THE LOGIC OF MODERN PHYSICS
CONTENTS PART I: MYSTERIES, METAPHORS, MODELS WHAT THE ANCIENTS KNEW HEAT HEAT IS A FORM OF ENERGY JUST A LITTLE HISTORY PREVIEW: THE CONCEPT OF FREE ENERGY HOW LIFE GENERATES ORDER THE PUZZLE OF BIOLOGICAL ORDER A PARADIGM FOR FREE ENERGY TRANSDUCTION EXCURSION: COMMERCIALS, PHILOSOPHY, PRAGMATICS HOW TO DO BETTER ON EXAMS (AND DISCOVER NEW PHYSICAL LAWS) DIMENSIONS AND UNITS USING DIMENSIONAL ANALYSIS TO CATCH ERRORS AND RECALL DE?NITIONS USING DIMENSIONAL ANALYSIS TO FORMULATE HYPOTHESES SOME NOTATIONAL CONVENTIONS INVOLVING ?UX AND DENSITY OTHER KEY IDEAS FROM PHYSICS AND CHEMISTRY MOLECULES ARE SMALL MOLECULES ARE PARTICULAR SPATIAL ARRANGEMENTS OF ATOMS MOLECULES HAVE DE?NITE INTERNAL ENERGIES LOW-DENSITY GASES OBEY A UNIVERSAL LAW THE BIG PICTURE TRACK 2 PROBLEMS WHAT’S INSIDE CELLS CELL PHYSIOLOGY INTERNAL GROSS ANATOMY EXTERNAL GROSS ANATOMY THE MOLECULAR PARTS LIST SMALL MOLECULES MEDIUM-SIZE MOLECULES BIG MOLECULES MACROMOLECULAR ASSEMBLIES BRIDGING THE GAP: MOLECULAR DEVICES THE PLASMA MEMBRANE MOLECULAR MOTORS ENZYMES AND REGULATORY PROTEINS THE OVERALL ?OW OF INFORMATION IN CELLS PART II: DI?USION, DISSIPATION, DRIVE THE MOLECULAR DANCE THE PROBABILISTIC FACTS OF LIFE DISCRETE DISTRIBUTIONS CONTINUOUS DISTRIBUTIONS MEAN AND VARIANCE ADDITION AND MULTIPLICATION RULES DECODING THE IDEAL GAS LAW TEMPERATURE RE?ECTS THE AVERAGE KINETIC ENERGY OF THERMAL MOTION THE COMPLETE DISTRIBUTION OF MOLECULAR VELOCITIES IS EXPERIMENTALLY MEASURABLE THE BOLTZMANN DISTRIBUTION ACTIVATION BARRIERS CONTROL REACTION RATES RELAXATION TO EQUILIBRIUM EXCURSION: A LESSON FROM HEREDITY ARISTOTLE WEIGHS IN IDENTIFYING THE PHYSICAL CARRIER OF GENETIC INFORMATION SCHR¨ODINGER’S SUMMARY: GENETIC INFORMATION IS STRUCTURAL RANDOM WALKS, FRICTION, AND DI?USION BROWNIAN MOTION JUST A LITTLE MORE HISTORY RANDOM WALKS LEAD TO DI?USIVE BEHAVIOR THE DI?USION LAW IS MODEL-INDEPENDENT FRICTION IS QUANTITATIVELY RELATED TO DI?USION EXCURSION: WHAT EINSTEIN DID AND DID NOT DO OTHER RANDOM WALKS THE CONFORMATION OF POLYMERS VISTA: RANDOM WALKS ON WALL STREET MORE ABOUT DI?USION DI?USION RULES THE SUBCELLULAR WORLD DI?USION OBEYS A SIMPLE EQUATION PRECISE STATISTICAL PREDICTION OF RANDOM PROCESSES FUNCTIONS, DERIVATIVES, AND SNAKES UNDER THE RUG FUNCTIONS DESCRIBE THE DETAILS OF QUANTITATIVE RELATIONSHIPS A FUNCTION OF TWO VARIABLES CAN BE VISUALIZED AS A LANDSCAPE BIOLOGICAL APPLICATIONS OF DI?USION THE PERMEABILITY OF ARTI?CIAL MEMBRANES IS DI?USIVE DI?USION SETS A FUNDAMENTAL LIMIT ON BACTERIAL METABOLISM THE NERNST RELATION SETS THE SCALE OF MEMBRANE POTENTIALS THE ELECTRICAL RESISTANCE OF A SOLUTION RE?ECTS FRICTIONAL DISSIPATION DI?USION FROM A POINT GIVES A SPREADING, GAUSSIAN PRO?LE LIFE IN THE SLOW LANE: THE LOW REYNOLDS-NUMBER WORLD FRICTION IN ?UIDS SEDIMENTATION SEPARATES PARTICLES BY DENSITY THE RATE OF SEDIMENTATION DEPENDS ON SOLVENT VISCOSITY IT’S HARD TO MIX A VISCOUS LIQUID LOW REYNOLDS NUMBER A CRITICAL FORCE DEMARCATES THE PHYSICAL REGIME DOMINATED BY FRICTION THE REYNOLDS NUMBER QUANTI?ES THE RELATIVE IMPORTANCE OF FRICTION AND INERTIA THE TIME REVERSAL PROPERTIES OF A DYNAMICAL LAW SIGNAL ITS DISSIPATIVE CHARACTER BIOLOGICAL APPLICATIONS SWIMMING AND PUMPING TO STIR OR NOT TO STIR? FORAGING, ATTACK, AND ESCAPE VASCULAR NETWORKS VISCOUS DRAG AT THE DNA REPLICATION FORK EXCURSION: THE CHARACTER OF PHYSICAL LAWS ENTROPY, TEMPERATURE, AND FREE ENERGY HOW TO MEASURE DISORDER ENTROPY THE STATISTICAL POSTULATE ENTROPY IS A CONSTANT TIMES THE MAXIMAL VALUE OF DISORDER TEMPERATURE HEAT ?OWS TO MAXIMIZE DISORDER TEMPERATURE IS A STATISTICAL PROPERTY OF A SYSTEM IN EQUILIBRIUM THE SECOND LAW ENTROPY INCREASES SPONTANEOUSLY WHEN A CONSTRAINT IS REMOVED THREE REMARKS OPEN SYSTEMS THE FREE ENERGY OF A SUBSYSTEM RE?ECTS THE COMPETITION BETWEEN ENTROPY AND ENERGY ENTROPIC FORCES CAN BE EXPRESSED AS DERIVATIVES OF THE FREE ENERGY FREE ENERGY TRANSDUCTION IS MOST E?CIENT WHEN IT PROCEEDS IN SMALL, CONTROLLED STEPS THE BIOSPHERE AS A THERMAL ENGINE MICROSCOPIC SYSTEMS THE BOLTZMANN DISTRIBUTION FOLLOWS FROM THE STATISTICAL POSTULATE KINETIC INTERPRETATION OF THE BOLTZMANN DISTRIBUTION THE MINIMUM FREE ENERGY PRINCIPLE ALSO APPLIES TO MICROSCOPIC SUBSYSTEMS THE FREE ENERGY DETERMINES THE POPULATIONS OF COMPLEX TWO-STATE SYSTEMS EXCURSION: “RNA FOLDING AS A TWO-STATE SYSTEM” BY J LIPHARDT, I TINOCO, JR , AND C BUS- TAMANTE ENTROPIC FORCES AT WORK MICROSCOPIC VIEW OF ENTROPIC FORCES FIXED-VOLUME APPROACH FIXED-PRESSURE APPROACH OSMOTIC PRESSURE EQUILIBRIUM OSMOTIC PRESSURE OBEYS THE IDEAL GAS LAW OSMOTIC PRESSURE CREATES A DEPLETION FORCE BETWEEN LARGE MOLECULES BEYOND EQUILIBRIUM: OSMOTIC ?OW OSMOTIC FORCES ARISE FROM THE RECTI?CATION OF BROWNIAN MOTION OSMOTIC ?OW IS QUANTITATIVELY RELATED TO FORCED PERMEATION A REPULSIVE INTERLUDE ELECTROSTATIC INTERACTIONS ARE CRUCIAL FOR PROPER CELL FUNCTIONING THE GAUSS LAW CHARGED SURFACES ARE SURROUNDED BY NEUTRALIZING ION CLOUDS THE REPULSION OF LIKE-CHARGED SURFACES ARISES FROM COMPRESSING THEIR ION CLOUDS OPPOSITELY CHARGED SURFACES ATTRACT BY COUNTERION RELEASE SPECIAL PROPERTIES OF WATER LIQUID WATER CONTAINS A LOOSE NETWORK OF HYDROGEN BONDS THE HYDROGEN-BOND NETWORK A?ECTS THE SOLUBILITY OF SMALL MOLECULES IN WATER WATER GENERATES AN ENTROPIC ATTRACTION BETWEEN NONPOLAR OBJECTS CHEMICAL FORCES AND SELF-ASSEMBLY CHEMICAL POTENTIAL µ MEASURES THE AVAILABILITY OF A PARTICLE SPECIES CHEMICAL REACTIONS CHEMICAL EQUILIBRIUM OCCURS WHEN CHEMICAL FORCES BALANCE ?G GIVES A UNIVERSAL CRITERION FOR THE DIRECTION OF A CHEMICAL REACTION KINETIC INTERPRETATION OF COMPLEX EQUILIBRIA THE PRIMORDIAL SOUP WAS NOT IN CHEMICAL EQUILIBRIUM DISSOCIATION IONIC AND PARTIALLY IONIC BONDS DISSOCIATE READILY IN WATER THE STRENGTHS OF ACIDS AND BASES RE?ECT THEIR DISSOCIATION EQUILIBRIUM CONSTANTS THE CHARGE ON A PROTEIN VARIES WITH ITS ENVIRONMENT ELECTROPHORESIS CAN GIVE A SENSITIVE MEASURE OF PROTEIN COMPOSITION SELF-ASSEMBLY OF AMPHIPHILES EMULSIONS FORM WHEN AMPHIPHILIC MOLECULES REDUCE THE OIL-WATER INTERFACE TENSION MICELLES SELF-ASSEMBLE SUDDENLY AT A CRITICAL CONCENTRATION EXCURSION: ON ?TTING MODELS TO DATA SELF-ASSEMBLY IN CELLS BILAYERS SELF-ASSEMBLE FROM TWO-TAILED AMPHIPHILES VISTA: MACROMOLECULAR FOLDING AND AGGREGATION ANOTHER TRIP TO THE KITCHEN PART III: MOLECULES, MACHINES, MECHANISMS COOPERATIVE TRANSITIONS IN MACROMOLECULES ELASTICITY MODELS OF POLYMERS WHY PHYSICS WORKS (WHEN IT DOES WORK) FOUR PHENOMENOLOGICAL PARAMETERS CHARACTERIZE THE ELASTICITY OF A LONG, THIN ROD POLYMERS RESIST STRETCHING WITH AN ENTROPIC FORCE STRETCHING SINGLE MACROMOLECULES THE FORCE–EXTENSION CURVE CAN BE MEASURED FOR SINGLE DNA MOLECULES A SIMPLE TWO-STATE SYSTEM QUALITATIVELY EXPLAINS DNA STRETCHING AT LOW FORCE EIGENVALUES FOR THE IMPATIENT MATRICES AND EIGENVALUES MATRIX MULTIPLICATION COOPERATIVITY THE TRANSFER MATRIX TECHNIQUE ALLOWS A MORE ACCURATE TREATMENT OF BEND COOPERATIVITY DNA ALSO EXHIBITS LINEAR STRETCHING ELASTICITY AT MODERATE APPLIED FORCE COOPERATIVITY IN HIGHER-DIMENSIONAL SYSTEMS GIVES RISE TO IN?NITELY SHARP PHASE TRAN- SITIONS THERMAL, CHEMICAL, AND MECHANICAL SWITCHING THE HELIX–COIL TRANSITION CAN BE OBSERVED USING POLARIZED LIGHT THREE PHENOMENOLOGICAL PARAMETERS DESCRIBE A GIVEN HELIX–COIL TRANSITION CALCULATION OF THE HELIX-COIL TRANSITION DNA ALSO DISPLAYS A COOPERATIVE “MELTING” TRANSITION APPLIED MECHANICAL FORCE CAN INDUCE COOPERATIVE STRUCTURAL TRANSITIONS IN MACRO- MOLECULES ALLOSTERY HEMOGLOBIN BINDS FOUR OXYGEN MOLECULES COOPERATIVELY ALLOSTERY INVOLVES RELATIVE MOTION OF MOLECULAR SUBUNITS VISTA: PROTEIN SUBSTATES