THE BIG PICTURE
PART I MYSTERIES METAPHORS MODELS 1 1 WHAT THE ANCIENTS KNEW 2 2 WHAT S INSIDE CELLS 30 PART II DIFFUSION DISSIPATION DRIVE 64 3 THE MOLECULAR DANCE 65 4 RANDOM WALKS FRICTION AND DIFFUSION 98 5 LIFE IN THE SLOW LANE THE LOW REYNOLDS NUMBER WORLD 141 6 ENTROPY TEMPERATURE AND FREE ENERGY 173 7 ENTROPIC FORCES AT WORK 216 8 CHEMICAL FORCES AND SELF ASSEMBLY 259 PART III MOLECULES MACHINES MECHANISMS 298 9 COOPERATIVE TRANSITIONS IN MACROMOLECULES 299 10 ENZYMES AND MOLECULAR MACHINES 351 11 MOLECULAR MACHINES IN MEMBRANES 409 12 NERVE IMPULSES 441 CONTENTS PART I MYSTERIES METAPHORS MODELS 1 CHAPTER 1 WHAT THE ANCIENTS KNEW ALTHOUGH THERE IS NO DIRECT CONNECTION BETWEEN BEER AND THE FIRST LAW OF THERMODYNAMICS THE IN UENCE OF JOULE S PROFES SIONAL EXPERTISE IN BREWING TECHNOLOGY ON HIS SCIENTI C WORK IS CLEARLY DISCERNIBLE HANS CHRISTIAN VON BAEYER WARMTH DIS PERSES AND TIME PASSES THE MODEST GOAL OF THIS BOOK IS TO TAKE YOU FROM THE MID NINETEENTH CENTURY WHERE RST YEAR PHYSICS COURSES OFTEN END TO THE SCIENCE HEADLINES YOU READ THIS MORNING IT S A LONG ROAD TO GET TO OUR DESTINATION ON TIME WE LL NEED TO FOCUS TIGHTLY ON JUST A FEW CORE ISSUES INVOLVING THE INTERPLAY BETWEEN ENERGY INFORMATION AND LIFE WE WILL EVENTUALLY ERECT A FRAMEWORK BASED ON ONLY A FEW PRINCIPLES IN WHICH TO BEGIN ADDRESSING THESE ISSUES IT S NOT ENOUGH SIMPLY TO ENUNCIATE A HANDFUL OF KEY IDEAS OF COURSE IF IT WERE THEN THIS BOOK COULD HAVE BEEN PUBLISHED ON A SINGLE WALLET CARD THE PLEASURE THE DEPTH THE CRAFT OF OUR SUBJECT LIE IN THE DETAILS OF HOW LIVING ORGANISMS WORK OUT THE SOLUTIONS TO THEIR CHALLENGES WITHIN THE FRAMEWORK OF PHYSICAL LAW THE AIM OF THE BOOK IS TO SHOW YOU A FEW OF THESE DETAILS TO CLOTHE THE ETERNAL MATHEMATICAL BONES OF PHYSICAL LAW WITH THE WET CONTINGENT ESH OF LIFE EACH CHAPTER OF THIS BOOK OPENS WITH A BIOLOGICAL QUESTION AND A TERSE SLOGAN ENCAPSULATING A PHYSICAL IDEA RELEVANT TO THE QUESTION THINK ABOUT THESE AS YOU READ THE CHAPTER BIOLOGICAL QUESTION HOW CAN LIVING ORGANISMS BE SO HIGHLY ORDERED PHYSICAL IDEA THE OW OF ENERGY CAN LEAVE BEHIND INCREASED ORDER 1 1 HEAT LIVING ORGANISMS EAT GROW REPRODUCE AND COMPUTE THEY DO THESE THINGS IN WAYS THAT APPEAR TOTALLY DI ERENT FROM MAN MADE MACHINES ONE KEY DI ERENCE INVOLVES THE ROLE OF TEMPERATURE FOR EXAMPLE IF YOU CHILL YOUR VACUUM CLEANER OR EVEN YOUR TELEVISION TO A DEGREE ABOVE FREEZING THESE APPLIANCES CONTINUE TO WORK NE BUT TRY THIS WITH A GRASSHOPPER OR EVEN A BACTERIUM AND YOU ND THAT LIFE PROCESSES PRACTICALLY STOP AFTER ALL THAT S WHY YOU OWN A FREEZER IN THE RST 2 PROCESSES OF LIFE AND WILL BECOME A CENTRAL OBSESSION OF THIS BOOK THIS CHAPTER WILL DEVELOP SOME PLAUSIBLE BUT PRELIMINARY IDEAS ABOUT THIS INTERPLAY PART II OF THE BOOK WILL SHARPEN THESE INTO PRECISE QUANTITATIVE TOOLS 1 1 1 HEAT IS A FORM OF ENERGY WHEN A ROCK OF MASS M FALLS FREELY ITS ALTITUDE Z AND VELOCITY V CHANGE TOGETHER IN JUST SUCH A WAY AS TO ENSURE THAT THE QUANTITY E MGZ 1 2MV2 STAYS CONSTANT WHERE G IS THE ACCELERATION OF GRAVITY AT EARTH S SURFACE WE SAY THAT ENERGY IS CONSERVED EXAMPLE SHOW THIS SOLUTION WE NEED TO SHOW THAT THE TIME DERIVATIVE DE DT EQUALS ZERO TAKING V TO BE THE VELOCITY IN THE UPWARD DIRECTION Z WE HAVE V DZ DT USING THE CHAIN RULE FROM CALCULUS THEN GIVES DE DT MV G DV DT BUT THE ACCELERATION DV DT IS ALWAYS EQUAL TO G IN FREE FALL HENCE DE DT 0 THROUGHOUT THE MOTION THE ENERGY IS A CONSTANT G LEIBNITZ OBTAINED THIS RESULT IN 1693 WE CALL THE RST TERM OF E THAT IS MGZ THE POTENTIAL ENERGY OF THE ROCK AND THE SECOND TERM 1 2MV2 ITS KINETIC ENERGY WE LL CALL THEIR SUM THE MECHANICAL ENERGY OF THE ROCK NOW SUPPOSE OUR ROCK LANDS IN SOME MUD AT Z 0 THE INSTANT BEFORE IT LANDS ITS KINETIC ENERGY IS NONZERO AND SO E IS NONZERO TOO AN INSTANT LATER THE ROCK IS AT REST IN THE MUD AND ITS TOTAL MECHANICAL ENERGY IS ZERO APPARENTLY MECHANICAL ENERGY IS NOT CONSERVED IN THE PRESENCE OF MUD EVERY RST YEAR PHYSICS STUDENT LEARNS WHY A MYSTERIOUS FRICTIONAL E ECT IN THE MUD DRAINED O THE MECHANICAL ENERGY OF THE ROCK THE GENIUS OF ISAAC NEWTON LAY IN PART IN HIS REALIZING THAT THE LAWS OF MOTION WERE BEST STUDIED IN THE CONTEXT OF THE MOTIONS OF CANNONBALLS AND PLANETS WHERE COMPLICATIONS LIKE FRICTIONAL E ECTS ARE TINY HERE THE CONSERVATION OF ENERGY SO APPARENTLY FALSE ON EARTH IS MOST CLEARLY SEEN IT TOOK ANOTHER TWO CENTURIES BEFORE OTHERS WOULD ARRIVE AT A PRECISE STATEMENT OF THE MORE SUBTLE IDEA THAT FRICTION CONVERTS MECHANICAL ENERGY INTO THERMAL FORM WHEN THERMAL ENERGY IS PROPERLY ACCOUNTED FOR THE ENERGY ACCOUNTS BALANCE 1 1 THAT IS THE ACTUAL CONSERVED QUANTITY IS NOT THE MECHANICAL ENERGY BUT THE TOTAL ENERGY THE SUM OF THE MECHANICAL ENERGY PLUS HEAT BUT WHAT IS FRICTION WHAT IS HEAT ON A PRACTICAL LEVEL IF ENERGY IS CONSERVED IF IT CANNOT BE CREATED OR DESTROYED THEN WHY MUST WE BE CAREFUL NOT TO WASTE IT INDEED WHAT COULD WASTE MEAN WE LL NEED TO LOOK A BIT MORE DEEPLY BEFORE WE REALLY UNDERSTAND IDEA 1 1 IDEA 1 1 SAYS THAT FRICTION IS NOT A PROCESS OF ENERGY LOSS BUT RATHER OF ENERGY CONVERSION JUST AS THE FALL OF A ROCK CONVERTS POTENTIAL TO KINETIC ENERGY YOU MAY HAVE SEEN AN ILLUSTRATION OF ENERGY CONVERSION IN A GRAMMAR SCHOOL EXERCISE EXPLORING THE PATHWAYS THAT COULD TAKE ENERGY FROM THE SUN AND CONVERT IT TO USEFUL WORK FOR EXAMPLE A TRIP UP A HILL FIGURE 1 1 A POINT YOUR SCHOOLTEACHER MAY NOT HAVE MENTIONED IS THAT IN PRINCIPLE ALL THE ENERGY CONVERSIONS IN FIGURE 1 1 ARE TWO WAY LIGHT FROM THE SUN CAN GENERATE ELECTRICITY USING A SOLAR CELL THAT ENERGY CAN BE PARTIALLY CONVERTED BACK TO LIGHT USING A LIGHT BULB AND SO ON THE KEY WORD HERE IS PARTIALLY WE NEVER GET ALL THE ORIGINAL ENERGY BACK IN THIS WAY SOME IS LOST AS HEAT BOTH IN THE SOLAR CELL AND THE LIGHT BULB THE WORD LOST HERE IMPLIES NOT THAT ENERGY ISN T CONSERVED IT IS BUT THAT THE BIG PICTURE 3