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

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

2. Spectrofluorimetry fluorescence: absorbing light and re-emitting it at a longer wavelength fluorophore: NADH (340 nm/460 nm) tryptophan (275-295 nm/330-340 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

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

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)

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)

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+

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

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

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

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)}

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, 0.125 multiples of the KM

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

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

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

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

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