg (Ser Chim ) 29,223 (1955) 350
paper 7JA Schellman The Stability of Hydrogen-Bonded Peptide
Structures in Aqueous Solution Compt Rend Trav Lab Carlsberg
(Ser Chim ) 29, 230 (1955) 357
paper 8JA Schellman The Factors Affecting the Stability of Hydrogen-
Bonded Polypeptide Structures in Solution J Phys Chem 62,
1485 (1958) 387
paper 9 J Applequist and V Damle Thermodynamics of the Helix-Coil
Equilibrium in Oligoadenylic Acid from Hypochromicity Studies
J Am Chem Soc 87,1450 (1965) 397
paper 10 D C Poland and H A Scheraga Statistical Mechanics of
Noncovalent Bonds in Polyamino Acids II Combinatorial Formu
lation for Short Chains, Including Hydrophobic Bonding in
Random Coil Biopolymers 3, 283 (1965) 406
paper 11 D C Poland and H A Scheraga Statistical Mechanics of
Noncovalent Bonds in Polyamino Acids III Interhelical Hydro-
phobic Bonds in Short Chains Biopolymers 3, 305 (1965) 428
paper 12 L Peller On a Model for the Helix-Coil Transition in Polypep
tides / Phys Chem 63, 1194,1199 (1959)
I The Model and its Thermal Behavior 437
II The Influence of Solvent Composition and Charge Interactions
on the Transition 443
paper 13 T L Hill Generalization of the One-Dimensional Ising Model
Applicable to Helix Transitions in Nucleic Acids and Proteins J
Chem Phys 30, 383 (1959) 451
paper 14 S Lifson and B H Zimm Simplified Theory of the Helix-Coil
Transition in DNA Based on a Grand Partition Function
Biopolymers 1, 15 (1963) 456
XV
CONTENTS
paper 15 S Lifson Partition Functions of Linear-Chain Molecules / Chem
Phys 40, 3705 (1964) 465
paper 16 A Litan and S Lifson Statistical-Mechanical Treatment of
Multistranded Polynucleotide Molecules / Chem Phys 42, 2528
(1965) 471
paper 17 B H Zimm and J K Bragg Theory of the Phase Transition
between Helix and Random Coil in Polypeptide Chains / Chem
Phys 31, 526 (1959) 476
paper 18 K Nagai Configurational Changes of Polypeptide Molecules in
the Helix-Coil Transition, I / Phys Soc Japan 15,407 (1960) 486
paper 19 A Miyake, R Chujo, and H Adachi Local Regularity of Chain
Substances / Polymer Sei 46, 163, 169, 177 (1960)
Local Regularity of Chain Substances I 496
Local Regularity of Chain Substances II 502
Local Regularity of Chain Substances III 509
paper 20 S Lifson and A Roig On the Theory of Helix-Coil Transition
in Polypeptides J Chem Phys 34,1963 (1961) 517
paper 21 D Poland and H A Scheraga Comparison of Theories of the
Helix-Coil Transition in Polypeptides J Chem Phys 43, 2071
(1965) 529
paper 22 D Poland, J N Vournakis, and H A Scheraga Cooperative
Interactions in Single-Strand Oligomers of Adenylic Acid
Biopolymers 4, 223 (1966) 533
paper 23 J H Gibbs and E A DiMarzio Statistical Mechanics of Helix-Coil
Transitions in Biological Macromolecules / Chem Phys 30,
271 (1959) 546
paper 24 A Litan A Statistical Mechanical Treatment of the Open Ends in
a Double-Stranded Polynucleotide Molecule Biopolymers 2, 279
(1964) 558
paper 25 B H Zimm and S A Rice The Helix-Coil Transition in Charged
Macromolecules Mol Phys 3, 391 (1960) 562
paper 26 J N Vournakis, D Poland, and H A Scheraga Anti-Cooperative
Interactions in Single-Strand Oligomers of Deoxyriboadenylic
Acid Bioploymers5,403 (1967) 579
Appendix: American Documentation Institute, Auxiliary
Publications Project, Photoduplication Service, Library of
Congress, Washington, DC, Document 9262
paper 27 G W Lehman and J P McTague Melting of DNA / Chem
Phys 49, 3170 (1968) 606
paper 28 S Lifson Theory of the Helix-Coil Transition in DNA Considered
as a Copolymer Biopolymers 1,25 (1963) 616
XVI
CONTENTS
paper 29 S Lifson and G Allegra On the Theory of Order-Disorder
Transition and Copolymer Structure of DNA Biopolymers 2, 65
(1964) 624
paper 30 G Allegra The Calculation of Average Functions of Local
Conformations for a Non-Interacting Copolymer System with
Neighbor Interactions J Polymer Sei Part C, 16, 2815 (1967) 628
paper 31 H Reiss, D A McQuarrie, J P McTague, and E R Cohen
On the Melting of Copolymeric DNA J Chem Phys 44, 4567
(1966) 638
paper 32 M FixmanandD Zeroka Helix-Coil Transition in Heterogeneous
Chains I Protein Model J Chem Phys 48, 5223 (1968) 653
paper 33 B H Zimm Theory of “Melting” of the Helical Form in Double
Chains of the DNA Type J Chem Phys 33, 1349 (1960) 661
paper 34 D M Crothers, N R Kallenbach, and B H Zimm The Melting
Transition of Low-Molecular-Weight DNA: Theory and Experi
ment J Mol Biol 11, 802 (1965) 669
paper 35 D M Crothers and N R Kallenbach On the Helix-Coil Tran
sition in Heterogeneous Polymers J Chem Phys 45,917 (1966) 688
paper 36 M Go Statistical Mechanics of Biopolymers and Its Application
to the Melting Transition of Polynücleotides J Phys Soc Japan
23, 597 (1967) 699
paper 37 D M Crothers Calculation of Melting Curves for DNA
Biopolymers 6, 1391 (1968) 711
paper 38 D Poland and H A Scheraga Phase Transitions in One Dimen
sion and the Helix-Coil Transition in Polyamino Acids J Chem
Phys 45, 1456 (1966) 725
paper 39 D Poland and H A Scheraga Occurrence of a Phase Transition
in Nucleic Acid Models J Chem Phys 45, 1464 (1966) 733
paper 40 M E Fisher Effect of Excluded Volume on Phase Transitions in
Biopolymers J Chem Phys 45, 1469 (1966) 739
paper 41 P J Flory and W G Miller A General Treatment of Helix-Coil
Equilibria in Macromolecular Systems J Mol Biol 15, 284
(1966) 744
paper 42 K Nagai Dimensional Change of Polypeptide Molecules in the
Helix-Coil Transition Region II J Chem Phys 34, 887 (1961) 758
paper 43 M E Baur and L H Nosanow Simple Model for the Helix-Coil
Transition in Polypeptides J Chem Phys 38, 578 (1963) 776
paper 44 J Applequist On the Helix-Coil Equilibrium in Polypeptides
J Chem Phys 38, 934 (1963) 781
Author Index 789
Subject Index 792
xvii
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| record_format | marc |
| series2 | Molecular biology |
| spelling | Poland, Douglas Verfasser aut Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules by Douglas Poland and Harold A. Scheraga New York u.a. Acad. Pr. 1970 XVII, 797 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Molecular biology Biologia Molecular E Macromolecular larpcal Polymères Biochemistry Biopolymers Macromolecular Substances Statistical mechanics Helix-Knäuel-Umwandlung (DE-588)4330170-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Biopolymere (DE-588)4006893-6 gnd rswk-swf Biopolymere (DE-588)4006893-6 s Helix-Knäuel-Umwandlung (DE-588)4330170-8 s Statistische Mechanik (DE-588)4056999-8 s DE-604 Scheraga, Harold A. Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258667&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Poland, Douglas Scheraga, Harold A. Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules Biologia Molecular E Macromolecular larpcal Polymères Biochemistry Biopolymers Macromolecular Substances Statistical mechanics Helix-Knäuel-Umwandlung (DE-588)4330170-8 gnd Statistische Mechanik (DE-588)4056999-8 gnd Biopolymere (DE-588)4006893-6 gnd |
| subject_GND | (DE-588)4330170-8 (DE-588)4056999-8 (DE-588)4006893-6 |
| title | Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules |
| title_auth | Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules |
| title_exact_search | Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules |
| title_full | Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules by Douglas Poland and Harold A. Scheraga |
| title_fullStr | Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules by Douglas Poland and Harold A. Scheraga |
| title_full_unstemmed | Theory of helix-coil transitions in biopolymers Statistical mechanical theory of order-disorder transitions in biological macromolecules by Douglas Poland and Harold A. Scheraga |
| title_short | Theory of helix-coil transitions in biopolymers |
| title_sort | theory of helix coil transitions in biopolymers statistical mechanical theory of order disorder transitions in biological macromolecules |
| title_sub | Statistical mechanical theory of order-disorder transitions in biological macromolecules |
| topic | Biologia Molecular E Macromolecular larpcal Polymères Biochemistry Biopolymers Macromolecular Substances Statistical mechanics Helix-Knäuel-Umwandlung (DE-588)4330170-8 gnd Statistische Mechanik (DE-588)4056999-8 gnd Biopolymere (DE-588)4006893-6 gnd |
| topic_facet | Biologia Molecular E Macromolecular Polymères Biochemistry Biopolymers Macromolecular Substances Statistical mechanics Helix-Knäuel-Umwandlung Statistische Mechanik Biopolymere |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258667&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT polanddouglas theoryofhelixcoiltransitionsinbiopolymersstatisticalmechanicaltheoryoforderdisordertransitionsinbiologicalmacromolecules AT scheragaharolda theoryofhelixcoiltransitionsinbiopolymersstatisticalmechanicaltheoryoforderdisordertransitionsinbiologicalmacromolecules |