Enzyme economy in metabolic networks

Metabolic systems are governed by a compromise between metabolic benefit and enzyme cost. This hypothesis and its consequences can be studied by kinetic models in which enzyme profiles are chosen by optimality principles. In enzyme-optimal states, active enzymes must provide benefits: a higher enzyme level must provide a metabolic benefit to justify the additional enzyme cost. This entails general relations between metabolic fluxes, reaction elasticities, and enzyme costs, the laws of metabolic economics. The laws can be formulated using economic potentials and loads, state variables that quantify how metabolites, reactions, and enzymes affect the metabolic performance in a steady state. Economic balance equations link them to fluxes, reaction elasticities, and enzyme levels locally in the network. Economically feasible fluxes must be free of futile cycles and must lead from lower to higher economic potentials, just like thermodynamics makes them lead from higher to lower chemical potentials. Metabolic economics provides algebraic conditions for economical fluxes, which are independent of the underlying kinetic models. It justifies and extends the principle of minimal fluxes and shows how to construct kinetic models in enzyme-optimal states, where all enzymes have a positive influence on the metabolic performance

Characteristics of the polymer transport in ratchet systems

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.Comment: 35 pages, 17 figures, to appear in Phys. Rev.

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

On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials

An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Hardy-supercritical singular potentials. Extensions to other linear and nonlinear singular PDEs are discussed.Comment: 22 page