Frank Anthony Ferrone

Given a set of kinetic data, then, the preceding discussions suggest the following approach to its analysis. 1.1. For purposes of establishing the reaction, ignore the final stages and concentrate on the initial 10–20% of the reaction at first. A globally optimized model may be based on a faulty assumption for the initial steps. Thus, although the whole data set may look reasonably well fit, the reaction could be misrepresented, and thus the fit unhelpful if accuracy at the later stages has come at the expense of the initial phase of the reaction.2.2. What is the time course of the initial reaction? (A) Is the reaction exponential? Exponential growth gives dramatic lag times (see Fig. 3), whereas nonexponential “lag times” have a visible signal from time 0 (i.e., Fig. 2). If the data set shows the abrupt appearance of signals after a period of quiescence, the chances are excellent that the time course is exponential. High sensitivity measurement of the signal at times during the lag phase should be used to confirm the exponential nature quantitatively. Exponential reactions mean a secondary pathway is operative. (a) A cascade (tn) can look similar to an exponential, but may proceed from a multistep single-path reaction. Thus the exponential needs to be ascertained with some accuracy. (b) It is possible that some or all of the lag results from a stochastic process, i.e., formation of a single nucleus being observed. This, however, is likely to be accompanied by a secondary process, as few techniques are sensitive enough to detect a single polymer at a time, and having one nucleus form many polymers is a hallmark of a secondary process. Thus, the reproducibility of the kinetics must be established to rule out stochastics. If data show wide variation, stochastic methods as described earlier may be employed. (c) Given a secondary process, one must separate the primary nucleation process from the secondary process (by stochastic means or by use of the product B2A, as described earlier). (B) If the reaction does not begin with an exponential, is it parabolic? If so, it falls in the general class of linear polymerizations.3.3. What is the concentration dependence of the reaction(s)? This will separate nucleation processes from growth, and so on.4.4. If the initial reaction is neither exponential nor parabolic, a reaction mechanism needs to be proposed and evaluated. Solving the resulting equations is best done by linearization, which has the best chance of giving equations whose solutions and their sensitivity to parameters are readily understood. If this proves fruitful, full numeric solutions may be useful.5.5. At this point, the full reaction may be considered to completion.6.6. The physical basis of the description (sizes of parameters and their dependencies) needs to be finally considered to ensure that the mathematical success of the description rests on tenable physical grounds.

This chapter focuses on the modulated excitement spectroscopy in hemoglobin (Hb). Modulated excitation is a kinetic perturbation method that uses frequency-domain techniques to observe small relaxations that may be partially masked by larger amplitude processes of lesser interest. Because it is basically a repetitive technique, it has found use thus far in reversible photolysis reactions, and there it has been used to study conformational change in Hb. This chapter also discusses the pulse methods to set the scope of the kinetic problems that are addressed by modulated excitation. Modulated excitation uses a beam that is repeatedly turned on and off, with observation of the accompanying optical changes. In this sense it is a means of performing the necessary averaging. Stability is assured by modulating a constant light output, rather than requiring pulse-to-pulse repetition. However, an unexpected bonus appears in the ability to adjust the phase of the detection system.

The thermodynamics of gelation of hemoglobin S partially saturated with oxygen have been investigated. The total concentration (solubility) and fractional saturation of the solution phase in equilibrium with polymerized hemoglobin was determined by near-infrared spectrophotometry after sedimentation of the polymers. The fractional saturation of the aligned polymer phase was determined from linear dichroism measurements. Using this data and the two-phase model for the gel, we calculate gel binding curves which agree well with those recently reported by Gill et al. (J. Mol. Biol. 130:175, 1979) confirming the validity of the two-phase model. The polymer binding curve is noncooperative and can be explained by an allosteric model in which no R-state molecules polymerize, and T-state molecules are excluded from the polymer by about 600 calories/mole for each molecule of oxygen bound.