Mathematical programming techniques for analysis and design of biotechnological systems.
The complexity of biotechnological systems does not allow their study without the use of advanced mathematical programming techniques. Metabolic flux quantification and optimal synthesis and design of multiproduct plants are problems with this characteristic, and are addressed in this thesis. The metabolic flux quantification employing labeling balances is formulated as a nonlinear optimization problem that is solved by the minimization of the difference between experimental measurements and predictions of the metabolic network model. This problem is generated by the necessity of estimating the rates of biochemical reactions that characterize the metabolism. The mathematical model for this class of problems is composed by balances of metabolites and isotopes; the former are linear whereas the latter are nonlinear and, in this work, are modeled by a modification of the atom mapping matrix technique. A spatial branch & bound algorithm was developed to quantify the metabolic fluxes, that considers the existence of local optima; in this algorithm, the global search is developed by the division of the searching region (branching) and the generation of sequences of bounds (bounding) that converge to the global solution. As a case study, fluxes in central metabolism of Saccharomyces cerevisiae were estimated. The results confirm the existence of local solutions and the necessity of develop a global search strategy; the central fluxes in the obtained global solution are similar to those ones obtained by an evolutionary algorithm. To solve problems of synthesis and design of multiproduct biotechnological systems, the most employed approaches are the sequential selection and sizing of the unit operations, and the fixing of sizing and time parameters (employing values from laboratory or pilot plants); nevertheless, both approaches generate suboptimal solutions. On the other hand, the simultaneous solution of the synthesis and design of multiproduct biotechnological systems generates large size mixed-integer nonlinear models (MINLP), due to the combination of options into the processing with nonlinear constraints from the operation models. As case study, a plant for production of insulin, hepatitis B vaccine, tissue plasminogen activator and superoxide dismutase was considered, by three hosts: yeast (S. cerevisiae) with extra or intracellular expression, Escherichia coli and mammalian cells. The design must satisfy the production target for each product, minimizing the capital cost and considering the selection of hosts, the operations and the number of parallel units in each stage. The obtained results show that the formulation of decisions by the big-M approach allows the solution of the generated MINLP model and that consideration of several products with different processing sequences and conditions generates large idleness at the equipment and increases the total cost of the design. In the case study it was observed that the allocation of storage tanks has a limited effect on cost reduction, but the simultaneous implementation of flexible scheduling, design of auxiliary equipments and intermediate storage tanks allow the generation of satisfactory designs.
Advisor:Jose Mauricio Pinto; Roberto de Campos Giordano; Andreas Karoly Gombert; Reginaldo Guirardello; Jorge Andrey Wilhelms Gut; Jose Mauricio Pinto
School:Universidade de São Paulo
Source Type:Master's Thesis
Keywords:global optimization mathematical programming metabolic flux quantification mixed-integer synthesis and design of multiproduct plants
Date of Publication:09/02/2005