Preface and outline .......................................... xiii
1 Introduction ............................................... 1
1.1 Relevance of biomolecular research ......................... 1
1.2 Proteins ................................................... 3
1.2.1 The trinity of amino acid sequence, structure, and
function ............................................ 3
1.2.2 Ribosomal synthesis of proteins ..................... 6
1.2.3 From sequence to function: The protein folding
process ............................................. 7
1.3 Molecular modeling ......................................... 9
1.3.1 Covalent bonds ...................................... 9
1.3.2 Effective noncovalent interactions and nanoscopic
modeling: Toward a semiclassical all-atom
representation ..................................... 11
1.4 All-atom peptide modeling ................................. 12
1.5 The mesoscopic perspective ................................ 14
1.5.1 Why coarse-graining...? The origin of the
hydrophobic force .................................. 15
1.5.2 Coarse-grained hydrophobic-polar modeling .......... 17
1.6 Polymers .................................................. 20
1.6.1 DNA and RNA ........................................ 20
1.6.2 Modeling free DNA .................................. 22
1.6.3 Flexible, attractively self-interacting polymers ... 23
1.6.4 Elastic polymers ................................... 27
2 Statistical mechanics: A modern review .................... 31
2.1 The theory of everything .................................. 31
2.2 Thermodynamics and statistical mechanics .................. 33
2.2.1 The thermodynamic limit ............................ 33
2.2.2 Thermodynamics of closed systems: The canonical
ensemble ........................................... 34
2.2.3 Thermodynamic equilibrium and the statistical
nature of entropy .................................. 36
2.3 Thermal fluctuations and the statistical path integral .... 43
2.4 Phase and pseudophase transitions ......................... 46
2.5 Relevant degrees of freedom ............................... 48
2.5.1 Coarse-grained modeling on mesoscopic scales ....... 48
2.5.2 Macroscopic relevant degrees of freedom: The
free-energy landscape .............................. 49
2.6 Kinetic free-energy barrier and transition state .......... 51
2.7 Microcanonical statistical analysis ...................... 53
2.7.1 Temperature as a derived quantity .................. 54
2.7.2 Identification of first-order transitions by
Maxwell construction ............................... 55
2.7.3 Systematic classification of transitions by
inflection-point analysis .......................... 62
3 The complexity of minimalistic lattice models for
protein folding ........................................... 67
3.1 Evolutionary aspects ...................................... 67
3.2 Self-avoiding walks and contact matrices .................. 68
3.3 Exact statistical analysis of designing sequences ......... 69
3.4 Exact density of states and thermodynamics ................ 76
4 Monte Carlo and chain growth methods for molecular
simulations ............................................... 81
4.1 Introduction .............................................. 81
4.2 Conventional Markov-chain Monte Carlo sampling ............ 82
4.2.1 Ergodicity and finite time series .................. 82
4.2.2 Statistical error and bias ......................... 84
4.2.3 Binning-jackknife error analysis ................... 88
4.3 Systematic data smoothing by using Bezier curves .......... 93
4.3.1 Construction of a Bezier curve ..................... 93
4.3.2 Smooth Bezier functions for discrete noisy data
sets ............................................... 96
4.4 Markov processes and stochastic sampling strategies ...... 100
4.4.1 Master equation ................................... 100
4.4.2 Selection and acceptance probabilities ............ 101
4.4.3 Simple sampling ................................... 102
4.4.4 Metropolis sampling ............................... 103
4.5 Reweighting methods ...................................... 104
4.5.1 Single-histogram reweighting ...................... 104
4.5.2 Multiple-histogram reweighting .................... 105
4.6 Generalized-ensemble Monte Carlo methods ................. 108
4.6.1 Replica-exchange Monte Carlo method: Parallel
tempering ......................................... 108
4.6.2 Simulated tempering ............................... 109
4.6.3 Multicanonical sampling ........................... 109
4.6.4 Wang-Landau method ................................ 117
4.7 Elementary Monte Carlo updates ........................... 118
4.8 Lattice polymers: Monte Carlo sampling vs. Rosenbluth
chain growth ............................................. 123
4.9 Pruned-enriched Rosenbluth method: Go with the winners ... 126
4.10 Canonical chain growth with PERM ......................... 127
4.11 Multicanonical chain-growth algorithm .................... 129
4.11.1 Multicanonical sampling of Rosenbluth-weighted
chains ............................................ 129
4.11.2 Iterative determination of the density of states .. 130
4.12 Random number generators ................................. 133
4.13 Molecular dynamics ....................................... 134
5 First insights to freezing and collapse of flexible
polymers ................................................. 137
5.1 Conformational transitions of flexible homopolymers ...... 137
5.2 Energetic fluctuations of finite-length polymers ......... 138
5.2.1 Peak structure of the specific heat ............... 138
5.2.2 Simple-cubic lattice polymers ..................... 139
5.2.3 Polymers on the face-centered cubic lattice ....... 141
5.3 The 0 transition ......................................... 144
5.4 Freezing and collapse in the thermodynamic limit ......... 147
6 Crystallization of elastic polymers ...................... 149
6.1 Lennard-Jones clusters ................................... 149
6.2 Perfect icosahedra ....................................... 150
6.3 Liquid-solid transitions of elastic flexible polymers .... 152
6.3.1 Finitely extensible nonlinear elastic Lennard-
Jones polymers .................................... 152
6.3.2 Classification of geometries ...................... 153
6.3.3 Ground states ..................................... 155
6.3.4 Thermodynamics of liquid-solid transitions
toward complete icosahedra ........................ 156
6.3.5 Liquid-solid transitions of elastic polymers ...... 158
6.3.6 Long-range effects ................................ 162
6.4 Systematic analysis of compact phases .................... 164
6.5 Dependence of structural phases on the range of
nonbonded interactions ................................... 165
7 Structural phases of semiflexible polymers ............... 175
7.1 Structural hyperphase diagram ............................ 175
7.2 Variation of chain length ................................ 180
8 Generic tertiary folding properties of proteins on
mesoscopic scales ........................................ 181
8.1 A simple model for a parallel β helix lattice protein .... 181
8.2 Protein folding as a finite-size effect .................. 184
8.3 Hydrophobic-polar off-lattice heteropolymers ............. 185
9 Protein folding channels and kinetics of two-state
folding .................................................. 191
9.1 Similarity measure and order parameter ................... 192
9.2 Identification of characteristic folding channels ........ 195
9.3 Go kinetics of folding transitions ....................... 198
9.3.1 Coarse-grained Go modeling ........................ 199
9.3.2 Thermodynamics .................................... 201
9.3.3 Kinetics .......................................... 204
9.3.4 Mesoscopic heteropolymers vs. real proteins ....... 208
9.4 Microcanonical effects ................................... 209
9.5 Two-state cooperativity in helix-coil transitions ........ 213
10 Inducing generic secondary structures by constraints ..... 217
10.1 The intrinsic nature of secondary structures ............. 217
10.2 Polymers with thickness constraint ....................... 218
10.2.1 Global radius of curvature ........................ 218
10.2.2 Modeling flexible polymers with constraints ....... 219
10.2.3 Thickness-dependent ground-state properties ....... 220
10.2.4 Structural phase diagram of tube-like polymers .... 222
10.3 Secondary-structure phases of a hydrophobic-polar
heteropolymer model ...................................... 223
11 Statistical analyses of aggregation processes ............ 227
11.1 Pseudophase separation in nucleation processes of
polymers ................................................. 227
11.2 Mesoscopic hydrophobic-polar aggregation model ........... 228
11.3 Order parameter of aggregation and fluctuations .......... 229
11.4 Statistical analysis in various ensembles ................ 230
11.4.1 Multicanonical results ............................ 230
11.4.2 Canonical perspective ............................. 233
11.4.3 Microcanonical interpretation: The backbending
effect ............................................ 235
11.5 Aggregation transition in larger heteropolymer systems ... 239
12 Hierarchical nature of phase transitions ................. 243
12.1 Aggregation of semiflexible polymers ..................... 243
12.2 Structural transitions of semiflexible polymers with
different bending rigidities ............................. 244
12.3 Hierarchies of subphase transitions ...................... 247
12.4 Hierarchical peptide aggregation processes ............... 249
12.5 Hierarchical aggregation of GNNQQNY ...................... 252
13 Adsorption of polymers at solid substrates .............. 255
13.1 Structure formation at hybrid interfaces of soft and
solid matter ............................................. 255
13.2 Minimalistic modeling and simulation of hybrid
interfaces ............................................... 256
13.3 Contact-density chain-growth algorithm ................... 258
13.4 Pseudophase diagram of a flexible polymer near an
attractive substrate ..................................... 259
13.4.1 Solubility-temperature pseudophase diagram ........ 260
13.4.2 Contact-number fluctuations ....................... 261
13.4.3 Anisotropic behavior of gyration tensor
components ........................................ 263
13.5 Alternative view: The free-energy landscape .............. 264
13.6 Continuum model of adsorption ............................ 269
13.6.1 Off-lattice modeling .............................. 269
13.6.2 Energetic and structural quantities for phase
characterization by canonical statistical
analysis .......................................... 270
13.6.3 Comparative discussion of structural
fluctuations ...................................... 271
13.6.4 Adsorption parameters ............................. 273
13.6.5 The pseudophase diagram of the hybrid system in
continuum ......................................... 274
13.7 Comparison with lattice results .......................... 277
13.8 Systematic microcanonical analysis of adsorption
transitions .............................................. 279
13.8.1 Dependence on the surface attraction strength ..... 280
13.8.2 Chain-length dependence ........................... 282
13.8.3 Translational entropy ............................. 284
13.9 Polymer adsorption at a nanowire ......................... 286
13.9.1 Modeling the polymer-nanowire complex ............. 287
13.9.2 Structural phase diagram .......................... 288
14 Hybrid protein-substrate interfaces ...................... 293
14.1 Steps toward bionanotechnology ........................... 293
14.2 Substrate-specific peptide adsorption .................... 294
14.2.1 Hybrid lattice model .............................. 294
14.2.2 Influence of temperature and solubility on
substrate-specific peptide adsorption ............. 295
14.3 Semiconductor-binding synthetic peptides ................. 301
14.4 Thermodynamics of semiconductor-binding peptides in
solution ................................................. 303
14.5 Modeling a hybrid peptide-silicon interface .............. 307
14.5.1 Introduction ...................................... 307
14.5.2 Si(100), oxidation, and the role of water ......... 308
14.5.3 The hybrid model .................................. 309
14.6 Sequence-specific peptide adsorption at silicon (100)
surface .................................................. 312
14.6.1 Thermal fluctuations and deformations upon
binding ........................................... 312
14.6.2 Secondary-structure contents of the peptides ...... 313
14.6.3 Order parameter of adsorption and nature of
adsorption transition ............................. 315
15 Concluding remarks and outlook ........................... 319
References .................................................... 323
Index ......................................................... 337
|
