Biochemical Thermodynamics Andy Howard Biochemistry, Fall 2010 IIT 08/25/2010 Biology 403: Thermodynamics 1 Thermodynamics matters! Thermodynamics tells us which reactions will go forward and which ones wont. 08/25/2010
Biology 403: Thermodynamics p. 2 of 49 Thermodynamics Thermodynamics: Topics in Thermodynamics Basics Why we care
The laws Enthalpy Thermodynamic properties 08/25/2010 Units Entropy Solvation & binding to surfaces Biology 403: Thermodynamics p. 3 of 49 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 08/25/2010 Biology 403: Thermodynamics p. 4 of 49 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 Theyre related by Go = -RT ln Keq 08/25/2010 Biology 403: Thermodynamics p. 5 of 49 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! 08/25/2010 Biology 403: Thermodynamics p. 6 of 49 Why we care G Reaction Coord. Free energy is directly related to the
equilibrium of a reaction It doesnt tell us how fast the system will come to equilibrium Kinetics, and the way that enzymes influence kinetics, tell us about rates Today well focus on equilibrium energetics; well call that thermodynamics 08/25/2010 Biology 403: Thermodynamics p. 7 of 49 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. 08/25/2010 Biology 403: Thermodynamics p. 8 of 49 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 doesnt produce secondary products 08/25/2010 Biology 403: Thermodynamics p. 9 of 49 iClicker quiz, continued Which type of biopolymer is sometimes branched? (a) DNA (b) Protein (c) Polysaccharide (d) RNA
(e) Theyre all branched. 08/25/2010 Biology 403: Thermodynamics p. 10 of 49 iClicker quiz, concluded Free G 4. The red curve Energy represents the reaction pathway for an uncatalyzed reaction. Which
one is the pathway for a catalyzed reaction? 08/25/2010 A D B C Reaction Coordinate Biology 403: Thermodynamics
p. 11 of 49 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. 08/25/2010 Biology 403: Thermodynamics p. 12 of 49 What do we mean by systems,
closed, open, and isolated? A system is the portion of the universe with which were concerned (e.g., an organism or a rock or an ecosystem) If it doesnt exchange energy or matter with the outside, its isolated. If it exchanges energy but not matter, its closed If it exchanges energy & matter, its open 08/25/2010 Biology 403: Thermodynamics p. 13 of 49
That makes sense if It makes sense Boltzmann Gibbs 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 dont enter or leave An organism is not an isolated system: so S can decrease within an organism! 08/25/2010 Biology 403: Thermodynamics p. 14 of 49
Enthalpy, H Closely related to energy: H = E + PV Therefore changes in H are: Kamerlingh H = E + PV + VP Onnes Most, but not all, biochemical systems have constant V, P: H = E Related to amount of heat content in a system 08/25/2010 Biology 403: Thermodynamics
p. 15 of 49 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 08/25/2010 Biology 403: Thermodynamics
p. 16 of 49 Units Energy unit: Joule (kg m2 s-2) 1 kJ/mol = 103J/(6.022*1023) James Prescott Joule = 1.661*10-21 J 1 cal = 4.184 J: so 1 kcal/mol = 6.948 *10-21 J 1 eV = 1 e * J/Coulomb = 1.602*10-19 C * 1 J/C = 1.602*10-19 J = 96.4 kJ/mol = 23.1 kcal/mol
08/25/2010 Biology 403: Thermodynamics p. 17 of 49 Typical energies in biochemistry Go 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 08/25/2010
Biology 403: Thermodynamics p. 18 of 49 Entropy Related to disorder: Boltzmann: S = k ln k=Boltzmann constant = 1.38*10-23 J K-1 Note that k = R / N0 is the number of degrees of freedom in the system Entropy in 1 mole = N0S = Rln Number of degrees of freedom can be calculated for simple atoms 08/25/2010
Biology 403: Thermodynamics p. 19 of 49 Components of entropy Liquid propane (as surrogate): 08/25/2010 Type of Entropy kJ (molK)-1 Translational 36.04 Rotational
23.38 Vibrational 1.05 Electronic 0 Total 60.47 Biology 403: Thermodynamics p. 20 of 49
Real biomolecules Entropy is mostly translational and rotational, as above Enthalpy is mostly electronic Translational entropy = (3/2) R ln Mr So when a molecule dimerizes, the total translational entropy decreases (theres half as many molecules, but ln Mr only goes up by ln 2) Rigidity decreases entropy 08/25/2010 Biology 403: Thermodynamics p. 21 of 49
Entropy in solvation: solute When molecules go into solution, their entropy increases because theyre freer to move around 08/25/2010 Biology 403: Thermodynamics p. 22 of 49 Entropy in solvation: Solvent Solvent entropy usually decreases because solvent molecules must become more ordered around solute
Overall effect: often slightly negative 08/25/2010 Biology 403: Thermodynamics p. 23 of 49 Thermodynamics Special topics in Thermodynamics Free energy Equilibrium Work Coupled reactions ATP: energy currency Other high-energy compounds
Dependence on concentration 08/25/2010 Biology 403: Thermodynamics p. 24 of 49 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.
08/25/2010 Biology 403: Thermodynamics p. 25 of 49 Apolar molecules in water Water molecules tend to form ordered structure surrounding apolar molecule Entropy decreases because theyre so ordered 08/25/2010 Biology 403: Thermodynamics
p. 26 of 49 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 theyre trapped Solvent molecules are displaced and liberated from the protein surface 08/25/2010 Biology 403: Thermodynamics p. 27 of 49
Free Energy Gibbs: Free Energy Equation G = H - TS So if isothermal, G = H - TS Gibbs showed that a reaction will be spontaneous (proceed to right) if and only if G < 0 08/25/2010 Biology 403: Thermodynamics p. 28 of 49 Standard free energy of formation, Gof
Difference between compounds free energy & sum of free energy of the elements from which it is composed Substance Gof, kJ/mol Substance Gof, kJ/mol Lactate -516 Pyruvate -474
-394 08/25/2010 Biology 403: Thermodynamics p. 29 of 49 Free energy and equilibrium Gibbs: Go = -RT ln keq Rewrite: keq = exp(-Go/RT) keq is equilibrium constant; formula depends on reaction type For aA + bB cC + dD, keq = ([C]c[D]d)/([A]a[B]b)
If all the proportions are equal, keq = ([C][D])/([A][B]) These values ([C], [D] ) denotes the concentrations at equilibrium 08/25/2010 Biology 403: Thermodynamics p. 30 of 49 Spontaneity and free energy Thus if reaction is just spontaneous, i.e. Go = 0, then keq = 1 If Go < 0, then keq > 1: Exergonic If Go > 0, then keq < 1: Endergonic You may catch me saying exoergic
and endoergic from time to time: these mean the same things. 08/25/2010 Biology 403: Thermodynamics p. 31 of 49 Free energy as a source of work Change in free energy indicates that the reaction could be used to perform useful work If Go < 0, we can do work If Go > 0, we need to do work to make the reaction occur
08/25/2010 Biology 403: Thermodynamics p. 32 of 49 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 08/25/2010
Biology 403: Thermodynamics p. 33 of 49 Coupled reactions Often a single enzyme catalyzes 2 reactions, shoving them together: reaction 1, A B: Go1 < 0 reaction 2, C D: Go2 > 0 Coupled reaction: A + C B + D: GoC = Go1 + Go2 If GoC < 0, then reaction 1 is driving reaction 2! 08/25/2010
Biology 403: Thermodynamics p. 34 of 49 How else can we win? Concentration of product may play a role As well discuss in a moment, the actual free energy depends on Go 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 08/25/2010
Biology 403: Thermodynamics p. 35 of 49 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 08/25/2010
Biology 403: Thermodynamics p. 36 of 49 Hydrolysis of ATP Hydrolysis at the rightmost high-energy bond: ATP + H2O ADP + Pi Go = -33kJ/mol Hydrolysis of middle bond: ATP + H2O AMP + PPi Go = -33kJ/mol BUT PPi + H2O 2 Pi, Go = -33 kJ/mol So, appropriately coupled, we get roughly
twice as much! 08/25/2010 Biology 403: Thermodynamics p. 37 of 49 ATP as energy currency Any time we wish to drive a reaction that has Go < +30 kJ/mol, we can couple it to ATP hydrolysis and come out ahead If the reaction we want has Go < +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 08/25/2010
Biology 403: Thermodynamics p. 38 of 49 Coin analogy Think of store of ATP as a roll of quarters Vendors dont give change Use one quarter for some reactions, two for others Inefficient for buying $0.35 items 08/25/2010 Biology 403: Thermodynamics p. 39 of 49
Other high-energy compounds Creatine phosphate: ~ $0.40 Phosphoenolpyruvate: ~ $0.35 So for some reactions, theyre more efficient than ATP 08/25/2010 Biology 403: Thermodynamics p. 40 of 49 Why not use those always? Theres no such thing as a free lunch! In order to store a compound, you have to create it in the first place
So an intermediate-energy currency is the most appropriate 08/25/2010 Biology 403: Thermodynamics p. 41 of 49 Dependence on Concentration Actual G of a reaction is related to the concentrations / activities of products and reactants: G = Go + RT ln [products]/[reactants] If all products and reactants are at 1M, then the second term drops
away; thats why we describe Go as the standard free energy 08/25/2010 Biology 403: Thermodynamics p. 42 of 49 Is [A] = [B] = 1M realistic? No, but it doesnt 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! 08/25/2010 Biology 403: Thermodynamics p. 43 of 49 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 even if Go > 0 08/25/2010
Biology 403: Thermodynamics p. 44 of 49 Example: glycolysis Later this semester well spend at least one lecture looking at glycolysis, one of the fundamental pathways Some of the glycolytic reactions have Go or Go > 0 But all have G values that are negative or zero because of this concentration effect 08/25/2010
Biology 403: Thermodynamics p. 45 of 49 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 Reversing a reaction reverses the sign of G. 08/25/2010 Biology 403: Thermodynamics
p. 46 of 49 A bit more detail Suppose we couple two equations: A + B C + D, Go = x C + F B + G, Go = y The result is: A+B+C+FB+C+D+G or A + F D + G, Go = x + y since B & C appear on both sides 08/25/2010 Biology 403: Thermodynamics p. 47 of 49
Slightly more complex Suppose we couple two equations: A + B C + D, Go = x H + A J + C, Go = z Reverse the second equation: J + C A + H, Go = -z Add this to 1st eqn. & simplify: B + J D + H, Go = x - z since A & C appear on both sides 08/25/2010 Biology 403: Thermodynamics p. 48 of 49
What do we mean by hydrolysis? It simply means a reaction with water Typically involves cleaving a bond: U + H2O V + W is described as hydrolysis of U to yield V and W 08/25/2010 Biology 403: Thermodynamics p. 49 of 49
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