The MIS algorithm proposed in [43,44] was then applied to compute all possible minimal perturbation sets to force the network into desired steady state or phenotype.

either high or low) in the desired final steady state .

Given a regulatory network, MIS patterns represent a set of simultaneous perturbations (or treatments) to force the network into a desired steady state , where a subset of nodes remain at a fixed expression level of either low or high [41,42].

The term minimal implies that no other subset of an M18 pattern can lead to the desired steady state behavior.

However, for a given network, there can be more than one MIS patterns to generate the same steady state .

The physiologically relevant combinations of ligands were discovered by applying the recently proposed MIS algorithm [43,44] to predict all minimal perturbations in the inferred regulatory network that can transition TEM into desired steady states (Table 4).

The state of the network at a given instant can change depending on the state of the other nodes and can ultimately stabilize into attractors of either a single state ( steady state ) or an oscillating set of states (cycling attractors) [2].

The Boolean steady state of the network has been shown to correspond to the cellular states for various regulatory networks in the past [3].

Boolean modeling of steady state transitions helps in understanding the influence of perturbations on system wide behavior and has been used to identify the key molecular mechanisms controlling gene expression [4,5,6] and regulation [7,8], cell differentiation [9] and signal transduction [10,11,12,13,14,15,16,17,18,19,20].

Therefore blood and tumor TEM can be viewed as two distinct cell steady state behaviors and ivdTEM as an intermediate state (Tables 2 and 3).

blood TEM) steady states respectively.

For the computation of the PRC, we evolved the model until it reached a steady state and then applied pulses of current (0.5 ms duration and 0.5 nA amplitude) at random times with a mean period between perturbations of 2.5 HZ.

In both cases, the algorithm employed to compute the PRC differed from that used in the single compartment model and resembled the one adopted in [42, 43]: briefly, after evolving the model until it reached a steady state , we identified two spike times to and t1 such that the 181 1‘1 — to was of the appropriate duration.

Similarly, it is often necessary to wait until PCs reach a steady state firing rate before initiating the repeated stimulation protocol.

1A), employed to speedup convergence to the firing rate steady state and reduce very slow fluctuations.

Additionally, we set the simulation temperature to 28°C, in order to span a broader range of steady state firing frequencies, particularly in the low end of the spectrum.

Any kinetic scheme, reversible or irreversible, that obeys a similar set of equations at steady state Will have a linear-fractional dose-response.

In steady state , the neW product obeys [X’] = q[X] [P] With mass which mimics a CLS step.

Reversible and irreversible reactions could be combined as long as the steady state conditions resemble the equilibrium conditions (2) and the mass conservation conditions have bilinear form.

In steady state , the concentrations obey the equilibrium conditions and the mass conservation conditions where X?

We have shown that one important ingredient affecting the dynamical behavior of the chain is noise, which plays a key role in onset of the pattern formation, i.e., the transition from the initial chain of vegetative cells to the steady state in which heterocysts coexist with vegetative cyanobacteria.

(5) for the steady state .

Taking into account the difference between the relaxation times of the constituents of the model, given by the inverses of d* (see Table 1), we can interpret it as composed of two temporally separated systems: a rapid one, formed by HetR and NtcA, showing fast dynamics that relaxes to its steady state almost instantaneously and a slow one, composed of PatS and cN, whose evolution is dictated by the values of HetR and thA in their instantaneous equilibrium.

The steady state is very robust against perturbations since it is far from the bifurcation region and there is a significant distance to the saddle in the qr — qa plane.