Πέμπτη, 20 Ιουνίου 2019

Computational Neuroscience

Slow-gamma frequencies are optimally guarded against effects of neurodegenerative diseases and traumatic brain injuries


We introduce a computational model for the cellular level effects of firing rate filtering due to the major forms of neuronal injury, including demyelination and axonal swellings. Based upon experimental and computational observations, we posit simple phenomenological input/output rules describing spike train distortions and demonstrate that slow-gamma frequencies in the 38–41 Hz range emerge as the most robust to injury. Our signal-processing model allows us to derive firing rate filters at the cellular level for impaired neural activity with minimal assumptions. Specifically, we model eight experimentally observed spike train transformations by discrete-time filters, including those associated with increasing refractoriness and intermittent blockage. Continuous counterparts for the filters are also obtained by approximating neuronal firing rates from spike trains convolved with causal and Gaussian kernels. The proposed signal processing framework, which is robust to model parameter calibration, is an abstraction of the major cellular-level pathologies associated with neurodegenerative diseases and traumatic brain injuries that affect spike train propagation and impair neuronal network functionality. Our filters are well aligned with the spectrum of dynamic memory fields including working memory, visual consciousness, and other higher cognitive functions that operate in a frequency band that is - at a single cell level - optimally guarded against common types of pathological effects. In contrast, higher-frequency neural encoding, such as is observed with short-term memory, are susceptible to neurodegeneration and injury.

Spatiotemporal discrimination in attractor networks with short-term synaptic plasticity


We demonstrate that a randomly connected attractor network with dynamic synapses can discriminate between similar sequences containing multiple stimuli suggesting such networks provide a general basis for neural computations in the brain. The network contains units representing assemblies of pools of neurons, with preferentially strong recurrent excitatory connections rendering each unit bi-stable. Weak interactions between units leads to a multiplicity of attractor states, within which information can persist beyond stimulus offset. When a new stimulus arrives, the prior state of the network impacts the encoding of the incoming information, with short-term synaptic depression ensuring an itinerancy between sets of active units. We assess the ability of such a network to encode the identity of sequences of stimuli, so as to provide a template for sequence recall, or decisions based on accumulation of evidence. Across a range of parameters, such networks produce the primacy (better final encoding of the earliest stimuli) and recency (better final encoding of the latest stimuli) observed in human recall data and can retain the information needed to make a binary choice based on total number of presentations of a specific stimulus. Similarities and differences in the final states of the network produced by different sequences lead to predictions of specific errors that could arise when an animal or human subject generalizes from training data, when the training data comprises a subset of the entire stimulus repertoire. We suggest that such networks can provide the general purpose computational engines needed for us to solve many cognitive tasks.

Neural network model of an amphibian ventilatory central pattern generator


The neuronal multiunit model presented here is a formal model of the central pattern generator (CPG) of the amphibian ventilatory neural network, inspired by experimental data from Pelophylax ridibundus. The kernel of the CPG consists of three pacemakers and two follower neurons (buccal and lung respectively). This kernel is connected to a chain of excitatory and inhibitory neurons organized in loops. Simulations are performed with Izhikevich-type neurons. When driven by the buccal follower, the excitatory neurons transmit and reorganize the follower activity pattern along the chain, and when driven by the lung follower, the excitatory and inhibitory neurons of the chain fire in synchrony. The additive effects of synaptic inputs from the pacemakers on the buccal follower account for (1) the low frequency buccal rhythm, (2) the intra-burst high frequency oscillations, and (3) the episodic lung activity. Chemosensitivity to acidosis is implemented by an increase in the firing frequency of one of the pacemakers. This frequency increase leads to both a decrease in the buccal burst frequency and an increase in the lung episode frequency. The rhythmogenic properties of the model are robust against synaptic noise and pacemaker jitter. To validate the rhythm and pattern genesis of this formal CPG, neurograms were built from simulated motoneuron activity, and compared with experimental neurograms. The basic principles of our model account for several experimental observations, and we suggest that these principles may be generic for amphibian ventilation.

Short term memory properties of sensory neural architectures


A functional role of the cerebral cortex is to form and hold representations of the sensory world for behavioral purposes. This is achieved by a sheet of neurons, organized in modules called cortical columns, that receives inputs in a peculiar manner, with only a few neurons driven by sensory inputs through thalamic projections, and a vast majority of neurons receiving mainly cortical inputs. How should cortical modules be organized, with respect to sensory inputs, in order for the cortex to efficiently hold sensory representations in memory? To address this question we investigate the memory performance of trees of recurrent networks (TRN) that are composed of recurrent networks, modeling cortical columns, connected with each others through a tree-shaped feed-forward backbone of connections, with sensory stimuli injected at the root of the tree. On these sensory architectures two types of short-term memory (STM) mechanisms can be implemented, STM via transient dynamics on the feed-forward tree, and STM via reverberating activity on the recurrent connectivity inside modules. We derive equations describing the dynamics of such networks, which allow us to thoroughly explore the space of possible architectures and quantify their memory performance. By varying the divergence ratio of the tree, we show that serial architectures, where sensory inputs are successively processed in different modules, are better suited to implement STM via transient dynamics, while parallel architectures, where sensory inputs are simultaneously processed by all modules, are better suited to implement STM via reverberating dynamics.

A computational model of large conductance voltage and calcium activated potassium channels: implications for calcium dynamics and electrophysiology in detrusor smooth muscle cells


The large conductance voltage and calcium activated potassium (BK) channels play a crucial role in regulating the excitability of detrusor smooth muscle, which lines the wall of the urinary bladder. These channels have been widely characterized in terms of their molecular structure, pharmacology and electrophysiology. They control the repolarising and hyperpolarising phases of the action potential, thereby regulating the firing frequency and contraction profiles of the smooth muscle. Several groups have reported varied profiles of BK currents and I-V curves under similar experimental conditions. However, no single computational model has been able to reconcile these apparent discrepancies. In view of the channels' physiological importance, it is imperative to understand their mechanistic underpinnings so that a realistic model can be created. This paper presents a computational model of the BK channel, based on the Hodgkin-Huxley formalism, constructed by utilising three activation processes — membrane potential, calcium inflow from voltage-gated calcium channels on the membrane and calcium released from the ryanodine receptors present on the sarcoplasmic reticulum. In our model, we attribute the discrepant profiles to the underlying cytosolic calcium received by the channel during its activation. The model enables us to make heuristic predictions regarding the nature of the sub-membrane calcium dynamics underlying the BK channel's activation. We have employed the model to reproduce various physiological characteristics of the channel and found the simulated responses to be in accordance with the experimental findings. Additionally, we have used the model to investigate the role of this channel in electrophysiological signals, such as the action potential and spontaneous transient hyperpolarisations. Furthermore, the clinical effects of BK channel openers, mallotoxin and NS19504, were simulated for the detrusor smooth muscle cells. Our findings support the proposed application of these drugs for amelioration of the condition of overactive bladder. We thus propose a physiologically realistic BK channel model which can be integrated with other biophysical mechanisms such as ion channels, pumps and exchangers to further elucidate its micro-domain interaction with the intracellular calcium environment.

From receptive profiles to a metric model of V1


In this work we show how to construct connectivity kernels induced by the receptive profiles of simple cells of the primary visual cortex (V1). These kernels are directly defined by the shape of such profiles: this provides a metric model for the functional architecture of V1, whose global geometry is determined by the reciprocal interactions between local elements. Our construction adapts to any bank of filters chosen to represent a set of receptive profiles, since it does not require any structure on the parameterization of the family. The connectivity kernel that we define carries a geometrical structure consistent with the well-known properties of long-range horizontal connections in V1, and it is compatible with the perceptual rules synthesized by the concept of association field. These characteristics are still present when the kernel is constructed from a bank of filters arising from an unsupervised learning algorithm.

A coarse-graining framework for spiking neuronal networks: from strongly-coupled conductance-based integrate-and-fire neurons to augmented systems of ODEs


Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We extend our partitioned-ensemble average (PEA) formalism proposed in Zhang et al. (Journal of Computational Neuroscience, 37(1), 81–104, 2014a) to systematically coarse grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived here successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations


Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

Slowdown of BCM plasticity with many synapses


During neural development sensory stimulation induces long-term changes in the receptive field of the neurons that encode the stimuli. The Bienenstock-Cooper-Munro (BCM) model was introduced to model and analyze this process computationally, and it remains one of the major models of unsupervised plasticity to this day. Here we show that for some stimulus types, the convergence of the synaptic weights under the BCM rule slows down exponentially as the number of synapses per neuron increases. We present a mathematical analysis of the slowdown that shows also how the slowdown can be avoided.

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability


We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABAA receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABAA mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABAA activity remains impaired. Thus the combination of deficient GABAA activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Alexandros Sfakianakis
Anapafseos 5 . Agios Nikolaos

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