Solution of the cascade problem with unknown parameter δ . Solution for the cascade problem with unknown propensities. Probability distribution function (top row) and marginal probability distribution function of each species (bottom row) at time t = 0 s, t = 30 s, and t = 600 s (approximately steady state). The left column presents the results for a value δ = 0.01, while the central one is for δ = 0.025 and the left one for δ = 0.045. Note that all the results are obtained in one execution of the program. The four-dimensional hypercube containing the solution space, whose dimensions are the concentrations of the two proteins, the value of δ and time, is then cut by the hyperplanes defined by the different values of δ and time to give these plots.