Application of the Second Rule of Transient-State Kinetic Isotope Effects to an Enzymatic Mechanism

Abstract

The transient-state kinetic approach reveals the formation and subsequent interconversions of intermediates in real-time. Its potential for the mechanistic resolution of enzymatic and other complex chemical mechanisms has been severely limited however by the lack of a rigorous and applicable theoretical basis in contrast to that of the less direct but soundly based algebraic algorithms of the steady-state approach. Having recently established three rigorously derived fundamental Rules of transient-state kinetics applicable to realistic multiple step reactions, we present here the successful application of the very counter-intuitive Second Rule to the resolution of the mechanism of the L-phenylalanine dehydrogenase catalyzed reaction.The steady-state kinetic approach has provided the overwhelming portion of what we now know about the mechanisms of enzymatic catalysis. While any such experiment provides only a single pair of parameters (V and V/K m ), their interpretation rests on a large body of rigorously derived algebraic formulations. Variation of pH, reactant and product concentrations, and kinetic isotope effects (KIEs) combined with X-ray crystallographic structures have produced many detailed mechanisms interpretable in terms of physical organic chemical theory(1). Yet, we are still a very long way from a thorough understanding of the phenomenon of enzymatic catalysis.In contrast to the steady-state approach, transient state kinetic experiments typically provide a wide variety of optical phenomena tracking the formation and interconversions of enzyme bound-intermediates in real time. The effectiveness of the transient (pre-steady state) approach, however, has been severely limited by the lack of a coherent body of rigorous analytical theorems applicable to the results of transient-state (stopped-flow) experimental data (2). The necessity of interpreting our experimental results has led us to develop such a theory.Kinetic isotope effects (KIEs) are an important tool for the steady-state kineticist (3). By definition, a steady state KIE is defined as a single value at zero-time. In contrast, transientstate KIEs (tKIEs) are strongly time dependent and may be presumed to contain significantly more extensive mechanistic information. To our knowledge, no analytic theory applicable to realistic enzyme mechanisms for tKIEs existed prior to this report. Experimental and theoretical developments described here have now provided a solid basis for the development of such a body of theory. † Transient State KineticsThe transient state absorbance versus wavelength and time array was obtained using an Applied Photophysics SX-18MV stopped flow apparatus by assembling a series of side-byside single-wavelength time traces, in which a solution containing enzyme and h-or d-L-Phe in one syringe is mixed with a solution containing enzyme and NAD in the other. The spectra were collected at 1 nm and 0.05 ms intervals. An individual experiment such as that portrayed in Figure 3a takes approximately 20 min to produce an ...

The Application of Transient-State Kinetic Isotope Effects to the Resolution of Mechanisms of Enzyme-Catalyzed Reactions

“…The deconvolution of an individual "time slice" of this array into specific components is shown in Figure 5b. Application of the First and Second rules to that data are shown in Figures 5-7 (from reference [10]). Figure 3 where C and D follow the sum of the red and blue components respectively.…”

“…Red-shifted components are indicated by diamond shaped symbols and blue-shifted components by circles. Open symbols denote h-substituted components; closed symbols indicate d-substituted components [10].…”

“…The application of these rules to the phenylalanine dehydrogenase catalyzed reaction [10] represents the first model-independent, assumption free and multi-step applicable approach to the mechanistic resolution of transient-state enzyme kinetic data. As such, it represents the current state of the art.…”