Index of papers in PLOS Comp. Biol. that mention

**steady state**

Computing minimal all perturbations sets in ivdTEM regulatory network | 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. |

Computing minimal all perturbations sets in ivdTEM regulatory network | either high or low) in the desired final steady state . |

Construction of dynamical models from the experimental data using TEM differentiated in vitro | 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]. |

Construction of dynamical models from the experimental data using TEM differentiated in vitro | The term minimal implies that no other subset of an M18 pattern can lead to the desired steady state behavior. |

Construction of dynamical models from the experimental data using TEM differentiated in vitro | However, for a given network, there can be more than one MIS patterns to generate the same steady state . |

Discussion | 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). |

Introduction | 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]. |

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

Introduction | 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]. |

The plasticity of TEM predicted computationally was validated experimentally using TEM differentiated in vitro | 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). |

The plasticity of TEM predicted computationally was validated experimentally using TEM differentiated in vitro | blood TEM) steady states respectively. |

steady state is mentioned in 12 sentences in this paper.

Topics mentioned in this paper:

- regulatory network (22)
- cytokine (20)
- breast cancer (16)

AMSN | It should however be noted, that our model eXplores the DTT under steady state conditions only. |

Effect of Dopamine on the DTT | This steady state effect of dopamine is often modelled by changing the weight of cortico-striatal synapses for D1 ([0) and for D2 (ICZ) [27]. |

Effect of Dopamine on the DTT | Consistent with experimental observations, our model suggests that an increase in steady state dopamine levels would (1) increase the firing rate of D1 MSNs [28] , thereby (2) introducing a preference for ‘Go’ type actions or dyskinesia. |

Model limitations | Thirdly, our model explores the striatal dynamics at steady states , since the model showed stable fixed points. |

Model predictions and explanation of experimental data | In our model, an increase in the steady state level of dopamine changes the DTT to higher cortical input rates, thereby increasing the region in which D1 MSNs can have their firing rate exceed those of D2 MSNs (Fig 7A). |

Model predictions and explanation of experimental data | In our model, a decrease in the steady state dopamine level results in an increase in the range of cortical input for which D2 MSNs have a higher firing rate than D1 MSNs. |

steady state is mentioned in 6 sentences in this paper.

Topics mentioned in this paper:

- firing rates (89)
- basal ganglia (21)
- feedforward (15)

Discussion | Other modeling approaches using perturbation data to unravel the network structure rely on modular response analysis (MRA), which requires steady state assumptions and linear equation based modeling. |

Discussion | Positive feedback loops have been shown to cause bistable behavior [49] and must be contained in the system's structure to enable more than one steady state [50]. |

Introduction | In contrast to related methods, which rely on the concept of sign consistency and require a steady state assumption [30, 34], exploitation of the dependency matrix is well-suited for the analysis of transient effects. |

Ordinary differential equation modeling | During the parameter estimation, no steady state conditions have been utilized. |

Ordinary differential equation modeling | We assume that non-stimulated measurements of signalling components in our data set is sufficient for training the system to an initial steady state in an unstimulated setting. |

steady state is mentioned in 5 sentences in this paper.

Topics mentioned in this paper:

- phosphorylation (52)
- signaling pathways (32)
- MAPK (29)

Modeling | 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. |

Modeling | 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. |

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

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

by | 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. |

steady state is mentioned in 5 sentences in this paper.

Topics mentioned in this paper:

- firing rate (115)
- computational modeling (5)
- single cell (5)

Competitive lL-2 uptake by regulatory T cells | Fig 3), the IL-2 concentration attains a spatially inhomogeneous steady state more rapidly, with the overall IL-2 concentration being lower (Fig 4C and 4D and 82A Fig). |

Discussion | In contrast to immune cell signaling with a typical time scale of many hours during which diffusive gradients reach steady state , the transient behavior on shorter time scales is of particular interest for morphogen gradients [51,54]. |

Homogeneous cytokine secretion and uptake | As diffusion is fast (D = 10um2/s, see Table 1), it reaches a steady state after about LZ/D = 0.5 s, Where L is the cell-to-cell distance in the case of high cell-density. |

Homogeneous cytokine secretion and uptake | Thus, it is sufficient to consider the diffusion equation in steady state in the extracellular domain with flux boundary condition at the cell surface: c(r) is the cytokine concentration at distance r from the center of the cell, A is the Laplace operator in spherical coordinates, p is the cell radius, and q is the cytokine secretion rate. |

steady state is mentioned in 4 sentences in this paper.

Topics mentioned in this paper:

- cytokine (143)
- T cells (36)
- cell-to-cell (12)

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

Equivalent irreversible kinetic scheme for the theory | In steady state , the neW product obeys [X’] = q[X] [P] With mass which mimics a CLS step. |

Equivalent irreversible kinetic scheme for the theory | 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. |

Theory of non-cooperative gene induction | In steady state , the concentrations obey the equilibrium conditions and the mass conservation conditions where X? |

steady state is mentioned in 4 sentences in this paper.

Topics mentioned in this paper:

- Hill coefficient (7)
- gene eXpression (6)
- transcriptional (5)

Discussion | 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. |

Regulatory equations | (5) for the steady state . |

Unicellular dynamics | 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. |

Unicellular dynamics | 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. |

steady state is mentioned in 4 sentences in this paper.

Topics mentioned in this paper: