A theoretical framework for analyzing coupled neuronal networks: Application to the olfactory system

Odor modality is transmitted to cortical brain regions from the olfactory bulb

Odor perception is the impetus for important animal behaviors with two predominate modes of processing: odors pass through the front of the nose (orthonasal) while inhaling and sniffing, or through the rear (retronasal) during exhalation and while eating. Despite the importance of olfaction for an animal's well-being and that ortho and retro naturally occur, it is unknown how the modality (ortho vs. retro) is even transmitted to cortical brain regions, which could significantly affect how odors are processed and perceived. Using multielectrode array recordings in tracheotomized anesthetized rats, which decouples ortho-retro modality from breathing, we show that mitral cells in rat olfactory bulb can reliably and directly transmit orthonasal versus retronasal modality with ethyl butyrate, a common food odor. Drug manipulations affecting synaptic inhibition via GABAA lead to worse decoding of ortho versus retro, independent of whether overall inhibition increases or decreases, suggesting that the olfactory bulb circuit may naturally favor encoding this important aspect of odors. Detailed data analysis paired with a firing rate model that captures population trends in spiking statistics shows how this circuit can encode odor modality. We have not only demonstrated that ortho/retro information is encoded to downstream brain regions but also used modeling to demonstrate a plausible mechanism for this encoding; due to synaptic adaptation, it is the slower time course of the retronasal stimulation that causes retronasal responses to be stronger and less sensitive to inhibitory drug manipulations than orthonasal responses.NEW & NOTEWORTHY Whether ortho (sniffing odors) versus retro (exhalation and eating) is encoded from the olfactory bulb to other brain areas is not completely known. Using multielectrode array recordings in anesthetized rats, we show that the olfactory bulb transmits this information downstream via spikes. Altering inhibition degrades ortho/retro information on average. We use theory and computation to explain our results, which should have implications on cortical processing considering that only food odors occur retronasally.

The Effects of Background Noise on a Biophysical Model of Olfactory Bulb Mitral Cells

The spiking activity of mitral cells (MC) in the olfactory bulb is a key attribute in olfactory sensory information processing to downstream cortical areas. A more detailed understanding of the modulation of MC spike statistics could shed light on mechanistic studies of olfactory bulb circuits and olfactory coding. We study the spike response of a recently developed single-compartment biophysical MC model containing seven known ionic currents and calcium dynamics subject to constant current input with background white noise. We observe rich spiking dynamics even with constant current input, including multimodal peaks in the interspike interval distribution (ISI). Although weak-to-moderate background noise for a fixed current input does not change the firing rate much, the spike dynamics can change dramatically, exhibiting non-monotonic spike variability not commonly observed in standard neuron models. We explain these dynamics with a phenomenological model of the ISI probability density function. Our study clarifies some of the complexities of MC spiking dynamics.

Odor-evoked increases in olfactory bulb mitral cell spiking variability

The spiking variability of neural networks has important implications for how information is encoded to higher brain regions. It has been well documented by numerous labs in many cortical and motor regions that spiking variability decreases with stimulus onset, yet whether this principle holds in the OB has not been tested. In stark contrast to this common view, we demonstrate that the onset of sensory input can cause an increase in the variability of neural activity in the mammalian OB. We show this in both anesthetized and awake rodents. Furthermore, we use computational models to describe the mechanisms of this phenomenon. Our findings establish sensory evoked increases in spiking variability as a viable alternative coding strategy.

A stochastic model for interacting neurons in the olfactory bulb

We focus on interacting neurons organized in a block-layered network devoted to the information processing from the sensory system to the brain. Specifically, we consider the firing activity of olfactory sensory neurons, periglomerular, granule and mitral cells in the context of the neuronal activity of the olfactory bulb. We propose and investigate a stochastic model of a layered and modular network to describe the dynamic behavior of each prototypical neuron, taking into account both its role (excitatory/inhibitory) and its location within the network. We adopt specific Gauss-Markov processes suitable to provide reliable estimates of the firing activity of the different neurons, given their linkages. Furthermore, we study the impact of selective excitation/inhibition on the information transmission by means of simulations and numerical estimates obtained through a Volterra integral approach.

Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models

Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces are considered. By assuming quasi-steady-state activity, one can neglect the complex temporal dynamics; however, in many cases the quasi-steady-state assumption fails. Here, we develop a new reduction method for a general heterogeneous firing-rate model receiving background correlated noisy inputs that accurately handles highly non-equilibrium statistics and interactions of heterogeneous cells. Our method involves solving an efficient set of nonlinear ODEs, rather than time-consuming Monte Carlo simulations or high-dimensional PDEs, and it captures the entire set of first and second order statistics while allowing significant heterogeneity in all model parameters.

Top-down inputs drive neuronal network rewiring and context-enhanced sensory processing in olfaction

Much of the computational power of the mammalian brain arises from its extensive top-down projections. To enable neuron-specific information processing these projections have to be precisely targeted. How such a specific connectivity emerges and what functions it supports is still poorly understood. We addressed these questions in silico in the context of the profound structural plasticity of the olfactory system. At the core of this plasticity are the granule cells of the olfactory bulb, which integrate bottom-up sensory inputs and top-down inputs delivered by vast top-down projections from cortical and other brain areas. We developed a biophysically supported computational model for the rewiring of the top-down projections and the intra-bulbar network via adult neurogenesis. The model captures various previous physiological and behavioral observations and makes specific predictions for the cortico-bulbar network connectivity that is learned by odor exposure and environmental contexts. Specifically, it predicts that-after learning-the granule-cell receptive fields with respect to sensory and with respect to cortical inputs are highly correlated. This enables cortical cells that respond to a learned odor to enact disynaptic inhibitory control specifically of bulbar principal cells that respond to that odor. For this the reciprocal nature of the granule cell synapses with the principal cells is essential. Functionally, the model predicts context-enhanced stimulus discrimination in cluttered environments ('olfactory cocktail parties') and the ability of the system to adapt to its tasks by rapidly switching between different odor-processing modes. These predictions are experimentally testable. At the same time they provide guidance for future experiments aimed at unraveling the cortico-bulbar connectivity.

Investigating the Correlation-Firing Rate Relationship in Heterogeneous Recurrent Networks

The structure of spiking activity in cortical networks has important implications for how the brain ultimately codes sensory signals. However, our understanding of how network and intrinsic cellular mechanisms affect spiking is still incomplete. In particular, whether cell pairs in a neural network show a positive (or no) relationship between pairwise spike count correlation and average firing rate is generally unknown. This relationship is important because it has been observed experimentally in some sensory systems, and it can enhance information in a common population code. Here we extend our prior work in developing mathematical tools to succinctly characterize the correlation and firing rate relationship in heterogeneous coupled networks. We find that very modest changes in how heterogeneous networks occupy parameter space can dramatically alter the correlation-firing rate relationship.