Fast-SNP: a fast matrix pre-processing algorithm for efficient loopless flux optimization of metabolic models

Abstract

Motivation: Computation of steady-state flux solutions in large metabolic models is routinely performed using flux balance analysis based on a simple LP (Linear Programming) formulation. A minimal requirement for thermodynamic feasibility of the flux solution is the absence of internal loops, which are enforced using ‘loopless constraints’. The resulting loopless flux problem is a substantially harder MILP (Mixed Integer Linear Programming) problem, which is computationally expensive for large metabolic models.Results: We developed a pre-processing algorithm that significantly reduces the size of the original loopless problem into an easier and equivalent MILP problem. The pre-processing step employs a fast matrix sparsification algorithm—Fast- sparse null-space pursuit (SNP)—inspired by recent results on SNP. By finding a reduced feasible ‘loop-law’ matrix subject to known directionalities, Fast-SNP considerably improves the computational efficiency in several metabolic models running different loopless optimization problems. Furthermore, analysis of the topology encoded in the reduced loop matrix enabled identification of key directional constraints for the potential permanent elimination of infeasible loops in the underlying model. Overall, Fast-SNP is an effective and simple algorithm for efficient formulation of loop-law constraints, making loopless flux optimization feasible and numerically tractable at large scale.Availability and Implementation: Source code for MATLAB including examples is freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization uses Gurobi, CPLEX or GLPK (the latter is included with the algorithm).Contact: lars.nielsen@uq.edu.auSupplementary information: Supplementary data are available at Bioinformatics online.

Accelerating flux balance calculations in genome-scale metabolic models by localizing the application of loopless constraints

“…Single-organism models Using the seven models tested in Saa and Nielsen (2016) excluding the toy model therein, we compared the performance between (1) ll-FVA using the original loopless constraint (referred to as ll-FVA), (2) ll-FVA with Fast-SNP preprocessing (referred to as Fast-SNP), (3) FVA with null-space-based LLCs, i.e., imposing LLCs on in Step 6 in section 2.6 without EFM calculations (referred to as NS-LLC), and (4) FVA with EFMbased LLCs (referred to as EFM-LLC). In the models tested, NS-LLC and EFM-LLC show 10~150x reduction in computational needs (in CPU time) compared to ll-FVA and 4~10x reduction compared to Fast-SNP (Table 1).…”

“…The original constraints for loopless flux calculations imposed on all internal reactions. (C) The previously proposed Fast-SNP(Saa and Nielsen, 2016) to find a minimal null-space. G R3 , G R4 , y R3 , y R4 become uncoupled from the rest of the formulation and can be precalculated.…”

Essentiality of local topology and regulation in kinetic metabolic modeling

“…Inspired by the minimal metabolic pathways (Bordbar et al, 2014c), we represented the highly-coupled subnetworks with the SLB of null space of the corresponding stoichiometric matrix, which is biologically explained as the minimal and indecomposable coupled components, and satisfy the constraint of thermodynamic and mass balance of element reactions. Different from infinite ordinary linear basis vectors of null space of stoichiometric matrix, there is a unique and globally optimal sparsest basis group of null space (Bordbar et al, 2014c; Saa & Nielsen, 2016). Briefly, the orthonormal null space N C k is initially defined by singular value decomposition (SVD) for the stoichiometric matrix S C k of subnetwork C k , here additional artificial exchange reactions are introduced in S C k to maintain the mass balance of reactions in subnetwork C k (more details can be found in Appendix file 1 Method S1).…”

“…This process is repeated until all the number of non-zero entries in N C k has converged on a minimum (Bordbar et al, 2014b). Here we utilized the advantage of sparse regularization of null space N C k to solve the minimum L1-norm of null space N C k of S C k (Saa & Nielsen, 2016). And the detailed process is showcased in Appendix file 1 Method S1, which finds , a minimal sparse basis representation of N C k in at most 2 r k linear programming optimization runs (where r k = l k − rank ( S C k ), l k is the number of columns (reactions) in S C k ), and then each of linear programming problem can be formulated as follows: where the is the SLB of null space of S C k at the m th runs, the lb and ub are lower and upper bound of , respectively.…”

Variant Calling pipeline for Next Generation Sequence Data – A review

“…Annotation of SNPs involves extraction of biological information base on nucleic acid and protein sequence. Commonly used annotation tools are SNPeff (Cingolani et al, 2012), VEP-Variant Effect Predictor (McLaren et al, 2010), ANNOVAR (Wang et al, 2010) , PolyPhen-2 (Adzhubei et al, 2010), SIFT (Ng and Henikoff, 2003) and FAST-SNP (Saa and Nielsen, 2016).…”