Learning spiking neuronal networks with artificial neural networks: neural oscillations.

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.

Multi-band oscillations emerge from a simple spiking network.

In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), and gamma (30-120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales (e.g., various ion channels or multiple types of inhibitory neurons) or oscillatory inputs to produce rhythms in multi-bands. Here, we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then, we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus, our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.

Orientation Tuning and End-stopping in Macaque V1 Studied with Two-photon Calcium Imaging.

Orientation tuning is a fundamental response property of V1 neurons and has been extensively studied with single-/multiunit recording and intrinsic signal optical imaging. Long-term 2-photon calcium imaging allows simultaneous recording of hundreds of neurons at single neuron resolution over an extended time in awake macaques, which may help elucidate V1 orientation tuning properties in greater detail. We used this new technology to study the microstructures of orientation functional maps, as well as population tuning properties, in V1 superficial layers of 5 awake macaques. Cellular orientation maps displayed horizontal and vertical clustering of neurons according to orientation preferences, but not tuning bandwidths, as well as less frequent pinwheels than previous estimates. The orientation tuning bandwidths were narrower than previous layer-specific single-unit estimates, suggesting more precise orientation selectivity. Moreover, neurons tuned to cardinal and oblique orientations did not differ in quantities and bandwidths, likely indicating minimal V1 representation of the oblique effect. Our experimental design also permitted rough estimates of length tuning. The results revealed significantly more end-stopped cells at a more superficial 150 µm depth (vs. 300 µm), but unchanged orientation tuning bandwidth with different length tuning. These results will help construct more precise models of V1 orientation processing.

Space-variant Shack-Hartmann wavefront sensing based on affine transformation estimation.

The space-variant wavefront reconstruction problem inherently exists in deep tissue imaging. In this paper, we propose a framework of Shack-Hartmann wavefront space-variant sensing with extended source illumination. The space-variant wavefront is modeled as a four-dimensional function where two dimensions are in the spatial domain and two are in the Fourier domain with priors that both gently vary. Here, the affine transformation is used to characterize the wavefront space-variant function. Correspondingly, the zonal and modal methods are both escalated to adapt to four-dimensional representation and reconstruction. Experiments and simulations show double to quadruple improvements in space-variant wavefront reconstruction accuracy compared to the conventional space-invariant correlation method.

Fast whole-body motor neuron calcium imaging of freely moving Caenorhabditis elegans without coverslip pressed.

Caenorhabditis elegans (C. elegans) is an ideal model organism for studying neuronal functions at the system level. This article develops a customized system for whole-body motor neuron calcium imaging of freely moving C. elegans without the coverslip pressed. Firstly, we proposed a fast centerline localization algorithm that could deal with most topology-variant cases costing only 6 ms for one frame, not only benefits for real-time localization but also for post-analysis. Secondly, we implemented a full-time two-axis synchronized motion strategy by adaptively adjusting the motion parameters of two motors in every short-term motion step (~50 ms). Following the above motion tracking configuration, the tracking performance of our system has been demonstrated to completely support the high spatiotemporal resolution calcium imaging on whole-body motor neurons of wild-type (N2) worms as well as two mutants (unc-2, unc-9), even the instantaneous speed of worm moving without coverslip pressed was extremely up to 400 µm/s.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure.

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

Upconversion Nanoparticles-Based Multiplex Protein Activation to Neuron Ablation for Locomotion Regulation.

The optogenetic neuron ablation approach enables noninvasive remote decoding of specific neuron function within a complex living organism in high spatiotemporal resolution. However, it suffers from shallow tissue penetration of visible light with low ablation efficiency. This study reports a upconversion nanoparticle (UCNP)-based multiplex proteins activation tool to ablate deep-tissue neurons for locomotion modulation. By optimizing the dopant contents and nanoarchitecure, over 300-fold enhancement of blue (450-470 nm) and red (590-610 nm) emissions from UCNPs is achieved upon 808 nm irradiation. Such emissions simultaneously activate mini singlet oxygen generator and Chrimson, leading to boosted near infrared (NIR) light-induced neuronal ablation efficiency due to the synergism between singlet oxygen generation and intracellular Ca2+ elevation. The loss of neurons severely inhibits reverse locomotion, revealing the instructive role of neurons in controlling motor activity. The deep penetrance NIR light makes the current system feasible for in vivo deep-tissue neuron elimination. The results not only provide a rapidly adoptable platform to efficient photoablate single- and multiple-cells, but also define the neural circuits underlying behavior, with potential for development of remote therapy in diseases.

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 Mechanism for Synaptic Copy Between Neural Circuits.

Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking may be enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.

Temporal multiplexing of the scientific grade camera for hyper-frame-rate imaging.

In order to maximize the spatio-temporal resolution of the scientific grade camera at width-limited ROI, this paper proposes a new hyper-frame-rate imaging method by temporal multiplexing the sub-region of the image sensor. In the system, a dual-axis scanning galvanometer is localized at the relay pupil plane and a high quality scan lens is utilized to form an image-side telecentric path. Following this path can overcome bandwidth waste in the conventional exposure and readout mode, and maintain other performances of image sensors. As a result, the sCMOS camera has performed 432fps over 820 × 700 pixel arrays to record the dynamic heartbeat of zebrafish larvae.

High cost-efficient and computational gigapixel video camera based on commercial lenses and CMOS chips.

The state-of-the-art commercial telephoto lens has already provided us almost one giga space-bandwidth product. Since the single-image sensor cannot take such sampling capacity, we implement a four-parallel-boresight imaging system by using four such lenses and use 64 image sensors to complete full field of view (FOV) imaging for achieving 0.8 gigapixel over 15.6°×10.5°. Multiple sensors mosaicking can make most online computation and data transfer in parallel, and help us to realize a gigapixel video camera. Meanwhile, according to the four-parallel-boresight configuration, the flat image plane simplifies the image registration and image stitching, and allows us to keep high imaging performance in full frame following geometric and optical calibration and correction. Furthermore, considering that working distance changes do bring additional x/y offsets between sensor arrays, we propose a computation-based method and introduce an eight-axis automatic motion mechanism into the system to perform the online active displacement. Our prototype camera using 16 sensors has been validated in 50 m indoor conditions and 145 m outdoor condition experiments, respectively. The effective angular resolution under the 0.2 giga 24 Hz video output is 18 µrad, which is two times the lens instantaneous FOV. Compared with other gigapixel cameras, it is superior in terms of optical system simplicity and cost efficiency, which would potentially benefit numerous unmanned aerial vehicle photogrammetric applications that pursue high angular resolution over moderate FOV.

Mutual Information and Information Gating in Synfire Chains.

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains-SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Segmentation and classification of two-channel C. elegans nucleus-labeled fluorescence images.

BACKGROUND: Aging is characterized by a gradual breakdown of cellular structures. Nuclear abnormality is a hallmark of progeria in human. Analysis of age-dependent nuclear morphological changes in Caenorhabditis elegans is of great value to aging research, and this calls for an automatic image processing method that is suitable for both normal and abnormal structures. RESULTS: Our image processing method consists of nuclear segmentation, feature extraction and classification. First, taking up the challenges of defining individual nuclei with fuzzy boundaries or in a clump, we developed an accurate nuclear segmentation method using fused two-channel images with seed-based cluster splitting and k-means algorithm, and achieved a high precision against the manual segmentation results. Next, we extracted three groups of nuclear features, among which five features were selected by minimum Redundancy Maximum Relevance (mRMR) for classifiers. After comparing the classification performances of several popular techniques, we identified that Random Forest, which achieved a mean class accuracy (MCA) of 98.69%, was the best classifier for our data set. Lastly, we demonstrated the method with two quantitative analyses of C. elegans nuclei, which led to the discovery of two possible longevity indicators. CONCLUSIONS: We produced an automatic image processing method for two-channel C. elegans nucleus-labeled fluorescence images. It frees biologists from segmenting and classifying the nuclei manually.

Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains.

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Recently experimental evidence has been presented suggesting that neural information is encoded and transferred in packets, i.e., in stereotypical, correlated spiking patterns of neural activity. Due to their relevance to coherent spiking, synfire chains are one of the main theoretical constructs that have been appealed to in order to describe coherent spiking and information transfer phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited the classical synfire chain's ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by streaming input, processes the input, then makes a decision based on the processed information and shuts itself down.

A mechanism for graded, dynamically routable current propagation in pulse-gated synfire chains and implications for information coding.

Neural oscillations can enhance feature recognition (Azouz and Gray Proceedings of the National Academy of Sciences of the United States of America, 97, 8110-8115 2000), modulate interactions between neurons (Womelsdorf et al. Science, 316, 1609-01612 2007), and improve learning and memory (Markowska et al. The Journal of Neuroscience, 15, 2063-2073 1995). Numerical studies have shown that coherent spiking can give rise to windows in time during which information transfer can be enhanced in neuronal networks (Abeles Israel Journal of Medical Sciences, 18, 83-92 1982; Lisman and Idiart Science, 267, 1512-1515 1995, Salinas and Sejnowski Nature Reviews. Neuroscience, 2, 539-550 2001). Unanswered questions are: 1) What is the transfer mechanism? And 2) how well can a transfer be executed? Here, we present a pulse-based mechanism by which a graded current amplitude may be exactly propagated from one neuronal population to another. The mechanism relies on the downstream gating of mean synaptic current amplitude from one population of neurons to another via a pulse. Because transfer is pulse-based, information may be dynamically routed through a neural circuit with fixed connectivity. We demonstrate the transfer mechanism in a realistic network of spiking neurons and show that it is robust to noise in the form of pulse timing inaccuracies, random synaptic strengths and finite size effects. We also show that the mechanism is structurally robust in that it may be implemented using biologically realistic pulses. The transfer mechanism may be used as a building block for fast, complex information processing in neural circuits. We show that the mechanism naturally leads to a framework wherein neural information coding and processing can be considered as a product of linear maps under the active control of a pulse generator. Distinct control and processing components combine to form the basis for the binding, propagation, and processing of dynamically routed information within neural pathways. Using our framework, we construct example neural circuits to 1) maintain a short-term memory, 2) compute time-windowed Fourier transforms, and 3) perform spatial rotations. We postulate that such circuits, with automatic and stereotyped control and processing of information, are the neural correlates of Crick and Koch's zombie modes.

Dimensional reduction of a V1 ring model with simple and complex cells.

In this paper, we extend a framework for constructing low-dimensional dynamical systems models of mammalian primary visual cortex to a cortical network model that incorporates the full nonlinear effects of complex cells. The procedure consists of capturing the essential dynamics in a low-dimensional subspace using empirical methods, then recasting the equations in the reduced vector space. Previously, we considered visual cortical network models consisting of only simple cells with nearly linear responses to external stimuli. Here we show that fully nonlinear effects can be incorporated by examining the dimensional reduction of an idealized ring model of V1 with both simple and complex cells. We found it expedient to divide the subspace into four separate neuronal populations: excitatory simple, excitatory complex, inhibitory simple and inhibitory complex. In order to reproduce the fluctuation-driven dynamics in this reduced space, we incorporated (1) white noises with different intensities into individual neuronal populations, and (2) firing rate estimates to capture the probability of firing due to subthreshold fluctuations. With a more accurate, fitted connectivity, our modified dimensional reduced models can reproduce the firing rates, circular variances and modulation ratios observed in the original ring model.

Improved dimensionally-reduced visual cortical network using stochastic noise modeling.

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.

C. elegans enteric motor neurons fire synchronized action potentials underlying the defecation motor program.

C. elegans neurons were thought to be non-spiking until our recent discovery of action potentials in the sensory neuron AWA; however, the extent to which the C. elegans nervous system relies on analog or digital coding is unclear. Here we show that the enteric motor neurons AVL and DVB fire synchronous all-or-none calcium-mediated action potentials following the intestinal pacemaker during the rhythmic C. elegans defecation behavior. AVL fires unusual compound action potentials with each depolarizing calcium spike mediated by UNC-2 followed by a hyperpolarizing potassium spike mediated by a repolarization-activated potassium channel EXP-2. Simultaneous behavior tracking and imaging in free-moving animals suggest that action potentials initiated in AVL propagate along its axon to activate precisely timed DVB action potentials through the INX-1 gap junction. This work identifies a novel circuit of spiking neurons in C. elegans that uses digital coding for long-distance communication and temporal synchronization underlying reliable behavioral rhythm.

Dendritic Morphology Affects the Velocity and Amplitude of Back-propagating Action Potentials.

The back-propagating action potential (bpAP) is crucial for neuronal signal integration and synaptic plasticity in dendritic trees. Its properties (velocity and amplitude) can be affected by dendritic morphology. Due to limited spatial resolution, it has been difficult to explore the specific propagation process of bpAPs along dendrites and examine the influence of dendritic morphology, such as the dendrite diameter and branching pattern, using patch-clamp recording. By taking advantage of Optopatch, an all-optical electrophysiological method, we made detailed recordings of the real-time propagation of bpAPs in dendritic trees. We found that the velocity of bpAPs was not uniform in a single dendrite, and the bpAP velocity differed among distinct dendrites of the same neuron. The velocity of a bpAP was positively correlated with the diameter of the dendrite on which it propagated. In addition, when bpAPs passed through a dendritic branch point, their velocity decreased significantly. Similar to velocity, the amplitude of bpAPs was also positively correlated with dendritic diameter, and the attenuation patterns of bpAPs differed among different dendrites. Simulation results from neuron models with different dendritic morphology corresponded well with the experimental results. These findings indicate that the dendritic diameter and branching pattern significantly influence the properties of bpAPs. The diversity among the bpAPs recorded in different neurons was mainly due to differences in dendritic morphology. These results may inspire the construction of neuronal models to predict the propagation of bpAPs in dendrites with enormous variation in morphology, to further illuminate the role of bpAPs in neuronal communication.

Differences in action potential propagation speed and axon initial segment plasticity between neurons from Sprague-Dawley rats and C57BL/6 mice.

Action potentials (APs) in neurons are generated at the axon initial segment (AIS). AP dynamics, including initiation and propagation, are intimately associated with neuronal excitability and neurotransmitter release kinetics. Most learning and memory studies at the single-neuron level have relied on the use of animal models, most notably rodents. Here, we studied AP initiation and propagation in cultured hippocampal neurons from Sprague-Dawley (SD) rats and C57BL/6 (C57) mice with genetically encoded voltage indicator (GEVI)-based voltage imaging. Our data showed that APs traveled bidirectionally in neurons from both species; forward-propagating APs (fpAPs) had a different speed than backpropagating APs (bpAPs). Additionally, we observed distinct AP propagation characteristics in AISs emerging from the somatic envelope compared to those originating from dendrites. Compared with rat neurons, mouse neurons exhibited higher bpAP speed and lower fpAP speed, more distally located ankyrin G (AnkG) in AISs, and longer Nav1.2 lengths in AISs. Moreover, during AIS plasticity, AnkG and Nav1.2 showed distal shifts in location and shorter lengths of labeled AISs in rat neurons; in mouse neurons, however, they showed a longer AnkG-labeled length and more distal Nav1.2 location. Our findings suggest that hippocampal neurons in SD rats and C57 mice may have different AP propagation speeds, different AnkG and Nav1.2 patterns in the AIS, and different AIS plasticity properties, indicating that comparisons between these species must be carefully considered.