A class of exact solutions for biomacromolecule diffusion-reaction in live cells

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo.     

MNPs-IHSPN nanoparticles in multi-application with absorption of bio drugs in vitro

The aim of this project is to investigate the method of using a common buffer to determine the degree of stabilization and secretion of two drug molecules that have been analyzed in vitro. First, magnetic nanoparticles were synthesized and their structure was identified by instruments such as XPS (X-ray photoelectron spectroscopy) and FT-IR (Fourier transform infrared spectroscopy). The main purpose of this study was to investigate the stabilization and release of methotrexate on the surface of magnetic nanoparticles. The two temperatures were 37 and 25°, respectively. After reaction with the biomolecules, the adsorption rate for both drug molecules was about 60–80. PBS buffer was also used for diffusion of biomolecules and the results were analyzed by spectrophotometer analysis. With these results, the adsorption of cysteine and MTX was more than 60% and its release rate in MNPS-IHSPN was up to 90%, which means that high-strength stabilization and release by magnetic nanoparticles under external magnetic field and in vitro confirmed. The result of this project for the exchange of drugs by the surface of magnetic nanoparticles to repair damaged cells in the body of living organisms can be generalized.