Interestingly, without this constraint we were not able to determine a parameter configuration matching the simulation results to in vitro measurements.

Before we extensively discuss the simulation results , we first thoroughly validate the model and its current parametrization.

The simulation results with the adapted model are depicted in Fig.

According to our simulation results , only a concisely regulated interplay between redox-dependent and self-induced auto-/paracrine WNT signaling can explain the nuclear fi-catenin dynamics observed experimentally during the initial phase of differentiation:

In summary, our simulation results suggest a twofold activation mechanism that drives the early differentiation process in human progenitor cells.

Simulation result for Raft/Receptor dynamics.

We also tested the sensitivity of the structure obtained to the evolutionary goal by comparing simulation results with different goals having the same rank.

We show simulation results of networks with L = 4 (5 layers of nodes) and 6 nodes in each layer (D = 6).

Each column in this figure shows simulation results for a different goal, and each row shows a different network layer.

We show simulation results of a simple nonlinear problem mimicking a 4-pixel retina.

(B) Typical example of simulation results .

We show simulation results when the goal consisted of a matrix of deficient rank (1 , 2 or 3) to which some level of noise was added (see Methods), so mathematically speaking goals had full rank, such that some of the eigenvalues were relatively small.

Generically, in fields as diverse as artificial neural networks [30] and evolution of biological networks, simulations result in highly connected networks with no bow-tie [31—37].

Additional figures and simulation results as follows: 1.Parameter sensitivity test, 2.

3(c)-(f) demonstrates that the analytical results slightly underestimate the simulation results to a small degree, especially if the mutated strain’s growth rate is high and R2 is close to K, but becomes more accurate as R2 increases and generally provides a good approximation.

Nevertheless, even in this case, Equation 7 accurately matches up with simulation results in this parameter range, although some inaccuracies arise for K = 1,000 (81 Fig).

Contains additional information on derivations, and further comparisons against simulation results (Mathematica NB format).