Globally convergent algorithms for finding zeros of duplomonotone mappings

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function.This work was supported by the National Research Fund, Luxembourg, co-funded under the Marie Curie Actions of the European Commission (FP7-COFUND), and by the U.S. Department of Energy, Offices of Advanced Scientific Computing Research and the Biological and Environmental Research as part of the Scientific Discovery Through Advanced Computing program, grant #DE-SC0010429

Accelerating the DC algorithm for smooth functions

We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction for the objective function evaluated at this point. Our algorithms are based on a combination of DCA together with a line search step that uses this descent direction. Convergence of the algorithms is proved and the rate of convergence is analysed under the Łojasiewicz property of the objective function. We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the Łojasiewicz property. Numerical tests on various biochemical models clearly show that our algorithms outperform DCA, being on average more than four times faster in both computational time and the number of iterations. Numerical experiments show that the algorithms are globally convergent to a non-equilibrium steady state of various biochemical networks, with only chemically consistent restrictions on the network topology.F. J. Aragón Artacho was supported by MINECO of Spain and ERDF of EU, as part of the Ramón y Cajal program (RYC-2013-13327) and the Grant MTM2014-59179-C2-1-P. R. M. Fleming and P. T. Vuong were supported by the U.S. Department of Energy, Offices of Advanced Scientific Computing Research and the Biological and Environmental Research as part of the Scientific Discovery Through Advanced Computing program, Grant #DE-SC0010429

Recon3D enables a three-dimensional view of gene variation in human metabolism

Genome-scale network reconstructions have helped uncover the molecular basis of metabolism. Here we present Recon3D, a computational resource that includes three-dimensional (3D) metabolite and protein structure data and enables integrated analyses of metabolic functions in humans. We use Recon3D to functionally characterize mutations associated with disease, and identify metabolic response signatures that are caused by exposure to certain drugs. Recon3D represents the most comprehensive human metabolic network model to date, accounting for 3,288 open reading frames (representing 17% of functionally annotated human genes), 13,543 metabolic reactions involving 4,140 unique metabolites, and 12,890 protein structures. These data provide a unique resource for investigating molecular mechanisms of human metabolism. Recon3D is available at http://vmh.life

Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity

We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for the Levenberg–Marquardt parameter and analyse the local convergence of the method under Hölder metric subregularity of the function defining the equation and Hölder continuity of its gradient mapping. Further, we analyse the local convergence of the method under the additional assumption that the Łojasiewicz gradient inequality holds. We finally report encouraging numerical results confirming the theoretical findings for the problem of computing moiety conserved steady states in biochemical reaction networks. This problem can be cast as finding a solution of a system of nonlinear equations, where the associated mapping satisfies the Łojasiewicz gradient inequality assumption

A constraint-based modelling approach to metabolic dysfunction in Parkinson's disease

One of the hallmarks of sporadic Parkinson's disease is degeneration of dopaminergic neurons in the pars compacta of the substantia nigra. The aetiopathogenesis of this degeneration is still not fully understood, with dysfunction of many biochemical pathways in different subsystems suggested to be involved. Recent advances in constraint-based modelling approaches hold great potential to systematically examine the relative contribution of dysfunction in disparate pathways to dopaminergic neuronal degeneration, but few studies have employed these methods in Parkinson's disease research. Therefore, this review outlines a framework for future constraint-based modelling of dopaminergic neuronal metabolism to decipher the multi-factorial mechanisms underlying the neuronal pathology of Parkinson's disease

Cardinality optimization in constraint-based modelling: application to human metabolism

Motivation: several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution.Results: by approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction.Availability and implementation: open source scripts to reproduce the results are here https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox

Functional characterization of alternate optimal solutions of Escherichia coli's transcriptional and translational machinery.

The constraint-based reconstruction and analysis approach has recently been extended to describe Escherichia coli's transcriptional and translational machinery. Here, we introduce the concept of reaction coupling to represent the dependency between protein synthesis and utilization. These coupling constraints lead to a significant contraction of the feasible set of steady-state fluxes. The subset of alternate optimal solutions (AOS) consistent with maximal ribosome production was calculated. The majority of transcriptional and translational reactions were active for all of these AOS, showing that the network has a low degree of redundancy. Furthermore, all calculated AOS contained the qualitative expression of at least 92% of the known essential genes. Principal component analysis of AOS demonstrated that energy currencies (ATP, GTP, and phosphate) dominate the network's capability to produce ribosomes. Additionally, we identified regulatory control points of the network, which include the transcription reactions of sigma70 (RpoD) as well as that of a degradosome component (Rne) and of tRNA charging (ValS). These reactions contribute significant variance among AOS. These results show that constraint-based modeling can be applied to gain insight into the systemic properties of E. coli's transcriptional and translational machinery

opencobra/cobratoolbox: The COBRA Toolbox 2.0

The COnstraint-Based Reconstruction and Analysis Toolbo