ORIGINAL RESEARCH

Towards a computational prediction for the tumor selective accumulation of paramagnetic nanoparticles in retinoblastoma cells

Johansen RJ1,2, Bukhvostov AA3, Ermakov KV3, Kuznetsov DA2,3
About authors

1 Department of Mathematics and Computer Science, University of Southern Denmark, Odense, DK-5230, Denmark

2 N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow

3 Department of Medical Nanobiotechnologies,
Pirogov Russian National Research Medical University, Moscow

Correspondence should be addressed: Dmitry A. Kuznetsov
Ostrovityanova 1, Moscow, 117997; ur.liam@onanzuk

About paper

Acknowledgments: this work was performed due to an exceptional technical assistance kindly provided by Erasmus-Plus DK06811/2020 Program associates affiliated with the Southern Denmark University at Odense, Denmark, and, most specifically, by Ms. Patricia Wladycziewski, SDU Erasmus chief supervising officer.

Received: 2018-06-27 Accepted: 2018-08-18 Published online: 2018-12-30
|
Fig. 1. Structure of PMC16 (cyclohexyl(C60)porphyrin), Me2+ — carrying and releasing nanoparticles with the marked membranotropic/amphiphilic properties [1]
Fig. 2. The NP uptake selectivity prediction in a complete accessibility of intracellular ligands. P — [NP] uptaken, units per cell; P0 — intracellular initial concentration of NP-ligands; KS — Gompertz equation vectoral K; K1 — an NP uptake steady state constant; K2 — an efficient constant of saturation of a cellular ligand pool at [NP] → 0.5 Pmax
Fig. 3. Probabilistic model for NPs distribution between RB and the neighboring RT cells as a function of the discriminative cell cycle turnover. Z-elimination coefficient for malignant and the RB-surrounding normal cells (RT) estimated for the drug efficiency duration time (σ) and the drug-free cell functioning time interval (ω). σ is normally distributed within a variation range of σ = σ/10, where remain constant while the inner rate of the “newborn” cell appearance is λ = 2, for a starting population size x(0) = 5
Table 1. Population turnover in Y79 and WERI-RB-1 cell lines