biochemical thermodynamics andy howard biochemistry, spring 2008 iit
TRANSCRIPT
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