Gamma oscillation in functional brain networks is involved in the spontaneous remission of depressive behavior induced by chronic restraint stress in mice

Additional file 1: Table S1. Statistical results of the cross-correlation in Fig. 2c

Gating of memory encoding of time-delayed cross-frequency MEG networks revealed by graph filtration based on persistent homology

To explain gating of memory encoding, magnetoencephalography (MEG) was analyzed over multi-regional network of negative correlations between alpha band power during cue (cue-alpha) and gamma band power during item presentation (item-gamma) in Remember (R) and No-remember (NR) condition. Persistent homology with graph filtration on alpha-gamma correlation disclosed topological invariants to explain memory gating. Instruction compliance (R-hits minus NR-hits) was significantly related to negative coupling between the left superior occipital (cue-alpha) and the left dorsolateral superior frontal gyri (item-gamma) on permutation test, where the coupling was stronger in R than NR. In good memory performers (R-hits minus false alarm), the coupling was stronger in R than NR between the right posterior cingulate (cue-alpha) and the left fusiform gyri (item-gamma). Gating of memory encoding was dictated by inter-regional negative alpha-gamma coupling. Our graph filtration over MEG network revealed these inter-regional time-delayed cross-frequency connectivity serve gating of memory encoding

Molecular neuroanatomy: mouse-human homologies and the landscape of genes implicated in language disorders

The distinctiveness of brain structures and circuits depends on interacting gene products, yet the organization of these molecules (the "transcriptome") within and across brain areas remains unclear. High-throughput, neuroanatomically-specific gene expression datasets such as the Allen Human Brain Atlas (AHBA) and Allen Mouse Brain Atlas (AMBA) have recently become available, providing unprecedented opportunities to quantify molecular neuroanatomy. This dissertation seeks to clarify how transcriptomic organization relates to conventional neuroanatomy within and across species, and to introduce the use of gene expression data as a bridge between genotype and phenotype in complex behavioral disorders. The first part of this work examines large-scale, regional transcriptomic organization separately in the mouse and human brain. The use of dimensionality reduction methods and cross-sample correlations both revealed greater similarity between samples drawn from the same brain region. Sample profiles and differentially expressed genes across regions in the human brain also showed consistent anatomical specificity in a second human dataset with distinct sampling properties. The frequent use of mouse models in clinical research points to the importance of comparing molecular neuroanatomical organization across species. The second part of this dissertation describes three comparative approaches. First, at genome scale, expression profiles within homologous brain regions tended to show higher similarity than those from non-homologous regions, with substantial variability across regions. Second, gene subsets (defined using co-expression relationships or shared annotations), which provide region-specific, cross-species molecular signatures were identified. Finally, brain-wide expression patterns of orthologous genes were compared. Neuron and oligodendrocyte markers were more correlated than expected by chance, while astrocyte markers were less so. The localization and co-expression of genes reflect functional relationships that may underlie high-level functions. The final part of this dissertation describes a database of genes that have been implicated in speech and language disorders, and identifies brain regions where they are preferentially expressed or co-expressed. Several brain structures with functions relevant to four speech and language disorders showed co-expression of genes associated with these disorders. In particular, genes associated with persistent developmental stuttering showed stronger preferential co-expression in the basal ganglia, a structure of known importance in this disorder

Structure-Function Network Mapping and Its Assessment via Persistent Homology

Understanding the relationship between brain structure and function is a fundamental problem in network neuroscience. This work deals with the general method of structure-function mapping at the whole-brain level. We formulate the problem as a topological mapping of structure-function connectivity via matrix function, and find a stable solution by exploiting a regularization procedure to cope with large matrices. We introduce a novel measure of network similarity based on persistent homology for assessing the quality of the network mapping, which enables a detailed comparison of network topological changes across all possible thresholds, rather than just at a single, arbitrary threshold that may not be optimal. We demonstrate that our approach can uncover the direct and indirect structural paths for predicting functional connectivity, and our network similarity measure outperforms other currently available methods. We systematically validate our approach with (1) a comparison of regularized vs. non-regularized procedures, (2) a null model of the degree-preserving random rewired structural matrix, (3) different network types (binary vs. weighted matrices), and (4) different brain parcellation schemes (low vs. high resolutions). Finally, we evaluate the scalability of our method with relatively large matrices (2514x2514) of structural and functional connectivity obtained from 12 healthy human subjects measured non-invasively while at rest. Our results reveal a nonlinear structure-function relationship, suggesting that the resting-state functional connectivity depends on direct structural connections, as well as relatively parsimonious indirect connections via polysynaptic pathways

Promises and pitfalls of topological data analysis for brain connectivity analysis

Acknowledgment The authors thank Jakub Kopal for sharing the preprocessed fMRI time series and Barbora Bučková for sharing scripts for classification pipelinePeer reviewedPublisher PD

Distances and Isomorphism between Networks and the Stability of Network Invariants

We develop the theoretical foundations of a network distance that has recently been applied to various subfields of topological data analysis, namely persistent homology and hierarchical clustering. While this network distance has previously appeared in the context of finite networks, we extend the setting to that of compact networks. The main challenge in this new setting is the lack of an easy notion of sampling from compact networks; we solve this problem in the process of obtaining our results. The generality of our setting means that we automatically establish results for exotic objects such as directed metric spaces and Finsler manifolds. We identify readily computable network invariants and establish their quantitative stability under this network distance. We also discuss the computational complexity involved in precisely computing this distance, and develop easily-computable lower bounds by using the identified invariants. By constructing a wide range of explicit examples, we show that these lower bounds are effective in distinguishing between networks. Finally, we provide a simple algorithm that computes a lower bound on the distance between two networks in polynomial time and illustrate our metric and invariant constructions on a database of random networks and a database of simulated hippocampal networks

Micro-connectomics: probing the organization of neuronal networks at the cellular scale.

Defining the organizational principles of neuronal networks at the cellular scale, or micro-connectomics, is a key challenge of modern neuroscience. In this Review, we focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originated with Ramón y Cajal's conservation laws. First, we summarize results from studies in intact small organisms and in samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization of neuronal networks. Various results suggest that many aspects of neuronal network organization are indeed the outcome of competition between these two fundamental selection pressures.This work was supported by the National Institute of Health Research (NIHR) Cambridge Biomedical Research Centre.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the Nature Publishing Group