Team:Vanderbilt/Modeling/Circuits
To give the user some sense of how well the optimization algorithm is working, it would be prudent to give an initial output to let the user know how well their circuit should hold up under selective pressures. Therefore we have created the crude measure of Expected Evolutionary Stability or EES. The EES of a sequence is correlated to how likely that sequence is to mutate in such a way as to change or reduce the function of the sequence.
The actual calculation of the EES is very simple to understand. It is a weighted sum, where each component contributes part of the total EES. The factors used to create the EES were outlined in Designing and Engineering evolutionary robust genetic circuits. These factors are: Level of Expression, Sequence Homology, and whether the circuit is induced or constitutive. The first two factors are real numbers. Where Level of Expression can be anything from 0 to 1. The level of expression is measured using relative level of fluorescence; the data set used was drawn from the IGEM Standard Registry (contributed by Professor Christopher Anderson). The Anderson Promoters are a family of related constitutive promoters whose activity were measured, and normalized so that the highest level of expression related to 1, and the lowest level relates to 0. Sequence Homology is a real number between 0 and 1, where 0 means that there is zero amount of homology in the sequence, and 1 is a sequence consisting of just one repeated subsequence. Finally, the induced vs. constitutive is a binary value, meaning it can either be 0 or 1, not both or anything in between.
The weights for these factors are based purely on empirical evidence. They are the ratios of evolutionary half-lives as outlined in Designing and Engineering evolutionary robust genetic circuits. For each of the three factors in the weighted sum, the authors ran experiments for each and looked at how the evolutionary half lives changed. With more empirical data, these weights could become more precise, leading to a more accurate indicator or EES. As the current model stands the weights are called alpha, beta, and gamma. Alpha is the coefficient of expression level, and it is based solely on one experiment from Designing and Engineering evolutionary robust genetic circuits, and has the value 10. Beta is based on a series of experiments from the Designing and Engineering evolutionary robust genetic circuits, and is the ratio of the fluorescence level corresponding to the highest level of homology to the lowest level of homology. Beta is also scaled by the ratio of those standard deviations, to give a more conservative estimate. Beta has a value of 4.7446. Gamma, the coefficient corresponding to whether a circuit is induced vs. constitutive is the average of fluorescence levels corresponding to the induced and constitutive experiments. Gamma has the value 1.2. These weights only represent the first application of this weighted sum method. Given more empirical evidence, and more refined methods for measuring expression level of a circuit it would increase the accuracy and efficacy of this method for determining Expected Evolutionary Stability.
Figure EES_I shows the theoretical EES for an induced circuit. The colors of the plotted points correlate to how evolutionarily stable the strand is, where red is the worst, green is mid-range, and blue is the optimal EES. As we can see, there is a strong negative correlation with both Homology and Expression level. Also, it can be seen that the range for an induced circuit goes up to a much higher value than the range of a constitutive circuit, reinforcing how the model is setup. Figure EES_C is very similar to that of Figure EES, however it is for a set of theoretical circuits which are designed to be constitutive rather than induced.
