Collective behavior of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus delivered to that neuron. The neuronal PRCs can be classified as having either purely positive value (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming excitatory unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that Feedforward loops favour synchronization of type I neurons, while feedback loops destroy their synchronization tendency. The results are robust to large directed networks constructed from only feedforward or mostly feedback loops, and high synchronization level observed for directed acyclic graphs with type I neurons. The synchronizability of type I neurons depends on both the directionality of the connectivity network and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.

The structure of the brain network shows modularity at multiple spatial scales. The effect of the modular structure on the brain dynamics has been the focus of several studies in recent years but many aspects remain to be explored. For example, it is not well-known how the delays in the transmission of signals between the neurons and the brain regions, interact with the modular structure to determine the brain dynamics. In this paper, we show an important impact of the delays on the collective dynamics of the brain network with modular structure; that is, the degree of the synchrony between different brain regions is dependent on the frequency. In particular, we show that increasing the frequency the network transits from a global synchrony state to an asynchronous state, through a transition region over which the local synchrony inside the modules is stronger than the global synchrony. When the delays are dependent on the distance between the nodes, the modular structure of different spatial scales appears in the correlation matrix over different specific frequency bands, so that, finer spatial modular structure reveal in higher frequency bands. The results are justified by a simple theoretical argument and elaborated by simulations on several simplified modular networks and the connectome with different spatial resolutions..

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by the accumulation of abnormal beta-amyloid (Aβ) and hyperphosphorylated Tau (pTau). These proteinopathies disrupt neuronal activity, causing, among others, an excessive and hypersynchronous neuronal firing that promotes hyperexcitability and leads to brain network dysfunction and cognitive deficits. In this study, we used computational network modeling to build a causal inference framework to explain AD-related abnormal brain activity. We constructed personalized brain network models with a set of working points to enable maximum dynamical complexity for each brain. Structural brain topographies were combined, either with excitotoxicity, or postsynaptic depression, as two leading mechanisms of the Aβ and pTau on neuronal activity. By applying various levels of these putative mechanisms to the limbic regions that typically present, with the earliest and largest protein burden, we found that the excitotoxicity is sufficient and necessary to reproduce empirical biomarkers two biometrics associated with AD pathology: homotopic dysconnectivity and a decrease in limbic network dynamical fluidity. This observation was shown not only in the clinical groups (aMCI and AD), but also in healthy subjects that were virtually-diseased with excitotoxicity as these abnormal proteins can accumulate before the appearance of any cognitive changes. The same findings were independently confirmed by a mechanistic deep learning inference framework. Taken together, our results show the crucial role of protein burden-induced hyperexcitability in altering macroscopic brain network dynamics, and offer a mechanistic link between structural and functional biomarkers of cognitive dysfunction due to AD.

The brain functional network extracted from the BOLD signals reveals the correlated activity of the different brain regions, which is hypothesized to underlie the integration of the information across functionally specialized areas. Functional networks are not static and change over time and in different brain states, enabling the nervous system to engage and disengage different local areas in specific tasks on demand. Due to the low temporal resolution, however, BOLD signals do not allow the exploration of spectral properties of the brain dynamics over different frequency bands which are known to be important in cognitive processes. Recent studies using imaging tools with a high temporal resolution has made it possible to explore the correlation between the regions at multiple frequency bands. These studies introduce the frequency as a new dimension over which the functional networks change, enabling brain networks to transmit multiplex of information at any time. In this computational study, we explore the functional connectivity at different frequency ranges and highlight the role of the distance between the nodes in their correlation. We run the generalized Kuramoto model with delayed interactions on top of the brain's connectome and show that how the transmission delay and the strength of the connections, affect the correlation between the pair of nodes over different frequency bands.