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Bipolar disorder (BD) and major depressive disorder (MDD) are severe mood disorders that belong to the most debilitating diseases worldwide. Differentiating both mood disorders often poses a major clinical challenge, leading to frequent misdiagnoses. Objective biomarkers able to differentiate individuals with BD and MDD therefore represent a psychiatric research field of utmost importance. Recent studies have applied resting-state fMRI paradigms and found promising results differentiating both disorders based on the acquired data. However, most of these studies have focused their efforts on acutely depressed patients. Thus, it remains unclear whether the aberrations remain in a symptomless disease state.
The here presented study addresses these issues by evaluating the ability to differentiate both disorders from one another by conducting a between-group comparison of functional brain network connectivity (FNC) obtained from resting-state fMRI data. Data were collected from 20 BD, 15 MDD patients and 30 age- and gender-matched healthy controls (HC). Graph theoretical analyses were applied to detect differences in functional network organization between the groups on a global and regional network level.
Network analysis detected frontal, temporal and subcortical nodes in emotion regulation areas such as the limbic system and associated regions exhibiting significant differences in network integration and segregation in BD compared to MDD patients and HC. Participants with MDD and HC only differed in frontal and insular network centrality.
These results indicate that a significantly altered brain network topology in the limbic system might be a trait marker specific to BD. Brain network analysis in these regions may therefore be used to differentiate euthymic BD not only from HC but also from patients with MDD.
Introduction: Previous studies have established graph theoretical analysis of functional network connectivity (FNC) as a potential tool to detect neurobiological underpinnings of psychiatric disorders. Despite the promising outcomes in studies that examined FNC aberrancies in bipolar disorder (BD) and major depressive disorder (MDD), there is still a lack of research comparing both mood disorders, especially in a nondepressed state. In this study, we used graph theoretical network analysis to compare brain network properties of euthymic BD, euthymic MDD and healthy controls (HC) to evaluate whether these groups showed distinct features in FNC.
Methods: We collected resting‐state functional magnetic resonance imaging (fMRI) data from 20 BD patients, 15 patients with recurrent MDD as well as 30 age‐ and gender‐matched HC. Graph theoretical analyses were then applied to investigate functional brain networks on a global and regional network level.
Results: Global network analysis revealed a significantly higher mean global clustering coefficient in BD compared to HC. We further detected frontal, temporal and subcortical nodes in emotion regulation areas such as the limbic system and associated regions exhibiting significant differences in network integration and segregation in BD compared to MDD patients and HC. Participants with MDD and HC only differed in frontal and insular network centrality.
Conclusion: In conclusion, our findings indicate that a significantly altered brain network topology in the limbic system might be a trait marker specific to BD. Brain network analysis in these regions may therefore be used to differentiate euthymic BD not only from HC but also from patients with MDD.
The graph theoretical analysis of structural magnetic resonance imaging (MRI) data has received a great deal of interest in recent years to characterize the organizational principles of brain networks and their alterations in psychiatric disorders, such as schizophrenia. However, the characterization of networks in clinical populations can be challenging, since the comparison of connectivity between groups is influenced by several factors, such as the overall number of connections and the structural abnormalities of the seed regions. To overcome these limitations, the current study employed the whole-brain analysis of connectional fingerprints in diffusion tensor imaging data obtained at 3 T of chronic schizophrenia patients (n = 16) and healthy, age-matched control participants (n = 17). Probabilistic tractography was performed to quantify the connectivity of 110 brain areas. The connectional fingerprint of a brain area represents the set of relative connection probabilities to all its target areas and is, hence, less affected by overall white and gray matter changes than absolute connectivity measures. After detecting brain regions with abnormal connectional fingerprints through similarity measures, we tested each of its relative connection probability between groups. We found altered connectional fingerprints in schizophrenia patients consistent with a dysconnectivity syndrome. While the medial frontal gyrus showed only reduced connectivity, the connectional fingerprints of the inferior frontal gyrus and the putamen mainly contained relatively increased connection probabilities to areas in the frontal, limbic, and subcortical areas. These findings are in line with previous studies that reported abnormalities in striatal–frontal circuits in the pathophysiology of schizophrenia, highlighting the potential utility of connectional fingerprints for the analysis of anatomical networks in the disorder.
Background: Network science provides powerful access to essential organizational principles of the brain. The aim of this study was to investigate longitudinal evolution of gray matter networks in early relapsing–remitting MS (RRMS) compared with healthy controls (HCs) and contrast network dynamics with conventional atrophy measurements.
Methods: For our longitudinal study, we investigated structural cortical networks over 1 year derived from 3T MRI in 203 individuals (92 early RRMS patients with mean disease duration of 12.1 ± 14.5 months and 101 HCs). Brain networks were computed based on cortical thickness inter-regional correlations and fed into graph theoretical analysis. Network connectivity measures (modularity, clustering coefficient, local efficiency, and transitivity) were compared between patients and HCs, and between patients with and without disease activity. Moreover, we calculated longitudinal brain volume changes and cortical atrophy patterns.
Results: Our analyses revealed strengthening of local network properties shown by increased modularity, clustering coefficient, local efficiency, and transitivity over time. These network dynamics were not detectable in the cortex of HCs over the same period and occurred independently of patients’ disease activity. Most notably, the described network reorganization was evident beyond detectable atrophy as characterized by conventional morphometric methods.
Conclusion: In conclusion, our findings provide evidence for gray matter network reorganization subsequent to clinical disease manifestation in patients with early RRMS. An adaptive cortical response with increased local network characteristics favoring network segregation could play a primordial role for maintaining brain function in response to neuroinflammation.
Attention-deficit/hyperactivity disorder (ADHD) is one of the most common neurodevelopmental disorders with significant and often lifelong effects on social, emotional, and cognitive functioning. Influential neurocognitive models of ADHD link behavioral symptoms to altered connections between and within functional brain networks. Here, we investigate whether network-based theories of ADHD can be generalized to understanding variations in ADHD-related behaviors within the normal (i.e., clinically unaffected) adult population. In a large and representative sample, self-rated presence of ADHD symptoms varied widely; only eight out of 291 participants scored in the clinical range. Subject-specific brain-network graphs were modeled from functional MRI resting-state data and revealed significant associations between (non-clinical) ADHD symptoms and region-specific profiles of between-module and within-module connectivity. Effects were located in brain regions associated with multiple neuronal systems including the default-mode network, the salience network, and the central executive system. Our results are consistent with network perspectives of ADHD and provide further evidence for the relevance of an appropriate information transfer between task-negative (default-mode) and task-positive brain regions. More generally, our findings support a dimensional conceptualization of ADHD and contribute to a growing understanding of cognition as an emerging property of functional brain networks.
Individual differences in general cognitive ability (i.e., intelligence) have been linked to individual variations in the modular organization of functional brain networks. However, these analyses have been limited to static (time-averaged) connectivity, and have not yet addressed whether dynamic changes in the configuration of brain networks relate to general intelligence. Here, we used multiband functional MRI resting-state data (N = 281) and estimated subject-specific time-varying functional connectivity networks. Modularity optimization was applied to determine individual time-variant module partitions and to assess fluctuations in modularity across time. We show that higher intelligence, indexed by an established composite measure, the Wechsler Abbreviated Scale of Intelligence (WASI), is associated with higher temporal stability (lower temporal variability) of brain network modularity. Post-hoc analyses reveal that subjects with higher intelligence scores engage in fewer periods of extremely high modularity — which are characterized by greater disconnection of task-positive from task-negative networks. Further, we show that brain regions of the dorsal attention network contribute most to the observed effect. In sum, our study suggests that investigating the temporal dynamics of functional brain network topology contributes to our understanding of the neural bases of general cognitive abilities.
The neuroanatomical connectivity of cortical circuits is believed to follow certain rules, the exact origins of which are still poorly understood. In particular, numerous nonrandom features, such as common neighbor clustering, overrepresentation of reciprocal connectivity, and overrepresentation of certain triadic graph motifs have been experimentally observed in cortical slice data. Some of these data, particularly regarding bidirectional connectivity are seemingly contradictory, and the reasons for this are unclear. Here we present a simple static geometric network model with distance-dependent connectivity on a realistic scale that naturally gives rise to certain elements of these observed behaviors, and may provide plausible explanations for some of the conflicting findings. Specifically, investigation of the model shows that experimentally measured nonrandom effects, especially bidirectional connectivity, may depend sensitively on experimental parameters such as slice thickness and sampling area, suggesting potential explanations for the seemingly conflicting experimental results.
In nature, society and technology many disordered systems exist, that show emergent behaviour, where the interactions of numerous microscopic agents result in macroscopic, systemic properties, that may not be present on the microscopic scale. Examples include phase transitions in magnetism and percolation, for example in porous unordered media, biological, and social systems. Also technological systems that are explicitly designed to function without central control instances, like their prime example the Internet, or virtual networks, like the World Wide Web, which is defined by the hyperlinks from one web page to another, exhibit emergent properties. The study of the common network characteristics found in previously seemingly unrelated fields of science and the urge to explain their emergence, form a scientific field in its own right, the science of complex networks. In this field, methodologies from physics, leading to simplification and generalization by abstraction, help to shift the focus from the implementation's details on the microscopic level to the macroscopic, coarse grained system level. By describing the macroscopic properties that emerge from microscopic interactions, statistical physics, in particular stochastic and computational methods, has proven to be a valuable tool in the investigation of such systems. The mathematical framework for the description of networks is graph theory, in hindsight founded by Euler in 1736 and an active area of research since then. In recent years, applied graph theory flourished through the advent of large scale data sets, made accessible by the use of computers. A paradigm for microscopic interactions among entities that locally optimize their behaviour to increase their own benefit is game theory, the mathematical framework of decision finding. With first applications in economics e.g. Neumann (1944), game theory is an approved field of mathematics. However, game theoretic behaviour is also found in natural systems, e.g. populations of the bacterium Escherichia coli, as described by Kerr (2002). In the present work, a combination of graph theory and game theory is used to model the interactions of selfish agents that form networks. Following brief introductions to graph theory and game theory, the present work approaches the interplay of local self-organizing rules with network properties and topology from three perspectives. To investigate the dynamics of topology reshaping, coupling of the so called iterated prisoners' dilemma (IPD) to the network structure is proposed and studied in Chapter 4. In dependence of a free parameter in the payoff matrix, the reorganization dynamics result in various emergent network structures. The resulting topologies exhibit an increase in performance, measured by a variance of closeness, of a factor 1.2 to 1.9, depending in the chosen free parameter. Presented in Chapter 5, the second approach puts the focus on a static network structure and studies the cooperativity of the system, measured by the fixation probability. Heterogeneous strategies to distribute incentives for cooperation among the players are proposed. These strategies allow to enhance the cooperative behaviour, while requiring fewer total investments. Putting the emphasis on communication networks in Chapters 6 and 7, the third approach investigates the use of routing metrics to increase the performance of data packet transport networks. Algorithms for the iterative determination of such metrics are demonstrated and investigated. The most successful of these algorithms, the hybrid metric, is able to increase the throughput capacity of a network by a factor of 7. During the investigation of the iterative weight assignments a simple, static weight assignment, the so called logKiKj metric, is found. In contrast to the algorithmic metrics, it results in vanishing computational costs, yet it is able to increase the performance by a factor of 5.
Proteins are biological macromolecules playing essential roles in all living organisms.
Proteins often bind with each other forming complexes to fulfill their function. Such protein complexes assemble along an ordered pathway. An assembled protein complex can often be divided into structural and functional modules. Knowing the order of assembly and the modules of a protein complex is important to understand biological processes and treat diseases related to misassembly.
Typical structures of the Protein Data Bank (PDB) contain two to three subunits and a few thousand atoms. Recent developments have led to large protein complexes being resolved. The increasing number and size of the protein complexes demand for computational assistance for the visualization and analysis. One such large protein complex is respiratory complex I accounting for 45 subunits in Homo sapiens.
Complex I is a well understood protein complex that served as case study to validate our methods.
Our aim was to analyze time-resolved Molecular Dynamics (MD) simulation data, identify modules of a protein complex and generate hypotheses for the assembly pathway of a protein complex. For that purpose, we abstracted the topology of protein complexes to Complex Graphs of the Protein Topology Graph Library (PTGL). The subunits are represented as vertices, and spatial contacts as edges. The edges are weighted with the number of contacts based on a distance threshold. This allowed us to apply graph-theoretic methods to visualize and analyze protein complexes.
We extended the implementations of two methods to achieve a computation of Complex Graphs in feasible runtimes. The first method skipped checks for contacts using the information which residues are sequential neighbors. We extended the method to protein complexes and structures containing ligands. The second method introduced spheres encompassing all atoms of a subunit and skipped the check for contacts if the corresponding spheres do not overlap. Both methods combined allowed skipping up to 93 % of the checks for contacts for sample complexes of 40 subunits compared to up to 10 % of the previous implementation. We showed that the runtime of the combined method scaled linearly with the number of atoms compared to a non-linear scaling of the previous implementation We implemented a third method fixing the assignment of an orientation to secondary structure elements. We placed a three-dimensional vector in each secondary structure element and computed the angle between secondary structure elements to assign an orientation. This method sped up the runtime especially for large structures, such as the capsid of human immunodeficiency virus, for which the runtime decreased from 43 to less than 9 hours.
The feasible runtimes allowed us to investigate two data sets of MD trajectories of respiratory complex I of Thermus thermophilus that we received. The data sets differ only by whether ubiquinone is bound to the complex. We implemented a pipeline, PTGLdynamics, to compute the contacts and Complex Graphs for all time steps of the trajectories. We investigated different methods to track changes of contacts during the simulation and created a heat map put onto the three-dimensional structure visualizing the changes. We also created line plots to visualize the changes of contacts over the course of the simulation. Both visualizations helped spotting outstandingly flexible or rigid regions of the structure or time points of the simulation in which major dynamics occur.
We introduced normalizations of the edge weights of Complex Graphs for identi-fying modules and predicting the assembly pathway. The idea is to normalize the number of contacts for the number of residues of a subunit. We defined five different normalizations.
To identify structural and functional modules, we applied the Leiden graph clustering algorithm to the Complex Graphs of respiratory complex I and the respiratory supercomplex. We examined the results for the different normalizations of the weights of the Complex Graphs. The absolute edge weight produced the best result identifying three of four modules that have been defined in the literature for respiratory complex I.
We applied agglomerative hierarchical clustering to the edges of a Complex Graph to create hypotheses of the assembly pathway. The rationale was that subunits with an extensive interface in the final structure assemble early. We tested our method against two existing methods on a data set of 21 proteins with reported assembly pathways. Our prediction outperformed the other methods and ran in feasible runtimes of a few minutes at most.
We also tested our method on respiratory complex I, the respiratory supercomplex and the respiratory megacomplex. We compared the results for the different normalizations with an assembly pathway of respiratory complex I described in the literature. We transformed the assembly pathways to dendrograms and compared the predictions to the reference using the Robinson-Foulds distance and clustering information distance. We analyzed the landscape of the clustering information distance by generating random dendrograms and showed that our result is far better than expected at random. We showed in a detailed analysis that the assembly prediction using one normalization was able to capture key features of the assembly pathway that has been proposed in the literature.
In conclusion, we presented different applications of graph theory to automatically analyze the topology of protein complexes. Our programs run in feasible runtimes even for large complexes. We showed that graph-theoretic modeling of the protein structure can be used to analyze MD simulation data, identify modules of protein complexes and predict assembly pathways.