Journal of Computational Neuroscience最新文献

Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Previous theoretical work has studied how such Hebbian plasticity rules shape network connectivity when firing rates are constant, or slowly varying in time. However, oscillations and fluctuations, which can arise through sensory inputs or intrinsic brain mechanisms, are ubiquitous in neuronal circuits. Here we study how oscillatory and fluctuating inputs shape recurrent network connectivity given a temporally asymmetric plasticity rule. We do this analytically using a separation of time scales approach for pairs of neurons, and then show that the analysis can be extended to understand the structure in large networks. In the case of oscillatory inputs, the resulting network structure is strongly affected by the phase relationship between drive to different neurons. In large networks, distributed phases tend to lead to hierarchical clustering. The analysis for stochastic inputs reveals a rich phase plane in which there is multistability between different possible connectivity motifs. Our results may be of relevance for understanding the effect of sensory-driven inputs, which are by nature time-varying, on synaptic plasticity, and hence on learning and memory.

This paper presents an in-depth theoretical analysis of the orientation selectivity properties of simple cells and complex cells, that can be well modelled by the generalized Gaussian derivative model for visual receptive fields, with the purely spatial component of the receptive fields determined by oriented affine Gaussian derivatives for different orders of spatial differentiation. A detailed mathematical analysis is presented for the three different cases of either: (i) purely spatial receptive fields, (ii) space-time separable spatio-temporal receptive fields and (iii) velocity-adapted spatio-temporal receptive fields. Closed-form theoretical expressions for the orientation selectivity curves for idealized models of simple and complex cells are derived for all these main cases, and it is shown that the orientation selectivity of the receptive fields becomes more narrow, as a scale parameter ratio $\kappa$ , defined as the ratio between the scale parameters in the directions perpendicular to vs. parallel with the preferred orientation of the receptive field, increases. It is also shown that the orientation selectivity becomes more narrow with increasing order of spatial differentiation in the underlying affine Gaussian derivative operators over the spatial domain. A corresponding theoretical orientation selectivity analysis is also presented for purely spatial receptive fields according to an affine Gabor model, showing that: (i) the orientation selectivity becomes more narrow when making the receptive fields wider in the direction perpendicular to the preferred orientation of the receptive field; while (ii) an additional degree of freedom in the affine Gabor model does, however, also strongly affect the orientation selectivity properties.

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.

Traveling waves of neuronal spiking activity are commonly observed across the brain, but their intrinsic function is still a matter of investigation. Experiments suggest that they may be valuable in the consolidation of memory or learning, indicating that consideration of traveling waves in the presence of plasticity might be important. A possible outcome of this consideration is that the synaptic pathways, necessary for the propagation of these waves, will be modified by the waves themselves. This will create a feedback loop where both the traveling waves and the strengths of the available synaptic pathways will change. To computationally investigate this, we model a sheet of cortical tissue by considering a quasi two-dimensional network of model neurons locally connected with plastic synaptic weights using Spike-Timing Dependent Plasticity (STDP). By using different stimulation conditions (central, stochastic, and alternating stimulation), we demonstrate that starting from a random network, traveling waves with STDP will form and strengthen propagation pathways. With progressive formation of traveling waves, we observe increases in synaptic weight along the direction of wave propagation, increases in propagation speed when pathways are strengthened over time, and an increase in the local order of synaptic weights. We also present evidence that the interaction between traveling waves and plasticity can serve as a mechanism of network-wide competition between available pathways. With an improved understanding of the interactions between traveling waves and synaptic plasticity, we can approach a fuller understanding of mechanisms of learning, computation, and processing within the brain.

The brain's ability to learn and distinguish rapid sequences of events is essential for timing-dependent tasks, such as those in sports and music. However, the mechanisms underlying this ability remain an active area of research. Here, we present a Pavlovian-conditioned spiking neural network model that may help elucidate these mechanisms. Using "three-factor learning rule," we conditioned an initially random spiking neural network to discriminate a specific spatiotemporal stimulus - a sequence of two or three pulses delivered within $\sim 10$ ms to two or three distinct neuronal subpopulations - from other pulse sequences differing by only a few milliseconds. Through conditioning, a feedforward structure emerges that encodes the target pattern's temporal information into specific topographic arrangements of stimulated subpopulations. In the readout phase, discrimination of different inputs is achieved by evaluating the shape and peak-shift characteristics of the spike density functions (SDFs) of input-triggered population bursts. The network's dynamic range - defined by the duration over which pulse sequences are processed accurately - is limited to around 10 ms, as determined by the duration of the input-triggered population burst. However, by introducing axonal conduction delays, we show that the network can generate "superbursts," producing a more complex and extended SDF lasting up to $\sim$ 30 ms, and potentially much longer. This extension effectively broadens the network's dynamic range for processing temporal sequences. We propose that such conditioning mechanisms may provide insight into the brain's ability to perceive and interpret complex spatiotemporal sensory information encountered in real-world contexts.

Childhood absence epilepsy (CAE) is a paediatric generalized epilepsy disorder with a confounding feature of resolving in adolescence in a majority of cases. In this study, we modelled how the small-scale (synapse-level) effect of progesterone metabolite allopregnanolone induces a large-scale (network-level) effect on a thalamocortical circuit associated with this disorder. In particular, our goal was to understand the role of sex steroid hormones in the spontaneous remission of CAE. The conductance-based computational model consisted of single-compartment cortical pyramidal, cortical interneurons, thalamic reticular and thalamocortical relay neurons, each described by a set of ordinary differential equations. Excitatory and inhibitory synapses were mediated by AMPA, GABAa and GABAb receptors. The model was implemented using the NetPyne modelling tool and the NEURON simulator. It was found that the action of allopregnanolone (ALLO) on individual GABAa-receptor mediated synapses can have an ameliorating effect on spike-wave discharges (SWDs) associated with absence seizures. This effect is region-specific and most significant in the thalamus, particularly the synapses between thalamic reticular neurons. The remedying effect of allopregnanolone on SWDs may possibly be true only for individuals that are predisposed to remission due to intrinsic connectivity differences or differences in tonic inhibition. These results are a useful first-step and prescribe directions for further investigation into the role of ALLO together with these differences to distinguish between models for CAE-remitting and non-remitting individuals.

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.