Index of papers in PLOS Comp. Biol. that mention

**differential equation**

Supporting Information | Translating the logical network models into ordinary differential equation models, and intervention target validation for the ordinary differential equation models. |

Supporting Information | Validation of the intervention targets in Table 1 for the T -LGL leukemia differential equation network model and single interventions from control sets with more than one node in Table 1 for the T -LGL leukemia differential equation network model. |

Supporting Information | Validation of the stable motif control intervention targets in Table 2 for the helper T cell differential equation network model. |

The control targets transcend the logical modeling framework | To address this, we translate the studied Boolean network models into ordinary differential equation (ODE) models using the method described by Wittmann et al. |

differential equation is mentioned in 6 sentences in this paper.

Topics mentioned in this paper:

- T cell (26)
- network model (20)
- initial conditions (18)

Comparing pathogen growth against death rate | If there are two strains spreading concurrently, the deterministic rate of change of immunity, y, and the second strain x2, is given by the following set of differential equations: |

Comparing pathogen growth against death rate | This can be seen by forming dxz / dy as before, and after substituting either (p2 —> (p2 c or 02 —> az/c, one sees that each transformation results in the same rescaled differential equation (Section 3 of 81 Text): |

Model outline | Our analytical approach involves using a set of deterministic differential equations to ascertain pathogen spread in a stochastic birth-death process, where an infection (or immune cell) can only either die or produce 1 offspring. |

Model outline | By dividing Equation 1 by Equation 2, we obtain a differential equation for x1 as a function of y: |

Model outline | This differential equation is straightforward to solve (Section 1 of 81 Text), and yields the following function for x1(y): |

Supporting Information | In-depth mathematical analyses of the differential equations used, and how to derive the emergence probability if affected by immune growth (Equation 10 in the main text). |

differential equation is mentioned in 6 sentences in this paper.

Topics mentioned in this paper:

- immune response (39)
- growth rate (30)
- immune cells (23)

Abstract | By combining time-resolved quantitative experimental data generated in primary mouse hepatocytes with interaction graph and ordinary differential equation modeling, we identify and experimentally validate a network structure that represents the experimental data best and indicates specific crosstalk mechanisms. |

Experimental Prediction of | Ordinary differential equation (ODE) modeling utilizes the entire information of the time resolved data. |

Introduction | To analyze the impact of crosstalk and feedback regulation, dynamic modeling approaches using coupled ordinary differential equations (ODEs) are most suited and allow quantitative insights [24, 35—38]. |

Ordinary differential equation model selection | Ordinary differential equation model selection |

Ordinary differential equation modeling | Ordinary differential equation modeling |

differential equation is mentioned in 5 sentences in this paper.

Topics mentioned in this paper:

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

Abstract | This framework allows us to formulate the essential dynamical ingredients of the genetic circuit of a single cyanobacterium into a set of differential equations describing the time evolution of the concentrations of the relevant molecular products. |

Methods | (16) is a set of stochastic differential equations (SDE) so its numerical integration requires generating a statistical representative trajectory for a discrete set of time-values. |

Regulatory equations | In this section we translate the genetic circuit previously described into a set of differential equations , for Which we follow the derivation in [46—48]. |

Regulatory equations | Finally we introduce the differential equations governing cyanobacterial reaction to nitrogen deprivation. |

Strains of cyanobacteria. Heterocyst patterns | We used a Runge-Kutta method for the numerical integration of stochastic differential equations |

differential equation is mentioned in 5 sentences in this paper.

Topics mentioned in this paper:

Adherens Junction Segmentation | The time needed to travel from each point x E Voronoi(v) to the verteX v is found as the solution to the partial differential equation : with boundary condition T (v) = O. |

Adherens Junction Segmentation | This equation is a well known partial differential equation known as the Eikonal equation. |

Introduction | [15, 16] have built a Partial Differential Equation framework to filter image noise, segment cell nuclei, locate the cell membrane and model the evolution of cell shapes to track the cells. |

Introduction | A 2D simplification of the 3D Partial Differential Equation framework introduced in [15] has been reported in [22]. |

differential equation is mentioned in 4 sentences in this paper.

Topics mentioned in this paper: