Adjoint systems for models of cell signaling pathways and their application to parameter fitting

Area of Science:

• Systems Biology
• Computational Biology
• Biophysics

Background:

• Cell signaling pathways are often modeled using nonlinear ordinary differential equations.
• Fitting these models requires optimizing parameters based on discrete time-point measurements.
• Adjoint sensitivity analysis is a key technique for gradient computation in parameter optimization.

Purpose of the Study:

• To present and apply a novel adjoint sensitivity analysis method for fitting continuous-discrete time models of biological systems.
• To demonstrate the efficacy of the Generalized Backpropagation Through Time (GBPTT) method.

Main Methods:

• The study employs a structural formulation of adjoint sensitivity analysis known as Generalized Backpropagation Through Time (GBPTT).
• This method is particularly effective for hybrid systems that combine continuous and discrete time dynamics.
• The NF-kB regulatory module, a critical component of the innate immune response, is used as a case study.

Main Results:

• The GBPTT method provides an efficient way to compute the gradient of the performance index with respect to model parameters.
• The application to the NF-kB model demonstrates the method's suitability for complex biological systems.
• Successful fitting of the model parameters is achieved using the developed approach.

Conclusions:

• Generalized Backpropagation Through Time (GBPTT) is a powerful and efficient tool for fitting mathematical models of cell signaling pathways.
• The method is well-suited for hybrid continuous-discrete time systems commonly encountered in systems biology.
• This work facilitates a deeper understanding of biological regulatory modules, such as the NF-kB pathway.