Team:UANL Mty-Mexico/Modeling

Mathematical models that represent the dynamic behavior of biological systems are a quite prolific field of work and are pilar 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 englobes enough information 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 and Hill equations.

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 fluoroscence units data, which should be enough for inter-system comparisons, i.e., to compare the temperature-dependent gene regulation features of different RNATs; an extension for protein concentration units is also proposed and waits for experimental validation.

After considering the effect of their metallothioneins (As-binding proteins), GlpF, ArsB and ArsR, they ended with the following time derivative:

\begin{equation} \large\frac{\mathrm{d[As(III)in] } }{\mathrm{d} x} = -ArsR_{As}-MBPArsR_{As} -n_{f}\cdot fMT_{As} -k_{1} ArsB_{As} + \frac{k_{2}V_{s}GlpF_{As}}{V_{c}} \end{equation}

RNA thermometers (RNATs) are RNA sequences that range from 40 to more than a 100 nucleotides commonly found in the 5' untranslated region of some genes and that regulate in cis their translation without the need of other factors [Kortmann and Narberhaus, (2012); Narberhaus, (2009)]. These RNAT sequences show certain three dimensional structures, some of which interact with the ribosome binding site (RBS) of their regulated genes and hinders the proccessivity of the ribosome complex at certain temperatures. The dynamics of the formation of these structures is temperature dependent and is the basis of the regulation of the translation rate of a given transcript [Chowdhury, S., et al.,(2006); Narberhaus, F., et al.,(2006)].

Functional RNAT have been found in different organisms, mainly pathogenic bacteria, and many others have been predicted in almost everyfrom a number of bioinformatic studies. They have been found to regulate the expression of virulence factors, heat and cold shock response factors and even proteins involved the development of some bacteriophages.

Their apparent widespread presence in living organisms has made RNATs attractive for some applications, specially the ones related to the replacement of chemical inducers and for the development of new drugs.

However, from the experience of those who have been working extensively with RNAT in the later years, the accurate bioinformatic prediction of functional RNAT has proven to be an exceptionally difficult task; the reasons for this are pointed to be the poor sequence conservation observed among RNATs and the gaps in our current understanding of the RNAT function, their structural diversity and the effect of other regulatory sequences far from the RBS region [Kortmann and Narberhaus, (2012); Waldminghaus, et al., (2007)].

The discovery of new RNATs has relied on a mixed approach that involves bioinformatics and experimental validation, as well as approaches that involve mutational libraries, synthetic constructions and directed evolution.

Even when the naturally found RNATs usually regulate the expression of transcription factors, the synthetic constructions made so far have focused mainly to characterize the effect of a given RNAT using a reporter protein (LacZ or a fluorescent protein) directly downstream of a RNAT. In our work, we intend to prove that RNATs can also be employed to effectively regulate the expression of transcription factors in synthetic circuits and point at possible applications for the circuit topologies that would be made feasible with this new kind of synthetic regulatory device.