FBApro: A fast, simple linear transformation for diverse metabolic modeling tasks

TL;DR

Constraint-based metabolic modeling traditionally relies on optimization to enforce steady-state fluxes. FBApro replaces optimization with a closed-form orthogonal projection onto the steady-state subspace, enabling fast, differentiable mapping from reference fluxes to feasible fluxes. The authors introduce FBAproPartial and FBAproFixed to handle partial measurements and fixed high-confidence reactions, respectively, and validate the approach on synthetic data and cancer-cell-line flux datasets, showing substantial speed advantages and robust denoising/imputation performance. Collectively, FBApro positions itself as a scalable, modular tool that can be embedded in gradient-based pipelines for high-throughput metabolic analysis and data integration.

Abstract

Constraint-based metabolic modeling is the predominant framework for simulating cellular metabolism. The central assumption of these models is that metabolism operates at a steady state, meaning that the production and consumption rates of each metabolite are balanced. This assumption imposes linear constraints on the fluxes of biochemical reactions. Flux Balance Analysis (FBA), a fundamental method in the field, is formulated as an optimization problem maximizing a cellular objective (e.g., growth) over the resulting linear subspace of steady state fluxes. Many other methods in the field are expressed either as a modification to FBA, or use FBA as a black box within an algorithm. Here, we propose a simple and general alternative to optimization that, for any flux vector, finds the closest flux distribution within the steady-state subspace. This operation corresponds to an orthogonal projection that enforces the steady-state assumption. We further introduce extensions to handle cases involving unknown or fixed fluxes through modified projections and tailored affine subspaces. The overall approach is computationally efficient, does not require a cellular objective, and is easy to implement. We validate our method and its variants on both synthetic and experimental datasets, demonstrating their speed and utility for denoising and imputing metabolic flux data, and for predicting steady-state fluxes from more readily available types of data. Code availability: The code implementing FBApro is available at https://github.com/Singh-Lab/FBApro. All code required to reproduce the figures in the paper is available, although the data used must be sourced separately. The repository also contains toy models and examples.

Figures (9)

• Figure 1: Amortized running time per sample, averaged over five replicas for one sample for benchmark methods, and five replicas for 100 samples for FBApro variants, for different methods on synthetic data generated from four model organism metabolic models.
• Figure 2: Spearman correlations between actual fluxes and predicted fluxes on synthetic datasets derived from the four model organism metabolic models. (a) Average performance across 10 samples for each model and the unmeasured 90% of the model reactions when input data consists of a subset of reactions with noisy flux measurements and the remainder of reactions with no measurements. No data is shown for FBA as it yielded fixed predictions across samples.
• Figure 3: Per sample correlations between model outputs and synthetic data derived from four model organism metabolic models, while varying either the fraction of reactions with measured fluxes or the amount of noise. (\ref{['fig:var_blanked_sample_frac']}), (\ref{['fig:var_blanked_sample_noise']}) Results for the missing/noisy experiment (where some reactions have no information about fluxes and other reactions have noisy flux measurements). (\ref{['fig:var_exact_sample_frac']}), (\ref{['fig:var_exact_sample_noise']}) Results for the noisy/exact experiment (where some reactions have exact flux measurements and the remaining have noisy flux measurements).
• Figure 4: Performance of methods when predicting fluxes from GE data and masked flux data.
• Figure 5: Running time of methods on synthetic data for four model organism models

Theorems & Definitions (1)

• Claim 2.1