1. Chap 6. Practical Methods for Kinetics and Equilibria
The basic requirement: monitoring the concentrations of reagents
Spectrophotometry
Spectrofluorimetry
Circular dichroism
Automatic titration of acid and base
Radioactive procedures
Label-free optical detection

2. 1. Spectrophotometry A: the absorbance I: the intensity of the light
Beer’s law
: the absorption coefficient
c: the concentration
l: the pathlength (in cm)
useful with chromophores
cf. NADH ( = 6.23  103 M-1cm-1 at 340 nm)
p-nitrophenolate ion ( = 1.8  104 M-1cm-1 at 340 nm)
possible errors: the breakdown of Beer’s law
- aggregation of chromophores
- high background abrobances
- too wide bandwidth of the monochromator
- turbid solutions

3. 2. Spectrofluorimetry
fluorescence: absorbing light and re-emitting it at a longer wavelength
fluorophore:
NADH (340 nm/460 nm)
tryptophan ( nm/ nm)
tyrosine (weaker than Trp, in the same region)
4-methylumbelliferone (7-hydroxy-4-
methylcoumarin)
more sensitive (100 folds) than spectrophotometry
no magnified change of the intensity
scattering light (Rayleigh or Raman scattering) by the solvent may intervene to detecting the emitted light
the compounds may decompose by photolysis

4. 2. Spectrofluorimetry (cont’d)
quenching:
- decay of an excited state by a collision with another
molecule or by a transfer of energy to another group
- useful for measuring the extent of binding
enhancing:
- increasing the intensity of fluorescence in different media or
by energy transfer
possible errors: some form of quenching
- the inadvertent addition of a substance
- concentration quenching: light absorption

5. 3. Circular Dichroism
Circular dichroism: different absorption for the right- and left-handed circularly polarized light
(cm M-1 or 103 cm2 mol-1)
: The ellipticity is defined as the angle of polarization and is measured in degrees
(deg cm2 dmol-1)

6. 3. Circular Dichroism (cont’d)
The a helix:
- a strong negative CD signal at 222 and 208 nm
a strong positive CD at 192 nm
The b sheet:
- weaker and more easily obscured
possible errors:
other chromophores absorbing
Tyr (194 and 224 nm)
His (at low pH, 222 nm)
Trp (218 and 196 nm)
the disulfide bonds (250 nm)

7. Automated spectrophotometric and spectrofluorimetric procedure
If the product can be detected by the spectroscopic methods, the spectroscopic assays are simplest and most accurate
Automated methods are less tedious, and much more reproducible and accurate
Coupled assays
using the second enzymatic reaction for the spectroscopic assay
- the formation of pyruvate: the conversion of NADH to NAD+

8. 4. Automatic Titration of Acid or Base
A hydrolytic reaction that releases acid may be followed by titration with base
possible errors: the buffering effect of dissolved CO2
pH-stat: keeping the pH of the solution to be constant by the automatic addition or base

9. 5. Radioactive Procedures
using radioactively labeled substrates: the most sensitive assay methods
necessary to separate the products from the starting materials: chromatography and high-voltage electrophoresis
possible errors:
- the emission may be quenched
- 3H transfer
- water, base, fluorescent lighting
scintillant: converting the radiation into light quanta that are registered as counts by a photomultiplier

10. 6. Label-Free Optical Detection
detecting the refractive index changes when a protein binding to the ligand
using an anchored ligand to a polymer
advantages:
- absolutely general
- specific
disadvantages:
- the heterogeneous condition causing reaction to slow

11. Plotting Kinetic Data 1. Exponentials a. single A  B, k
[B]t = [B]{1-exp(-kt)}
ln([B] - [B]t) = ln [B] - kt
b. The Gurrenheim method
when the endpoint cannot be determined
ln([B]t+t - [B]t) = constant – kt
c. Consecutive exponentials
when one of the rate constants is more than 5-10 times faster
[B] = X{exp(-k1t) - exp(-k1t)}

12. Plotting Kinetic Data (cont’d)
2. Second-order reactions
A + B  C, k2
using one of the reagents in large excess over the other: pseudo-first-order kinetics
3. Michaelis-Menten kinetics
using initial rates: the first 5% or less of the reaction
plots of Eadie or Hofstee
a good range of substrate concetrations: 8, 4, 2, 1, 0.5, 0.25, multiples of the KM

13. Determination of Protein-Ligand Dissociation Constants
Kinetics
- The KM for an enzymatic reaction is not always equal to the
dissociation constant of the enz-sub complex.
- The dissociation constants of competitive inhibitors:
2. Equilibrium dialysis
- a direct method to measure the concentrations of free and
enzyme-bound ligand
- need at least 1-2 hours for equilibrium: not suitable for
unstable ligands and enzymes
- nonequilibrium dialysis is available

14. Determination of Protein-Ligand Dissociation Constants (cont’d)
3. Equilibrium gel filtration
- the proteins moving faster than the ligands
- the proteins drag the bound ligands
- advantages: i. suitable for unstable or slightly reactive ligands
ii. some available gel for distinguishing between the size of one polymer and another
4. Ultracentrifugation
- the higher-molecular-weight complex of enzyme and the ligands sediments faster
- the best method for determining the state of oligomerization

15. Determination of Protein-Ligand Dissociation Constants (cont’d)
5. Filter assays
- Many proteins are adsorbed on nitrocellulose filters, while the free ligands are not retained
- Binding is not 100%
6. Spectroscopic methods
- not a direct measurement of the number of bound ligands
- A change of the spectroscopic signal by bound ligands is related to the fraction of the ligand-bound proteins

16. Determination of Protein-Ligand Dissociation Constants (cont’d)
7. Stoichiometric titration
- If the dissociation constant is low enough, it may be possible to determine the number of equivalents of ligand
8. Microcalorimetry
- using the heat of binding of a ligand to a protein

17. Measurement of protein concentration
using a dye such as Coomassie Blue
measuring the absorbance at 280 nm