Genomic signal processing: from matrix algebra to genetic networks.

Area of Science:

• Systems Biology
• Computational Biology
• Genomics

Background:

• DNA microarrays enable comprehensive recording of genomic signals governing cellular processes.
• Mathematical modeling of this genome-scale data is crucial for advancing biology and medicine, including diagnosis, treatment, and drug development.

Purpose of the Study:

• To review early data-driven mathematical models derived from genome-scale data.
• To demonstrate how these models, adapted from physical sciences frameworks, describe genetic networks and cellular functions.

Main Methods:

• Adaptation and generalization of matrix algebra frameworks, including singular value decomposition (SVD), generalized SVD, and pseudoinverse projection.
• Application of these models to analyze RNA expression data (yeast, human cell cycle) and DNA-binding data (yeast transcription factors, replication proteins).

Main Results:

• Development of models that mathematically describe genetic networks, correlating data patterns with cellular element activities.
• Simulation of experimental observations by reconstructing, rotating, and classifying data in subspaces representing cellular programs.
• Elucidation of RNA expression oscillations during the cell cycle, paralleling physical oscillator designs.
• Prediction of a novel regulatory mechanism linking DNA replication initiation with cell cycle-regulated RNA transcription in yeast.

Conclusions:

• These data-driven models provide a mathematical description of cellular systems, akin to physical systems.
• They have the capacity to elucidate design principles of cellular systems and guide the creation of synthetic ones.
• The models demonstrate predictive power for uncovering new biological principles and may form the foundation for future systems biology approaches.