Nikolaos V. Mantzaris

Associate Professor in Chemical and Biomolecular Engineering
Assistant Professor in Bioengineering

Research Interests:

Mathematical modeling of biological systems

Signal transduction and pattern formation

Cell population balances

Nonlinear control of bioprocesses

Particulate processes

Education:

Diploma, Chemical Engineering
National Technical University of Athens, Hellas (1989-1994)

Research Assistant, Microelectronics
National Center for Scientific Research, Hellas (1994-1995)

Ph.D., Chemical Engineering
University of Minnesota (1995-2000)

Postdoctoral Associate, Applied Mathematics
University of Minnesota (2000-2001)

Our research aims at understanding, optimizing and controlling the behavior of different types of biological systems with the use of mathematical modeling. The common thread lies in the methodology and the tools employed in order to accomplish such challenging goals. On one end, we are creating simplified caricature models that can capture essential, experimentally observed features of the system under consideration. The advantage of such an approach is that most of the dynamical analysis can be performed analytically using elements from bifurcation theory. On the other end, we are developing sophisticated two- and three-dimensional numerical algorithms, which, in combination with the intuition and understanding gained from the simplified model results, serve as the basis for studying the asymptotic as well as the transient behavior of the full, detailed models. Furthermore, due to the fact that biological processes are inherently nonlinear, we are constructing nonlinear feedback control laws using these models, in order to achieve important control objectives, which are implemented and tested via numerical simulations.

Signal Transduction and Biological Pattern Formation

From the unicellular level to the largest plants and animals, organisms have developed sophisticated signal detection and transduction systems used to sense their environment, and then accordingly adjust their behavior in order to find food and mates, initiate developmental changes, avoid harmful environments and in general perform a wide variety of functions that lead to patterns of astonishing harmony and complexity. There are two areas of current interest and concentration:

1. Calcium Dynamics: We are studying the signal transduction mechanisms that utilize intracellular calcium (Ca2+) to activate various processes, including muscle contraction, neuromodulation, insulin secretion etc. Intercellula calcium signaling is considered to play a key role in pathological conditions such as spreading depression, epilepsy, as well as arrhythmia in cardiac tissues. In order to control the effects of calcium wave propagation, it is necessary to first identify the relative importance of the complicated mechanisms involved in intercellular signaling through calcium waves.
   
2. Tumor-induced Angiogenesis: Tumor-induced angiogenesis is the process by which new blood capillaries grow into areas previously unoccupied by vascular tissue in the presence of a hypoxic tumor. It is a distinct stage of tumor growth, without which solid tumors (independent of cancer type) do not grow more than 1-2 mm in diameter and the tumor mass does not contain more than 100,000-1,000,000 cells. Recent discoveries of substances which inhibit the formation of these blood vessels have revolutionized cancer research. However, a fundamental understanding of the experimentally observed phenomena associated with tumor-induced angiogenesis is still lacking. To this end, mathematical modeling, dynamical analysis and simulation are of obvious importance.

Cell Population Balance Modeling

Cell population balance models are the only models proposed to date that take into account the heterogeneous nature of cell growth processes. Despite their undisputed accuracy, they have been underutilized for design and control purposes due to two main reasons: a) they are hard to solve and b) the functions that describe single-cell mechanisms and appear as parameters in these models are typically unknown. Our research focuses on overcoming these obstacles in several different ways:

1. Numerical Solution and Dynamical Studies: We are developing efficient algorithms that can accurately approximate the solution of cell population balance models and can help us analyze the underlying dynamical behavior of such systems.
2. Inverse Cell Population Balance Modeling: We are constructing the theoretical and computational framework that can utilize flow cytometric data in conjunction with the numerical solution of cell population balance models in order to determine the unknown parameters that describe specific single-cell mechanisms, such as growth, division, birth etc.
3. Cybernetic Modeling: We are working on applying cybernetic modeling principles at the single-cell level, with the objective to model division as well as transition between cell cycle stages.

Nonlinear Control of Bioprocesses

The large majority of model based control approaches that have been suggested in the literature to control bioprocesses are based on mathematical models that do not recognize the distributed nature of cell growth. However, various products of biotechnological interest are being produced only by specific cell subpopulations (e.g. subpopulations consisting of cells in certain cell cycle stages). Motivated by the fact that such processes can most effectively be described by cell population balance models we are developing feedback control laws that are based on such models. These control approaches require measurements of entire cell property distributions, which are now obtainable due to recent advances in online measurement technology. Moreover, the availability of the computational tools for the accurate solution of multi-variable cell population balance models provides the basis for controlling the dynamics of metabolic pathways and ultimately the production of important metabolites.

Particulate Processes

Particulate systems are abundant in chemical and biochemical engineering. Some examples include crystallization, comminution, aerosol, emulsion polymerization and microbial growth systems. Despite obvious differences, there is at least one important similarity between these systems: their dynamics can be mathematically described using population balance models, the numerical solution of which has been an active area of research for the last 30 years. However, most numerical methods have focused on the specifics of the problem of interest. We are working on a unified and general numerical approach for this class of problems, which will serve as a valuable computational interface for revealing important similarities in the dynamical behavior of these systems as well as for promoting the cross-fertilization of ideas and methodologies used to address common problems (e.g. inverse problems). Applications of immediate interest include the growth of filamentous organisms used in the production of antibiotics and kidney stone formation.

Selected Publications

1. Mantzaris, N.V. "Single-Cell Gene-Switching Networks and Heterogeneous Cell Population Phenotypes", Comp. Chem. Eng., (Accepted), (2004).
2. Mantzaris, N.V. and Daoutidis , P., "Cell Population Balance Modeling and Control in Continuous Bioreactors", Journal of Process Control, 14 (7), 775-784 (2004).
3. Mantzaris, N. V., Webb, S. and Othmer, H. G. "Mathematical Modeling of Tumor Induced Angiogenesis: A Review", Journal of Mathematical Biology (available on-line 2/6/04) (2004).
4. Fredrickson, A. G. and Mantzaris, N. V. “A New Set of Population Balance Equations for Microbial and Cell Cultures”, Chem. Eng. Sci., 57 (12), 2265-2278 (2002).
   
5. Mantzaris, N. V., Srienc, F. and Daoutidis P. “Nonlinear Productivity Control in using a Multi-Staged Cell Population Balance Model”, Chem. Eng. Sci., 57 (1), 1-14, (2002)
6. Mantzaris, N. V., Daoutidis P. and Srienc, F. “Numerical Solution of Multivariable Cell Population Balance Models. I: Finite Difference Methods”, Comp. & Chem. Eng., 25 (11-12), 1411-1440, (2001).
7. Mantzaris, N. V., Daoutidis P. and Srienc, F. “Numerical Solution of Multivariable Cell Population Balance Models. II: Spectral Methods”, Comp. & Chem. Eng., 25 (11-12), 1441-1462, (2001).
8. Mantzaris, N. V., Daoutidis P. and Srienc, F. “Numerical Solution of Multivariable Cell Population Balance Models. III: Finite Element Methods”, Comp. & Chem. Eng., 25 (11-12), 1463-1481, (2001).
9. Kelley, A. S., Mantzaris, N. V., Daoutidis, P., and Srienc, F. “Controlled Synthesis of Polyhydroxyalkanoic Nanostructures in R. eutropha”, Nano Letters, 1 (9), 481-485, (2001).
10. Mantzaris, N. V., Kelley, A. S., Daoutidis, P., and Srienc, F. “An Optimal Carbon Source Switching Strategy for the Production of PHA di-block Copolymers with Ralstonia eutropha” AIChE J. 47 (3), pages 727-743, (2001).

CHEMICAL & BIOMOLECULAR ENGINEERING DEPT. MS-362
Rice University PO Box 1892 Houston, Texas 77251-1892	E-mail: chbe@rice.edu	Phone: (713) 348-4902 FAX:(713) 348-5478