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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

Quantifying neuronal network dynamics through coarse-grained event trees.

Animals process information about many stimulus features simultaneously, swiftly (in a few 100 ms), and robustly (even when individual neurons do not themselves respond reliably). When the brain carries, codes, and certainly when it decodes information, it must do so through some coarse-grained projection mechanism. How can a projection retain information about network dynamics that covers multiple features, swiftly and robustly? Here, by a coarse-grained projection to event trees and to the event chains that comprise these trees, we propose a method of characterizing dynamic information of neuronal networks by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). We demonstrate, through idealized point neuron simulations in small networks, that this event tree analysis can reveal, with high reliability, information about multiple stimulus features within short realistic observation times. Then, with a large-scale realistic computational model of V1, we show that coarse-grained event trees contain sufficient information, again over short observation times, for fine discrimination of orientation, with results consistent with recent experimental observation.

Pseudo-Lyapunov exponents and predictability of Hodgkin-Huxley neuronal network dynamics.

We present a numerical analysis of the dynamics of all-to-all coupled Hodgkin-Huxley (HH) neuronal networks with Poisson spike inputs. It is important to point out that, since the dynamical vector of the system contains discontinuous variables, we propose a so-called pseudo-Lyapunov exponent adapted from the classical definition using only continuous dynamical variables, and apply it in our numerical investigation. The numerical results of the largest Lyapunov exponent using this new definition are consistent with the dynamical regimes of the network. Three typical dynamical regimes-asynchronous, chaotic and synchronous, are found as the synaptic coupling strength increases from weak to strong. We use the pseudo-Lyapunov exponent and the power spectrum analysis of voltage traces to characterize the types of the network behavior. In the nonchaotic (asynchronous or synchronous) dynamical regimes, i.e., the weak or strong coupling limits, the pseudo-Lyapunov exponent is negative and there is a good numerical convergence of the solution in the trajectory-wise sense by using our numerical methods. Consequently, in these regimes the evolution of neuronal networks is reliable. For the chaotic dynamical regime with an intermediate strong coupling, the pseudo-Lyapunov exponent is positive, and there is no numerical convergence of the solution and only statistical quantifications of the numerical results are reliable. Finally, we present numerical evidence that the value of pseudo-Lyapunov exponent coincides with that of the standard Lyapunov exponent for systems we have been able to examine.

Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type.

We discuss how to characterize long-time dynamics of non-smooth dynamical systems, such as integrate-and-fire (I&F) like neuronal network, using Lyapunov exponents and present a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for this large class of dynamics. These dynamics contain (i) jump conditions as in the firing-reset dynamics and (ii) degeneracy such as in the refractory period in which voltage-like variables of the network collapse to a single constant value. Using the networks of linear I&F neurons, exponential I&F neurons, and I&F neurons with adaptive threshold, we illustrate our method and discuss the rich dynamics of these networks.

A large-scale model of the locust antennal lobe.

The antennal lobe (AL) is the primary structure within the locust's brain that receives information from olfactory receptor neurons (ORNs) within the antennae. Different odors activate distinct subsets of ORNs, implying that neuronal signals at the level of the antennae encode odors combinatorially. Within the AL, however, different odors produce signals with long-lasting dynamic transients carried by overlapping neural ensembles, suggesting a more complex coding scheme. In this work we use a large-scale point neuron model of the locust AL to investigate this shift in stimulus encoding and potential consequences for odor discrimination. Consistent with experiment, our model produces stimulus-sensitive, dynamically evolving populations of active AL neurons. Our model relies critically on the persistence time-scale associated with ORN input to the AL, sparse connectivity among projection neurons, and a synaptic slow inhibitory mechanism. Collectively, these architectural features can generate network odor representations of considerably higher dimension than would be generated by a direct feed-forward representation of stimulus space.

Library-based numerical reduction of the Hodgkin-Huxley neuron for network simulation.

We present an efficient library-based numerical method for simulating the Hodgkin-Huxley (HH) neuronal networks. The key components in our numerical method involve (i) a pre-computed high resolution data library which contains typical neuronal trajectories (i.e., the time-courses of membrane potential and gating variables) during the interval of an action potential (spike), thus allowing us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations; (ii) an algorithm of spike-spike corrections within the groups of strongly coupled neurons to account for spike-spike interactions in a single large time step. By using the library method, 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 resolution in statistical quantifications of the network activity, such as average firing rate, interspike interval distribution, power spectra of voltage traces. Moreover, our large time steps using the library method can break the stability requirement of standard methods (such as Runge-Kutta (RK) methods) for the original dynamics. We compare our library-based method with RK methods, and find that our method can capture very well phase-locked, synchronous, and chaotic dynamics of HH neuronal networks. It is important to point out that, in essence, our library-based HH neuron solver can be viewed as a numerical reduction of the HH neuron to an integrate-and-fire (I&F) neuronal representation that does not sacrifice the gating dynamics (as normally done in the analytical reduction to an I&F neuron).

Fokker-Planck description of conductance-based integrate-and-fire neuronal networks.

Steady dynamics of coupled conductance-based integrate-and-fire neuronal networks in the limit of small fluctuations is studied via the equilibrium states of a Fokker-Planck equation. An asymptotic approximation for the membrane-potential probability density function is derived and the corresponding gain curves are found. Validity conditions are discussed for the Fokker-Planck description and verified via direct numerical simulations.

Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train.

We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1) -dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.