Team:CIDEB-UANL Mexico/Math-Improvement

Probability Equation - Concentration of Vip in E.Coli
Probability Equation - Return

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
In our variable of a stochastic model that we try to introduce it says that the overproduction of Vip3Ca3 will kill the host cell, in this case E.Coli, and in In the following article it supports our hypothesis about this situation, they investigated “the over production of seven membrane proteins in a E. Coli bacteriophage. In all seven cases, when the expression of the target membrane protein was induced, most of the host cell died, this make us think or suppose that the E. coli of our system can be affected by a similar case”. http://www.ncbi.nlm.nih.gov/pubmed/8757792

In another article it states that “The difficulties in recombinant overexpression of membrane proteins arise partly from the physical space limitations of the cell membrane, but overexpression can also be toxic to the host cell”, also we can inferred that the overproduction can cause a toxicity that can affect after the host cell die and affect the system or the worm white.

Also we suggest that after the host cell die, we can´t know if the worm white dies will be for the production of Vip3Ca3 or the toxicity that it release after its death.

We have to recall that the model it has to be in a control environment, in other words, in a lab with all the control of the variables in order that the entire model has a real function. The improvement it reaches a more reality to have other variables that are more specifically to an open environment.