Carlos Pozo

Optimization and evolution in metabolic pathways: Global optimization techniques in Generalized Mass Action models

Cells are natural factories that can adapt to changes in external conditions. Their adaptive responses to specific stress situations are a result of evolution. In theory, many alternative sets of coordinated changes in the activity of the enzymes of each pathway could allow for an appropriate adaptive readjustment of metabolism in response to stress. However, experimental and theoretical observations show that actual responses to specific changes follow fairly well defined patterns that suggest an evolutionary optimization of that response. Thus, it is important to identify functional effectiveness criteria that may explain why certain patterns of change in cellular components and activities during adaptive response have been preferably maintained over evolutionary time. Those functional effectiveness criteria define sets of physiological requirements that constrain the possible adaptive changes and lead to different operation principles that could explain the observed response. Understanding such operation principles can also facilitate biotechnological and metabolic engineering applications. Thus, developing methods that enable the analysis of cellular responses from the perspective of identifying operation principles may have strong theoretical and practical implications. In this paper we present one such method that was designed based on nonlinear global optimization techniques. Our methodology can be used with a special class of nonlinear kinetic models known as GMA models and it allows for a systematic characterization of the physiological requirements that may underlie the evolution of adaptive strategies.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

BackgroundDesign of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization.ResultsBased on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity.ConclusionsOur results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems

BackgroundThe estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens.ResultsThis work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied.ConclusionThe capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

Identifying the Preferred Subset of Enzymatic Profiles in Nonlinear Kinetic Metabolic Models via Multiobjective Global Optimization and Pareto Filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Using pareto filters to support risk management in optimization under uncertainty: Application to the strategic planning of chemical supply chains

Abstract Optimization under uncertainty has attracted recently an increasing interest in the process systems engineering literature. The inclusion of uncertainties in an optimization problem inevitably leads to the need to manage the associated risk in order to control the variability of the objective function in the uncertain parameters space. So far, risk management methods have focused on optimizing a single risk metric along with the expected performance. In this work we propose an alternative approach that can handle several risk metrics simultaneously. First, a multi-objective stochastic model containing a set of risk metrics is formulated. This model is then solved efficiently using a tailored decomposition strategy inspired on the Sample Average Approximation. After a normalization step, the resulting solutions are assessed using Pareto filters, which identify solutions showing better performance in the uncertain parameters space. The capabilities and benefits of our approach are illustrated through a design and planning supply chain case study.

Time for global action: an optimised cooperative approach towards effective climate change mitigation

The difficulties in climate change negotiations together with the recent withdrawal of the U.S. from the Paris Agreement call for new cooperative mechanisms to enable a resilient international response. In this study we propose an approach to aid such negotiations based on quantifying the benefits of interregional cooperation and distributing them among the participants in a fair manner. Our approach is underpinned by advanced optimisation techniques that automate the screening of millions of alternatives for differing levels of cooperation, ultimately identifying the most cost-effective solutions for meeting emission targets. We apply this approach to the Clean Power Plan, a related act in the U.S. aiming at curbing carbon emissions from electricity generation, but also being withdrawn. We find that, with only half of the states cooperating, the cost of electricity generation could be reduced by US

An Outer Approximation Algorithm for the Global Optimization of Regulated Metabolic Systems

41 billion per year, while simultaneously cutting carbon emissions by 68% below 2012 levels. These win–win scenarios are attained by sharing the emission targets and trading electricity among the states, which allows exploiting regional advantages. Fair sharing of dividends may be used as a key driver to spur cooperation since the global action to mitigate climate change becomes beneficial for all participants. Even if global cooperation remains elusive, it is worth trying since the mere cooperation of a few states leads to significant benefits for both the U.S. economy and the climate. These findings call on the U.S. to reconsider its withdrawal but also boost individual states to take initiative even in the absence of federal action.

A global optimization strategy to identify quantitative design principles for gene expression in yeast adaptation to heat shock

Abstract Understanding the evolution of cellular metabolism requires a number of techniques able to deal with its complexity. Adaptive responses observed in evolutive studies are expected to consist of an optimal set of changes in enzymes activities fulfilling important physiological constraints. Within this context, we present a novel approach to identify enzyme activity regions that contain feasible biological responses in evolution. The framework presented also allows to optimize the enzyme activity changes required to maximize certain fluxes in biotechnological applications. The method relies on solving nonlinear programming models via global optimization techniques.

Modelling and optimization framework for the multi-objective design of buildings

Abstract In this paper, we present a new method that is able of identifying the optimal enzyme activity changes that allow a system to meet a set of physiological constraints. The problem is formulated as a nonlinear programming (NLP) model, and it is solved by a novel bi-level global optimization algorithm that exploits its mathematical structure.

Electricity mix assessment of the EU member countries using DEA and EffMixF

Abstract Many energy strategies can be applied to a building to improve its energy efficiency without compromising comfort. The analysis becomes more complex when considering not only the energetic improvement but also the corresponding economic cost and especially when considering its multiple environmental impacts. This study presents a methodology for determining the optimal insulation thickness for external building surfaces. As a case study, we model a cubicle like building. It is representative for a conventional Mediterranean construction system and is situated in Lleida, representing a moderate climate in Spain. Our approach is based on a multi-objective optimization model that minimizes simultaneously the cost and eleven environmental impact indicators associated with both the energy consumption over the operational phase and the construction materials used (including the waste produced during the disposal phase). To simplify the problem we reduce the dimensionality of the multi-objective optimization problem identifying and removing in a systematic manner redundant criteria from the mathematical model. To accelerate the optimization analysis we apply a surrogate model which provides the global prediction of the objective functions, and an evaluation of uncertainty of the prediction of this model. Results show that this approach represents a practical tool for performing the dimensionality reduction of criteria and the acceleration of building design optimization through the use of a surrogate model.