# In Silico Modeling Study of Curcumin Diffusion and Cellular Growth
###### Abstract  
Curcumin can enhance cutaneous wound healing by improving fibroblast proliferation. However, its therapeutic properties are dose-dependent: high concentrations produce cytotoxic effects, whereas low concentrations benefit cell proliferation. Similarly, the type of administration and its moderation are key aspects, as an erroneous distribution may result in null or noxious activity to the organism. In silico models for curcumin diffusion work as predictive tools for evaluating curcumin's cytotoxic effects and establishing therapeutic windows. A 2D fibroblast culture growth model was created based on a model developed by [PERSON] and [PERSON]. Similarly, a curcumin diffusion model was developed by adjusting experimental release values obtained from [PERSON] et al. and fitted to [PERSON] and [PERSON]'s hyperbolic models. The release of six key curcumin concentrations was achieved. Both models were integrated using Morpheus software, and a scratch-wound assay simulated curcumin's dose-dependent effects on wound healing. The most beneficial effect was achieved at 0.25 uM, which exhibited the lowest cell-division period, the highest confluence (~60% for both release models, 447 initial cells), and the highest final cell population. The least beneficial effect was found at 20 uM, which inhibited cell division and achieved the lowest confluence (~34.30% for both release models, 447 initial cells). Confluence was shown to decrease as curcumin concentration increased, since higher concentrations of curcumin have inhibitory and cytotoxic effects. curcumin; fibroblasts; cell proliferation; diffusion; in silico model Article  
In Silico Modeling Study of Curcumin Diffusion and Cellular Growth  
[PERSON]  
1 Department of Physics and Mathematics, Universidad de Monterrey, Av. Morones Prieto 4500, San Pedro Garza Garcia 66288, N.L., Mexico 1
an antioxidant agent, curcumin accelerates the wound-healing process by decreasing the damage caused by oxygen free radicals [10]. Thus, this molecule has been described as a possible substitute for existing commercial treatments due to its accessibility, lower cost, and lower cytotoxicity [11; 12]. However, its therapeutic properties have been demonstrated to be dose-dependent [12; 13; 14; 15]. When administered in high concentrations, it has cytotoxic effects on the cell population, reducing its viability and growth [12; 13; 14; 16]. Moreover, the administration type and its moderation are essential since the drug delivery depends on the molecule's properties [17; 18]. Curcumin exhibits low solubility, low bioavailability, and fast metabolism [19]. An erroneous distribution may lead to secondary negative effects, as the molecule reaches sites outside its therapeutic window, causing null or noxious activity to the organism [18]. Even though there are reports of curcuminoids being classified as PAINS, in silico investigations have validated their binding and activity on specific proteins (casein kinase 1 and glycogen synthase kinase 3 beta) involved in the Wnt/\(\beta\)-catenin signaling pathway [20]. Molecular docking calculates curcumin derivatives' binding affinity to epidermal growth factor receptor and nuclear factor kB (NF-kB), known as cancer target proteins [21]. In most cases, the in silico results have been exemplarily validated using in vitro assays accordingly. Computational modeling is a widely used tool in biological research for prediction purposes and to guide experimental research [22]. Variables are used in these models to describe a simplified biological system or physiological process and are modified in simulations to visualize predictions for multiple hypothetical scenarios [23]. Wound healing and cell proliferation are extensively modeled processes [23], especially in respect of their behavior or response to the presence of a key variable. For instance, the authors of [24] proposed a model of the effects of epidermal growth factor, a protein secreted by fibroblasts, on keratinocyte migration.