The physical basis of biochemistry: the foundations of molecular biophysics
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| Format: | Book |
| Language: | English |
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New York, NY
Springer
2010
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXIX, 949 S. Ill., graph. Darst. |
| ISBN: | 9781441963239 |
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MARC
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| 100 | 1 | |a Bergethon, Peter R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The physical basis of biochemistry |b the foundations of molecular biophysics |c Peter R. Bergethon |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2010 | |
| 300 | |a XXIX, 949 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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IMAGE 1
CONTENTS
PART I PRINCIPLES OF BIOPHYSICAL INQUIRY
1 INTRODUCTION: TO THE STUDENT - FIRST EDITION . . . . . . . . . . . . 3
2 PHILOSOPHY AND PRACTICE OF BIOPHYSICAL STUDY . . . . . . . . . . . 5
2.1 WHAT IS BIOPHYSICAL CHEMISTRY AND WHY STUDY IT? . . . . . . 5
2.2 SCIENCE IS NOT CONTENT BUT A UNIQUE METHOD OF DISCOVERY . . 6 2.3
THE PROGRESSION OF INQUIRY GUIDES THE SCIENTIFIC MODELING PROCESS . . .
. . . . . . . . . . . . . . . . . . . . 8
2.4 A BRIEF HISTORY OF HUMAN METHODS OF INQUIRY REVEALS IMPORTANT
ASPECTS OF THE SCIENTIFIC METHOD . . . . . 9 2.5 THE GEDANKEN EXPERIMENT
IS A THOUGHT EXPERIMENT . . . . . 12 2.6 THE BEGINNINGS OF MODERN
SCIENCE- KEPLER AND GALILEO . . . 14 2.7 MODERN BIOPHYSICAL STUDIES
STILL FOLLOW THE
PARADIGM OF KEPLER AND GALILEO . . . . . . . . . . . . . . . . 16
2.7.1 DESCRIBE THE PHENOMENON - WHAT IS HAPPENING HERE? WHAT ARE THE
EMERGENT PROPERTIES OF THE SYSTEM? . . . . . . . . . . . . . . . 16
2.7.2 REDUCE THE PHENOMENON TO A SYSTEMS DESCRIPTION: IDENTIFY THE
COMPONENTS OF A SYSTEM - WHO AND WHAT IS INVOLVED? (WHAT ARE THE
ELEMENTS?) . . . . . . . . . . . . . . . . . . 17
2.7.3 ANALYSIS OF STRUCTURE - WHAT DOES IT LOOK LIKE? WHAT ARE THE
RELATIONSHIPS BETWEEN THE COMPONENTS? (WHAT ARE THE INTERACTION RULES
AND WHAT IS THE CONTEXT OF THE SYSTEM?) . . . 17
2.7.4 ANALYSIS OF DYNAMIC FUNCTION - WHAT IS THE MECHANISTIC OR
EXPLANATORY CAUSE OF THAT? . . . . . 18 FURTHER READING . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 20
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
IX
IMAGE 2
X CONTENTS
3 OVERVIEW OF THE BIOLOGICAL SYSTEM UNDER STUDY . . . . . . . . . 23
3.1 HIERARCHIES OF ABSTRACTION ARE ESSENTIAL IN THE STUDY OF BIOPHYSICAL
CHEMISTRY . . . . . . . . . . . . . . . . . . . 24
3.2 AN OVERVIEW OF THE CELL: THE ESSENTIAL BUILDING BLOCK OF LIFE . . .
. . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 THE CELL MEMBRANE IS A PHYSICAL BOUNDARY BETWEEN THE CELL SYSTEM
AND ITS SURROUNDINGS BUT THIS MEMBRANE IS ALSO PART OF THE BIOLOGICAL
SYSTEM . . . . . . . . . . . . 26
3.2.2 THE CYTOPLASMIC SPACE IS THE MATRIX OF THE INTRACELLULAR SYSTEM .
. . . . . . . . . . . . . . . . 26
3.2.3 THE ORGANELLES ARE SUBSYSTEMS THAT ARE FOUND WITHIN THE
CYTOPLASMIC SPACE BUT HAVE UNIQUE ENVIRONMENTS AND ARE THEREFORE COMPLEX
PHYSICAL SYSTEMS . . . 28
3.2.4 THE NUCLEAR SPACE IS AN INTRACELLULAR SPACE THAT IS SEPARATED FROM
THE CYTOPLASMIC SPACE BECAUSE OF THE SYSTEMS INTERACTIONS . . . . . 31
3.3 CONTROL MECHANISMS ARE ESSENTIAL PROCESS ELEMENTS OF THE BIOLOGICAL
STATE SPACE . . . . . . . . . . . . . . . . . 33
3.4 BIOLOGICAL ENERGY TRANSDUCTION IS AN ESSENTIAL PROCESS THAT PROVIDES
ENERGY TO ENSURE THE HIGH DEGREE OF ORGANIZATION NECESSARY FOR LIFE . .
. . . . . . . . 34
3.5 THE CELL IS A BUILDING BLOCK OF CHEMICAL AND BIOLOGICAL ORGANIZATION
AND ALSO A KEY TO THE STUDY OF BIOLOGICAL COMPLEXITY . . . . . . . . . .
. . . . . . . . . 44
3.6 A BRIEF HISTORY OF LIFE . . . . . . . . . . . . . . . . . . . . 45
3.7 EVOLUTION CAN BE MODELED AS A DYNAMIC PROCESS WITH MANY BIFURCATIONS
IN THE STATE SPACE OF LIFE . . . . . . 46
3.7.1 THE SCARCITY OF ENERGY AND CHEMICAL RESOURCES IS A FUNDAMENTAL
CHALLENGE ENCOUNTERED IN BIOLOGICAL EVOLUTION . . . . . . . . . 47
3.7.2 THE BIOCHEMICAL SOLUTION TO THE ENERGY LIMITATIONS CREATED A NEW
WASTE PROBLEM: GLOBAL OXYGENATION . . . . . . . . . . . . . . . . . 48
3.7.3 THE RESPONSE TO THE NEW BIOCHEMICAL ENVIRONMENT RESULTED IN A
BIOLOGICAL BIFURCATION: THE APPEARANCE OF THE EUKARYOTIC CELL . . . . .
. . . . . . . . . . . . . . . 49
3.7.4 COMPARTMENTALIZATION IS AN IMPORTANT REORDERING OF PHYSIOCHEMICAL
RELATIONSHIPS THAT CHANGES THE PHYSICAL ENVIRONMENT FROM SOLUTION
DOMINATED TO SURFACE DOMINATED . . . . . 52 FURTHER READING . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 54
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
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CONTENTS XI
4 PHYSICAL THOUGHTS, BIOLOGICAL SYSTEMS - THE APPLICATION OF MODELING
PRINCIPLES TO UNDERSTANDING BIOLOGICAL SYSTEMS . . 57 4.1 THE
INTERACTION BETWEEN FORMAL MODELS AND NATURAL SYSTEMS IS THE ESSENCE OF
PHYSICAL AND BIOPHYSICAL SCIENCE . 57 4.2 OBSERVABLES ARE THE LINK
BETWEEN OBSERVER AND REALITY . . 58 4.3 SYSTEMS SCIENCE GUIDES THE
LINKAGE OF NATURAL
AND FORMAL MODELS . . . . . . . . . . . . . . . . . . . . . . 60
4.4 ABSTRACTION AND APPROXIMATION MAY BE USEFUL BUT ARE NOT ALWAYS
CORRECT . . . . . . . . . . . . . . . . . . . . 61
4.5 THE CHOICES MADE IN OBSERVABLES AND MEASUREMENT INFLUENCE WHAT CAN
BE KNOWN ABOUT A SYSTEM . . . . . . . 62
4.6 THE SIMPLIFYING CONCEPT OF ABSTRACTION IS CENTRAL TO BOTH SCIENTIFIC
UNDERSTANDING AND MISCONCEPTION . . . . . . 64 4.7 EQUATIONS OF STATE
CAPTURE THE SYSTEM BEHAVIOR OR "SYSTEMNESS" . . . . . . . . . . . . . .
. . . . . . . . . . 65
4.8 EQUIVALENT DESCRIPTIONS CONTAIN THE SAME INFORMATION . . . . 67 4.9
SYMMETRY AND SYMMETRY OPERATIONS ALLOW MOLECULES TO BE PLACED IN GROUPS
. . . . . . . . . . . . . . . 69
4.10 THE GOODNESS OF THE MODEL DEPENDS ON WHERE YOU LOOK WITH
BIFURCATION LEADING TO NEW DISCOVERY . . . . . . 71 4.11 BIFURCATIONS IN
STATE SPACE CHARACTERIZE COMPLEX SYSTEMS . 72 4.12 CATASTROPHES AND
CHAOS ARE EXAMPLES OF FORMAL
MATHEMATICAL SYSTEMS THAT MAY CAPTURE IMPORTANT BEHAVIORS OF NATURAL
SYSTEMS . . . . . . . . . . . . . . . . . 74
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
5 PROBABILITY AND STATISTICS . . . . . . . . . . . . . . . . . . . . . .
81
5.1 AN OVERVIEW OF PROBABILITY AND STATISTICS . . . . . . . . . . . 82
5.2 DISCRETE PROBABILITY COUNTS THE NUMBER OF WAYS THINGS CAN HAPPEN . .
. . . . . . . . . . . . . . . . . . . . 82
5.3 SPECIFIC TECHNIQUES ARE NEEDED FOR DISCRETE COUNTING . . . 84 5.3.1
MULTIPLICATION COUNTS POSSIBLE OUTCOMES OF SUCCESSIVE EVENTS . . . . . .
. . . . . . . . . . . 85
5.3.2 PERMUTATIONS ARE COUNTS OF LINEUPS . . . . . . . . . 86
5.3.3 COMBINATIONS ARE COUNTS OF COMMITTEES . . . . . . 86
5.3.4 COUNTING INDISTINGUISHABLE VERSUS DISTINGUISHABLE ENTITIES REQUIRE
DIFFERENT TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . 87
5.4 COUNTING CONDITIONAL AND INDEPENDENT EVENTS THAT OCCUR IN MULTISTAGE
EXPERIMENTS REQUIRE SPECIAL CONSIDERATIONS . . . . . . . . . . . . . . .
. . . . . . . . . . 87
5.5 DISCRETE DISTRIBUTIONS COME FROM COUNTING UP THE OUTCOMES OF
REPEATED EXPERIMENTS . . . . . . . . . . . . 89
5.5.1 THE MULTINOMIAL COEFF ICIENT . . . . . . . . . . . . . 89
IMAGE 4
XII CONTENTS
5.5.2 THE BINOMIAL DISTRIBUTION CAPTURES THE PROBABILITY OF SUCCESS IN
THE CASE OF TWO POSSIBLE OUTCOMES . . . . . . . . . . . . . . . . . . 91
5.5.3 THE POISSON DISTRIBUTION REQUIRES FEWER PARAMETERS FOR CALCULATION
THAN THE BINOMIAL DISTRIBUTION . . . . . . . . . . . . . . . . 91
5.6 CONTINUOUS PROBABILITY IS REPRESENTED AS A DENSITY OF LIKELIHOOD
RATHER THAN BY COUNTING EVENTS . . . . . . . . 94
5.6.1 SOME MATHEMATICAL PROPERTIES OF PROBABILITY DENSITY FUNCTIONS . .
. . . . . . . . . . . . . . . . 95
5.6.2 THE EXPONENTIAL DENSITY FUNCTION IS USEFUL FOR LIFETIME ANALYSIS .
. . . . . . . . . . . . . . . . 98
5.6.3 THE GAUSSIAN DISTRIBUTION IS A BELL-SHAPED CURVE . 99 5.6.4
STIRLING'S FORMULA CAN BE USED TO APPROXIMATE THE FACTORIALS OF LARGE
NUMBERS . . . . . . . . . . . . . . . . . . . . . . . 101
5.6.5 THE BOLTZMANN DISTRIBUTION FINDS THE MOST PROBABLE DISTRIBUTION OF
PARTICLES IN THERMAL EQUILIBRIUM . . . . . . . . . . . . . . . . . . . .
. . 102
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
105
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
105
PART II FOUNDATIONS
6 ENERGY AND FORCE - THE PRIME OBSERVABLES . . . . . . . . . . . . 109
6.1 EXPERIMENTAL MODELS ARE A CAREFUL ABSTRACTION OF EITHER DESCRIPTIVE
OR EXPLANATORY MODELS . . . . . . . . . 109
6.2 POTENTIAL ENERGY SURFACES ARE TOOLS THAT HELP FIND STRUCTURE THROUGH
THE MEASUREMENT OF ENERGY . . . . . . . . 110
6.3 CONSERVATIVE SYSTEMS FIND MAXIMAL CHOICE BY BALANCING KINETIC AND
POTENTIAL ENERGIES OVER TIME . . . 113 6.4 FORCES IN BIOLOGICAL SYSTEMS
DO THE WORK THAT INFLUENCES STRUCTURE AND FUNCTION . . . . . . . . . . .
. . . . 115
6.4.1 THE CONCEPT OF FORCES AND FIELDS IS DERIVED FROM NEWTON'S LAWS OF
MOTION . . . . . . . . . . . 115
6.4.2 FORCE AND MASS ARE RELATED THROUGH ACCELERATION . 116 6.4.3 THE
PRINCIPLE OF CONSERVATION LEADS TO THE CONCEPT OF A FORCE FIELD . . . .
. . . . . . . . . . . 117
6.4.4 ENERGY IS A MEASURE OF THE CAPACITY TO DO WORK . . 118 FURTHER
READING . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
123
7 BIOPHYSICAL FORCES IN MOLECULAR SYSTEMS . . . . . . . . . . . . . 125
7.1 FORM AND FUNCTION IN BIOMOLECULAR SYSTEMS ARE GOVERNED BY A LIMITED
NUMBER OF FORCES . . . . . . . . . . 126
IMAGE 5
CONTENTS XIII
7.2 MECHANICAL MOTIONS CAN DESCRIBE THE BEHAVIOR OF GASES AND THE
MIGRATION OF CELLS . . . . . . . . . . . . . . 127
7.2.1 MOTION IN ONE AND TWO DIMENSIONS . . . . . . . . . 127
7.2.2 MOTION UNDER CONSTANT ACCELERATION . . . . . . . . 128
7.2.3 PROJECTILE MOTION IN A CONSTANT POTENTIAL ENERGY FIELD . . . . . .
. . . . . . . . . . . . . . . 129
7.3 THE KINETIC THEORY OF GASES EXPLAINS THE PROPERTIES OF GASES BASED
ON MECHANICAL INTERACTIONS OF MOLECULES . . 129 7.3.1 COLLISIONS ARE
IMPACTS IN WHICH OBJECTS EXCHANGE MOMENTUM . . . . . . . . . . . . . . .
. 130
7.3.2 REVIEWING THE PHENOMENOLOGY OF DILUTE GASES SHEDS LIGHT ON
MOLECULAR MECHANICS . . . . . 131 7.3.3 THE PRESSURE OF A GAS IS DERIVED
FROM THE TRANSFER OF AN EXTREMELY SMALL AMOUNT OF
MOMENTUM FROM AN ATOM TO THE WALL OF A VESSEL . . 134 7.3.4 THE LAW OF
EQUIPARTITION OF ENERGY IS A CLASSICAL TREATMENT OF ENERGY DISTRIBUTION
. . . . . 138 7.3.5 THE REAL BEHAVIOR OF GASES CAN BE BETTER
MODELED BY ACCOUNTING FOR ATTRACTIVE AND REPULSIVE FORCES BETWEEN
MOLECULES . . . . . . . . 141
7.4 THE ELECTRIC FORCE IS THE ESSENTIAL INTERACTION THAT LEADS TO THE
CHEMICAL NATURE OF THE UNIVERSE . . . . . . . . 144
7.4.1 ELECTROSTATICS DEFINE ELECTRICAL FORCES BETWEEN STATIONARY CHARGES
. . . . . . . . . . . . . 144
7.4.2 THE ELECTRIC FIELD IS ASSOCIATED WITH A CHARGED OBJECT . . . . . .
. . . . . . . . . . . . . . 147
7.4.3 ELECTRIC DIPOLES ARE OPPOSITE CHARGES THAT ARE SEPARATED IN SPACE
. . . . . . . . . . . . . . . . 151
7.4.4 THE ELECTRIC FLUX IS A PROPERTY OF THE ELECTRIC FIELD . 152 7.4.5
GAUSS' LAW RELATES THE ELECTRIC FIELD TO AN ELECTRIC CHARGE . . . . . .
. . . . . . . . . . . . . . 153
7.4.6 A POINT CHARGE WILL ACCELERATE IN AN ELECTRIC FIELD . 154 7.4.7
THE ELECTRIC POTENTIAL IS THE CAPACITY TO DO ELECTRICAL WORK . . . . . .
. . . . . . . . . . . . . . 155
7.4.8 EQUIPOTENTIAL SURFACES ARE COMPRISED OF LINES OF CONSTANT
POTENTIAL . . . . . . . . . . . . . . 158
7.4.9 CALCULATING POTENTIAL FIELDS . . . . . . . . . . . . . 158
7.4.10 CAPACITORS STORE ELECTROSTATIC FIELD ENERGY . . . . . 160 7.5
WAVE MOTION IS IMPORTANT IN ELECTROMAGNETIC AND MECHANICAL INTERACTIONS
IN BIOLOGICAL SYSTEMS . . . . . . . . 162
7.5.1 PULSES ARE THE STARTING POINT FOR UNDERSTANDING WAVE MOTION . . .
. . . . . . . . . . 163
7.5.2 THE WAVEFUNCTION IS A MATHEMATICAL EXPRESSION FOR WAVE MOTION IN
TERMS OF SPACE AND TIME . . . . . . . . . . . . . . . . . . 164
IMAGE 6
XIV CONTENTS
7.5.3 SUPERPOSITION AND INTERFERENCE ARE FUNDAMENTAL PROPERTIES OF WAVE
INTERACTION . . . . . 165 7.5.4 THE VELOCITY OF A WAVE PULSE IS A
FUNCTION OF THE TRANSMISSION MEDIUM . . . . . . . . . . . . . 166
7.5.5 REFLECTION AND TRANSMISSION OF A WAVE DEPENDS ON THE INTERFACE
BETWEEN TWO PHASES OF DIFFERENT SPEEDS OF PROPAGATION . . . . . . 167
7.6 HARMONIC WAVES ARE THE RESULT OF A SINUSOIDAL OSCILLATION . 167
7.6.1 WAVELENGTH, FREQUENCY, AND VELOCITY . . . . . . . . 168
7.6.2 POLARIZATION . . . . . . . . . . . . . . . . . . . . . . 169
7.6.3 SUPERPOSITION AND INTERFERENCE - WAVES OF THE SAME FREQUENCY . . .
. . . . . . . . . . . . . . 171
7.7 ENERGY AND INTENSITY OF WAVES . . . . . . . . . . . . . . . . 174
7.7.1 SOUND AND HUMAN EAR . . . . . . . . . . . . . . . . 175
7.8 STANDING WAVES . . . . . . . . . . . . . . . . . . . . . . . . 176
7.9 SUPERPOSITION AND INTERFERENCE - WAVES OF DIFFERENT FREQUENCIES . .
. . . . . . . . . . . . . . . . . . . . . . . . 179
7.10 COMPLEX WAVEFORMS . . . . . . . . . . . . . . . . . . . . . . 181
7.11 WAVE PACKETS . . . . . . . . . . . . . . . . . . . . . . . . . .
182
7.12 DISPERSION . . . . . . . . . . . . . . . . . . . . . . . . . . .
184
7.13 THE WAVE EQUATION . . . . . . . . . . . . . . . . . . . . . . 185
7.14 WAVES IN TWO AND THREE DIMENSIONS . . . . . . . . . . . . . 186
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
189
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
189
8 PHYSICAL PRINCIPLES: QUANTUM MECHANICS . . . . . . . . . . . . . 191
8.1 THE STORY OF THE DISCOVERY OF QUANTUM MECHANICS IS AN INSTRUCTIVE
HISTORY OF HOW SCIENTIFIC IDEAS ARE MODIFIED 192 8.2 FROM THE STANDPOINT
OF THE PHILOSOPHY OF EPISTEMOLOGICAL SCIENCE, THE QUANTUM REVOLUTION
ENDED AN AGE OF CERTAINTY . . . . . . . . . . . . . . . . . . . 192
8.3 THE ULTRAVIOLET CATASTROPHE IS A TERM THAT REFERS TO A HISTORICAL
FAILURE OF CLASSICAL THEORY . . . . . . . . . . 194
8.3.1 THERMAL RADIATION . . . . . . . . . . . . . . . . . . 195
8.3.2 BLACKBODY RADIATION . . . . . . . . . . . . . . . . . 195
8.3.3 CLASSICAL THEORY OF CAVITY RADIATION . . . . . . . . 197
8.3.4 PLANCK'S THEORY OF CAVITY RADIATION . . . . . . . . . 199
8.3.5 QUANTUM MODEL MAKING - EPISTEMOLOGICAL REFLECTIONS ON THE MODEL .
. . . . . . . . . . . . . . 200
8.4 THE CONCEPT OF HEAT CAPACITY WAS MODIFIED BY QUANTUM MECHANICAL
CONSIDERATIONS . . . . . . . . . . . . . 202
8.5 THE PHOTOELECTRIC EFFECT AND THE PHOTON-PARTICLE PROPERTIES OF
RADIATION COULD BE UNDERSTOOD USING PLANCK'S QUANTA . . . . . . . . . .
. . . . . . . . . . . . . . 203
8.6 ELECTROMAGNETIC RADIATION HAS A DUAL NATURE . . . . . . . . 205
IMAGE 7
CONTENTS XV
8.7 DE BROGLIE'S POSTULATE DEFINES THE WAVELIKE PROPERTIES OF PARTICLES
. . . . . . . . . . . . . . . . . . . . . 206
8.8 THE ELECTRON MICROSCOPE EMPLOYS PARTICLES AS WAVES TO FORM IMAGES .
. . . . . . . . . . . . . . . . . . . . . . . 207
8.9 THE UNCERTAINTY PRINCIPLE IS AN ESSENTIAL CONCLUSION OF THE QUANTUM
VIEWPOINT . . . . . . . . . . . . . . . . . . . 209
8.10 AN HISTORICAL APPROACH TO UNDERSTANDING ATOMIC STRUCTURE AND THE
ATOM . . . . . . . . . . . . . . . . . . . . 210
8.10.1 ATOMIC SPECTRA . . . . . . . . . . . . . . . . . . . . 213
8.10.2 BOHR'S MODEL . . . . . . . . . . . . . . . . . . . . . 215
8.11 QUANTUM MECHANICS REQUIRES THE CLASSICAL TRAJECTORY ACROSS A
POTENTIAL ENERGY SURFACE TO BE REPLACED BY THE WAVEFUNCTION . . . . . .
. . . . . . . . . . . 218
8.11.1 THE SCHROEDINGER EQUATION . . . . . . . . . . . . . . 220
8.12 SOLUTIONS TO THE TIME-INDEPENDENT SCHROEDINGER THEORY . . . 224
8.12.1 LINEAR MOTION - ZERO POTENTIAL FIELD . . . . . . . . 224
8.12.2 THE STEP POTENTIAL . . . . . . . . . . . . . . . . . . 226
8.12.3 THE BARRIER POTENTIAL . . . . . . . . . . . . . . . . . 227
8.12.4 THE SQUARE WELL POTENTIAL . . . . . . . . . . . . . . 229
8.12.5 THE HARMONIC OSCILLATOR . . . . . . . . . . . . . . . 232
8.12.6 ROTATIONAL AND ANGULAR MOTION . . . . . . . . . . . 233
8.13 BUILDING THE ATOMIC MODEL - ONE-ELECTRON ATOMS . . . . . . 235 8.14
BUILDING THE ATOMIC MODEL - MULTI-ELECTRON ATOMS . . . . . 238 8.14.1
FERMIONS AND BOSONS . . . . . . . . . . . . . . . . . 238
8.14.2 SELF-CONSISTENT FIELD THEORY FINDS APPROXIMATE WAVEFUNCTIONS FOR
MULTI-ELECTRON ATOMS . . . . . . . . . . . . . . . . . 239
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
240
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
241
9 CHEMICAL PRINCIPLES . . . . . . . . . . . . . . . . . . . . . . . . .
243
9.1 KNOWING THE DISTRIBUTION OF ELECTRONS IN MOLECULES IS ESSENTIAL FOR
UNDERSTANDING CHEMICAL STRUCTURE AND BEHAVIOR . . . . . . . . . . . . .
. . . . . . . . . . . . . 243
9.2 THE NATURE OF CHEMICAL INTERACTIONS . . . . . . . . . . . . . 244
9.3 ELECTROSTATIC FORCES DESCRIBE THE INTERACTIONS FROM SALT CRYSTALS TO
VAN DER WAALS ATTRACTION . . . . . . . . . . . 244
9.3.1 ION-ION INTERACTIONS . . . . . . . . . . . . . . . . . 244
9.3.2 ION-DIPOLE INTERACTIONS . . . . . . . . . . . . . . . 245
9.3.3 ION-INDUCED DIPOLE INTERACTIONS . . . . . . . . . . . 246
9.3.4 VAN DER WAALS INTERACTIONS . . . . . . . . . . . . . . 246
9.4 COVALENT BONDS INVOLVE A TRUE SHARING OF ELECTRONS BETWEEN ATOMS . .
. . . . . . . . . . . . . . . . . . . . . . 249
9.4.1 LEWIS STRUCTURES ARE A FORMAL SHORTHAND THAT DESCRIBE COVALENT
BONDS . . . . . . . . . . . . 250
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XVI CONTENTS
9.4.2 VSEPR THEORY PREDICTS MOLECULAR STRUCTURE . . . . 250 9.4.3
MOLECULAR ORBITAL THEORY IS AN APPROXIMATION TO A FULL QUANTUM
MECHANICAL TREATMENT OF COVALENT INTERACTIONS . . . 251
9.5 HYDROGEN BONDS ARE A UNIQUE HYBRID OF INTERACTIONS AND PLAY A
FUNDAMENTAL ROLE IN THE BEHAVIOR OF BIOLOGICAL SYSTEMS . . . . . . . . .
. . . . . . . . . . . . 262
9.6 BIOLOGICAL SYSTEMS ARE MADE FROM A LIMITED NUMBER OF ELEMENTS . . .
. . . . . . . . . . . . . . . . . . . 264
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
266
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
267
10 MEASURING THE ENERGY OF A SYSTEM: ENERGETICS AND THE FIRST LAW OF
THERMODYNAMICS . . . . . . . . . . . . . . . 269
10.1 HISTORICALLY HEAT WAS THOUGHT TO BE A FLUID OR "THE CALORIC" 269
10.2 THE THERMODYNAMIC MODELING SPACE IS A SYSTEMIC APPROACH TO
DESCRIBING THE WORLD . . . . . . . . . . . . . . 271
10.2.1 SYSTEMS, SURROUNDINGS, AND BOUNDARIES . . . . . . . 272
10.2.2 PROPERTIES OF A THERMODYNAMIC SYSTEM . . . . . . . 272
10.2.3 EXTENSIVE AND INTENSIVE VARIABLES . . . . . . . . . . 273
10.2.4 THE STATE OF A SYSTEM . . . . . . . . . . . . . . . . 274
10.2.5 HOW MANY PROPERTIES ARE REQUIRED TO DEFINE THE STATE OF A SYSTEM?
. . . . . . . . . . . . 275
10.2.6 CHANGES IN STATE . . . . . . . . . . . . . . . . . . . 276
10.3 THE FIRST LAW STATES THAT "THE ENERGY OF THE UNIVERSE IS CONSERVED"
. . . . . . . . . . . . . . . . . . . . . . . . . 276
10.3.1 SPECIALIZED BOUNDARIES ARE IMPORTANT TOOLS FOR DEFINING
THERMODYNAMIC SYSTEMS . . . . . . . . 278
10.3.2 EVALUATING THE ENERGY OF A SYSTEM REQUIRES MEASURING WORK AND
HEAT TRANSFER . . . . . . . . . 280
10.4 THE HEAT CAPACITY IS A PROPERTY THAT CAN REFLECT THE INTERNAL
ENERGY OF A SYSTEM . . . . . . . . . . . . . . . . . . 283
10.5 ENTHALPY IS DEFINED WHEN A SYSTEM IS HELD AT CONSTANT PRESSURE . .
. . . . . . . . . . . . . . . . . . . . . 285
THOUGHT QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . .
289
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
289
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
290
11 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS . . . . . . . . 293
11.1 THE ARROW OF TIME AND IMPOSSIBLE EXISTENCE OF PERPETUAL MOTION
MACHINES ARE BOTH MANIFESTATIONS OF THE SECOND LAW OF THERMODYNAMICS . .
. 294 11.1.1 THE MOVEMENT OF A SYSTEM TOWARD
EQUILIBRIUM IS THE NATURAL DIRECTION . . . . . . . . . 295
11.2 THE DESIGN OF A PERFECT HEAT ENGINE IS AN IMPORTANT THOUGHT
EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . 295
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CONTENTS XVII
11.2.1 REVERSIBLE PATHS HAVE UNIQUE PROPERTIES COMPARED TO IRREVERSIBLE
PATHS . . . . . . . . . . . . 296
11.2.2 A CARNOT CYCLE IS A REVERSIBLE PATH HEAT ENGINE . . 301 11.2.3
ENTROPY IS THE RESULT OF THE CONSIDERATION OF A CARNOT CYCLE . . . . . .
. . . . . . . . . . . . . . 305
11.3 A MECHANICAL/KINETIC APPROACH TO ENTROPY . . . . . . . . . 307
11.3.1 THE STATISTICAL BASIS OF A MECHANISTIC THEORY IS REFLECTED BY
SYSTEM PROPERTIES . . . . . . 308
11.3.2 FLUCTUATIONS CAN BE MEASURED STATISTICALLY . . . . . 309 11.4
STATISTICAL THERMODYNAMICS YIELDS THE SAME CONCLUSIONS AS CLASSICAL
TREATMENT OF THERMODYNAMICS . . . 310
11.4.1 THE ENSEMBLE METHOD IS A THOUGHT EXPERIMENT INVOLVING MANY
PROBABILITY EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . 310
11.4.2 THE CANONICAL ENSEMBLE IS AN EXAMPLE OF THE ENSEMBLE METHOD . . .
. . . . . . . . . . . . 312
11.4.3 THE DISTRIBUTION OF ENERGY AMONG ENERGY STATES IS AN IMPORTANT
DESCRIPTION OF A SYSTEM . . . 316 11.4.4 HEAT FLOW CAN BE DESCRIBED
STATISTICALLY . . . . . . 317 11.4.5 INTERNAL MOLECULAR MOTIONS, ENERGY
AND
STATISTICAL MECHANICS ARE RELATED BY A PARTITION FUNCTION . . . . . . .
. . . . . . . . . . . . 320
11.5 ENTROPY CAN BE DESCRIBED AND UNDERSTOOD ON A STATISTICAL BASIS . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
11.5.1 DIFFERENT STATISTICAL DISTRIBUTIONS ARE NEEDED FOR DIFFERENT
CONDITIONS . . . . . . . . . . . 321
11.5.2 PHENOMENOLOGICAL ENTROPY CAN BE LINKED TO STATISTICAL ENTROPY . .
. . . . . . . . . . . . . . . 323
11.6 THE THIRD LAW OF THERMODYNAMICS DEFINES AN ABSOLUTE MEASURE OF
ENTROPY . . . . . . . . . . . . . . . . . 324
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
324
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
325
12 WHICH WAY IS THAT SYSTEM GOING? THE GIBBS FREE ENERGY . . . 327 12.1
THE GIBBS FREE ENERGY IS A STATE FUNCTION THAT INDICATES THE DIRECTION
AND POSITION OF A SYSTEM'S EQUILIBRIUM . . . . . . . . . . . . . . . . .
. . . . . . . . . 327
12.2 THE GIBBS FREE ENERGY HAS SPECIFIC PROPERTIES . . . . . . . . 329
12.3 THE FREE ENERGY PER MOLE, * , IS AN IMPORTANT THERMODYNAMIC
QUANTITY . . . . . . . . . . . . . . . . . . . 333
12.4 THE CONCEPT OF ACTIVITY RELATES AN IDEAL SYSTEM TO A REAL SYSTEM .
. . . . . . . . . . . . . . . . . . . . . . . 333
12.5 THE APPLICATION OF FREE ENERGY CONSIDERATIONS TO MULTIPLE-COMPONENT
SYSTEMS . . . . . . . . . . . . . . . 334
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XVIII CONTENTS
12.6 THE CHEMICAL POTENTIAL IS AN IMPORTANT DRIVING FORCE IN BIOCHEMICAL
SYSTEMS . . . . . . . . . . . . . . . . . . . . 335
12.6.1 CHARACTERISTICS OF * . . . . . . . . . . . . . . . . . . 336
12.7 ENTROPY AND ENTHALPY CONTRIBUTE TO CALCULATIONS OF THE FREE ENERGY
OF MIXING . . . . . . . . . . . . . . . . . 337
12.8 FINDING THE CHEMICAL EQUILIBRIUM OF A SYSTEM IS POSSIBLE BY MAKING
FREE ENERGY CALCULATIONS . . . . . . . . 340
12.8.1 DERIVATION OF THE ACTIVITY . . . . . . . . . . . . . . 340
12.8.2 ACTIVITY OF THE STANDARD STATE . . . . . . . . . . . . 341
12.8.3 THE EQUILIBRIUM EXPRESSION . . . . . . . . . . . . . 342
12.9 THE THERMODYNAMICS OF GALVANIC CELLS IS DIRECTLY RELATED TO THE
GIBBS FREE ENERGY . . . . . . . . . . . . . . . 345
12.10 FREE ENERGY CHANGES RELATE THE EQUILIBRIUM POSITION OF BIOCHEMICAL
REACTIONS . . . . . . . . . . . . . . . . . . . 348
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
348
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
349
13 THE THERMODYNAMICS OF PHASE EQUILIBRIA . . . . . . . . . . . . . 351
13.1 THE CONCEPT OF PHASE EQUILIBRIUM IS IMPORTANT IN BIOCHEMICAL
SYSTEMS . . . . . . . . . . . . . . . . . . . . 351
13.2 THERMODYNAMICS OF TRANSFER BETWEEN PHASES . . . . . . . . 353
13.3 THE PHASE RULE RELATES THE NUMBER OF VARIABLES OF STATE TO THE
NUMBER OF COMPONENTS AND PHASES AT EQUILIBRIUM . . . . . . . . . . . . .
. . . . . . . . . . . . . 353
13.4 THE EQUILIBRIUM BETWEEN DIFFERENT PHASES IS GIVEN BY THE CLAPEYRON
EQUATION . . . . . . . . . . . . . . . . . . . 355
13.4.1 COLLIGATIVE PROPERTIES VARY WITH SOLUTE CONCENTRATION . . . . . .
. . . . . . . . . . . . . . . 358
13.4.2 THE ACTIVITY COEFFICIENT CAN BE MEASURED BY CHANGES IN THE
COLLIGATIVE PROPERTIES . . . . . . . 361
13.5 SURFACE PHENOMENA ARE AN IMPORTANT EXAMPLE OF PHASE INTERACTION . .
. . . . . . . . . . . . . . . . . . . . . . 362
13.6 BINDING EQUILIBRIA RELATE SMALL MOLECULE BINDING TO LARGER ARRAYS .
. . . . . . . . . . . . . . . . . . . . . . . 364
13.6.1 BINDING AT A SINGLE SITE . . . . . . . . . . . . . . . 366
13.6.2 MULTIPLE BINDING SITES . . . . . . . . . . . . . . . . 367
13.6.3 BINDING WHEN SITES ARE EQUIVALENT AND INDEPENDENT . . . . . . . .
. . . . . . . . . . . . . . 368
13.6.4 EQUILIBRIUM DIALYSIS AND SCATCHARD PLOTS . . . . . . 370 13.6.5
BINDING IN THE CASE OF NON-EQUIVALENT SITES . . . . . 373 13.6.6
COOPERATIVITY IS A MEASURE OF NON-INDEPENDENT BINDING . . . . . . . . .
. . . . . 374
13.6.7 THE ACID-BASE BEHAVIOR OF BIOMOLECULES REFLECTS PROTON BINDING .
. . . . . . . . . . . . . . 379
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
383
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
383
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CONTENTS XIX
PART III BUILDING A MODEL OF BIOMOLECULAR STRUCTURE
14 WATER: A UNIQUE SOLVENT AND VITAL COMPONENT OF LIFE . . . . . . 389
14.1 AN INTRODUCTION TO THE MOST FAMILIAR OF ALL LIQUIDS . . . . . 389
14.2 THE PHYSICAL PROPERTIES OF WATER ARE CONSISTENT WITH A HIGH DEGREE
OF INTERMOLECULAR INTERACTION . . . . . . . . . 391
14.3 CONSIDERING THE PROPERTIES OF WATER AS A LIQUID . . . . . . . 392
14.4 THE STRUCTURE OF MONOMOLECULAR WATER CAN BE DESCRIBED USING A
VARIETY OF MODELS . . . . . . . . . . . . . 394
14.5 THE CAPACITY OF WATER TO FORM HYDROGEN BONDS UNDERLIES ITS UNUSUAL
PROPERTIES . . . . . . . . . . . . . . . 398
14.6 THE STRUCTURE AND DYNAMICS OF LIQUID WATER RESULTS IN "ORDERED
DIVERSITY" THAT IS PROBABLY DISTINCT FROM ICE . . 402 14.7 HYDROPHOBIC
FORCES REFERENCE INTERACTIONS BETWEEN WATER AND OTHER MOLECULES . . . .
. . . . . . . . . . . . . . 405
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
407
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
408
15 ION-SOLVENT INTERACTIONS . . . . . . . . . . . . . . . . . . . . . .
409
15.1 THE NATURE OF ION-SOLVENT INTERACTIONS CAN BE DISCOVERED THROUGH
THE PROGRESSION OF INQUIRY . . . . . . . . 409
15.2 THE BORN MODEL IS A THERMODYNAMIC CYCLE THAT TREATS THE INTERACTION
ENERGY BETWEEN A SIMPLIFIED ION AND A STRUCTURELESS SOLVENT . . . . . .
. . . . . . . . . . 410
15.2.1 BUILDING THE MODEL . . . . . . . . . . . . . . . . . . 411
15.2.2 CHOOSING AN EXPERIMENTAL OBSERVABLE TO TEST THE MODEL . . . . . .
. . . . . . . . . . . . . . 414
15.3 ADDING WATER STRUCTURE TO THE SOLVENT CONTINUUM . . . . . . 418
15.3.1 THE ENERGY OF ION-DIPOLE INTERACTIONS DEPENDS ON GEOMETRY . . . .
. . . . . . . . . . . . 419
15.3.2 DIPOLES IN AN ELECTRIC FIELD: A MOLECULAR PICTURE OF THE
DIELECTRIC CONSTANTS . . . . . . . . . . 420
15.3.3 WHAT HAPPENS WHEN THE DIELECTRIC IS LIQUID WATER? . . . . . . . .
. . . . . . . . . . . . . . . . 426
15.4 EXTENDING THE ION-SOLVENT MODEL BEYOND THE BORN MODEL . . 429
15.4.1 RECALCULATING THE NEW MODEL . . . . . . . . . . . . 430
15.5 SOLUTIONS OF INORGANIC IONS . . . . . . . . . . . . . . . . . . 435
15.6 ION-SOLVENT INTERACTIONS IN BIOLOGICAL SYSTEMS . . . . . . . . 437
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
438
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
438
16 ION-ION INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . . .
. 441
16.1 ION-ION INTERACTIONS CAN BE MODELED AND THESE MODELS CAN BE
EXPERIMENTALLY VALIDATED AND REFINED . . . . 441 16.2 THE DEBYE-HUECKEL
MODEL IS A CONTINUUM MODEL THAT RELATES A DISTRIBUTION OF NEARBY IONS TO
A
CENTRAL REFERENCE ION . . . . . . . . . . . . . . . . . . . . . 444
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XX CONTENTS
16.3 THE PREDICTIONS GENERATED BY THE DEBYE-HUECKEL MODEL CAN BE
EXPERIMENTALLY EVALUATED . . . . . . . . . . . 453
16.4 MORE RIGOROUS TREATMENT OF ASSUMPTIONS LEADS TO AN IMPROVED
PERFORMANCE OF THE DEBYE-HUECKEL MODEL . . 455 16.5 CONSIDERATION OF
OTHER INTERACTIONS IS NECESSARY TO ACCOUNT FOR THE LIMITS OF THE
DEBYE-HUECKEL MODEL . . . . 457
16.5.1 BJERRUM SUGGESTED THAT ION PAIRING COULD AFFECT THE CALCULATION
OF ION-ION INTERACTIONS . . . . 457 FURTHER READING . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 458
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
459
17 LIPIDS IN AQUEOUS SOLUTION . . . . . . . . . . . . . . . . . . . . .
461
17.1 BIOLOGICAL MEMBRANES FORM AT THE INTERFACE BETWEEN AQUEOUS AND
LIPID PHASES . . . . . . . . . . . . . . . . . . . 461
17.2 AQUEOUS SOLUTIONS CAN BE FORMED WITH SMALL NONPOLAR MOLECULES . . .
. . . . . . . . . . . . . . . . . . . 462
17.3 AQUEOUS SOLUTIONS OF ORGANIC IONS ARE AN AMALGAM OF ION-SOLVENT AND
NONPOLAR SOLUTE INTERACTION . . . . . . . . 465
17.3.1 SOLUTIONS OF SMALL ORGANIC IONS . . . . . . . . . . . 465
17.3.2 SOLUTIONS OF LARGE ORGANIC IONS . . . . . . . . . . . 466
17.4 LIPIDS CAN BE PLACED INTO SEVERAL MAJOR CLASSES . . . . . . . 468
17.5 THE ORGANIZATION OF LIPIDS INTO MEMBRANES OCCURS WHEN AQUEOUS AND
LIPID PHASES COME IN CONTACT . . . . . . 474 17.6 THE PHYSICAL
PROPERTIES OF LIPID MEMBRANES . . . . . . . . . 478
17.6.1 PHASE TRANSITIONS IN LIPID MEMBRANES . . . . . . . . 478
17.6.2 THERE ARE SPECIFIC AND LIMITED MOTIONS AND MOBILITIES FOUND IN
MEMBRANES . . . . . . . . . 479
17.7 BIOLOGICAL MEMBRANES: A MORE COMPLETE PICTURE . . . . . . 482
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
483
18 MACROMOLECULES IN SOLUTION . . . . . . . . . . . . . . . . . . . . .
485
18.1 THE PHYSICAL INTERACTIONS OF POLYMERS IN SOLUTION ARE NOT UNIQUE
BUT MODELING THE INTERACTIONS WILL REQUIRE DIFFERENT CONSIDERATIONS THAN
THOSE OF SMALLER MOLECULES . . . . . . . . . . . . . . . . . . . . . . .
486
18.2 THERMODYNAMICS OF SOLUTIONS OF POLYMERS . . . . . . . . . . 487
18.2.1 THE ENTROPY OF MIXING FOR A POLYMER SOLUTION REQUIRES A
STATISTICAL APPROACH . . . . . . 489
18.2.2 THE ENTHALPY OF MIXING IN A POLYMER SOLUTION IS DOMINATED BY VAN
DER WAALS INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . 493
18.2.3 THE FREE ENERGY OF MIXING RELATES ENTHALPY AND ENTROPY IN THE
STANDARD MANNER . . . . . . . . . 498
18.2.4 CALCULATION OF THE PARTIAL SPECIFIC VOLUME AND CHEMICAL POTENTIAL
. . . . . . . . . . . . . . . . 499
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CONTENTS XXI
18.2.5 VAPOR PRESSURE MEASUREMENTS CAN EXPERIMENTALLY BE USED TO
INDICATE INTERACTION ENERGIES . . . . . . . . . . . . . . . . . 504
18.3 THE CONFORMATION OF SIMPLE POLYMERS CAN BE MODELED BY A RANDOM WALK
AND A MARKOV PROCESS . . . . . 505 18.4 THE MAJOR CLASSES OF BIOCHEMICAL
SPECIES FORM MACROMOLECULAR STRUCTURES . . . . . . . . . . . . . . . 506
18.4.1 NUCLEIC ACIDS ARE THE BASIS FOR GENETIC INFORMATION STORAGE AND
PROCESSING . . . . . . . . . 506
18.4.2 CARBOHYDRATE POLYMERS ARE DOMINATED BY HYDROPHILIC INTERACTIONS
WITH WATER . . . . . . . 513
18.4.3 THE POLYMERS OF AMINO ACIDS, PROTEINS ARE BY FAR THE MOST DIVERSE
AND COMPLEX OF ALL BIOLOGICAL POLYMER FAMILIES . . . . . . . . . . . . .
515
18.5 NONPOLAR POLYPEPTIDES IN SOLUTION . . . . . . . . . . . . . . 523
18.6 POLAR POLYPEPTIDES IN SOLUTION . . . . . . . . . . . . . . . . .
527
18.7 TRANSITIONS OF STATE . . . . . . . . . . . . . . . . . . . . . .
531
18.8 THE PROTEIN FOLDING PROBLEM . . . . . . . . . . . . . . . . . 538
18.9 PATHOLOGICAL PROTEIN FOLDING . . . . . . . . . . . . . . . . . .
542
18.9.1 ALZHEIMER'S DISEASE . . . . . . . . . . . . . . . . . 544
18.9.2 FAMILIAL AMYLOIDOTIC POLYNEUROPATHY . . . . . . . . 545
18.9.3 SPONGIFORM ENCEPHALOPATHIES . . . . . . . . . . . . 546
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
549
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
551
19 MOLECULAR MODELING - MAPPING BIOCHEMICAL STATE SPACE . . . . 553 19.1
THE PREDICTION OF MACROMOLECULAR STRUCTURE AND FUNCTION IS A GOAL OF
MOLECULAR MODELING . . . . . . . . . . 553
19.2 MOLECULAR MODELING IS BUILT ON FAMILIAR PRINCIPLES . . . . . 554
19.3 EMPIRICAL METHODS USE CAREFULLY CONSTRUCTED PHYSICAL MODELS . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 555
19.3.1 STICKS AND STONES . . . . . . . . . . . . . . . . . . . 555
19.3.2 THE RAMACHANDRAN PLOT IS THE "ART OF THE POSSIBLE" . 557 19.3.3
SECONDARY STRUCTURE PREDICTION IN PROTEINS IS AN IMPORTANT CHALLENGE IN
MOLECULAR MODELING . . . 563 19.4 COMPUTATIONAL METHODS ARE THE ULTIMATE
GEDANKEN EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . .
569
19.5 MOLECULAR MECHANICS IS A NEWTONIAN OR CLASSICAL MECHANICAL MODELING
APPROACH . . . . . . . . . . . . . . . . 571
19.5.1 BOND STRETCHING . . . . . . . . . . . . . . . . . . . 574
19.5.2 BOND BENDING . . . . . . . . . . . . . . . . . . . . 576
19.5.3 TORSIONAL OR DIHEDRAL POTENTIAL FUNCTIONS . . . . . . 576 19.5.4
VAN DER WAALS INTERACTIONS . . . . . . . . . . . . . . 577
19.5.5 ELECTROSTATIC INTERACTIONS . . . . . . . . . . . . . . . 578
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XXII CONTENTS
19.6 QUANTUM MECHANICAL METHODS ARE COMPUTATIONAL DIFFICULT BUT
THEORETICALLY "PURE" . . . . . . . . . . . . . . . 579
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
581
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
582
20 THE ELECTRIFIED INTERPHASE . . . . . . . . . . . . . . . . . . . . .
. 583
20.1 THE INTERPHASE IS FORMED WHEN PHASES MEET . . . . . . . . . 583
20.2 A DETAILED STRUCTURAL DESCRIPTION OF THE INTERPHASE IS A TASK FOR
PHYSICAL STUDY . . . . . . . . . . . . . . . . . . 587
20.3 THE SIMPLEST PICTURE OF THE INTERPHASE IS THE HELMHOLTZ-PERRIN
MODEL . . . . . . . . . . . . . . . . . . 589
20.4 THE BALANCE BETWEEN THERMAL AND ELECTRICAL FORCES IS SEEN AS
COMPETITION BETWEEN DIFFUSE-LAYER VERSUS DOUBLE-LAYER INTERPHASE
STRUCTURES . . . . . . . . . . 590
20.5 THE STERN MODEL IS A COMBINATION OF THE CAPACITOR AND DIFFUSE LAYER
MODELS . . . . . . . . . . . . . . . . . . . 591
20.6 A MORE COMPLETE PICTURE OF THE DOUBLE-LAYER FORMS WITH ADDED DETAIL
. . . . . . . . . . . . . . . . . . . . . . . 593
20.7 COLLOIDAL SYSTEMS AND THE ELECTRIFIED INTERFACE GIVE RISE TO THE
LYOPHILIC SERIES . . . . . . . . . . . . . . . . . . 595
20.8 SALTING OUT CAN BE UNDERSTOOD IN TERMS OF ELECTRIFIED INTERPHASE
BEHAVIOR . . . . . . . . . . . . . . . . 599
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
600
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
600
PART IV FUNCTION AND ACTION BIOLOGICAL STATE SPACE
21 TRANSPORT - A NON-EQUILIBRIUM PROCESS . . . . . . . . . . . . . . 605
21.1 TRANSPORT IS AN IRREVERSIBLE PROCESS AND DOES NOT OCCUR AT
EQUILIBRIUM . . . . . . . . . . . . . . . . . . . . . . 605
21.2 THE PRINCIPLES OF NON-EQUILIBRIUM THERMODYNAMICS CAN BE RELATED TO
THE MORE FAMILIAR EQUILIBRIUM TREATMENT WITH THE IDEA OF LOCAL
EQUILIBRIUM . . . . . . . . . 606
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
610
22 FLOW IN A CHEMICAL POTENTIAL FIELD: DIFFUSION . . . . . . . . . . .
611
22.1 TRANSPORT IN CHEMICAL, ELECTRICAL, PRESSURE, AND THERMAL GRADIENTS
ARE ALL TREATED WITH THE SAME MATHEMATICS . . . . . . . . . . . . . . .
. . . . . . . . . . . 611
22.2 DIFFUSION OR THE FLOW OF PARTICLES DOWN A CONCENTRATION GRADIENT
CAN BE DESCRIBED PHENOMENOLOGICALLY . . . . . . . . . . . . . . . . . .
. . . . 612
22.3 THE RANDOM WALK FORMS THE BASIS FOR A MOLECULAR PICTURE OF FLUX . .
. . . . . . . . . . . . . . . . . . . . . . . 616
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
622
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
622
IMAGE 15
CONTENTS XXIII
23 FLOW IN AN ELECTRIC FIELD: CONDUCTION . . . . . . . . . . . . . . .
625
23.1 TRANSPORT OF CHARGE OCCURS IN AN ELECTRIC FIELD . . . . . . . 625
23.1.1 IONIC SPECIES CAN BE CLASSIFIED AS TRUE OR POTENTIAL ELECTROLYTES
. . . . . . . . . . . . . . . 626
23.2 DESCRIBING A SYSTEM OF IONIC CONDUCTION INCLUDES ELECTRONIC,
ELECTRODIC, AND IONIC ELEMENTS . . . . . . . . . . 627
23.3 THE FLOW OF IONS DOWN A ELECTRICAL GRADIENT CAN BE DESCRIBED
PHENOMENOLOGICALLY . . . . . . . . . . . . 631
23.4 A MOLECULAR VIEW OF IONIC CONDUCTION . . . . . . . . . . . . 637
23.5 INTERIONIC FORCES AFFECT CONDUCTIVITY . . . . . . . . . . . . . 640
23.6 PROTON CONDUCTION IS A SPECIAL CASE THAT HAS A MIXED MECHANISM . .
. . . . . . . . . . . . . . . . . . . . . . . . . 643
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
646
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
647
24 FORCES ACROSS MEMBRANES . . . . . . . . . . . . . . . . . . . . . 649
24.1 ENERGETICS AND FORCE IN MEMBRANES . . . . . . . . . . . . . . 649
24.2 THE DONNAN EQUILIBRIUM IS DETERMINED BY A BALANCE BETWEEN CHEMICAL
AND ELECTRICAL POTENTIAL IN A TWO-PHASE SYSTEM . . . . . . . . . . . . .
. . . . . . . 650
24.3 ELECTRIC FIELDS ACROSS MEMBRANES ARE OF SUBSTANTIAL MAGNITUDE . . .
. . . . . . . . . . . . . . . . . . . . . . . . 653
24.3.1 DIFFUSION AND CONCENTRATION POTENTIALS ARE COMPONENTS OF THE
TRANSMEMBRANE POTENTIAL . . . . 653 24.3.2 THE GOLDMAN CONSTANT FIELD
EQUATION IS AN EXPRESSION USEFUL FOR
QUANTITATIVE DESCRIPTION OF THE BIOLOGICAL ELECTROCHEMICAL POTENTIAL . .
. . . . . . . . . . . . 656
24.4 ELECTROSTATIC PROFILES OF THE MEMBRANE ARE POTENTIAL ENERGY
SURFACES DESCRIBING FORCES IN THE VICINITY OF MEMBRANES . . . . . . . .
. . . . . . . . . . . . . . . . . . . 657
24.5 THE ELECTROCHEMICAL POTENTIAL IS A THERMODYNAMIC TREATMENT OF THE
GRADIENTS ACROSS A CELLULAR MEMBRANE . . . 661 24.6 TRANSPORT THROUGH
THE LIPID BILAYER OF DIFFERENT MOLECULES REQUIRES VARIOUS MECHANISMS . .
. . . . . . . . . 661
24.6.1 MODES OF TRANSPORT INCLUDE PASSIVE, FACILITATED, AND ACTIVE
PROCESSES . . . . . . . . . . . 661
24.6.2 WATER TRANSPORT THROUGH A LIPID PHASE INVOLVES PASSIVE AND PORE
SPECIFIC MECHANISMS . . . 663 FURTHER READING . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 666
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
667
25 KINETICS - CHEMICAL KINETICS . . . . . . . . . . . . . . . . . . . .
669
25.1 THE EQUILIBRIUM STATE IS FOUND BY CHEMICAL THERMODYNAMICS BUT
CHEMICAL KINETICS TELLS THE STORY OF GETTING THERE . . . . . . . . . . .
. . . . . . . . 670
IMAGE 16
XXIV CONTENTS
25.2 A HISTORICAL PERSPECTIVE ON THE DEVELOPMENT OF CHEMICAL KINETICS .
. . . . . . . . . . . . . . . . . . . . . 671
25.3 KINETICS HAS A SPECIFIC AND SYSTEMIC LANGUAGE . . . . . . . 675
25.3.1 MECHANISM AND ORDER . . . . . . . . . . . . . . . . 675
25.4 ORDER OF A REACTION RELATES THE CONCENTRATION OF REACTANTS TO THE
REACTION VELOCITY . . . . . . . . . . . . . 676
25.5 EXPRESSIONS OF THE RATE LAWS ARE IMPORTANT PROPERTIES OF A REACTION
. . . . . . . . . . . . . . . . . . . . 677
25.5.1 ZERO ORDER REACTIONS . . . . . . . . . . . . . . . . . 677
25.5.2 FIRST-ORDER REACTIONS . . . . . . . . . . . . . . . . . 679
25.5.3 SECOND-ORDER REACTIONS . . . . . . . . . . . . . . . 680
25.5.4 EXPERIMENTAL DETERMINATION OF A RATE LAW REQUIRES MEASUREMENT OF
TWO OBSERVABLES, TIME AND CONCENTRATION . . . . . . . . . . . . . . .
681
25.6 ELEMENTARY REACTIONS ARE THE ELEMENTS OF THE SYSTEM THAT DEFINES A
CHEMICAL MECHANISM . . . . . . . . . 681
25.7 REACTION MECHANISMS ARE A SYSTEM OF INTERACTING ELEMENTS
(MOLECULES) IN THE CONTEXT OF A POTENTIAL ENERGY SURFACE . . . . . . . .
. . . . . . . . . . . . . . . . . 682
25.7.1 COLLISION THEORY . . . . . . . . . . . . . . . . . . . 682
25.7.2 SURPRISES IN THE COLLISION THEORY STATE SPACE REQUIRE
RE-EVALUATION OF THE ABSTRACTION . . . . . . 686 25.7.3 TRANSITION-STATE
THEORY IS A QUANTUM MECHANICAL EXTENSION OF THE CLASSICAL FLAVOR
OF COLLISION THEORY . . . . . . . . . . . . . . . . . . 687
25.7.4 THE POTENTIAL ENERGY SURFACE UNIFIES THE MODELS . . 691 25.8
SOLUTION KINETICS ARE MORE COMPLICATED THAN THE SIMPLE KINETIC BEHAVIOR
OF GASES . . . . . . . . . . . . . . . 699
25.9 ENZYMES ARE MACROMOLECULAR CATALYSTS WITH ENORMOUS EFF ICIENCY . .
. . . . . . . . . . . . . . . . . . . . 699
25.9.1 ENZYME KINETICS . . . . . . . . . . . . . . . . . . . 702
25.9.2 ENZYMES CAN BE CHARACTERIZED BY KINETIC PROPERTIES . . . . . . .
. . . . . . . . . . . . . . . . 704
25.9.3 ENZYMES ARE COMPLEX SYSTEMS SUBJECT TO BIOPHYSICAL CONTROL . . .
. . . . . . . . . . . . . . 707
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
710
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
710
26 DYNAMIC BIOELECTROCHEMISTRY - CHARGE TRANSFER IN BIOLOGICAL SYSTEMS .
. . . . . . . . . . . . . . . . . . . . . . . . . 713
26.1 ELECTROKINETICS AND ELECTRON CHARGE TRANSFER DEPEND ON ELECTRICAL
CURRENT FLOW IN BIOCHEMICAL SYSTEMS . . . . . 713 26.2 ELECTROKINETIC
PHENOMENA OCCUR WHEN THE ELEMENTS OF THE BIOLOGICAL ELECTRICAL DOUBLE
LAYER EXPERIENCE
EITHER MECHANICAL OR ELECTRICAL TRANSPORT . . . . . . . . . . . 714
IMAGE 17
CONTENTS XXV
26.2.1 THE ZETA POTENTIAL IS MEASURED AT THE OUTER HELMHOLTZ PLANE OF
THE ELECTRICAL DOUBLE LAYER . . . 714 26.2.2 A STREAMING POTENTIAL
RESULTS WHEN FLUID FLOWS IN A CYLINDER . . . . . . . . . . . . . . . . .
. 715
26.2.3 ELECTRO-OSMOSIS IS THE TRANSPORT OF SOLVENT COINCIDENT WITH
ELECTRICAL INDUCED FLUX OF ELECTROLYTES . . . . . . . . . . . . . . . .
. . . . 716
26.2.4 ELECTROPHORESIS DESCRIBES THE MOTION OF PARTICLES WITH AN
ELECTRICAL DOUBLE LAYER IN AN ELECTRICAL FIELD . . . . . . . . . . . . .
. . . . . 717
26.2.5 A SEDIMENTATION POTENTIAL ARISES WHEN WITH THE MOVEMENT OF A
PARTICLE RELATIVE TO A STATIONARY SOLVENT . . . . . . . . . . . . . . .
. . . 721
26.2.6 ELECTROKINETIC PHENOMENA CAN HAVE A ROLE IN BIOLOGICAL SYSTEMS .
. . . . . . . . . . . . . . . 721
26.3 ELECTRON TRANSFER IS AN ESSENTIAL FORM OF BIOLOGICAL CHARGE
TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . 722
26.3.1 DYNAMIC ELECTROCHEMISTRY IS THE STUDY OF ELECTRON TRANSFER AND
THEIR KINETICS . . . . . . . . . 722
26.3.2 ELECTRON TRANSFER IS A QUANTUM MECHANICAL PHENOMENON . . . . . .
. . . . . . . . . . . . . . . 726
26.3.3 ELECTRON CHARGE TRANSFER CAN OCCUR IN PROTEINS . . . 730 FURTHER
READING . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
737
PART V METHODS FOR THE MEASURING STRUCTURE AND FUNCTION
27 SEPARATION AND CHARACTERIZATION OF BIOMOLECULES BASED ON MACROSCOPIC
PROPERTIES . . . . . . . . . . . . . . . . . . . . . 741
27.1 INTRODUCTION: MECHANICAL MOTION INTERACTS WITH MASS, SHAPE, CHARGE,
AND PHASE TO ALLOW ANALYSIS OF MACROMOLECULAR STRUCTURE . . . . . . . .
. . . . . . . . . 742
27.2 BUOYANT FORCES ARE THE RESULT OF DISPLACEMENT OF THE MEDIUM BY AN
OBJECT . . . . . . . . . . . . . . . . . . 742
27.2.1 MOTION THROUGH A MEDIUM RESULTS IN A RETARDING FORCE PROPORTIONAL
TO SPEED . . . . . . . . 743
27.2.2 FRICTIONAL COEFFICIENTS CAN BE USED IN THE ANALYSIS OF
MACROMOLECULAR STRUCTURE . . . . . . . . 744
27.2.3 THE CENTRIFUGE IS A DEVICE THAT PRODUCES MOTION BY GENERATING
CIRCULAR MOTION WITH CONSTANT SPEED . . . . . . . . . . . . . . . . . .
. . 745
27.2.4 SEDIMENTATION OCCURS WHEN PARTICLES EXPERIENCE MOTION CAUSED BY
GRAVITATIONAL OR EQUIVALENT FIELDS . . . . . . . . . . . . . . . . . 748
IMAGE 18
XXVI CONTENTS
27.2.5 DRAG FORCES ON MOLECULES IN MOTION ARE PROPORTIONAL TO THE
VELOCITY OF THE PARTICLE . . . . . . 755 27.2.6 FLUIDS WILL MOVE AND BE
TRANSPORTED WHEN PLACED UNDER A SHEARING STRESS FORCE . . . . . . . .
756
27.3 SYSTEMS STUDY IN THE BIOLOGICAL SCIENCE REQUIRES METHODS OF
SEPARATION AND IDENTIFICATION TO DESCRIBE THE "STATE OF A BIOLOGICAL
SYSTEM" . . . . . . . . . . . . . . . 760
27.4 ELECTROPHORESIS IS A PRACTICAL APPLICATION OF MOLECULAR MOTION IN
AN ELECTRICAL FIELD BASED ON CHARGE AND MODIF IED BY CONFORMATION AND
SIZE . . . . . . . 760
27.5 CHROMATOGRAPHIC TECHNIQUES ARE BASED ON THE DIFFERENTIAL
PARTITIONING OF MOLECULES BETWEEN TWO PHASES IN RELATIVE MOTION . . . .
. . . . . . . . . . . . . . . 763
27.6 THE MOTION INDUCED BY A MAGNETIC INTERACTION IS ESSENTIAL FOR
DETERMINATION OF MOLECULAR MASS IN MODERN BIOLOGICAL INVESTIGATIONS . .
. . . . . . . . . . . . . 767
27.6.1 MAGNETIC FIELDS ARE VECTOR FIELDS OF MAGNETIC FORCE THAT CAN BE
FOUND THROUGHOUT SPACE . . . . . . . . . . . . . . . . . . 768
27.6.2 MAGNETS INTERACT WITH ONE ANOTHER THROUGH THE MAGNETIC FIELD . .
. . . . . . . . . . . . . . . . 770
27.6.3 CURRENT LOOPS IN B FIELDS EXPERIENCE TORQUE . . . . 771 27.6.4
THE PATH OF MOVING POINT CHARGES IN A B FIELD IS ALTERED BY THE
INTERACTION . . . . . . . . . . 771
27.6.5 THE MASS SPECTROMETER IS WIDELY USED FOLLOWING VARIOUS SEPARATION
TECHNIQUES TO CHARACTERIZE BIOLOGICAL SAMPLES . . . . . . . . . . . 772
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
775
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
775
28 ANALYSIS OF MOLECULAR STRUCTURE WITH ELECTRONIC SPECTROSCOPY . 779
28.1 THE INTERACTION OF LIGHT WITH MATTER ALLOWS INVESTIGATION OF
BIOCHEMICAL PROPERTIES . . . . . . . . . . . . 780
28.2 THE MOTION OF A DIPOLE RADIATOR GENERATES ELECTROMAGNETIC RADIATION
. . . . . . . . . . . . . . . . . . . 780
28.3 OPTICAL INTERACTIONS CAN BE TREATED AT VARYING LEVELS OF
ABSTRACTION . . . . . . . . . . . . . . . . . . . . . . . . . 780
28.4 ATOMIC AND MOLECULAR ENERGY LEVELS ARE A QUANTUM PHENOMENON THAT
PROVIDE A WINDOW ON MOLECULAR STRUCTURE . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 782
28.4.1 THERE ARE POINTS OF MAXIMUM INFLECTION OCCURRING AT PARTICULAR
WAVELENGTHS . . . . . . . . . 783
28.4.2 EACH MAXIMUM HAS A DIFFERENT INTENSITY . . . . . . 786
28.4.3 THE MAXIMA ARE SPREAD TO SOME DEGREE AND ARE NOT SHARP . . . . .
. . . . . . . . . . . . . 787
IMAGE 19
CONTENTS XXVII
28.5 ABSORPTION SPECTROSCOPY HAS IMPORTANT APPLICATIONS TO BIOCHEMICAL
ANALYSIS . . . . . . . . . . . . . . . . . . . . 789
28.5.1 ABSORPTION SPECTROSCOPY IS A POWERFUL TOOL IN THE EXAMINATION OF
DILUTE SOLUTIONS . . . . . . . . 793
28.6 FLUORESCENCE AND PHOSPHORESCENCE OCCUR WHEN TRAPPED PHOTON ENERGY
IS RE-RADIATED AFTER A FINITE LIFETIME . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 794
28.7 ELECTRON PARAMAGNETIC RESONANCE (EPR) AND NUCLEAR MAGNETIC
RESONANCE (NMR) DEPEND ON INTERACTIONS BETWEEN PHOTONS AND MOLECULES IN
A MAGNETIC FIELD . . . . . 797 28.7.1 THE SOLENOID SHAPES THE MAGNETIC
FIELD IN A
MANNER SIMILAR TO THE PARALLEL-PLATE CAPACITOR . . . 798 28.7.2
MAGNETISM IN MATTER HAS DISTINCT PROPERTIES . . . . 798 28.7.3 ATOMS CAN
HAVE MAGNETIC MOMENTS . . . . . . . . 800
28.7.4 EPR SPECTROSCOPY ALLOWS EXPLORATION OF MOLECULAR STRUCTURE BY
INTERACTION WITH THE MAGNETIC MOMENT OF AN ELECTRON . . . . . . . . 803
28.7.5 NMR SPECTROSCOPY EMPLOYS THE MAGNETIC PROPERTIES OF CERTAIN
NUCLEI FOR DETERMINING STRUCTURE . . . . . . . . . . . . . . . . . . . .
. . . 804
28.7.6 FURTHER STRUCTURAL INFORMATION CAN BE FOUND BY NMR STUDIES OF
NUCLEI OTHER THAN PROTONS . . . . . . . . . . . . . . . . . . . . . . .
. 809
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
812
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
813
29 MOLECULAR STRUCTURE FROM SCATTERING PHENOMENA . . . . . . . . . 815
29.1 THE INTERFERENCE PATTERNS GENERATED BY THE INTERACTION OF WAVES
WITH POINT SOURCES IS A VALUABLE TOOL IN THE ANALYSIS OF STRUCTURE . . .
. . . . . . . . . . . . . . . . . . . 815
29.2 DIFFRACTION IS THE RESULT OF THE REPROPAGATION OF A WAVE . . . 819
29.3 X-RAY DIFFRACTION IS A POWERFUL FOOL FOR STRUCTURE DETERMINATION .
. . . . . . . . . . . . . . . . . . . . . . . . 822
29.4 SCATTERING OF LIGHT RATHER THAN ITS ABSORPTION CAN BE USED TO PROBE
MOLECULAR STRUCTURE AND INTERACTION . . . . 831 29.4.1 RAYLEIGH
SCATTERING . . . . . . . . . . . . . . . . . . 831
29.4.2 RAMAN SCATTERING . . . . . . . . . . . . . . . . . . . 833
29.4.3 CIRCULAR DICHROISM AND OPTICAL ROTATION . . . . . . 834
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
835
30 ANALYSIS OF STRUCTURE - MICROSCOPY . . . . . . . . . . . . . . . .
837
30.1 SEEING IS BELIEVING . . . . . . . . . . . . . . . . . . . . . . 837
30.2 THE LIGHT MICROSCOPE ALLOWS VISUALIZATION OF STRUCTURES ON THE
DIMENSIONAL SCALE OF THE WAVELENGTH OF A PHOTON . . . . . . . . . . . .
. . . . . . . . 839
30.3 VISUALIZATION REQUIRES SOLVING THE PROBLEM OF CONTRAST . . . 843
IMAGE 20
XXVIII CONTENTS
30.3.1 DARK FIELD MICROSCOPY . . . . . . . . . . . . . . . . 843
30.3.2 PHASE MICROSCOPY . . . . . . . . . . . . . . . . . . 843
30.3.3 POLARIZATION MICROSCOPY . . . . . . . . . . . . . . . 845
30.3.4 HISTOCHEMISTRY . . . . . . . . . . . . . . . . . . . . 847
30.3.5 FLUORESCENCE MICROSCOPY . . . . . . . . . . . . . . 848
30.4 SCANNING PROBE MICROSCOPY CREATES AN IMAGE OF A STRUCTURES BY
INTERACTIONS ON A MOLECULAR SCALE . . . . . . . . 849
30.4.1 SCANNING TUNNELING MICROSCOPY . . . . . . . . . . . 850
30.4.2 SCANNING FORCE MICROSCOPY . . . . . . . . . . . . . 852
30.4.3 NEAR-FIELD OPTICAL MICROSCOPY, OUTSIDE THE CLASSICAL LIMITS . . .
. . . . . . . . . . . . . . . . . 854
FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
854
PROBLEM SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
855
31 EPILOGUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 857
NOW TRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
857
32 PHYSICAL CONSTANTS . . . . . . . . . . . . . . . . . . . . . . . . .
. 859
CONVERSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
859
APPENDIX A: MATHEMATICAL METHODS . . . . . . . . . . . . . . . . . . . .
861
A.1 UNITS AND MEASUREMENT . . . . . . . . . . . . . . . . . . . . 861
A.2 EXPONENTS AND LOGARITHMS . . . . . . . . . . . . . . . . . . 862
A.3 TRIGONOMETRIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . 865
A.4 EXPANSION SERIES . . . . . . . . . . . . . . . . . . . . . . . . 869
A.5 DIFFERENTIAL AND INTEGRAL CALCULUS . . . . . . . . . . . . . . . 870
A.6 PARTIAL DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . .
870
A.7 VECTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
872
A.7.1 ADDITION AND SUBTRACTION . . . . . . . . . . . . . . . 872
A.7.2 MAGNITUDE OF A VECTOR . . . . . . . . . . . . . . . . 873
A.7.3 MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . 873
APPENDIX B: QUANTUM ELECTRODYNAMICS . . . . . . . . . . . . . . . . . .
875
APPENDIX C: THE PRE-SOCRATIC ROOTS OF MODERN SCIENCE . . . . . . . . .
877
APPENDIX D: THE POISSON FUNCTION . . . . . . . . . . . . . . . . . . . .
. 879
APPENDIX E: ASSUMPTIONS OF A THEORETICAL TREATMENT OF THE IDEAL GAS LAW
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 881
APPENDIX F: THE DETERMINATION OF THE FIELD FROM THE POTENTIAL IN
CARTESIAN COORDINATES . . . . . . . . . . . . . . . . . . . . . . 883
APPENDIX G: GEOMETRICAL OPTICS . . . . . . . . . . . . . . . . . . . . .
. 885
G.1 REFLECTION AND REFRACTION OF LIGHT . . . . . . . . . . . . . . 885
G.2 MIRRORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
886
G.2.1 THE PLANE MIRROR . . . . . . . . . . . . . . . . . . . 886
G.2.2 THE CONCAVE MIRROR . . . . . . . . . . . . . . . . . 887
IMAGE 21
CONTENTS XXIX
G.3 IMAGE FORMATION BY REFRACTION . . . . . . . . . . . . . . . . 889
G.4 PRISMS AND TOTAL INTERNAL REFLECTION . . . . . . . . . . . . . . 891
APPENDIX H: THE COMPTON EFFECT . . . . . . . . . . . . . . . . . . . . .
893
APPENDIX I: HAMILTON'S PRINCIPLE OF LEAST ACTION/FERMAT'S PRINCIPLE OF
LEAST TIME . . . . . . . . . . . . . . . . . . . . . . . 895
APPENDIX J: DERIVATION OF THE ENERGY OF INTERACTION BETWEEN TWO IONS . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897
APPENDIX K: DERIVATION OF THE STATEMENT, Q REV Q IRREV . . . . . . . .
. . 899
APPENDIX L: DERIVATION OF THE CLAUSIUS-CLAPEYRON EQUATION . . . . . .
901
APPENDIX M: DERIVATION OF THE VAN'T HOFF EQUATION FOR OSMOTIC PRESSURE .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903
APPENDIX N: FICTITIOUS AND PSEUDOFORCES - THE CENTRIFUGAL FORCE . . .
905
APPENDIX O: DERIVATION OF THE WORK TO CHARGE AND DISCHARGE A RIGID
SPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907
APPENDIX P: REVIEW OF CIRCUITS AND ELECTRIC CURRENT . . . . . . . . . .
909
P.1 CURRENT DENSITY AND FLUX . . . . . . . . . . . . . . . . . . . 909
P.1.1 OHM'S LAW . . . . . . . . . . . . . . . . . . . . . . 910
P.2 CIRCUITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
911
P.2.1 USEFUL LEGAL RELATIONS . . . . . . . . . . . . . . . . 911
P.2.2 KIRCHOFF'S RULES . . . . . . . . . . . . . . . . . . . 911
P.2.3 CAPACITORS IN SERIES AND PARALLEL . . . . . . . . . . . 912
P.2.4 RESISTORS IN SERIES AND PARALLEL . . . . . . . . . . . . 913
P.2.5 RC CIRCUITS AND RELATIONS . . . . . . . . . . . . . . 913
P.3 MEASURING INSTRUMENTS . . . . . . . . . . . . . . . . . . . . . 916
P.3.1 AMMETERS, VOLTMETERS, OHMMETERS . . . . . . . . . 917
APPENDIX Q: FERMI'S GOLDEN RULE . . . . . . . . . . . . . . . . . . . .
. 919
APPENDIX R: THE TRANSITION FROM REACTANT TO PRODUCT: ADIABATIC AND
NON-ADIABATIC TRANSITIONS . . . . . . . . . . . . . 921
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 923 |
| any_adam_object | 1 |
| author | Bergethon, Peter R. |
| author_facet | Bergethon, Peter R. |
| author_role | aut |
| author_sort | Bergethon, Peter R. |
| author_variant | p r b pr prb |
| building | Verbundindex |
| bvnumber | BV036723956 |
| classification_rvk | WD 2000 WD 2200 |
| classification_tum | CHE 802f |
| ctrlnum | (OCoLC)695853798 (DE-599)DNB1000754413 |
| 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 | Chemie / Pharmazie Biologie Chemie |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-20T10:49:20Z |
| institution | BVB |
| isbn | 9781441963239 |
| language | English |
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| physical | XXIX, 949 S. Ill., graph. Darst. |
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| spelling | Bergethon, Peter R. Verfasser aut The physical basis of biochemistry the foundations of molecular biophysics Peter R. Bergethon 2. ed. New York, NY Springer 2010 XXIX, 949 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biophysikalische Chemie (DE-588)4291844-3 gnd rswk-swf Molekulare Biophysik (DE-588)4170391-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Biophysikalische Chemie (DE-588)4291844-3 s DE-604 Molekulare Biophysik (DE-588)4170391-1 s 1\p DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3439937&prov=M&dok_var=1&dok_ext=htm Inhaltstext SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020641772&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bergethon, Peter R. The physical basis of biochemistry the foundations of molecular biophysics Biophysikalische Chemie (DE-588)4291844-3 gnd Molekulare Biophysik (DE-588)4170391-1 gnd |
| subject_GND | (DE-588)4291844-3 (DE-588)4170391-1 (DE-588)4123623-3 |
| title | The physical basis of biochemistry the foundations of molecular biophysics |
| title_auth | The physical basis of biochemistry the foundations of molecular biophysics |
| title_exact_search | The physical basis of biochemistry the foundations of molecular biophysics |
| title_full | The physical basis of biochemistry the foundations of molecular biophysics Peter R. Bergethon |
| title_fullStr | The physical basis of biochemistry the foundations of molecular biophysics Peter R. Bergethon |
| title_full_unstemmed | The physical basis of biochemistry the foundations of molecular biophysics Peter R. Bergethon |
| title_short | The physical basis of biochemistry |
| title_sort | the physical basis of biochemistry the foundations of molecular biophysics |
| title_sub | the foundations of molecular biophysics |
| topic | Biophysikalische Chemie (DE-588)4291844-3 gnd Molekulare Biophysik (DE-588)4170391-1 gnd |
| topic_facet | Biophysikalische Chemie Molekulare Biophysik Lehrbuch |
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