Biochemical ThermodynamicsBiochemical Thermodynamics

Andy Howard

Biochemistry, Spring 2008IIT

Thermodynamics matters!Thermodynamics matters!

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

KineticsKinetics

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‡

RegulationRegulation

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 regulationTypical 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 biologyMolecular 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 ofThe molecules ofmolecular biologymolecular 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 isNH-(CHR)-CO; side chains are 20 ribosomally encoded styles

Steps in molecular biology:Steps in molecular biology:the the Central DogmaCentral 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 TaxonomyEvolution 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

QuantitationQuantitation

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 biochemistryMathematics 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

ExponentialsExponentials

Many important biochemical equations are expressed in the formY = ef(x)

… which can also be writtenY = exp(f(x))

The number e is the base of the natural logarithm system and is, very roughly, 2.718281828459045

I.e., it’s 2.7 1828 1828 45 90 45

LogarithmsLogarithms

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 = xa logx(Y) = a

In particular, Y = exp(a) = ealnY = loge(Y) = a

Algebra of logarithmsAlgebra of logarithms

logv(A) = logu(A) / logu(v)

logu(A/B) = logu(A) - logu(B)

logu(AB) = Blogu(A)

log10(A) = ln(A) / ln(10)= ln(A) / 2.30258509299= 0.4342944819 * ln(A)

ln(A) = log10(A) / log10e= log10(A) / 0.4342944819= 2.30258509299 * log10(A)

What we’ll discussWhat 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 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

G

ReactionCoord.

… … 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

iClicker quiz, continuediClicker quiz, continued

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

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?

Reaction Coordinate

G

A

B C

D

Laws of ThermodynamicsLaws of Thermodynamics

Traditionally four (0, 1, 2, 3)Can be articulated in various waysFirst law: The energy of a closed

system is constant.Second law: Entropy of a closed

system increases.

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 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, 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 J1 cal = 4.184 J:

so 1 kcal/mol = 6.948 *10-21 J1 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

Typical energies in biochemistryTypical 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/molvan der Waals force: ~ 1 kJ/molSee 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 entropicIncreases 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 - TSGibbs 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

ffDifference 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 workIf 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 two reactions, shoving them together:A B Go

1 < 0 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 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 changeUse one quarter for some reactions,

two for othersInefficient for buying $0.35 items

Other high-energy compoundsOther high-energy compounds

Creatine phosphate: ~ $0.40Phosphoenolpyruvate: ~ $0.35So 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 withdrawl of a product from availability

If that happens, [product]/[reactant]shrinks, the second term becomes negative, and G < 0 even if Go > 0