Reconstructing noisy intracellular expression dynamics using neural stochastic differential equations, Part II: Applications in cell biophysics

Within individual cells, signaling pathways and gene expression are highly dynamic and noisy. Trajectories of protein concentrations vary across different cells due to cell heterogeneity (extrinsic noise). In addition, intrinsic noise results from the inherent stochasticity of biochemical reactions within a cell, which can be modeled using stochastic differential equations (SDEs). However, directly inferring and recapturing intrinsic noise within experimental data remains a challenge. In this work, we apply our recently developed Wasserstein distance-based neural SDE (nSDE) reconstruction approach to accurately reconstruct SDE models of transcription factor (NF$\kappa$B) dynamics from single-cell trajectory data. By simulating trajectories with given noise and training a neural network to learn these noise levels, we then input experimentally measured trajectories and determine their underlying intrinsic noise. Thus, by leveraging simulation and experimentally measured NF$\kappa$B abundance trajectories we are able to train a neural network that defines the high-dimensional SDE representing the stochastic dynamics of the NF$\kappa$B system.