DOTcvpSB, a software toolbox for dynamic optimization in systems biology

<p>Abstract</p> <p>Background</p> <p>Mathematical optimization aims to make a system or design as effective or functional as possible, computing the quality of the different alternatives using a mathematical model. Most models in systems biology have a dynamic nature, usually described by sets of differential equations. Dynamic optimization addresses this class of systems, seeking the computation of the optimal time-varying conditions (control variables) to minimize or maximize a certain performance index. Dynamic optimization can solve many important problems in systems biology, including optimal control for obtaining a desired biological performance, the analysis of network designs and computer aided design of biological units.</p> <p>Results</p> <p>Here, we present a software toolbox, DOTcvpSB, which uses a rich ensemble of state-of-the-art numerical methods for solving continuous and mixed-integer dynamic optimization (MIDO) problems. The toolbox has been written in MATLAB and provides an easy and user friendly environment, including a graphical user interface, while ensuring a good numerical performance. Problems are easily stated thanks to the compact input definition. The toolbox also offers the possibility of importing SBML models, thus enabling it as a powerful optimization companion to modelling packages in systems biology. It serves as a means of handling generic black-box models as well.</p> <p>Conclusion</p> <p>Here we illustrate the capabilities and performance of DOTcvpSB by solving several challenging optimization problems related with bioreactor optimization, optimal drug infusion to a patient and the minimization of intracellular oscillations. The results illustrate how the suite of solvers available allows the efficient solution of a wide class of dynamic optimization problems, including challenging multimodal ones. The toolbox is freely available for academic use.</p

State-controlled epidemic in a game against a novel pathogen

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool. In our game-theoretical framework, the state is playing against a pathogen by introducing non-pharmaceutical interventions to fulfil its socio-political goals, such as guaranteeing hospital care to all needed patients, keeping the country functioning, while the applied social restrictions should be as soft as possible. With the inclusion of activity and economic sector dependent transmission rate, optimal control of lockdowns and health care capacity management is calculated. We identify the presence and length of a pre-symptomatic infectious stage of the disease to have the greatest effect on the probability to cause a pandemic. Here we show that contrary to intuition, the state should not strive for the great expansion of its health care capacities even if its goal is to provide care for all requiring it and minimize the cost of lockdowns

Theoretical Foundation of the Control of Pollination by Hoverflies in a Greenhouse

We propose a conceptual model for pollination and fertilization of tomato flowers in greenhouses crops by hoverflies, when the maximal number of adult pollinators maintained by the crops is less than what is needed for an economically successful pollination in greenhouses. The model consists of a two-stage process for additional feeding of hoverfly to maintain the pollinator density at the economically desired level. First, with a stochastic model, we calculate the density of flies necessary for the economically successful pollination, determined according to the economically expected yield. Second, using a deterministic optimal control model, we find a minimum cost supplementary feeding strategy. In summary, we theoretically demonstrate, at the present stage of the research without validations in case studies, that optimal supplementary feeding can maintain the economically desired hoverfly density

ANALISIS KESTABILAN DAN STRATEGI PEMBERIAN MAKANAN OPTIMAL PADA MODEL PERTUMBUHAN MIKROALGA DALAM BIOREAKTOR FED-BATCH

Beberapa negara di dunia mulai beralih ke sumber energi alternatif untuk memenuhi kebutuhan bahan bakarnya. Salah satu bahan bakar alternatif yang banyak dikembangkan adalah biodiesel. Bahan baku pembuatan biodesel dapat diperoleh antara lain dengan cara budidaya mikroalga dalam bioreaktor fed-batch. Selain dibutuhkan pengetahuan tentang dinamika pertumbuhan mikroalga, dibutuhkan pula pengendalian optimal untuk meningkatkan produktivitas budidaya mikroalga. Dalam tesis ini dibahas model matematika pertumbuhan mikroalga dalam bioreaktor fed-batch, analisis kestabilan titik kesetimbangan, dan strategi pemberian makanan yang optimal menggunakan Prinsip Minimum Pontryagin. Model pertumbuhan mikroalga dalam bioreaktor fed-batch memiliki dua titik kesetimbangan, yaitu titik kesetimbangan trivial dan nontrivial. Titik kesetimbangan trivial bersifat stabil asimtotik dengan syarat laju pengenceran lebih besar daripada laju pertumbuhan maksimal mikroalga. Sedangkan titik kesetimbangan nontrivial bersifat tak stabil. Hasil simulasi numerik dengan DOTcvpSB menunjukkan bahwa model pertumbuhan mikroalga dengan pengendalian dalam pemberian makanan menghasilkan hasil panen yang lebih banyak dan biaya yang lebih minimum daripada model pertumbuhan mikroalga tanpa pengendalian

A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available

A control-theoretic approach to dynamic optimization of metabolic networks

The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-ane model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic ux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a nite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Dierential-Algebraic system. In the innite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available

Robust network calibration and therapy design in systems biology

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 115-123).Mathematical modeling of biological networks is under active research, receiving attention for its ability to quantitatively represent the modeler's systems-level understanding of network functionalities. Computational methods that enhance the usefulness of mathematical models are thus being increasingly sought after, as they face a variety of difficulties that originate from limitations in model accuracy and experimental precision. This thesis explores robust optimization as a tool to counter the effects of these uncertainty-based difficulties in calibrating biological network models and in designing protocols for cancer immunotherapy. The robust approach to network calibration and therapy design aims to account for the worst-case uncertainty scenario that could threaten successful determination of network parameters or therapeutic protocols, by explicitly identifying and sampling the region of potential uncertainties corresponding to worst-case. Through designating individual numerical ranges that uncertain model parameters are each expected to lie within, the region of uncertainties is defined as a hypercube that encompasses a particular uncertainty range along each of its dimensions. For investigating its applicability to parameter estimation, the performance of the optimization method that embodies this robust approach is examined in the context of a model of a unit belonging to the mitogen-activated protein kinase pathway. For its significance in therapeutic design, the method is applied to both a canonical mathematical model of the tumor-immune system and a model specific to treating superficial bladder cancer with Bacillus Calmette-Guirin, which have both been selected to examine the plausibility of applying the method to either discrete-dose or continuous-dose administrations of immunotherapeutic agents. The robust optimization method is evaluated against a standard optimization method by comparing the relative robustness of their respective estimated parameters or designed therapies. Further analysis of the results obtained using the robust method points to properties and limitations, and in turn directions for improvement, of existing models and design frameworks for applying the robust method to network calibration and protocol design. An alternative mathematical formulation to solving the worst-case optimization problem is also studied, one that replaces the sampling process of the previous method with a linearization of the objective function's parameter space over the region of uncertainties. This formulation's relative computational efficiency additionally gives rise to a novel approach to experimental guidance directed at improving modeling efforts under uncertainties, which may potentially further fuel the advancement of quantitative systems biological research.by Bo S. Kim.Ph.D

BENEFICIAL INSECTS IN GREENHOUSES: A STUDY OF SOME ASPECTS OF CANNIBALISM AND POLLINATION.

Tesis doctoral en período de exposición públicaDoctorado en Ciencias Aplicadas al Medio Ambiente (RD99/11) (8904