The enzyme-substrate complex as a cat state: A toy quantum analog

We introduce a quantum model system incorporating qualitative aspects of tunneling in enzyme action and analyze the possibilities of quantum superposition of several conformations of the enzyme-substrate complex. There is a potential barrier in each conformation which for simplicity's sake is assumed to be of zero width making the system explicitly solvable. Such a system exhibits generic features of quantum dynamics that should be present to some extent in real enzyme action. We find that depending on the parameters of the system, the rate of conversion of substrate to product can be either enhanced or suppressed in relation to the rates that can be achieved in fixed conformations. There are also solutions in which a component of the quantum state exists as a bound state, something that cannot happen in a fixed conformation. This may provide some measure of stability to the complex. Paradoxically enough, superposition of a finite barrier with an infinite barrier can also enhance the conversion of substrate to product in relation to the finite barrier alone. We suggest that binding to a superposition of conformations could be preferred in relation to binding to a fixed conformation, and analyze the conditions in living cells that could support enzyme action by conformations in superposition.