Evidence for a short-lived resonance state in enzyme catalysis via rate-equation convolution

At the cellular level, all biological function relies on enzymes to provide catalytic acceleration of essential biochemical processes driving cellular metabolism. The enzyme is presumed to lower the activation energy barrier separating reactants from products, but the precise mechanism remains unresolved. Here we examine the temperature dependence of the enzyme-catalyzed dissociation of p-nitrophenyl-α-D-glucopyranoside (pNPG), a chromogenic analog for maltose, isomaltose, and sucrose disaccharide sugars, into p-nitrophenol (pNP) and glucose (monosaccharide). The enzymes of interest are the wild type and mutant forms of glucosidase MalL produced by the probiotic bacterium Bacillus subtilis. The per-enzyme production rates k(T) for the pNPG→ glucose reaction all show a characteristic temperature profile with an Arrhenius-like (approximately exponential) slow acceleration at low temperatures, rising through a point of inflexion to reach a maximum, then turning over to decline steeply towards zero production at high temperatures. This asymmetric profile is found to be well fitted by convolving an exponential growth function f(T) with a Gaussian temperature distribution g(T) to produce an exponentially modified Gaussian function h(T). To give a physical interpretation of the convolution components, we make the temperature mapping Θ≡T_{ref}-T where T_{ref} marks the temperature at which a given mutant becomes fully denatured (unfolded) and therefore inactive, then convert the convolution components to probability density functions which obey the convolution theorem of statistics. Working in Θ space, we identify f(Θ) as the density function for an Arrhenius-like transition from ground-state A to metastable-state B, and g(Θ) as the Gaussian distribution of offset-temperature fluctuations for the metastable state. By mapping the standard thermodynamic relations for temperature and energy fluctuations to the enzyme frame of reference, we are able to derive an expression for the lifetime for the metastable B state. For the 15 enzyme experiments, we obtain a mean value 〈Δt〉≳(29.0±1.3)×10^{-15}s, in remarkably good agreement with the ∼30-fs estimate for the period of glycosidic bond oscillations extracted from published infrared spectroscopy. We suggest that the metastable B state provides a low-energy target that has the effect of lowering the activation energy barrier by presenting an alternative axis for the reaction coordinate.