Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Abstract

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small-to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

Optimization and profile calculation of ODE models using second order adjoint sensitivity analysis

“…For these problem classes, the constraint TR and IP optimization algorithms as implemented in are the state-of-the-art methods. Additionally, new algorithms, which can exploit the additional curvature information, available through exact Hessian computation, in novel ways are steadily developed ( Fröhlich et al , 2017b ). Either directions of negative curvature can be used to escape saddle-points efficiently ( Dauphin et al , 2014 ), or third-order approximations of the objective functions are constructed iteratively from the Hessians along the trajectory of optimization to improve the convergence order ( Martinez and Raydan, 2017 ).…”

Parameter estimation and uncertainty quantification for systems biology models

“…However, the forward sensitivity method generates an ODE system of size equal to the number of original equations times number of parameters [23]. Stiff numerical integrators (e.g., CVODE [28]) have a computational complexity limited by that of matrix multiplication [7], which is n 3 with a naive implementation and roughly n 2.38 with the best known algorithm (for a system of n equations). This complexity limits the capacity to solve very large ODE systems.…”

“…Various software tools such as COPASI [5], Data2Dynamics [6], AMICI [7], and PyBioNetFit [8] make parameterization of detailed models possible without the need for problem-specific code. PyBioNetFit and AMICI are the newest of these tools, and both provide features that are complementary to those available in older tools.…”

Optimization and uncertainty analysis of ODE models using 2nd order adjoint sensitivity analysis

“…For these problem classes, the constraint trust-region and interior-point optimization algorithms as implemented in fmincon are the state-of-theart methods. Additionally, new algorithms, which can exploit the additional curvature information, available through exact Hessian computation, in novel ways are steadily developed (see Fröhlich et al (2017b)). Either directions of negative curvature can be used to escape saddle-points efficiently (Dauphin et al, 2014), or third-order approximations of the objective functions are constructed iteratively from the Hessians along the trajectory of optimization to improve the convergence order (Martinez & Raydan, 2017).…”