Lecture 24 Thermodynamics in Biology

A Simple Thought Experiment

Driving Forces for Natural Processes Enthalpy –Tendency toward lowest energy state Form stablest bonds Entropy –Tendency to maximize randomness

Enthalpy and Bond Strength Enthalpy = ∆H = heat change at constant pressure Units –cal/mole or joule/mole 1 cal = 4.18 joule Sign –∆H is negative for a reaction that liberates heat

Entropy and Randomness

Entropy = S = measure of randomness –cal/deg·mole T∆S = change of randomness For increased randomness, sign is “+”

“System” Definition

Cells and Organisms: Open Systems Material exchange with surroundings –Fuels and nutrients in (glucose) –By-products out (CO 2 ) Energy exchange –Heat release (fermentation) –Light release (fireflies) –Light absorption (plants)

1 st Law of Thermodynamics Energy is conserved, but transduction is allowed Transduction

2 nd Law of Thermodynamics In all spontaneous processes, total entropy of the universe increases

2 nd Law of Thermodynamics ∆S system + ∆S surroundings = ∆S universe > 0 A cell (system) can decrease in entropy only if a greater increase in entropy occurs in surroundings C 6 H 12 O 6 + 6O 2  6CO 2 + 6H 2 O complex simple

Entropy: A More Rigorous Definition From statistical mechanics: –S = k lnW k = Boltzmann constant = 1.38  10 –23 J/K W = number of ways to arrange the system S = 0 at absolute zero (-273ºC)

Gibbs Free Energy Unifies 1 st and 2 nd laws ∆G –Gibbs free energy –Useful work available in a process ∆G = ∆H – T∆S –∆H from 1 st law Kind and number of bonds –T∆S from 2 nd law Order of the system

∆G Driving force on a reaction Work available  distance from equilibrium ∆G = ∆H – T∆S –State functions Particular reaction T P Concentration (activity) of reactants and products

Equilibrium ∆G = ∆H – T∆S = 0 So ∆H = T∆S –∆H is measurement of enthalpy –T∆S is measurement of entropy Enthalpy and entropy are exactly balanced at equilibrium

Effects of ∆H and ∆S on ∆G Voet, Voet, and Pratt. Fundamentals of Biochemistry

Standard State and ∆Gº Arbitrary definition, like sea level [Reactants] and [Products] –1 M or 1 atmos (activity) T = 25ºC = 298K P = 1 atmosphere Standard free energy change = ∆Gº

Biochemical Conventions: ∆Gº Most reactions at pH 7 in H 2 O Simplify ∆Gº and K eq by defining [H + ] = 10 –7 M [H 2 O] = unity Biochemists use ∆Gº and K eq

Relationship of ∆G to ∆Gº ∆G is real and ∆Gº is standard For A in solution –G A = G A + RT ln[A] For reaction aA + bB  cC + dD –∆G = ∆Gº + RT ln –Constant Variable (from table) º [C] c [D] d [A] a [B] b }

Relationship Between ∆Gº and K eq ∆G = ∆Gº + RT ln At equilibrium, ∆G = 0, so –∆Gº = –RT ln –∆Gº = –RT ln K eq [C] c [D] d [A] a [B] b [C] c [D] d [A] a [B] b

Relationship Between K eq and ∆Gº

Will Reaction Occur Spontaneously? When: –∆G is negative, forward reaction tends to occur –∆G is positive, back reaction tends to occur –∆G is zero, system is at equilibrium ∆G = ∆Gº + RT ln [C] c [D] d [A] a [B] b

A Caution About ∆Gº Even when a reaction has a large, negative ∆Gº, it may not occur at a measurable rate Thermodynamics –Where is the equilibrium point? Kinetics –How fast is equilibrium approached? Enzymes change rate of reactions, but do not change K eq

∆Gº is Additive (State Function) Reaction A  B B  C Sum: A  C Also: B  A Free energy change ∆G 1 º ∆G 2 º ∆G 1 º + ∆G 2 º – ∆G 1 º

Coupling Reactions Glucose + HPO 4 2–  Glucose-6-P ATP  ADP + HPO 4 2– ATP + Glucose  ADP + Glucose-6-P ∆Gº kcal/mol kJ/mol –7.3 – 30.5 –4.0 – 16.7

Resonance Forms of P i –– –– –– ––

Phosphate Esters and Anhydrides

Hydrolysis of Glucose-6-Phosphate ∆Gº = –3.3 kcal/mol = –13.8 kJ/mol

High ∆Gº Hydrolysis Compounds ∆Gº = –14.8 kcal/mol = –61.9 kJ/mol

High ∆Gº Hydrolysis Compounds ∆Gº = –11.8 kcal/mol = –49.3 kJ/mol

High ∆Gº Hydrolysis Compounds ∆Gº = –10.3 kcal/mol = –43 kJ/mol

Phosphate Anhydrides (Pyrophosphates) ∆Gº = –7.3 kcal/mol = –30.5 kJ/mol

Thiol Esters ∆Gº = –7.5 kcal/mol = –31.4 kJ/mol

Thiol Esters Thiol ester less resonance-stabilized

“High-Energy” Compounds Large ∆Gº hydrolysis –Bond strain (electrostatic repulsion) in reactant ATP –Products stabilized by ionization Acyl-P –Products stabilized by isomerization PEP –Products stabilized by resonance Creatine-P

“High-Energy” Compounds “High-energy” compound is one with a ∆Gº below –6 kcal/mol (–25 kJ/mol)

High-Energy Compounds

Group Transfer Potential

Lecture 25 Chemical Sense in Metabolism