Biochemical Thermodynamics Andy Howard Biochemistry, Spring 2008 IIT

Thermodynamics matters! Thermodynamics tells us which reactions will go forward and which ones won’t.

Kinetics Rate of reaction is dependent on Kelvin temperature T and on activation barrier  G ‡ preventing conversion from one site to the other Rate = Qexp(-  G ‡ /RT) Job of an enzyme is to reduce  G ‡

Regulation Biological reactions are regulated in the sense that they’re catalyzed by enzymes, so the presence or absence of the enzyme determines whether the reaction will proceed The enzymes themselves are subject to extensive regulation so that the right reactions occur in the right places and times

Typical enzymatic regulation Suppose enzymes are involved in converting A to B, B to C, C to D, and D to F. E is the enzyme that converts A to B: (E) A  B  C  D  F In many instance F will inhibit (interfere) with the reaction that converts A to B by binding to a site on enzyme E so that it can’t bind A. This feedback inhibition helps to prevent overproduction of F—homeostasis.

Molecular biology This phrase means something much more specific than biochemistry: It’s the chemistry of replication, transcription, and translation, i.e., the ways that genes are reproduced and expressed. Most of you have taken biology 214 or its equivalent; we’ll review some of the contents of that course here.

The molecules of molecular biology Deoxyribonucleic acid: polymer; backbone is deoxyribose-phosphate; side chains are nitrogenous ring compounds RNA: polymer; backbone is ribose- phosphate; side chains as above Protein: polymer: backbone is NH-(CHR)-CO; side chains are 20 ribosomally encoded styles

Steps in molecular biology: the Central Dogma DNA replication (makes accurate copy of existing double-stranded DNA prior to mitosis) Transcription (RNA version of DNA message is created) Translation (mRNA copy of gene serves as template for making protein: 3 bases of RNA per amino acid of synthesized rotein)

Evolution and Taxonomy Traditional studies of interrelatedness of organisms focused on functional similarities This enables production of phylogenetic trees Molecular biology provides an alternative, possibly more quantitative, approach to phylogenetic tree-building More rigorous hypothesis-testing possible

Quantitation Biochemistry is a quantitative science. Results in biochemistry are rarely significant unless they can be couched in quantifiable terms. Thermodynamic & kinetic behavior of biochemical systems must be described quantitatively. Even the descriptive aspects of biochemistry, e.g. the compartmentalization of reactions and metabolites into cells and into particular parts of cells, must be characterized numerically.

Mathematics in biochemistry Ooo: I went into biology rather than physics because I don’t like math Too bad. You need some here: but not much. Biggest problem in past years: exponentials and logarithms

Exponentials Many important biochemical equations are expressed in the form Y = e f(x) … which can also be written Y = exp(f(x)) The number e is the base of the natural logarithm system and is, very roughly, I.e., it’s

Logarithms First developed as computational tools because they convert multiplication problems into addition problems They have a fundamental connection with raising a value to a power: Y = x a  log x (Y) = a In particular, Y = exp(a) = e a  lnY = log e (Y) = a

Algebra of logarithms log v (A) = log u (A) / log u (v) log u (A/B) = log u (A) - log u (B) log u (A B ) = Blog u (A) log 10 (A) = ln(A) / ln(10) = ln(A) / = * ln(A) ln(A) = log 10 (A) / log 10 e = log 10 (A) / = * log 10 (A)

What we’ll discuss Why we care about thermodynamics The laws of thermodynamics Enthalpy Thermodynamic properties Units Entropy Solvation & binding to surfaces Free energy Equilibrium Work Coupled reactions ATP: energy currency Other high-energy compounds Dependence on concentration

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.

… 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.

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

iClicker quiz, continued Which type of biopolymer is sometimes branched? (a) DNA (b) Protein (c) Polysaccharide (d) RNA

iClicker quiz, concluded 4. The red curve represents the reaction pathway for an uncatalyzed reaction. Which one is the pathway for a catalyzed reaction? Reaction Coordinate G A B C D

Laws of Thermodynamics Traditionally four (0, 1, 2, 3) Can be articulated in various ways First law: The energy of a closed system is constant. Second law: Entropy of a closed system increases.

That makes sense if… It makes sense provided that we understand the words! Energy. Hmm. Capacity to do work. Entropy: Disorder. (Boltzmann): S = kln  Closed system: one in which energy and matter don’t enter or leave An organism is not a closed system: so S can decrease within an organism! Boltzmann Gibbs

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

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

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

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

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

Components of entropy Liquid propane (as surrogate): Type of EntropykJ (molK) -1 Translational36.04 Rotational23.38 Vibrational1.05 Electronic0 Total60.47

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

Entropy in solvation: solute When molecules go into solution, their entropy increases because they’re freer to move around

Entropy in solvation: Solvent Solvent entropy usually decreases because solvent molecules must become more ordered around solute Overall effect: often slightly negative

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.

Apolar molecules in water Water molecules tend to form ordered structure surrounding apolar molecule Entropy decreases because they’re so ordered

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

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

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

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 )

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.

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

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

Coupled reactions Often a single enzyme catalyzes two reactions, shoving them together: 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!

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

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

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 twice as much!

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

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

Other high-energy compounds Creatine phosphate: ~ $0.40 Phosphoenolpyruvate: ~ $0.35 So for some reactions, they’re more efficient than ATP

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

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!

How does this matter? Often coupled reactions involve withdrawl of a product from availability If that happens, [product]/[reactant] shrinks, the second term becomes negative, and  G 0