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Modeling overview

Distribution of drugs throughout tissues is very important for the effective therapy. We built pharmacokinetic models to simulate distribution of biological drugs produced by the engineered microencapsulated cells which would be implanted into the liver to treat hepatitis C and into the heart for the therapy of myocardial ischaemia, in comparison to the standard therapy.

Pharmacokinetic models suggest that the proposed type of delivery should decrease the systemic side effects and the required dose of biological drugs.

Mathematical modeling was used to simulate different types of epigenetic switches (mutual repressor switch, based on the classic toggle switch and its extended version with introduction of additional positive feedback loops), where experimental parameters were incorporated into the model. Our models led to some non-intuitive results concerning the introduction of non-linearity into the system, which was verified by experimental results.

We constructed deterministic and stochastic models to analyze both of our switches and developed two additional modeling approaches:

  • a quantitative model based on the available experimental data;
  • a new modeling algorithm, called C#Sim, based on object-oriented programming approach.

All models consistently demonstrate that:

  • the mutual repressor switch is unlikely to exhibit bistability in a realistic experimental setting using monomeric transcription factors;
  • the positive feedback loop switch is, in terms of robustness, far superior to the mutual repressor switch based on non-cooperative orthogonal DNA-binding domains of transcription factors, exhibiting bistability in more demanding (non-ideal) conditions.

Therefore we predicted that the mutual repressor switch would not exhibit bistable behavior, while the positive feedback loop switch should be stable. These assessments were confirmed by experimental results, with the positive feedback loop switch clearly exhibiting bistability.

Modeling of epigenetic switches and thorough parameter space analysis made it possible to provide our wet-lab with answers to questions regarding how our switches may behave in different scenarios - e.g., how different amounts of constructs defining the positive feedback loop switch may affect bistability, what is the effect of leaky transcription, can the positive feedback loops replace the need for transcription factor cooperativity to obtain bistability, why the mutual repressor switch may not work, etc. This way, our experimental work was interwoven with dry-lab modeling.

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.

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