The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion-modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non-Markovian rate equations onto Markovian ones with time-independent rate constants is not a good approximation at short times. We then developed a non-Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion-modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady-state response in a phosphorylation-dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation-dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle-based computer simulations.

DJ-1 is a homodimeric protein that is centrally involved in various human diseases including Parkinson disease (PD). DJ-1 protects against oxidative damage and mitochondrial dysfunction through a homeostatic control of reactive oxygen species (ROS). DJ-1 pathology results from a loss of function, where ROS readily oxidizes a highly conserved and functionally essential cysteine (C106). The over-oxidation of DJ-1 C106 leads to a dynamically destabilized and biologically inactivated protein. An analysis of the structural stability of DJ-1 as a function of oxidative state and temperature may provide further insights into the role the protein plays in PD progression. NMR spectroscopy, circular dichroism, analytical ultracentrifugation sedimentation equilibrium, and molecular dynamics simulations were utilized to investigate the structure and dynamics of the reduced, oxidized (C106-SO2 - ), and over-oxidized (C106-SO3 - ) forms of DJ-1 for temperatures ranging from 5°C to 37°C. The three oxidative states of DJ-1 exhibited distinct temperature-dependent structural changes. A cold-induced aggregation occurred for the three DJ-1 oxidative states by 5°C, where the over-oxidized state aggregated at significantly higher temperatures than both the oxidized and reduced forms. Only the oxidized and over-oxidized forms of DJ-1 exhibited a mix state containing both folded and partially denatured protein that likely preserved secondary structure content. The relative amount of this denatured form of DJ-1 increased as the temperature was lowered, consistent with a cold-denaturation. Notably, the cold-induced aggregation and denaturation for the DJ-1 oxidative states were completely reversible. The dramatic changes in the structural stability of DJ-1 as a function of oxidative state and temperature are relevant to its role in PD and its functional response to oxidative stress.