Modular networks emerge from multiconstraint optimization

Extreme trophic tales: deciphering bacterial diversity and potential functions in oligotrophic and hypereutrophic lakes

BACKGROUND

Oligotrophy and hypereutrophy represent the two extremes of lake trophic states, and understanding the distribution of bacterial communities across these contrasting conditions is crucial for advancing aquatic microbial research. Despite the significance of these extreme trophic states, bacterial community characteristics and co-occurrence patterns in such environments have been scarcely interpreted. To bridge this knowledge gap, we collected 60 water samples from Lake Fuxian (oligotrophic) and Lake Xingyun (hypereutrophic) during different hydrological periods.

RESULTS

Employing 16S rRNA gene sequencing, our findings revealed distinct community structures and metabolic potentials in bacterial communities of hypereutrophic and oligotrophic lake ecosystems. The hypereutrophic ecosystem exhibited higher bacterial α- and β-diversity compared to the oligotrophic ecosystem. Actinobacteria dominated the oligotrophic Lake Fuxian, while Cyanobacteria, Proteobacteria, and Bacteroidetes were more prevalent in the hypereutrophic Lake Xingyun. Functions associated with methanol oxidation, methylotrophy, fermentation, aromatic compound degradation, nitrogen/nitrate respiration, and nitrogen/nitrate denitrification were enriched in the oligotrophic lake, underscoring the vital role of bacteria in carbon and nitrogen cycling. In contrast, functions related to ureolysis, human pathogens, animal parasites or symbionts, and phototrophy were enriched in the hypereutrophic lake, highlighting human activity-related disturbances and potential pathogenic risks. Co-occurrence network analysis unveiled a more complex and stable bacterial network in the hypereutrophic lake compared to the oligotrophic lake.

CONCLUSION

Our study provides insights into the intricate relationships between trophic states and bacterial community structure, emphasizing significant differences in diversity, community composition, and network characteristics between extreme states of oligotrophy and hypereutrophy. Additionally, it explores the nuanced responses of bacterial communities to environmental conditions in these two contrasting trophic states.

Mesoscopic architecture enhances communication across the macaque connectome revealing structure-function correspondence in the brain

Analyzing the brain in terms of organizational structures at intermediate scales provides an approach to unravel the complexity arising from interactions between its large number of components. Focusing on a wiring diagram that spans the cortex, basal ganglia, and thalamus of the macaque brain, we identify robust modules in the network that provide a mesoscopic-level description of its topological architecture. Surprisingly, we find that the modular architecture facilitates rapid communication across the network, instead of localizing activity as is typically expected in networks having community organization. By considering processes of diffusive spreading and coordination, we demonstrate that the specific pattern of inter- and intramodular connectivity in the network allows propagation to be even faster than equivalent randomized networks with or without modular structure. This pattern of connectivity is seen at different scales and is conserved across principal cortical divisions, as well as subcortical structures. Furthermore, we find that the physical proximity between areas is insufficient to explain the modular organization, as similar mesoscopic structures can be obtained even after factoring out the effect of distance constraints on the connectivity. By supplementing the topological information about the macaque connectome with physical locations, volumes, and functions of the constituent areas and analyzing this augmented dataset, we reveal a counterintuitive role played by the modular architecture of the brain in promoting global coordination of its activity. It suggests a possible explanation for the ubiquity of modularity in brain networks.

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.

Graph theoretical analysis of functional network for comprehension of sign language

Signed languages are natural human languages using the visual-motor modality. Previous neuroimaging studies based on univariate activation analysis show that a widely overlapped cortical network is recruited regardless whether the sign language is comprehended (for signers) or not (for non-signers). Here we move beyond previous studies by examining whether the functional connectivity profiles and the underlying organizational structure of the overlapped neural network may differ between signers and non-signers when watching sign language. Using graph theoretical analysis (GTA) and fMRI, we compared the large-scale functional network organization in hearing signers with non-signers during the observation of sentences in Chinese Sign Language. We found that signed sentences elicited highly similar cortical activations in the two groups of participants, with slightly larger responses within the left frontal and left temporal gyrus in signers than in non-signers. Crucially, further GTA revealed substantial group differences in the topologies of this activation network. Globally, the network engaged by signers showed higher local efficiency (t₍₂₄₎=2.379, p=0.026), small-worldness (t₍₂₄₎=2.604, p=0.016) and modularity (t₍₂₄₎=3.513, p=0.002), and exhibited different modular structures, compared to the network engaged by non-signers. Locally, the left ventral pars opercularis served as a network hub in the signer group but not in the non-signer group. These findings suggest that, despite overlap in cortical activation, the neural substrates underlying sign language comprehension are distinguishable at the network level from those for the processing of gestural action.

Modes of Large-Scale Brain Network Organization during Threat Processing and Posttraumatic Stress Disorder Symptom Reduction during TF-CBT among Adolescent Girls

Posttraumatic stress disorder (PTSD) is often chronic and disabling across the lifespan. The gold standard treatment for adolescent PTSD is Trauma-Focused Cognitive-Behavioral Therapy (TF-CBT), though treatment response is variable and mediating neural mechanisms are not well understood. Here, we test whether PTSD symptom reduction during TF-CBT is associated with individual differences in large-scale brain network organization during emotion processing. Twenty adolescent girls, aged 11–16, with PTSD related to assaultive violence completed a 12-session protocol of TF-CBT. Participants completed an emotion processing task, in which neutral and fearful facial expressions were presented either overtly or covertly during 3T fMRI, before and after treatment. Analyses focused on characterizing network properties of modularity, assortativity, and global efficiency within an 824 region-of-interest brain parcellation separately during each of the task blocks using weighted functional connectivity matrices. We similarly analyzed an existing dataset of healthy adolescent girls undergoing an identical emotion processing task to characterize normative network organization. Pre-treatment individual differences in modularity, assortativity, and global efficiency during covert fear vs neutral blocks predicted PTSD symptom reduction. Patients who responded better to treatment had greater network modularity and assortativity but lesser efficiency, a pattern that closely resembled the control participants. At a group level, greater symptom reduction was associated with greater pre-to-post-treatment increases in network assortativity and modularity, but this was more pronounced among participants with less symptom improvement. The results support the hypothesis that modularized and resilient brain organization during emotion processing operate as mechanisms enabling symptom reduction during TF-CBT.

Growth, collapse, and self-organized criticality in complex networks

Network growth is ubiquitous in nature (e.g., biological networks) and technological systems (e.g., modern infrastructures). To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands. We find that a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverges from the synchronous state in a cascading manner within a relatively short time period. In particular, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis reveals that the collapse size is approximately algebraically distributed, indicating the emergence of self-organized criticality. We demonstrate the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.

Thermodynamics of random reaction networks

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Modular network evolution under selection for robustness to noise

Real networks often exhibit modularity, which is defined as the degree to which a network can be decomposed into several subnetworks. The question of how a modular network arises is still open to discussion. The leading hypothesis is that high modularity evolves under multiple goals, which are decomposable to subproblems, as well as under the evolutionary constraint that selection prefers sparse links in a network. In the present study, we investigate an alternative evolutionary constraint entailing increased robustness to noise. To examine this, we present noise-interfused network models involving an analytically solvable linear system and biologically inspired nonlinear systems. The models demonstrate that it is possible to evolve a modular network under both modularly changing goal orientations and enhancing robustness to noise, thereby reducing sensitivity to noise. By performing theoretical analyses of linear systems, it is shown that the evolutionary constraint enforces the establishment of well-balanced noise sensitivities of multiple noise sources and leads to a modular network underlying a modular structure in goals. Moreover, computer simulations confirm that the presented mechanisms of modular network evolution are robust to variations of nonlinearity in network functions. Our findings suggest a positive role for the presence of noise in network evolution.

Mutation rules and the evolution of sparseness and modularity in biological systems

Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity – the near decomposability of the system into modules with distinct functionality. Recent work suggests that modularity can evolve in a variety of circumstances, including goals that vary in time such that they share the same subgoals (modularly varying goals), or when connections are costly. Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than on connection cost or variations in the goal. We use simulations of evolution with different mutation rules. We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations. In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers – a better model for the effects of biological mutations – led to sparseness naturally. When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they tend to reduce interactions, and to keep small interaction terms small.

Social climber attachment in forming networks produces a phase transition in a measure of connectivity

The formation and fragmentation of networks are typically studied using percolation theory, but most previous research has been restricted to studying a phase transition in cluster size, examining the emergence of a giant component. This approach does not study the effects of evolving network structure on dynamics that occur at the nodes, such as the synchronization of oscillators and the spread of information, epidemics, and neuronal excitations. We introduce and analyze an alternative link-formation rule, called social climber (SC) attachment, that may be combined with arbitrary percolation models to produce a phase transition using the largest eigenvalue of the network adjacency matrix as the order parameter. This eigenvalue is significant in the analyses of many network-coupled dynamical systems in which it measures the quality of global coupling and is hence a natural measure of connectivity. We highlight the important self-organized properties of SC attachment and discuss implications for controlling dynamics on networks.

Modular Organization of Functional Network Connectivity in Healthy Controls and Patients with Schizophrenia during the Resting State

Neuroimaging studies have shown that functional brain networks composed from select regions of interest have a modular community structure. However, the organization of functional network connectivity (FNC), comprising a purely data-driven network built from spatially independent brain components, is not yet clear. The aim of this study is to explore the modular organization of FNC in both healthy controls (HCs) and patients with schizophrenia (SZs). Resting state functional magnetic resonance imaging data of HCs and SZs were decomposed into independent components (ICs) by group independent component analysis (ICA). Then weighted brain networks (in which nodes are brain components) were built based on correlations between ICA time courses. Clustering coefficients and connectivity strength of the networks were computed. A dynamic branch cutting algorithm was used to identify modules of the FNC in HCs and SZs. Results show stronger connectivity strength and higher clustering coefficient in HCs with more and smaller modules in SZs. In addition, HCs and SZs had some different hubs. Our findings demonstrate altered modular architecture of the FNC in schizophrenia and provide insights into abnormal topological organization of intrinsic brain networks in this mental illness.

Interplay between structure and dynamics in adaptive complex networks: emergence and amplification of modularity by adaptive dynamics

Many real networks display modular organization, which can influence dynamical clustering on the networks. Therefore, there have been proposals put forth recently to detect network communities by using dynamical clustering. In this paper, we study how the feedback from dynamical clusters can shape the network connection weights with a weight-adaptation scheme motivated from Hebbian learning in neural systems. We show that such a scheme generically leads to the formation of community structure in globally coupled chaotic oscillators. The number of communities in the adaptive network depends on coupling strength c and adaptation strength r. In a modular network, the adaptation scheme will enhance the intramodule connection weights and weaken the intermodule connection strengths, generating effectively separated dynamical clusters that coincide with the communities of the network. In this sense, the modularity of the network is amplified by the adaptation. Thus, for a network with a strong community structure, the adaptation scheme can evidently reflect its community structure by the resulting amplified weighted network. For a network with a weak community structure, the statistical properties of synchronization clusters from different realizations can be used to amplify the modularity of the communities so that they can be detected reliably by the other traditional algorithms.

Network growth under the constraint of synchronization stability

While it is well recognized that realistic networks are typically growing with time, the dynamical features of their growing processes remain to be explored. In the present paper, incorporating the requirement of synchronization stability into the conventional models of network growth, we will investigate how the growing process of a complex network is influenced by, and also will influence, the network collective dynamics. Our study shows that, constrained by the synchronization stability, the network will be growing in a selective and dynamical fashion. In particular, we find that the chance for a new node to be accepted by the growing network could have a large variation, i.e., it follows roughly a power-law distribution. Furthermore, we find that, with the dynamical growth, the network is always developed into structures of clear scale-free features, despite the form of the link attachment (preferential or random). The dynamical properties of network growth are studied using the method of eigenvalue analysis, and they are verified by direct simulations of coupled chaotic oscillators. Our study implies that, driven by the network collective dynamics, network growth could also be highly dynamical.

Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. The coordination of many different co-occurring processes at this level underlies the command and control of overall network activity. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations such as, optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Even including information about the genetic relatedness of the cells cannot account for the observed modular structure. Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.

Dynamical reconnection and stability constraints on cortical network architecture

Stability under dynamical changes to network connectivity is invoked alongside previous criteria to constrain brain network architecture. A new hierarchical network is introduced that satisfies all these constraints, unlike more commonly studied regular, random, and small-world networks. It is shown that hierarchical networks can simultaneously have high clustering, short path lengths, and low wiring costs, while being robustly stable under large scale reconnection of substructures.

Phase of Ising spins on modular networks analogous to social polarization

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks, corresponding to consensus formation in society, we observe two distinct phases: (i) ordering within each module at a critical temperature followed by (ii) global ordering at a lower temperature. This indicates polarization of society into groups having contrary opinions can persist indefinitely even when mutual interactions between agents favor consensus.

Organization of modular networks

We examine the global organization of heterogeneous equilibrium networks consisting of a number of well-distinguished interconnected parts-"communities" or modules. We develop an analytical approach allowing us to obtain the statistics of connected components and the intervertex distance distribution in these modular networks, and to describe their global organization and structure. In particular, we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks. We demonstrate that even a relatively small number of shortcuts unite the networks into one. In more precise terms, if the number of interlinks is any finite fraction of the total number of connections, then the intervertex distance distribution approaches a delta -function peaked form, and so the network is united.