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.

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.

persstemc1

Beginner2022-07-02Added 18 answers

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.

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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