Team:UANL Mty-Mexico/Modeling

Mathematical models that represent the dynamic behavior of biological systems are a quite prolific field of work and are pillar for Systems Biology. A number of deterministic and stochastic formalisms have been developed at different abstraction levels that range from the molecular to the population levels.

In principle, a model that is simple but that is good enough to describe and make predictions, with a degree of certainty, about the phenomenon under scrutiny, would be desirable.

Deterministic mathematical models that describe the behavior of genetic circuits and the interactions of the proteins they encode are usually built upon mass action kinetics theory.

Aside from the common objection that they are not suitable to describe systems that show a low number of particles, we believe that a deterministc model at a molecular level of these kind of systems and the degree of certainty with which they can be used for inter-system comparison or usage, do not outweigh the costs of the experimental determination of parameters.

Here we propose a model for the description and comparison of the behavior of the effect of RNA thermometers or RNATs on the expression of a reporter protein. The model is tested with relative fluorescence units data, which are not hard to obtain, and the model and its parameters should allow for inter-system comparisons, i.e., to compare the temperature-dependent gene regulation features of different RNATs; an extension that works with protein concentration units is also proposed, along with a potential application in metabolic engineering, and waits for experimental validation.

We present a model for the relation between time, temperature and the change in fluorescence (measured in Relative Fluorescent Units or RFUs) of an E. coli culture that harbors a genetic construction where a fluorescent protein is under control of a RNAT.

We took as reference for the RFUs the amount of fluorescence emited by an E. coli K12 culture transformed with a constitutively expressed part BBa_E1010 (for RFP expression) or BBa_E0040 (for GFP expression) per unit of Optical Density at 600nm light (OD₆₀₀) after 8hr of growth at 37°C in LB medium.

In this way the amount of fluorescence emited by our culture was calculated as follows:

\begin{equation} \large \frac{\frac{F_{sample}}{F_{standard}} \end{equation}

where F_sample is the OD₆₀₀-normalized fluorescence emited by a sample, while F_standard is the OD₆₀₀-normalized fluorescence measurement for the corresponding standard culture (again, BBa_E1010 for RFP and BBa_E0040 for GFP).