Inferring dynamic topology for decoding spatiotemporal structures in complex heterogeneous networks

Data-Efficient Inference of Nonlinear Oscillator Networks

Decoding the connectivity structure of a network of nonlinear oscillators from measurement data is a difficult yet essential task for understanding and controlling network functionality. Several data-driven network inference algorithms have been presented, but the commonly considered premise of ample measurement data is often difficult to satisfy in practice. In this paper, we propose a data-efficient network inference technique by combining correlation statistics with the model-fitting procedure. The proposed approach can identify the network structure reliably in the case of limited measurement data. We compare the proposed method with existing techniques on a network of Stuart-Landau oscillators, oscillators describing circadian gene expression, and noisy experimental data obtained from Rössler Electronic Oscillator network.

Synchronization, clustering, and weak chimeras in a densely coupled transcription-based oscillator model for split circadian rhythms

The synchronization dynamics for the circadian gene expression in the suprachiasmatic nucleus is investigated using a transcriptional circadian clock gene oscillator model. With global coupling in constant dark (DD) conditions, the model exhibits a one-cluster phase synchronized state, in dim light (dim LL), bistability between one- and two-cluster states and in bright LL, a two-cluster state. The two-cluster phase synchronized state, where some oscillator pairs synchronize in-phase, and some anti-phase, can explain the splitting of the circadian clock, i.e., generation of two bouts of daily activities with certain species, e.g., with hamsters. The one- and two-cluster states can be reached by transferring the animal from DD or bright LL to dim LL, i.e., the circadian synchrony has a memory effect. The stability of the one- and two-cluster states was interpreted analytically by extracting phase models from the ordinary differential equation models. In a modular network with two strongly coupled oscillator populations with weak intragroup coupling, with appropriate initial conditions, one group is synchronized to the one-cluster state and the other group to the two-cluster state, resulting in a weak-chimera state. Computational modeling suggests that the daily rhythms in sleep-wake depend on light intensity acting on bilateral networks of suprachiasmatic nucleus (SCN) oscillators. Addition of a network heterogeneity (coupling between the left and right SCN) allowed the system to exhibit chimera states. The simulations can guide experiments in the circadian rhythm research to explore the effect of light intensity on the complexities of circadian desynchronization.

On quantification and maximization of information transfer in network dynamical systems

Information flow among nodes in a complex network describes the overall cause-effect relationships among the nodes and provides a better understanding of the contributions of these nodes individually or collectively towards the underlying network dynamics. Variations in network topologies result in varying information flows among nodes. We integrate theories from information science with control network theory into a framework that enables us to quantify and control the information flows among the nodes in a complex network. The framework explicates the relationships between the network topology and the functional patterns, such as the information transfers in biological networks, information rerouting in sensor nodes, and influence patterns in social networks. We show that by designing or re-configuring the network topology, we can optimize the information transfer function between two chosen nodes. As a proof of concept, we apply our proposed methods in the context of brain networks, where we reconfigure neural circuits to optimize excitation levels among the excitatory neurons.

Data-Driven Control of Neuronal Networks with Population-Level Measurement

Controlling complex networks of nonlinear neurons is an important problem pertinent to various applications in engineering and natural sciences. While in recent years the control of neural populations with comprehensive biophysical models or simplified models, e.g., phase models, has seen notable advances, learning appropriate controls directly from data without any model assumptions remains a challenging and less developed area of research. In this paper, we address this problem by leveraging the network's local dynamics to iteratively learn an appropriate control without constructing a global model of the system. The proposed technique can effectively regulate synchrony in a neuronal network using only one input and one noisy population-level output measurement. We provide a theoretical analysis of our approach and illustrate its robustness to system variations and its generalizability to accommodate various physical constraints, such as charge-balanced inputs.

Partitioned estimation methodology of biological neuronal networks with topology-based module detection

Parameter estimation of neuronal networks is closely related with information processing mechanisms in neural systems. Estimation of synaptic parameters for neuronal networks was an time consuming task. Due to complex interactions between neurons, computational efficiency and accuracy of estimation methods is relatively low. Meanwhile, inherent topological properties such as core-periphery and modular structures are not fully considered in estimation. In order to improve the efficiency and accuracy of estimation, this study proposes a two-stage PartitionMLE method which introduces detected neuronal modules as topological constraints in estimation. The proposed PartitionMLE method firstly decomposes the system into multiple non-overlapping neuronal modules, by performing topology-based module detection. Dynamic parameters including intra-modular and inter-modular parameters are estimated in two stages, using detected hubs to connect non-overlapping neuronal modules. The contributions of PartitionMLE method are two-folds: reducing estimation errors and improving the model interpretability. Experiments about neuronal networks consisting of Hodgkin-Huxley (HH) and leaky integrate-and-firing (LIF) neurons validated the effectiveness of the PartitionMLE method, with comparison to the single-stage MLE method.

A new approach for extracting information from protein dynamics

Increased ability to predict protein structures is moving research focus towards understanding protein dynamics. A promising approach is to represent protein dynamics through networks and take advantage of well-developed methods from network science. Most studies build protein dynamics networks from correlation measures, an approach that only works under very specific conditions, instead of the more robust inverse approach. Thus, we apply the inverse approach to the dynamics of protein dihedral angles, a system of internal coordinates, to avoid structural alignment. Using the well-characterized adhesion protein, FimH, we show that our method identifies networks that are physically interpretable, robust, and relevant to the allosteric pathway sites. We further use our approach to detect dynamical differences, despite structural similarity, for Siglec-8 in the immune system, and the SARS-CoV-2 spike protein. Our study demonstrates that using the inverse approach to extract a network from protein dynamics yields important biophysical insights.

Statistical inference links data and theory in network science

The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domain-specific applications often occur in isolation, risking an effective disconnect between theoretical and methodological advances and the way network science is employed in practice. Here we address this risk constructively, discussing good practices to guarantee more successful applications and reproducible results. We endorse designing statistically grounded methodologies to address challenges in network science. This approach allows one to explain observational data in terms of generative models, naturally deal with intrinsic uncertainties, and strengthen the link between theory and applications.

Theoretical models and structures recovered from measured data serve for analysis of complex networks. The authors discuss here existing gaps between theoretical methods and real-world applied networks, and potential ways to improve the interplay between theory and applications.

Reconstruction of Tree Network via Evolutionary Game Data Analysis

As one of the most effective technologies for network reconstruction, compressive sensing can recover signals from a small amount of observed data through sparse search or greedy algorithms in the assumption that the unknown signal is sufficiently sparse on a specific basis. However, there often occurs loss of precision even failure in the process of reconstruction without enough prior information. Therefore, the purpose of this article is to solve the problem of low reconstruction accuracy by mining implicit structural information in the network. Specifically, we propose a novel and efficient algorithm (MCM_TRA) for reconstructing the structure of the K -forked tree network. Based on evolutionary game dynamics, the modified clustering method (MCM) classifies all nodes into two sets, then a two-stage reconstruction algorithm (TRA) is illustrated to recover the node signals in different sets. The experimental results demonstrate that the MCM_TRA enhances the reconstruction accuracy prominently than previous algorithms. Moreover, extensive sensitivity analysis shows that the reconstruction effect can be promoted for a broad range of parameters, which further indicates the superiority of the proposed method.

Deciphering clock cell network morphology within the biological master clock, suprachiasmatic nucleus: From the perspective of circadian wave dynamics

The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of ~10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (~25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained ‘indegree distribution’ as well as a ‘physical range distribution of afferent clock cells.’ Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced “phase-singularities.” The successful, realistic networks have several common features: 1) “indegree” and “outdegree” should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN.

A new approach for extracting information from protein dynamics

Increased ability to predict protein structures is moving research focus towards understanding protein dynamics. A promising approach is to represent protein dynamics through networks and take advantage of well-developed methods from network science. Most studies build protein dynamics networks from correlation measures, an approach that only works under very specific conditions, instead of the more robust inverse approach. Thus, we apply the inverse approach to the dynamics of protein dihedral angles, a system of internal coordinates, to avoid structural alignment. Using the well-characterized adhesion protein, FimH, we show that our method identifies networks that are physically interpretable, robust, and relevant to the allosteric pathway sites. We further use our approach to detect dynamical differences, despite structural similarity, for Siglec-8 in the immune system, and the SARS-CoV-2 spike protein. Our study demonstrates that using the inverse approach to extract a network from protein dynamics yields important biophysical insights.

Remarkable Sensitivity of Young Honey Bee Workers to Multiple Non-photic, Non-thermal, Forager Cues That Synchronize Their Daily Activity Rhythms

Honey bees live in colonies containing tens of thousands of workers that coordinate their activities to produce efficient colony-level behavior. In free-foraging colonies, nest bees are entrained to the forager daily phase of activity even when experiencing conflicting light-dark illumination regime, but little is known on the cues mediating this potent social synchronization. We monitored locomotor activity in an array of individually caged bees in which we manipulated the contact with neighbour bees. We used circular statistics and coupling function analyses to estimate the degree of social synchronization. We found that young bees in cages connected to cages housing foragers showed stronger rhythms, better synchronization with each other, higher coupling strength, and a phase more similar to that of the foragers compared to similar bees in unconnected cages. These findings suggest that close distance contacts are sufficient for social synchronization or that cage connection facilitated the propagation of time-giving social cues. Coupling strength was higher for bees placed on the same tray compared with bees at a similar distance but on a different tray, consistent with the hypothesis that substrate borne vibrations mediate phase synchronization. Additional manipulation of the contact between cages showed that social synchronization is better among bees in cages connected with tube with a single mesh partition compared to sealed tubes consistent with the notion that volatile cues act additively to substrate borne vibrations. These findings are consistent with self-organization models for social synchronization of activity rhythms and suggest that the circadian system of honey bees evolved remarkable sensitivity to non-photic, non-thermal, time giving entraining cues enabling them to tightly coordinate their behavior in the dark and constant physical environment of their nests.

Computational Approaches and Tools as Applied to the Study of Rhythms and Chaos in Biology

The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.

Social synchronization of circadian rhythms with a focus on honeybees

Many animals benefit from synchronizing their daily activities with conspecifics. In this hybrid paper, we first review recent literature supporting and extending earlier evidence for a lack of clear relationship between the level of sociality and social entrainment of circadian rhythms. Social entrainment is specifically potent in social animals that live in constant environments in which some or all individuals do not experience the ambient day-night cycles. We next focus on highly social honeybees in which there is good evidence that social cues entrain the circadian clocks of nest bees and can override the influence of conflicting light-dark cycles. The current understanding of social synchronization in honeybees is consistent with self-organization models in which surrogates of forager activity, such as substrate-borne vibrations and colony volatiles, entrain the circadian clocks of bees dwelling in the dark cavity of the nest. Finally, we present original findings showing that social synchronization is effective even in an array of individually caged callow bees placed on the same substrate and is improved for bees in connected cages. These findings reveal remarkable sensitivity to social time-giving cues and show that bees with attenuated rhythms (weak oscillators) can nevertheless be socially synchronized to a common phase of activity. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

Inferring causality in biological oscillators

MOTIVATION

Fundamental to biological study is identifying regulatory interactions. The recent surge in time-series data collection in biology provides a unique opportunity to infer regulations computationally. However, when components oscillate, model-free inference methods, while easily implemented, struggle to distinguish periodic synchrony and causality. Alternatively, model-based methods test the reproducibility of time series given a specific model but require inefficient simulations and have limited applicability.

RESULTS

We develop an inference method based on a general model of molecular, neuronal and ecological oscillatory systems that merges the advantages of both model-based and model-free methods, namely accuracy, broad applicability and usability. Our method successfully infers the positive and negative regulations within various oscillatory networks, e.g. the repressilator and a network of cofactors at the pS2 promoter, outperforming popular inference methods.

AVAILABILITY AND IMPLEMENTATION

We provide a computational package, ION (Inferring Oscillatory Networks), that users can easily apply to noisy, oscillatory time series to uncover the mechanisms by which diverse systems generate oscillations. Accompanying MATLAB code under a BSD-style license and examples are available at https://github.com/Mathbiomed/ION. Additionally, the code is available under a CC-BY 4.0 License at https://doi.org/10.6084/m9.figshare.16431408.v1.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Parallel residual projection: a new paradigm for solving linear inverse problems

A grand challenge to solve a large-scale linear inverse problem (LIP) is to retain computational efficiency and accuracy regardless of the growth of the problem size. Despite the plenitude of methods available for solving LIPs, various challenges have emerged in recent times due to the sheer volume of data, inadequate computational resources to handle an oversized problem, security and privacy concerns, and the interest in the associated incremental or decremental problems. Removing these barriers requires a holistic upgrade of the existing methods to be computationally efficient, tractable, and equipped with scalable features. We, therefore, develop the parallel residual projection (PRP), a parallel computational framework involving the decomposition of a large-scale LIP into sub-problems of low complexity and the fusion of the sub-problem solutions to form the solution to the original LIP. We analyze the convergence properties of the PRP and accentuate its benefits through its application to complex problems of network inference and gravimetric survey. We show that any existing algorithm for solving an LIP can be integrated into the PRP framework and used to solve the sub-problems while handling the prevailing challenges.

Real-time Inference and Detection of Disruptive EEG Networks for Epileptic Seizures

Recent studies in brain science and neurological medicine paid a particular attention to develop machine learning-based techniques for the detection and prediction of epileptic seizures with electroencephalogram (EEG). As a noninvasive monitoring method to record brain electrical activities, EEG has been widely used for capturing the underlying dynamics of disruptive neuronal responses across the brain in real-time to provide clinical guidance in support of epileptic seizure treatments in practice. In this study, we introduce a novel dynamic learning method that first infers a time-varying network constituted by multivariate EEG signals, which represents the overall dynamics of the brain network, and subsequently quantifies its topological property using graph theory. We demonstrate the efficacy of our learning method to detect relatively strong synchronization (characterized by the algebraic connectivity metric) caused by abnormal neuronal firing during a seizure onset. The computational results for a realistic scalp EEG database show a detection rate of 93.6% and a false positive rate of 0.16 per hour (FP/h); furthermore, our method observes potential pre-seizure phenomena in some cases.

Application of Random Forest and ICON Models Combined with Weather Forecasts to Predict Soil Temperature and Water Content in a Greenhouse

Climate change might potentially cause extreme weather events to become more frequent and intense. It could also enhance water scarcity and reduce food security. More efficient water management techniques are thus required to ensure a stable food supply and quality. Maintaining proper soil water content and soil temperature is necessary for efficient water management in agricultural practices. The usage of water and fertilizers can be significantly improved with a precise water content prediction tool. In this study, we proposed a new framework that combines weather forecast data, numerical models, and machine learning methods to simulate and predict the soil temperature and volumetric water content in a greenhouse. To test the framework, we performed greenhouse experiments with cherry tomatoes. The numerical models and machine learning methods we selected were Newton’s law of cooling, HYDRUS-1D, the random forest model, and the ICON (inferring connections of networks) model. The measured air temperature, soil temperature, and volumetric water content during the cultivation period were used for model calibration and validation. We compared the performances of the models for soil temperature and volumetric water content predictions. The results showed that the random forest model performed a more accurate prediction than other methods under the limited information provided from greenhouse experiments. This approach provides a framework that can potentially learn best water management practices from experienced farmers and provide intelligent information for smart greenhouse management.

A numerical investigation of the effect of external resistance and applied potential on the distribution of periodicity and chaos in the anodic dissolution of nickel

Low density, elongation, and suppression of the shrimp-like structures in the resistance-potential phase diagrams have been observed in the oscillatory dissolution of nickel.

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

The organization of the basal ganglia functional connectivity network is non-linear in Parkinson's disease

The motor symptoms in Parkinson's disease (PD) have been linked to changes in the excitatory/inhibitory interactions of centers involved in the cortical-subcortical closed-loop circuits which connect basal ganglia (BG) and the brain cortex. This approach may explain some motor symptoms of PD but not others, which has driven the study of BG from new perspectives. Besides their cortical-subcortical linear circuits, BG have a number of subcortical circuits which directly or indirectly connect each BG with all the others. This suggests that BG may work as a complex network whose output is the result of massive functional interactions between all of their nuclei (decentralized network; DCN), more than the result of the linear excitatory/inhibitory interactions of the cortical-subcortical closed-loops. The aim of this work was to study BG as a DCN, and to test whether the DCN behavior of BG changes in PD. BG activity was recorded with MRI methods and their complex interactions were studied with a procedure based on multiple correspondence analysis, a data-driven multifactorial method which can work with non-linear multiple interactions. The functional connectivity of twenty parkinsonian patients and eighteen age-matched controls were studied during resting and when they were performing sequential hand movements. Seven functional configurations were identified in the control subjects during resting, and some of these interactions changed with motor activity. Five of the seven interactions found in control subjects changed in Parkinson's disease. The BG response to the motor task was also different in PD patients and controls. These data show the basal ganglia as a decentralized network where each region can perform multiple functions and each function is performed by multiple regions. This framework of BG interactions may provide new explanations concerning motor symptoms of PD which are not explained by current BG models.

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The classical basal ganglia model is based on linear excitatory/inhibitory interactions.

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The classical model only explains part of the motor disorders of Parkinson's disease.

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fcMRI images were studied with Multiple Correspondence Analysis (MCA).

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MCA showed multiple non-linear interactions between basal ganglia.

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Parkinson's disease induced marked changes of non-linear basal ganglia interactions.