Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.National Institutes of Health (U.S.) (Grant P50-GM068762)National Institutes of Health (U.S.) (Grant R24-DK090963)United States. Army Research Office (Grant W911NF-09-0001)German Research Foundation (Grant GSC 111

Identifying Drug Effects via Pathway Alterations using an Integer Linear Programming Optimization Formulation on Phosphoproteomic Data

Understanding the mechanisms of cell function and drug action is a major endeavor in the pharmaceutical industry. Drug effects are governed by the intrinsic properties of the drug (i.e., selectivity and potency) and the specific signaling transduction network of the host (i.e., normal vs. diseased cells). Here, we describe an unbiased, phosphoproteomicbased approach to identify drug effects by monitoring drug-induced topology alterations. With the proposed method, drug effects are investigated under several conditions on a cell-type specific signaling network. First, starting with a generic pathway made of logical gates, we build a cell-type specific map by constraining it to fit 13 key phopshoprotein signals under 55 experimental cases. Fitting is performed via a formulation as an Integer Linear Program (ILP) and solution by standard ILP solvers; a procedure that drastically outperforms previous fitting schemes. Then, knowing the cell topology, we monitor the same key phopshoprotein signals under the presence of drug and cytokines and we re-optimize the specific map to reveal the drug-induced topology alterations. To prove our case, we make a pathway map for the hepatocytic cell line HepG2 and we evaluate the effects of 4 drugs: 3 selective inhibitors for the Epidermal Growth Factor Receptor (EGFR) and a non selective drug. We confirm effects easily predictable from the drugs’ main target (i.e. EGFR inhibitors blocks the EGFR pathway) but we also uncover unanticipated effects due to either drug promiscuity or the cell’s specific topology. An interesting finding is that the selective EGFR inhibitor Gefitinib is able to inhibit signaling downstream the Interleukin-1alpha (IL-1α) pathway; an effect that cannot be extracted from binding affinity based approaches. Our method represents an unbiased approach to identify drug effects on a small to medium size pathways and is scalable to larger topologies with any type of signaling perturbations (small molecules, 3 RNAi etc). The method is a step towards a better picture of drug effects in pathways, the cornerstone in identifying the mechanisms of drug efficacy and toxicity

Training Signaling Pathway Maps to Biochemical Data with Constrained Fuzzy Logic: Quantitative Analysis of Liver Cell Responses to Inflammatory Stimuli

Predictive understanding of cell signaling network operation based on general prior knowledge but consistent with empirical data in a specific environmental context is a current challenge in computational biology. Recent work has demonstrated that Boolean logic can be used to create context-specific network models by training proteomic pathway maps to dedicated biochemical data; however, the Boolean formalism is restricted to characterizing protein species as either fully active or inactive. To advance beyond this limitation, we propose a novel form of fuzzy logic sufficiently flexible to model quantitative data but also sufficiently simple to efficiently construct models by training pathway maps on dedicated experimental measurements. Our new approach, termed constrained fuzzy logic (cFL), converts a prior knowledge network (obtained from literature or interactome databases) into a computable model that describes graded values of protein activation across multiple pathways. We train a cFL-converted network to experimental data describing hepatocytic protein activation by inflammatory cytokines and demonstrate the application of the resultant trained models for three important purposes: (a) generating experimentally testable biological hypotheses concerning pathway crosstalk, (b) establishing capability for quantitative prediction of protein activity, and (c) prediction and understanding of the cytokine release phenotypic response. Our methodology systematically and quantitatively trains a protein pathway map summarizing curated literature to context-specific biochemical data. This process generates a computable model yielding successful prediction of new test data and offering biological insight into complex datasets that are difficult to fully analyze by intuition alone.National Institutes of Health (U.S.) (NIH grant P50-GM68762)National Institutes of Health (U.S.) (Grant U54-CA112967)United States. Dept. of Defense (Institute for Collaborative Biotechnologies

Animal welfare in studies on murine tuberculosis : assessing progress over a 12-year period and the need for further improvement

There is growing concern over the welfare of animals used in research, in particular when these animals develop pathology. The present study aims to identify the main sources of animal distress and to assess the possible implementation of refinement measures in experimental infection research, using mouse models of tuberculosis (TB) as a case study. This choice is based on the historical relevance of mouse studies in understanding the disease and the present and long-standing impact of TB on a global scale. Literature published between 1997 and 2009 was analysed, focusing on the welfare impact on the animals used and the implementation of refinement measures to reduce this impact. In this 12-year period, we observed a rise in reports of ethical approval of experiments. The proportion of studies classified into the most severe category did however not change significantly over the studied period. Information on important research parameters, such as method for euthanasia or sex of the animals, were absent in a substantial number of papers. Overall, this study shows that progress has been made in the application of humane endpoints in TB research, but that a considerable potential for improvement remains.Nuno H. Franco is funded by Fundação para a Ciência e Tecnologia (SFRH/BD/38337/2007). This work is funded by FEDER funds through the Operational Competitiveness Programme - COMPETE and by national funds through FCT - Fundação para a Ciência e Tecnologia under the project FCOMP-01-0124-FEDER-022718 (PEst-C/SAU/LA0002/2011

Positional Cloning of “Lisch-like”, a Candidate Modifier of Susceptibility to Type 2 Diabetes in Mice

In 404 Lepob/ob F2 progeny of a C57BL/6J (B6) x DBA/2J (DBA) intercross, we mapped a DBA-related quantitative trait locus (QTL) to distal Chr1 at 169.6 Mb, centered about D1Mit110, for diabetes-related phenotypes that included blood glucose, HbA1c, and pancreatic islet histology. The interval was refined to 1.8 Mb in a series of B6.DBA congenic/subcongenic lines also segregating for Lepob. The phenotypes of B6.DBA congenic mice include reduced β-cell replication rates accompanied by reduced β-cell mass, reduced insulin/glucose ratio in blood, reduced glucose tolerance, and persistent mild hypoinsulinemic hyperglycemia. Nucleotide sequence and expression analysis of 14 genes in this interval identified a predicted gene that we have designated “Lisch-like” (Ll) as the most likely candidate. The gene spans 62.7 kb on Chr1qH2.3, encoding a 10-exon, 646–amino acid polypeptide, homologous to Lsr on Chr7qB1 and to Ildr1 on Chr16qB3. The largest isoform of Ll is predicted to be a transmembrane molecule with an immunoglobulin-like extracellular domain and a serine/threonine-rich intracellular domain that contains a 14-3-3 binding domain. Morpholino knockdown of the zebrafish paralog of Ll resulted in a generalized delay in endodermal development in the gut region and dispersion of insulin-positive cells. Mice segregating for an ENU-induced null allele of Ll have phenotypes comparable to the B.D congenic lines. The human ortholog, C1orf32, is in the middle of a 30-Mb region of Chr1q23-25 that has been repeatedly associated with type 2 diabetes

A Network-Based Multi-Target Computational Estimation Scheme for Anticoagulant Activities of Compounds

BACKGROUND: Traditional virtual screening method pays more attention on predicted binding affinity between drug molecule and target related to a certain disease instead of phenotypic data of drug molecule against disease system, as is often less effective on discovery of the drug which is used to treat many types of complex diseases. Virtual screening against a complex disease by general network estimation has become feasible with the development of network biology and system biology. More effective methods of computational estimation for the whole efficacy of a compound in a complex disease system are needed, given the distinct weightiness of the different target in a biological process and the standpoint that partial inhibition of several targets can be more efficient than the complete inhibition of a single target. METHODOLOGY: We developed a novel approach by integrating the affinity predictions from multi-target docking studies with biological network efficiency analysis to estimate the anticoagulant activities of compounds. From results of network efficiency calculation for human clotting cascade, factor Xa and thrombin were identified as the two most fragile enzymes, while the catalytic reaction mediated by complex IXa:VIIIa and the formation of the complex VIIIa:IXa were recognized as the two most fragile biological matter in the human clotting cascade system. Furthermore, the method which combined network efficiency with molecular docking scores was applied to estimate the anticoagulant activities of a serial of argatroban intermediates and eight natural products respectively. The better correlation (r = 0.671) between the experimental data and the decrease of the network deficiency suggests that the approach could be a promising computational systems biology tool to aid identification of anticoagulant activities of compounds in drug discovery. CONCLUSIONS: This article proposes a network-based multi-target computational estimation method for anticoagulant activities of compounds by combining network efficiency analysis with scoring function from molecular docking

Differential metabolic activity and discovery of therapeutic targets using summarized metabolic pathway models

Abstract In spite of the increasing availability of genomic and transcriptomic data, there is still a gap between the detection of perturbations in gene expression and the understanding of their contribution to the molecular mechanisms that ultimately account for the phenotype studied. Alterations in the metabolism are behind the initiation and progression of many diseases, including cancer. The wealth of available knowledge on metabolic processes can therefore be used to derive mechanistic models that link gene expression perturbations to changes in metabolic activity that provide relevant clues on molecular mechanisms of disease and drug modes of action (MoA). In particular, pathway modules, which recapitulate the main aspects of metabolism, are especially suitable for this type of modeling. We present Metabolizer, a web-based application that offers an intuitive, easy-to-use interactive interface to analyze differences in pathway metabolic module activities that can also be used for class prediction and in silico prediction of knock-out (KO) effects. Moreover, Metabolizer can automatically predict the optimal KO intervention for restoring a diseased phenotype. We provide different types of validations of some of the predictions made by Metabolizer. Metabolizer is a web tool that allows understanding molecular mechanisms of disease or the MoA of drugs within the context of the metabolism by using gene expression measurements. In addition, this tool automatically suggests potential therapeutic targets for individualized therapeutic interventions