# (6da) Modelling and Optimal Control of Non-Viral siRNA Delivery

Authors:
University College London
University College London

Gene therapy gives great new hope to the patients with life-threatening diseases such as cancer and HIV (Al-Dosari and Gao, 2009). This approach can be defined as the insertion of genetic materials including RNA and DNA into selected cells in the body for obtaining a therapeutic effect by inhibiting gene expression associated with the pathogenesis, or correcting a genetic defect so as to obtain normal gene expression (Parra-Guillen et al., 2010). Vehicles used for gene delivery to transfer the genetic information into a cell are called vectors, which could be divided into two main groups: viral and non-viral (Liu and Huang, 2002). A successful approach depends on the effectiveness and safety of the delivery of therapeutic genetic materials (Wang et al., 2013). Thus, knowledge of the effects (pharmacodynamics) and kinetics (pharmacokinetics) of therapeutic agents in the body is critical (Urso et al., 2002).

In the current work, mathematical and computational modeling is used for analysis, optimisation and control of gene delivery. A pharmacokinetic model was developed using the experimental data reported in the literature to describe the transport of genetic material between the various compartments. The model development involves estimating the rate constants of siRNA translocation over the intracellular barriers. Parameter estimation is one of the important steps for developing high-fidelity mathematical models. This is based on minimizing an objective function (the error function) given by the summed square of the difference between the experimental data and the model predictions. Techniques that are used for solving the parameter estimation problems are chosen based on the model types of the system. The focus of this study is on systems involving ordinary differential equations (ODEs). The parameter estimation methodology is based on a simultaneous algorithm in which the solution of the model equations is the part of the overall optimisation problem. The dynamic model equations are converted into a system of algebraic equations using an Artificial Neural Network (ANN) transformation (Dua and Dua, 2012).

Then, the estimated rate constants of siRNA translocation are used to simulate the intracellular pharmacokinetic profile of siRNA delivery by non-viral nano-carrier (NC) to represent the intracellular endosome and cytoplasm exposure of siRNA. Following that, the developed models are used to obtain optimal gene infusion rates. The current work includes developing a pharmacodynamic model and providing a balance between two main and conflicting objectives: high efficacy and low toxicity. So, a mathematical formulation for optimal control of siRNA delivery was developed. Various practical constraints are also incorporated for the gene delivery problems. One of the important and practical constraints is on the time to take into account the cell multiplication so that the effect is manifested before the cell division takes place. Thus, a mathematical modeling and control framework to incorporate the time constraints for cell division has been developed.

References

AL-DOSARI, M. S. & GAO, X. 2009. Nonviral Gene Delivery: Principle, Limitations, and Recent Progress. AAPS Journal, 11, 671-681.

DUA, V. & DUA, P. 2012. A Simultaneous Approach for Parameter Estimation of a System of Ordinary Differential Equations, Using Artificial Neural Network Approximation. Industrial & Engineering Chemistry Research, 51, 1809-1814.

LIU, F. & HUANG, L. 2002. Development of non-viral vectors for systemic gene delivery. Journal of Controlled Release, 78, 259-266.

PARRA-GUILLEN, Z. P., GONZALEZ-ASEGUINOLAZA, G., BERRAONDO, P. & TROCONIZ, I. F. 2010. Gene Therapy: A Pharmacokinetic/Pharmacodynamic Modelling Overview. Pharmaceutical Research, 27, 1487-1497.

URSO, R., BLARDI, P. & GIORGI, G. 2002. A short introduction to pharmacokinetics. Eur Rev Med Pharmacol Sci, 6, 33-44.

WANG, W. W., LI, W. Z., MA, N. & STEINHOFF, G. 2013. Non-Viral Gene Delivery Methods. Current Pharmaceutical Biotechnology, 14, 46-60.