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Exactly 100 years ago, Louis Lapicque published a paper on the excitability of nerves that is often cited in the context of integrate-and-fire neurons. We discuss Lapicque’s contributions along with a translation of the original publication. [ABSTRACT FROM AUTHOR]

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions have been reported, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these 'historical' graphs, both in their directed (original) and symmetrized (a common preprocessing step) forms, and provide a set of measures that can be consistently applied across graphs (directed or undirected, with or without self-loops). We focus on simple structural characterizations of network connectivity and find that in many measures, the networks studied are captured by simple random graph models. In a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in the networks studied is not well captured by existing abstract graph models in their first- and second-order connectivity. [ABSTRACT FROM AUTHOR]

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections. [ABSTRACT FROM AUTHOR]

Lateral inhibition is a well documented aspect of neural architecture in the main sensory systems. Existing accounts of lateral inhibition focus on its role in sharpening distinctions between inputs that are closely related. However, these accounts fail to explain the functional role of inhibition in cortical columns, such as those in V1, where neurons have similar response properties. In this paper, we outline a model of position tracking using cortical columns of integrate-and-fire and Hodgkin-Huxley-type neurons which respond optimally to a particular location, to show that negatively correlated firing patterns arise from lateral inhibition in cortical columns and that this provides a clear benefit for population coding in terms of stability, accuracy, estimation time and neural resources. [ABSTRACT FROM AUTHOR]

Biological data suggests that activity patterns emerging in small- and large-scale neural systems may play an important role in performing the functions of the neural system, and in particular, neural computations. It is proposed in this paper that neural systems can be understood in terms of pattern computation and abstract communication systems theory. It is shown that analysing high-resolution surface EEG data, it is possible to determine abstract probabilistic rules that describe how emerging activity patterns follow earlier activity patterns. The results indicate the applicability of the proposed approach for understanding the working of complex neural systems. [ABSTRACT FROM AUTHOR]

The mechanical complexities of rotating an object through the gravity field present a formidable challenge to the human central nervous system (CNS). The current study documents the finger force patterns selected by the CNS when performing one-, two-, and four-finger grasping while holding an object statically at various orientations with respect to vertical. Numerous mechanically ‘‘unnecessary’’ behaviors were observed. These included: nonzero tangential forces for horizontal handle orientations, large internal forces (i.e., those in excess of equilibrium requirements) for all orientations, and safety margins between 50 and 90%. Additionally, none of the investigated measures were constant across orientations or could be represented as a simple trigonometric function of orientation. Nonetheless, all measures varied in systematic (and sometimes symmetric) ways with orientation. The results suggest that the CNS selects force patterns that are based on mechanical principles but also that are not simply related to object orientation. This study is complemented by a second paper that provides an in-depth analysis of the mechanics of nonvertical grasping and accounts for many of the observed results with numerical optimization (see Part II - current issue). Together, the papers demonstrate that the CNS is likely to utilize optimization processes when controlling prehensile actions. [ABSTRACT FROM AUTHOR]

Abstract. This paper presents a handwriting generation model that takes advantage of the asymptotic impulse response of neuromuscular networks to produce and control complex two-dimensional synergistic movements. A parametric definition of a ballistic stroke in the context of the kinematic theory of rapid human movements is given. Two types of parameters are used: command and system parameters. The first group provides a representation of the action plan while the second takes into account the temporal properties of the neuromuscular systems executing that plan. Handwriting is described as the time superimposition of basic discontinuous strokes that results in a continuous summation of delta-lognormal velocity vectors. The model leads to trajectory reconstruction, both in the spatial and in the kinematic domain. According to this new paradigm, the angular velocity does not have to be controlled independently and continuously; it naturally emerges from the vectorial summation process. Several psychophysical phenomena related to two-dimensional movements are explained and analyzed in the context of the model: the speed/accuracy tradeoffs, spatial scaling, the isochrony principle, the two-thirds power law, effector independence, etc. The overall approach also shows how basic handwriting characteristics (dimension, slant, baseline, shape, etc.) are affected and controlled using an action plan made up of virtual targets fed into a neuromuscular synergy that is governed by a delta-lognormal law. [ABSTRACT FROM AUTHOR]

Abstract. Presented in this paper is a neural network model that can be used to investigate the possible sell-organizing mechanisms occurring during the early ontogeny of spinal neural circuits in the vertebrate motor system. The neural circuit is composed of multiple types of neurons which correspond to motorneurons, Renshaw cells and a hypothetical class of interneurons. While the connectivity of this circuit is genetically predetermined, the efficacies of these connections - the synaptic strengths evolve in accordance with activity-dependent mechanisms which are initiated by the intrinsic, autonomous activity present in the developing spinal cord. Using Oja's rule, a modified Hebbian learning scheme for adjusting the values of the connections, the network stably self-organizes developing, in the process, reciprocally activated motorneuron pools analogous to those which exist in vive. [ABSTRACT FROM AUTHOR]

Oscillatory activity is ubiquitous in nervous systems, with solid evidence that synchronisation mechanisms underpin cognitive processes. Nevertheless, its informational content and relationship with behaviour are still to be fully understood. In addition, cognitive systems cannot be properly appreciated without taking into account brain-body- environment interactions. In this paper, we developed a model based on the Kuramoto Model of coupled phase oscillators to explore the role of neural synchronisation in the performance of a simulated robotic agent in two different minimally cognitive tasks. We show that there is a statistically significant difference in performance and evolvability depending on the synchronisation regime of the network. In both tasks, a combination of information flow and dynamical analyses show that networks with a definite, but not too strong, propensity for synchronisation are more able to reconfigure, to organise themselves functionally and to adapt to different behavioural conditions. The results highlight the asymmetry of information flow and its behavioural correspondence. Importantly, it also shows that neural synchronisation dynamics, when suitably flexible and reconfigurable, can generate minimally cognitive embodied behaviour. [ABSTRACT FROM AUTHOR]

A fundamental problem in neuroscience, to which Prof. Segundo has made seminal contributions, is to understand how action potentials represent events in the external world. The aim of this paper is to review the issue of neural coding in the context of the rodent whiskers, an increasingly popular model system. Key issues we consider are: the role of spike timing; mechanisms of spike timing; decoding and context-dependence. Significant insight has come from the development of rigorous, information theoretic frameworks for tackling these questions, in conjunction with suitably designed experiments. We review both the theory and experimental studies. In contrast to the classical view that neurons are noisy and unreliable, it is becoming clear that many neurons in the subcortical whisker pathway are remarkably reliable and, by virtue of spike timing with millisecond-precision, have high bandwidth for conveying sensory information. In this way, even small (~200 neuron) subcortical modules are able to support the sensory processing underlying sophisticated whisker-dependent behaviours. Future work on neural coding in cortex will need to consider new findings that responses are highly dependent on context, including behavioural and internal states. [ABSTRACT FROM AUTHOR]

Parameters in diffusion neuronal models are divided into two groups; intrinsic and input parameters. Intrinsic parameters are related to the properties of the neuronal membrane and are assumed to be known throughout the paper. Input parameters characterize processes generated outside the neuron and methods for their estimation are reviewed here. Two examples of the diffusion neuronal model, which are based on the integrate-and-fire concept, are investigated—the Ornstein–Uhlenbeck model as the most common one and the Feller model as an illustration of state-dependent behavior in modeling the neuronal input. Two types of experimental data are assumed—intracellular describing the membrane trajectories and extracellular resulting in knowledge of the interspike intervals. The literature on estimation from the trajectories of the diffusion process is extensive and thus the stress in this review is set on the inference made from the interspike intervals. [ABSTRACT FROM AUTHOR]

The Hodgkin–Huxley (HH) neuron is a nonlinear system with two stable states: A fixed point and a limit cycle. Both of them co-exist. The behavior of this neuron can be switched between these two equilibria, namely spiking and resting respectively, by using a perturbation method. The change from spiking to resting is named Spike Annihilation, and the transition from resting to spiking is named Spike Generation. Our intention is to determine if the HH neuron in 2D is controllable (i.e., if it can be driven from a quiescent state to a spiking state and vice versa). It turns out that the general system is unsolvable.1 In this paper, first of all,2 we analytically prove the existence of a brief current pulse, which, when delivered to the HH neuron during its repetitively firing state, annihilates its spikes. We also formally derive the characteristics of this brief current pulse. We then proceed to explore experimentally, by using numerical simulations, the properties of this pulse, namely the range of time when it can be inserted (the minimum phase and the maximum phase), its magnitude, and its duration. In addition, we study the solution of annihilating the spikes by using two successive stimuli, when the first is, of its own, unable to annihilate the neuron. Finally, we investigate the inverse problem of annihilation, namely the spike generation problem, when the neuron switches from resting to firing. [ABSTRACT FROM AUTHOR]

The paper introduces mirror neuron system II (MNS2), a new version of the MNS model (Oztop and Arbib in Biol Cybern 87 (2):116–140, 2002) of action recognition learning by mirror neurons of the macaque brain. The new model uses a recurrent architecture that is biologically more plausible than that of the original model. Moreover, MNS2 extends the capacity of the model to address data on audio-visual mirror neurons and on the response of mirror neurons when the target object was recently visible but is currently hidden. [ABSTRACT FROM AUTHOR]

Rhythmic body motions observed in animal locomotion are known to be controlled by neuronal circuits called central pattern generators (CPGs). It appears that CPGs are energy efficient controllers that cooperate with biomechanical and environmental constraints through sensory feedback. In particular, the CPGs tend to induce rhythmic motion of the body at a natural frequency, i.e., the CPGs are entrained to a mechanical resonance by sensory feedback. The objective of this paper is to uncover the mechanism of entrainment resulting from the dynamic interaction of the CPG and mechanical system. We first develop multiple CPG models for the reciprocal inhibition oscillator (RIO) and examine through numerical experiments whether they can be entrained to a simple pendulum. This comparative study identifies the neuronal properties essential for the entrainment. We then analyze the simplest model that captures the essential dynamics via the method of harmonic balance. It is shown that robust entrainment results from a strong, positive-feedback coupling of a lightly damped mechanical system and the RIO consisting of neurons with the complete adaptation property [ABSTRACT FROM AUTHOR]

This paper describes a neuro-musculo-skeletal model of the human lower body which has been developed with the aim of studying the effects of spinal cord injury on locomotor abilities. The model represents spinal neural control modules corresponding to central pattern generators, muscle spindle based reflex pathways, golgi tendon organ based pathways and cutaneous reflex pathways, which are coupled to the lower body musculo-skeletal dynamics. As compared to other neuro-musculo-skeletal models which aim to provide a description of the possible mechanisms involved in the production of locomotion, the goal of the model here is to understand the role of the known spinal pathways in locomotion. Thus, while other models focus primarily on functionality at the overall system level, the model here emphasizes functional and topological correspondance with the biological system at the level of the subcomponents representing spinal pathways. Such a model is more suitable for the detailed investigation of clinical questions related to spinal control of locomotion. The model is used here to perform preliminary experiments addressing the following issues: (1) the significance of spinal reflex modalities for walking and (2) the relative criticality of the various reflex modalities. The results of these experiments shed new light on the possible role of the reflex modalities in the regulation of stance and walking speed. The results also demonstrate the use of the model for the generation of hypothesis which could guide clinical experimentation. In the future, such a model may have applications in clinical diagnosis, as it can be used to identify the internal state of the system which provides the closest behavioral fit to a patient’s pathological condition. [ABSTRACT FROM AUTHOR]

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons. [ABSTRACT FROM AUTHOR]

Principal components analysis (PCA) has not been very much in vogue within the field of movement coordination even though it is useful to reduce data dimensionality and to reveal underlying data structures. Traditionally, studies of coordination between two joints have predominantly made use of relative phase analyses. This has resulted in the identification of principal constraints that govern the Central Nervous System’s organization and the control of coordination patterns. However, relative phase analyses on pairwise joints have some drawbacks because they are not optimal for revealing convergent patterns among multijoint coordination modes and for unraveling generic control strategies. In this paper, we present a method to analyze multijoint coordination based on the properties of PC, more specifically the eigenvalues and eigenvectors of the covariance matrix. The comparison between relative phase analysis and PCA shows that both provide similar and consistent results, underscoring the latter technique’s sensitivity to the study of coordination performance. In addition, it provides a method for automatic pattern detection as well as an index of performance for each joint within the context of the global coordination pattern. Finally, the merit of the PCA technique within the context of central pattern generators (CPG) will be discussed. [ABSTRACT FROM AUTHOR]

In the present paper, we propose a novel neural procedure for signal processing and coding based on the subthreshold oscillations and resonance of the neural membrane potential that could be used by real neurons to perform frequency spectra analysis and information coding of incoming signals. Taking into account the biophysical properties of the neural membranes, we note that the subthreshold resonant behaviour they exhibit can be used to analyse incoming signals and represent them in the frequency domain. We study the reliability of the representation of signals depending on the biophysical parameters of the neurons, the fault-tolerance of this coding scheme and its robustness against noise and in the presence of spikes. The principal characteristics of our system are the use of the physical phenomenon of neural resonance (rarely considered in the literature for signal coding); it fits well with the biophysical parameters of most neurons that exhibit subthreshold oscillations; it is compatible with experimental data; and it can be easily integrated in a more general model of information processing and coding that includes communication between neurons based on spikes. [ABSTRACT FROM AUTHOR]

Abstract. Secondary vestibular neurons exhibit a wide variety of responses to a head movement, with the response of each secondary neuron depending upon the particular primary afferents converging onto it. A single head movement is thereby registered in a distributed manner. This paper focuses on implications of afferent convergence to the relative timing of secondary neuron response modulation during rotational movements about a combination of horizontal axes. In particular, the neurons of interest are those that receive input from afferents innervating the vertical semicircular canals, and the movements of interest are those that have a sinusoidal component about one vertical canal axis and a sinusoidal component about another, approximately orthogonal, vertical canal axis. Under these conditions, the present research shows that it is possible for two or more secondary neurons to have a different relative timing of response (i.e., different relative phase of the periodic modulation in firing rate) for different head movements, and for the neurons to switch their order of response for different movements. For particular head movements, those same neurons will respond in phase. From the point of view of the nervous system, the relative timing of neuron responses may tell which movement is taking place, but with certain restrictions as discussed in the present paper. Shown here is that, among those head movements for which the two components of rotation may be at any phase relative to one another and have any relative amplitude, an in-phase response of just two neurons cannot identify a... [ABSTRACT FROM AUTHOR]

Abstract. It has been well established that extra-retinal information is used in the perception of visual direction and distance. Furthermore, a number of studies have established that both efference copy and afferent discharge contribute to the extra-retinal signal. Despite this, no model currently exists to explain how the signals which arise through oculomotor control contribute to perception. This paper attempts to provide such a framework. The first part of the paper outlines the framework [the cyclopean equilibrium point (EP) model] and considers the binoculus or cyclopean eye from the perspective of a current account of motor control (the EP hypothesis). An existing model is used to describe how the nervous system could utilise available efference copy and afferent extra retinal signals when determining the direction and distance of cyclopean fixation. Although the cyclopean EP model is speculative, it allows for a parsimonious framework when considering the oculomotor contribution to perception. The model has the additional advantage of being consistent with current theories regarding the control and perception of limb movement. The second part of the paper shows that the model is biologically plausible, demonstrates the use of the proposed model in describing the central control of eye movements with regard to non-conjugate peripheral adaptation and reconciles seemingly disparate empirical findings. [ABSTRACT FROM AUTHOR]

Abstract. In a previous paper [Kilmer (1996) Neural Netw 9:567 573] we developed a differential equation model of how a stable focus of attention could be maintained in a higher mammalian brain. The so-called TRC model consisted of interconnected modules, with each module comprised of a simple representations of parts of the reticular thalamic nucleus, specific thalamic nuclei, nonspecific thalamic nuclei, and cortex, together with the known excitatory and inhibitory interconnections between them. TRC was analyzed only for steady states under zero inputs. Here we analyze the behavior of TRC_2, a substantially modified and reinterpreted TRC, for steady attention and attention-switching behavior under nonzero inputs. We show that TRC_2 always converges to a unique mode of primary attention, and that it allows concurrently one or more other modes of weak attention, which experience suggests occurs often. A crucial postulate for TRC_2 is that a mode alpha does not actively compete against other modes unless primary attention is paid to mode alpha. This postulate should be testable experimentally. [ABSTRACT FROM AUTHOR]

Detection of looming obstacles is a vital task for both natural and artificial systems. Locusts possess a visual nervous system with an extensively studied obstacle detection pathway, culminating in the lobula giant movement detector (LGMD) neuron. While numerous models of this system exist, none to date have incorporated recent data on the anatomy and function of feedforward and global inhibitory systems in the input network of the LGMD. Moreover, the possibility that global and lateral inhibition shape the feedforward inhibitory signals to the LGMD has not been investigated. To address these points, a novel model of feedforward inhibitory neurons in the locust optic lobe was developed based on the recent literature. This model also incorporated global and lateral inhibition into the afferent network of these neurons, based on their observed behaviour in existing data and the posited role of these mechanisms in the inputs to the LGMD. Tests with the model showed that it accurately replicates the behaviour of feedforward inhibitory neurons in locusts; the model accurately coded for stimulus angular size in an overall linear fashion, with decreasing response saturation and increasing linearity as stimulus size increased or approach velocity decreased. The model also exhibited only phasic responses to the appearance of a grating, along with sustained movement by it at constant speed. By observing the effects of altering inhibition schemes on these responses, it was determined that global inhibition serves primarily to normalize growing excitation as collision approaches, and keeps coding for subtense angle linear. Lateral inhibition was determined to suppress tonic responses to wide-field stimuli translating at constant speed. Based on these features being shared with characterizations of the LGMD input network, it was hypothesized that the feedforward inhibitory neurons and the LGMD share the same excitatory afferents; this necessitates further investigation. [ABSTRACT FROM AUTHOR]

Animals exhibit remarkable feats of behavioral flexibility and multifunctional control that remain challenging for robotic systems. The neural and morphological basis of multifunctionality in animals can provide a source of bioinspiration for robotic controllers. However, many existing approaches to modeling biological neural networks rely on computationally expensive models and tend to focus solely on the nervous system, often neglecting the biomechanics of the periphery. As a consequence, while these models are excellent tools for neuroscience, they fail to predict functional behavior in real time, which is a critical capability for robotic control. To meet the need for real-time multifunctional control, we have developed a hybrid Boolean model framework capable of modeling neural bursting activity and simple biomechanics at speeds faster than real time. Using this approach, we present a multifunctional model of Aplysia californica feeding that qualitatively reproduces three key feeding behaviors (biting, swallowing, and rejection), demonstrates behavioral switching in response to external sensory cues, and incorporates both known neural connectivity and a simple bioinspired mechanical model of the feeding apparatus. We demonstrate that the model can be used for formulating testable hypotheses and discuss the implications of this approach for robotic control and neuroscience. [ABSTRACT FROM AUTHOR]

Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm. [ABSTRACT FROM AUTHOR]

Motor synergies have been investigated since the 1980s as a simplifying representation of motor control by the nervous system. This way of representing finger positional data is in particular useful to represent the kinematics of the human hand. Whereas, so far, the focus has been on kinematic synergies, that is common patterns in the motion of the hand and fingers, we hereby also investigate their force aspects, evaluated through surface electromyography (sEMG). We especially show that force-related motor synergies exist, i.e. that muscle activation during grasping, as described by the sEMG signal, can be grouped synergistically; that these synergies are largely comparable to one another across human subjects notwithstanding the disturbances and inaccuracies typical of sEMG; and that they are physiologically feasible representations of muscular activity during grasping. Potential applications of this work include force control of mechanical hands, especially when many degrees of freedom must be simultaneously controlled. [ABSTRACT FROM AUTHOR]

In the past years, several frequency-domain causality measures based on vector autoregressive time series modeling have been suggested to assess directional connectivity in neural systems. The most followed approaches are based on representing the considered set of multiple time series as a realization of two or three vector-valued processes, yielding the so-called Geweke linear feedback measures, or as a realization of multiple scalar-valued processes, yielding popular measures like the directed coherence (DC) and the partial DC (PDC). In the present study, these two approaches are unified and generalized by proposing novel frequency-domain causality measures which extend the existing measures to the analysis of multiple blocks of time series. Specifically, the block DC (bDC) and block PDC (bPDC) extend DC and PDC to vector-valued processes, while their logarithmic counterparts, denoted as multivariate total feedback $$f^\mathrm{m}$$ and direct feedback $$g^\mathrm{m}$$, represent into a full multivariate framework the Geweke's measures. Theoretical analysis of the proposed measures shows that they: (i) possess desirable properties of causality measures; (ii) are able to reflect either direct causality (bPDC, $$g^\mathrm{m})$$ or total (direct + indirect) causality (bDC, $$f^\mathrm{m})$$ between time series blocks; (iii) reduce to the DC and PDC measures for scalar-valued processes, and to the Geweke's measures for pairs of processes; (iv) are able to capture internal dependencies between the scalar constituents of the analyzed vector processes. Numerical analysis showed that the proposed measures can be efficiently estimated from short time series, allow to represent in an objective, compact way the information derived from the causal analysis of several pairs of time series, and may detect frequency domain causality more accurately than existing measures. The proposed measures find their natural application in the evaluation of directional interactions in neurophysiological settings where several brain activity signals are simultaneously recorded from multiple regions of interest. [ABSTRACT FROM AUTHOR]

In this study, we investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments with modified neural activity patterns in the prefrontal and perirhinal cortex regions. Our motivation for recovering this well-known learning prescription is two-fold: first, the switch-like nature of the induced synaptic bonds, as there is evidence that biological synaptic transitions might occur in a discrete stepwise fashion. Second, the possibility that in the mammalian brain, unused, silent synapses might be pruned in the long-term. Besides the usual pattern and network capacities, we calculate the synaptic capacity of the model, a recently proposed measure where only the functional subset of synapses is taken into account. We find that in terms of network capacity, Willshaw learning is strongly affected by the pattern coding rates, which have to be kept fixed and very low at any time to achieve a non-zero capacity in the large network limit. The information carried per functional synapse, however, diverges and is comparable to that of the pattern association case, even for more realistic moderately low activity levels that are a function of network size. [ABSTRACT FROM AUTHOR]

In the nervous system, the representation of signals is based predominantly on the rate and timing of neuronal discharges. In most everyday tasks, the brain has to carry out a variety of mathematical operations on the discharge patterns. Recent findings show that even single neurons are capable of performing basic arithmetic on the sequences of spikes. However, the interaction of the two spike trains, and thus the resulting arithmetic operation may be influenced by the stochastic properties of the interacting spike trains. If we represent the individual discharges as events of a random point process, then an arithmetical operation is given by the interaction of two point processes. Employing a probabilistic model based on detection of coincidence of random events and complementary computer simulations, we show that the point process statistics control the arithmetical operation being performed and, particularly, that it is possible to switch from subtraction to division solely by changing the distribution of the inter-event intervals of the processes. Consequences of the model for evaluation of binaural information in the auditory brainstem are demonstrated. The results accentuate the importance of the stochastic properties of neuronal discharge patterns for information processing in the brain; further studies related to neuronal arithmetic should therefore consider the statistics of the interacting spike trains. [ABSTRACT FROM AUTHOR]

In a noisy system, such as the nervous system, can movements be precisely controlled as experimentally demonstrated? We point out that the existing theory of motor control fails to provide viable solutions. However, by adopting a generalized approach to the nonconvex optimization problem with the Young measure theory, we show that a precise movement control is possible even with stochastic control signals. Numerical results clearly demonstrate that a considerable significant improvement of movement precisions is achieved. Our generalized approach proposes a new way to solve optimization problems in biological systems when a precise control is needed. [ABSTRACT FROM AUTHOR]

A mirror system is active both when an animal executes a class of actions (self-actions) and when it sees another execute an action of that class. Much attention has been given to the possible roles of mirror systems in responding to the actions of others but there has been little attention paid to their role in self-actions. In the companion article (Bonaiuto et al. Biol Cybern 96:9–38, 2007) we presented MNS2, an extension of the Mirror Neuron System model of the monkey mirror system trained to recognize the external appearance of its own actions as a basis for recognizing the actions of other animals when they perform similar actions. Here we further extend the study of the mirror system by introducing the novel hypotheses that a mirror system may additionally help in monitoring the success of a self-action and may also be activated by recognition of one’s own apparent actions as well as efference copy from one’s intended actions. The framework for this computational demonstration is a model of action sequencing, called augmented competitive queuing, in which action choice is based on the desirability of executable actions. We show how this “what did I just do?” function of mirror neurons can contribute to the learning of both executability and desirability which in certain cases supports rapid reorganization of motor programs in the face of disruptions. [ABSTRACT FROM AUTHOR]

The joint influence of recurrent feedback and noise on gain control in a network of globally coupled spiking leaky integrate-and-fire neurons is studied theoretically and numerically. The context of our work is the origin of divisive versus subtractive gain control, as mixtures of these effects are seen in a variety of experimental systems. We focus on changes in the slope of the mean firing frequency-versus-input bias ( f – I) curve when the gain control signal to the cells comes from the cells’ output spikes. Feedback spikes are modeled as alpha functions that produce an additive current in the current balance equation. For generality, they occur after a fixed minimum delay. We show that purely divisive gain control, i.e. changes in the slope of the f – I curve, arises naturally with this additive negative or positive feedback, due to a linearizing actions of feedback. Negative feedback alone lowers the gain, accounting in particular for gain changes in weakly electric fish upon pharmacological opening of the feedback loop as reported by Bastian (J Neurosci 6:553–562, 1986). When negative feedback is sufficiently strong it further causes oscillatory firing patterns which produce irregularities in the f – I curve. Small positive feedback alone increases the gain, but larger amounts cause abrupt jumps to higher firing frequencies. On the other hand, noise alone in open loop linearizes the f – I curve around threshold, and produces mixtures of divisive and subtractive gain control. With both noise and feedback, the combined gain control schemes produce a primarily divisive gain control shift, indicating the robustness of feedback gain control in stochastic networks. Similar results are found when the “input” parameter is the contrast of a time-varying signal rather than the bias current. Theoretical results are derived relating the slope of the f – I curve to feedback gain and noise strength. Good agreement with simulation results are found for inhibitory and excitatory feedback. Finally, divisive feedback is also found for conductance-based feedback (shunting or excitatory) with and without noise. [ABSTRACT FROM AUTHOR]

Sound localization requires comparison between the inputs to the left and right ears. One important aspect of this comparison is the differences in arrival time to each side, also called interaural time difference (ITD). A prevalent model of ITD detection, consisting of delay lines and coincidence-detector neurons, was proposed by Jeffress (J Comp Physiol Psychol 41:35–39, 1948). As an extension of the Jeffress model, the process of detecting and encoding ITD has been compared to an effective cross-correlation between the input signals to the two ears. Because the cochlea performs a spectrotemporal decomposition of the input signal, this cross-correlation takes place over narrow frequency bands. Since the cochlear tonotopy is arranged in series, sounds of different frequencies will trigger neural activity with different temporal delays. Thus, the matching of the frequency tuning of the left and right inputs to the cross-correlator units becomes a ‘timing’ issue. These properties of auditory transduction gave theoretical support to an alternative model of ITD-detection based on a bilateral mismatch in frequency tuning, called the ‘stereausis’ model. Here we first review the current literature on the owl’s nucleus laminaris, the equivalent to the medial superior olive of mammals, which is the site where ITD is detected. Subsequently, we use reverse correlation analysis and stimulation with uncorrelated sounds to extract the effective monaural inputs to the cross-correlator neurons. We show that when the left and right inputs to the cross-correlators are defined in this manner, the computation performed by coincidence-detector neurons satisfies conditions of cross-correlation theory. We also show that the spectra of left and right inputs are matched, which is consistent with predictions made by the classic model put forth by Jeffress. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An important problem in neuroscience is to obtain quantitative knowledge of how information is represented, or encoded, in the signals that nerve cells process and transmit. Sensory receptors have provided important models for the study of neural coding because their inputs can often be relatively easily controlled and measured, while the resultant activity is recorded. A variety of engineering concepts have been successfully applied to physiological sciences, particularly those related to control of dynamic systems. Linear systems analysis was one of the earliest methods used to probe sensory coding, and measurements such as step responses and frequency responses have become standard tools for describing sensory functions. Modern systems analysis has evolved to provide accurate and efficient linear identification of encoding in sensory receptors that use either graded potentials or action potentials. It has also led to nonlinear systems analysis, the creation of parametric nonlinear models, and measures of information coding by sensory neurons. These methods promise to provide important new knowledge about sensory systems in the future, especially when complemented with parallel biophysical and molecular studies of sensory neurons. Mechanoreceptors provided some of the earliest preparations for the investigation of neural coding, and both the linear and nonlinear properties of wide variety of vertebrate and invertebrate mechanoreceptors continue to be explored. [ABSTRACT FROM AUTHOR]

Reduced models have long been used as a tool for the analysis of the complex activity taking place in neurons and their coupled networks. Recent advances in experimental and theoretical techniques have further demonstrated the usefulness of this approach. Despite the often gross simplification of the underlying biophysical properties, reduced models can still present significant difficulties in their analysis, with the majority of exact and perturbative results available only for the leaky integrate-and-fire model. Here an elementary numerical scheme is demonstrated which can be used to calculate a number of biologically important properties of the general class of non-linear integrate-and-fire models. Exact results for the first-passage-time density and spike-train spectrum are derived, as well as the linear response properties and emergent states of recurrent networks. Given that the exponential integrate-fire model has recently been shown to agree closely with the experimentally measured response of pyramidal cells, the methodology presented here promises to provide a convenient tool to facilitate the analysis of cortical-network dynamics. [ABSTRACT FROM AUTHOR]

The dynamic I– V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons. [ABSTRACT FROM AUTHOR]

The increase in complexity of computational neuron models makes the hand tuning of model parameters more difficult than ever. Fortunately, the parallel increase in computer power allows scientists to automate this tuning. Optimization algorithms need two essential components. The first one is a function that measures the difference between the output of the model with a given set of parameter and the data. This error function or fitness function makes the ranking of different parameter sets possible. The second component is a search algorithm that explores the parameter space to find the best parameter set in a minimal amount of time. In this review we distinguish three types of error functions: feature-based ones, point-by-point comparison of voltage traces and multi-objective functions. We then detail several popular search algorithms, including brute-force methods, simulated annealing, genetic algorithms, evolution strategies, differential evolution and particle-swarm optimization. Last, we shortly describe Neurofitter, a free software package that combines a phase–plane trajectory density fitness function with several search algorithms. [ABSTRACT FROM AUTHOR]

Most simple neuron models are only able to model traditional spiking behavior. As physiologists discover and classify different electrical phenotypes, computational neuroscientists become interested in using simple phenomenological models that can exhibit these different types of spiking patterns. The Hindmarsh–Rose model is a three-dimensional relaxation oscillator which can show both spiking and bursting patterns and has a chaotic regime. We test the predictive powers of the Hindmarsh–Rose model on two different test databases. We show that the Hindmarsh–Rose model can predict the spiking response of rat layer 5 neocortical pyramidal neurons on a stochastic input signal with a precision comparable to the best known spiking models. We also show that the Hindmarsh–Rose model can capture qualitatively the electrical footprints in a database of different types of neocortical interneurons. When the model parameters are fit from sub-threshold measurements only, the model still captures well the electrical phenotype, which suggests that the sub-threshold signals contain information about the firing patterns of the different neurons. [ABSTRACT FROM AUTHOR]

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations. [ABSTRACT FROM AUTHOR]

The mushroom body is a prominent invertebrate neuropil strongly associated with learning and memory. We built a high-level computational model of this structure using simplified but realistic models of neurons and synapses, and developed a learning rule based on activity dependent pre-synaptic facilitation. We show that our model, which is consistent with mushroom body Drosophila data and incorporates Aplysia learning, is able to both acquire and later recall CS–US associations. We demonstrate that a highly divergent input connectivity to the mushroom body and strong periodic inhibition both serve to improve overall learning performance. We also examine the problem of how synaptic conductance, driven by successive training events, obtains a value appropriate for the stimulus being learnt. We employ two feedback mechanisms: one stabilises strength at an initial level appropriate for an association; another prevents strength increase for established associations. [ABSTRACT FROM AUTHOR]

Stable signal transmission is crucial for information processing by the brain. Synfire-chains, defined as feed-forward networks of spiking neurons, are a well-studied class of circuit structure that can propagate a packet of single spikes while maintaining a fixed packet profile. Here, we studied the stable propagation of spike bursts, rather than single spike activities, in a feed-forward network of a general class of excitable bursting neurons. In contrast to single spikes, bursts can propagate stably without converging to any fixed profiles. Spike timings of bursts continue to change cyclically or irregularly during propagation depending on intrinsic properties of the neurons and the coupling strength of the network. To find the conditions under which bursts lose fixed profiles, we propose an analysis based on timing shifts of burst spikes similar to the phase response analysis of limit-cycle oscillators. [ABSTRACT FROM AUTHOR]

The self-organizing map (SOM) algorithm produces artificial neural maps by simulating competition and cooperation among neurons. We study the consequences of input background activity on simulated self-organization, using the SOM, of the retinotopic map in the superior colliculus. The colliculus not only represents its inputs but also uses them to localize saccadic targets. Using the colliculus as a test-bed enables us to quantify the results of self- organization both descriptively, in terms of input–output mutual information, and functionally, in terms of the probability of error (expected distortion) in localizing targets. We find that mutual information is low, and distortion is high, when the SOM operates in the presence of input background activity but without the cooperative component (no neighbor training). Cooperation (training neighbors) greatly increases mutual information and greatly decreases expected distortion. Our simulation results extend theoretical work suggesting that cooperative mechanisms are needed to increase the information content of neural representations. They also identify input background activity as a factor affecting the self-organization of information-transmitting channels in the nervous system. [ABSTRACT FROM AUTHOR]

Evoked potentials are the transient electrical responses caused by changes in the brain following stimuli. This work uses a physiology-based continuum model of neuronal activity in the human brain to calculate theoretical cortical auditory evoked potentials (CAEPs) from the model’s linearized response. These are fitted to experimental data, allowing the fitted parameters to be related to brain physiology. This approach yields excellent fits to CAEP data, which can then be compared to fits of EEG spectra. It is shown that the differences between resting eyes-open EEG and standard CAEPs can be explained by changes in the physiology of populations of neurons in corticothalamic pathways, with notable similarities to certain aspects of slow-wave sleep. This pilot study demonstrates the ability of our model-based fitting method to provide information on the underlying physiology of the brain that is not available using standard methods. [ABSTRACT FROM AUTHOR]

Functional magnetic resonance imaging (fMRI) was used to assess the contributions of movement preparation and execution of a visuomotor task in a cerebral motor network. The functional connectivity of the voxel time series between brain regions in the frequency space was investigated by performing spectral analysis of fMRI time series. The regional interactivities between the two portions of the supplementary motor area (pre-SMA and SMA-proper) and the primary motor cortex (M1), defined as a seed region, were evaluated. The spectral parameter of coherence was used to describe a correlation structure in the frequency domain between two voxel-based time series and to infer the strength of the functional interaction within our presumed motor network of connections. The results showed meaningful differences of the functional interactions between the two portions of the SMA and the M1 area depending on the task conditions. This approach demonstrated the existence of a functional dissociation between the pre-SMA and SMA-proper subregions. We therefore conclude that spectral analysis is useful for identifying functional interactions of brain regions and might provide a powerful tool to quantify changes in connectivity profiles associated with various components of an experimental task. [ABSTRACT FROM AUTHOR]

A recent continuum model of the large scale electrical activity of the cerebral cortex is generalized to include cholinergic modulation. In this model, dynamic modulation of synaptic strength acts over the time scales of nicotinic and muscarinic receptor action. The cortical model is analyzed to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses to changes in subcortical input. ACh increases the firing rate in steady states of the system. Changing ACh concentration does not introduce oscillatory behavior into the system, but increases the overall spectral power. Model responses to pulses in subcortical input are affected by the tonic level of ACh concentration, with higher levels of ACh increasing the magnitude firing rate response of excitatory cortical neurons to pulses of subcortical input. Numerical simulations are used to explore the temporal dynamics of the model in response to changes in ACh concentration. Evidence is seen of a transition from a state in which intracortical inputs are emphasized to a state where thalamic afferents have enhanced influence. Perturbations in ACh concentration cause changes in the firing rate of cortical neurons, with rapid responses due to fast acting facilitatory effects of nicotinic receptors on subcortical afferents, and slower responses due to muscarinic suppression of intracortical connections. Together, these numerical simulations demonstrate that the actions of ACh could be a significant factor modulating early components of evoked response potentials. [ABSTRACT FROM AUTHOR]

The article highlights various quantitative investigations of electrical nerve excitation treated as polarization. The term polarization was vague until the study of W. Nerst gave it a foundation based on chemical physics. As Nernst has remarked, semi-permeable membranes placed in an electrolytic conductor can lead to a polarization.

We demonstrate that a previously presented flexible silicon–neuron architecture can implement three disparate conductance-based neuron models with both fast and slow dynamics. By exploiting the real-time nature of this physical implementation, we mapped the model dynamics across a large region of parameter space. We also found that two of these dynamically different models represent points in a contiguous bursting space that spans between the two models. By systematically varying the model parameters, we also found that multiple, diverse trajectories in parameter space connected the two canonical bursting points. In addition, we found that the combination of parameter values keeps the neuron in the bursting region. These findings demonstrate the usefulness of the silicon–neuron architecture as a neural-modeling tool and illustrate its versatility as a platform for a multi-behavioral neuron that resembles its living analog. [ABSTRACT FROM AUTHOR]

Accumulating evidence suggests that the plasticity of extrinsic thalamocortical inputs in cortical layer IV may be guided or instructed by earlier plasticity events in the intrinsic, horizontal connections within the extragranular cortical layers. We analyse a rate-based model of the plasticity of a set of extrinsic afferents in the presence of a pre-existing (and fixed) plexus of intrinsic, overall excitatory horizontal connections between a set of target neurons. We determine conditions under which afferent synaptic pattern formation respects this pre-existing lateral structure. We find three broad regimes under which extrinsic afferent plasticity may violate this structure: the initial pattern of extrinsic afferent innervation of the target cells is far from balanced; the gain of the extrinsic afferents greatly exceeds the overall scale of the strength of lateral excitation; the target cell horizontal coupling matrix is sparse. If none of these conditions is satisfied, then extrinsic afferent plasticity respects the pre-existing lateral connectivity, so that afferent synaptic pattern formation conforms to the pattern of lateral excitation. [ABSTRACT FROM AUTHOR]

We consider the issue of how to read out the information from nonstationary spike train ensembles. Based on the theory of censored data in statistics, we propose a ‘censored’ maximum-likelihood estimator (CMLE) for decoding the input in an unbiased way when the spike activity is observed over time windows of finite length. Compared with a rate-based, moment estimator, the CMLE is proved consistently more efficient, particularly with nonstationary inputs. Using our approach, we show that a dynamical input to a group of neurons can be inferred accurately and with high temporal resolution (50 ms) using as few as about one spike per neuron within each decoding window. By applying our theoretical results to a population coding setting, we then demonstrate that a spiking neural network can encode spatial information in such a way to allow fast and precise tracking of a moving target. [ABSTRACT FROM AUTHOR]

Many models of eyeblink conditioning assume that there is a simple linear relationship between the firing patterns of neurons in the interpositus nucleus and the time course of the conditioned response (CR). However, the complexities of muscle behaviour and plant dynamics call this assumption into question. We investigated the issue by implementing the most detailed model available of the rabbit nictitating membrane response (Bartha and Thompson in Biol Cybern 68:135–143, 1992a and in Biol Cybern 68:145–154, 1992b), in which each motor unit of the retractor bulbi muscle is represented by a Hill-type model, driven by a non-linear activation mechanism designed to reproduce the isometric force measurements of Lennerstrand (J Physiol 236:43–55, 1974). Globe retraction and NM extension are modelled as linked second order systems. We derived versions of the model that used a consistent set of SI units, were based on a physically realisable version of calcium kinetics, and used simulated muscle cross-bridges to produce force. All versions showed similar non-linear responses to two basic control strategies. (1) Rate-coding with no recruitment gave a sigmoidal relation between control signal and amplitude of CR, reflecting the measured relation between isometric muscle force and stimulation frequency. (2) Recruitment of similar strength motor units with no rate coding gave a sublinear relation between control signal and amplitude of CR, reflecting the increase in muscle stiffness produced by recruitment. However, the system response could be linearised by either a suitable combination of rate-coding and recruitment, or by simple recruitment of motor units in order of (exponentially) increasing strength. These plausible control strategies, either alone or in combination, would in effect present the cerebellum with the simplified virtual plant that is assumed in many models of eyeblink conditioning. Future work is therefore needed to determine the extent to which motor neuron firing is in fact linearly related to the nictitating membrane response. [ABSTRACT FROM AUTHOR]