The price of information transfer in living cells
Here we provide the detail of the chemical Langevin approximation of the enzymatic push pull loop and hence the algorithm to reproduce scatter points (green and blue clouds) in Fig. 3 of the maintext (shown as follows).
Note: Apply our mathematica notebook with mathematica v.11 or higher.
chemical Langevin approximation: In this notebook, we provide the details of chemical Langevin solution, the coefficients of power spectra, the variances of input X/output Y, and hence the mutual information as a function of γk, κ-r, ρ-r, and parameters choice. Using our result for mutual information, one can easily reproduce the following Fig. A and B.
derivation_of_Fig_3: In this notebook, we provide the algorithm to reproduce scatter points (green and blue clouds) in figure D to I (shown as follows). Insert our data for 1/1.5/2 bits generated by this algorithm, one can easily reproduce figure C.
