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

08/27/2009 Biology 401: Thermodynamics 1

Biochemical ThermodynamicsBiochemical Thermodynamics

Andy Howard

Biochemistry, Fall 2009IIT

08/27/2009 Biology 401: Thermodynamics p. 2 of 45

Thermodynamics matters!Thermodynamics matters!

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


ThermodynamicsThermodynamics

• 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


Energy in biological systemsEnergy 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


ThermodynamicsThermodynamics

•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 Go = -RT ln Keq


Thermodynamics!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!


Why we careWhy 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

GReactionCoord.


… … but first: iClicker quiz!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, continuediClicker 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


iClicker quiz, continuediClicker quiz, continued

•Which type of biopolymer is sometimes branched?(a) DNA(b) Protein(c) Polysaccharide(d) RNA(e) They’re all branched.


iClicker quiz, concludediClicker 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

BD

C

Reaction Coordinate

Free Energy


Laws of ThermodynamicsLaws 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.


What do we mean by What do we mean by systems, systems, closed, open, and isolated?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


That makes sense if…That makes sense if…

• It makes senseprovided 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


Enthalpy, Enthalpy, HH

• Closely related to energy:H = E + PV

• Therefore changes in H are:H = E + PV + VP

•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 Kinds of thermodynamic propertiesproperties

• 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


UnitsUnits

•Energy unit: Joule (kg m2 s-2)•1 kJ/mol = 103J/(6.022*1023)

= 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

James Prescott Joule


Typical energies in Typical energies in biochemistrybiochemistry

•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


EntropyEntropy

• 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


Components of entropyComponents of entropy

Liquid propane (as surrogate):

Type of Entropy kJ (molK)-1

Translational 36.04

Rotational 23.38

Vibrational 1.05

Electronic 0

Total 60.47


Real biomoleculesReal 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(there’s half as many molecules,but ln Mr only goes up by ln 2)

• Rigidity decreases entropy


Entropy in solvation: soluteEntropy in solvation: solute

•When molecules go into solution, their entropy increases because they’re freer to move around


Entropy in solvation: SolventEntropy 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!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 waterApolar molecules in water

•Water molecules tend to form ordered structure surrounding apolar molecule

• Entropy decreases because they’re so ordered


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


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


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/mol

Lactate -516 Pyruvate -474

Succinate -690 Glycerol -488

Acetate -369 Oxaloacetate -797

HCO3- -394


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)


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.


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


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


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: Go

C = Go1 + Go

2

•If GoC < 0,

then reaction 1 is driving reaction 2!


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


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


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 2 Pi, Go = -33 kJ/mol

•So, appropriately coupled, we get roughly twice as much!


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


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


Other high-energy compoundsOther high-energy compounds

•Creatine phosphate: ~ $0.40

•Phosphoenolpyruvate: ~ $0.35

•So for some reactions, they’re more efficient than ATP


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


Is that realistic?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] = 1even if all the concentrations are small

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


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


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

•This is how you solve the homework problem!


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


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 + Wis described as hydrolysis of Uto yield V and W

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

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Transcript of 08/27/2009Biology 401: Thermodynamics1 Biochemical Thermodynamics Andy Howard Biochemistry, Fall...