Optimal resource allocation enables mathematical exploration of microbial metabolic configurations.

Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of power grids remains to be explored. Based on a simple model of networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most networks display damped oscillations, even when their units - and linear chains of these units - behave in a non-oscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a new interpretation of business cycles and of oscillating or pulsating processes. The network structure of material flows itself turns out to be a source of instability, and cyclical variations are an inherent feature of decentralized adjustments. In particular, we show how to treat production and networks as transport problems governed by balance equations and equations for the adaptation of production speeds. The stability and dynamic behavior of networks is investigated for different topologies, including sequential chains, supply circles, supply ladders, and supply hierarchies. Moreover, analytical conditions for absolute and convective instabilities are derived. The empirically observed bullwhip effect in chains is explained as a form of convective instability based on resonance effects. An application of this theory to the optimization of production networks has large optimization potentials.

Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. The key object of interest in systems biology, synthetic biology, and molecular programming is chemical reaction networks (CRNs) which formalizes coupled chemical reactions in a well-mixed solution. CRNs are pivotal for our understanding of biological regulatory and metabolic networks, as well as for programming engineered molecular behavior. Although it is clear that small CRNs are capable of complex dynamics and computational behavior, it remains difficult to explore the space of CRNs in search for desired functionality. We use Alloy, a tool for expressing structural constraints and behavior in software systems, to enumerate CRNs with declaratively specified properties. We show how this framework can enumerate CRNs with a variety of structural constraints including biologically motivated catalytic networks and metabolic networks, and seesaw networks motivated by DNA nanotechnology. We also use the framework to explore analog function computation in rate-independent CRNs. By computing the desired output value with stoichiometry rather than with reaction rates (in the sense that X → Y+Y computes multiplication by 2), such CRNs are completely robust to the choice of reaction rates or rate law. We find the smallest CRNs computing the max, minmax, abs and ReLU (rectified linear unit) functions in a natural subclass of rate-independent CRNs where rate-independence follows from structural network properties.

Metabolism is a complex network of biochemical reactions that cells use to obtain free energy transduced from nutrients and synthesize new cellular components. Understanding the wiring of metabolism can aid in metabolic engineering to boost certain metabolic functions, or, alternatively, inspire interventions to block undesired metabolism, for example, of parasites. The challenge is that interventions to metabolic networks should be studied in the context of the entire, extensive cellular metabolic networks. Incoming and outgoing fluxes may be readily measured but how fluxes are distributed within the metabolic network often remains a black box. Systems biology offers a toolset to shine light inside this black box: constraint-based metabolic models can predict intracellular flux distributions. But how to construct such a model? In this chapter, we will guide you through the steps to make a constraint-based model out of the genome sequence and demonstrate that it may be easier than it sounds. We provide a walkthrough of model construction, curation and validation-with a specific focus on protistan parasites and their lifecycle stages. While genomes can help to infer the entirety of metabolic potential encoded in the organism's genome (a so-called genome-scale metabolic model), cells do not necessarily express all metabolic enzymes simultaneously. This is particularly relevant for parasites as the different lifecycle stages rely on different sets of metabolic enzymes and host-imposed constraints. We discuss approaches to restrict the genome-wide network to become lifecycle stage specific and how you can test and use the resulting models.

Understanding the relationship between the structure of chemical reaction networks and their reaction dynamics is essential for unveiling the design principles of living organisms. However, while some network-structural features are known to relate to the steady-state characteristics of chemical reaction networks, mathematical frameworks describing the links between out-of-steady-state dynamics and network structure are still underdeveloped. Here, we characterize the out-of-steady-state behavior of a class of artificial chemical reaction networks consisting of the ligation and splitting reactions of polymers. Within this class, we examine minimal networks that can convert a given set of sources (e.g., nutrients) to a specified set of targets (e.g., biomass precursors). By exploring the dynamics of the models with a simple setup, we find three distinct types of relaxation dynamics after perturbation from a steady-state: exponential-, power-law-, and plateau-dominated. We computationally show that we can predict this out-of-steady-state dynamical behavior from just three features computed from the network’s stoichiometric matrix, namely, (1) the rank gap, determining the existence of a steady-state; (2) the left null-space, being related to conserved quantities in the dynamics; and (3) the stoichiometric cone, dictating the range of achievable chemical concentrations. We further demonstrate that these three quantities relates to the type of relaxation dynamics of combinations of our minimal networks, larger networks with many redundant pathways, and a real example of a metabolic network. The relationship between the topological features of reaction networks and the relaxation dynamics presented here are useful clues for understanding the design of metabolic reaction networks as well as industrially useful chemical production pathways.

BackgroundOne central goal of computational systems biology is the mathematical modelling of complex metabolic reaction networks. The first and most time-consuming step in the development of such models consists in the stoichiometric reconstruction of the network, i. e. compilation of all metabolites, reactions and transport processes relevant to the considered network and their assignment to the various cellular compartments. Therefore an information system is required to collect and manage data from different databases and scientific literature in order to generate a metabolic network of biochemical reactions that can be subjected to further computational analyses.ResultsThe computer program METANNOGEN facilitates the reconstruction of metabolic networks. It uses the well-known database of biochemical reactions KEGG of biochemical reactions as primary information source from which biochemical reactions relevant to the considered network can be selected, edited and stored in a separate, user-defined database. Reactions not contained in KEGG can be entered manually into the system. To aid the decision whether or not a reaction selected from KEGG belongs to the considered network METANNOGEN contains information of SWISSPROT and ENSEMBL and provides Web links to a number of important information sources like METACYC, BRENDA, NIST, and REACTOME. If a reaction is reported to occur in more than one cellular compartment, a corresponding number of reactions is generated each referring to one specific compartment. Transport processes of metabolites are entered like chemical reactions where reactants and products have different compartment attributes. The list of compartmentalized biochemical reactions and membrane transport processes compiled by means of METANNOGEN can be exported as an SBML file for further computational analysis. METANNOGEN is highly customizable with respect to the content of the SBML output file, additional data-fields, the graphical input form, highlighting of project specific search terms and dynamically generated Web-links.ConclusionMETANNOGEN is a flexible tool to manage information for the design of metabolic networks. The program requires Java Runtime Environment 1.4 or higher and about 100 MB of free RAM and about 200 MB of free HD space. It does not require installation and can be directly Java-webstarted from .

Isolating pure microbial cultures and cultivating them in the laboratory on defined media is used to more fully characterize the metabolism and physiology of organisms. However, identifying an appropriate growth medium for a novel isolate remains a challenging task. Even organisms with sequenced and annotated genomes can be difficult to grow, despite our ability to build genome-scale metabolic networks that connect genomic data with metabolic function. The scientific literature is scattered with information about defined growth media used successfully for cultivating a wide variety of organisms, but to date there exists no centralized repository to inform efforts to cultivate less characterized organisms by bridging the gap between genomic data and compound composition for growth media. Here we present MediaDB, a manually curated database of defined media that have been used for cultivating organisms with sequenced genomes, with an emphasis on organisms with metabolic network models. The database is accessible online, can be queried by keyword searches or downloaded in its entirety, and can generate exportable individual media formulation files. The data assembled in MediaDB facilitate comparative studies of organism growth media, serve as a starting point for formulating novel growth media, and contribute to formulating media for in silico investigation of metabolic networks. MediaDB is freely available for public use at https://mediadb.systemsbiology.net.

As an important research direction in the field of artificial intelligence, neural networks have made significant progress in many fields such as image recognition and natural language processing in recent years. The mathematical principles behind it, particularly ordinary and partial differential equations, play a pivotal role in describing the dynamic behavior and learning processes of neural networks. Therefore, the study of the mathematical principles of these two and their application in neural networks has important theoretical significance and practical value. This paper first introduces the mathematical principles of ordinary differential equations and their applications in neural networks, then expounds the mathematical principles of partial differential equations and their applications in neural networks, and finally analyzes the limitations of existing research and looks forward to future development. By systematically reviewing the application of ordinary differentiation and partial differentiation in neural networks, this paper provides a new perspective and idea for related research. At the same time, the research in this paper is helpful to deepen the understanding of the dynamic behavior of neural networks, promote the development of neural network theory, and provide a theoretical basis for model design and optimization in practical applications.

Associative classification (AC) is a branch of data mining that utilizes association rules (ARs) for classification. ARs are extracted from databases that satisfy some statistical criteria such as minimal support. However, in some practical applications, useful ARs may be found among infrequent, but closely related, itemsets that are filtered out by high minimal support. In this study, a new measure, named “condenseness,” is presented for evaluating whether infrequent ruleitems that are filtered out by minimal support can form strong ARs for classification. For an infrequent ruleitem, the condenseness is the average of lift of all ARs that can be generated from the ruleitem. A ruleitem with a high condenseness means that its elements are closely related and can serve for AC even if it does not have high support. Based on the concept of condenseness, a new associative classifier is developed and presented – condensed association rules for classification (CARC). CARC generates ARs using a modified Apriori algorithm and develops new strategies of rule inference. With the condenseness measure and strategies for rule inference, more useful ARs can be produced and improve the effectiveness of association classification. Empirical evidences show that CARC mitigates the problems caused by setting too high/low minimal support and has a better performance on classification.

Nonlinear dynamics and chaos in fractional-order neural networks

This paper provides a mathematical explanation for the phenomenon of \triadic closure so often seen in social networks. It appears to be a natural con- sequence when network change is constrained to be continuous. The concept of chordless cycles in the network's \irreducible spine is used in the analysis of the network's dynamic behavior. A surprising result is that as networks undergo random, but continuous, pertur- bations they tend to become more structured and less chaotic. In this paper we explore the behavior of networks as they change under a sequence of simple, \continuous transformations. We will start with a random network and apply a sequence of transformations which randomly adds edges (or connections) to it and randomly deletes edges. Periodically we observe the resulting network. The structure, or topology, of these show considerable similarity to that appearing in social networks. The rather surprising conclusion will be that \random change, provided it is continuous, leads to a less chaotic and more regular structure. This provides a purely mathematical basis for the presence of \triadic closure in social networks.

A new era of the electrical grid began due to the high integration of the inverter-based resources. Typically, resources are connected to the electrical grid using grid-following control techniques. Overall system inertia reduces as these resources replace rotating synchronous machines. Grid-forming control is one of the solutions introduced to overcome the challenges in the electrical grid due to the increase in inverters. With the increase of inverter-based resources in both transmission and distribution networks and the introduction of new inverter controls, it is important to understand how power system voltage and frequency dynamics are affected. In this paper, a 100% inverter-based resource electrical network is studied across both transmission and distribution networks while considering different inverter control configurations and different methods of current limiting. Moreover, the increasing penetration of inverter-based resources poses challenges to transmission planning as the dynamic interaction between distribution and transmission can no longer be ignored. In this regard, an aggregated distribution network model is proposed for transmission planning studies to accurately represent the distribution network's dynamic behavior at different grid-forming and grid-following inverter ratios.

Improving the controllability of power networks is crucial as they are highly complex networks operating in synchrony; even minor perturbations can cause desynchronization and instability. To that end, one needs to assess the criticality of key network components (buses and lines) in terms of their impact on system performance. Traditional methods to identify the key nodes/edges in power networks often rely on static centrality measures based on the network's topological structure ignoring the network's dynamic behavior. In this paper, using multimachine power network models and a new control-theoretic edge centrality matrix (ECM) approach, we: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> quantify the influence of edges (i.e., the line susceptances) in terms of controllability performance metrics, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> identify the most <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">influential</i> lines, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(iii)</i> compute near-optimal edge modifications that improve the power network controllability. Employing various IEEE power network benchmarks, we validate the effectiveness of the ECM-based algorithm and demonstrate improvements in system reachability, control, and damping performance.

The reactivity of palladium complexes of bidentate diaryl phosphane ligands (P(2)) was studied in the reaction of nitrobenzene with CO in methanol. Careful analysis of the reaction mixtures revealed that, besides the frequently reported reduction products of nitrobenzene [methyl phenyl carbamate (MPC), N,N'-diphenylurea (DPU), aniline, azobenzene (Azo) and azoxybenzene (Azoxy)], large quantities of oxidation products of methanol were co-produced (dimethyl carbonate (DMC), dimethyl oxalate (DMO), methyl formate (MF), H(2)O, and CO). From these observations, it is concluded that several catalytic processes operate simultaneously, and are coupled via common catalytic intermediates. Starting from a P(2)Pd(0) compound formed in situ, oxidation to a palladium imido compound P(2)Pd(II)=NPh, can be achieved by de-oxygenation of nitrobenzene 1) with two molecules of CO, 2) with two molecules of CO and the acidic protons of two methanol molecules, or 3) with all four hydrogen atoms of one methanol molecule. Reduction of P(2)Pd(II)=NPh to P(2)Pd(0) makes the overall process catalytic, while at the same time forming Azo(xy), MPC, DPU and aniline. It is proposed that the Pd-imido species is the central key intermediate that can link together all reduction products of nitrobenzene and all oxidation products of methanol in one unified mechanistic scheme. The relative occurrence of the various catalytic processes is shown to be dependent on the characteristics of the catalysts, as imposed by the ligand structure.

General rate equations and their applications for cyclic reaction networks: multi-pathway systems

Data science is introduced to identify the reactant, product, and reaction path in the chemical reaction network. Cobalt catalyzed hydroformylation is investigated where the reaction network is built via first principles calculations. The closeness centrality and high frequency node are found to be the reactant cobalt tetracarbonyl hydride. In addition, betweenness centrality uncovers three reaction paths which have the products of aldehyde, CH2O, and CO2, respectively. The energy profile determines that the reaction path leading to aldehyde is energetically favored; thus, the reaction path for cobalt catalyzed hydroformylation is identified without kinetics. Hence, the proposed approach can act as a first step towards understanding the complex chemical reaction network and towards further kinetic understanding of the chemical reaction.