Investigating the ability of astrocytes to drive neural network synchrony.

Recent experimental works have implicated astrocytes as a significant cell type underlying several neuronal processes in the mammalian brain, from encoding sensory information to neurological disorders. Despite this progress, it is still unclear how astrocytes are communicating with and driving their neuronal neighbors. While previous computational modeling works have helped propose mechanisms responsible for driving these interactions, they have primarily focused on interactions at the synaptic level, with microscale models of calcium dynamics and neurotransmitter diffusion. Since it is computationally infeasible to include the intricate microscale details in a network-scale model, little computational work has been done to understand how astrocytes may be influencing spiking patterns and synchronization of large networks. We overcome this issue by first developing an "effective" astrocyte that can be easily implemented to already established network frameworks. We do this by showing that the astrocyte proximity to a synapse makes synaptic transmission faster, weaker, and less reliable. Thus, our "effective" astrocytes can be incorporated by considering heterogeneous synaptic time constants, which are parametrized only by the degree of astrocytic proximity at that synapse. We then apply our framework to large networks of exponential integrate-and-fire neurons with various spatial structures. Depending on key parameters, such as the number of synapses ensheathed and the strength of this ensheathment, we show that astrocytes can push the network to a synchronous state and exhibit spatially correlated patterns.

Effect of Interglomerular Inhibitory Networks on Olfactory Bulb Odor Representations.

Lateral inhibition is a fundamental feature of circuits that process sensory information. In the mammalian olfactory system, inhibitory interneurons called short axon cells (SACs) comprise the first network mediating lateral inhibition between glomeruli, the functional units of early olfactory coding and processing. The connectivity of this network and its impact on odor representations is not well understood. To explore this question, we constructed a computational model of the interglomerular inhibitory network using detailed characterizations of SAC morphologies taken from mouse olfactory bulb (OB). We then examined how this network transformed glomerular patterns of odorant-evoked sensory input (taken from previously-published datasets) as a function of the selectivity of interglomerular inhibition. We examined three connectivity schemes: selective (each glomerulus connects to few others with heterogeneous strength), nonselective (glomeruli connect to most others with heterogenous strength), or global (glomeruli connect to all others with equal strength). We found that both selective and nonselective interglomerular networks could mediate heterogeneous patterns of inhibition across glomeruli when driven by realistic sensory input patterns, but that global inhibitory networks were unable to produce input-output transformations that matched experimental data and were poor mediators of intensity-dependent gain control. We further found that networks whose interglomerular connectivities were tuned by sensory input profile decorrelated odor representations moreeffectively. These results suggest that, despite their multiglomerular innervation patterns, SACs are capable of mediating odorant-specific patterns of inhibition between glomeruli that could, theoretically, be tuned by experience or evolution to optimize discrimination of particular odorants.SIGNIFICANCE STATEMENT Lateral inhibition is a key feature of circuitry in many sensory systems including vision, audition, and olfaction. We investigate how lateral inhibitory networks mediated by short axon cells (SACs) in the mouse olfactory bulb (OB) might shape odor representations as a function of their interglomerular connectivity. Using a computational model of interglomerular connectivity derived from experimental data, we find that SAC networks, despite their broad innervation patterns, can mediate heterogeneous patterns of inhibition across glomeruli, and that the canonical model of global inhibition does not generate experimentally observed responses to stimuli. In addition, inhibitory connections tuned by input statistics yield enhanced decorrelation of similar input patterns. These results elucidate how the organization of inhibition between neural elements may affect computations.

A Computational model of the mammalian external tufted cell.

We introduce a novel detailed conductance-based model of the bursting activity in external tufted (ET) cells of the olfactory bulb. We investigate the mechanisms underlying their bursting, and make experimentally-testable predictions. The ionic currents included in the model are specific to ET cells, and their kinetic and other parameters are based on experimental recordings. We validate the model by showing that its bursting characteristics under various conditions (e.g. blocking various currents) are consistent with experimental observations. Further, we identify the bifurcation structure and dynamics that explain bursting behavior. This analysis allows us to make predictions of the response of the cell to current pulses at different burst phases. We find that depolarizing (but not hyperpolarizing) inputs received during the interburst interval can advance burst timing, creating the substrate for synchronization by excitatory connections. It has been hypothesized that such synchronization among the ET cells within one glomerulus might help coordinate the glomerular output. Next we investigate model parameter sensitivity and identify parameters that play the most prominent role in controlling each burst characteristic, such as the burst frequency and duration. Finally, the response of the cell to periodic inputs is examined, reflecting the sniffing-modulated input that these cell receive in vivo. We find that individual cells can be better entrained by inputs with higher, rather than lower, frequencies than the intrinsic bursting frequency of the cell. Nevertheless, a heterogeneous population of ET cells (as may be found in a glomerulus) is able to produce reliable periodic population responses even at lower input frequencies.

Receptor recharge time drastically reduces the number of captured particles.

Many diverse biological systems are described by randomly moving particles that can be captured by traps in their environment. Examples include neurotransmitters diffusing in the synaptic cleft before binding to receptors and prey roaming an environment before capture by predators. In most cases, the traps cannot capture particles continuously. Rather, each trap must wait a transitory "recharge" time after capturing a particle before additional captures. This recharge time is often overlooked. In the case of instant recharge, the average number of particles captured before they escape grows linearly in the total number of particles. In stark contrast, we prove that for any nonzero recharge time, the average number of captured particles grows at most logarithmically in the total particle number. This is a fundamental effect of recharge, as it holds under very general assumptions on particle motion and spatial domain. Furthermore, we characterize the parameter regime in which a given recharge time will dramatically affect a system, allowing researchers to easily verify if they need to account for recharge in their specific system. Finally, we consider a few examples, including a neural system in which recharge reduces neurotransmitter bindings by several orders of magnitude.

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes.

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

Role of intraglomerular circuits in shaping temporally structured responses to naturalistic inhalation-driven sensory input to the olfactory bulb.

Olfaction in mammals is a dynamic process driven by the inhalation of air through the nasal cavity. Inhalation determines the temporal structure of sensory neuron responses and shapes the neural dynamics underlying central olfactory processing. Inhalation-linked bursts of activity among olfactory bulb (OB) output neurons [mitral/tufted cells (MCs)] are temporally transformed relative to those of sensory neurons. We investigated how OB circuits shape inhalation-driven dynamics in MCs using a modeling approach that was highly constrained by experimental results. First, we constructed models of canonical OB circuits that included mono- and disynaptic feedforward excitation, recurrent inhibition and feedforward inhibition of the MC. We then used experimental data to drive inputs to the models and to tune parameters; inputs were derived from sensory neuron responses during natural odorant sampling (sniffing) in awake rats, and model output was compared with recordings of MC responses to odorants sampled with the same sniff waveforms. This approach allowed us to identify OB circuit features underlying the temporal transformation of sensory inputs into inhalation-linked patterns of MC spike output. We found that realistic input-output transformations can be achieved independently by multiple circuits, including feedforward inhibition with slow onset and decay kinetics and parallel feedforward MC excitation mediated by external tufted cells. We also found that recurrent and feedforward inhibition had differential impacts on MC firing rates and on inhalation-linked response dynamics. These results highlight the importance of investigating neural circuits in a naturalistic context and provide a framework for further explorations of signal processing by OB networks.

Investigating navigation strategies in the Morris Water Maze through deep reinforcement learning.

Navigation is a complex skill with a long history of research in animals and humans. In this work, we simulate the Morris Water Maze in 2D to train deep reinforcement learning agents. We perform automatic classification of navigation strategies, analyze the distribution of strategies used by artificial agents, and compare them with experimental data to show similar learning dynamics as those seen in humans and rodents. We develop environment-specific auxiliary tasks and examine factors affecting their usefulness. We suggest that the most beneficial tasks are potentially more biologically feasible for real agents to use. Lastly, we explore the development of internal representations in the activations of artificial agent neural networks. These representations resemble place cells and head-direction cells found in mouse brains, and their presence has correlation to the navigation strategies that artificial agents employ.

Spike phase locking in CA1 pyramidal neurons depends on background conductance and firing rate.

Oscillatory activity in neuronal networks correlates with different behavioral states throughout the nervous system, and the frequency-response characteristics of individual neurons are believed to be critical for network oscillations. Recent in vivo studies suggest that neurons experience periods of high membrane conductance, and that action potentials are often driven by membrane potential fluctuations in the living animal. To investigate the frequency-response characteristics of CA1 pyramidal neurons in the presence of high conductance and voltage fluctuations, we performed dynamic-clamp experiments in rat hippocampal brain slices. We drove neurons with noisy stimuli that included a sinusoidal component ranging, in different trials, from 0.1 to 500 Hz. In subsequent data analysis, we determined action potential phase-locking profiles with respect to background conductance, average firing rate, and frequency of the sinusoidal component. We found that background conductance and firing rate qualitatively change the phase-locking profiles of CA1 pyramidal neurons versus frequency. In particular, higher average spiking rates promoted bandpass profiles, and the high-conductance state promoted phase-locking at frequencies well above what would be predicted from changes in the membrane time constant. Mechanistically, spike rate adaptation and frequency resonance in the spike-generating mechanism are implicated in shaping the different phase-locking profiles. Our results demonstrate that CA1 pyramidal cells can actively change their synchronization properties in response to global changes in activity associated with different behavioral states.

Frequency separation by an excitatory-inhibitory network.

We consider a situation in which individual features of the input are represented in the neural system by different frequencies of periodic firings. Thus, if two of the features are presented concurrently, the input to the system will consist of a superposition of two periodic trains. In this paper we present an algorithm that is capable of extracting the individual features from the composite signal by separating the signal into periodic spike trains with different frequencies. We show that the algorithm can be implemented in a biophysically based excitatory-inhibitory network model. The frequency separation process works over a range of frequencies determined by time constants of the model's intrinsic variables. It does not rely on a "resonance" phenomenon and is not tuned to a discrete set of frequencies. The frequency separation is still reliable when the timing of incoming spikes is noisy.

Estimating three synaptic conductances in a stochastic neural model.

We present a method for the reconstruction of three stimulus-evoked time-varying synaptic input conductances from voltage recordings. Our approach is based on exploiting the stochastic nature of synaptic conductances and membrane voltage. Starting with the assumption that the variances of the conductances are known, we use a stochastic differential equation to model dynamics of membrane potential and derive equations for first and second moments that can be solved to find conductances. We successfully apply the new reconstruction method to simulated data. We also explore the robustness of the method as the assumptions of the underlying model are relaxed. We vary the noise levels, the reversal potentials, the number of stimulus repetitions, and the accuracy of conductance variance estimation to quantify the robustness of reconstruction. These studies pave the way for the application of the method to experimental data.

Analyzing Neuronal Networks Using Discrete-Time Dynamics.

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect's Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.

Role of trap recharge time on the statistics of captured particles.

We consider n particles diffusing freely in a domain. The boundary contains absorbing escape regions, where the particles can escape, and traps, where the particles can be captured. Modeled after biological examples such as receptors in the synaptic cleft and ambush predators waiting for prey, these traps, or capture regions, must recharge between captures. We are interested in characterizing the time courses of the number of particles remaining in the domain, the number of cumulative captures, and the number of available capture regions. We find that under certain conditions, the number of cumulative captures increases linearly in time with a slope and duration determined explicitly by the recharge rate of the capture regions. This recharge rate also determines the mean and variance of the clearance time, defined as the time it takes for all particles to leave the domain. Further, we find that while a finite recharge rate will always result in a lower number of captured particles when compared to instantaneous recharging, it can either increase or decrease the amount of variability. Lastly, we extend the model to partially absorbing traps in order to investigate the dynamics of receptor activation within an idealized synaptic cleft. We find that the width of the domain controls the amount of time that these receptors are activated, while the number of receptors controls the amplitude of activation. Our mathematical results are derived from considering this system in several ways: as a full spatial diffusion process with recharging traps, as a continuous-time Markov process on a discrete state space, and as a system of ordinary differential equations in a mean-field approximation.

Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation.

We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N --> infinity. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.

Diversity of Evoked Astrocyte Ca2+ Dynamics Quantified through Experimental Measurements and Mathematical Modeling.

Astrocytes are a major cell type in the mammalian brain. They are not electrically excitable, but generate prominent Ca2+ signals related to a wide variety of critical functions. The mechanisms driving these Ca2+ events remain incompletely understood. In this study, we integrate Ca2+ imaging, quantitative data analysis, and mechanistic computational modeling to study the spatial and temporal heterogeneity of cortical astrocyte Ca2+ transients evoked by focal application of ATP in mouse brain slices. Based on experimental results, we tune a single-compartment mathematical model of IP3-dependent Ca2+ responses in astrocytes and use that model to study response heterogeneity. Using information from the experimental data and the underlying bifurcation structure of our mathematical model, we categorize all astrocyte Ca2+ responses into four general types based on their temporal characteristics: Single-Peak, Multi-Peak, Plateau, and Long-Lasting responses. We find that the distribution of experimentally-recorded response types depends on the location within an astrocyte, with somatic responses dominated by Single-Peak (SP) responses and large and small processes generating more Multi-Peak responses. On the other hand, response kinetics differ more between cells and trials than with location within a given astrocyte. We use the computational model to elucidate possible sources of Ca2+ response variability: (1) temporal dynamics of IP3, and (2) relative flux rates through Ca2+ channels and pumps. Our model also predicts the effects of blocking Ca2+ channels/pumps; for example, blocking store-operated Ca2+ (SOC) channels in the model eliminates Plateau and Long-Lasting responses (consistent with previous experimental observations). Finally, we propose that observed differences in response type distributions between astrocyte somas and processes can be attributed to systematic differences in IP3 rise durations and Ca2+ flux rates.

Adaptation and inhibition underlie responses to time-varying interaural phase cues in a model of inferior colliculus neurons.

A mathematical model was developed for exploring the sensitivity of low-frequency inferior colliculus (IC) neurons to interaural phase disparity (IPD). The formulation involves a firing-rate-type model that does not include spikes per se. The model IC neuron receives IPD-tuned excitatory and inhibitory inputs (viewed as the output of a collection of cells in the medial superior olive). The model cell possesses cellular properties of firing rate adaptation and postinhibitory rebound (PIR). The descriptions of these mechanisms are biophysically reasonable, but only semi-quantitative. We seek to explain within a minimal model the experimentally observed mismatch between responses to IPD stimuli delivered dynamically and those delivered statically (McAlpine et al. 2000; Spitzer and Semple 1993). The model reproduces many features of the responses to static IPD presentations, binaural beat, and partial range sweep stimuli. These features include differences in responses to a stimulus presented in static or dynamic context: sharper tuning and phase shifts in response to binaural beats, and hysteresis and "rise-from-nowhere" in response to partial range sweeps. Our results suggest that dynamic response features are due to the structure of inputs and the presence of firing rate adaptation and PIR mechanism in IC cells, but do not depend on a specific biophysical mechanism. We demonstrate how the model's various components contribute to shaping the observed phenomena. For example, adaptation, PIR, and transmission delay shape phase advances and delays in responses to binaural beats, adaptation and PIR shape hysteresis in different ranges of IPD, and tuned inhibition underlies asymmetry in dynamic tuning properties. We also suggest experiments to test our modeling predictions: in vitro simulation of the binaural beat (phase advance at low beat frequencies, its dependence on firing rate), in vivo partial range sweep experiments (dependence of the hysteresis curve on parameters), and inhibition blocking experiments (to study inhibitory tuning properties by observation of phase shifts).