(253c) Constraints on Information Flow in Metabolic Networks

Metabolism, like all open systems, is fundamentally constrained by flows of mass, energy, and information. Mass balance has formed the basis of systems-level metabolic analysis in both FBA and kinetic modelling methodologies, and thermodynamic consistency is now readily considered at scale in metabolic modelling (1, 2). However, informational constraints in metabolic networks remain unexplored, despite the fact that biological systems are awash with information that they have evolved to use to maintain homeostasis, and that understanding such constraints in gene circuits and signal transduction systems has proven useful for their characterization and engineering (3). Uncovering the constraints on information flow within the context of metabolism could enable the design and optimization of next-generation metabolic systems for chemical transformation, including those which make use of small-molecule regulation of enzyme activity in place of/in addition to engineered gene circuits, and those which employ engineered autocatalytic metabolic cycles, as in many novel C1-utilizing systems (e.g. 4). These have the potential to radically transform the space of available feedstocks for bioprocesses, perhaps enabling the valorization of CO₂ and CH₄ at scale in the production of carbon-negative chemicals, for example. However, the regulation and stability of such systemsis not well understood because of the rapid time scale over which small-molecule regulation (SMR) of enzyme activity operates relative to transcriptional regulation. In particular, which metabolites in the network are informational at this level of metabolic control and how that information is naturally transferred (or not, as is relevant to instability) throughout the metabolic and small-molecule regulatory networks (SMRN) are both completely unexplored areas of investigation.

Here, a very simple representative metabolic subsystem - the branchpoint - is modelled under varied constraining scenarios. Sensitivity analysis is used to show that thermodynamic constraints on the consumption of metabolites at branchpoints and saturation kinetics of their consuming enzymes have the combined effect of limiting the amount of information that can be transferred in the metabolic network alone (i.e. without regulation). This is because thermodynamic constraints enforce operation of one downstream branch near equilibrium, causing the others to be pushed far from equilibrium and enforcing their operation near saturation. As a result, fluctuations in upstream fluxes may not be propagated to some pathways downstream of branchpoints in the network, and this represents a loss of information about changing upstream conditions. It is then shown that enzyme inhibition by the metabolites at such branchpoints maximally transfers information, thereby providing a structural mechanism for preventing such information loss. This is because inhibition operates most effectively when the inhibitor is near saturation - the same conditions in which information is lost. To understand if information loss minimization is a "design principle" of metabolic regulation, a genome-wide analysis of a novel E. coli small-molecule regulatory network (SMRN) reconstruction is used to show that inhibitors are indeed significantly more likely to be positioned at branch points with multiple downstream branches and strong thermodynamic constraints. These are points of maximum potential information loss in the network, and the overabundance of inhibitors at such points suggests that indeed minimizing information loss is a broad design goal of metabolic regulation.

Practically-speaking, identification of the structural aspects which render some metabolites informational about upstream fluctuations will no doubt help metabolic engineers to identify metabolites in both native and engineered pathways that they can use to manipulate flux distributions, perhaps dynamically, and also to stabilize engineered metabolic cycles, especially those which are autocatalytic. Understanding the natural constraints on information in metabolic networks is essential to uncovering such native internal sources of metabolic information and the mechanisms by which they correlate fluxes. Both of these must be exploited by engineers to optimize online balancing of metabolite pools for production pathways in which flux correlation is key to stability and productivity maximization. This work will thus begin to enable consideration of the rapid dynamics and related stability criteria of nascent one carbon-assimilation pathways by providing a roadmap to understanding the structures underlying such dynamics and stability.

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   All Biomass Carbon from CO2. Cell, 179(6):1255–1263.e12, (2019)

Figure caption:

A. In the representative branching system, substrate S is produced at a rate u and consumed by two downstream enzymes to produce P₁ and P₂. The thermodynamic parameter of the constraining branch, ∆Gâ—¦_max , enforces accumula tion of S if this branch is reverse-favoured, ∆Gâ—¦ max ≫ 0, enforcing operation of the unconstrained, forward-favoured branch in a state far from equilibrium (P₂/S → 0) and close to saturation. However, if the constraining branch is favourable in the forward direction (∆Gâ—¦max ≪ 0), accumulation of S is not guaranteed. B. Elasticities (ε^v_S), or scaled sensitivities, for each branch of the system under varied thermodynamic constraint in the constraining branch. The sensitivity of the constraining branch is maximized for strongly constrained systems, in which this branch is enforced to operate closer to equilibrium. In the same conditions, enforced accumulation of substrate enforces low sensitivity in the unconstrained branch because it is constrained to operate closer to saturation. K_eq,2 = 10⁴ here. C. Elasticities (ε^v) for catalysis and inhibition with varying degree of cooperativity as a function of either substrate, S, or inhibitor, x_I, concentration, respectively, for the system in (A) solved at steady state for varied u. The inhibition elasticity, |ε^v_xI|, increases to a maximum as the inhibitor concentration increases to saturation, whereas the elasticity for catalysis, ε^v_S , decreases to zero as the substrate concentration increases to saturation. η is the degree of cooperativity for inhibition; more cooperativity yields larger maximum elasticities. K_eq,1 = K_eq,2 = 1000 here. C. Steady-state S concentration depends on the constraining thermodynamic parameter. As ∆Gâ—¦_max is increased, ε^vI_S grows to a maximum, while ε^v_S is minimized. In highly constrained systems, perturbations to S will not be propagated in the unconstrained branch, but inhibition by S maximally propagates these perturbations in the same conditions. K_S = 0.1, K_P = 1, V_m = 1, k = 10, K_I = 1, for representative curves in (B) and (C). E. Lower bound information loss estimated for a given parameter set via lumped elasticities, |a|. For catalysis, |a| decreases asymptotically to 0 as the substrate concentration increases, as indicated by the blue arrow. Information loss via catalysis thus increases rapidly as saturation is approached. Conversely, for inhibition |a| increases to 1 (for η = 1) as the inhibitor concentration increases, as indicated by the black arrow. Thus, near-perfect information transfer is possible as the inhibitor concentration approaches saturation. Inhibition maximally preserves information at saturation, while catalysis can only do so when substrate concentration is 0. (F) Bivariate density distributions of thermodynamic constraints and out-degrees for reactions producing inhibitors and those producing non-regulatory metabolites. Out-degree is the number of reactions for which a given metabolite is a substrate in our SMRN reconstruction. Reactions producing inhibitors are characterized by large thermodynamic constraints and high out-degrees relative to non-regulatory reactions.