Journal of Computational Neuroscience最新文献

We study the impact of bursts on spike statistics and neural signal transmission. We propose a stochastic burst algorithm that is applied to a burst-free spike train and adds a random number of temporally-jittered burst spikes to each spike. This simple algorithm ignores any possible stimulus-dependence of bursting but allows to relate spectra and signal-transmission characteristics of burst-free and burst-endowed spike trains. By averaging over the various statistical ensembles, we find a frequency-dependent factor connecting the linear and also the second-order susceptibility of the spike trains with and without bursts. The relation between spectra is more complicated: besides a frequency-dependent multiplicative factor it also involves an additional frequency-dependent offset. We confirm these relations for the (burst-free) spike trains of a stochastic integrate-and-fire neuron and identify frequency ranges in which the transmission is boosted or diminished by bursting. We then consider bursty spike trains of electroreceptor afferents of weakly electric fish and approach the role of burst spikes as follows. We compare the spectral statistics of the bursty spike train to (i) that of a spike train with burst spikes removed and to (ii) that of the spike train in (i) endowed by bursts according to our algorithm. Significant spectral features are explained by our signal-independent burst algorithm, e.g. the burst-induced boosting of the nonlinear response. A difference is seen in the information transfer for the original bursty spike train and our burst-endowed spike train. Our algorithm is thus helpful to identify different effects of bursting.

Deficient gamma oscillations in the prefrontal cortex (PFC) of individuals with schizophrenia (SZ) are proposed to arise from alterations in the excitatory drive to fast-spiking interneurons (E $\to$ I) and in the inhibitory drive from these interneurons to excitatory neurons (I $\to$ E). Consistent with this idea, prior postmortem studies showed lower levels of molecular and structural markers for the strength of E $\to$ I and I $\to$ E synapses and also greater variability in E $\to$ I synaptic strength in PFC of SZ. Moreover, simulating these alterations in a network of quadratic integrate-and-fire (QIF) neurons revealed a synergistic effect of their interactions on reducing gamma power. In this study, we aimed to investigate the dynamical nature of this synergistic interaction at macroscopic level by deriving a mean-field description of the QIF model network that consists of all-to-all connected excitatory neurons and fast-spiking interneurons. Through a series of numerical simulations and bifurcation analyses, findings from our mean-field model showed that the macroscopic dynamics of gamma oscillations are synergistically disrupted by the interactions among lower strength of E $\to$ I and I $\to$ E synapses and greater variability in E $\to$ I synaptic strength. Furthermore, the two-dimensional bifurcation analyses showed that this synergistic interaction is primarily driven by the shift in Hopf bifurcation due to lower E $\to$ I synaptic strength. Together, these simulations predict the nature of dynamical mechanisms by which multiple synaptic alterations interact to robustly reduce PFC gamma power in SZ, and highlight the utility of mean-field model to study macroscopic neural dynamics and their alterations in the illness.

Firing rate models for describing the mean-field activities of neuronal ensembles can be used effectively to study network function and dynamics, including synchronization and rhythmicity of excitatory-inhibitory populations. However, traditional Wilson-Cowan-like models, even when extended to include an explicit dynamic synaptic activation variable, are found unable to capture some dynamics such as Interneuronal Network Gamma oscillations (ING). Use of an explicit delay is helpful in simulations at the expense of complicating mathematical analysis. We resolve this issue by introducing a dynamic variable, u, that acts as an effective delay in the negative feedback loop between firing rate (r) and synaptic gating of inhibition (s). In effect, u endows synaptic activation with second order dynamics. With linear stability analysis, numerical branch-tracking and simulations, we show that our r-u-s rate model captures some key qualitative features of spiking network models for ING. We also propose an alternative formulation, a v-u-s model, in which mean membrane potential v satisfies an averaged current-balance equation. Furthermore, we extend the framework to E-I networks. With our six-variable v-u-s model, we demonstrate in firing rate models the transition from Pyramidal-Interneuronal Network Gamma (PING) to ING by increasing the external drive to the inhibitory population without adjusting synaptic weights. Having PING and ING available in a single network, without invoking synaptic blockers, is plausible and natural for explaining the emergence and transition of two different types of gamma oscillations.

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields - and predictions of the model - stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature - such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface - demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

Activity in layer 2/3 of the mouse primary visual cortex has been shown to depend both on visual input and the mouse's locomotion. Moreover, this activity is altered by a mismatch between the observed visual flow and the predicted visual flow from locomotion. Here, I present a simple computational model that explains previously reported recordings from layer 2/3 neurons in mice. In my model, layer 2/3 encodes the velocity difference between the estimate from visual flow and the prediction from locomotion using a neural population code. Moreover, I describe a hypothesized mechanism for how the brain may carry out computations of variables encoded in population codes. This mechanism may point to a general principle for computing any mathematical function in the brain.

The hippocampal formation is critical for episodic memory, with area Cornu Ammonis 3 (CA3) a necessary substrate for auto-associative pattern completion. Recent theoretical and experimental evidence suggests that the formation and retrieval of cell assemblies enable these functions. Yet, how cell assemblies are formed and retrieved in a full-scale spiking neural network (SNN) of CA3 that incorporates the observed diversity of neurons and connections within this circuit is not well understood. Here, we demonstrate that a data-driven SNN model quantitatively reflecting the neuron type-specific population sizes, intrinsic electrophysiology, connectivity statistics, synaptic signaling, and long-term plasticity of the mouse CA3 is capable of robust auto-association and pattern completion via cell assemblies. Our results show that a broad range of assembly sizes could successfully and systematically retrieve patterns from heavily incomplete or corrupted cues after a limited number of presentations. Furthermore, performance was robust with respect to partial overlap of assemblies through shared cells, substantially enhancing memory capacity. These novel findings provide computational evidence that the specific biological properties of the CA3 circuit produce an effective neural substrate for associative learning in the mammalian brain.

We demonstrate a model of chirp-velocity sensitivity in the inferior colliculus (IC) that retains the tuning to amplitude modulation (AM) that was established in earlier models. The mechanism of velocity sensitivity is sequence detection by octopus cells of the posteroventral cochlear nucleus, which have been proposed in physiological studies to respond preferentially to the order of arrival of cross-frequency inputs of different amplitudes. Model architecture is based on coincidence detection of a combination of excitatory and inhibitory inputs. Chirp-sensitivity of the IC output is largely controlled by the strength and timing of the chirp-sensitive octopus-cell inhibitory input. AM tuning is controlled by inhibition and excitation that are tuned to the same frequency. We present several example neurons that demonstrate the feasibility of the model in simulating realistic chirp-sensitivity and AM tuning for a wide range of characteristic frequencies. Additionally, we explore the systematic impact of varying parameters on model responses. The proposed model can be used to assess the contribution of IC chirp-velocity sensitivity to responses to complex sounds, such as speech.

We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption can be satisfied by introducing a piece-wise polynomial approximation of the nonlinear voltage-dependent magnesium block of NMDAR current. We study the dynamics of the resulting system for two example cases of excitatory cortical neurons and inhibitory striatal neurons. Bifurcation diagrams are presented comparing the different dynamical regimes as compared to the case of linear NMDAR currents, along with sample comparison simulation time series demonstrating different possible oscillatory solutions. The omission of the nonlinearity of NMDAR currents results in a shift in the range (and possible disappearance) of the constant high firing rate regime, along with a modulation in the amplitude and frequency power spectrum of oscillations. Moreover, nonlinear NMDAR action is seen to be state-dependent and can have opposite effects depending on the type of neurons involved and the level of input firing rate received. The presented model can serve as a computationally efficient building block in whole brain network models for investigating the differential modulation of different types of synapses under neuromodulatory influence or receptor specific malfunction.