Range-finding initial

If an approximate Km value for the enzyme-substrate combination of interest is known, a full-scale kinetic assay may be done immediately. However, often an approximate value is not known and it is necessary first to do a range finding or suck and see preliminary assay. For such an assay, a concentrated substrate solution is prepared and tenfold serial dilutions of the substrate are made so that a range of substrate concentrations is available within which the experimenter is confident the Km value lies. Initial velocities are determined at each substrate concentration, and data may he plotted either hyperholically (as V versus [S]) or with [S] values expressed as logio values. In the latter case, a sigmoidal curve is fitted to data with a three parameter logistic equation (O Eq. 4) ... 

Figure C4.1.3 Range-finding and the effect of enzyme concentration on the time course of a reaction. The dotted lines show the true initial rate. Only assay C will be reliable if a fixed-time assay is used.

In accord with the findings of several other groups including Appell, et al. (7), the conversions were found to be base promoted. The present study included a range of initial pH values, and focused on a comparison of the results in H20 with those from a substitution in parallel experiments of D20. 

In initial range-finding experiments, it is often practical to do one-factor-at-a-time experiments (4), followed by factorial screening designs using many factors (4,7), each at two levels. As we are interested in the properties of the concentration-response curve (particularly the difference between the asymptotes, the steepness of the responsive region, and the variation around the curve), it is important to quickly move to study the full curve. For cell-culture assays performed in 96-well plates, an effective approach is to assign... 

Determination of the activity coefficients of the non-volatile solute in a solution is difficult. If electrolytes (ions) are present, the activities can be obtained from experimental electromotive force (EMF) measurements. However, for non-electrolyte and non-volatile solutes an indirect method is applied to find initially the activity of the solvent over a range of solute concentrations, and then the Gibbs-Duhem equation is integrated to find the solute activity. If the solution is saturated, then it is easy to calculate the activity coefficient... 

These range-finding results and data from the literature can be used to provide the initial target assay range. For example, erythropoietin concentrations in nonsmokers, smokers, and cancer patients are shown in Table 6.2. The concentrations, 9.2, 15.2, and 21.9mU/mL for nonsmokers (A =25), smokers (N = 14), and cancer patients (N= 10), respectively, illustrate the need for establishing normal ranges in a target population. 

As we showed in Section III the available criteria which guarantee asymptotic stability in the large of solutions of Eqs. (1) or Eq. (18) are fairly restrictive. One is therefore motivated to consider somewhat weaker requirements, for example, under what hypothesis on K i) does it follow that the solutions of Eqs. (1) are bounded on 0 < t < oo, but not necessarily such that they tend to constant equilibrium values as f-> 00. Or one might try to find realistic and applicable criteria which, if satisfied, would imply asymptotic stability of solutions of Eqs. (1) for a finite range of initial values. Presumably these assumptions would be weaker than those implying asymptotic stability in the large and easier to satisfy in practice. 

---