What is the main difference between solutions of linear ODEs

What is the main difference between solutions of linear ODE\'s and nonlinear ODE\'s assuming the linear/non linear ODE satisfy the conditions for existence - uniqueness of theorems 2.4.1 and 2.4.2 Theorem 2.4.1: If the function p & g are continuous on an open interval I: d

Solution

Statistical inference of biological networks such as gene regulatory networks, signaling pathways and metabolic networks can contribute to build a picture of complex interactions that take place in the cell. However, biological systems considered as dynamical, non-linear and generally partially observed processes may be difficult to estimate even if the structure of interactions is given.

Results: Using the same approach as Sitz et al. proposed in another context, we derive non-linear state-space models from ODEs describing biological networks. In this framework, we apply Unscented Kalman Filtering (UKF) to the estimation of both parameters and hidden variables of non-linear state-space models. We instantiate the method on a transcriptional regulatory model based on Hill kinetics and a signaling pathway model based on mass action kinetics. We successfully use synthetic data and experimental data to test our approach.

Conclusion: This approach covers a large set of biological networks models and gives rise to simple and fast estimation algorithms. Moreover, the Bayesian tool used here directly provides uncertainty estimates on parameters and hidden states. Let us also emphasize that it can be coupled with structure inference methods used in Graphical Probabilistic Models.