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Table 1 Sufficient conditions to optimize the forward signaling. The second column reports combined parameter ranges able to enhance the forward response for convex (χ≤0) and logistic-like (χ>0) curves, deduced analytically from the criteria of efficient forward signaling. The third column refers to conditions obtained below, with a numerical method based on a random parameter sampling and maximizing the likelihood of these parameters with respect to the forward signaling (See Discussion section)

From: Signaling cascades transmit information downstream and upstream but unlikely simultaneously

Parameters Suff. conditions for Maximizing likelihood
  χ≤0 χ>0 (cf. discussion below)
\(a = \frac {K^{1}}{Y_{T}}\) >1 1 a 31
\(b = \frac {K^{0}}{Y_{T}}\) <1 <1 b i 1
\(1/e = \frac {k^{0}\,Y_{T}}{k^{1}\,E_{T}}\) 1 1 1/e i >1
\(c-e = \frac {E_{T}}{Y_{T}}\) 1 1 c i e i <1
\(\frac {a}{b} = \frac {K^{1}}{K^{0}}\) >1 1 a i /b i >1