Peroxide-dependent enzymes often suffer from irreversible oxidative deactivation by the peroxide co-substrate. Transition metal mediated in situ generation of H2O2 offers continuous peroxide feeding in low concentration. However, free metal complexes often interact non-selectively with proteins, leading to mutual deactivation of metal catalysts and enzymes. Here, we report a spatial isolation strategy using zirconium-based metal-organic frameworks (UiO-67) to immobilize the transition metal catalytic unit [Cp*Rh(bpy)Cl]⁺. The porous MOF structure acts as a molecular sieve, excluding enzymes from the Rh sites on the framework, thus protecting both catalysts from mutual deactivation. The Rh modified UiO-67 (Rh@UiO-67) catalyzes the flavin-mediated electron transfer from formate to oxygen, generating H2O2 in a formate oxidase mimicking fashion. Its protein compatibility allows Rh@UiO-67 to fuel peroxyzymes for stable oxyfunctionalization. Compared to natural formate oxidase, this system also shows high stability to various pH and temperatures, enabling its application in versatile conditions.

Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this problematic convergence behaviour using a Cramér Rao Lower Bound (CRLB) analysis. An analytical expression for the CRLB diverges for spatial frequency components that approach the diffraction limit from below. The resulting mean noise variance per pixel diverges for large images. These results imply that a regular optimum of the likelihood does not exist, and that RL deconvolution is necessarily ill-convergent.

Richardson-Lucy deconvolution can offer an increase in contrast, but converges poorly, and is sensitive to noise. We show that the Cramér Rao Lower Bound (CRLB) diverges, which explains the problematic behaviour.