Statistical physics of biomolecules: an introduction
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| Format: | Buch |
| Sprache: | English |
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CRC
2010
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| Beschreibung: | XXI, 334 S. Ill., graph. Darst. |
| ISBN: | 9781420073782 1420073788 |
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| 100 | 1 | |a Zuckerman, Daniel M. |e Verfasser |0 (DE-588)1019320796 |4 aut | |
| 245 | 1 | 0 | |a Statistical physics of biomolecules |b an introduction |c Daniel M. Zuckerman |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC |c 2010 | |
| 300 | |a XXI, 334 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
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| adam_text |
Titel: Statistical physics of biomolecules
Autor: Zuckerman, Daniel M
Jahr: 2010
Contents
Preface.xix
Acknowledgments.xxi
Chapter 1 Proteins Don't Know Biology. 1
1.1 Prologue: Statistical Physics of Candy, Dirt, and Biology. 1
1.1.1 Candy. 1
1.1.2 Clean Your House, Statistically.2
1.1.3 More Seriously.3
1.2 Guiding Principles .4
1.2.1 Proteins Don't Know Biology.4
1.2.2 Nature Has Never Heard of Equilibrium.4
1.2.3 Entropy Is Easy.5
1.2.4 Three Is the Magic Number for Visualizing Data.5
1.2.5 Experiments Cannot Be Separated from "Theory".5
1.3 About This Book.5
1.3.1 What Is Biornolecular Statistical Physics?.5
1.3.2 What's in This Book, and What's Not.6
1.3.3 Background Expected of the Student.7
1.4 Molecular Prologue: A Day in the Life of Butane.7
1.4.1 Exemplary by Its Stupidity.9
1.5 What Does Equilibrium Mean to a Protein?.9
1.5.1 Equilibrium among Molecules.9
1.5.2 Internal Equilibrium.10
1.5.3 Time and Population Averages .11
1.6 A Word on Experiments .11
1.7 Making Movies: Basic Molecular Dynamics Simulation.12
1.8 Basic Protein Geometry.14
1.8.1 Proteins Fold.14
1.8.2 There Is a Hierarchy within Protein Structure.14
1.8.3 The Protein Geometry We Need to Know,
for Now .15
1.8.4 The AminoAcid.16
1.8.5 The Peptide Plane.17
1.8.6 The Two Main Dihedral Angles Are Not
Independent.17
1.8.7 Correlations Reduce Configuration Space, but Not
Enough to Make Calculations Easy.18
1.8.8 Another Exemplary Molecule: Alanine Dipeptide.18
vi» Contents
1.9 A Note on the Chapters.18
Further Reading.19
Chapter2 The Heart oflt All: Probabi lity Theory.21
2.1 Introduction.21
2.1.1 The Monty Hall Problem.21
2.2 Basics of One-Dimensional Distributions.22
2.2.1 What Is a Distribution?.22
2.2.2 Make Sure It's a Density! .25
2.2.3 There May Be More than One Peak:
Multimodality.25
2.2.4 Cumulative Distribution Functions.26
2.2.5 Averages.28
2.2.6 Sampling and Samples.29
2.2.7 The Distribution of a Sum of Increments:
Convolutions.31
2.2.8 Physical and Mathematical Origins of Some
Common Distributions.34
2.2.9 Change of Variables.36
2.3 Fluctuations and Error.36
2.3.1 Variance and Higher "Moments".37
2.3.2 The Standard Deviation Gives the Scale of a
Unimodal Distribution.38
2.3.3 The Variance of a Sum (Convolution).39
2.3.4 A Note on Diffusion.40
2.3.5 Beyond Variance: Skewed Distributions
and Higher Moments.41
2.3.6 Error (Not Variance).41
2.3.7 Contidence Intervals.43
2.4 Two+ Dimensions: Protection and Correlation.43
2.4.1 Projection/Marginalization.44
2.4.2 Correlations, in a Sentence.45
2.4.3 Statistical Independence.46
2.4.4 Linear Correlation.46
2.4.5 More Complex Correlation.48
2.4.6 Physical Origins of Correlations.50
2.4.7 Joint Probability and Conditional Probability.51
2.4.8 Correlations in Time.52
2.5 Simple Statistics Help Reveal a Motor Protein's
Mechanism .54
2.6 Additional Problems: Trajeetory Analysis.54
Further Reading.55
Contents ix
Chapter 3 Big Lessons from Simple Systems: Equilibrium Statistical
Mechanics in One Dimension.57
3.1 Introduction.57
3.1.1 Looking Ahead .57
3.2 Energy Landscapes Are Probability Distributions.58
3.2.1 Translating Probability Coneepts into the
Language of Statistical Mechanics.60
3.2.2 Physical Ensembles and the Connection with
Dynamics.61
3.2.3 Simple States and the Harmonie Approximation .61
3.2.4 A Hint of Fluctuations: Average Does Not Mean
Most Probable .63
3.3 States, Not Contigurations.65
3.3.1 Relative Populations.65
3.4 Free Energy: It's Just Common Sense. If You Believe in
Probability.66
3.4.1 Getting Ready: Relative Populations.67
3.4.2 Finally. the Free Energy.68
3.4.3 More General Harmonie Wells.69
3.5 Entropy: It's Just a Name.70
3.5.1 Entropy as (the Log of) Width: Double
Square Wells.71
3.5.2 Entropy as Width in Harmonie Wells .73
3.5.3 That Awful ]T p Inp Formula.74
3.6 Summing Up .76
3.6.1 States Get the Fancy Names because They're Most
Important.76
3.6.2 It's the Differences That Matter.77
3.7 Molecular Intuition from Simple Systems.78
3.7.1 Temperature Dependence: A One-Dimensional
Model of Protein Folding.78
3.7.2 Discrete Models.80
3.7.3 A Note on 1D Multi-Particle Systems.81
3.8 Loose Ends: Proper Dimensions, Kinetic Energy .81
Further Reading.83
Chapter 4 Nature Doesn't Calculate Partilion Functions: Elementary
Dynamics and Equilibrium.85
4. i Introduction.85
4.1.1 Equivalence of Time and Configurational Averages. 86
4.1.2 An Aside: Does Equilibrium Exist?.86
x Contents
4.2 Newtonian Dynamics: Deterministic but Not Predictable.87
4.2.1 The Probabilistic ("Stochastic") Picture of
Dynamics.89
4.3 Barrier Crossing?Activated Processes.89
4.3.1 A Quick Preview of Barrier Crossing .89
4.3.2 Catalysts Accelerate Rates by Lowering Barriers.91
4.3.3 A Decomposition of the Rate.91
4.3.4 More on Arrhenius Factors and Their Limitations.92
4.4 Flux Balance: The Definition of Equilibrium.92
4.4.1 "Detailed Balance" and a More Precise Definition
of Equilibrium.94
4.4.2 Dynamics Causes Equilibrium Populations.94
4.4.3 The Fundamental Differential Equation.95
4.4.4 Are Rates Constant in Time? (Advanced).95
4.4.5 Equilibrium Is "Self-Healing".96
4.5 Simple Diffusion, Again.97
4.5.1 The Diffusion Constant and the Square-Root Law
of Diffusion.98
4.5.2 Diffusion and Binding. 100
4.6 More on Stochastic Dynamics: The Langevin Equation. 100
4.6.1 Overdamped, or "Brownian," Motion and Its
Simulation. 102
4.7 Key Tools: The Correlation Time and Function. 103
4.7.1 Quantifying Time Correlations: The
Autocorrelation Function. 104
4.7.2 Data Analysis Guided by Time Correlation
Functions. 105
4.7.3 The Correlation Time Helps to Connect Dynamics
and Equilibrium. 106
4.8 Tying It All Together. 106
4.9 So Many Ways to ERR: Dynamics in Molecular
Simulation. 107
4.10 Mini-Project: Double-Well Dynamics. 108
Further Reading. 109
Chapter 5 Molecules Are Correlated! Multidimensional Statistical
Mechanics. 111
5.1 Introduction. 111
5.1.1 Many Atoms in One Molecule and/or Many
Molecules. 111
5.1.2 Working toward Thermodynamics. 112
5.1.3 Toward Understanding Simulations. 112
5.2 A More-than-Two-Dimensional Prelude. 112
5.2.1 One 'Atom" in Two Dimensions. 113
5.2.2 Two Ideal (Noninteracting) "Atoms" in 2D. 114
Contents xi
5.2.3 A Diatomic "Moleeule" in 2D. 115
5.2.4 Lessons Learned in Two Dimensions. 119
5.3 Coordinates and Forcefields. 119
5.3.1 Cartesian Coordinates. 119
5.3.2 Internal Coordinates. 120
5.3.3 A Forcefield Is Just a Potential Energy
Function. 121
5.3.4 Jacobian Factors for Internal Coordinates
(Advanced). 123
5.4 The Single-Molecule Partition Function. 124
5.4.1 Three Atoms Is Too Many for an Exact
Calculation. 125
5.4.2 The General Unimolecular Partition Function. 126
5.4.3 Back to Probability Theory and Correlations . 127
5.4.4 Technical Aside: Degeneracy Number. 128
5.4.5 Some Lattice Models Can Be Solved Exactly. 129
5.5 Multimolecular Systems. 130
5.5.1 Partition Functions for Systems of Identical
Molecules. 131
5.5.2 Ideal Systems?Uncorrelated by Definition. 132
5.5.3 Nonideal Systems. 132
5.6 The Free Energy Still Gives the Probability. 133
5.6.1 The Entropy Still Embodies Width (Volume). 134
5.6.2 Defining States. 134
5.6.3 Discretization Again Implies 5 ~ ? J^plnp . 135
5.7 Summary. 135
Further Reading. 135
Chapter 6 From Complexity to Simplicity: The Potential of Mean Force. 137
6.1 Introduction: PMFs Are Every where. 137
6.2 The Potential of Mean Force Is Like a Free Energy. 137
6.2.1 The PMF Is Exactly Related to a Projection. 138
6.2.2 Proportionality Functions for PMFs. 140
6.2.3 PMFs Are Easy to Compute from a Good
Simulation. 141
6.3 The PMF May Not Yield the Reaction Rate or Transition
State. 142
6.3.1 Is There Such a Thing as a Reaction Coordinate? . 143
6.4 The Radial Distribution Function. 144
6.4.1 What to Expect for g(r). 145
6.4.2 g(r) Is Easy to Get from a Simulation. 146
6.4.3 The PMF Differs from the "Bare" Pair Potential . 148
6.4.4 From g(r) to Thermodynamics in Pairwise
Systems . 149
6.4.5 g(r) Is Experimentally Measurable. 149
xii Contents
6.5 PMFs Are the Typical Basis for "Knowledge-Based"
("Statistical") Potentials . 150
6.6 Summary: The Meaning, Uses, and Limitations of
the PMF. 150
Further Reading. 151
Chapter 7 What's Free about "Free" Energy? Essential Thermodynamics. 153
7.1 Introduction. 153
7.1.1 An Apology: Thermodynamics Does Matter!. 153
7.2 Statistical Thermodynamics: Can You Take a Derivative? . 154
7.2.1 Quick Reference on Derivatives. 154
7.2.2 Averages and Entropy, via First Derivatives. 155
7.2.3 Fluctuations from Second Derivatives. 157
7.2.4 The Specific Heat, Energy Fluctuations, and the
(Un)folding Transition . 157
7.3 You Love the Ideal Gas. 158
7.3.1 Free Energy and Entropy of the Ideal Gas. 159
7.3.2 The Equation of State for the Ideal Gas. 160
7.4 Boring but True: The First Law Describes Energy
Conservation. 160
7.4.1 Applying the First Law to the Ideal Gas: Heating
at Constant Volume. 161
7.4.2 Why Is It Called "Free" Energy, Anyway? The
Ideal Gas Teils All. 162
7.5 G vs. F: Other Free Energies and Why They (Sort of)
Matter. 164
7.5.1 G, Constant Pressure, Fluctuating Volume?A
Statistical View. 164
7.5.2 When Is It Important to Use G Instead of F?. 166
7.5.3 Enthalpy and the Thermodynamic
Definition of G. 168
7.5.4 Another Derivative Connection?Getting
PfromF. 169
7.5.5 Summing Up: G vs. F. 170
7.5.6 Chemical Potential and Fluctuating Particle
Numbers. 171
7.6 Overview of Free Energies and Derivatives. 173
7.6.1 The Pertinent Free Energy Depends on the
Conditions. 173
7.6.2 Free Energies Are "State Functions". 174
7.6.3 First Derivatives of Free Energies Yield
Averages. 174
7.6.4 Second Derivatives Yield
Fluctuations/Susceptibilities. 174
Contents xiii
7.7 The Second Law and (Sometimes) Free Energy
Minimization. 175
7.7.1 A Kinetic View Is Helpful . 175
7.7.2 Spontaneous Heat Flow and Entropy. 175
7.7.3 The Second Law for Free
Energies?Minimization, Sometimes. 177
7.7.4 PMFs and Free Energy Minimization for
Proteins?BeWarned! . 179
7.7.5 The Second Law for Your House: Refrigerators
Are Heaters . 181
7.7.6 Summing Up: The Second Law. 181
7.8 Calorimetry: A Key Thermodynamic Technique. 182
7.8.1 Integrating the Specific Heat Yields Both Enthalpy
and Entropy. 182
7.8.2 Differential Scanning Calorimetry for Protein
Folding. 183
7.9 The Bare-Bones Essentials of Thermodynamics. 183
7.10 Key Topics Omitted from This Chapter. 184
Further Reading. 184
Chapter 8 The Most Important Molecule: Electro-Statistics of Water. 185
8.1 Basics of Water Structure. 185
8.1.1 Waler Is Tetrahedral because of Its Electron
Orbitals. 185
8.1.2 Hydrogen Bonds. 185
8.1.3 Ice. 186
8.1.4 Fluctuating H-Bonds in Water. 187
8.1.5 Hydronium Ions, Protons, and Quantum
Fluctuations. 187
8.2 Water Molecules Are Structural Elements in Many Crystal
Structures. 188
8.3 The pH of Water and Acid-Base Ideas. 188
8.4 Hydrophobie Effect. 190
8.4.1 Hydrophobicity in Protein and Membrane
Structure. 190
8.4.2 Statistical/Entropic Explanation ofthe
Hydrophobie Effect. 190
8.5 Water Is a Strong Dielectric . 192
8.5.1 Basics of Dielectric Behavior. 193
8.5.2 Dielectric Behavior Results from Polarizability. 194
8.5.3 Water Polarizes Primarily due to
Reorientation. 195
8.5.4 Charges Prefer Water Solvation to a Nonpolar
Environment . 196
8.5.5 Charges on Protein in Water = Complicated!. 196
xiv Contents
8.6 Charges in Water + Salt = Screening. 197
8.6.1 Statistical Mechanics of Electrostatic Systems
(Technical). 198
8.6.2 First Approximation: The Poisson-Boltzmann
Equation.200
8.6.3 Second Approximation: Debye-Hückel Theory.200
8.6.4 Counterion Condensation on DNA. 202
8.7 A Brief Word on Solubility. 202
8.8 Summary.203
8.9 Additional Problem: Understanding Differential
Electrostatics .203
Further Reading.204
Chapter 9 Basics of Binding and Allostery.205
9.1 A Dynamieal View of Binding: On- and Off-Rates.205
9.1.1 Time-Dependent Binding: The Basic Differential
Equation.207
9.2 Macroscopic Equilibrium and the Binding Constant.208
9.2.1 Interpreting Kd.209
9.2.2 The Free Energy of Binding AG,1*"1 Is Based on a
Reference State.210
9.2.3 Measuring A'j by a "Generic" Titration
Experiment.211
9.2.4 Measuring Kd from Isothermal Titration
Calorimetry .211
9.2.5 Measuring Afd by Measuring Rates.212
9.3 A Structural-Thermodynamic View of Binding .212
9.3.1 Pictures of Binding: "Lock and Key" vs.
"Induced Fit".212
9.3.2 Many Factors Affect Binding. 213
9.3.3 Entropy-Enthalpy Compensation.215
9.4 Understanding Relative Affinities: AAG and
Thermodynamic Cycles.216
9.4.1 The Sign of AAG Has Physical Meaning. 216
9.4.2 Competitive Binding Experiments.218
9.4.3 "Alchemical" Computations of Relative
Affinities.218
9.5 Energy Storage in "Fuels" Like ATP. 220
9.6 Direct Statistical Mechanics Description of
Binding.221
9.6.1 What Are the Right Partition Functions?.221
9.7 Allostery and Cooperativity . 222
9.7.1 Basic Ideas of Allostery.222
9.7.2 Quantifying Cooperativity with the Hill Constant . 224
Contents
9.7.3 Further Analysis of Allostery: MWC and KNF
Models.227
9.8 Elementary Enzymatic Catalysis.229
9.8.1 The Steady-State Concept. 230
9.8.2 The Michaelis-Menten "Velocity".231
9.9 pHANDpÄTa .231
9.9.1 pH.232
9.9.2 pKä. 232
9.10 Summary.233
Further Reading.233
Chapter 10 Kinetics of Conformational Change and Protein Folding. 235
10.1 Introduction: Basins, Substates, and States. 235
10.1.1 Separating Timescales to Define Kinetic
Models.235
10.2 Kinetic Analysis of Multistate Systems. 238
10.2.1 Revisiting the Two-State System.238
10.2.2 A Three-State System: One Intermediate. 242
10.2.3 The Effective Rate in the Presence of an
Intermediate. 246
10.2.4 The Rate When There Are Parallel Pathways.250
10.2.5 Is There Such a Thing as Nonequilibrium
Kinetics?. 251
10.2.6 Formalism for Systems Described by Many
States-. 252
10.3 Conformational and Allosteric Changes in Proteins. 252
10.3.1 What Is the "Mechanism" of a Conformational
Change?.252
10.3.2 Induced and Spontaneous Transitions. 253
10.3.3 Allosteric Mechanisms. 254
10.3.4 Multiple Pathways.255
10.3.5 Processivity vs. Stochasticity. 255
10.4 Protein Folding. 256
10.4.1 Protein Folding in the Cell. 257
10.4.2 The Levinthal Paradox. 258
10.4.3 Just Another Type of Conformational
Change?.258
10.4.4 What Is the Unfolded State?. 259
10.4.5 Multiple Pathways, Multiple Intermediates. 260
10.4.6 Two-State Systems, J Values, and Chevron
Plots. 262
10.5 Summary. 264
Further Reading . 264
xvi Contents
Chapter 11 Ensemble Dynamics: From Trajectories to Diffusion
and Kinetics. 265
11.1 Introduction: Back to Trajectories and Ensembles.265
11.1.1 Why We Should Care about Trajectory
Ensembles.265
11.1.2 Anatomy of a Transition Trajectory.266
11.1.3 Three General Ways to Describe Dynamics.267
11.2 One-Dimensional Ensemble Dynamics.271
11.2.1 Derivation of the One-Dimensional Trajectory
Energy: The "Action".272
11.2.2 Physical Interpretation of the Action.274
11.3 Four Key Trajectory Ensembles.275
11.3.1 Initialized Nonequilibrium Trajectory
Ensembles . 275
11.3.2 Steady-State Nonequilibrium Trajectory
Ensembles.275
11.3.3 The Equilibrium Trajectory Ensemble.276
11.3.4 Transition Path Ensembles. 276
11.4 From Trajectory Ensembles to Observables.278
11.4.1 Configuration-Space Distributions from
Trajectory Ensembles.279
11.4.2 Finding Intermediates in the Path Ensemble.280
11.4.3 The Commitment Probability and a
Transition-State Definition . 280
11.4.4 Probability Flow, or Current. 281
11.4.5 What Is the Reaction Coordinate?. 281
11.4.6 From Trajectory Ensembles to Kinetic Rates.282
11.4.7 More General Dynamical Observables from
Trajectories.283
11.5 Diffusion and Beyond: Evolving Probability
Distributions.283
11.5.1 Diffusion Derived from Trajectory Probabilities . 284
11.5.2 Diffusion on a Linear Landscape. 285
11.5.3 The Diffusion (Differential) Equation.287
11.5.4 Fokker-Planck/Smoluchowski Picture for
Arbitrary Landscapes . 289
11.5.5 The Issue of History Dependence. 291
11.6 The Jarzynski Relation and Single-Molecule
Phenomena. 293
11.6.1 Revisiting the Second Law of Thermodynamics . 294
11.7 Summary. 294
Further Reading. 295
Contents xvii
Chapter 12 A Statistical Perspective on Biomolecular Simulation .297
12.1 Introduction: Ideas, Not Recipes.297
12.1.1 Do Simulations Matter in Biophysics?.297
12.2 First, Choose Your Model: Detailed or Simplitied. 298
12.2.1 Atomistic and "Detailed" Models. 299
12.2.2 Coarse Graining and Related Ideas. 299
12.3 "Basic" Simulations Emulate Dynamics. 300
12.3.1 Timescale Problems, Sampling Problems.301
12.3.2 Energy Minimization vs. Dynamics/Sampling . 304
12.4 Metropolis Monte Carlo: A Basic Method and
Variations.305
12.4.1 Simple Monte Carlo Can Be Quasi-Dynamic.305
12.4.2 The General Metropolis-Hastings Algorithm . 306
12.4.3 MC Variations: Replica Exchange and Beyond . 307
12.5 Another Basic Method: Reweighting and Its Variations . 309
12.5.1 Reweighting and Annealing. 310
12.5.2 Polymer-Growth Ideas. 311
12.5.3 Removing Weights by "Resampling" Methods. 312
12.5.4 Correlations Can Arise Even without Dynamics . 313
12.6 Discrete-State Simulations.313
12.7 How to Judge Equilibrium Simulation Quality.313
12.7.1 Visiting All Important States. 314
12.7.2 Ideal Sampling as a Key Conceptual Reference . 314
12.7.3 Uncertainty in Observables and Averages.314
12.7.4 Overall Sampling Quality. 315
12.8 Free Energy and PMF Calculations. 316
12.8.1 PMF and Configurational Free Energy
Calculations . 317
12.8.2 Thermodynamic Free Energy Differences Include
All Space. 318
12.8.3 Approximate Methods for Drug Design.320
12.9 Path Ensembles: Sampling Trajectories .321
12.9.1 Three Strategies for Sampling Paths.321
12.10Protein Folding: Dynamics and Structure Prediction. 322
12.11 Summary. 323
Further Reading. 323
Index . 325 |
| any_adam_object | 1 |
| author | Zuckerman, Daniel M. |
| author_GND | (DE-588)1019320796 |
| author_facet | Zuckerman, Daniel M. |
| author_role | aut |
| author_sort | Zuckerman, Daniel M. |
| author_variant | d m z dm dmz |
| building | Verbundindex |
| bvnumber | BV025602695 |
| classification_rvk | WD 2200 |
| classification_tum | PHY 821f |
| ctrlnum | (OCoLC)699656111 (DE-599)BVBBV025602695 |
| dewey-full | 572 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 572 - Biochemistry |
| dewey-raw | 572 |
| dewey-search | 572 |
| dewey-sort | 3572 |
| dewey-tens | 570 - Biology |
| discipline | Physik Biologie |
| format | Book |
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| id | DE-604.BV025602695 |
| illustrated | Illustrated |
| indexdate | 2025-02-11T11:01:26Z |
| institution | BVB |
| isbn | 9781420073782 1420073788 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020197970 |
| oclc_num | 699656111 |
| open_access_boolean | |
| owner | DE-11 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-188 DE-384 |
| owner_facet | DE-11 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-188 DE-384 |
| physical | XXI, 334 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC |
| record_format | marc |
| spelling | Zuckerman, Daniel M. Verfasser (DE-588)1019320796 aut Statistical physics of biomolecules an introduction Daniel M. Zuckerman Boca Raton, Fla. [u.a.] CRC 2010 XXI, 334 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biomolekül (DE-588)4135124-1 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Biomolekül (DE-588)4135124-1 s Statistische Physik (DE-588)4057000-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020197970&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zuckerman, Daniel M. Statistical physics of biomolecules an introduction Biomolekül (DE-588)4135124-1 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4135124-1 (DE-588)4057000-9 |
| title | Statistical physics of biomolecules an introduction |
| title_auth | Statistical physics of biomolecules an introduction |
| title_exact_search | Statistical physics of biomolecules an introduction |
| title_full | Statistical physics of biomolecules an introduction Daniel M. Zuckerman |
| title_fullStr | Statistical physics of biomolecules an introduction Daniel M. Zuckerman |
| title_full_unstemmed | Statistical physics of biomolecules an introduction Daniel M. Zuckerman |
| title_short | Statistical physics of biomolecules |
| title_sort | statistical physics of biomolecules an introduction |
| title_sub | an introduction |
| topic | Biomolekül (DE-588)4135124-1 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Biomolekül Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020197970&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zuckermandanielm statisticalphysicsofbiomoleculesanintroduction |