Team:CIDEB-UANL Mexico/Math-Improvement

Probability Equation

We tried to modify our model with a probability equation from an article of the National Institute for Mathematical and Biological Synthesis, Knoxville, Tennessee, United States of America published in the internet page PLOS ONE with the name Is Thermosensing Property of RNA Thermometers Unique? This work looks for the probability of finding a RNA at an openness way using its temperature, intercept and slope parameters time. This would describe the chance of finding our riboswitch k115017 open or closed. Making a smooth change in the fold of the thermosensor and the increase decrease slopes in our simulations.

"P_i(T) is the probability of finding the window at position “i” in a gene, open at temperature (C), a_i and b_i are the intercept and slope parameters of how the log-odds of finding an open window at position “i”, log(p_i(T)/1- p_i(T)), changes with temperature. The ratio –a_i/b_i indicates the temperature at which the probability of openness of a window is 0.5."

Our team used the last data of –a_i/b_i = T when openness is 0.5, to get “a_i” expressed in b ( a_i= -T*b_i) and have our own goods ; to find b the authors of the articles, compared across the 100 genes, found that values were not significantly greater than zero for 24 genes at p value is 0.05, so b value is 0.157. This implies that a small fraction of genes did not show a significant change in openness of its RBS with temperature over the range of temperatures considered. Then we place our control temperature in the isolated equation and get a= -32*0.157 to get the “a” value that was negative 5.024.

But there were some problems using the p_i(T) formula in the matlab simulations like malfunction of the equation at the moment of seen graphs or the incorrect insertion of parameters in the simulation, so finally the team decided to leave it apart of the graphics.

We mention this special formula because it was the solution of the fast growth and decrease of the concentrations of the RNAs and proteins in E.Coli. We run out of time and it was almost imposible to experiment with it and get better results, but heres the small advance we made with all this.

The graph shows the probability of the increase in openness of an RNA thermometer. b was compared across the 100 genes, they found that values were not significantly greater than zero for 24 genes at p value= 0.05 and remember that ai and bi are the intercept and slope parameters of how the log-odds of finding an open window at position “i”, log(pi(T)/1- pi(T)), changes with temperature. So it can be conclude that a small fraction of genes did not show a significant change in openness of its RBS considering the range of temperature and this indicates that RNA thermometers do not have a great change from non-thermometers in increasing the openness of RBS with temperature.

Concentration of Vip in E.Coli

Another variable that we have to consider is the saturation of Vip3Ca3 in E.Coli in the environment that we want to put it on, in this case, is the gel that serves as a way of transportation. We found an article talks about this oversautration - " They investigated the over-production of seven membrane proteins in an Escherichia coli-bacteriophage." http://www.ncbi.nlm.nih.gov/pubmed/8757792 At the beginning, we assume that our variables are going to behave continuously and without noise, so it is a deterministic model but we consider that the overproduction in this medium is a variable of an stochastic model because it is a factor that affect our system and the production, in other words, is a noise that we have consider if we want to check the way that the system is going to work.

If the production of Vip3Ca3 oversaturates in the bacteria E.Coli, it will die, the medium where our bacteria is will disappear and the production of Vip3Ca3 will stop. Also, another situation that we need to observe... if the white worm dies, the reasons could be the production of Vip3Ca3 or the aftermath of the rests of E.Coli and other factors of the system. The implement of new stochastic equations to this model should answer these variables and make a more realistic modeling of our equation, but there isn’t a perfect model, you can only approach to it.