871 research outputs found
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks
Flux balance analysis has proven an effective tool for analyzing metabolic
networks. In flux balance analysis, reaction rates and optimal pathways are
ascertained by solving a linear program, in which the growth rate is maximized
subject to mass-balance constraints. A variety of cell functions in response to
environmental stimuli can be quantified using flux balance analysis by
parameterizing the linear program with respect to extracellular conditions.
However, for most large, genome-scale metabolic networks of practical interest,
the resulting parametric problem has multiple and highly degenerate optimal
solutions, which are computationally challenging to handle. An improved
multi-parametric programming algorithm based on active-set methods is
introduced in this paper to overcome these computational difficulties.
Degeneracy and multiplicity are handled, respectively, by introducing
generalized inverses and auxiliary objective functions into the formulation of
the optimality conditions. These improvements are especially effective for
metabolic networks because their stoichiometry matrices are generally sparse;
thus, fast and efficient algorithms from sparse linear algebra can be leveraged
to compute generalized inverses and null-space bases. We illustrate the
application of our algorithm to flux balance analysis of metabolic networks by
studying a reduced metabolic model of Corynebacterium glutamicum and a
genome-scale model of Escherichia coli. We then demonstrate how the critical
regions resulting from these studies can be associated with optimal metabolic
modes and discuss the physical relevance of optimal pathways arising from
various auxiliary objective functions. Achieving more than five-fold
improvement in computational speed over existing multi-parametric programming
tools, the proposed algorithm proves promising in handling genome-scale
metabolic models.Comment: Accepted in J. Optim. Theory Appl. First draft was submitted on
August 4th, 201
Dynamic Bounds on Stochastic Chemical Kinetic Systems Using Semidefinite Programming
Applying the method of moments to the chemical master equation (CME)
appearing in stochastic chemical kinetics often leads to the so-called closure
problem. Recently, several authors showed that this problem can be partially
overcome using moment-based semidefinite programs (SDPs). In particular, they
showed that moment-based SDPs can be used to calculate rigorous bounds on
various descriptions of the stochastic chemical kinetic system's stationary
distribution(s) -- for example, mean molecular counts, variances in these
counts, and so on. In this paper, we show that these ideas can be extended to
the corresponding dynamic problem, calculating time-varying bounds on the same
descriptions
The Per2 Negative Feedback Loop Sets the Period in the Mammalian Circadian Clock Mechanism
Processes that repeat in time, such as the cell cycle, the circadian rhythm, and seasonal variations, are prevalent in biology. Mathematical models can represent our knowledge of the underlying mechanisms, and numerical methods can then facilitate analysis, which forms the foundation for a more integrated understanding as well as for design and intervention. Here, the intracellular molecular network responsible for the mammalian circadian clock system was studied. A new formulation of detailed sensitivity analysis is introduced and applied to elucidate the influence of individual rate processes, represented through their parameters, on network functional characteristics. One of four negative feedback loops in the model, the Per2 loop, was uniquely identified as most responsible for setting the period of oscillation; none of the other feedback loops were found to play as substantial a role. The analysis further suggested that the activity of the kinases CK1δ and CK1ɛ were well placed within the network such that they could be instrumental in implementing short-term adjustments to the period in the circadian clock system. The numerical results reported here are supported by previously published experimental data
Dynamic flux balance modeling to increase the production of high-value compounds in green microalgae
Background
Photosynthetic organisms can be used for renewable and sustainable production of fuels and high-value compounds from natural resources. Costs for design and operation of large-scale algae cultivation systems can be reduced if data from laboratory scale cultivations are combined with detailed mathematical models to evaluate and optimize the process.
Results
In this work we present a flexible modeling formulation for accumulation of high-value storage molecules in microalgae that provides quantitative predictions under various light and nutrient conditions. The modeling approach is based on dynamic flux balance analysis (DFBA) and includes regulatory models to predict the accumulation of pigment molecules. The accuracy of the model predictions is validated through independent experimental data followed by a subsequent model-based fed-batch optimization. In our experimentally validated fed-batch optimization study we increase biomass and β-carotene density by factors of about 2.5 and 2.1, respectively.
Conclusions
The analysis shows that a model-based approach can be used to develop and significantly improve biotechnological processes for biofuels and pigments
Metabolic modeling of synthesis gas fermentation in bubble column reactors
Background A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas) streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngas fermentation technology is underway, an unmet need is the development of integrated metabolic and transport models for industrially relevant syngas bubble column reactors. Results We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngas fermenting bacterium Clostridium ljungdahlii as the microbial catalyst. Our modeling approach involved combining a genome-scale reconstruction of C. ljungdahlii metabolism with multiphase transport equations that govern convective and dispersive processes within the spatially varying column. The reactor model was spatially discretized to yield a large set of ordinary differential equations (ODEs) in time with embedded linear programs (LPs) and solved using the MATLAB based code DFBAlab. Simulations were performed to analyze the effects of important process and cellular parameters on key measures of reactor performance including ethanol titer, ethanol-to-acetate ratio, and CO and H2 conversions. Conclusions Our computational study demonstrated that mathematical modeling provides a complementary tool to experimentation for understanding, predicting, and optimizing syngas fermentation reactors. These model predictions could guide future cellular and process engineering efforts aimed at alleviating bottlenecks to biochemical production in syngas bubble column reactors
Spatiotemporal modeling of microbial metabolism
Background
Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention.
Results
We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution.
Conclusions
Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems
Global optimization of hybrid systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2006.Includes bibliographical references (p. 339-353).Systems that exhibit both discrete state and continuous state dynamics are called hybrid systems. In most nontrivial cases, these two aspects of system behavior interact to such a significant extent that they cannot be decoupled effectively by any kind of abstraction and must be analyzed simultaneously. Hybrid system models are important in many areas of science and engineering, including flip-flops and latching relays, manufacturing systems, air-traffic management systems, controller synthesis, switched systems, chemical process systems, signaling and decision making mechanisms in (biological) cells, robotic systems, safety interlock systems, and embedded systems. The primary focus of this thesis is to explore deterministic methods for the global optimization of hybrid systems. While the areas of modeling, simulation and sensitivity analysis of hybrid systems have received much attention, there are many challenging difficulties associated with the optimization of such systems. The contents of this thesis represent the first steps toward deterministic global optimization of hybrid systems in the continuous time domain. There are various reasons for wanting to solve optimization problems globally.(cont.) In particular, there are many applications which demand that the global solution be found, for example, formal safety verification problems and parameter estimation problems. In the former case, a suboptimal local solution could falsely indicate that all safety specifications are met, leading to disastrous consequences if, in actuality, a global solution exists which provides a counter example that violates some safety specification. In the latter case, a suboptimal local solution could falsely indicate that a proposed model structure did not match experimental data in a statistically significant manner, leading to the false rejection of a valid model structure. In addition, for many optimization problems in engineering, the presence of nonlinear equality constraints makes the optimization problem nonconvex such that local optimization methods can often fail to produce a single feasible point, even though the problem is indeed feasible. The control parameterization framework is employed for the solution of the optimization problem with continuous time hybrid systems embedded. A major difficulty of such a framework lies in the fact that the mode sequence of the embedded hybrid system changes in the space of the optimization decision variables for most nontrivial problems.(cont.) This makes the resulting optimization problem nonsmooth because the parametric sensitivities of the hybrid system do not exist everywhere, thus invalidating efficient gradient based optimization solvers. In this thesis, the general optimization problem is decomposed into three subproblems, and tackled individually: (a) when the mode sequence is fixed, and the transition times are fixed; (b) when the mode sequence is allowed to vary, and the transition times are fixed; and (c) when the mode sequence is fixed, and the transition times are allowed to vary. Because even these subproblems are nontrivial to solve, this thesis focuses on hybrid systems with linear time varying ordinary differential equations describing the continuous dynamics, and proposes various methods to exploit the linear structure. However, in the course of solving the last subproblem, a convexity theory for general, nonlinear hybrid systems is developed, which can be easily extended for general, nonlinear hybrid systems. Subproblem (a) is the easiest to solve. A convexity theory is presented that allows convex relaxations of general, nonconvex Bolza type functions to be constructed for the optimization problem. This allows a deterministic branch-and-bound framework to be employed for the global optimization of the subproblem.(cont.) Subproblems (b) and (c) are much more difficult to solve, and require the exploitation of structure. For subproblem (b), a hybrid superstructure is proposed that enables the linear structure to be retained. A branch-and-cut framework with a novel dynamic bounds tightening heuristic is proposed, and it is shown that the generation of cuts from dynamic bounds tightening can have a dramatic impact on the solution of the problem. For subproblem (c), a time transformation is employed to transform the problem into one with fixed transition times, but nonlinear dynamics. A convexity theory is developed for constructing convex relaxations of general, nonconvex Bolza type functions with the nonlinear hybrid system embedded, along with the development of bounding methods, based on the theory of differential inequalities. A novel bounding technique that exploits the time transformation is also introduced, which can provide much tighter bounds than that furnished utilizing differential inequalities.by Cha Kun Lee.Ph.D
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Dynamic Simulation and Optimization of Nuclear Hydrogen Production Systems
This project is part of a research effort to design a hydrogen plant and its interface with a nuclear reactor. This project developed a dynamic modeling, simulation and optimization environment for nuclear hydrogen production systems. A hybrid discrete/continuous model captures both the continuous dynamics of the nuclear plant, the hydrogen plant, and their interface, along with discrete events such as major upsets. This hybrid model makes us of accurate thermodynamic sub-models for the description of phase and reaction equilibria in the thermochemical reactor. Use of the detailed thermodynamic models will allow researchers to examine the process in detail and have confidence in the accurary of the property package they use
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