Exploring the Genetic Heterogeneity of Alzheimer's Disease: Evidence for Genetic Subtypes.

Background: Alzheimer's disease (AD) exhibits considerable phenotypic heterogeneity, suggesting the potential existence of subtypes. AD is under substantial genetic influence, thus identifying systematic variation in genetic risk may provide insights into disease origins. Objective: We investigated genetic heterogeneity in AD risk through a multi-step analysis. Methods: We performed principal component analysis (PCA) on AD-associated variants in the UK Biobank (AD cases = 2,739, controls = 5,478) to assess structured genetic heterogeneity. Subsequently, a biclustering algorithm searched for distinct disease-specific genetic signatures among subsets of cases. Replication tests were conducted using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset (AD cases = 500, controls = 470). We categorized a separate set of ADNI individuals with mild cognitive impairment (MCI; n = 399) into genetic subtypes and examined cognitive, amyloid, and tau trajectories. Results: PCA revealed three distinct clusters ("constellations") driven primarily by different correlation patterns in a region of strong LD surrounding the MAPT locus. Constellations contained a mixture of cases and controls, reflecting disease-relevant but not disease-specific structure. We found two disease-specific biclusters among AD cases. Pathway analysis linked bicluster-associated variants to neuron morphogenesis and outgrowth. Disease-relevant and disease-specific structure replicated in ADNI, and bicluster 2 exhibited increased cerebrospinal fluid p-tau and cognitive decline over time. Conclusions: This study unveils a hierarchical structure of AD genetic risk. Disease-relevant constellations may represent haplotype structure that does not increase risk directly but may alter the relative importance of other genetic risk factors. Biclusters may represent distinct AD genetic subtypes. This structure is replicable and relates to differential pathological accumulation and cognitive decline over time.

Heterogeneity analysis provides evidence for a genetically homogeneous subtype of bipolar-disorder.

Bipolar Disorder (BD) is a complex disease. It is heterogeneous, both at the phenotypic and genetic level, although the extent and impact of this heterogeneity is not fully understood. One way to assess this heterogeneity is to look for patterns in the subphenotype data, identify a more phenotypically homogeneous set of subjects, and perform a genome-wide association-study (GWAS) and subsequent secondary analyses restricted to this homogeneous subset. Because of the variability in how phenotypic data was collected by the various BD studies over the years, homogenizing the phenotypic data is a challenging task, and so is replication. As members of the Psychiatric Genomics Consortium (PGC), we have access to the raw genotypes of 18,711 BD cases and 29,738 controls. This amount of data makes it possible for us to set aside the intricacies of phenotype and allow the genetic data itself to determine which subjects define a homogeneous genetic subgroup. In this paper, we leverage recent advances in heterogeneity analysis to look for distinct homogeneous genetic BD subgroups (or biclusters) that manifest the broad phenotype we think of as Bipolar Disorder. As our data was generated by 27 studies and genotyped on a variety of platforms (OMEX, Affymetrix, Illumina), we use a biclustering algorithm capable of covariate-correction. Covariate-correction is critical if we wish to distinguish disease-related signals from those which are a byproduct of ancestry, study or genotyping platform. We rely on the raw genotyped data and do not include any data generated through imputation. We first apply this covariate-corrected biclustering algorithm to a cohort of 2524 BD cases and 4106 controls from the Bipolar Disease Research Network (BDRN: OMEX). We find evidence of genetic heterogeneity delineating a statistically significant bicluster comprising a subset of BD cases which exhibits a disease-specific pattern of differential-expression across a subset of SNPs. This pattern replicates across the remaining data-sets collected by the PGC containing 5781/8289 (OMEX), 3581/7591 (Illumina), and 6825/9752(Affymetrix) cases/controls, respectively. This bicluster includes subjects diagnosed with bipolar type-I, as well as subjects diagnosed with bipolar type-II. However, the bicluster is enriched for bipolar type-I over type-II and may represent a collection of correlated genetic risk-factors. By investigating the bicluster-informed polygenic-risk-scoring (PRS), we find that the disease-specific pattern highlighted by the bicluster can be leveraged to eliminate noise from our GWAS analyses and improve not only risk prediction, particularly when using only a relatively small subset (e.g., ~ 1%) of the available SNPs, but also SNP replication. Though our primary focus is only the analysis of disease-related signal, we also identify replicable control-related heterogeneity. Covariate-corrected biclustering of raw genetic data appears to be a promising route for untangling heterogeneity and identifying replicable homogeneous genetic subtypes of complex disease. It may also prove useful in identifying protective effects within the control group. This approach circumvents some of the difficulties presented by subphenotype data collected by meta-analyses or 23 andMe, e.g., missingness, assessment variation, and reliance on self-report.

Robust ab initio solution of the cryo-EM reconstruction problem at low resolution with small data sets.

Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional projection views of particles frozen at unknown orientations. This is accomplished by using a suite of software tools to (i) identify particles in large micrographs, (ii) obtain low-resolution reconstructions, (iii) refine those low-resolution structures, and (iv) finally match the obtained electron scattering density to the constituent atoms that make up the macromolecule or macromolecular complex of interest. Here, we focus on the second stage of the reconstruction pipeline: obtaining a low resolution model from picked particle images. Our goal is to create an algorithm that is capable of ab initio reconstruction from small data sets (on the order of a few thousand selected particles). More precisely, we propose an algorithm that is robust, automatic, and fast enough that it can potentially be used to assist in the assessment of particle quality as the data is being generated during the microscopy experiment.

Exploring the genetic heterogeneity of Alzheimer's disease: Evidence for genetic subtypes.

Background: Alzheimer's disease (AD) exhibits heterogeneity in cognitive impairment, atrophy, and pathological accumulation, suggesting the potential existence of subtypes. AD is under substantial genetic influence, thus identifying systematic variation in genetic risk may provide insights into disease origins. Objective: We investigated genetic heterogeneity in AD risk through a multi-step analysis. Methods: We performed principal component analysis (PCA) on AD-associated variants in the UK Biobank (AD cases=2,739, controls=5,478) to assess the presence of structured genetic heterogeneity. Subsequently, a biclustering algorithm searched for distinct disease-specific genetic signatures among subsets of cases. Replication tests were conducted using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset (AD cases=500, controls=470). We categorized a separate set of ADNI individuals with mild cognitive impairment (MCI; n=399) into genetic subtypes and examined cognitive, amyloid, and tau trajectories. Results: PCA revealed three distinct clusters ("constellations") within AD-associated variants containing a mixture of cases and controls, reflecting disease-relevant structure. We found two disease-specific biclusters among AD cases. Pathway analysis linked bicluster-associated variants to neuron morphogenesis and outgrowth, including genes related to cellular components and development-modulating factors. Both disease-relevant and disease-specific structure replicated in ADNI. Individuals with genetic signatures resembling bicluster 2 exhibited increased CSF p-tau and cognitive decline over time. Conclusions: This study unveils a hierarchical structure of AD genetic risk. Disease-relevant constellations may represent differential biological vulnerability that is itself not sufficient to increase risk. Biclusters may represent distinct AD genetic subtypes. This structure replicates in an independent dataset and relates to differential pathological accumulation and cognitive decline over time.

A time-series analysis of blood-based biomarkers within a 25-year longitudinal dolphin cohort.

Causal interactions and correlations between clinically-relevant biomarkers are important to understand, both for informing potential medical interventions as well as predicting the likely health trajectory of any individual as they age. These interactions and correlations can be hard to establish in humans, due to the difficulties of routine sampling and controlling for individual differences (e.g., diet, socio-economic status, medication). Because bottlenose dolphins are long-lived mammals that exhibit several age-related phenomena similar to humans, we analyzed data from a well controlled 25-year longitudinal cohort of 144 dolphins. The data from this study has been reported on earlier, and consists of 44 clinically relevant biomarkers. This time-series data exhibits three starkly different influences: (A) directed interactions between biomarkers, (B) sources of biological variation that can either correlate or decorrelate different biomarkers, and (C) random observation-noise which combines measurement error and very rapid fluctuations in the dolphin's biomarkers. Importantly, the sources of biological variation (type-B) are large in magnitude, often comparable to the observation errors (type-C) and larger than the effect of the directed interactions (type-A). Attempting to recover the type-A interactions without accounting for the type-B and type-C variation can result in an abundance of false-positives and false-negatives. Using a generalized regression which fits the longitudinal data with a linear model accounting for all three influences, we demonstrate that the dolphins exhibit many significant directed interactions (type-A), as well as strong correlated variation (type-B), between several pairs of biomarkers. Moreover, many of these interactions are associated with advanced age, suggesting that these interactions can be monitored and/or targeted to predict and potentially affect aging.

Olfactory encoding within the insect antennal lobe: The emergence and role of higher order temporal correlations in the dynamics of antennal lobe spiking activity.

In this review, we focus on the antennal lobe (AL) of three insect species - the fruit fly, sphinx moth, and locust. We first review the experimentally elucidated anatomy and physiology of the early olfactory system of each species; empirical studies of AL activity, however, often focus on assessing firing rates (averaged over time scales of about 100 ms), and hence the AL odor code is often analyzed in terms of a temporally evolving vector of firing rates. However, such a perspective necessarily misses the possibility of higher order temporal correlations in spiking activity within a single cell and across multiple cells over shorter time scales (of about 10 ms). Hence, we then review our prior theoretical work, where we constructed biophysically detailed, species-specific AL models within the fly, moth, and locust, finding that in each case higher order temporal correlations in spiking naturally emerge from model dynamics (i.e., without a prioriincorporation of elements designed to produce correlated activity). We therefore use our theoretical work to argue the perspective that temporal correlations in spiking over short time scales, which have received little experimental attention to-date, may provide valuable coding dimensions (complementing the coding dimensions provided by the vector of firing rates) that nature has exploited in the encoding of odors within the AL. We further argue that, if the AL does indeed utilize temporally correlated activity to represent odor information, such an odor code could be naturally and easily deciphered within the Mushroom Body.

Dynamics of sensory integration of olfactory and mechanical stimuli within the response patterns of moth antennal lobe neurons.

Odors emanating from a biologically relevant source are rapidly embedded within a windy, turbuluent medium that folds and spins filaments into fragmented strands of varying sizes. Environmental odor plumes therefore exhibit complex spatiotemporal dynamics, and rarely yield an easily discernible concentration gradient marking an unambiguous trail to an odor source. Thus, sensory integration of chemical input, encoding odor identity or concentration, and mechanosensory input, encoding wind speed, is a critical task that animals face in resolving the complex dynamics of odor plumes and tracking an odor source. In insects, who employ olfactory navigation as their primary means of foraging for food and finding mates, the antennal lobe (AL) is the first brain structure that processes sensory odor information. Although the importance of chemosensory and mechanosensory integration is widely recognized, the AL itself has traditionally been viewed purely from the perspective of odor encoding, with little attention given to its role as a bimodal integrator. In this work, we seek to explore the AL as a model for studying sensory integration - it boasts well-understood architecture, well-studied olfactory responses, and easily measurable cells. Using a moth model, we present experimental data that clearly demonstrates that AL neurons respond, in dynamically distinct ways, to both chemosensory and mechanosensory input; mechanosensory responses are transient and temporally precise, while olfactory responses are long-lasting but lack temporal precision. We further develop a computational model of the AL, show that our model captures odor response dynamics reported in the literature, and examine the dynamics of our model with the inclusion of mechanosensory input; we then use our model to pinpoint dynamical mechanisms underlying the bimodal AL responses revealed in our experimental work. Finally, we propose a novel hypothesis about the role of mechanosensory input in sculpting AL dynamics and the implications for biological odor tracking.

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.

A loop-counting method for covariate-corrected low-rank biclustering of gene-expression and genome-wide association study data.

A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices (i.e., 'loops') within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS).

Role of the locus coeruleus in the emergence of power law wake bouts in a model of the brainstem sleep-wake system through early infancy.

Infant rats randomly cycle between the sleeping and waking states, which are tightly correlated with the activity of mutually inhibitory brainstem sleep and wake populations. Bouts of sleep and wakefulness are random; from P2-P10, sleep and wake bout lengths are exponentially distributed with increasing means, while during P10-P21, the sleep bout distribution remains exponential while the distribution of wake bouts gradually transforms to power law. The locus coeruleus (LC), via an undeciphered interaction with sleep and wake populations, has been shown experimentally to be responsible for the exponential to power law transition. Concurrently during P10-P21, the LC undergoes striking physiological changes - the LC exhibits strong global 0.3 Hz oscillations up to P10, but the oscillation frequency gradually rises and synchrony diminishes from P10-P21, with oscillations and synchrony vanishing at P21 and beyond. In this work, we construct a biologically plausible Wilson Cowan-style model consisting of the LC along with sleep and wake populations. We show that external noise and strong reciprocal inhibition can lead to switching between sleep and wake populations and exponentially distributed sleep and wake bout durations as during P2-P10, with the parameters of inhibition between the sleep and wake populations controlling mean bout lengths. Furthermore, we show that the changing physiology of the LC from P10-P21, coupled with reciprocal excitation between the LC and wake population, can explain the shift from exponential to power law of the wake bout distribution. To our knowledge, this is the first study that proposes a plausible biological mechanism, which incorporates the known changing physiology of the LC, for tying the developing sleep-wake circuit and its interaction with the LC to the transformation of sleep and wake bout dynamics from P2-P21.

Intrinsic and Network Mechanisms Constrain Neural Synchrony in the Moth Antennal Lobe.

Projection-neurons (PNs) within the antennal lobe (AL) of the hawkmoth respond vigorously to odor stimulation, with each vigorous response followed by a ~1 s period of suppression-dubbed the "afterhyperpolarization-phase," or AHP-phase. Prior evidence indicates that this AHP-phase is important for the processing of odors, but the mechanisms underlying this phase and its function remain unknown. We investigate this issue. Beginning with several physiological experiments, we find that pharmacological manipulation of the AL yields surprising results. Specifically, (a) the application of picrotoxin (PTX) lengthens the AHP-phase and reduces PN activity, whereas (b) the application of Bicuculline-methiodide (BIC) reduces the AHP-phase and increases PN activity. These results are curious, as both PTX and BIC are inhibitory-receptor antagonists. To resolve this conundrum, we speculate that perhaps (a) PTX reduces PN activity through a disinhibitory circuit involving a heterogeneous population of local-neurons, and (b) BIC acts to hamper certain intrinsic currents within the PNs that contribute to the AHP-phase. To probe these hypotheses further we build a computational model of the AL and benchmark our model against our experimental observations. We find that, for parameters which satisfy these benchmarks, our model exhibits a particular kind of synchronous activity: namely, "multiple-firing-events" (MFEs). These MFEs are causally-linked sequences of spikes which emerge stochastically, and turn out to have important dynamical consequences for all the experimentally observed phenomena we used as benchmarks. Taking a step back, we extract a few predictions from our computational model pertaining to the real AL: Some predictions deal with the MFEs we expect to see in the real AL, whereas other predictions involve the runaway synchronization that we expect when BIC-application hampers the AHP-phase. By examining the literature we see support for the former, and we perform some additional experiments to confirm the latter. The confirmation of these predictions validates, at least partially, our initial speculation above. We conclude that the AL is poised in a state of high-gain; ready to respond vigorously to even faint stimuli. After each response the AHP-phase functions to prevent runaway synchronization and to "reset" the AL for another odor-specific response.

A coarse-grained framework for spiking neuronal networks: between homogeneity and synchrony.

Homogeneously structured networks of neurons driven by noise can exhibit a broad range of dynamic behavior. This dynamic behavior can range from homogeneity to synchrony, and often incorporates brief spurts of collaborative activity which we call multiple-firing-events (MFEs). These multiple-firing-events depend on neither structured architecture nor structured input, and are an emergent property of the system. Although these MFEs likely play a major role in the neuronal avalanches observed in culture and in vivo, the mechanisms underlying these MFEs cannot easily be captured using current population-dynamics models. In this work we introduce a coarse-grained framework which illustrates certain dynamics responsible for the generation of MFEs. By using a new kind of ensemble-average, this coarse-grained framework can not only address the nucleation of MFEs, but can also faithfully capture a broad range of dynamic regimes ranging from homogeneity to synchrony.

Distribution of correlated spiking events in a population-based approach for Integrate-and-Fire networks.

Randomly connected populations of spiking neurons display a rich variety of dynamics. However, much of the current modeling and theoretical work has focused on two dynamical extremes: on one hand homogeneous dynamics characterized by weak correlations between neurons, and on the other hand total synchrony characterized by large populations firing in unison. In this paper we address the conceptual issue of how to mathematically characterize the partially synchronous "multiple firing events" (MFEs) which manifest in between these two dynamical extremes. We further develop a geometric method for obtaining the distribution of magnitudes of these MFEs by recasting the cascading firing event process as a first-passage time problem, and deriving an analytical approximation of the first passage time density valid for large neuron populations. Thus, we establish a direct link between the voltage distributions of excitatory and inhibitory neurons and the number of neurons firing in an MFE that can be easily integrated into population-based computational methods, thereby bridging the gap between homogeneous firing regimes and total synchrony.

Coding of odors by temporal binding within a model network of the locust antennal lobe.

The locust olfactory system interfaces with the external world through antennal receptor neurons (ORNs), which represent odors in a distributed, combinatorial manner. ORN axons bundle together to form the antennal nerve, which relays sensory information centrally to the antennal lobe (AL). Within the AL, an odor generates a dynamically evolving ensemble of active cells, leading to a stimulus-specific temporal progression of neuronal spiking. This experimental observation has led to the hypothesis that an odor is encoded within the AL by a dynamically evolving trajectory of projection neuron (PN) activity that can be decoded piecewise to ascertain odor identity. In order to study information coding within the locust AL, we developed a scaled-down model of the locust AL using Hodgkin-Huxley-type neurons and biologically realistic connectivity parameters and current components. Using our model, we examined correlations in the precise timing of spikes across multiple neurons, and our results suggest an alternative to the dynamic trajectory hypothesis. We propose that the dynamical interplay of fast and slow inhibition within the locust AL induces temporally stable correlations in the spiking activity of an odor-dependent neural subset, giving rise to a temporal binding code that allows rapid stimulus detection by downstream elements.

Spatiotemporal dynamics of neuronal population response in the primary visual cortex.

One of the fundamental questions in system neuroscience is how the brain encodes external stimuli in the early sensory cortex. It has been found in experiments that even some simple sensory stimuli can activate large populations of neurons. It is believed that information can be encoded in the spatiotemporal profile of these collective neuronal responses. Here, we use a large-scale computational model of the primary visual cortex (V1) to study the population responses in V1 as observed in experiments in which monkeys performed visual detection tasks. We show that our model can capture very well spatiotemporal activities measured by voltage-sensitive-dye-based optical imaging in V1 of the awake state. In our model, the properties of horizontal long-range connections with NMDA conductance play an important role in the correlated population responses and have strong implications for spatiotemporal coding of neuronal populations. Our computational modeling approach allows us to reveal intrinsic cortical dynamics, separating them from those statistical effects arising from averaging procedures in experiment. For example, in experiments, it was shown that there was a spatially antagonistic center-surround structure in optimal weights in signal detection theory, which was believed to underlie the efficiency of population coding. However, our study shows that this feature is an artifact of data processing.

Emergent dynamics in a model of visual cortex.

This paper proposes that the network dynamics of the mammalian visual cortex are highly structured and strongly shaped by temporally localized barrages of excitatory and inhibitory firing we call 'multiple-firing events' (MFEs). Our proposal is based on careful study of a network of spiking neurons built to reflect the coarse physiology of a small patch of layer 2/3 of V1. When appropriately benchmarked this network is capable of reproducing the qualitative features of a range of phenomena observed in the real visual cortex, including spontaneous background patterns, orientation-specific responses, surround suppression and gamma-band oscillations. Detailed investigation into the relevant regimes reveals causal relationships among dynamical events driven by a strong competition between the excitatory and inhibitory populations. It suggests that along with firing rates, MFE characteristics can be a powerful signature of a regime. Testable predictions based on model observations and dynamical analysis are proposed.

Dynamics of spiking neurons: between homogeneity and synchrony.

Randomly connected networks of neurons driven by Poisson inputs are often assumed to produce "homogeneous" dynamics, characterized by largely independent firing and approximable by diffusion processes. At the same time, it is well known that such networks can fire synchronously. Between these two much studied scenarios lies a vastly complex dynamical landscape that is relatively unexplored. In this paper, we discuss a phenomenon which commonly manifests in these intermediate regimes, namely brief spurts of spiking activity which we call multiple firing events (MFE). These events do not depend on structured network architecture nor on structured input; they are an emergent property of the system. We came upon them in an earlier modeling paper, in which we discovered, through a careful benchmarking process, that MFEs are the single most important dynamical mechanism behind many of the V1 phenomena we were able to replicate. In this paper we explain in a simpler setting how MFEs come about, as well as their potential dynamic consequences. Although the mechanism underlying MFEs cannot easily be captured by current population dynamics models, this phenomena should not be ignored during analysis; there is a growing body of evidence that such collaborative activity may be a key towards unlocking the possible functional properties of many neuronal networks.

Blood vessel adaptation with fluctuations in capillary flow distribution.

Throughout the life of animals and human beings, blood vessel systems are continuously adapting their structures - the diameter of vessel lumina, the thickness of vessel walls, and the number of micro-vessels - to meet the changing metabolic demand of the tissue. The competition between an ever decreasing tendency of luminal diameters and an increasing stimulus from the wall shear stress plays a key role in the adaptation of luminal diameters. However, it has been shown in previous studies that the adaptation dynamics based only on these two effects is unstable. In this work, we propose a minimal adaptation model of vessel luminal diameters, in which we take into account the effects of metabolic flow regulation in addition to wall shear stresses and the decreasing tendency of luminal diameters. In particular, we study the role, in the adaptation process, of fluctuations in capillary flow distribution which is an important means of metabolic flow regulation. The fluctuation in the flow of a capillary group is idealized as a switch between two states, i.e., an open-state and a close-state. Using this model, we show that the adaptation of blood vessel system driven by wall shear stress can be efficiently stabilized when the open time ratio responds sensitively to capillary flows. As micro-vessel rarefaction is observed in our simulations with a uniformly decreased open time ratio of capillary flows, our results point to a possible origin of micro-vessel rarefaction, which is believed to induce hypertension.

Functional roles for synaptic-depression within a model of the fly antennal lobe.

Several experiments indicate that there exists substantial synaptic-depression at the synapses between olfactory receptor neurons (ORNs) and neurons within the drosophila antenna lobe (AL). This synaptic-depression may be partly caused by vesicle-depletion, and partly caused by presynaptic-inhibition due to the activity of inhibitory local neurons within the AL. While it has been proposed that this synaptic-depression contributes to the nonlinear relationship between ORN and projection neuron (PN) firing-rates, the precise functional role of synaptic-depression at the ORN synapses is not yet fully understood. In this paper we propose two hypotheses linking the information-coding properties of the fly AL with the network mechanisms responsible for ORN-->AL synaptic-depression. Our first hypothesis is related to variance coding of ORN firing-rate information--once stimulation to the ORNs is sufficiently high to saturate glomerular responses, further stimulation of the ORNs increases the regularity of PN spiking activity while maintaining PN firing-rates. The second hypothesis proposes a tradeoff between spike-time reliability and coding-capacity governed by the relative contribution of vesicle-depletion and presynaptic-inhibition to ORN-->AL synaptic-depression. Synaptic-depression caused primarily by vesicle-depletion will give rise to a very reliable system, whereas an equivalent amount of synaptic-depression caused primarily by presynaptic-inhibition will give rise to a less reliable system that is more sensitive to small shifts in odor stimulation. These two hypotheses are substantiated by several small analyzable toy models of the fly AL, as well as a more physiologically realistic large-scale computational model of the fly AL involving 5 glomerular channels.

Coarse-grained event tree analysis for quantifying Hodgkin-Huxley neuronal network dynamics.

We present an event tree analysis of studying the dynamics of the Hodgkin-Huxley (HH) neuronal networks. Our study relies on a coarse-grained projection to event trees and to the event chains that comprise these trees by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). This projection can retain information about network dynamics that covers multiple features, swiftly and robustly. We demonstrate that for even small differences in inputs, some dynamical regimes of HH networks contain sufficiently higher order statistics as reflected in event chains within the event tree analysis. Therefore, this analysis is effective in discriminating small differences in inputs. Moreover, we use event trees to analyze the results computed from an efficient library-based numerical method proposed in our previous work, where a pre-computed high resolution data library of typical neuronal trajectories during the interval of an action potential (spike) allows us to avoid resolving the spikes in detail. In this way, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable statistical accuracy in terms of average firing rate and power spectra of voltage traces. Our numerical simulation results show that the library method is efficient in the sense that the results generated by using this numerical method with much larger time steps contain sufficiently high order statistical structure of firing events that are similar to the ones obtained using a regular HH solver. We use our event tree analysis to demonstrate these statistical similarities.