3,257 research outputs found
Inferring Chemical Reaction Patterns Using Rule Composition in Graph Grammars
Modeling molecules as undirected graphs and chemical reactions as graph
rewriting operations is a natural and convenient approach tom odeling
chemistry. Graph grammar rules are most naturally employed to model elementary
reactions like merging, splitting, and isomerisation of molecules. It is often
convenient, in particular in the analysis of larger systems, to summarize
several subsequent reactions into a single composite chemical reaction. We use
a generic approach for composing graph grammar rules to define a chemically
useful rule compositions. We iteratively apply these rule compositions to
elementary transformations in order to automatically infer complex
transformation patterns. This is useful for instance to understand the net
effect of complex catalytic cycles such as the Formose reaction. The
automatically inferred graph grammar rule is a generic representative that also
covers the overall reaction pattern of the Formose cycle, namely two carbonyl
groups that can react with a bound glycolaldehyde to a second glycolaldehyde.
Rule composition also can be used to study polymerization reactions as well as
more complicated iterative reaction schemes. Terpenes and the polyketides, for
instance, form two naturally occurring classes of compounds of utmost
pharmaceutical interest that can be understood as "generalized polymers"
consisting of five-carbon (isoprene) and two-carbon units, respectively
Conditions for duality between fluxes and concentrations in biochemical networks
Mathematical and computational modelling of biochemical networks is often
done in terms of either the concentrations of molecular species or the fluxes
of biochemical reactions. When is mathematical modelling from either
perspective equivalent to the other? Mathematical duality translates concepts,
theorems or mathematical structures into other concepts, theorems or
structures, in a one-to-one manner. We present a novel stoichiometric condition
that is necessary and sufficient for duality between unidirectional fluxes and
concentrations. Our numerical experiments, with computational models derived
from a range of genome-scale biochemical networks, suggest that this
flux-concentration duality is a pervasive property of biochemical networks. We
also provide a combinatorial characterisation that is sufficient to ensure
flux-concentration duality. That is, for every two disjoint sets of molecular
species, there is at least one reaction complex that involves species from only
one of the two sets. When unidirectional fluxes and molecular species
concentrations are dual vectors, this implies that the behaviour of the
corresponding biochemical network can be described entirely in terms of either
concentrations or unidirectional fluxes
Systems approaches to modelling pathways and networks.
Peer reviewedPreprin
Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis
A fundamental result in metabolic pathway analysis states that every flux
mode can be decomposed into a sum of elementary modes. However, only a
decomposition without cancelations is biochemically meaningful, since a
reversible reaction cannot have different directions in the contributing
elementary modes. This essential requirement has been largely overlooked by the
metabolic pathway community.
Indeed, every flux mode can be decomposed into elementary modes without
cancelations. The result is an immediate consequence of a theorem by
Rockafellar which states that every element of a linear subspace is a conformal
sum (a sum without cancelations) of elementary vectors (support-minimal
vectors). In this work, we extend the theorem, first to "subspace cones" and
then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's
and Carath\'eodory's theorems, two fundamental results in polyhedral geometry.
We note that, in general, elementary vectors need not be support-minimal, in
fact, they are conformally non-decomposable and form a unique minimal set of
conformal generators.
Our treatment is mathematically rigorous, but suitable for systems
biologists, since we give self-contained proofs for our results and use
concepts motivated by metabolic pathway analysis. In particular, we study cones
defined by linear subspaces and nonnegativity conditions - like the flux cone -
and use them to analyze general polyhedral cones and polyhedra.
Finally, we review applications of elementary vectors and conformal sums in
metabolic pathway analysis
A Taxonomy of Causality-Based Biological Properties
We formally characterize a set of causality-based properties of metabolic
networks. This set of properties aims at making precise several notions on the
production of metabolites, which are familiar in the biologists' terminology.
From a theoretical point of view, biochemical reactions are abstractly
represented as causal implications and the produced metabolites as causal
consequences of the implication representing the corresponding reaction. The
fact that a reactant is produced is represented by means of the chain of
reactions that have made it exist. Such representation abstracts away from
quantities, stoichiometric and thermodynamic parameters and constitutes the
basis for the characterization of our properties. Moreover, we propose an
effective method for verifying our properties based on an abstract model of
system dynamics. This consists of a new abstract semantics for the system seen
as a concurrent network and expressed using the Chemical Ground Form calculus.
We illustrate an application of this framework to a portion of a real
metabolic pathway
Algebraic shortcuts for leave-one-out cross-validation in supervised network inference
Supervised machine learning techniques have traditionally been very successful at reconstructing biological networks, such as protein-ligand interaction, protein-protein interaction and gene regulatory networks. Many supervised techniques for network prediction use linear models on a possibly nonlinear pairwise feature representation of edges. Recently, much emphasis has been placed on the correct evaluation of such supervised models. It is vital to distinguish between using a model to either predict new interactions in a given network or to predict interactions for a new vertex not present in the original network. This distinction matters because (i) the performance might dramatically differ between the prediction settings and (ii) tuning the model hyperparameters to obtain the best possible model depends on the setting of interest. Specific cross-validation schemes need to be used to assess the performance in such different prediction settings. In this work we discuss a state-of-the-art kernel-based network inference technique called two-step kernel ridge regression. We show that this regression model can be trained efficiently, with a time complexity scaling with the number of vertices rather than the number of edges. Furthermore, this framework leads to a series of cross-validation shortcuts that allow one to rapidly estimate the model performance for any relevant network prediction setting. This allows computational biologists to fully assess the capabilities of their models
- …