Calcium Dynamics in Neurons with ER: From Differential Equations to Hybrid Differential Equation and Deep Neural Network Models

Qingguang Guan (The University of Southern Mississipi)

Monday 20th May 12:20-13:00 Lecture Theatre 116

Abstract

Many biological processes are modeled using differential equations. We will demonstrate the well-posedness of a calcium model based on partial differential equations (PDEs) and ordinary differential equations (ODEs), and then discuss the numerical methods to solve it. However, determining the underlying equations analytically becomes highly challenging due to the complexity and unknown factors inherent in these biological processes. Our research aims to employ deep neural networks (DNNs) to model the open probability of ion channels, a task that can prove to be intricate when tackled with ODEs. The distinctive contribution of this research lies in reducing the number of unknowns required to model the open probability. When trained with valid data, the same neural network architecture can be employed for different ion channels, such as sodium, potassium, and calcium. Further based on given data, we can build more physiologically reasonable DNN models which can be customized. Subsequently, we integrated the DNN model into calcium dynamics in neurons with endoplasmic reticulum, resulting in a hybrid model that combines PDEs and deep neural networks. Numerical results are provided to demonstrate the flexibility and effectiveness of the DNN model.

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