Alexander Bockmayr

Branch and Infer: a Unifying Framework for Integer and Finite Domain Constraint Programming

We introduce branch and infer, a unifying framework for integer linear programming and finite domain constraint programming. We use this framework to compare the two approaches with respect to their modeling and solving capabilities, to introduce symbolic constraint abstractions into integer programming, and to discuss possible combinations of the two approaches.

A model-based method for investigating bioenergetic processes in autotrophically growing eukaryotic microalgae: Application to the green algae Chlamydomonas reinhardtii

A constraint‐based modeling approach was developed to investigate the metabolic response of the eukaryotic microalgae Chlamydomonas reinhardtii under photoautotrophic conditions. The model explicitly includes thermodynamic and energetic constraints on the functioning metabolism. A mixed integer linear programming method was used to determine the optimal flux distributions with regard to this set of constraints. It enabled us, in particular, to highlight the existence of a light‐driven respiration depending on the incident photon flux density in photobioreactors functioning in physical light limitation.

Temporal constraints in the logical analysis of regulatory networks

Starting from the logical description of gene regulatory networks developed by R. Thomas, we introduce an enhanced modeling approach based on timed automata. We obtain a refined qualitative description of the dynamical behavior by exploiting not only information on ratios of kinetic parameters related to synthesis and decay, but also constraints on the time delays associated with the operations of the system. We develop a formal framework for handling such temporal constraints using timed automata, discuss the relationship with the original Thomas formalism, and demonstrate the potential of our approach by analyzing an illustrative gene regulatory network of bacteriophage @l.

Exploring metabolic pathways in genome-scale networks via generating flux modes

MOTIVATION The reconstruction of metabolic networks at the genome scale has allowed the analysis of metabolic pathways at an unprecedented level of complexity. Elementary flux modes (EFMs) are an appropriate concept for such analysis. However, their number grows in a combinatorial fashion as the size of the metabolic network increases, which renders the application of EFMs approach to large metabolic networks difficult. Novel methods are expected to deal with such complexity. RESULTS In this article, we present a novel optimization-based method for determining a minimal generating set of EFMs, i.e. a convex basis. We show that a subset of elements of this convex basis can be effectively computed even in large metabolic networks. Our method was applied to examine the structure of pathways producing lysine in Escherichia coli. We obtained a more varied and informative set of pathways in comparison with existing methods. In addition, an alternative pathway to produce lysine was identified using a detour via propionyl-CoA, which shows the predictive power of our novel approach. AVAILABILITY The source code in C++ is available upon request.

Using Hybrid Concurrent Constraint Programming to Model Dynamic Biological Systems

Systems biology is a new area in biology that aims at achieving a systems-level understanding of biological systems. While current genome projects provide a huge amount of data on genes or proteins, lots of research is still necessary to understand how the different parts of a biological system interact in order to perform complex biological functions. Computational models that help to analyze, explain or predict the behavior of biological systems play a crucial role in systems biology. The goal of this paper is to show that hybrid concurrent constraint programming [11] may be a promising alternative to existing modeling approaches in systems biology. Hybrid cc is a declarative compositional programming language with a well-defined semantics. It allows one to model and simulate the dynamics of hybrid systems, which exhibit both discrete and continuous change. We show that Hybrid cc can be used naturally to model a variety of biological phenomena, such as reaching thresholds, kinetics, gene interaction or biological pathways.

F2C2: a fast tool for the computation of flux coupling in genome-scale metabolic networks

BackgroundFlux coupling analysis (FCA) has become a useful tool in the constraint-based analysis of genome-scale metabolic networks. FCA allows detecting dependencies between reaction fluxes of metabolic networks at steady-state. On the one hand, this can help in the curation of reconstructed metabolic networks by verifying whether the coupling between reactions is in agreement with the experimental findings. On the other hand, FCA can aid in defining intervention strategies to knock out target reactions.ResultsWe present a new method F2C2 for FCA, which is orders of magnitude faster than previous approaches. As a consequence, FCA of genome-scale metabolic networks can now be performed in a routine manner.ConclusionsWe propose F2C2 as a fast tool for the computation of flux coupling in genome-scale metabolic networks. F2C2 is freely available for non-commercial use at https://sourceforge.net/projects/f2c2/files/.

Incorporating time delays into the logical analysis of gene regulatory networks

Based on the logical description of gene regulatory networks developed by R. Thomas, we introduce an enhanced modelling approach that uses timed automata. It yields a refined qualitative description of the dynamics of the system incorporating information not only on ratios of kinetic constants related to synthesis and decay, but also on the time delays occurring in the operations of the system. We demonstrate the potential of our approach by analysing an illustrative gene regulatory network of bacteriophage λ.

On the Chvátal rank of polytopes in the 0/1 cube

Abstract Given a polytope P⊆ R n , the Chvatal–Gomory procedure computes iteratively the integer hull PI of P. The Chvatal rank of P is the minimal number of iterations needed to obtain PI. It is always finite, but already the Chvatal rank of polytopes in R 2 can be arbitrarily large. In this paper, we study polytopes in the 0/1 cube, which are of particular interest in combinatorial optimization. We show that the Chvatal rank of any polytope P⊆[0,1]n is O (n 3 log n) and prove the linear upper and lower bound n for the case P∩ Z n =∅ .

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi-steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle.

Fast thermodynamically constrained flux variability analysis

MOTIVATION Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints. RESULTS We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected. AVAILABILITY AND IMPLEMENTATION Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de/arnem/fast-tfva.html. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.