Curcumin Hydrogel Diffusion Model and PQQGDH Visualization
Secondly, it is important to note that the maximum concentration that enters the bloodstream is dependent on the distance the curcumin must travel. This is defined as the total thickness of skin the particles must travel, and we consider open air, which can exist the deepness of a wound, as negligible distance for curcumin since there is no resistance. Alternatively, this may be useful for age differences or special conditions, which may alter the thickness of skin and thus if there wasn’t a wound, this mode could still apply.
With these two assumptions in mind, we used MATLAB’s pdepe function to numerically solve Fick’s law with the above assumptions/conditions and represent the information in three different ways: a 3D graph, a heat map, and a phase map. With this model we were able to determine concentration of curcumin in the bloodstream at various times and distances between the hydrogel and blood vessel. It is indeed true that the greater the depth of skin (which means small wound) has a small curcumin concentration. On the other hand, the deeper the wound (less depth of skin that curcumin has to travel), the larger the blood-curcumin concentration. This is ideally what we want since smaller wounds like have a lower amount of or chance for P. aeruginosa infection, so conserve curcumin, the hydrogel should release less curcumin, represented by a lower blood-curcumin concentration.
Fick's Law
References
[1] Bader RA, Herzog KT, Kao WJ. A study of diffusion in poly(ethyleneglycol)-gelatin based semi-interpenetrating networks for use in wound healing. Polym Bull (Berl). 2009 Mar 1;62(3):10.1007/s00289-008-0023-x. doi: 10.1007/s00289-008-0023-x. PMID: 24311827; PMCID: PMC3848884.
[2] Using PDEPE for Ficks second law ? - MATLAB Answers - MATLAB Central [Internet]. [cited 2023 Oct 11]. Available from: link
Animation of the PQQGDH active site
Model of curcumin concentration dependent on time and depth of blood vessels based on Fick’s law. Individuals with thick skin (adults vs children) will have deeper blood vessels, and thus their concentration of curcumin over time will be less than that of less thick skin. In application to wounds, the deeper the wound (meaning less epithelial tissue), the faster curcumin will diffuse into the bloodstream.
Boundary curves of PDE numerical solution. The plot condenses figure 2 into distinct regions with boundaries that may help in approximating the curcumin concentration based on the two independent variables. While other confounding variables may affect the true concentration, placing boundary curves provides ranges that the true concentration is expected to be in.
Heat map of curcumin concentration data. Using the same PDE solution, the total concentration of curcumin in blood was numerically determined at multiple points plotted in two dimensions, resulting in the above heat map.
Water soluble pyrroloquinoline quinone glucose dehydrogenase (PQQGDH) derived from A.calcoaceticus is a homodimer. Subunits labeled cyan and green, Ca2+ ions grey, PQQ yellow, and glucose orange-pink. Waters modeled as a ball and stick.
Structure can be found from here.
Close-up model of PQQ co-factor bound to GDH
Binding of PQQ and Glucose in the active site, with and without the protein backbone. Protein main chain atoms are dark purple, with nitrogens being blue and oxygens being red. Active site residues are pink. Ca2+ is modeled as grey orb, PQQ is lavender, and glucose is orange-pink. Waters are represented in stick model format. Dashed lines represent polar contacts (mostly hydrogen bonds).