Initial reaction rate data for lactic dehydrogenase / pyruvate, lactic dehydrogenase / lactate and malic dehydrogenase / malate enzyme reactions were analyzed to obtain activation free energy changes of -329, -195 and -221 cal/mole, respectively, for rate increases associated with time-specific irradiation of the crystalline substrates prior to dissolution and incorporation in the reaction solutions. These energies, presumably, correspond to conformational or vibrational changes in the reactants or the activated complex. For the lactic dehydrogenase / pyruvate reaction, it is estimated that on the order of 10% of the irradiation energy (546 nm, 400 footcandles for 5 seconds) would be required to produce the observed reaction rate increase if a presumed photoproduct is consumed stoichiometrically with the pyruvate substrate. These findings are consistent with the proposition that the observed reaction rate enhancement involves photoproducts derived from oscillatory atmospheric gas reactions at the crystalline enzyme substrate surfaces rather than photo-excitations of the substrate molecules, per se.
Transition-state theory and its associated free energy of activation serve as the primary tools in conceptualization of models for enzyme catalysis mechanisms. These models are becoming increasingly elaborate, and hypothetical, as they struggle to account for the enzyme's specificity and efficiency (e.g., see Ma et al., [1]). Modeling necessarily is based on the assumption that all relevant features of the catalytic process are taken into consideration. With regard to this point, a body of experimental work referred to as the Comorosan effect may prove relevant. Here, we present an evaluation of some implications of that work from a transition-state theory perspective.
The Comorosan effect is a phenomenon in which the initial velocity of an enzymatic reaction is increased as a consequence of utilizing substrate that had been irradiated in the crystalline state, for a specific time duration, prior to dissolution and incorporation in the reaction mixture. This behavior has been observed for the reactions of over twenty enzymes isolated from multiple sources (see Table 1) and, thus, may reflect a very common, perhaps even fundamental, property of enzyme catalysis. To date, it has not been established how the relevant irradiation energy is absorbed by the crystalline material, how it is transformed on dissolution, nor how it is manifest in producing an enhanced in vitro enzymatic reaction rate. No assessment of the energetics attendant to the observed reaction rate stimulation has been reported. For overviews of much of the published work in this area, see Comorosan et al , [2,3].
Comorosan [4,5] sought to explain the phenomenon as due to photo-excitation of the irradiated crystalline enzyme substrate molecules, per se, to special “biological observable” quantum states detectable only with the extreme sensitivity of enzymes. The purpose of this theoretical investigation is to derive an estimate of the magnitude of the energy that is involved, particularly with respect to Comorosan’s model. We applied the transition-state theory of reaction rates to kinetic data published by Comorosan and coworkers for three enzyme reactions, the lactic dehydrogenase interconversions of pyruvate and lactate [6] and the malic dehydrogenase conversion of malate to αoxaloacetate [7].
In the simplest representation of transition-state theory [8] for an enzymatic reaction, one has:
where k 1 is the rate constant describing formation of the activated complex and k 2 that for its conversion to product. Formation of the transition-state complex requires a free energy of activation, ΔG*, usually illustrated as a barrier along the reaction coordinate.
The basic modeling assumption made here is that the energy absorbed and transferred from the irradiated crystals, in whatever form, serves to reduce ΔG*, thereby increasing the reaction rate. In general, this might be achieved either by raising the free energy level of the free reactants or of the Michaelis-Menten complex (if considered distinct from the transition-state complex), or by lowering that of the transition-state complex.
The rate, v, of the reaction can be expressed as:
x (rate of traversing the energy barrier) .
The rate of traversing the energy barrier is given by κK B T/h , where κ is a transmission coefficient giving the probability that formation of the complex will lead to reaction, K B is Boltzmann’s constant, T is the absolute temperature and h is Planck’s constant. The transmission coefficient usually is assumed to be unity or very nearly so, and will be taken as such here. Thus,
The equilibrium constant for the complex, K*, is given by:
From thermodynamics one has: -ΔG* = RT ln(K*) , or, correspondingly, K* = exp(-ΔG*/RT).
On the other hand, one may write:
Equating the two expressions for v gives: Of interest here is the limiting (maximal) rate of reaction, that is, the initial reaction rate, achieved when all reactants are present in excess relative to the enzyme. This is the effective rate at an instant after t = 0 and before a significant portion of any reactant can be removed or product accumulated.
In modeling the experimental data at hand, we assumed that irradiation of the crystalline substrate creates an entity, or precursor thereof, which though unidentified, we shall designate as Є. Inspection of the published reaction rate curves strongly suggest that it is consumed in the course of the reaction, the presumed product being here designated Є'.
This entity may, or may not, be identifiable with excited molecules of the substrate. In the subsequent enzyme assay, two simultaneous reactions can proceed:
(1) S + E S:E P + E and
(2) Є + S + E Є:S:E P + E + Є'
(for notational simplicity, the cofactor, NADH or NAD + , is not represented).
Here, two competing models may be envisioned. If Є corresponds simply to an excited state of the substrate, as proposed by Comorosan, then the activation energy barrier for the catalyzed reaction will be reduced as a
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