Equilibria & Kinetics In Analysis

Relevance to Biochemical Analysis

Significant in:

(A) chemical conversions being used for biochemical analysis (refer Sections 1.3-1.4)
(B) distribution between phases in heterogeneous systems, eg chromatography, osmometry.

Will consider only (A)
ie application to chemical conversion analysis

Endpoint Assays and Rate Assays

                              
Endpoint (or terminal) assay:
Allow reaction to proceed until no further conversion. Measure total concentration change from beginning to end ie increase (Dc) in product concentration, or decrease (Dc') in analyte concentration.
Dc = Dc' = initial concn. of analyte.

Rate (or kinetic assay):
Measure concentration of analyte or product in initial stages only of the reaction (usually <5 mins.) Determine INITIAL RATE (= SLOPE of the line as close as possible to start of reaction).

Measurement and Interpretation of Rate

Automated instrument may make readings at two set times, say 1 min and 5 mins after initiating reaction.
Computes the rate between these two times

TWO DISTINCT AND DIFFERENT PURPOSES OF RATE MEASUREMENT

(i) ENZYME ASSAY

in contrast to

(ii) SUBSTRATE ASSAY using an enzyme reaction.

(i) ENZYME ASSAY

Aim is to determine concentration of active enzyme, making use of the fact that rates of enzyme-catalysed reactions are proportional to the concentration of active enzyme.

Require rate measurement not sensitive substrate concentration .

So need [substrate] >>K_m. Then kinetics are zero order with respect to substrate as rate approaches V_max (Region 1 in Figure below).

(ii) SUBSTRATE ASSAY

Aim is to determine concentration of substrate by choosing conditions where rate is proportional to substrate concentration (ie 1st order). So need [substrate] << K_m (Region 2 in Figure above).

Conditions for Successful Endpoint (Terminal) Assay

Generally requires that at least 99% conversion of analyte to product occurs before the reaction stops (reaches equilibrium).

Possibility of >= 99% conversion is favoured by:

1. A high equilibrium constant (K) for the conversion reaction, and
2. Being able to use large excess of reagent for the chemical conversion of analyte.

Examples will be given in tutorial time.

"Tricks of the Trade"

Sometimes when the equilibrium constant is too small, a trapping reaction is used to drive a reaction beyond the 99% level and thereby allow endpoint assay.

eg   Assay of serum lactate using lactate dehydrogenase (LD)

K = 2.3 x 10^-5 at pH 7, too small to allow 99% conversion.

Add SEMICARBAZIDE or HYDRAZINE to reaction mixture - form a stable complex with pyruvate, ie "trapping" the pyruvate so its concentration drops almost to zero, and reaction driven forward. Measure increase in A₃₄₀ due to NADH.
In other cases, if reaction involves H⁺, adjust pH to promote progress of reaction beyond 99%. Might choose pH away from enzyme's optimum and sacrifice some speed of reaction to allow favourable equilibrium.

Conditions for Successful Rate (Kinetic) Assay
Rate measure for enzyme assay:

More straightforward because use of high [substrate] and approx zero order conditions, so rate doesn't change much as substrate is consumed. Linear progress of reaction makes it easy to measure rate (though complications include reverse reaction, product inhibition)

Rate measure for substrate assay:

More difficult because

1. Requirement for [substrate] << K_m means low initial concentrations of substrate must be used - places great demands on the sensitivity of the detection method.
2. Depletion of substrate by reaction --> decrease in rate (because on 1st order part of Michaelis-Menten curve). So only a small amount of reaction can be allowed to occur in order to approximate to the initial rate - accentuates problem of sensitivity of detection.
3. Rates of enzyme reactions are very sensitive to pH, activators, inhibitors, temperature. Care needed to control these variables in all standards and samples.

To overcome (i) and (ii), enzyme-substrate cycling using a coupled enzyme system can sometimes be applied (Holme & Peck 2E pp 305-307, 3E pp 299-301).

Why Use a Rate Assay for Substrate in Preference to Endpoint Assay?

* Faster (avoid waiting for reaction completion)
* No requirement for >= 99% conversion. Need only sufficient conversion over first few minutes to make initial rate measurement.