08/27/2009Biology 401: Thermodynamics1 Biochemical Thermodynamics Andy Howard Biochemistry, Fall 2009 IIT

08/27/2009Biology 401: Thermodynamicsp. 2 of 45 Thermodynamics matters! Thermodynamics tells us which reactions will go forward and which ones won’t.

08/27/2009Biology 401: Thermodynamicsp. 3 of 45 Thermodynamics Thermodynamics: Basics –Why we care –The laws –Enthalpy –Thermodynamic properties –Units –Entropy Special topics in Thermodynamics –Solvation & binding to surfaces –Free energy –Equilibrium –Work –Coupled reactions –ATP: energy currency –Other high-energy compounds –Dependence on concentration

08/27/2009Biology 401: Thermodynamicsp. 4 of 45 Energy in biological systems We distinguish between thermodynamics and kinetics: Thermodynamics characterizes the energy associated with equilibrium conditions in reactions Kinetics describes the rate at which a reaction moves toward equilibrium

08/27/2009Biology 401: Thermodynamicsp. 5 of 45 Thermodynamics Equilibrium constant is a measure of the ratio of product concentrations to reactant concentrations at equilibrium Free energy is a measure of the available energy in the products and reactants They’re related by  G o = -RT ln K eq

08/27/2009Biology 401: Thermodynamicsp. 6 of 45 Thermodynamics! Horton et al put this in the middle of chapter 10; Garrett & Grisham are smart enough to put it in the beginning. You can tell which I prefer!

08/27/2009Biology 401: Thermodynamicsp. 7 of 45 Why we care Free energy is directly related to the equilibrium of a reaction It doesn’t tell us how fast the system will come to equilibrium Kinetics, and the way that enzymes influence kinetics, tell us about rates Today we’ll focus on equilibrium energetics; we’ll call that thermodynamics GG Reaction Coord.

08/27/2009Biology 401: Thermodynamicsp. 8 of 45 … but first: iClicker quiz! 1. Which of the following statements is true? –(a) All enzymes are proteins. –(b) All proteins are enzymes. –(c) All viruses use RNA as their transmittable genetic material. –(d) None of the above.

08/27/2009Biology 401: Thermodynamicsp. 9 of 45 iClicker quiz, continued 2. Biopolymers are generally produced in reactions in which building blocks are added head to tail. Apart from the polymer, what is the most common product of these reactions? (a) Water (b) Ammonia (c) Carbon Dioxide (d) Glucose (e) None of the above. Polymerization doesn’t produce secondary products

08/27/2009Biology 401: Thermodynamicsp. 10 of 45 iClicker quiz, continued Which type of biopolymer is sometimes branched? (a) DNA (b) Protein (c) Polysaccharide (d) RNA (e) They’re all branched.

08/27/2009Biology 401: Thermodynamicsp. 11 of 45 iClicker quiz, concluded 4. The red curve represents the reaction pathway for an uncatalyzed reaction. Which one is the pathway for a catalyzed reaction? G A B D C Reaction Coordinate Free Energy

08/27/2009Biology 401: Thermodynamicsp. 12 of 45 Laws of Thermodynamics Traditionally four (0, 1, 2, 3) Can be articulated in various ways First law: The energy of an isolated system is constant. Second law: Entropy of an isolated system increases.

08/27/2009Biology 401: Thermodynamicsp. 13 of 45 What do we mean by systems, closed, open, and isolated? A system is the portion of the universe with which we’re concerned (e.g., an organism or a rock or an ecosystem) If it doesn’t exchange energy or matter with the outside, it’s isolated. If it exchanges energy but not matter, it’s closed If it exchanges energy & matter, it’s open

08/27/2009Biology 401: Thermodynamicsp. 14 of 45 That makes sense if… It makes sense provided that we understand the words! Energy. Hmm. Capacity to do work. Entropy: Disorder. (Boltzmann): S = kln  Isolated system: one in which energy and matter don’t enter or leave An organism is not an isolated system: so S can decrease within an organism! Boltzmann Gibbs

08/27/2009Biology 401: Thermodynamicsp. 15 of 45 Enthalpy, H Closely related to energy: H = E + PV Therefore changes in H are:  H =  E + P  V + V  P Most, but not all, biochemical systems have constant V, P:  H =  E Related to amount of heat content in a system Kamerlingh Onnes

08/27/2009Biology 401: Thermodynamicsp. 16 of 45 Kinds of thermodynamic properties Extensive properties: Thermodynamic properties that are directly related to the amount (e.g. mass, or # moles) of stuff present (e.g. E, H, S) Intensive properties: not directly related to mass (e.g. P, T) E, H, S are state variables; work, heat are not

08/27/2009Biology 401: Thermodynamicsp. 17 of 45 Units Energy unit: Joule (kg m 2 s -2 ) 1 kJ/mol = 10 3 J/(6.022*10 23 ) = 1.661* J 1 cal = J: so 1 kcal/mol = * J 1 eV = 1 e * J/Coulomb = 1.602* C * 1 J/C = 1.602* J = 96.4 kJ/mol = 23.1 kcal/mol James Prescott Joule

08/27/2009Biology 401: Thermodynamicsp. 18 of 45 Typical energies in biochemistry  G o for hydrolysis of high-energy phosphate bond in adenosine triphosphate: 33kJ/mol = 7.9kcal/mol = 0.34 eV Hydrogen bond: 4 kJ/mol=1 kcal/mol van der Waals force: ~ 1 kJ/mol See textbook for others

08/27/2009Biology 401: Thermodynamicsp. 19 of 45 Entropy Related to disorder: Boltzmann: S = k ln  k= Boltzmann constant = 1.38* J K -1 Note that k = R / N 0  is the number of degrees of freedom in the system Entropy in 1 mole = N 0 S = Rln  Number of degrees of freedom can be calculated for simple atoms

08/27/2009Biology 401: Thermodynamicsp. 20 of 45 Components of entropy Liquid propane (as surrogate): Type of EntropykJ (molK) -1 Translational36.04 Rotational23.38 Vibrational1.05 Electronic0 Total60.47

08/27/2009Biology 401: Thermodynamicsp. 21 of 45 Real biomolecules Entropy is mostly translational and rotational, as above Enthalpy is mostly electronic Translational entropy = (3/2) R ln M r So when a molecule dimerizes, the total translational entropy decreases (there’s half as many molecules, but ln M r only goes up by ln 2) Rigidity decreases entropy

08/27/2009Biology 401: Thermodynamicsp. 22 of 45 Entropy in solvation: solute When molecules go into solution, their entropy increases because they’re freer to move around

08/27/2009Biology 401: Thermodynamicsp. 23 of 45 Entropy in solvation: Solvent Solvent entropy usually decreases because solvent molecules must become more ordered around solute Overall effect: often slightly negative

08/27/2009Biology 401: Thermodynamicsp. 24 of 45 Entropy matters a lot! Most biochemical reactions involve very small ( < 10 kJ/mol) changes in enthalpy Driving force is often entropic Increases in solute entropy often is at war with decreases in solvent entropy. The winner tends to take the prize.

08/27/2009Biology 401: Thermodynamicsp. 25 of 45 Apolar molecules in water Water molecules tend to form ordered structure surrounding apolar molecule Entropy decreases because they’re so ordered

08/27/2009Biology 401: Thermodynamicsp. 26 of 45 Binding to surfaces Happens a lot in biology, e.g. binding of small molecules to relatively immobile protein surfaces Bound molecules suffer a decrease in entropy because they’re trapped Solvent molecules are displaced and liberated from the protein surface

08/27/2009Biology 401: Thermodynamicsp. 27 of 45 Free Energy Gibbs: Free Energy Equation G = H - TS So if isothermal,  G =  H - T  S Gibbs showed that a reaction will be spontaneous (proceed to right) if and only if  G < 0

08/27/2009Biology 401: Thermodynamicsp. 28 of 45 Standard free energy of formation,  G o f Difference between compound’s free energy & sum of free energy of the elements from which it is composed Substance  G o f, kJ/mol Substance  G o f, kJ/mol Lactate -516 Pyruvate -474 Succinate -690 Glycerol -488 Acetate -369 Oxaloacetate -797 HCO

08/27/2009Biology 401: Thermodynamicsp. 29 of 45 Free energy and equilibrium Gibbs:  G o = -RT ln K eq Rewrite: K eq = exp(-  G o /RT) K eq is equilibrium constant; formula depends on reaction type For aA + bB  cC + dD, K eq = ([C] c [D] d )/([A] a [B] b )

08/27/2009Biology 401: Thermodynamicsp. 30 of 45 Spontaneity and free energy Thus if reaction is just spontaneous, i.e.  G o = 0, then K eq = 1 If  G o 1: Exergonic If  G o > 0, then K eq < 1: Endergonic You may catch me saying “exoergic” and “endoergic” from time to time: these mean the same things.

08/27/2009Biology 401: Thermodynamicsp. 31 of 45 Free energy as a source of work Change in free energy indicates that the reaction could be used to perform useful work If  G o < 0, we can do work If  G o > 0, we need to do work to make the reaction occur

08/27/2009Biology 401: Thermodynamicsp. 32 of 45 What kind of work? Movement (flagella, muscles) Chemical work: –Transport molecules against concentration gradients –Transport ions against potential gradients To drive otherwise endergonic reactions –by direct coupling of reactions –by depletion of products

08/27/2009Biology 401: Thermodynamicsp. 33 of 45 Coupled reactions Often a single enzyme catalyzes 2 reactions, shoving them together: reaction 1, A  B:  G o 1 0 Coupled reaction: A + C  B + D:  G o C =  G o 1 +  G o 2 If  G o C < 0, then reaction 1 is driving reaction 2!

08/27/2009Biology 401: Thermodynamicsp. 34 of 45 How else can we win? Concentration of product may play a role As we’ll discuss in a moment, the actual free energy depends on  G o and on concentration of products and reactants So if the first reaction withdraws product of reaction B away, that drives the equilibrium of reaction 2 to the right

08/27/2009Biology 401: Thermodynamicsp. 35 of 45 Adenosine Triphosphate ATP readily available in cells Derived from catabolic reactions Contains two high-energy phosphate bonds that can be hydrolyzed to release energy: O O - || | (AMP)-O~P-O~P-O - | || O - O

08/27/2009Biology 401: Thermodynamicsp. 36 of 45 Hydrolysis of ATP Hydrolysis at the rightmost high-energy bond: ATP + H 2 O  ADP + P i  G o = -33kJ/mol Hydrolysis of middle bond: ATP + H 2 O  AMP + PP i  G o = -33kJ/mol BUT PP i  2 P i,  G o = -33 kJ/mol So, appropriately coupled, we get roughly twice as much!

08/27/2009Biology 401: Thermodynamicsp. 37 of 45 ATP as energy currency Any time we wish to drive a reaction that has  G o < +30 kJ/mol, we can couple it to ATP hydrolysis and come out ahead If the reaction we want has  G o < +60 kJ/mol, we can couple it to ATP  AMP and come out ahead So ATP is a convenient source of energy — an energy currency for the cell

08/27/2009Biology 401: Thermodynamicsp. 38 of 45 Coin analogy Think of store of ATP as a roll of quarters Vendors don’t give change Use one quarter for some reactions, two for others Inefficient for buying $0.35 items

08/27/2009Biology 401: Thermodynamicsp. 39 of 45 Other high-energy compounds Creatine phosphate: ~ $0.40 Phosphoenolpyruvate: ~ $0.35 So for some reactions, they’re more efficient than ATP

08/27/2009Biology 401: Thermodynamicsp. 40 of 45 Dependence on Concentration Actual  G of a reaction is related to the concentrations / activities of products and reactants:  G =  G o + RT ln [products]/[reactants] If all products and reactants are at 1M, then the second term drops away; that’s why we describe  G o as the standard free energy

08/27/2009Biology 401: Thermodynamicsp. 41 of 45 Is that realistic? No, but it doesn’t matter; as long as we can define the concentrations, we can correct for them Often we can rig it so [products]/[reactants] = 1 even if all the concentrations are small Typically [ATP]/[ADP] > 1 so ATP coupling helps even more than 33 kJ/mol!

08/27/2009Biology 401: Thermodynamicsp. 42 of 45 How does this matter? Often coupled reactions involve withdrawal of a product from availability If that happens, [product] / [reactant] shrinks, the second term becomes negative, and  G 0

08/27/2009Biology 401: Thermodynamicsp. 43 of 45 How to solve energy problems involving coupled equations General principles: –If two equations are added, their energetics add –An item that appears on the left and right side of the combined equation can be cancelled This is how you solve the homework problem!

08/27/2009Biology 401: Thermodynamicsp. 44 of 45 A bit more detail Suppose we couple two equations: A + B  C + D,  G o ’ = x C + F  B + G,  G o ’ = y The result is: A + B + C + F  B + C + D + G or A + F  D + G,  G o ’ = x + y … since B and C appear on both sides

08/27/2009Biology 401: Thermodynamicsp. 45 of 45 What do we mean by hydrolysis? It simply means a reaction with water Typically involves cleaving a bond: U + H 2 O  V + W is described as hydrolysis of U to yield V and W