Logarithmic diffusion and porous media equations: a unified description

Understanding Diffusion in a Single-Metal Organic Framework Crystal Used for Sensing Applications

Metal-organic frameworks (MOFs) stand out as remarkable materials renowned for their exceptionally high surface area and large number of pores, making them invaluable for diverse sensing applications including gas, biomedical, chemical, and optical sensing. Traditional methods of molecule infusion and release often involve a large number of crystals with varying shapes and sizes, leading to averaged outcomes across a heterogeneous crystal population. In this study, we present continuous monitoring of the infusion and release dynamics of model drug molecules, specifically vitamin B12, within individual Tb-mesoMOF crystals. Our findings underscore the critical influence of crystal size and shape on the infusion and diffusion processes and corresponding color change, underscoring the necessity to account for these factors in the design of large-scale systems. Leveraging optical microscopy, we employed a histogram-based algorithm for image processing, enabling automated tracking of diffusion phenomena. This investigation offers crucial insights into the dynamics of these processes, laying the groundwork for optimizing parameters in future sensing systems.

Approximate analytical time-dependent solutions to describe large-amplitude local calcium transients in the presence of buffers

Local Ca(2+) signaling controls many neuronal functions, which is often achieved through spatial localization of Ca(2+) signals. These nanodomains are formed due to combined effects of Ca(2+) diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca(2+) diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca(2+) levels up to 50 microM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca(2+)] transients, which participate in various physiological processes.