Agostarawz

2022-07-01

I am studying bioinformatics. I am trying to solve a problem. So we have a gene, whose initial value ${x}_{0}$ at time t=0 is ${x}_{0}$=1. A perturbation of factor −0.9789812 is applied to it, such that, at time t=10, its value is 0.0210359. The gene is measured at time-points t=[0,1,2...,10]. How can I know the calculate the values at time t=1,2,...,10, given the only information I have is the value at ${x}_{0}$ and and the perturbation applied ? I am giving the data here
x = [1.0000000,0.3482754,0.1304151,0.0575881,0.0332433,0.0251052,0.0223848,0.0214755,0.0211715,0.0210698,0.0210359]
But I want to know how would I generate this data. I tried the exponential decay function and the values do not correspond to the ones I have in my data set.
So if the gene has an initial value of 1 and a perturbation of −0.9789812 is applied to it, at the final reading of the gene at time t = 10 is 1−0.9789812 = 0.0210188. The decay is not linear, it seems like it has an exponential curve but I dont know how to fit it.
Note that the only information I have is the initial value of the gene, the perturbation applied. I want to be able to calculate the values of gene at any time given this information.

Even if your model is correct and exponential decay is expected, real work data rarely fits perfectly.
I expect that you are familiar with cases of linear relationships e.g. y=ax or y=ax+b. In these cases, you could plot the points on a graph and find the line of best fit.
If the expected relationship is $y={e}^{-ax}$ then this does not work but note that log(y)=−ax so the relationship between log(y) and x is linear. So, plot log(y) rather than y and try to find the line of best fit.

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