Encoding of Time-varying Stimuli in Populations of Cultured Neurons

We wondered whether random populations of dissociated cultured cortical neurons, despite of their lack of structure and/or regional specialization, are capable of modulating their neural activity as the effect of a time-varying stimulation – a simulated ‘sensory’ afference. More specifically, we used localized low-frequency, non-periodic trains of stimuli to simulate sensory afferences, and asked how much information about the original trains of stimuli could be extracted from the neural activity recorded at the different sites. Furthermore, motivated by the results of studies performed both in vivo and in vitro on different preparations, which suggested that isolated spikes and bursts may play different roles in coding time-varying signals, we explored the amount of such ‘sensory’ information that could be associated to these different firing modes. Finally, we asked whether and how such ‘sensory’ information is transferred from the sites of stimulation (i.e., the ‘sensory’ areas), to the other regions of the neural populations. To do this we applied stimulus reconstruction techniques and information theoretic concepts that are typically used to investigate neural coding in sensory systems. Our main results are that (1) slow variations of the rate of stimulation are coded into isolated spikes and in the time of occurrence of bursts (but not in the bursts’ temporal structure); (2) increasing the rate of stimulation has the effect of increasing the proportion of isolated spikes in the average evoked response and their importance in coding for the stimuli; and, (3) the ability to recover the time course of the pattern of stimulation is strongly related to the degree of functional connectivity between stimulation and recording sites. These observations parallel similar findings in intact nervous systems regarding the complementary roles of bursts and tonic spikes in encoding sensory information. Our results also have interesting implications in the field of neuro-robotic interfaces. In fact, the ability of populations of neurons to code information is a prerequisite for obtaining hybrid systems, in which neuronal populations are used to control external devices.     

Neural population codes

In many regions of the brain, information is represented by patterns of activity occurring over populations of neurons. Understanding the encoding of information in neural population activity is important both for grasping the fundamental computations underlying brain function, and for interpreting signals that may be useful for the control of prosthetic devices. We concentrate on the representation of information in neurons with Poisson spike statistics, in which information is contained in the average spike firing rate. We analyze the properties of population codes in terms of the tuning functions that describe individual neuron behavior. The discussion centers on three computational questions: first, what information is encoded in a population; second, how does the brain compute using populations; and third, when is a population optimal? To answer these questions, we discuss several methods for decoding population activity in an experimental setting. We also discuss how computation can be performed within the brain in networks of interconnected populations. Finally, we examine questions of optimal design of population codes that may help to explain their particular form and the set of variables that are best represented. We show that for population codes based on neurons that have a Poisson distribution of spike probabilities, the behavior and computational properties of the code can be understood in terms of the tuning properties of individual cells.     

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Distributed processing and temporal codes in neuronal networks

The cerebral cortex presents itself as a distributed dynamical system with the characteristics of a small world network. The neuronal correlates of cognitive and executive processes often appear to consist of the coordinated activity of large assemblies of widely distributed neurons. These features require mechanisms for the selective routing of signals across densely interconnected networks, the flexible and context dependent binding of neuronal groups into functionally coherent assemblies and the task and attention dependent integration of subsystems. In order to implement these mechanisms, it is proposed that neuronal responses should convey two orthogonal messages in parallel. They should indicate (1) the presence of the feature to which they are tuned and (2) with which other neurons (specific target cells or members of a coherent assembly) they are communicating. The first message is encoded in the discharge frequency of the neurons (rate code) and it is proposed that the second message is contained in the precise timing relationships between individual spikes of distributed neurons (temporal code). It is further proposed that these precise timing relations are established either by the timing of external events (stimulus locking) or by internal timing mechanisms. The latter are assumed to consist of an oscillatory modulation of neuronal responses in different frequency bands that cover a broad frequency range from <2 Hz (delta) to >40 Hz (gamma) and ripples. These oscillations limit the communication of cells to short temporal windows whereby the duration of these windows decreases with oscillation frequency. Thus, by varying the phase relationship between oscillating groups, networks of functionally cooperating neurons can be flexibly configurated within hard wired networks. Moreover, by synchronizing the spikes emitted by neuronal populations, the saliency of their responses can be enhanced due to the coincidence sensitivity of receiving neurons in very much the same way as can be achieved by increasing the discharge rate. Experimental evidence will be reviewed in support of the coexistence of rate and temporal codes. Evidence will also be provided that disturbances of temporal coding mechanisms are likely to be one of the pathophysiological mechanisms in schizophrenia. This article was part of LNCS 5286 (2008), Maria Marinaro, Silvia Scarpetta, Yoko Yamaguchi (eds.), “Dynamic Brain—from Neural Spikes to Behaviors, 12th International Summer School on Neural Networks Erice, Italy, December 2007 Revised Lectures” and summarized some of the putative functions of temporal codes resulting either from the timing of external events (feed forward/bottom up) or from internal timing mechanisms (top down). For comprehensive reviews of the theoretical prerequisites of synchronization in these processes see Yamaguchi and Shimizu (1994) and Shimizu et al. (1985).     

Auditory information coding by modeled cochlear nucleus neurons

In this paper we use information theory to quantify the information in the output spike trains of modeled cochlear nucleus globular bushy cells (GBCs). GBCs are part of the sound localization pathway. They are known for their precise temporal processing, and they code amplitude modulations with high fidelity. Here we investigated the information transmission for a natural sound, a recorded vowel. We conclude that the maximum information transmission rate for a single neuron was close to 1,050 bits/s, which corresponds to a value of approximately 5.8 bits per spike. For quasi-periodic signals like voiced speech, the transmitted information saturated as word duration increased. In general, approximately 80% of the available information from the spike trains was transmitted within about 20 ms. Transmitted information for speech signals concentrated around formant frequency regions. The efficiency of neural coding was above 60% up to the highest temporal resolution we investigated (20 μs). The increase in transmitted information to that precision indicates that these neurons are able to code information with extremely high fidelity, which is required for sound localization. On the other hand, only 20% of the information was captured when the temporal resolution was reduced to 4 ms. As the temporal resolution of most speech recognition systems is limited to less than 10 ms, this massive information loss might be one of the reasons which are responsible for the lack of noise robustness of these systems.     

Candidate codes in the gustatory system of caterpillars

Larvae of tobacco hornworms offer unique opportunities to relate the electrophysiological output of identified chemosensory neurons to specific behavioral responses. Larvae can discriminate among three preferred plants with only eight functioning gustatory receptors. They can be induced to prefer any one of the plants, and these preferences can be reversed. All eight neurons respond to each plant sap. Two fire too infrequently to permit detailed analysis. Analyses of the remaining six show that all electrophysiological responses consist of phasic and tonic components. Only the "salt best" cell fires during the phasic period. Temporal analysis of the spike train during this period shows that tomato and tobacco could be distinguished from Jerusalem cherry but not from each other by a rate code. Measurements of behavioral response times together with the nonspecificity of this with respect of food plants, unacceptable plants, and sodium chloride eliminate a phasic period rate code as a probable mechanism for complex discrimination. Events occurring in the tonic period, when all cells are firing, suggest a major role for this period. Analyses of variance in the interval frequencies of the large and medium spikes suggest that a variance code could allow discrimination among the three plants as long as both cells were firing at the same time. Evidence has been found for temporal patterning in the tonic response of the "salt best" cell to Jerusalem cherry but is absent elsewhere. The most likely basis for coding the difference between each of the three plants is across- fiber patterning in which the relative rates of firing and the variances of all the sensory neurons in the tonic phase are critical.     

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     

The multiple codes of nucleotide sequences

Nucleotide sequences carry genetic information of many different kinds, not just instructions for protein synthesis (triplet code). Several codes of nucleotide sequences are discussed including: (1) the translation framing code, responsible for correct triplet counting by the ribosome during protein synthesis; (2) the chromatin code, which provides instructions on appropriate placement of nucleosomes along the DNA molecules and their spatial arrangement; (3) a putative loop code for single-stranded RNA-protein interactions. The codes are degenerate and corresponding messages are not only interspersed but actually overlap, so that some nucleotides belong to several messages simultaneously. Tandemly repeated sequences frequently considered as functionless “junk” are found to be grouped into certain classes of repeat unit lengths. This indicates some functional involvement of these sequences. A hypothesis is formulated according to which the tandem repeats are given the role of weak enhancer-silencers that modulate, in a copy number-dependent way, the expression of proximal genes. Fast amplification and elimination of the repeats provides an attractive mechanism of species adaptation to a rapidly changing environment.     

Using sensory weighting to model the influence of canal,otolith and visual cues on spatial orientation and eye movements

 The sensory weighting model is a general model of sensory integration that consists of three processing layers. First, each sensor provides the central nervous system (CNS) with information regarding a specific physical variable. Due to sensor dynamics, this measure is only reliable for the frequency range over which the sensor is accurate. Therefore, we hypothesize that the CNS improves on the reliability of the individual sensor outside this frequency range by using information from other sensors, a process referred to as “frequency completion.” Frequency completion uses internal models of sensory dynamics. This “improved” sensory signal is designated as the “sensory estimate” of the physical variable. Second, before being combined, information with different physical meanings is first transformed into a common representation; sensory estimates are converted to intermediate estimates. This conversion uses internal models of body dynamics and physical relationships. Third, several sensory systems may provide information about the same physical variable (e.g., semicircular canals and vision both measure self-rotation). Therefore, we hypothesize that the “central estimate” of a physical variable is computed as a weighted sum of all available intermediate estimates of this physical variable, a process referred to as “multicue weighted averaging.” The resulting central estimate is fed back to the first two layers. The sensory weighting model is applied to three-dimensional (3D) visual–vestibular interactions and their associated eye movements and perceptual responses. The model inputs are 3D angular and translational stimuli. The sensory inputs are the 3D sensory signals coming from the semicircular canals, otolith organs, and the visual system. The angular and translational components of visual movement are assumed to be available as separate stimuli measured by the visual system using retinal slip and image deformation. In addition, both tonic (“regular”) and phasic (“irregular”) otolithic afferents are implemented. Whereas neither tonic nor phasic otolithic afferents distinguish gravity from linear acceleration, the model uses tonic afferents to estimate gravity and phasic afferents to estimate linear acceleration. The model outputs are the internal estimates of physical motion variables and 3D slow-phase eye movements. The model also includes a smooth pursuit module. The model matches eye responses and perceptual effects measured during various motion paradigms in darkness (e.g., centered and eccentric yaw rotation about an earth-vertical axis, yaw rotation about an earth-horizontal axis) and with visual cues (e.g., stabilized visual stimulation or optokinetic stimulation). Received: 20 September 2000 / Accepted in revised form: 28 September 2001     

Chemical codes of sensory neurons innervating the guinea-pig adrenal gland

Retrograde neuronal tracing in combination with double-labelling immunofluorescence was applied to distinguish the chemical coding of guinea-pig primary sensory neurons projecting to the adrenal medulla and cortex. Seven subpopulations of retrogradely traced neurons were identified in thoracic spinal ganglia T1-L1. Five subpopulations contained immunolabelling either for calcitonin gene-related peptide (CGRP) alone (I), or for CGRP, together with substance (P (II), substance P/dynorphin (III), substance P/cholecystokinin (IV), and substance P/nitric oxide synthase (V), respectively. Two additional subpopulations of retrogradely traced neurons were distinct from these groups: neurofilament-immunoreactive neurons (VI), and cell bodies that were nonreactive to either of the antisera applied (VII). Nerve fibres in the adrenal medulla and cortex were equipped with the mediator combinations I, II, IV and VI. An additional meshwork of fibres solely labelled for nitric oxide synthase was visible in the medulla. Medullary as well as cortical fibres along endocrine tissue apparently lacked the chemical code V, while in the external cortex some fibres exhibited code III. Some intramedullary neuronal cell bodies revealed immunostaining for nitric oxide synthase, CGRP or substance P, providing an additional intrinsic adrenal innervation. Perikarya, immunolabelled for nitric oxide synthase, however, were too few to match with the large number of intramedullary nitric oxide synthase-immunoreactive fibres. A non-sensory participation is also supposed for the particularly dense intramedullary network of solely neurofilament-immunoreactive nerve fibres. The findings give evidence for a differential sensory innervation of the guineapig adrenal cortex and medulla. Specific sensory neuron subpopulations suggest that nervous control of adrenal functions is more complex than hitherto believed.     

Motor pattern selection by combinatorial code of interneuronal pathways

We use a modeling approach to examine ideas derived from physiological network analyses, pertaining to the switch of a motor control network between two opposite control modes. We studied the femur–tibia joint control system of the insect leg, and its switch between resistance reflex in posture control and “active reaction” in walking, both elicited by the same sensory input. The femur–tibia network was modeled by fitting the responses of model neurons to those obtained in animals. The strengths of 16 interneuronal pathways that integrate sensory input were then assigned three different values and varied independently, generating a database of more than 43 million network variants. We demonstrate that the same neural network can produce the two different behaviors, depending on the combinatorial code of interneuronal pathways. That is, a switch between behaviors, such as standing to walking, can be brought about by altering the strengths of selected sensory integration pathways. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

大脑中的抉择神经元

近年来神经科学领域的进展表明,大脑中不仅存在如位置神经元之类的特异性编码感觉信息的神经元,也存在能够特异性地反映动物思考过程的神经元。在一系列以侧内顶叶(LIP)为目标的猕猴电生理实验中,人们发现LIP神经元的动作电位发放率可以反映抉择思考的过程。抉择的研究为我们打开了一个研究大脑高级认知功能的窗口。抉择神经元的发现表明了大脑的高级认知功能是基于与感觉信息处理类似的神经计算原理。     

Object localization with whiskers

Rats use their large facial hairs (whiskers) to detect, localize and identify objects in their proximal three-dimensional (3D) space. Here, we focus on recent evidence of how object location is encoded in the neural sensory pathways of the rat whisker system. Behavioral and neuronal observations have recently converged to the point where object location in 3D appears to be encoded by an efficient orthogonal scheme supported by primary sensory-afferents: each primary-afferent can signal object location by a spatial (labeled-line) code for the vertical axis (along whisker arcs), a temporal code for the horizontal axis (along whisker rows), and an intensity code for the radial axis (from the face out). Neuronal evidence shows that (i) the identities of activated sensory neurons convey information about the vertical coordinate of an object, (ii) the timing of their firing, in relation to other reference signals, conveys information about the horizontal object coordinate, and (iii) the intensity of firing conveys information about the radial object coordinate. Such a triple-coding scheme allows for efficient multiplexing of 3D object location information in the activity of single neurons. Also, this scheme provides redundancy since the same information may be represented in the activity of many neurons. These features of orthogonal coding increase accuracy and reliability. We propose that the multiplexed information is conveyed in parallel to different readout circuits, each decoding a specific spatial variable. Such decoding reduces ambiguity, and simplifies the required decoding algorithms, since different readout circuits can be optimized for a particular variable.     

Stochasticity,spikes and decoding: sufficiency and utility of order statistics

For over 75 years it has been clear that the number of spikes in a neural response is an important part of the neuronal code. Starting as early as the 1950’s with MacKay and McCullough, there has been speculation over whether each spike and its exact time of occurrence carry information. Although it is obvious that the firing rate carries information it has been less clear as to whether there is information in exactly timed patterns, when they arise from the dynamics of the neurons and networks, as opposed to when they represent some strong external drive that entrains them. One strong null hypothesis that can be applied is that spike trains arise from stochastic sampling of an underlying deterministic temporally modulated rate function, that is, there is a time-varying rate function. In this view, order statistics seem to provide a sufficient theoretical construct to both generate simulated spike trains that are indistinguishable from those observed experimentally, and to evaluate (decode) the data recovered from experiments. It remains to learn whether there are physiologically important signals that are not described by such a null hypothesis. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

The vestibular system implements a linear-nonlinear transformation in order to encode self-motion

Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (～50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways.     

Pituitary adenylate cyclase-activating polypeptide and islet amyloid polypeptide in primary sensory neurons

Primary sensory neurons serve a dual role as afferent neurons, conveying sensory information from the periphery to the central nervous system, and as efferent effectors mediating, e.g., neurogenic inflammation. Neuropeptides are crucial for both these mechanisms in primary sensory neurons. In afferent functions, they act as messengers and modulators in addition to a principal transmitter; by release from peripheral terminals, they induce an efferent response, “neurogenic inflammation,” which comprises vasodilatation, plasma extravasation, and recruitment of immune cells. In this article, we introduce two novel members of the sensory neuropeptide family: pituitary adenylate cyclase-activating polypeptide (PACAP) and islet amyloid polypeptide (IAPP). Whereas PACAP, a vasoactive intestinal polypeptide-resembling peptide, predominantly occurs in neuronal elements, IAPP, which is structurally related to calcitonin gene-related peptide, is most widely known as a pancreatic β-cell peptide; as such, it has been recognized as a constituent of amyloid deposits in type 2 diabetes. In primary sensory neurons, under normal conditions, both peptides are predominantly expressed in small-sized nerve cell bodies, suggesting a role in nociception. On axotomy, the expression of PACAP is rapidly induced, whereas that of IAPP is reduced. Such a regulation of PACAP suggests that it serves a protective role during nerve injury, but that of IAPP may indicate that it is an excitatory messenger under normal conditions. In contrast, in localized adjuvant-induced inflammation, expression of both peptides is rapidly induced. For IAPP, studies in IAPP-deficient mice support the notion that IAPP is a pronociceptive peptide, because these mutant mice display a reduced nociceptive response when challenged with formalin.     

Identification of head motions by central vestibular neurons receiving linear and angular input

Most naturally occurring displacements of the head in space, due to either an external perturbation of the body or a self-generated, volitional head movement, apply both linear and angular forces to the head. The vestibular system detects linear and angular accelerations of the head separately, but the succeeding control of gaze and posture often relies upon the combined processing of linear and angular motion information. Thus, the output of a secondary neuron may reflect the linear, the angular, or both components of the head motion. Although the vestibular system is typically studied in terms of separate responses to linear and angular acceleration of the head, many secondary and higher-order neurons in the vestibular system do, in fact, receive information from both sets of motion sensors. The present paper develops methods to analyze responses of neurons that receive both types of information, and focuses on responses to sinusoidal motions composed of a linear and an angular component. We show that each neuron has a preferred motion, but a single neuron cannot code for a single motion. However, a pair of neurons can code for a motion by the relative phases of firing-rate modulation. In this way, information about motion is enhanced by neurons combining information about linear and angular motion. Received: 5 November 1998 / Accepted in revised form: 19 March 1999     

Sensory processing and the network mechanisms for reading neuronal population codes

In many neuronal systems, information appears to be represented in the activity of populations of neurons. Such neuronal population codes must also be read out, or interpreted, by downstream networks. Recent studies in both vertebrate and invertebrate systems have begun to elucidate some of the general mechanisms underlying these processes. Directed behaviors, that involve a directional response to a directional sensory input, have been a particularly useful context for these studies because, among other things, their input-output relationship is easily defined and experimentally controlled. We have recently shown that the neuronal network underlying a directed behavior in the medicinal leech utilizes a specific population coding scheme based on a neuronal population vector. A population vector of mechanosensory neuron activity correlates well with behavioral output and the connectivity of the downstream network is well suited for accurately reading out this population code. Accepted: 17 April 1999     

The mechanism of rate remapping in the dentate gyrus

Rate remapping is a recently revealed neural code in which sensory information modulates the firing rate of hippocampal place cells. The mechanism underlying rate remapping is unknown. Its characteristic modulation, however, must arise from the interaction of the two major inputs to the hippocampus, the medial entorhinal cortex (MEC), in which grid cells represent the spatial position of the rat, and the lateral entorhinal cortex (LEC), in which cells represent the sensory properties of the environment. We have used computational methods to elucidate the mechanism by which this interaction produces rate remapping. We show that the convergence of LEC and MEC inputs, in conjunction with a competitive network process mediated by feedback inhibition, can account quantitatively for this phenomenon. The same principle accounts for why different place fields of the same cell vary independently as sensory information is altered. Our results show that rate remapping can be explained in terms of known mechanisms.     

How do bees learn and recognize visual patterns?

The basic task of perceptual systems is the recognition and localization of objects. The central nervous system has to solve these problems on the basis of the excitation patterns of sensory nerves, in spite of the fact that these provide only ambiguous information about objects. Two processing principles seem to be fundamental for an efficient formation of object representations: the extraction of characteristic features and the ability to assess similarities between different objects. This article reviews investigations in which different training paradigms were applied in order to explore the honeybee's capacities to learn and recognize visual patterns. One aim of these experiments is to assess whether insects use similar processing mechanisms as vertebrates, for instance human beings. By comparing the computational performance of perceptual systems in animals with different evolutionary history we can hope to learn more about the operation of basic rules in nervous systems. “The messages which the brain receives have not the least similarity with the stimuli. They consist in pulses of given intensities and frequencies, characteristic for the transmitting nerve-fiber, which ends at a definite place of the cortex. ... From this information it produces the image of the world by a process which can metaphorically be called a consummate piece of combinatorial mathematics: it sorts out of the maze of indifferent and varying signals, invariant shapes and relations which form the world of ordinary experience.” Max Born (1949) Received: 4 October 1997 / Accepted in revised form: 26 August 1998