scholarly journals A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks

2019 ◽  
Author(s):  
M. Ali Al-Radhawi ◽  
David Angeli ◽  
Eduardo D. Sontag
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Extensive Study ◽  
Biochemical Networks ◽  
Reaction Networks ◽  
Post Translational Modification ◽  
Unified Framework ◽  
Biochemical Reaction Networks ◽  
Computational Framework ◽  
Three Body

AbstractComplex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally. The kinetics can also change with environmental variations.This work addresses the following question: given a set of reactions and without assuming a particular form for the kinetics, what can we say about the asymptotic behavior of the network? Specifically, it introduces a class of networks that are “structurally (mono) attractive” meaning that they are incapable of exhibiting multiple steady states, oscillation, or chaos by virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function called a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence.An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. Basic motifs, three-body binding, and genetic networks are studied first. The work then focuses on cellular signalling networks including various post-translational modification cascades, phosphotransfer and phosphorelay networks, T-cell kinetic proofreading, and ERK signalling. The Ribosome Flow Model is also studied.Author summaryA theoretical and computational framework is developed for the identification of biochemical networks that are “structurally attractive”. This means that they only allow global point attractors and they cannot exhibit any other asymptotic behavior such as multi-stability, oscillations, or chaos for any choice of the kinetics. They are characterized by the existence of energy-like functions. A computational package is made available for usage by a wider community. Many relevant networks in molecular biology satisfy the assumptions, and some are analyzed for the first time.

scholarly journals Universal scaling across biochemical networks on Earth

2019 ◽  
Vol 5 (1) ◽  
pp. eaau0149 ◽  
Author(s):  
Hyunju Kim ◽  
Harrison B. Smith ◽  
Cole Mathis ◽  
Jason Raymond ◽  
Sara I. Walker
Keyword(s):  
Scaling Laws ◽  
Network Size ◽  
Biochemical Networks ◽  
Biochemical Network ◽  
Reaction Networks ◽  
Biochemical Reaction Networks ◽  
Global Database ◽  
Universal Scaling ◽  
Planetary Scale ◽  
Domains Of Life

The application of network science to biology has advanced our understanding of the metabolism of individual organisms and the organization of ecosystems but has scarcely been applied to life at a planetary scale. To characterize planetary-scale biochemistry, we constructed biochemical networks using a global database of 28,146 annotated genomes and metagenomes and 8658 cataloged biochemical reactions. We uncover scaling laws governing biochemical diversity and network structure shared across levels of organization from individuals to ecosystems, to the biosphere as a whole. Comparing real biochemical reaction networks to random reaction networks reveals that the observed biological scaling is not a product of chemistry alone but instead emerges due to the particular structure of selected reactions commonly participating in living processes. We show that the topology of biochemical networks for the three domains of life is quantitatively distinguishable, with >80% accuracy in predicting evolutionary domain based on biochemical network size and average topology. Together, our results point to a deeper level of organization in biochemical networks than what has been understood so far.

scholarly journals SMGen: A Generator of Synthetic Models of Biochemical Reaction Networks

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 119
Author(s):  
Simone G. Riva ◽  
Paolo Cazzaniga ◽  
Marco S. Nobile ◽  
Simone Spolaor ◽  
Leonardo Rundo ◽  
...  
Keyword(s):  
Biochemical Networks ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Computational Systems Biology ◽  
Biochemical Reaction Networks ◽  
Asymmetric Reaction ◽  
Computational Performance ◽  
Set Up ◽  
Definition Of ◽  
Synthetic Models

Several software tools for the simulation and analysis of biochemical reaction networks have been developed in the last decades; however, assessing and comparing their computational performance in executing the typical tasks of computational systems biology can be limited by the lack of a standardized benchmarking approach. To overcome these limitations, we propose here a novel tool, named SMGen, designed to automatically generate synthetic models of reaction networks that, by construction, are characterized by relevant features (e.g., system connectivity and reaction discreteness) and non-trivial emergent dynamics of real biochemical networks. The generation of synthetic models in SMGen is based on the definition of an undirected graph consisting of a single connected component that, generally, results in a computationally demanding task; to speed up the overall process, SMGen exploits a main–worker paradigm. SMGen is also provided with a user-friendly graphical user interface, which allows the user to easily set up all the parameters required to generate a set of synthetic models with any number of reactions and species. We analysed the computational performance of SMGen by generating batches of symmetric and asymmetric reaction-based models (RBMs) of increasing size, showing how a different number of reactions and/or species affects the generation time. Our results show that when the number of reactions is higher than the number of species, SMGen has to identify and correct a large number of errors during the creation process of the RBMs, a circumstance that increases the running time. Still, SMGen can generate synthetic models with hundreds of species and reactions in less than 7 s.

scholarly journals Self-Aware Distributed Consensus Building for Sensor Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Lei Chen ◽  
Jeff Frolik
Keyword(s):  
Asymptotic Behavior ◽  
Sensor Networks ◽  
Extensive Study ◽  
Practical Implementation ◽  
Consensus Building ◽  
Optimal Parameters ◽  
Distributed Consensus ◽  
Systematic Analysis ◽  
Second Derivatives ◽  
Derivatives Of

Distributed consensus building promises to improve the robustness and reliability of sensor networks and thus is an active topic of research. Whereas extensive study has been done on the theoretical analysis of the asymptotic behavior of consensus building, one important issue that is crucial to the practical implementation of sensor networks was rarely explored, namely, the criteria to determine whether consensus has been attained. In this paper, we propose an approach that allows each node in a network to make the decision by itself, based on the second derivatives of its own state. The approach does not rely on the states of other nodes, leads to substantial saving of communication resources, and is resilient to connection failure. We perform a systematic analysis of the approach and, as a consequence, derive the optimal parameters that minimize the upper bound of the number of required iterations to reach consensus.

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