09/01/2009 Biology 401: Thermodynamics II 1

Thermodynamics, concludedThermodynamics, concluded

Andy HowardBiochemistry, Fall 2009

IIT

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Thermodynamics matters!Thermodynamics matters!

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

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ThermodynamicsThermodynamics

•Special topics in Thermodynamics– Free energy– Equilibrium– Work– Coupled reactions– ATP: energy currency– Other high-energy compounds– Dependence on concentration

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Entropy matters a lot!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.

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Apolar molecules in waterApolar molecules in water

•Water molecules tend to form ordered structure surrounding apolar molecule

• Entropy decreases because they’re so ordered

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Binding to surfacesBinding 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

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Free EnergyFree Energy

•Gibbs: Free Energy EquationG = 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

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Standard free energy of Standard free energy of formation, formation, GGoo

ff

•Difference between compound’s free energy & sum of free energy of the elements from which it is composed

Substance Gof, kJ/mol Substance Go

f, kJ/molLactate -516 Pyruvate -474Succinate -690 Glycerol -488Acetate -369 Oxaloacetate -797

HCO3- -394

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Free energy and equilibriumFree 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)

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Spontaneity and free energySpontaneity 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.

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Free energy as a source of workFree 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

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What kind of work?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

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Coupled reactionsCoupled reactions

•Often a single enzyme catalyzes 2 reactions, shoving them together:reaction 1, A B: Go

1 < 0 reaction 2, C D: Go

2 > 0 •Coupled reaction:

A + C B + D: GoC = Go

1 + Go2

•If GoC < 0,

then reaction 1 is driving reaction 2!

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How else can we win?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 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

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Adenosine TriphosphateAdenosine 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

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Hydrolysis of ATPHydrolysis 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!

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ATP as energy currencyATP 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 hasGo < +60 kJ/mol, we can couple it toATP AMP and come out ahead

• So ATP is a convenient source of energy — an energy currency for the cell

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Coin analogyCoin analogy

•Think of store of ATPas a roll of quarters

•Vendors don’t give change•Use one quarter for some reactions,

two for others• Inefficient for buying $0.35 items

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Other high-energy compoundsOther high-energy compounds

•Creatine phosphate: ~ $0.40•Phosphoenolpyruvate: ~ $0.35•So for some reactions, they’re more

efficient than ATP

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Why not use those always? Why not use those always?

•There’s 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

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Dependence on ConcentrationDependence 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; that’s why we describe Go as the standard free energy

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Is [A] = [B] = 1M… realistic?Is [A] = [B] = 1M… 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] = 1even if all the concentrations are small

• Typically [ATP]/[ADP] > 1 so ATP coupling helps even more than 33 kJ/mol!

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How does this matter?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

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How to solve energy problems How to solve energy problems involving coupled equationsinvolving 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.

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A bit more detailA bit more detail

•Suppose we couple two equations:A + B C + D, Go’ = xC + F B + G, Go’ = y

•The result is:A + B + C + F B + C + D + GorA + F D + G, Go’ = x + y

•… since B and C appear on both sides

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Slightly more complex…Slightly more complex…

•Suppose we couple two equations:A + B C + D, Go’ = xH + 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 and C appear on both sides

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What do we mean by What do we mean by hydrolysishydrolysis??• It simply means a reaction with water•Typically involves cleaving a bond:•U + H2O V + W

is described as hydrolysis of Uto yield V and W