Discovering Neuronal Cell Types and Their Gene Expression Profiles Using a Spatial Point Process Mixture Model
Furong Huang, Animashree Anandkumar, Christian Borgs, Jennifer Chayes, Ernest Fraenkel, Michael Hawrylycz, Ed Lein, Alessandro Ingrosso, Srinivas Turaga
Cataloging the neuronal cell types that comprise circuitry of individual brain regions is a major goal of modern neuroscience and the BRAIN initiative. Single-cell RNA sequencing can now be used to measure the gene expression profiles of individual neurons and to categorize neurons based on their gene expression profiles. While the single-cell techniques are extremely powerful and hold great promise, they are currently still labor intensive, have a high cost per cell, and, most importantly, do not provide information on spatial distribution of cell types in specific regions of the brain. We propose a complementary approach that uses computational methods to infer the cell types and their gene expression profiles through analysis of brain-wide single-cell resolution in situ hybridization (ISH) imagery contained in the Allen Brain Atlas (ABA). We measure the spatial distribution of neurons labeled in the ISH image for each gene and model it as a spatial point process mixture, whose mixture weights are given by the cell types which express that gene. By fitting a point process mixture model jointly to the ISH images, we infer both the spatial point process distribution for each cell type and their gene expression profile. We validate our predictions of cell type-specific gene expression profiles using single cell RNA sequencing data, recently published for the mouse somatosensory cortex. Jointly with the gene expression profiles, cell features such as cell size, orientation, intensity and local density level are inferred per cell type.
Discovering the 'Neural Code' from multi-neuronal spike trains is an important task in neuroscience. For such an analysis, it is important to unearth interesting regularities in the spiking patterns. In this report, we present an efficient method for automatically discovering synchrony, synfire chains, and more general sequences of neuronal firings. We use the Frequent Episode Discovery framework of Laxman, Sastry, and Unnikrishnan (2005), in which the episodes are represented and recognized using finite-state automata. Many aspects of functional connectivity between neuronal populations can b…
Discovering frequent episodes in event sequences is an interesting data mining task. In this paper, we argue that this framework is very effective for analyzing multi-neuronal spike train data. Analyzing spike train data is an important problem in neuroscience though there are no data mining approaches reported for this. Motivated by this application, we introduce different temporal constraints on the occurrences of episodes. We present algorithms for discovering frequent episodes under temporal constraints. Through simulations, we show that our method is very effective for analyzing spike tra…
When the human brain manifests the birth of organised communication among local and large-scale neuronal populations activity remains undescribed. We report, in resting-state EEG source-estimates of 100 infants at term age, the existence of macro-scale dynamic functional connectivity, which have rich topological organisations, distinct spectral fingerprints and scale-invariance temporal dynamics. These functional networks encompass the default mode, primary sensory-limbic system, thalamo-frontal, thalamo-sensorimotor and visual-limbic system confined in the delta and low-alpha frequency interv…
Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magneto-encephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here, we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multi-scale mean-field theory where the neuron is considered in interaction with a "mean" extracellular medium (characterized by a specific impedance). We first show that, as …
Recordings of whole brain activity with single neuron resolution are now feasible in simple organisms. Yet, it is still challenging to appropriately simplify such complex, noisy, and multivariate data in order to reveal general principles of nervous system function. Here, we develop a method that allows us to extract global brain dynamics from pan-neuronal imaging. Success of this method is rooted in a surprising mathematical connection between dimensionality reduction and a general class of thermodynamic systems. Application of this theoretical framework to the nervous system of C. elegans re…
Nowadays, it is possible to record the activity of hundreds of cells at the same time in behaving animals. However, these data are often treated and analyzed as if they consisted of many independently recorded neurons. How can neuronal populations be uniquely used to learn about cognition? We describe recent work that shows that populations of simultaneously recorded neurons are fundamental to understand the basis of decision-making, including processes such as ongoing deliberations and decision confidence, which generally fall outside the reach of single-cell analysis. Thus, neuronal populati…
Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the diff…
Neurons in the central nervous system are affected by complex and noisy signals due to fluctuations in their cellular environment and in the inputs they receive from many other cells 1,2. Such noise usually increases the probability that a neuron will send out a signal to its target cells 2-5. In stochastic resonance, which occurs in many physical and biological systems, an optimal response is found at a particular noise amplitude 6-9. We have found that in a classical neuronal model the opposite can occur - that noise can subdue or turn off repetitive neuronal activity in both single cells an…
The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables.
We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous $1/f^2$ scaling within the power spectrum. We develop a quantitative model that treats the generation of these fields in an analogous way to that of electronic shot noise, and use this model to specifically address the cause of this $1/f^2$ Brownian noise. The model gives way to two analytically tractable solutions, both displaying Brownian noise: 1) uncorrelated cells that display sharp initial activity, whose…
Many systems in Nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behaviour of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the sam…
In this correspondence information theoretical tools are used to investigate the statistical properties of modeled cochlear nucleus globular bushy cell spike trains. The firing patterns are obtained from a simulation software that generates sample spike trains from any auditory input. Here we analyze for the first time the responses of globular bushy cells to voiced and unvoiced speech sounds. Classical entropy estimates, such as the direct method, are improved upon by considering a time-varying and time-dependent entropy estimate. With this method we investigated the relationship between the …
Epileptic seizures are characterised by abnormal brain dynamics at multiple scales, engaging single neurons, neuronal ensembles and coarse brain regions. Key to understanding the cause of such emergent population dynamics, is capturing the collective behaviour of neuronal activity at multiple brain scales. In this thesis I make use of the larval zebrafish to capture single cell neuronal activity across the whole brain during epileptic seizures. Firstly, I make use of statistical physics methods to quantify the collective behaviour of single neuron dynamics during epileptic seizures. Here, I de…
Starting from the morphological-functional assumption of the fractal brain, a mathematical model is given by activating brain non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms. The postulation of a scale covariance principle in Schrodinger type representation of the brain geodesics implies the spectral functionality of the brain dynamics through mechanisms of tunelling, percolation etc., while in the hydrodynamical type representation, it implies their structural functionality through mechanisms of wave schock, solitons type etc. For ext…
Brain-Computer Interfaces (BCI) arose as systems that merge computing systems with the human brain to facilitate recording, stimulation, and inhibition of neural activity. Over the years, the development of BCI technologies has shifted towards miniaturization of devices that can be seamlessly embedded into the brain and can target single neuron or small population sensing and control. We present a motivating example highlighting vulnerabilities of two promising micron-scale BCI technologies, demonstrating the lack of security and privacy principles in existing solutions. This situation opens t…
Graph theoretical analyses of nervous systems usually omit the aspect of connection polarity, due to data insufficiency. The chemical synapse network of Caenorhabditis elegans is a well-reconstructed directed network, but the signs of its connections are yet to be elucidated. Here, we present the gene expression-based sign prediction of the ionotropic chemical synapse connectome of C. elegans (3,638 connections and 20,589 synapses total), incorporating available presynaptic neurotransmitter and postsynaptic receptor gene expression data for three major neurotransmitter systems. We made predict…
Cell ensembles, originally proposed by Donald Hebb in 1949, are subsets of synchronously firing neurons and proposed to explain basic firing behavior in the brain. Despite having been studied for many years no conclusive evidence has been presented yet for their existence and involvement in information processing such that their identification is still a topic of modern research, especially since simultaneous recordings of large neuronal population have become possible in the past three decades. These large recordings pose a challenge for methods allowing to identify individual neurons forming…
University of Pennsylvania（宾夕法尼亚大学）；Wu Tsai Institute, Yale University（耶鲁大学吴氏研究所）；Northeastern University（东北大学）；Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Yale University（耶鲁大学）
For complex life to evolve, a sophisticated nervous system for handling its complexities was fundamental. The demand resulted in the emergence of brain's computational facility, the neuronal network. This facet of the brain is attested solidly by its inspired scientific computational neural nets which (mathematically) resolve and solve many complex problems. The presumptive general semblance of the computational operation between the two systems allows for the inference that the process in brain's neural domain also renders complexities for solution, as sets of parametric equations, like the b…
Brain activity can be measured using magnetic fields located at some distance from the brain, a technique called magneto-encephalography (MEG). The origin of such magnetic fields are the ionic currents involved in neuronal activity. While these processes are well known at the microscopic scale, it is less clear how large populations of neurons generate magnetic fields. Here, we attempt to make such a link by deriving a mean-field theory of magnetic field generation by populations of neurons. We use the concept of current dipoles to build a theory that can be applied to populations of neurons. …
We consider a spike-generating stationary Markov process whose transition probabilities are known. We show that there is a canonical potential whose Gibbs distribution, obtained from the Maximum Entropy Principle (MaxEnt), is the equilibrium distribution of this process. We provide a method to compute explicitly and exactly this potential as a linear combination of spatio-temporal interactions. In particular, our results establish an explicit relation between Maximum Entropy models and neuro-mimetic models used in spike train statistics.
Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect information processing, such as thresholding and gain scaling. These properties can be mathematically studied using generalised phenomenological models, such as the Fitzhugh-Nagumo model and the mirrored FHN. The FHN model shows that each excitability type corresponds to one specific type of bifurcation in the phase plane: Type I underlies a saddle-node on invarian…
Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide …
The Chinese University of Hong Kong（香港中文大学）；Southeast University（东南大学）；Cornell University（康奈尔大学）
Throughout history, the development of artificial intelligence, particularly artificial neural networks, has been open to and constantly inspired by the increasingly deepened understanding of the brain, such as the inspiration of neocognitron, which is the pioneering work of convolutional neural networks. Per the motives of the emerging field: NeuroAI, a great amount of neuroscience knowledge can help catalyze the next generation of AI by endowing a network with more powerful capabilities. As we know, the human brain has numerous morphologically and functionally different neurons, while artifi…
We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branc…
Recent efforts in neuroscience research seek to obtain detailed anatomical neuronal wiring maps as well as information on how neurons in these networks engage in dynamic activities. Although the entire connectivity map of the nervous system of C. elegans has been known for more than 25 years, this knowledge has not been sufficient to predict all functional connections underlying behavior. To approach this goal, we developed a two-photon technique for brain-wide calcium imaging in C. elegans using wide-field temporal focusing (WF-TEFO). Pivotal to our results was the use of a nuclear-localized,…
Experimental observations of neuroscience suggest that the brain is working a probabilistic way when computing information with uncertainty. This processing could be modeled as Bayesian inference. However, it remains unclear how Bayesian inference could be implemented at the level of neuronal circuits of the brain. In this study, we propose a novel general-purpose neural implementation of probabilistic inference based on a ubiquitous network of cortical microcircuits, termed winner-take-all (WTA) circuit. We show that each WTA circuit could encode the distribution of states defined on a variab…
Phase-amplitude coupling (PAC) describes the phenomenon where the power of a high-frequency oscillation evolves with the phase of a low-frequency one. We propose a model that explains the emergence of PAC in two commonly-accepted architectures in the brain, namely, a high-frequency neural oscillation driven by an external low-frequency input and two interacting local oscillations with distinct, locally-generated frequencies. We further propose an interconnection structure for brain regions and demonstrate that low-frequency phase synchrony can integrate high-frequency activities regulated by l…
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After…
This paper deals with the EEG/MEG neuroimaging problem: given measurements of scalp electric potential differences (EEG: electroencephalogram) and extracranial magnetic fields (MEG: magnetoencephalogram), find the 3D distribution of the generating electric neuronal activity. This problem has no unique solution. Only particular solutions with "good" localization properties are of interest, since neuroimaging is concerned with the localization of brain function. In this paper, a general family of linear imaging methods with exact, zero error localization to point-test sources is presented. One p…
Recent remarkable advances in the experimental techniques have provided a background for inferring neuronal couplings from point process data that includes a great number of neurons. Here, we propose a systematic procedure for pre- and post-processing generic point process data in an objective manner, to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch--Pitts model. The procedure involves two steps: (1) determining time-bin size for transforming the point-process data into discrete-time binary data and (2) screening relevant couplings from t…
