Transcript thermodynamics

Biochemical Thermodynamics
Andy Howard
Biochemistry, Spring 2008
IIT
Thermodynamics matters!

Thermodynamics tells us which
reactions will go forward and which
ones won’t.
Kinetics
Rate of reaction is dependent on
Kelvin temperature T and on
activation barrier DG‡ preventing
conversion from one site to the other
 Rate = Qexp(-DG‡/RT)
 Job of an enzyme is to reduce DG‡
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Regulation
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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 regulation
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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 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 of
molecular biology

Deoxyribonucleic acid: polymer;
backbone is deoxyribose-phosphate; side
chains are nitrogenous ring compounds
 RNA: polymer; backbone is ribosephosphate; side chains as above
 Protein: polymer: backbone is
NH-(CHR)-CO; side chains are 20
ribosomally encoded styles
Steps in molecular biology:
the Central 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 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
Quantitation
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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 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
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Exponentials
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Many important biochemical equations are
expressed in the form
Y = ef(x)
 … which can also be written
Y = 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
Logarithms

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) = ea
lnY = loge(Y) = a
Algebra 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 discuss
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Why we care about
thermodynamics
 The laws of
thermodynamics
 Enthalpy
 Thermodynamic
properties
 Units
 Entropy
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Solvation & binding to
surfaces
Free energy
Equilibrium
Work
Coupled reactions
ATP: energy currency
Other high-energy
compounds
Dependence on
concentration
Why we care

DG
Reaction
Coord.
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
… 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, continued
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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, continued
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Which type of biopolymer is
sometimes branched?
(a) DNA
(b) Protein
(c) Polysaccharide
(d) RNA
iClicker quiz, concluded
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G
4. The red curve
represents the
reaction pathway
for an uncatalyzed
reaction. Which
one is the
pathway for a
catalyzed
reaction?
A
D
B C
Reaction Coordinate
Laws of Thermodynamics
Traditionally four (0, 1, 2, 3)
 Can be articulated in various ways
 First law: The energy of a closed
system is constant.
 Second law: Entropy of a closed
system increases.
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That makes sense if…
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Boltzmann Gibbs
It makes sense
provided that we understand the words!
Energy. Hmm. Capacity to do work.
Entropy: Disorder. (Boltzmann): S = klnW
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!
Enthalpy, H

Closely related to energy:
H = E + PV
 Therefore changes in H are: Kamerlingh Onnes
DH = DE + PDV + VDP
 Most, but not all, biochemical systems
have constant V, P:
DH = DE
 Related to amount of heat content in a
system
Kinds of thermodynamic
properties
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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
Units
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
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Typical energies in biochemistry
• DGo 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
Entropy
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Related to disorder: Boltzmann:
S = k ln W
k=Boltzmann constant = 1.38*10-23 J K-1
 Note that k = R / N0
• W is the number of degrees of freedom in
the system
 Entropy in 1 mole = N0S = RlnW
 Number of degrees of freedom can be
calculated for simple atoms
Components 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 biomolecules
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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: solute
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When molecules go into solution,
their entropy increases because
they’re freer to move around
Entropy in solvation: Solvent
Solvent entropy usually decreases
because solvent molecules must
become more ordered around solute
 Overall effect: often slightly negative
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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 water
Water molecules tend to form
ordered structure surrounding apolar
molecule
 Entropy decreases because they’re
so ordered
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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 they’re trapped
 Solvent molecules are displaced and
liberated from the protein surface

Free Energy
Gibbs: Free Energy Equation
G = H - TS
 So if isothermal, DG = DH - TDS
 Gibbs showed that a reaction will be
spontaneous (proceed to right) if and
only if DG < 0
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Standard free energy of
formation, DGof
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Difference between compound’s free
energy & sum of free energy of the
elements from which it is composed
Substance DGof, kJ/mol
Substance
DGof, kJ/mol
Lactate
-516
Pyruvate
-474
Succinate
-690
Glycerol
-488
Acetate
-369
Oxaloacetate
-797
HCO3-
-394
Free energy and equilibrium
Gibbs: DGo = -RT ln Keq
• Rewrite: Keq = exp(-DGo/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 energy
• Thus if reaction is just spontaneous,
i.e. DGo = 0, then Keq = 1
• If DGo < 0, then Keq > 1: Exergonic
• If DGo > 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 work
Change in free energy indicates that
the reaction could be used to
perform useful work
 If DGo < 0, we can do work
 If DGo > 0, we need to do work to
make the reaction occur
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What kind of work?
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Movement (flagella, muscles)
 Chemical work:
– Transport molecules against concentration
gradients
– Transport ions against potential gradients
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To drive otherwise endergonic reactions
– by direct coupling of reactions
– by depletion of products
Coupled reactions
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•
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Often a single enzyme catalyzes two
reactions, shoving them together:
A  B DGo1 < 0
C  D DGo2 > 0
Coupled reaction:
A + C  B + D DGoC = DGo1 + DGo2
If DGoC < 0,
then reaction 1 is driving reaction 2!
How else can we win?
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Concentration of product may play a role
 As we’ll discuss in a moment, the actual
free energy depends on DGo 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 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 ATP
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•
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Hydrolysis at the rightmost high-energy
bond:
ATP + H2O  ADP + Pi
DGo = -33kJ/mol
Hydrolysis of middle bond:
ATP + H2O  AMP + PPi
DGo = -33kJ/mol
BUT PPi  2 Pi, DGo = -33 kJ/mol
So, appropriately coupled, we get twice as
much!
ATP as energy currency
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Any time we wish to drive a reaction that
has DGo < +30 kJ/mol, we can couple it to
ATP hydrolysis and come out ahead
 If the reaction we want has
DGo < +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
Coin analogy
Think of store of ATP
as 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 compounds
Creatine phosphate: ~ $0.40
 Phosphoenolpyruvate: ~ $0.35
 So for some reactions, they’re more
efficient than ATP
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Dependence on Concentration
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Actual DG of a reaction is related to
the concentrations / activities of
products and reactants:
DG = DGo + RT ln [products]/[reactants]
If all products and reactants are at
1M, then the second term drops
away; that’s why we describe DGo as
the standard free energy
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] = 1
even 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?
Often coupled reactions involve
withdrawl of a product from
availability
 If that happens, [product]/[reactant]
shrinks, the second term becomes
negative, and DG < 0 even if DGo > 0
