The protein cost of metabolic fluxes: prediction from enzymatic rate laws and cost minimization

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 3.8 and 2.7, respectively, for the two kinds of data. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified

Microbial carbon use efficiency: accounting for population, community, and ecosystem-scale controls over the fate of metabolized organic matter

Microbial carbon use efficiency (CUE) is a critical regulator of soil organic matter dynamics and terrestrial carbon fluxes, with strong implications for soil biogeochemistry models. While ecologists increasingly appreciate the importance of CUE, its core concepts remain ambiguous: terminology is inconsistent and confusing, methods capture variable temporal and spatial scales, and the significance of many fundamental drivers remains inconclusive. Here we outline the processes underlying microbial efficiency and propose a conceptual framework that structures the definition of CUE according to increasingly broad temporal and spatial drivers where (1) CUEP reflects population-scale carbon use efficiency of microbes governed by species-specific metabolic and thermodynamic constraints, (2) CUEC defines community-scale microbial efficiency as gross biomass production per unit substrate taken up over short time scales, largely excluding recycling of microbial necromass and exudates, and (3) CUEE reflects the ecosystem-scale efficiency of net microbial biomass production (growth) per unit substrate taken up as iterative breakdown and recycling of microbial products occurs. CUEE integrates all internal and extracellular constraints on CUE and hence embodies an ecosystem perspective that fully captures all drivers of microbial biomass synthesis and decay. These three definitions are distinct yet complementary, capturing the capacity for carbon storage in microbial biomass across different ecological scales. By unifying the existing concepts and terminology underlying microbial efficiency, our framework enhances data interpretation and theoretical advances

An objective function exploiting suboptimal solutions in metabolic networks

Background: Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power. Results: We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation. Conclusion: Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network

How enzyme economy shapes metabolic fluxes

Metabolic fluxes are governed by physical and economic principles. Stationarity constrains them to a subspace in flux space and thermodynamics makes them lead from higher to lower chemical potentials. At the same time, fluxes in cells represent a compromise between metabolic performance and enzyme cost. To capture this, some flux prediction methods penalise larger fluxes by heuristic cost terms. Economic flux analysis, in contrast, postulates a balance between enzyme costs and metabolic benefits as a necessary condition for fluxes to be realised by kinetic models with optimal enzyme levels. The constraints are formulated using economic potentials, state variables that capture the enzyme labour embodied in metabolites. Generally, fluxes must lead from lower to higher economic potentials. This principle, which resembles thermodynamic constraints, can complement stationarity and thermodynamic constraints in flux analysis. Futile modes, which would be incompatible with economic potentials, are defined algebraically and can be systematically removed from flux distributions. Enzymes that participate in potential futile modes are likely targets of regulation. Economic flux analysis can predict high-yield and low-yield strategies, and captures preemptive expression, multi-objective optimisation, and flux distributions across several cells living in symbiosis. Inspired by labour value theories in economics, it justifies and extends the principle of minimal fluxes and provides an intuitive framework to model the complex interplay of fluxes, metabolic control, and enzyme costs in cells

Spectral signatures of photosynthesis I: Review of Earth organisms

Why do plants reflect in the green and have a 'red edge' in the red, and should extrasolar photosynthesis be the same? We provide: 1) a brief review of how photosynthesis works; 2) an overview of the diversity of photosynthetic organisms, their light harvesting systems, and environmental ranges; 3) a synthesis of photosynthetic surface spectral signatures; 4) evolutionary rationales for photosynthetic surface reflectance spectra with regard to utilization of photon energy and the planetary light environment. Given the surface incident photon flux density spectrum and resonance transfer in light harvesting, we propose some rules with regard to where photosynthetic pigments will peak in absorbance: a) the wavelength of peak incident photon flux; b) the longest available wavelength for core antenna or reaction center pigments; and c) the shortest wavelengths within an atmospheric window for accessory pigments. That plants absorb less green light may not be an inefficient legacy of evolutionary history, but may actually satisfy the above criteria.Comment: 69 pages, 7 figures, forthcoming in Astrobiology March 200

Selection theorem for systems with inheritance

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of "natural" selection. Estimations of the asymptotic dimension are presented. After some initial time, solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow over time and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t goes to infinity. The drift equations for peak motion are obtained. Various types of distribution stability are studied: internal stability (stability with respect to perturbations that do not extend the support), external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of self-synchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinite-dimensional space is discussed, and the notion of "completely thin" sets is introduced. Key words: Dynamics; Attractor; Evolution; Entropy; Natural selectionComment: 46 pages, the final journal versio