A few organizational items
• Tentative topic for research project (paper) is due Feb. 1 (this week,
okay)
• Outline of research project is due March 9 (before spring break)
• We are going to have a pizza & movie night, when would be a good
date/time?
• We’ll put books on reserve.
• Graduate students: Please remember presentation, choose own paper,
or paper from paper list on web site
Introduction-3
Thermodynamics
Homework 3
1.
(due Mo, Feb. 6):
2.
3.
4.
Consider the isomerization reaction of Dihydroxyacetone phosphate (DHP) to
Glyceraldehyde 3-phosphate (GP) which occurs in glycolysis. At equilibrium the
ratio of GP to DHP is 0.0475 at 25C and pH 7 (standard conditions). (a) What is
the standard free energy change for this reaction? (b) If the initial concentration
of DHP is 2 x 10-4 M and that of GP is 3 x 10-6 M, what is DG for that state? Is it
higher or lower than the value in (a)? In which direction will the reaction proceed
(toward DHP or GP)?
van Holde, Problem 2.5
van Holde, Problem 2.7
Van Holde, Problem 2.8
(Solutions to odd-numbered problems are in back of book).
Reading:
Van Holde, Chapter 1
Van Holde Chapter 3.1 to 3.3
Van Holde Chapter 2
Van Holde Chapter 4 (cursory reading)
Paper list (for presentations) is posted on web site
Introduction-3
Thermodynamics
•
In this section, we are asking, in which direction will a biochemical
reaction proceed?.
•
This will depend on two quantities:
1. The enthalpy, DH, of the reaction. This corresponds to the sum of all the
potential energies we discussed in Introduction-2.
2. The entropy, DS of the reaction. This relates to the number of ways the
system can adopt.
•
In other words, it will depend on the Gibbs’ free energy, DG of the
reaction:
DG  DH  TDS
0
0
0
Enthalpy
Definition: H = E +PV (is a state function)
• Why is it useful?
– The enthalpy change between the initial and final states of a
biochemical process, DH, is the easily measured heat that it
generates or absorbs.
– H is a state function. DH of a reaction only depends on initial
state and final state of reaction; it does not matter what goes on
between.
Example: Measuring enthalpy of oxidation of glucose to CO2 and H2O directly in muscles
would be very difficult. But, since enthalpy is a state function, we can measure the
enthalpy of this reaction in any apparatus (e.g. a constant pressure calorimeter) and
get the same result. We don’t even need to know the reaction mechanism, as long as
we know the beginning and end state.
Most biochemical processes occur in liquids or solids (rather than gases), so volume
changes are small. To a good approximation, we can often neglect the difference between
DH and DE in biochemistry and simply talk about the change in ‘energy’ accompanying a
reaction. This is the potential energy we discussed in Introduction-2.
Entropy
• Still, the enthalpy alone cannot tell us if a reaction occurs
spontaneously (by itself).
• Two examples:
–
When two blocks are brought in contact, heat flows from the hot one to the cold one, never
vice versa (‘reaction’ occurs, but enthalpy of system stays the same).
–
Two bulbs of equal volume connected by a stopcock. All molecules are on one side first;
when the stopcock is opened, molecules diffuse back and forth, until they are equally
distributed (‘reaction’ occurs, but enthalpy of system stays the same).
Total number of states: 2N.
The number of ways W of putting L of the N molecules
into the right bulb is:
N!
WL 
L!( N  L )!
Most probable state: highest value of WL
Here: L = N/2.
Entropy
In chemical systems, the number of ways, W, of arranging a system in a
particular state is huge. Define entropy of a system:
S  kB lnW
kB … Boltzmann constant
kB = 1.38*10-23 J/K
S is function of state
For gas bulb example (previous slide):
Entropy of the system is S = kB*lnW = kB*ln2N = kB*Nln2
Entropy of all molecules on one side: WN = 1  S=0.
Entropy of having N/2 molecules in each bulb is largest.
The laws of random change cause any system of reasonable size to
spontaneously adopt its most probable arrangement, the one in which
entropy is a maximum, simply because it is so overwhelmingly
probable.
Once the most probable state has been reached, the system
stays there (macroscopically) and is said to have reached
equlibrium.
(Here: Assume all states have same energy)
Boltzmann’s grave, Vienna
Example:
A certain 100 amino-acid long polypeptide chain has only one alpha-helical
conformation but there are three possible orientations for each residue in the
random-coil state.
1. Calcuate DS for the conformational change
Random coil  alpha helix.
2. Does the entropy increase or decrease for this transition?
Examples of entropy
•
Quasi-reversible heat transfer (const
Temp):
q
DS 
T
•
Isothermal, reversible expansion of
gas from V1 to V2 (p. 84):
 V2 
DS  nR ln  
 V1 
•
Isothermal dilution of a solute from
concentration C1 to C2 (p. 85):
•
Entropy of mixing (p. 86):
Xi mole fraction of species i
n… number of moles of species i
 C1 
DS  nR ln  
 C2 
DS  R ni ln  X i 
i
Systems at constant temperature and pressure
(most biochemical systems)
• Define Gibbs free energy: G = H – TS
– Then dG = VdP – SdT
– For const. P & const. T systems (dP = dT = 0):
–  dG = 0.
What does this mean?
G must be an extremum (minimum) for
such a system to be at equilibrium!!
Gibbs free energy
• Is of enormous importance in deciding the direction
processes & equilibrium positions in biochemical
systems
• If DG for a particular process is negative, that process is
spontaneous, because it leads in the direction of
equilibrium.
DG  DH  TDS
0
0
0
DH and DS are equally important  Energy
minimization and entropy maximization play a part in
determining the position of equilibrium.
Gibbs free energy
DG  DH  TDS
0
0
0
DG   RT ln Keq
0
Gibbs free energy
The native and denatured forms of a protein are generally in equilibrium.
Native


Denatured
For a certain protein, (total conc 2.0 * 10-3 M) the concentration of the denatured
and native forms at 50°C and 100°C is given in the table.
Temp
Denatured (M)
Native (M)
50
5.1*10-6
2.0*10-3
100
2.8*10-4
1.7*10-3
1. Determine DH and DS for the folding reaction (assuming they are
independent of T)
2. Calculate DG for this protein at 25°C. Is the folding process spontaneous?
3. What is the denaturing temperature for this protein at standard conditions?
Van’t Hoff Plot
DG 0
DH 0  TDS 0
ln Keq  

RT
RT
ln K eq 
1  0 DH 
 DS 

R
T 
Van’t Hoff equation
Keq and DG0 are temperature dependent
Enthalpy can be
calculated from slope;
Measure Keq as a function of T:
ln Keq
Then get DS from van’t
Hoff equation
Slope: -DH/R
DH and DS are tempindependent over small temp
ranges.
1/T (1/K)
Gibbs free energy in real life
• For real biochemical reactions we need to
consider DG for the object under study
(e.g. protein, reaction, etc) AND DG for the
solvent (usually water)
• Water molecules form Hydrogen bonds
(enthalpy).
• “Fixing” water molecules will “cost”
decrease entropy of system (entropy).
DGtotal  DGreactants  DGwater
Application of Gibbs free energy to
protein and DNA stability
• Need to consider enthalpy part of protein/DNA. These are the potential
energies we discussed. Bonding potential, Hydrogen bonds, chargecharge interactions, dipole-dipole interactions, van-der-Waals, etc.
• Need to consider entropy part of protein/DNA. Folded protein has one
conformation (low entropy) and unfolded protein has many
conformations (high entropy).
• Need to consider enthalpy of water. Water forms many H-bonds.
• Need to consider entropy of water.
• Need to consider enthalpy of ions in solution (charge-charge
interactions)
• Need to consider entropy of ions in solution (binding (fixing) will lower
entropy).
Hydrophobic effect
• Perhaps most important contribution to
protein folding.
• Hydrophobic (non-polar) substances don’t
want to “touch” water.
–  hydrophobic residues are on protein inside
–  bases are on DNA inside (base-pairing (Hbonds), don’t contribute much)
Hydrophobic effect
It is an entropy effect:
Transfer of hydrophobic residues
from water to non-polar solvent
(e.g. benzene)
Often a small DH, but a large,
favorable DS component.
Why?
 Sticking a hydrophobic
substance into water, makes
the water form a fixed cavity
around the substance  This
“costs” (decreases) the entropy
of the water.
Hydrophobicity determines placement of amino acid in protein (related to protein
folding). In aqueous environment, hydrophobic residues hide inside; (this is reversed
in the membrane). Hydropathy – feeling about water; hydrophilic – likes water;
hydrophobic – does not like water.
DGtrans.vap  water
 aq
  RT  ln  P  , where P 
,   mole fraction
 nonaq
Kyte-Doolittle Scale:
They used vapor to water, others have used ethanol to water.
In this equation:
If Xaq > Xnonaq then DG is negative – hydrophilic
If Xnonaq > Xaq then DG is positive – hydrophobic
e.g. DGtransfer for val is 2.78, DGtransfer for Glu is - 8.59 (in Kcal/mole)
Non-polar
aa
aa
Kyte and Doolittle actually used combination of:
1.
2.
3.
0.69*DGtransfer + 2.32
48.1*(fraction 100% buried) – 4.5
16.45*(fraction 95% buried) – 4.71
They combined these three things to get a hydropathy index
that ranges from +5 (very hydrophobic) to -5 (very hydrophilic).
aa
aa
aa
aa
aa
aa
aa
aa
H2O
aa
aa