The word cybernetics has its roots in the Greek word \kybernetes" or \steers-man" and was coined by Norbert Wiener in 1948 to describe \the science of control and communication, in the animal and the machine". The discipline focuses on the way various complex systems (animals/machines) steer towards/maintain their goals utilizing information, models and control actions in the face of various disturbances. For a given animal/machine, cybernetics considers all the possible behaviors that the animal/machine can exhibit and then enquires about the constraints that result in a particular behavior. The thesis focuses on the application of principles of cybernetics to the modeling and optimization of bioreactors and lies at the interface of systems engineering and biology. Specifically, it lies at the interface of control theory and the growth behavior exhibited by microorganisms. The hypothesis of the present work is that the principles and tools of control theory can give novel insights into the growth behavior of microorganisms and that the growth behavior exhibited by microorganisms can in turn provide insights for the development of principles and tools of control theory. Mathematical models for the growth of microorganisms such as stoichiometric, optimal and cybernetic assume that microorganisms have evolved to become optimal with respect to certain cellular goals or objectives. Typical cellular goals used in the literature are the maximization of instantaneous/short term objectives such biomass yield, instantaneous growth rate, instantaneous ATP production rate etc. Since microorganisms live in a dynamic world, it is expected that the microorganisms have evolved towards maximizing long term goals. In the literature, it is often assumed that the maximization of a short term cellular goal results in the maximization of the long term cellular goal. However, in the systems engineering literature, it has long been recognized that the maximization of a short term goal does not necessarily result in the maximization of the long term goal. For example, maximization of product production in a fed-batch bioreactor involves two separate phases: a first phase in which the growth of microorganisms is maximized and a second phase in which the production of product is maximized. An analogous situation arises when the bacterium E. coli passes through the digestive tract of mammals wherein it first encounters the sugar lactose in the proximal portions and the sugar maltose in the distal portions. Mitchell et al. (2009) have experimentally shown that when E. coli encounters the sugar lactose, it expresses the genes of maltose operons anticipatorily which reduces its growth rate on lactose. This regulatory strategy of E. coli has been termed asymmetric anticipatory regulation (AAR) and is shown to be beneficial for long term cellular fitness by Mitchell et al. (2009). The cybernetic modeling framework for the growth of microorganisms, developed by Ramakrishna and co-workers, is extended in the present thesis for modeling the AAR strategy of E. coli. The developed model accurately captures the experimental observations of the AAR phenomenon, reveals the inherent advantages of the cybernetic modeling framework over other frameworks in explaining the AAR phenomenon, while at the same time suggesting a scope for the generalization of the cybernetic framework. As cybernetics is interested in all the possible behaviors that a machine (which is, in the present case, microorganism) can exhibit, a rigorous analysis of the optimal dynamic growth behavior of microorganisms under various constraints is carried out next using the methods of optimal control theory. An optimal control problem is formulated using a generalized version of the unstructured Monod model with the objective of maximization of cellular concentration at a fixed final time. Optimal control analysis of the above problem reveals that the long term objective of maximization of cellular concentration at a final time is equivalent to maximization of instantaneous growth rate for the growth of microorganisms under various constraints in a two substrate batch environment. In addition, reformulation of the above optimal control problem together with its necessary conditions of optimality reveals the existence of generalized governing dynamic equations of the structured cybernetic modeling framework. The dynamic behavior of the generalized equations of the cybernetic modeling framework is analyzed further to gain insights into the growth of microorganisms. For growth of microorganisms on a single growth limiting carbon substrate, the analysis reveals that the cybernetic model exhibits linear growth behavior, similar to that of the unstructured Contois model at high cellular concentrations, under appropriate constraints. During the growth of microorganisms on multiple substitutable substrates, the analysis reveals the existence of simple correlations that quantitatively predict the mixed substrate maximum specific growth rate from single substrate maximum specific growth rates during simultaneous consumption of the substrates in several cases. Further analysis of the cybernetic model of the growth of S. cerevisiae on the mixture of glucose and galactose reveals that S. cerevisiae exhibits sub-optimal dynamic growth with a long diauxic lag phase and suggests the possibility for S. cerevisiae to grow optimally with a significantly reduced diauxic lag period. Since cybernetics is interested in understanding the constraints under which a particular machine (microorganism) exhibits a particular behavior, a methodology is then developed for inferring the internal constraints experienced by the microorganisms from experimental data. The methodology is used for inferring the internal constraints experienced by E. coli during its growth on the mixture of glycerol and lactose. An interesting question in the study of the growth behavior of microorganisms concerns the objective that the microorganisms optimize. Several studies aim to determine these cellular objectives experimentally. A similar question that is relevant to the optimization of fed-batch bioreactors is \what are the objectives that are to be optimized by the feed flow rate in various time intervals for the optimization of a final objective?" It was mentioned previously that the maximization of product production in a fed-batch bioreactor involves maximization of growth of microorganisms first and the maximization of product production later. However, such guidelines can only be stated for relatively simple bioreactor optimization problems and no such guidelines exist for sufficiently complex problems. For complex problems, the answer to the above question requires the formulation and solution of a genetic programming problem which can be quite challenging. An alternative numerical solution methodology is developed in the present thesis to address the above question. The solution methodology involves the specification of bioreactor objectives in terms of the bioreactor trajectory in the state space of substrate concentration-volume. The equivalent control law of the sliding mode control technique is used for finding the inlet feed ow rate that tracks the bioreactor trajectory accurately. The search for the best bioreactor trajectory is carried out using the stochastic search technique genetic algorithm. The effectiveness of the developed solution methodology in determining the optimal bioreactor trajectory is demonstrated using three challenging bioreactor optimization problems.

<p>Regulation of metabolism in mammalian cells is achieved through a complex interplay between cellular signaling, metabolic reactions, and transcriptional changes. The modeling of metabolic fluxes in a cell requires the knowledge of all these mechanisms, some of which may be unknown. A cybernetic approach provides a framework to model these complex interactions through the implicit accounting of such regulatory mechanisms, assuming a biological “goal”. The goal-oriented control policies of cybernetic models have been used to predict metabolic phenomena ranging from complex substrate uptake patterns and dynamic metabolic flux distributions to the behavior of gene knockout strains. The premise underlying the cybernetic framework is that the regulatory processes affecting metabolism can be mathematically formulated as a cybernetic objective through variables that constrain the network to achieve a specified biological “goal”. </p><p>Cybernetic theory builds on the perspective that regulation is organized towards achieving goals relevant to an organism’s survival or displaying a specific phenotype in response to a stimulus. While cybernetic models have been established by prior work carried out in bacterial systems, we show its applicability to more complex biological systems with a predefined goal. We have modeled eicosanoid, a well-characterized set of inflammatory lipids derived from arachidonic acid, metabolism in mouse bone marrow derived macrophage (BMDM) cells stimulated by Kdo2-Lipid A (KLA, a chemical analogue of Lipopolysaccharide found on the surface of bacterial cells) and adenosine triphosphate (ATP, a danger signal released in response to surrounding cell death) using cybernetic control variables. Here, the cybernetic goal is inflammation; the hallmark of inflammation is the expression of cytokines which act as autocrine signals to stimulate a pro-inflammatory response. Tumor necrosis factor (TNF)-α is an exemplary pro-inflammatory marker and can be designated as a cybernetic objective for modeling eicosanoid—prostaglandin (PG) and leukotriene (LK)—metabolism. Transcriptomic and lipidomic data for eicosanoid biosynthesis and conversion were obtained from the LIPID Maps database. We show that the cybernetic model captures the complex regulation of PG metabolism and provides a reliable description of PG formation using the treatment ATP stimulation. We then validated our model by predicting an independent data set, the PG response of KLA primed ATP stimulated BMDM cells.</p><p>The process of inflammation is mediated by the production of multiple cytokines, chemokines, and lipid mediators each of which contribute to specific individual objectives. For such complex processes in mammalian systems, a cybernetic objective based on a single protein/component may not be sufficient to capture all the biological processes thereby necessitating the use of multiple objectives. The choice of the objective function has been made by intuitive considerations in this thesis. If objectives are conjectured, an argument can be made for numerous alternatives. Since regulatory effects are estimated from unregulated kinetics, one encounters the risk of multiplicity in this regard giving rise to multiple models. The best model is of course that which is able to predict a comprehensive set of perturbations. Here, we have extended our above model to also capture the dynamics of LKs. We have used migration as a biological goal for LK using the chemoattractant CCL2 as a key representative molecule describing cell activation leading to an inflammatory response where a goal composed of multiple cybernetic objectives is warranted. Alternative model objectives included relating both branches of the eicosanoid metabolic network to the inflammatory cytokine TNF-α, as well as the simple maximization of all metabolic products such that each equally contributes to the inflammatory system outcome. We were again able to show that all three cybernetic objectives describing the LK and PG branches for eicosanoid metabolism capture the complex regulation and provide a reliable description of eicosanoid formation. We performed simulated drug and gene perturbation analyses on the system to identify differences between the models and propose additional experiments to select the best cybernetic model.</p><p>The advantage to using cybernetic modeling is in its ability to capture system behavior without the same level of detail required for these interactions as standard kinetic modeling. Given the complexity of mammalian systems, the cybernetic goal for mammalian cells may not be based solely on survival or growth but on specific context dependent cellular responses. In this thesis, we have laid the groundwork for the application of cybernetic modeling in complex mammalian systems through a specific example case of eicosanoid metabolism in BMDM cells, illustrated the case for multiple objectives, and highlighted the extensibility of the cybernetic framework to other complex biological systems.</p>