Biochemical Thermodynamics
Andy Howard
Biochemistry, Fall 2009
IIT
08/27/2009
Biology 401: Thermodynamics
1
Thermodynamics matters!
• Thermodynamics tells
us which reactions will
go forward and which
ones won’t.
08/27/2009
Biology 401: Thermodynamics
p. 2 of 45
Thermodynamics
• Thermodynamics:
Basics
–
–
–
–
Why we care
The laws
Enthalpy
Thermodynamic
properties
– Units
– Entropy
08/27/2009
• Special topics in
Thermodynamics
– Solvation & binding to
surfaces
– Free energy
– Equilibrium
– Work
– Coupled reactions
– ATP: energy currency
– Other high-energy
compounds
– Dependence on
concentration
Biology 401: Thermodynamics
p. 3 of 45
Energy 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
08/27/2009
Biology 401: Thermodynamics
p. 4 of 45
Thermodynamics
• 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 DGo = -RT ln Keq
08/27/2009
Biology 401: Thermodynamics
p. 5 of 45
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!
08/27/2009
Biology 401: Thermodynamics
p. 6 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 7 of 45
… 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.
08/27/2009
Biology 401: Thermodynamics
p. 8 of 45
iClicker 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
08/27/2009
Biology 401: Thermodynamics
p. 9 of 45
iClicker quiz, continued
• Which type of biopolymer is
sometimes branched?
(a) DNA
(b) Protein
(c) Polysaccharide
(d) RNA
(e) They’re all branched.
08/27/2009
Biology 401: Thermodynamics
p. 10 of 45
iClicker quiz, concluded
•
Free
G
4. The red curve Energy
represents the
reaction pathway
for an uncatalyzed
reaction. Which
one is the
pathway for a
catalyzed
reaction?
08/27/2009
A
D
B
C
Reaction Coordinate
Biology 401: Thermodynamics
p. 11 of 45
Laws 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.
08/27/2009
Biology 401: Thermodynamics
p. 12 of 45
What do we mean by systems,
closed, open, and isolated?
• A system is the portion of the universe
•
•
•
08/27/2009
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
Biology 401: Thermodynamics
p. 13 of 45
That makes sense if…
• It makes sense
•
•
•
•
08/27/2009
Boltzmann Gibbs
provided that we understand the words!
Energy. Hmm. Capacity to do work.
Entropy: Disorder. (Boltzmann): S = klnW
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!
Biology 401: Thermodynamics
p. 14 of 45
Enthalpy, H
• Closely related to energy:
•
•
•
08/27/2009
H = E + PV
Therefore changes in H are:
Kamerlingh
DH = DE + PDV + VDP
Onnes
Most, but not all, biochemical systems
have constant V, P:
DH = DE
Related to amount of heat content in a
system
Biology 401: Thermodynamics
p. 15 of 45
Kinds of thermodynamic
properties
• Extensive properties:
•
•
08/27/2009
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
Biology 401: Thermodynamics
p. 16 of 45
Units
• Energy unit: Joule (kg m2 s-2)
• 1 kJ/mol = 103J/(6.022*1023)
James
Prescott
Joule
= 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
08/27/2009
Biology 401: Thermodynamics
p. 17 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 18 of 45
Entropy
• Related to disorder: Boltzmann:
•
•
•
•
08/27/2009
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
Biology 401: Thermodynamics
p. 19 of 45
Components of entropy
Liquid propane (as surrogate):
08/27/2009
Type of Entropy
kJ (molK)-1
Translational
36.04
Rotational
23.38
Vibrational
1.05
Electronic
0
Total
60.47
Biology 401: Thermodynamics
p. 20 of 45
Real biomolecules
• Entropy is mostly translational and
•
•
•
•
08/27/2009
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
Biology 401: Thermodynamics
p. 21 of 45
Entropy in solvation: solute
• When molecules go into solution,
their entropy increases because
they’re freer to move around
08/27/2009
Biology 401: Thermodynamics
p. 22 of 45
Entropy in solvation: Solvent
• Solvent entropy usually decreases
because solvent molecules must
become more ordered around
solute
• Overall effect: often slightly
negative
08/27/2009
Biology 401: Thermodynamics
p. 23 of 45
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.
08/27/2009
Biology 401: Thermodynamics
p. 24 of 45
Apolar molecules in water
• Water molecules tend to form ordered
•
08/27/2009
structure surrounding apolar molecule
Entropy decreases because they’re so
ordered
Biology 401: Thermodynamics
p. 25 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 26 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 27 of 45
Standard free energy of
formation, DGof
• 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
08/27/2009
Biology 401: Thermodynamics
p. 28 of 45
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)
08/27/2009
Biology 401: Thermodynamics
p. 29 of 45
Spontaneity and free energy
• Thus if reaction is just spontaneous, i.e.
•
•
•
08/27/2009
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.
Biology 401: Thermodynamics
p. 30 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 31 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 32 of 45
Coupled reactions
• Often a single enzyme catalyzes 2
•
•
08/27/2009
reactions, shoving them together:
reaction 1, A  B: DGo1 < 0
reaction 2, C  D: DGo2 > 0
Coupled reaction:
A + C  B + D: DGoC = DGo1 + DGo2
If DGoC < 0,
then reaction 1 is driving reaction 2!
Biology 401: Thermodynamics
p. 33 of 45
How else can we win?
• Concentration of product may play a
•
•
08/27/2009
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
Biology 401: Thermodynamics
p. 34 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 35 of 45
Hydrolysis of ATP
• Hydrolysis at the rightmost high-energy
•
•
•
08/27/2009
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
roughly twice as much!
Biology 401: Thermodynamics
p. 36 of 45
ATP as energy currency
• 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
08/27/2009
Biology 401: Thermodynamics
p. 37 of 45
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
08/27/2009
Biology 401: Thermodynamics
p. 38 of 45
Other high-energy compounds
• Creatine phosphate: ~ $0.40
• Phosphoenolpyruvate: ~ $0.35
• So for some reactions, they’re more
efficient than ATP
08/27/2009
Biology 401: Thermodynamics
p. 39 of 45
Dependence on Concentration
• 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
08/27/2009
Biology 401: Thermodynamics
p. 40 of 45
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!
08/27/2009
Biology 401: Thermodynamics
p. 41 of 45
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 DG < 0 even if DGo > 0
08/27/2009
Biology 401: Thermodynamics
p. 42 of 45
How to solve energy problems
involving 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!
08/27/2009
Biology 401: Thermodynamics
p. 43 of 45
A bit more detail
• Suppose we couple two equations:
A + B  C + D, DGo’ = x
C + F  B + G, DGo’ = y
• The result is:
A+B+C+FB+C+D+G
or
A + F  D + G, DGo’ = x + y
• … since B and C appear on both sides
08/27/2009
Biology 401: Thermodynamics
p. 44 of 45
What do we mean by
hydrolysis?
• It simply means a reaction with water
• Typically involves cleaving a bond:
• U + H2O  V + W
is described as hydrolysis of U
to yield V and W
08/27/2009
Biology 401: Thermodynamics
p. 45 of 45