EXPERIMENTAL DYNAMICS

By V. JAERY

SUMS OF INDEPENDENT RANDOM VARIABLES CONTINUOUS PROBABILITY DISTRIBUTIONS EXAMPLE: A CERTAIN CONTINUOUS PROBABILITY DISTRIBUTION EXPONENTIAL DISTRIBUTIONS: FLUORESCENCE LIFETIMES, RADIOACTIVE DECAY, AND DRUG ELIMINATION FROM THE BODY GAUSSIAN DISTRIBUTIONS THE CENTRAL LIMIT THEOREM PARAMETER ESTIMATION, EXPERIMENTAL ERRORS, AND COUNTING STATISTICS CHAPTER OUTLOOK PROBLEMS REFERENCES RANDOM WALKS: BROWNIAN MOTION AND THE TREE OF LIFE INTRODUCTION YOUR LEARNING GOALS FOR THIS CHAPTER BROWNIAN MOTION BROWNIAN MOTION AND THE ATOMIC HYPOTHESIS STATISTICAL PROPERTIES OF BROWNIAN MOTION RANDOM WALKS ONE-DIMENSIONAL BROWNIAN MOTION, MODELED AS A 1D RANDOM WALK RANDOM WALKS IN THE CONTINUUM LIMIT TWO- AND THREE-DIMENSIONAL RANDOM WALKS THE EINSTEIN RELATION AND HOW WE KNOW THERE ARE ATOMS ACTIN POLYMERIZATION ACTIN POLYMERIZATION AS A RANDOM WALK EXAMPLE: MOLECULAR MOTORS AS RANDOM WALKERS EVOLUTIONARY “GENETIC DRIFT” GAMBLER’S RUIN EXAMPLE: STACKED ODDS THE MORAN MODEL PROBABILITY THAT A MUTATION BECOMES FIXED IN THE POPULATION AND PHYLOGENETIC TREES DIFFUSION: MEMBRANE PERMEABILITY AND THE RATE OF ACTIN POLYMERIZATION THE DIFFUSION EQUATION PARTICLE FLUX AND FICK’S LAW PARTICLE NUMBER CONSERVATION AND FICK’S SECOND LAW THE STEADY-STATE, ONE-DIMENSIONAL DIFFUSION EQUATION DIFFUSION THROUGH A MEMBRANE OR A TUBE DIFFUSION THROUGH A MEMBRANE: MORE REALISTIC VERSION DIFFUSIVE CONDUCTANCE AND MEMBRANE PERMEABILITY DIFFUSION THROUGH MULTILAYER MEMBRANES EXAMPLE: CONCENTRATION BETWEEN THE LAYERS OF A TWO-LAYER MEMBRANE EXAMPLE: DIFFUSION ALONG A TUBE OF VARYING CROSS-SECTIONAL AREA EXAMPLE: A DIFFERENT PROCESS FOR TRANSMEMBRANE TRANSPORT AND CONDUCTANCES “IN PARALLEL” SPHERICAL COWS THE STEADY-STATE, SPHERICALLY SYMMETRIC DIFFUSION EQUATION EXAMPLE: DIFFUSION ENFORCES A FUNDAMENTAL LIMIT ON CELL SIZE THE RATE OF ACTIN POLYMERIZATION DIFFUSION TO CAPTURE AND DIFFUSION-LIMITED ACTIN POLYMERIZATION ACTIN POLYMERIZATION WITH FRACTIONAL CAPTURE EF?CIENCY EXAMPLE: DEPLETION AS A RESULT OF CAPTURE DIFFUSION PREDICTIONS COMPARED TO EXPERIMENTS ACTIN MONOMER DISSOCIATION RECEPTORS AND BIOLOGICAL SIGNALING EF?CIENCY RATES OF CHANGE: DRUGS, INFECTIONS, AND WEAPONS OF MASS DESTRUCTION RATES OF CHANGE ADMINISTERING THERAPEUTICS: CONTINUOUS INFUSION WITH ELIMINATION THE SAME EQUATIONS HAVE THE SAME SOLUTIONS SOLUTION BY DIRECT SUBSTITUTION REVISITED INITIAL CONDITIONS ADMINISTERING THERAPEUTICS: ORAL DOSAGE WITH ELIMINATION EXAMPLE: TUMOR SUPPRESSOR GENES AND TUMORIGENESIS: THE CASE OF RETINOBLASTOMA EXAMPLE: GENE EXPRESSION PROGRESSION OF HIV INFECTION IN AN INDIVIDUAL PATIENT EXAMPLE: BUILDING A MODEL OF HIV INFECTION NUMERICAL SOLUTION OF HIV INFECTION MODEL STEADY-STATE SOLUTIONS: LIVING WITH HIV HIV INFECTION PREDICTIONS COMPARED TO EXPERIMENTS NUCLEAR CHAIN REACTIONS AND ATOMIC BOMBS EXAMPLE: LINEAR CHAIN REACTION EQUATIONS AT EARLY TIMES STATISTICAL MECHANICS: BOLTZMANN FACTORS, PCR, AND BROWNIAN RATCHETS THE BOLTZMANN FACTOR EXAMPLE: ION CHANNELS EXAMPLE: MOLECULAR HEIGHT DISTRIBUTION PROTEIN AND NUCLEIC ACID FOLDING–UNFOLDING AND MICROSTATE MULTIPLICITY DNA UNZIPPING AND POLYMERASE CHAIN REACTION DNA ZIPPING AND UNZIPPING AS A RANDOM WALK CONNECTION TO THE SECOND LAW OF THERMODYNAMICS BROWNIAN RATCHETS BROWNIAN RATCHET MECHANISM OF HELICASE-CATALYZED UNZIPPING HELICASE TRANSLOCATION AS A RANDOM WALK CLASH OF THE TITANS EXAMPLE: FORCE GENERATION BY ACTIN POLYMERIZATION: ANOTHER BROWNIAN RATCHET BINDING AND REACTIONS LANGMUIR BINDING CURVE CHEMICAL EQUILIBRIUM AND THE LAW OF MASS ACTION ENTROPY, TEMPERATURE, AND THE IDEAL GAS LAW ENTROPY TEMPERATURE THE IDEAL GAS EQUATION OF STATE FLUID MECHANICS: LAMINAR FLOW, BLUSHING, AND MURRAY’S LAW PRESSURE AND HYDROSTATIC PRESSURE TWO TYPES OF FLUID BEHAVIOR: LAMINAR FLUID FLOW AND TURBULENT FLUID FLOW VISCOUS FORCES AND VISCOSITY REYNOLDS NUMBER HOW TO DESCRIBE LAMINAR FLUID FLOW VELOCITY PRO?LE IN A THIN CHANNEL FLOW RATE LAMINAR FLUID FLOW IN A CYLINDRICAL TUBE EXAMPLE: VELOCITY PRO?LE IN A CYLINDRICAL TUBE POISEUILLE’S LAW, BLUSHING, AND ATHEROSCLEROSIS STEADY-STATE APPROXIMATION FOR THE HUMAN CIRCULATORY SYSTEM FLOW CONDUCTANCE AND RESISTANCE FLOW CHANNELS “IN SERIES” AND LIQUID INCOMPRESSIBILITY FLOW CHANNELS “IN PARALLEL” EXAMPLE: SQUARE MICRO?UIDICS POWER DISSIPATION IN A VISCOUS FLUID FLOW MURRAY’S LAW AND THE “ENGINEERING” OF THE HUMAN CIRCULATORY SYSTEM