Mathematical modeling and analysis in biochemical engineering: past accomplishments and future opportunities.

This is a personal commentary on the history and future prospects of mathematical modeling and analysis in biochemical engineering. Major transitions in these fields were driven by the appearance of the Aiba, Humphrey, and Millis text, Fredrickson's guidance on conceptualizing mathematical representations of cell populations, and Ramkrishna's development of the cybernetic modeling approach. The value of mathematical models to organize data, to consider interactions in complex systems in a rational way, to correct the conventional wisdom, and to understand essential qualitative features of biological systems has been clearly documented in prior research. The impact of this research in biotechnology discovery has so far been limited, but this will change in the future if we are adept in recognizing emerging opportunities and in integrating new concepts and tools into our research. Mathematical structures and methods, allied with extraordinary contemporary computing power, are essential to the emerging field of functional genomics. Important in this quest is a hierarchy of powerful modeling, analysis, and computational tools which can capture essential quantitative features of available experimental data and use these effectively for analysis and design of metabolism.