Modeling overview

Pharmacokinetic modeling

A pharmacokinetic model was built to simulate drug distribution troughout body tissues. We used physiologically based design to construct a mathematical model and predict drug kinetics. Several models were built to compare standard therapies with localized therapeutical cells.

Calculations show that localized drug production accounts for better concentration ratios between target and non-target tissues and also maintains steady concentration levels through time. This has a potential to avoid many of the side effects with common therapies. In addition, with this therapy, drug concentration does not fluctuate as in standard therapy. Peaks in concentration contribute to side-effects while decreases in concentrations cause lower therapeutical effectiveness. Results suggest this prospective treatment provides a more efficient and safe alternative.

Deterministic and stochastic modeling

We modeled the mutual repressor switch and the positive feedback loop switch using deterministic and stochastic modeling approach. The deterministic model was based on the probabilistic interpretation of gene regulation and formalized as a set of ordinary differential equations. For each promoter, the probability of it being in an active state (i.e. a state leading to gene expression) was formulated mathematically, considering transcription factors bound to the corresponding binding sites. In this way, binding of an activator would result in activation of transcription from the minimal promoter, while binding of a repressor would result in an inactive promoter. Stochastic models were formulated as a set of reactions describing the dynamics of a switch and simulated using stochastic simulation algorithm.

Quantitative modeling

A quantitative model of switch dynamics extracted simulation parameters from the available experimental data of gene regulation and results obtained from our experiments using TAL regulators. This model also predicted that the positive feedback loop switch exhibits bistability without cooperative DNA binding.

C#Sim - a new object oriented hybrid modeling algorithm

We developed a new modeling algorithm, called C#Sim. This algorithm enabled us:

• to explicitly model transcription factor binding, especially competitive binding of TAL activators and repressors to the same binding site, characteristic of our positive feedback loop switch;
• to explicitly model a limited number of binding site repeats;
• to incorporate the stochasticity of gene expression into an otherwise deterministic approach.

The algorithm was designed in a modular, object-oriented way, allowing us to represent each mRNA and protein molecule as a separate entity with its own set of parameters. With C#Sim, gene regulatory networks can easily be constructed using a programming language and simulated as a series of related entities (i.e. objects) such as promoters, binding sites and genes. The algorithm was implemented in C# programming language (Figure 3).

We modeled both the mutual repressor switch and the positive feedback loop switch using C#Sim. The results obtained led to the same conclusions as other modeling methods.