On the Similarity of Functional Connectivity between Neurons Estimated across Timescales

A central objective in neuroscience is to understand how neurons interact. Such functional interactions have been estimated using signals recorded with different techniques and, consequently, different temporal resolutions. For example, spike data often have sub-millisecond resolution while some imaging techniques may have a resolution of many seconds. Here we use multi-electrode spike recordings to ask how similar functional connectivity inferred from slower timescale signals is to the one inferred from fast timescale signals. We find that functional connectivity is relatively robust to low-pass filtering—dropping by about 10% when low pass filtering at 10 hz and about 50% when low pass filtering down to about 1 Hz—and that estimates are robust to high levels of additive noise. Moreover, there is a weak correlation for physiological filters such as hemodynamic or Ca²⁺ impulse responses and filters based on local field potentials. We address the origin of these correlations using simulation techniques and find evidence that the similarity between functional connectivity estimated across timescales is due to processes that do not depend on fast pair-wise interactions alone. Rather, it appears that connectivity on multiple timescales or common-input related to stimuli or movement drives the observed correlations. Despite this qualification, our results suggest that techniques with intermediate temporal resolution may yield good estimates of the functional connections between individual neurons.     

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na⁺ and K⁺ channels, with generator potential and graded potential models lacking voltage-gated Na⁺ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na⁺ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.     

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.     

Spatial and temporal analysis of calcium-dependent electrical activity in guinea pig Purkinje cell dendrites

We have used the calcium indicator dye arsenazo III, together with a photodiode array, to record intracellular calcium changes simultaneously from all regions of individual guinea pig cerebellar Purkinje cells in slices. The optical signals, recorded with millisecond time resolution, are good indicators of calcium-dependent electrical events. For many cells the sensitivity of the recordings was high enough to detect signals from each array element without averaging. Consequently, it was possible to use these signals to follow the complex spatial and temporal patterns of plateau and spike potentials. Calcium entry corresponding to action potentials was detected from all parts of the dendritic field including the fine spiny branchlets, demonstrating that calcium action potentials spread over the entire arbor. Usually, the entire dendritic tree fired at once. But sometimes only restricted areas had signals at any one moment with transients detected in different regions at other times. In one cell, six separate zones were distinguished. These results show that calcium action potentials could be regenerative in some dendrites and could fail to propagate into others. Signals from plateau potentials were also detected from extensive areas in the dendritic field but were always smaller than those caused by a burst of action potentials.     

Information-Driven Active Audio-Visual Source Localization

We present a system for sensorimotor audio-visual source localization on a mobile robot. We utilize a particle filter for the combination of audio-visual information and for the temporal integration of consecutive measurements. Although the system only measures the current direction of the source, the position of the source can be estimated because the robot is able to move and can therefore obtain measurements from different directions. These actions by the robot successively reduce uncertainty about the source’s position. An information gain mechanism is used for selecting the most informative actions in order to minimize the number of actions required to achieve accurate and precise position estimates in azimuth and distance. We show that this mechanism is an efficient solution to the action selection problem for source localization, and that it is able to produce precise position estimates despite simplified unisensory preprocessing. Because of the robot’s mobility, this approach is suitable for use in complex and cluttered environments. We present qualitative and quantitative results of the system’s performance and discuss possible areas of application.     

Noise Suppression and Surplus Synchrony by Coincidence Detection

The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.     

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.     

Reconstruction of firing rate changes across neuronal populations by temporally deconvolved Ca2+ imaging

Methods to record action potential (AP) firing in many individual neurons are essential to unravel the function of complex neuronal circuits in the brain. A promising approach is bolus loading of Ca(2+) indicators combined with multiphoton microscopy. Currently, however, this technique lacks cell-type specificity, has low temporal resolution and cannot resolve complex temporal firing patterns. Here we present simple solutions to these problems. We identified neuron types by colocalizing Ca(2+) signals of a red-fluorescing indicator with genetically encoded markers. We reconstructed firing rate changes from Ca(2+) signals by temporal deconvolution. This technique is efficient, dramatically enhances temporal resolution, facilitates data interpretation and permits analysis of odor-response patterns across thousands of neurons in the zebrafish olfactory bulb. Hence, temporally deconvolved Ca(2+) imaging (TDCa imaging) resolves limitations of current optical recording techniques and is likely to be widely applicable because of its simplicity, robustness and generic principle.     

Information processing in the CNS: a supramolecular chemistry?

How does central nervous system process information? Current theories are based on two tenets: (a) information is transmitted by action potentials, the language by which neurons communicate with each other—and (b) homogeneous neuronal assemblies of cortical circuits operate on these neuronal messages where the operations are characterized by the intrinsic connectivity among neuronal populations. In this view, the size and time course of any spike is stereotypic and the information is restricted to the temporal sequence of the spikes; namely, the “neural code”. However, an increasing amount of novel data point towards an alternative hypothesis: (a) the role of neural code in information processing is overemphasized. Instead of simply passing messages, action potentials play a role in dynamic coordination at multiple spatial and temporal scales, establishing network interactions across several levels of a hierarchical modular architecture, modulating and regulating the propagation of neuronal messages. (b) Information is processed at all levels of neuronal infrastructure from macromolecules to population dynamics. For example, intra-neuronal (changes in protein conformation, concentration and synthesis) and extra-neuronal factors (extracellular proteolysis, substrate patterning, myelin plasticity, microbes, metabolic status) can have a profound effect on neuronal computations. This means molecular message passing may have cognitive connotations. This essay introduces the concept of “supramolecular chemistry”, involving the storage of information at the molecular level and its retrieval, transfer and processing at the supramolecular level, through transitory non-covalent molecular processes that are self-organized, self-assembled and dynamic. Finally, we note that the cortex comprises extremely heterogeneous cells, with distinct regional variations, macromolecular assembly, receptor repertoire and intrinsic microcircuitry. This suggests that every neuron (or group of neurons) embodies different molecular information that hands an operational effect on neuronal computation.     

Translation-invariant pattern recognition based on Synfire chains

Most of current neural network architectures are not suited to recognize a pattern at various displaced positions. This lack seems due to the prevailing neuron model which reduces a neuron's information transmission to its firing rate. With this information code, a neuronal assembly cannot distinguish between different combinations of its entities and therefore fails to represent the fine structure within a pattern. In our approach, the main idea of the correlation theory is accepted that spatial relationships in a pattern should be coded by temporal relations in the timing of action potentials. However, we do not assume that synchronized spikes are a sign for strong synapses between the neurons concerned. Instead, the synchronization of Synfire chains can be exploited to produce the relevant timing relationships between the neuronal signals. Therefore, we do not require fast synaptic plasticity to account for the precise timing of action potentials. In order to illustrate this claim, we propose a model for translation-invariant pattern recognition which does not depend on any changes in synaptic efficacies. Received: 14 June 1998 / Accepted in revised form: 9 January 1999     

Auditory Nerve Spike Generator Modeled as a Variable Attenuator Based on a Saddle Node on Invariant Circle Bifurcation

Mammalian inner hair cells transduce the sound waves amplified by the cochlear amplifier (CA) into a graded neurotransmitter release that activates channels on auditory nerve fibers (ANF). These synaptic channels then charge its dendritic spike generator. While the outer hair cells of the CA employ positive feedback, poising on Andronov-Hopf type instabilities which make them extremely sensitive to faint sounds and make CA output strongly nonlinear, the ANF appears to be based on different principles and a different type of dynamical instability. Its spike generator “digitizes” CA output into trains of action potentials and behaves as a linear filter, rate-coding sound intensity across a wide dynamic range. Here we model the spike generator as a 3 dimensional version of a saddle node on invariant circle (SNIC) bifurcation. The generic 2d SNIC increases its spike rate as the square root of the input current above its spiking threshold. We add negative feedback in the form of a low voltage-threshold potassium conductance that slows down the generator’s rate of increase of its spike rate. A Poisson random source simulates an inner hair cell, outputting a series of noisy periodic current pulses to the model ANF whose spikes phase lock to these pulses and have a linear frequency to current relation with a wide dynamic range. Also, the spike generator compartment has a cholinergic feedback connection from the olive and experiments show that such feedback is able to alter the amount of H conductance inside the generator compartment. We show that an olive able to decrease H would be able to shift the spike generator’s dynamic range to higher sound intensities. In a quiet environment by increasing H the olive would be able to make spike trains similar to those caused by synaptic input.     

Dynamic Electrode-to-Image (DETI) mapping reveals the human brain’s spatiotemporal code of visual information

A number of neuroimaging techniques have been employed to understand how visual information is transformed along the visual pathway. Although each technique has spatial and temporal limitations, they can each provide important insights into the visual code. While the BOLD signal of fMRI can be quite informative, the visual code is not static and this can be obscured by fMRI’s poor temporal resolution. In this study, we leveraged the high temporal resolution of EEG to develop an encoding technique based on the distribution of responses generated by a population of real-world scenes. This approach maps neural signals to each pixel within a given image and reveals location-specific transformations of the visual code, providing a spatiotemporal signature for the image at each electrode. Our analyses of the mapping results revealed that scenes undergo a series of nonuniform transformations that prioritize different spatial frequencies at different regions of scenes over time. This mapping technique offers a potential avenue for future studies to explore how dynamic feedforward and recurrent processes inform and refine high-level representations of our visual world.     

神经元放电阈值的可变性及其意义

神经元能够将不同时空模式的突触输入转化为时序精确的动作电位输出，这种灵活、可靠的信息编码方式是神经集群在动态环境或特定任务下产生所需活动模式的重要基础。动作电位的产生遵循全或无规律，只有当细胞膜电压达到放电阈值时，神经元才产生动作电位。放电阈值在细胞内和细胞间具有高度可变性，具体动态依赖于刺激输入和放电历史。特别是，放电阈值对动作电位起始前的膜电压变化十分敏感，这种状态依赖性产生的生物物理根源包括Na⁺失活和K⁺激活。在绝大多数神经元中，动作电位的触发位置是轴突起始端，这个位置处的阈值可变性是决定神经元对时空输入转化规律的关键因素。但是，电生理实验中动作电位的记录位置却通常是胞体或近端树突，此处的阈值可变性高于轴突起始端，而其产生的重要根源是轴突动作电位的反向传播。基于胞体测量的相关研究显示，放电阈值动态能够增强神经元的时间编码、特征选择、增益调控和同时侦测能力。本文首先介绍放电阈值的概念及量化方法，然后详细梳理近年来国内外关于放电阈值可变性及产生根源的研究进展，在此基础上归纳总结放电阈值可变性对神经元编码的重要性，最后对未来放电阈值的研究方向进行展望。     

Time-Warp–Invariant Neuronal Processing

Fluctuations in the temporal durations of sensory signals constitute a major source of variability within natural stimulus ensembles. The neuronal mechanisms through which sensory systems can stabilize perception against such fluctuations are largely unknown. An intriguing instantiation of such robustness occurs in human speech perception, which relies critically on temporal acoustic cues that are embedded in signals with highly variable duration. Across different instances of natural speech, auditory cues can undergo temporal warping that ranges from 2-fold compression to 2-fold dilation without significant perceptual impairment. Here, we report that time-warp–invariant neuronal processing can be subserved by the shunting action of synaptic conductances that automatically rescales the effective integration time of postsynaptic neurons. We propose a novel spike-based learning rule for synaptic conductances that adjusts the degree of synaptic shunting to the temporal processing requirements of a given task. Applying this general biophysical mechanism to the example of speech processing, we propose a neuronal network model for time-warp–invariant word discrimination and demonstrate its excellent performance on a standard benchmark speech-recognition task. Our results demonstrate the important functional role of synaptic conductances in spike-based neuronal information processing and learning. The biophysics of temporal integration at neuronal membranes can endow sensory pathways with powerful time-warp–invariant computational capabilities.     

Spatiotemporal Spike Coding of Behavioral Adaptation in the Dorsal Anterior Cingulate Cortex

The frontal cortex controls behavioral adaptation in environments governed by complex rules. Many studies have established the relevance of firing rate modulation after informative events signaling whether and how to update the behavioral policy. However, whether the spatiotemporal features of these neuronal activities contribute to encoding imminent behavioral updates remains unclear. We investigated this issue in the dorsal anterior cingulate cortex (dACC) of monkeys while they adapted their behavior based on their memory of feedback from past choices. We analyzed spike trains of both single units and pairs of simultaneously recorded neurons using an algorithm that emulates different biologically plausible decoding circuits. This method permits the assessment of the performance of both spike-count and spike-timing sensitive decoders. In response to the feedback, single neurons emitted stereotypical spike trains whose temporal structure identified informative events with higher accuracy than mere spike count. The optimal decoding time scale was in the range of 70–200 ms, which is significantly shorter than the memory time scale required by the behavioral task. Importantly, the temporal spiking patterns of single units were predictive of the monkeys’ behavioral response time. Furthermore, some features of these spiking patterns often varied between jointly recorded neurons. All together, our results suggest that dACC drives behavioral adaptation through complex spatiotemporal spike coding. They also indicate that downstream networks, which decode dACC feedback signals, are unlikely to act as mere neural integrators.     

Time-Warp–Invariant Neuronal Processing

Fluctuations in the temporal durations of sensory signals constitute a major source of variability within natural stimulus ensembles. The neuronal mechanisms through which sensory systems can stabilize perception against such fluctuations are largely unknown. An intriguing instantiation of such robustness occurs in human speech perception, which relies critically on temporal acoustic cues that are embedded in signals with highly variable duration. Across different instances of natural speech, auditory cues can undergo temporal warping that ranges from 2-fold compression to 2-fold dilation without significant perceptual impairment. Here, we report that time-warp–invariant neuronal processing can be subserved by the shunting action of synaptic conductances that automatically rescales the effective integration time of postsynaptic neurons. We propose a novel spike-based learning rule for synaptic conductances that adjusts the degree of synaptic shunting to the temporal processing requirements of a given task. Applying this general biophysical mechanism to the example of speech processing, we propose a neuronal network model for time-warp–invariant word discrimination and demonstrate its excellent performance on a standard benchmark speech-recognition task. Our results demonstrate the important functional role of synaptic conductances in spike-based neuronal information processing and learning. The biophysics of temporal integration at neuronal membranes can endow sensory pathways with powerful time-warp–invariant computational capabilities.     

Optical Recording of Suprathreshold Neural Activity with Single-cell and Single-spike Resolution

Signaling of information in the vertebrate central nervous system is often carried by populations of neurons rather than individual neurons. Also propagation of suprathreshold spiking activity involves populations of neurons. Empirical studies addressing cortical function directly thus require recordings from populations of neurons with high resolution. Here we describe an optical method and a deconvolution algorithm to record neural activity from up to 100 neurons with single-cell and single-spike resolution. This method relies on detection of the transient increases in intracellular somatic calcium concentration associated with suprathreshold electrical spikes (action potentials) in cortical neurons. High temporal resolution of the optical recordings is achieved by a fast random-access scanning technique using acousto-optical deflectors (AODs)¹. Two-photon excitation of the calcium-sensitive dye results in high spatial resolution in opaque brain tissue². Reconstruction of spikes from the fluorescence calcium recordings is achieved by a maximum-likelihood method. Simultaneous electrophysiological and optical recordings indicate that our method reliably detects spikes (>97% spike detection efficiency), has a low rate of false positive spike detection (< 0.003 spikes/sec), and a high temporal precision (about 3 msec) ³. This optical method of spike detection can be used to record neural activity in vitro and in anesthetized animals in vivo^3,4.     

Estimating Temporal Causal Interaction between Spike Trains with Permutation and Transfer Entropy

Estimating the causal interaction between neurons is very important for better understanding the functional connectivity in neuronal networks. We propose a method called normalized permutation transfer entropy (NPTE) to evaluate the temporal causal interaction between spike trains, which quantifies the fraction of ordinal information in a neuron that has presented in another one. The performance of this method is evaluated with the spike trains generated by an Izhikevich’s neuronal model. Results show that the NPTE method can effectively estimate the causal interaction between two neurons without influence of data length. Considering both the precision of time delay estimated and the robustness of information flow estimated against neuronal firing rate, the NPTE method is superior to other information theoretic method including normalized transfer entropy, symbolic transfer entropy and permutation conditional mutual information. To test the performance of NPTE on analyzing simulated biophysically realistic synapses, an Izhikevich’s cortical network that based on the neuronal model is employed. It is found that the NPTE method is able to characterize mutual interactions and identify spurious causality in a network of three neurons exactly. We conclude that the proposed method can obtain more reliable comparison of interactions between different pairs of neurons and is a promising tool to uncover more details on the neural coding.     

Ready steady slow: action preparation slows the subjective passage of time

Professional ball game players report the feeling of the ball ‘slowing-down’ before hitting it. Because effective motor preparation is critical in achieving such expert motor performance, these anecdotal comments imply that the subjective passage of time may be influenced by preparation for action. Previous reports of temporal illusions associated with action generally emphasize compensation for suppressed sensory signals that accompany motor commands. Here, we show that the time is perceived slowed-down during preparation of a ballistic reaching movement before action, involving enhancement of sensory processing. Preparing for a reaching movement increased perceived duration of a visual stimulus. This effect was tightly linked to action preparation, because the amount of temporal dilation increased with the information about the upcoming movement. Furthermore, we showed a reduction of perceived frequency for flickering stimuli and an enhanced detection of rapidly presented letters during action preparation, suggesting increased temporal resolution of visual perception during action preparation. We propose that the temporal dilation during action preparation reflects the function of the brain to maximize the capacity of sensory information-acquisition prior to execution of a ballistic movement. This strategy might facilitate changing or inhibiting the planned action in response to last-minute changes in the external environment.