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Modeling
Modeling in synthetic biology and iGEM Freiburg 2017
In synthetic biology, modeling can be applied to a wide range of topics. Our project allowed us to work on one of the most exciting: modeling of genetic circuits. In this subfield of mathematical and computational biology, ordinary differential equations (ODEs) are used to describe the transcriptional and translational process (Chen et al., 1999).
ODEs consist of a set of parameters and a system of functions and their derivatives. How they can be set up in their simplest form is shown below.
f'(t)=y(z)-k1*f(t)
z'(x)=k2*f(t)-k3*z(t)
The variables are functions of time t and are described as follows:
f(t) describes the mRNA concentration, y(z) the transcription function, k1 the mRNA degradation rate, z(t) the protein concentration, k2 the translation rate and k3 the protein degradation rate (Chen et al., 1999).
This system of ODEs can now be solved via numerical integration, but to obtain constants like k1, k2, k3, experimental data has to be produced that is suitable for a nonlinear regression (Ingalls et al., 2012).
The obtained model is to be compared with new experimental data in order to verify the parameter sets. If necessary, parameters or assumptions have to be corrected. Furthermore, if enough data is available, models can be utilized to optimize genetic circuits for a desired outcome.
Why did we choose an AND gate?
As already stated the HRE, CRE and NFAT binding site are enhancers, that could be utilized for more specific CAR expression. But the combination of these three enhancers in an AND-gate to even further boost the specificity of the CAR expression (Brophy et al., 2014) proved to be quite challenging, because using endogenes systems came with the drawback, that we had to generate a knockout or knockdown of either HIF1, VEGF-R, or TDAG8.
Generating a single knockout or knockdown is challenging enough but generating three to test all possibilities, so using modeling to find the best candidate seemed an attractive option, instead of choosing a random possibility.
In the first step literature values had to be obtained to describe the promoter kinetics. Papers were selected on the basis of cell lines that were used and the resolution of the kinetic characterisation.
The final constructs for the transfection are shown on the AND gate page (link to the AND gate page).
(Insert picture of the AND gate modeling scheme)
Creating an AND gate model
Simplified AND gate model
(Insert table with the simplified AND gate Model)
In our model, we assume that the expression of HIF1α and CAR comprises a basal and an induced expression. Also, we made the assumption that, due to the constitutive expression, the level of the monomer HIF1β stays constant over time. Potential loss as a result of dimerization and deviations in the expression was neglected. Therefore we set dHIF1β/dt = 0. Additionally, we work with the simplification that the kinetics for both input 1 and input 2 are completely independent from each other. The gene expression dependent on the input is described by an equation including the Hill coefficient. The concentration changes for every single protein account for all reactions containing it as a reactant or product. In the following, the ODEs describing the concentration changes of the single parts over time are listed:
dHIF1α/dt = kbasal_HIF1α + kstim_HIF1α*[VEGF]n_HIF/((KM)n_HIF+[VEGF]n_HIF - kdeg1_HIF1α*[HIF1α] - kdeg2_HIF1α*[HIF1α]*[O2] - kdim_HIF1αβ*[HIF1α]*[HIF1β] - kdiss_HIF1αβ*[HIF1αβ]
dCAR/dt = kbasal+ kstim_HIF1α*[HIF1αβ]n_HIF/((KM)n_HIF+[HIF1αβ]n_HIF - kdeg_CAR*[CAR]
dHIF1β/dt = kdiss_HIF1αβ*[HIF1αβ] - kdim_HIF1αβ*[HIF1α]*[HIF1β]
dHIF1αβ/dt = kdim_HIF1αβ*[HIF1α]*[HIF1β] - kdiss_HIF1αβ*[HIF1αβ]
As a large number of projects in synthetic biology are based on the manipulation of signaling pathways and genetic networks, it is in the researcher’s interest to work with software tools which apply general rate laws to particular reactions. In this context, we discovered data2dynamics, a program performing ODE simulations automatically thus facilitating the analysis of biological networks and their kinetics.
Results
All information about relevant parts, reactions, and reaction speeds are used to plot the concentrations of diverse species against the time. The graphs show the changes over time for the relative expression rates of CAR under varying VEGF concentrations / pH values and varying oxygen concentrations:
( insert graphs)
Evaluation and Outlook
(Insert results of modeling here)
