The closed-loop control of pathological brain activity is a challenging task. In this study, we investigated the sensitivity of continuous epileptiform short discharge generation to electrical stimulation applied at different phases between the discharges using an in vitro 4-AP-based model of epilepsy in rat hippocampal slices. As a measure of stimulation effectiveness, we introduced a sensitivity function, which we then measured in experiments and analyzed with different biophysical and abstract mathematical models, namely, (i) the two-order subsystem of our previous Epileptor-2 model, describing short discharge generation governed by synaptic resource dynamics; (ii) a similar model governed by shunting conductance dynamics (Epileptor-2B); (iii) the stochastic leaky integrate-and-fire (LIF)-like model applied for the network; (iv) the LIF model with potassium M-channels (LIF+KM), belonging to Class II of excitability; and (v) the Epileptor-2B model with after-spike depolarization. A semi-analytic method was proposed for calculating the interspike interval (ISI) distribution and the sensitivity function in LIF and LIF+KM models, which provided parametric analysis. Sensitivity was found to increase with phase for all models except the last one. The Epileptor-2B model is favored over other models for subthreshold oscillations in the presence of large noise, based on the comparison of ISI statistics and sensitivity functions with experimental data. This study also emphasizes the stochastic nature of epileptiform discharge generation and the greater effectiveness of closed-loop stimulation in later phases of ISIs.

We studied the single-particle Anderson localization problem for non-Hermitian systems on directed graphs. Random regular graph and various undirected standard random graph models were modified by controlling reciprocity and hopping asymmetry parameters. We found the emergence of left, biorthogonal, and right localized states depending on both parameters and graph structure properties such as node degree d. For directed random graphs, the occurrence of biorthogonal localization near exceptional points is described analytically and numerically. The clustering of localized states near the center of the spectrum and the corresponding mobility edge for left and right states are shown numerically. Structural features responsible for localization, such as topologically invariant nodes or drains and sources, were also described. Considering the diagonal disorder, we observed the disappearance of localization dependence on reciprocity around W∼20 for a random regular graph d=4. With a small diagonal disorder, the average biorthogonal fractal dimension drastically reduces. Around W∼5, localization scars occur within the spectrum, alternating as vertical bands of clustering of left and right localized states.

The marine flavobacterium Krokinobactereikastus light-driven sodium pump (KR2) generates an outward sodium ion current under 530 nm light stimulation, representing a promising optogenetic tool for seizure control. However, the specifics of KR2 application to suppress epileptic activity have not yet been addressed. In the present study, we investigated the possibility of KR2 photostimulation to suppress epileptiform activity in mouse brain slices using the 4-aminopyrindine (4-AP) model. We injected the adeno-associated viral vector (AAV-PHP.eB-hSyn-KR2-YFP) containing the KR2 sodium pump gene enhanced with appropriate trafficking tags. KR2 expression was observed in the lateral entorhinal cortex and CA1 hippocampus. Using whole-cell patch clamp in mouse brain slices, we show that KR2, when stimulated with LED light, induces a substantial hyperpolarization of entorhinal neurons. However, continuous photostimulation of KR2 does not interrupt ictal discharges in mouse entorhinal cortex slices induced by a solution containing 4-AP. KR2-induced hyperpolarization strongly activates neuronal HCN channels. Consequently, turning off photostimulation resulted in HCN channel-mediated rebound depolarization accompanied by a transient increase in spontaneous network activity. Using low-frequency pulsed photostimulation, we induced the generation of short HCN channel-mediated discharges that occurred in response to the light stimulus being turned off; these discharges reliably interrupt ictal activity. Thus, low-frequency pulsed photostimulation of KR2 can be considered as a potential tool for controlling epileptic seizures.

Apparent motion is a visual illusion in which stationary stimuli, flashing in distinct spatial locations at certain time intervals, are perceived as one stimulus moving between these locations. In the primary visual cortex, apparent-motion stimuli produce smooth spatio-temporal patterns of activity similar to those produced by continuously moving stimuli. An important prerequisite for producing such activity patterns is prolongation of responses to brief stimuli. Indeed, a brief stimulus can evoke in the visual cortex a long response, outlasting the stimulus by hundreds of milliseconds. Here we use firing-rate based models with simple ring structure, and biologically-detailed conductance-based refractory density (CBRD) model with retinotopic space representation to analyze the response retention and the origin of smooth profiles of activity in response to apparent-motion stimuli. We show that the strength of recurrent connectivity is the major factor that endorses neuronal networks with the ability for response retention. The same strengths of recurrent connections mediate the appearance of bump attractor in the ring models. Factors such as synaptic depression, NMDA receptor mediated currents, and conductances regulating spike adaptation influence response retention, but cannot substitute for the weakness of recurrent connections to reproduce response retention in models with weak connectivity. However, the weakness of lateral recurrent connections can be compensated by layering: in multi-layer models even with weaker connections the activity retains due to its feedforward propagation from layer to layer. Using CBRD model with retinotopic space representation we further show that smooth spatio-temporal profiles of activity in response to apparent-motion stimuli are produced in the models expressing response retention, but not in the models that fail to produce response retention. Together, these results demonstrate a link between response retention and the ability of neuronal networks to generate spatio-temporal patterns of activity, which are compatible with perception of apparent motion.

We investigated the structure of the functional networks of the human brain using data from the OASIS dataset. To construct functional networks from BOLD signals, we used the method of dynamic time warping (DTW), which allows one to take into account possible distortions and nonlinear effects when comparing two time series. We investigated the resulting functional networks in terms of graph entropy, a recently proposed thermodynamic approach to describing dynamics in complex networks. The graph entropy approach provides tools to investigate the information flows in networks on different timescales. We showed a high heterogeneity of the resulting individual functional networks, expressed in a significant mismatch of the characteristic excitation diffusion times between subjects. We also constructed an artificial network model with a hierarchy of temporal scales to explain the detected multiscale nature of some functional networks. No differences were found between the healthy subjects and subjects with different levels of clinical dementia rating. We hypothesize that the heterogeneity we found may be related to the personality traits of the subjects, and we intend to investigate this issue further.

Cortical neural networks in vivo are able to retain their activity evoked by a short stimulus. We compare and analyze two mathematical models of ring-structured networks of an orientational hypercolumn of the visual cortex in order to distinguish the contributions of recurrent connections, synaptic depression and slow synaptic kinetics into the retention effect. Comparison of a more elaborated model with the classical ring-model has helped to translate the mathematical analysis of the later model to the former one. As shown, the network with developed recurrent connections reproduces the retention effect compared to that in experiments. The synaptic depression prevents the effect, however the long-lasting excitatory synaptic current recovers the property. Accounting of the slow kinetics of the NMDA receptors, a characteristic post-peak plateau of activity is reproduced. The models show an invariance to contrast of visual stimuli. Simulations reveal a major role of strong excitatory recurrent connections in the retention effect.