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

Homework 3 (due Mo, Feb. 6):

Reading: Van Holde, Chapter 1

Van Holde Chapter 3.1 to 3.3

Van Holde Chapter 2

Van Holde Chapter 4 (cursory reading)

1. 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 25C 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 G for that state? Is it

higher or lower than the value in (a)? In which direction will the reaction proceed

(toward DHP or GP)?

2. van Holde, Problem 2.5

3. van Holde, Problem 2.7

4. Van Holde, Problem 2.8

(Solutions to odd-numbered problems are in back of book).

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, H, of the reaction. This corresponds to the sum of all the

potential energies we discussed in Introduction-2.

2. The entropy, S 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, G of the

reaction:

Introduction-3 Thermodynamics

000 STHG

Enthalpy• Why is it useful?

– The enthalpy change between the initial and final states of a

biochemical process, H, is the easily measured heat that it

generates or absorbs.

– H is a state function. H 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.

Definition: H = E +PV (is a state function)

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 H and E 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:

L

N !W

L!( N L )!

Most probable state: highest value of WL

Here: L = N/2.

BS k lnWkB … 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

EntropyIn chemical systems, the number of ways, W, of arranging a system in a

particular state is huge. Define entropy of a system:

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 S 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):

• Isothermal, reversible expansion of

gas from V1 to V2 (p. 84):

• 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

qS

T

2

1

VS nRln

V

1

2

CS nRln

C

i ii

S R n ln X

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 G for a particular process is negative, that process is

spontaneous, because it leads in the direction of

equilibrium.

H and S are equally important Energy minimization and entropy maximization play a part in determining the position of equilibrium.

000 STHG

Gibbs free energy

000 STHG

eqKRTG ln0

Gibbs free energy

The native and denatured forms of a protein are generally in equilibrium.

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 H and S for the folding reaction (assuming they are independent of T)

2. Calculate G for this protein at 25°C. Is the folding process spontaneous?

3. What is the denaturing temperature for this protein at standard conditions?

DenaturedNative

Van’t Hoff Plot

RT

STH

RT

GKeq

000

ln

Keq and G0 are temperature dependent

1/T (1/K)

ln Keq

Slope: -H/R

Enthalpy can be calculated from slope;

Then get S from van’t Hoff equation

H and S are temp-independent over small temp ranges.

Measure Keq as a function of T:

T

HS

RKeq

01ln

Van’t Hoff equation

Gibbs free energy in real life

• For real biochemical reactions we need to consider G for the object under study (e.g. protein, reaction, etc) AND G for the solvent (usually water)

• Water molecules form Hydrogen bonds (enthalpy).

• “Fixing” water molecules will “cost” decrease entropy of system (entropy).

total reactants waterG G G

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, charge-charge 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 (H-

bonds), 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 H, but a large, favorable S 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.

aqtrans.vap water

nonaq

G RT ln P , where P , mole fraction

Kyte-Doolittle Scale:They used vapor to water, others have used ethanol to water.In this equation: If Xaq > Xnonaq then G is negative – hydrophilic

If Xnonaq > Xaq then G is positive – hydrophobic

e.g. Gtransfer for val is 2.78, Gtransfer for Glu is - 8.59 (in Kcal/mole)

Kyte and Doolittle actually used combination of:

• 0.69*Gtransfer + 2.32• 48.1*(fraction 100% buried) – 4.5 • 16.45*(fraction 95% buried) – 4.71

aaaa

aa

aa aa

aa aa

aa

aa

aa

H2O

aa

aa

Non-polar

They combined these three things to get a hydropathy index that ranges from +5 (very hydrophobic) to -5 (very hydrophilic).