xCellerator

GRN (Genetic Regulatory Network Arrows)

GRN[v,β,n,h] is an uninstantiated function that encapsulates the parameters used in a Genetic Regulatory Network reaction. GRN arrow functions are based on neural-network (connectionist) models of genetic regulation.

GRN[v, β, n] is equivalent to GRN[v, β, n, 0].

GRN[v, β] is equivalent to GRN[v, β, 1, 0].

GRN[v] is equivalent to GRN[v, 1, 1, 0].

GRN[] is equivalent to GRN[1, 1, 1, 0].

The expressions GRN[...] and grn[...] are equivalent and may be used interchangeably.

The canonical form for a GRN reaction

The template for a GRN reaction is

Multiple reactancts will be combined togetherThe following forms are equivalent:

$interpret[{{{P,Q,R}\[RightTeeArrow]B,GRN[v,\[Beta],n,h]}}]$
$interpret[{{P + Q + R \[RightTeeArrow] B, GRN[v, \[Beta], n, h]}}]$

The sigmoidal activation function be replaced with any other previously defined function f, e.g.,

$interpret[{{P + Q + R \[RightTeeArrow] B, GRN[v, \[Beta], n, h, f]}}]$

A lambda-function can also be used:

$interpret[{{P + Q \[RightTeeArrow] B, GRN[v, \[Beta], n, h, 0.5*(1 + #/Sqrt[1 + #^2]) &]}}][[1, 1]]$