5 research outputs found
Signatures of arithmetic simplicity in metabolic network architecture
Metabolic networks perform some of the most fundamental functions in living
cells, including energy transduction and building block biosynthesis. While
these are the best characterized networks in living systems, understanding
their evolutionary history and complex wiring constitutes one of the most
fascinating open questions in biology, intimately related to the enigma of
life's origin itself. Is the evolution of metabolism subject to general
principles, beyond the unpredictable accumulation of multiple historical
accidents? Here we search for such principles by applying to an artificial
chemical universe some of the methodologies developed for the study of genome
scale models of cellular metabolism. In particular, we use metabolic flux
constraint-based models to exhaustively search for artificial chemistry
pathways that can optimally perform an array of elementary metabolic functions.
Despite the simplicity of the model employed, we find that the ensuing pathways
display a surprisingly rich set of properties, including the existence of
autocatalytic cycles and hierarchical modules, the appearance of universally
preferable metabolites and reactions, and a logarithmic trend of pathway length
as a function of input/output molecule size. Some of these properties can be
derived analytically, borrowing methods previously used in cryptography. In
addition, by mapping biochemical networks onto a simplified carbon atom
reaction backbone, we find that several of the properties predicted by the
artificial chemistry model hold for real metabolic networks. These findings
suggest that optimality principles and arithmetic simplicity might lie beneath
some aspects of biochemical complexity
Evolution under Fluctuating Environments Explains Observed Robustness in Metabolic Networks
A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments
Toolbox model of evolution of metabolic pathways on networks of arbitrary topology
In prokaryotic genomes the number of transcriptional regulators is known to
quadratically scale with the total number of protein-coding genes. Toolbox
model was recently proposed to explain this scaling for metabolic enzymes and
their regulators. According to its rules the metabolic network of an organism
evolves by horizontal transfer of pathways from other species. These pathways
are part of a larger "universal" network formed by the union of all
species-specific networks. It remained to be understood, however, how the
topological properties of this universal network influence the scaling law of
functional content of genomes. In this study we answer this question by first
analyzing the scaling properties of the toolbox model on arbitrary tree-like
universal networks. We mathematically prove that the critical branching
topology, in which the average number of upstream neighbors of a node is equal
to one, is both necessary and sufficient for the quadratic scaling. Conversely,
the toolbox model on trees with exponentially expanding, supercritical topology
is characterized by the linear scaling with logarithmic corrections. We further
generalize our model to include reactions with multiple substrates/products as
well as branched or cyclic metabolic pathways. Unlike the original model the
new version employs evolutionary optimized pathways with the smallest number of
reactions necessary to achieve their metabolic tasks. Numerical simulations of
this most realistic model on the universal network from the KEGG database again
produced approximately quadratic scaling. Our results demonstrate why, in spite
of their "small-world" topology, real-life metabolic networks are characterized
by a broad distribution of pathway lengths and sizes of metabolic regulons in
regulatory networks.Comment: 34 pages, 9 figures, 2 table
The compositional and evolutionary logic of metabolism
Metabolism displays striking and robust regularities in the forms of
modularity and hierarchy, whose composition may be compactly described. This
renders metabolic architecture comprehensible as a system, and suggests the
order in which layers of that system emerged. Metabolism also serves as the
foundation in other hierarchies, at least up to cellular integration including
bioenergetics and molecular replication, and trophic ecology. The
recapitulation of patterns first seen in metabolism, in these higher levels,
suggests metabolism as a source of causation or constraint on many forms of
organization in the biosphere.
We identify as modules widely reused subsets of chemicals, reactions, or
functions, each with a conserved internal structure. At the small molecule
substrate level, module boundaries are generally associated with the most
complex reaction mechanisms and the most conserved enzymes. Cofactors form a
structurally and functionally distinctive control layer over the small-molecule
substrate. Complex cofactors are often used at module boundaries of the
substrate level, while simpler ones participate in widely used reactions.
Cofactor functions thus act as "keys" that incorporate classes of organic
reactions within biochemistry.
The same modules that organize the compositional diversity of metabolism are
argued to have governed long-term evolution. Early evolution of core
metabolism, especially carbon-fixation, appears to have required few
innovations among a small number of conserved modules, to produce adaptations
to simple biogeochemical changes of environment. We demonstrate these features
of metabolism at several levels of hierarchy, beginning with the small-molecule
substrate and network architecture, continuing with cofactors and key conserved
reactions, and culminating in the aggregation of multiple diverse physical and
biochemical processes in cells.Comment: 56 pages, 28 figure