A note on estimation of dynamics of multiple gene expression based on singular value decomposition

Area of Science:

• Computational Biology
• Systems Biology
• Bioinformatics

Background:

• Analyzing high-dimensional gene expression data over time is crucial for understanding biological dynamics.
• Singular Value Decomposition (SVD) is employed to identify dominant trends (characteristic modes) in such data.
• Linear discrete-time dynamical systems offer a framework to model temporal dependencies in gene expression.

Purpose of the Study:

• To refine and evaluate a method combining SVD with linear dynamical systems for gene expression analysis.
• To develop and provide a practical MATLAB procedure for implementing this analytical approach.
• To investigate the method's robustness concerning missing data and the impact of data regularization on predictions.

Main Methods:

• Formulation of a non-linear optimization problem to obtain the dynamical model.
• Numerical solution of the optimization problem using standard MATLAB procedures.
• Testing the approach with publicly available gene expression datasets.

Main Results:

• A ready-to-use MATLAB procedure was developed for analyzing gene expression dynamics.
• The method's sensitivity to missing measurements and its data reconstruction capabilities were investigated.
• Potential consequences of data regularization on model outcomes, particularly for prediction, were discussed.

Conclusions:

• The combined SVD and linear dynamical system approach provides insights into gene expression dynamics.
• Overfitting represents a significant challenge that can arise from this analytical method.
• Careful consideration of data preprocessing techniques like regularization is essential for reliable model application.