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PubMed1998

Learning dynamical systems by recurrent neural networks from orbits.

This paper investigates the problem of approximating a dynamical system (DS) by a recurrent neural network (RNN) as one extension of the problem of approximating orbits by an RNN. We systematically investigate how an RNN can produce a DS on the visible state space to approximate a given DS and as a first step to the generalization problem for RNNs, we also investigate whether or not a DS produced by some RNN can be identified from several observed orbits of the DS. First, it is proved that RNNs without hidden units uniquely produce a certain class of DS. Next, neural dynamical systems (NDSs) are proposed as DSs produced by RNNs with hidden units. Moreover, affine neural dynamial systems (A-NDSs) are provided as nontrivial examples of NDSs and it is proved that any DS can be finitely approximated by an A-NDS with any precision. We propose an A-NDS as a DS that an RNN can actually produce on the visible state space to approximate the target DS. For the generalization problem of RNNs, a geometric criterion is derived in the case of RNNs without hidden units. This theory is also extended to the case of RNNs with hidden units for learning A-NDSs.

Journal Article↗
PubMed2006

A Bayesian dynamic model for influenza surveillance.

The severe acute respiratory syndrome (SARS) epidemic, the growing fear of an influenza pandemic and the recent shortage of flu vaccine highlight the need for surveillance systems able to provide early, quantitative predictions of epidemic events. We use dynamic Bayesian networks to discover the interplay among four data sources that are monitored for influenza surveillance. By integrating these different data sources into a dynamic model, we identify in children and infants presenting to the pediatric emergency department with respiratory syndromes an early indicator of impending influenza morbidity and mortality. Our findings show the importance of modelling the complex dynamics of data collected for influenza surveillance, and suggest that dynamic Bayesian networks could be suitable modelling tools for developing epidemic surveillance systems.

Bayes Theorem↗
PubMed2004

Using a quantitative blueprint to reprogram the dynamics of the flagella gene network.

Detailed understanding and control of biological networks will require a level of description similar to that of electronic engineering blueprints. Currently, however, even the best-studied systems are usually described using qualitative arrow diagrams. A quantitative blueprint requires in vivo measurements of (1) the relative strength of the interactions (numbers on the arrows) and (2) the functions that integrate multiple inputs. Here, we address this using a well-studied system, the flagella biosynthesis transcription network in Escherichia coli. We use theory and high-resolution experiments to obtain a quantitative blueprint with (1) numbers on the arrows, finding different hierarchies of activation coefficients for the two regulators, FlhDC and FliA; and (2) cis-regulatory input functions, which summate the input from the two regulators (SUM gates). We then demonstrate experimentally how this blueprint can be used to reprogram temporal expression patterns in this system, using controlled expression of the regulators or point mutations in their binding sites. The present approach can be used to define blueprints of other gene networks and to quantitatively reprogram their dynamics.

Algorithms↗
PubMed2006

Evolutionary dynamics of prokaryotic transcriptional regulatory networks.

The structure of complex transcriptional regulatory networks has been studied extensively in certain model organisms. However, the evolutionary dynamics of these networks across organisms, which would reveal important principles of adaptive regulatory changes, are poorly understood. We use the known transcriptional regulatory network of Escherichia coli to analyse the conservation patterns of this network across 175 prokaryotic genomes, and predict components of the regulatory networks for these organisms. We observe that transcription factors are typically less conserved than their target genes and evolve independently of them, with different organisms evolving distinct repertoires of transcription factors responding to specific signals. We show that prokaryotic transcriptional regulatory networks have evolved principally through widespread tinkering of transcriptional interactions at the local level by embedding orthologous genes in different types of regulatory motifs. Different transcription factors have emerged independently as dominant regulatory hubs in various organisms, suggesting that they have convergently acquired similar network structures approximating a scale-free topology. We note that organisms with similar lifestyles across a wide phylogenetic range tend to conserve equivalent interactions and network motifs. Thus, organism-specific optimal network designs appear to have evolved due to selection for specific transcription factors and transcriptional interactions, allowing responses to prevalent environmental stimuli. The methods for biological network analysis introduced here can be applied generally to study other networks, and these predictions can be used to guide specific experiments.

Amino Acid Motifs↗
PubMed2006

Regulatory dynamics of synthetic gene networks with positive feedback.

Biological processes are governed by complex networks ranging from gene regulation to signal transduction. Positive feedback is a key element in such networks. The regulation enables cells to adopt multiple internal expression states in response to a single external input signal. However, past works lacked a dynamical aspect of this system. To address the dynamical property of the positive feedback system, we employ synthetic gene circuits in Escherichia coli to measure the rise-time of both the no-feedback system and the positive feedback system. We show that the kinetics of gene expression is slowed down if the gene regulatory system includes positive feedback. We also report that the transition of gene switching behaviors from the hysteretic one to the graded one occurs. A mathematical model based on the chemical reactions shows that the response delay is an inherited property of the positive feedback system. Furthermore, with the aid of the phase diagram, we demonstrate the decline of the feedback activation causes the transition of switching behaviors. Our findings provide a further understanding of a positive feedback system in a living cell from a dynamical point of view.

Escherichia coli↗
PubMed2026

Investigating the mechanisms of PhIP-induced colorectal cancer through network toxicology, machine learning, and molecular dynamics simulation.

BACKGROUND: Over the past few years, 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP)- a compound from grilled or processed meats-has emerged as a major player in cancer development, especially colorectal cancer (CRC). This work dives into its potential links to CRC and uncovers the key genes that bridge this connection. METHODS: We tapped into various databases to pinpoint target genes tied to PhIP and CRC, then ran protein-protein interaction (PPI) analyses for visualization. Next, we explored underlying mechanisms through Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment. To nail down predictions, we tested 107 machine learning pipelines and picked the best one, validating its accuracy and the core genes' prognostic value across datasets. Next, molecular docking and dynamics simulations probed the interactions between these genes and PhIP. Finally, cell proliferation was assessed using Cell Counting Kit-8 (CCK-8) and 5-ethynyl-2'-deoxyuridine (EdU) assays, and polymerase chain reaction (PCR) was performed to validate the expression levels of the hub genes. RESULTS: Our analysis identified 39 overlapping genes, from which a machine learning model (glmBoost + Enet) identified six candidate targets: CDK4, CEBPB, COMT, SOX9, TIMP1, and TOP2A. To prioritize these, a hierarchical screening framework was applied. Molecular docking and dynamics simulations identified CDK4, COMT, and TIMP1 as the most stable interactors with PhIP. Functional assays confirmed that PhIP treatment significantly enhanced the proliferation of CRC cells. Crucially, quantitative PCR (qPCR) validation in multiple CRC cell lines identified TIMP1 as the primary target, showing the most consistent and significant upregulation upon PhIP exposure. CONCLUSIONS: In essence, these genes drive PhIP is role in CRC, offering novel insights into its molecular pathways. This could reshape how we tackle food-related pollutants, paving the way for better prevention and targeted therapies.

Colorectal cancer (CRC)↗
PubMed2026

Validating the potential mechanism and therapeutic effect of Qinlian Jiangxia decoction in the treatment of type 2 diabetes mellitus complicated with hyperlipidemia through network pharmacology, molecular docking, molecular dynamics simulation, andexperiments.

OBJECTIVE: To investigate the mechanism of action of Qinlian Jiangxia decoction (, QLJXD) in the treatment of type 2 diabetes mellitus (T2DM) complicated by hyperlipidemia using network pharmacology, molecular docking, molecular dynamics simulation and in vivo experiments. METHODS: Drug components, targets and disease targets were identified using databases such as TCM systems pharmacology database and analysis platform and GeneCards. The intersecting targets were subjected to protein-protein interaction analysis using the search tool for the retrieval of interacting genes/proteins database. Subsequently, Gene Ontology and Kyoto Encyclopedia of Genes and Genomes analysis of the intersecting targets were conducted using the Metascape platform to identify core components and targets. The results were validated using molecular docking, molecular dynamics simulations and in vivo experiments. RESULTS: QLJXD contains 76 active ingredients and 136 disease targets. The core ingredients are quercetin, β-sitosterol, wogonin and baicalein, while the core targets are fatty acid binding protein 4 (FABP4) and peroxisome proliferative activated receptor gamma (PPARG). Molecular docking and molecular dynamics simulations revealed that the core ingredients bound well to the core targets. Animal experiments demonstrated that QLJXD effectively inhibited the expression of FABP4 and increased the expression of PPARG, thereby enhancing disorders of glycolipid metabolism. CONCLUSION: The putative therapeutic efficacy of QLJXD in the management of T2DM complicated with hyperlipidemia may be ascribed to the synergistic actions of multiple components, such as quercetin, β-sitosterol, wogonin, and baicalein, which collectively modulate FABP4 and PPARG molecular targets.

Molecular Docking Simulation↗
PubMed1999

Dynamical analysis of gene networks requires both mRNA and protein expression information.

One of the important goals of biology is to understand the relationship between DNA sequence information and nonlinear cellular responses. This relationship is central to the ability to effectively engineer cellular phenotypes, pathways, and characteristics. Expression arrays for monitoring total gene expression based on mRNA can provide quantitative insight into which gene or genes are on or off; but this information is insufficient to fully predict dynamic biological phenomena. Using nonlinear stability analysis we show that a combination of gene expression information at the message level and at the protein level is required to describe even simple models of gene networks. To help illustrate the need for such information we consider a mechanistic model for circadian rhythmicity which shows agreement with experimental observations when protein and mRNA information are included and we propose a framework for acquiring and analyzing experimental and mathematically derived information about gene networks.

Animals↗
PubMed1990

The significance of sexual partner contact networks for the transmission dynamics of HIV.

The paper provides a brief review of the significance of heterogeneity in sexual behaviour to the transmission dynamics of HIV and the spread of AIDS. It addresses the formulation of mathematical models to encapsulate variability in the rate of sexual partner change, the structure of networks of sexual partner contact, and age dependency in sexual activity. A particular focus is the significance of high or low preference (or choice) of sexual partners from an individual's own sexual activity class (defined on the basis of partner change rate or other criteria). Numerical studies of model behaviour reveal that a high degree of assortativeness (high level of "like with like" mixing) results in a more rapid initial spread of HIV, a smaller overall epidemic, and the possibility of a multipeak or long and drawn out epidemic, by comparison with those induced by high degrees of disassortativeness (low level of "like with like" mixing) in sexual contact patterns. The structure of a sexual network is shown to be a major determinant of the temporal pattern and magnitude of an epidemic. The demographic impact of HIV in developing countries is also examined in the context of choice matrices based on age as well as sexual activity. The potential demographic impact of AIDS is shown to be enhanced by age dependency in levels of activity (high in the young and lower in older age classes), a male preference for females of younger age, and a higher efficiency of HIV transmission from male to female than vice versa. The paper ends with a discussion of the need for better quantitative data on sexual behaviour.

Adult↗
PubMed2000

Strain hardening of actin filament networks. Regulation by the dynamic cross-linking protein alpha-actinin.

Mechanical stresses applied to the plasma membrane of an adherent cell induces strain hardening of the cytoskeleton, i.e. the elasticity of the cytoskeleton increases with its deformation. Strain hardening is thought to mediate the transduction of mechanical signals across the plasma membrane through the cytoskeleton. Here, we describe the strain dependence of a model system consisting of actin filaments (F-actin), a major component of the cytoskeleton, and the F-actin cross-linking protein alpha-actinin, which localizes along contractile stress fibers and at focal adhesions. We show that the amplitude and rate of shear deformations regulate the resilience of F-actin networks. At low temperatures, for which the lifetime of binding of alpha-actinin to F-actin is long, F-actin/alpha-actinin networks exhibit strong strain hardening at short time scales and soften at long time scales. For F-actin networks in the absence of alpha-actinin or for F-actin/alpha-actinin networks at high temperatures, strain hardening appears only at very short time scales. We propose a model of strain hardening for F-actin networks, based on both the intrinsic rigidity of F-actin and dynamic topological constraints formed by the cross-linkers located at filaments entanglements. This model offers an explanation for the origin of strain hardening observed when shear stresses are applied against the cellular membrane.

Actin Cytoskeleton↗
PubMed2005

The implications of network structure for epidemic dynamics.

It has long been realised that the standard assumptions of mass-action mixing are a crude approximation of the true mechanistic processes that govern the transmission of infection. In particular, many infections can be considered to be spread through a limited network of contacts. Yet, despite the underlying discrepancies, mass-action models continue to be used and provide a remarkably accurate description of epidemic behaviour. Here, the differences between mass-action and network-based models are investigated. This allows us to determine when mass-action models are a reliable tool, and suggest ways in which their behaviour should be refined.

Cluster Analysis↗
PubMed1985

A dorsal spinal neural network in cat. III. Dynamic nonlinear analysis of responses to random stimulation of single type 1 cutaneous input fibers.

The input/output characteristics of a subset of dorsal horn neurons in laminae 3 and 4 [( L3,4:SA1,X], see INTRODUCTION; output cells) of cat have previously been examined in the resting unperturbed condition using single or paired input pulses introduced once every three seconds on single slowly adapting type 1 (SA1) cutaneous mechanoreceptor afferent fibers (1, 27, 28). The present study extends this description to the dynamic condition by use of a random-stimulation method developed for the characterization of multiport pulse-input/pulse-output nonlinear systems. A total of 58 SA1 receptor input channels to 29 [L3,4:SA1,X] network output cells were tested individually in 15 spinal cats with several random train stimuli of differing mean input rates [5, 10, 20, 30, 50 pulses per second (pps)]. Simultaneous stimulation of two input channels with independent random trains was performed in 16 units. In each case, zero-, first-, and second-order descriptions of network behavior were obtained; the second-order characteristics of interest were expressed in the form of excitability functions, which are directly comparable with those obtained from condition-test results. Preliminary testing with multiple input pulses suggested that, in addition to the strong second-order effects previously identified, third- and higher-order nonlinearities and effects with long time constants could generate significant rate effects. Nonetheless, first-order response characteristics obtained in the dynamic condition at the lowest mean input rate used (5 pps) were in each case qualitatively identical, though slightly smaller in magnitude, to the poststimulus time histograms (PST) obtained in the unperturbed condition. Second-order excitability functions were generally, but not always, similar to condition-test results in the eight cases in which comparisons were made. Furthermore, use of a complete second-order characterization to predict the output response to a different random input in five cases resulted in an average correlation with the observed output that was a 50% improvement over the linear model predictions. These results indicate strong second-order and weaker higher-order nonlinearities in the [L3,4:SA1,X] network. Three classes of channel-specific second-order excitability characteristics were identified into which the previous descriptions (28) can be incorporated. The general pattern was initial facilitation followed by inhibition. This was observed for both the early and late response components in about half the channels (class I).(ABSTRACT TRUNCATED AT 400 WORDS)

Afferent Pathways↗
PubMed2001

Computational design and nonlinear dynamics of a recurrent network model of the primary visual cortex.

Recurrent interactions in the primary visual cortex make its output a complex nonlinear transform of its input. This transform serves preattentive visual segmentation, that is, autonomously processing visual inputs to give outputs that selectively emphasize certain features for segmentation. An analytical understanding of the nonlinear dynamics of the recurrent neural circuit is essential to harness its computational power. We derive requirements on the neural architecture, components, and connection weights of a biologically plausible model of the cortex such that region segmentation, figure-ground segregation, and contour enhancement can be achieved simultaneously. In addition, we analyze the conditions governing neural oscillations, illusory contours, and the absence of visual hallucinations. Many of our analytical techniques can be applied to other recurrent networks with translation-invariant neural and connection structures.

Animals↗
PubMed2002

Comment on "Dynamics of some neural network models with delay".

Based upon numerical evidence, Ruan et al. [J. Ruan, L. Li, and W. Lin, Phys. Rev. E 63, 051906 (2001)] suggest that the delay differential equation dx/dt(t)=-x(t)+A tanh[x(t)]+B tanh[x(t-tau)] may display chaotic dynamics. As mentioned by Pakdaman and Malta [IEEE Trans. Neural Netw. 9, 231 (1998)], this equation presents a monotonic delayed feedback, so that it satisfies a Poincaré-Bendixson-like theorem, ruling out the existence of complex aperiodic dynamics.

Comment↗
PubMed2006

Computational neurogenetic modelling: a pathway to new discoveries in genetic neuroscience.

The paper presents a methodology for using computational neurogenetic modelling (CNGM) to bring new original insights into how genes influence the dynamics of brain neural networks. CNGM is a novel computational approach to brain neural network modelling that integrates dynamic gene networks with artificial neural network model (ANN). Interaction of genes in neurons affects the dynamics of the whole ANN model through neuronal parameters, which are no longer constant but change as a function of gene expression. Through optimization of interactions within the internal gene regulatory network (GRN), initial gene/protein expression values and ANN parameters, particular target states of the neural network behaviour can be achieved, and statistics about gene interactions can be extracted. In such a way, we have obtained an abstract GRN that contains predictions about particular gene interactions in neurons for subunit genes of AMPA, GABAA and NMDA neuro-receptors. The extent of sequence conservation for 20 subunit proteins of all these receptors was analysed using standard bioinformatics multiple alignment procedures. We have observed abundance of conserved residues but the most interesting observation has been the consistent conservation of phenylalanine (F at position 269) and leucine (L at position 353) in all 20 proteins with no mutations. We hypothesise that these regions can be the basis for mutual interactions. Existing knowledge on evolutionary linkage of their protein families and analysis at molecular level indicate that the expression of these individual subunits should be coordinated, which provides the biological justification for our optimized GRN.

Algorithms↗
PubMed1997

Associative Dynamics in a Chaotic Neural Network.

An associative network is constructed with chaotic neuron models interconnected through a conventional auto-associative matrix of synaptic weights. The associative dynamics of the network is analysed with spatio-temporal output patterns, quasi-energy function, distances between internal state vectors and orbital instability. The network shows a periodic response after a nonperiodic transient phase when the external stimulations are spatially constant. The retrieval characteristics and the duration in the transient phase are dependent on the initial conditions. The results imply that the transient dynamics can be interpreted as a memory searching process. The network also shows periodic responses with short and very long periods when external stimulations are not spatially constant, but corresponding to a stored pattern and an unstored pattern, respectively. The responses to the external stimulations can be utilized for a pattern recognition with nonliner dynamics. Copyright 1996 Elsevier Science Ltd.

Journal Article↗
PubMed2000

Dynamics of autocatalytic replicator networks based on higher-order ligation reactions.

A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c0 of replicating material. For small c0, in the hyperbolic growth regime, we recover the familiar dynamics of second-order replicator equations with its wealth of complex dynamics ranging from multi-stability to periodic and strange attractors as well as to heteroclinic orbits. For large c0, in the parabolic growth regime, product inhibition becomes dominating and we observe a single globally stable equilibrium tantamount to permanent coexistence. In an intermediate parameter range we sometimes observe a behavior that is reminiscent of 'survival of the fittest'. Independently replicating species (Schlögl's model) and the hypercycle are discussed in detail.

Catalysis↗
PubMed2004

Highly entangled polymer primitive chain network simulations based on dynamic tube dilation.

The concept of dynamic tube dilation (DTD) is here used to formulate a new simulation scheme to obtain the linear viscoelastic response of long chains with a large number of entanglements. The new scheme is based on the primitive chain network model previously proposed by some of the authors, and successfully employed to simulate linear and nonlinear behavior of moderately entangled polymers. Scaling laws are generated by the DTD concept, and allow for prediction of the linear response of very long chains on the basis of suitable simulations performed on shorter ones, without introducing adjustable parameters. Tests of the method against existing data for linear monodisperse polyisoprene and polystyrene show good quantitative agreement.

Journal Article↗