22 research outputs found
Maximizing Output and Recognizing Autocatalysis in Chemical Reaction Networks is NP-Complete
Background: A classical problem in metabolic design is to maximize the
production of desired compound in a given chemical reaction network by
appropriately directing the mass flow through the network. Computationally,
this problem is addressed as a linear optimization problem over the "flux
cone". The prior construction of the flux cone is computationally expensive and
no polynomial-time algorithms are known. Results: Here we show that the output
maximization problem in chemical reaction networks is NP-complete. This
statement remains true even if all reactions are monomolecular or bimolecular
and if only a single molecular species is used as influx. As a corollary we
show, furthermore, that the detection of autocatalytic species, i.e., types
that can only be produced from the influx material when they are present in the
initial reaction mixture, is an NP-complete computational problem. Conclusions:
Hardness results on combinatorial problems and optimization problems are
important to guide the development of computational tools for the analysis of
metabolic networks in particular and chemical reaction networks in general. Our
results indicate that efficient heuristics and approximate algorithms need to
be employed for the analysis of large chemical networks since even conceptually
simple flow problems are provably intractable
Unstable Cores are the source of instability in chemical reaction networks
In biochemical networks, complex dynamical features such as superlinear
growth and oscillations are classically considered a consequence of
autocatalysis. For the large class of parameter-rich kinetic models, which
includes Generalized Mass Action kinetics and Michaelis-Menten kinetics, we
show that certain submatrices of the stoichiometric matrix, so-called unstable
cores, are sufficient for a reaction network to admit instability and
potentially give rise to such complex dynamical behavior. The determinant of
the submatrix distinguishes unstable-positive feedbacks, with a single
real-positive eigenvalue, and unstable-negative feedbacks without real-positive
eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive
feedbacks that are Metzler matrices. Thus there are sources of dynamical
instability in chemical networks that are unrelated to autocatalysis. We use
such intuition to design non-autocatalytic biochemical networks with
superlinear growth and oscillations.Comment: 47 pages. Main text pp 1-14, Supplementary Information pp 15-47. 8
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Analysis of Generative Chemistries
For the modelling of chemistry we use undirected, labelled graphs as explicit models of molecules and graph transformation rules for modelling generalised chemical reactions. This is used to define artificial chemistries on the level of individual bonds and atoms, where formal graph grammars implicitly represent large spaces of chemical compounds. We use a graph rewriting formalism, rooted in category theory, called the Double Pushout approach, which directly expresses the transition state of chemical reactions. Using concurrency theory for transformation rules, we define algorithms for the composition of rewrite rules in a chemically intuitive manner that enable automatic abstraction of the level of detail in chemical pathways. Based on this rule composition we define an algorithmic framework for generation of vast reaction networks for specific spaces of a given chemistry, while still maintaining the level of detail of the model down to the atomic level. The framework also allows for computation with graphs and graph grammars, which is utilised to model non-trivial chemical systems. The graph generation relies on graph isomorphism testing, and we review the general individualisation-refinement paradigm used in the state-of-the-art algorithms for graph canonicalisation, isomorphism testing, and automorphism discovery.
We present a model for chemical pathways based on a generalisation of network flows from ordinary directed graphs to directed hypergraphs. The model allows for reasoning about the flow of individual molecules in general pathways, and the introduction of chemically motivated routing constraints. It further provides the foundation for defining specialised pathway motifs, which is illustrated by defining necessary topological constraints for both catalytic and autocatalytic pathways. We also prove that central types of pathway questions are NP-complete, even for restricted classes of reaction networks. The complete pathway model, including constraints for catalytic and autocatalytic pathways, is implemented using integer linear programming. This implementation is used in a tree search method to enumerate both optimal and near-optimal pathway solutions.
The formal methods are applied to multiple chemical systems: the enzyme catalysed beta-lactamase reaction, variations of the glycolysis pathway, and the formose process. In each of these systems we use rule composition to abstract pathways and calculate traces for isotope labelled carbon atoms. The pathway model is used to automatically enumerate alternative non-oxidative glycolysis pathways, and enumerate thousands of candidates for autocatalytic pathways in the formose process
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
Intrinsic and extrinsic thermodynamics for stochastic population processes with multi-level large-deviation structure
A set of core features is set forth as the essence of a thermodynamic
description, which derive from large-deviation properties in systems with
hierarchies of timescales, but which are \emph{not} dependent upon conservation
laws or microscopic reversibility in the substrate hosting the process. The
most fundamental elements are the concept of a macrostate in relation to the
large-deviation entropy, and the decomposition of contributions to
irreversibility among interacting subsystems, which is the origin of the
dependence on a concept of heat in both classical and stochastic
thermodynamics. A natural decomposition is shown to exist, into a relative
entropy and a housekeeping entropy rate, which define respectively the
\textit{intensive} thermodynamics of a system and an \textit{extensive}
thermodynamic vector embedding the system in its context. Both intensive and
extensive components are functions of Hartley information of the momentary
system stationary state, which is information \emph{about} the joint effect of
system processes on its contribution to irreversibility. Results are derived
for stochastic Chemical Reaction Networks, including a Legendre duality for the
housekeeping entropy rate to thermodynamically characterize fully-irreversible
processes on an equal footing with those at the opposite limit of
detailed-balance. The work is meant to encourage development of inherent
thermodynamic descriptions for rule-based systems and the living state, which
are not conceived as reductive explanations to heat flows
Using MapReduce Streaming for Distributed Life Simulation on the Cloud
Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp