The role of sensory network dynamics in generating a motor program

Neural manifold analysis of brain circuit dynamics in health and disease

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than those applicable to single-cell experiments. One approach that has gained recent popularity is neural manifold learning. This approach takes advantage of the fact that often, even though neural datasets may be very high dimensional, the dynamics of neural activity tends to traverse a much lower-dimensional space. The topological structures formed by these low-dimensional neural subspaces are referred to as "neural manifolds", and may potentially provide insight linking neural circuit dynamics with cognitive function and behavioral performance. In this paper we review a number of linear and non-linear approaches to neural manifold learning, including principal component analysis (PCA), multi-dimensional scaling (MDS), Isomap, locally linear embedding (LLE), Laplacian eigenmaps (LEM), t-SNE, and uniform manifold approximation and projection (UMAP). We outline these methods under a common mathematical nomenclature, and compare their advantages and disadvantages with respect to their use for neural data analysis. We apply them to a number of datasets from published literature, comparing the manifolds that result from their application to hippocampal place cells, motor cortical neurons during a reaching task, and prefrontal cortical neurons during a multi-behavior task. We find that in many circumstances linear algorithms produce similar results to non-linear methods, although in particular cases where the behavioral complexity is greater, non-linear methods tend to find lower-dimensional manifolds, at the possible expense of interpretability. We demonstrate that these methods are applicable to the study of neurological disorders through simulation of a mouse model of Alzheimer's Disease, and speculate that neural manifold analysis may help us to understand the circuit-level consequences of molecular and cellular neuropathology.

Integrated neural dynamics of sensorimotor decisions and actions

Recent theoretical models suggest that deciding about actions and executing them are not implemented by completely distinct neural mechanisms but are instead two modes of an integrated dynamical system. Here, we investigate this proposal by examining how neural activity unfolds during a dynamic decision-making task within the high-dimensional space defined by the activity of cells in monkey dorsal premotor (PMd), primary motor (M1), and dorsolateral prefrontal cortex (dlPFC) as well as the external and internal segments of the globus pallidus (GPe, GPi). Dimensionality reduction shows that the four strongest components of neural activity are functionally interpretable, reflecting a state transition between deliberation and commitment, the transformation of sensory evidence into a choice, and the baseline and slope of the rising urgency to decide. Analysis of the contribution of each population to these components shows meaningful differences between regions but no distinct clusters within each region, consistent with an integrated dynamical system. During deliberation, cortical activity unfolds on a two-dimensional "decision manifold" defined by sensory evidence and urgency and falls off this manifold at the moment of commitment into a choice-dependent trajectory leading to movement initiation. The structure of the manifold varies between regions: In PMd, it is curved; in M1, it is nearly perfectly flat; and in dlPFC, it is almost entirely confined to the sensory evidence dimension. In contrast, pallidal activity during deliberation is primarily defined by urgency. We suggest that these findings reveal the distinct functional contributions of different brain regions to an integrated dynamical system governing action selection and execution.

Robust dynamical invariants in sequential neural activity

By studying different sources of temporal variability in central pattern generator (CPG) circuits, we unveil fundamental aspects of the instantaneous balance between flexibility and robustness in sequential dynamics -a property that characterizes many systems that display neural rhythms. Our analysis of the triphasic rhythm of the pyloric CPG (Carcinus maenas) shows strong robustness of transient dynamics in keeping not only the activation sequences but also specific cycle-by-cycle temporal relationships in the form of strong linear correlations between pivotal time intervals, i.e. dynamical invariants. The level of variability and coordination was characterized using intrinsic time references and intervals in long recordings of both regular and irregular rhythms. Out of the many possible combinations of time intervals studied, only two cycle-by-cycle dynamical invariants were identified, existing even outside steady states. While executing a neural sequence, dynamical invariants reflect constraints to optimize functionality by shaping the actual intervals in which activity emerges to build the sequence. Our results indicate that such boundaries to the adaptability arise from the interaction between the rich dynamics of neurons and connections. We suggest that invariant temporal sequence relationships could be present in other networks, including those shaping sequences of functional brain rhythms, and underlie rhythm programming and functionality.

Dimensionality reduction in neuroscience

The nervous system extracts information from its environment and distributes and processes that information to inform and drive behaviour. In this task, the nervous system faces a type of data analysis problem, for, while a visual scene may be overflowing with information, reaching for the television remote before us requires extraction of only a relatively small fraction of that information. We could care about an almost infinite number of visual stimulus patterns, but we don't: we distinguish two actors' faces with ease but two different images of television static with significant difficulty. Equally, we could respond with an almost infinite number of movements, but we don't: the motions executed to pick up the remote are highly stereotyped and related to many other grasping motions. If we were to look at what was going on inside the brain during this task, we would find populations of neurons whose electrical activity was highly structured and correlated with the images on the screen and the action of localizing and picking up the remote.

Central nervous system transcriptome of Biomphalaria alexandrina, an intermediate host for schistosomiasis

Objective

Globally, more than 200 million people live at risk of the neglected tropical disease schistosomiasis (or snail fever). Larval schistosomes require the presence of specific snail species that act as intermediate hosts, supporting their multiplication and transformation into forms that can infect humans. This project was designed to generate a transcriptome from the central nervous system (CNS) of Biomphalaria alexandrina, the major intermediate host for Schistosoma mansoni in Egypt.

Results

A transcriptome was generated from five pooled central nervous systems dissected from uninfected specimens of B. alexandrina. Raw Illumina RNA-seq data (~ 20.3 million paired end reads of 150 base pairs length each) generated a transcriptome consisting of 144,213 transcript elements with an N50 contig size of 716 base pairs. Orthologs of 15,246 transcripts and homologs for an additional 16,810 transcripts were identified in the UniProtKB/Swiss-Prot database. The B. alexandrina CNS transcriptome provides a resource for future research exploring parasite-host interactions in a simpler nervous system. Moreover, increased understanding of the neural signaling mechanisms involved in the response of B. alexandrina to infection by S. mansoni larvae could lead to novel and highly specific strategies for the control of snail populations.

Electronic supplementary material

The online version of this article (10.1186/s13104-017-3018-6) contains supplementary material, which is available to authorized users.

Dynamical networks: Finding, measuring, and tracking neural population activity using network science

Systems neuroscience is in a headlong rush to record from as many neurons at the same time as possible. As the brain computes and codes using neuron populations, it is hoped these data will uncover the fundamentals of neural computation. But with hundreds, thousands, or more simultaneously recorded neurons come the inescapable problems of visualizing, describing, and quantifying their interactions. Here I argue that network science provides a set of scalable, analytical tools that already solve these problems. By treating neurons as nodes and their interactions as links, a single network can visualize and describe an arbitrarily large recording. I show that with this description we can quantify the effects of manipulating a neural circuit, track changes in population dynamics over time, and quantitatively define theoretical concepts of neural populations such as cell assemblies. Using network science as a core part of analyzing population recordings will thus provide both qualitative and quantitative advances to our understanding of neural computation.

A spiral attractor network drives rhythmic locomotion

The joint activity of neural populations is high dimensional and complex. One strategy for reaching a tractable understanding of circuit function is to seek the simplest dynamical system that can account for the population activity. By imaging Aplysia's pedal ganglion during fictive locomotion, here we show that its population-wide activity arises from a low-dimensional spiral attractor. Evoking locomotion moved the population into a low-dimensional, periodic, decaying orbit - a spiral - in which it behaved as a true attractor, converging to the same orbit when evoked, and returning to that orbit after transient perturbation. We found the same attractor in every preparation, and could predict motor output directly from its orbit, yet individual neurons' participation changed across consecutive locomotion bouts. From these results, we propose that only the low-dimensional dynamics for movement control, and not the high-dimensional population activity, are consistent within and between nervous systems.

Continuous lateral oscillations as a core mechanism for taxis in Drosophila larvae

Taxis behaviour in Drosophila larva is thought to consist of distinct control mechanisms triggering specific actions. Here, we support a simpler hypothesis: that taxis results from direct sensory modulation of continuous lateral oscillations of the anterior body, sparing the need for ‘action selection’. Our analysis of larvae motion reveals a rhythmic, continuous lateral oscillation of the anterior body, encompassing all head-sweeps, small or large, without breaking the oscillatory rhythm. Further, we show that an agent-model that embeds this hypothesis reproduces a surprising number of taxis signatures observed in larvae. Also, by coupling the sensory input to a neural oscillator in continuous time, we show that the mechanism is robust and biologically plausible. The mechanism provides a simple architecture for combining information across modalities, and explaining how learnt associations modulate taxis. We discuss the results in the light of larval neural circuitry and make testable predictions.

DOI:http://dx.doi.org/10.7554/eLife.15504.001

Dynamic trajectory of multiple single-unit activity during working memory task in rats

Working memory plays an important role in complex cognitive tasks. A popular theoretical view is that transient properties of neuronal dynamics underlie cognitive processing. The question raised here as to how the transient dynamics evolve in working memory. To address this issue, we investigated the multiple single-unit activity dynamics in rat medial prefrontal cortex (mPFC) during a Y-maze working memory task. The approach worked by reconstructing state space from delays of the original single-unit firing rate variables, which were further analyzed using kernel principal component analysis (KPCA). Then the neural trajectories were obtained to visualize the multiple single-unit activity. Furthermore, the maximal Lyapunov exponent (MLE) was calculated to quantitatively evaluate the neural trajectories during the working memory task. The results showed that the neuronal activity produced stable and reproducible neural trajectories in the correct trials while showed irregular trajectories in the incorrect trials, which may establish a link between the neurocognitive process and behavioral performance in working memory. The MLEs significantly increased during working memory in the correctly performed trials, indicating an increased divergence of the neural trajectories. In the incorrect trials, the MLEs were nearly zero and remained unchanged during the task. Taken together, the trial-specific neural trajectory provides an effective way to track the instantaneous state of the neuronal population during the working memory task and offers valuable insights into working memory function. The MLE describes the changes of neural dynamics in working memory and may reflect different neuronal population states in working memory.

Global segregation of cortical activity and metastable dynamics

Cortical activity exhibits persistent metastable dynamics. Assemblies of neurons transiently couple (integrate) and decouple (segregate) at multiple spatiotemporal scales; both integration and segregation are required to support metastability. Integration of distant brain regions can be achieved through long range excitatory projections, but the mechanism supporting long range segregation is not clear. We argue that the thalamocortical matrix connections, which project diffusely from the thalamus to the cortex and have long been thought to support cortical gain control, play an equally-important role in cortical segregation. We present a computational model of the diffuse thalamocortical loop, called the competitive cross-coupling (CXC) spiking network. Simulations of the model show how different levels of tonic input from the brainstem to the thalamus could control dynamical complexity in the cortex, directing transitions between sleep, wakefulness and high attention or vigilance. The model also explains how mutually-exclusive activity could arise across large portions of the cortex, such as between the default-mode and task-positive networks. It is robust to noise but does not require noise to autonomously generate metastability. We conclude that the long range segregation observed in brain activity and required for global metastable dynamics could be provided by the thalamocortical matrix, and is strongly modulated by brainstem input to the thalamus.

Modular deconstruction reveals the dynamical and physical building blocks of a locomotion motor program

The neural substrates of motor programs are only well understood for small, dedicated circuits. Here we investigate how a motor program is constructed within a large network. We imaged populations of neurons in the Aplysia pedal ganglion during execution of a locomotion motor program. We found that the program was built from a very small number of dynamical building blocks, including both neural ensembles and low-dimensional rotational dynamics. These map onto physically discrete regions of the ganglion, so that the motor program has a corresponding modular organization in both dynamical and physical space. Using this dynamic map, we identify the population potentially implementing the rhythmic pattern generator and find that its activity physically traces a looped trajectory, recapitulating its low-dimensional rotational dynamics. Our results suggest that, even in simple invertebrates, neural motor programs are implemented by large, distributed networks containing multiple dynamical systems.

Dimensionality reduction for large-scale neural recordings

Most sensory, cognitive and motor functions depend on the interactions of many neurons. In recent years, there has been rapid development and increasing use of technologies for recording from large numbers of neurons, either sequentially or simultaneously. A key question is what scientific insight can be gained by studying a population of recorded neurons beyond studying each neuron individually. Here, we examine three important motivations for population studies: single-trial hypotheses requiring statistical power, hypotheses of population response structure and exploratory analyses of large data sets. Many recent studies have adopted dimensionality reduction to analyze these populations and to find features that are not apparent at the level of individual neurons. We describe the dimensionality reduction methods commonly applied to population activity and offer practical advice about selecting methods and interpreting their outputs. This review is intended for experimental and computational researchers who seek to understand the role dimensionality reduction has had and can have in systems neuroscience, and who seek to apply these methods to their own data.

Estimation of neural firing rate: the wavelet density estimation approach

The computation of neural firing rates based on spike sequences has been introduced as a useful tool for extraction of an animal's behavior. Different estimating methods of such neural firing rates have been developed by neuroscientists, and among these methods, time histogram and kernel estimators have been used more than other approaches. In this paper, the problem in the estimation of firing rates using wavelet density estimators has been considered. The results of simulation study in estimation of underlying rates based on spike sequences sampled from two different variable firing rates show that the proposed wavelet density method provides better and more accurate estimation of firing rates with smooth results compared to two other classical approaches. Furthermore, the performance of a different family of wavelet density estimators in the estimation of the underlying firing rate of biological data have been compared with results of both time histogram and kernel estimators. All in all, the results show that the proposed method can be useful in the estimation of firing rate of neural spike trains.

Transformation of context-dependent sensory dynamics into motor behavior

The intrinsic dynamics of sensory networks play an important role in the sensory-motor transformation. In this paper we use conductance based models and electrophysiological recordings to address the study of the dual role of a sensory network to organize two behavioral context-dependent motor programs in the mollusk Clione limacina. We show that: (i) a winner take-all dynamics in the gravimetric sensory network model drives the typical repetitive rhythm in the wing central pattern generator (CPG) during routine swimming; (ii) the winnerless competition dynamics of the same sensory network organizes the irregular pattern observed in the wing CPG during hunting behavior. Our model also shows that although the timing of the activity is irregular, the sequence of the switching among the sensory cells is preserved whenever the same set of neurons are activated in a given time window. These activation phase locks in the sensory signals are transformed into specific events in the motor activity. The activation phase locks can play an important role in motor coordination driven by the intrinsic dynamics of a multifunctional sensory organ.

How sensory information is transformed into effective motor action is one of the most fundamental questions in neuroscience. As this question is difficult to assess experimentally, biophysical models of sensory, central and motor systems contribute to understand the information processing mechanisms involved in this transformation. Biophysical models can be informed by electrophysiological data in those situations where it is possible to record neural activity at all stages of sensory-motor processing. In this paper we use this approach to describe the dual dynamics of a multifunctional sensory organ in the mollusk Clione limacina and its transformation into two different motor programs. Our experimental and modeling results indicate that the sensory signals are modified to fit the changing behavioral context, and they are readily interpreted by the rest of the nervous system to produce the correct motor output.

Generalization of the dynamic clamp concept in neurophysiology and behavior

The idea of closed-loop interaction in in vitro and in vivo electrophysiology has been successfully implemented in the dynamic clamp concept strongly impacting the research of membrane and synaptic properties of neurons. In this paper we show that this concept can be easily generalized to build other kinds of closed-loop protocols beyond (or in addition to) electrical stimulation and recording in neurophysiology and behavioral studies for neuroethology. In particular, we illustrate three different examples of goal-driven real-time closed-loop interactions with drug microinjectors, mechanical devices and video event driven stimulation. Modern activity-dependent stimulation protocols can be used to reveal dynamics (otherwise hidden under traditional stimulation techniques), achieve control of natural and pathological states, induce learning, bridge between disparate levels of analysis and for a further automation of experiments. We argue that closed-loop interaction calls for novel real time analysis, prediction and control tools and a new perspective for designing stimulus-response experiments, which can have a large impact in neuroscience research.

Organization of Anti-Phase Synchronization Pattern in Neural Networks: What are the Key Factors?

Anti-phase oscillation has been widely observed in cortical neural network. Elucidating the mechanism underlying the organization of anti-phase pattern is of significance for better understanding more complicated pattern formations in brain networks. In dynamical systems theory, the organization of anti-phase oscillation pattern has usually been considered to relate to time delay in coupling. This is consistent to conduction delays in real neural networks in the brain due to finite propagation velocity of action potentials. However, other structural factors in cortical neural network, such as modular organization (connection density) and the coupling types (excitatory or inhibitory), could also play an important role. In this work, we investigate the anti-phase oscillation pattern organized on a two-module network of either neuronal cell model or neural mass model, and analyze the impact of the conduction delay times, the connection densities, and coupling types. Our results show that delay times and coupling types can play key roles in this organization. The connection densities may have an influence on the stability if an anti-phase pattern exists due to the other factors. Furthermore, we show that anti-phase synchronization of slow oscillations can be achieved with small delay times if there is interaction between slow and fast oscillations. These results are significant for further understanding more realistic spatiotemporal dynamics of cortico-cortical communications.

Autonomous head-mounted electrophysiology systems for freely behaving primates

Recent technological advances have led to new light-weight battery-operated systems for electrophysiology. Such systems are head mounted, run for days without experimenter intervention, and can record and stimulate from single or multiple electrodes implanted in a freely behaving primate. Here we discuss existing systems, studies that use them, and how they can augment traditional, physically restrained, 'in-rig' electrophysiology. With existing technical capabilities, these systems can acquire multiple signal classes, such as spikes, local field potential, and electromyography signals, and can stimulate based on real-time processing of recorded signals. Moving forward, this class of technologies, along with advances in neural signal processing and behavioral monitoring, have the potential to dramatically expand the scope and scale of electrophysiological studies.

Sequentially switching cell assemblies in random inhibitory networks of spiking neurons in the striatum

The striatum is composed of GABAergic medium spiny neurons with inhibitory collaterals forming a sparse random asymmetric network and receiving an excitatory glutamatergic cortical projection. Because the inhibitory collaterals are sparse and weak, their role in striatal network dynamics is puzzling. However, here we show by simulation of a striatal inhibitory network model composed of spiking neurons that cells form assemblies that fire in sequential coherent episodes and display complex identity-temporal spiking patterns even when cortical excitation is simply constant or fluctuating noisily. Strongly correlated large-scale firing rate fluctuations on slow behaviorally relevant timescales of hundreds of milliseconds are shown by members of the same assembly whereas members of different assemblies show strong negative correlation, and we show how randomly connected spiking networks can generate this activity. Cells display highly irregular spiking with high coefficients of variation, broadly distributed low firing rates, and interspike interval distributions that are consistent with exponentially tailed power laws. Although firing rates vary coherently on slow timescales, precise spiking synchronization is absent in general. Our model only requires the minimal but striatally realistic assumptions of sparse to intermediate random connectivity, weak inhibitory synapses, and sufficient cortical excitation so that some cells are depolarized above the firing threshold during up states. Our results are in good qualitative agreement with experimental studies, consistent with recently determined striatal anatomy and physiology, and support a new view of endogenously generated metastable state switching dynamics of the striatal network underlying its information processing operations.

Frequency-dependent spatiotemporal tuning properties of non-eye movement related vestibular neurons to three-dimensional translations in squirrel monkeys

Responses of vestibular-only translation sensitive (VOTS) neurons in vestibular nuclei of two squirrel monkeys were studied at multiple frequencies to three-dimensional translations and rotations. A novel frequency-dependent spatiotemporal analysis examined in each neuron whether complex models, with unrestricted response dynamics in three-dimensional (3D) space, provided significantly better fits than restricted models following simple, cosine rule. Subsequently, the statistically selected optimal model was used to predict the maximum translation direction, expressed as a unitary vector, Vt(max), and its associated sensitivity and phase across frequencies. Simple models were sufficient to quantify the 3D translational responses of 66% of neurons. Most VOTS neurons, complex or simple, exhibited flat-gain or low-pass response dynamics. The Vt(max) of simple neurons was fixed, whereas that of complex neurons changed with frequency. The spatial distribution of Vt(max) in simple neurons, which fell within 30 degrees of either the horizontal plane or/and the sagittal plane, was closely aligned with Vt(max) of vestibular afferents. In contrast, the frequency-dependent Vt(max) of most complex neurons migrated from the dorsoventral axis at higher frequency toward the horizontal plane, especially the interaural axis, at lower frequency. When the maximum rotation direction was estimated from responses of the same VOTS neurons to 1.2 Hz yaw, pitch, and roll rotations, complex neurons were more likely to respond to rotations activating vertical canals. Responses to 0.15-0.3 Hz linear accelerations produced by inertial or gravitational forces were indistinguishable in most complex neurons but significantly different in most simple neurons. These observations suggest that simple and complex VOTS neurons constitute distinctive vestibular pathways where complex neurons, exhibiting a novel spatiotemporal filtering mechanism in processing otolith-related signals, are well suited to drive tilt-related responses, whereas simple neurons probably mediate pure translation related responses.

Generating spatiotemporal joint torque patterns from dynamical synchronization of distributed pattern generators

Pattern generators found in the spinal cord are no more seen as simple rhythmic oscillators for motion control. Indeed, they achieve flexible and dynamical coordination in interaction with the body and the environment dynamics giving to rise motor synergies. Discovering the mechanisms underlying the control of motor synergies constitutes an important research question not only for neuroscience but also for robotics: the motors coordination of high dimensional robotic systems is still a drawback and new control methods based on biological solutions may reduce their overall complexity. We propose to model the flexible combination of motor synergies in embodied systems via partial phase synchronization of distributed chaotic systems; for specific coupling strength, chaotic systems are able to phase synchronize their dynamics to the resonant frequencies of one external force. We take advantage of this property to explore and exploit the intrinsic dynamics of one specified embodied system. In two experiments with bipedal walkers, we show how motor synergies emerge when the controllers phase synchronize to the body's dynamics, entraining it to its intrinsic behavioral patterns. This stage is characterized by directed information flow from the sensors to the motors exhibiting the optimal situation when the body dynamics drive the controllers (mutual entrainment). Based on our results, we discuss the relevance of our findings for modeling the modular control of distributed pattern generators exhibited in the spinal cord, and for exploring the motor synergies in robots.

Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity

We consider the problem of extracting smooth, low-dimensional neural trajectories that summarize the activity recorded simultaneously from many neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional, noisy spiking activity in a compact form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the spike trains are first smoothed over time, then a static dimensionality-reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way and that account for spiking variability, which may vary both across neurons and across time. We then present a novel method for extracting neural trajectories-Gaussian-process factor analysis (GPFA)-which unifies the smoothing and dimensionality-reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that the proposed extensions improved the predictive ability of the two-stage methods. The predictive ability was further improved by going to GPFA. From the extracted trajectories, we directly observed a convergence in neural state during motor planning, an effect that was shown indirectly by previous studies. We then show how such methods can be a powerful tool for relating the spiking activity across a neural population to the subject's behavior on a single-trial basis. Finally, to assess how well the proposed methods characterize neural population activity when the underlying time course is known, we performed simulations that revealed that GPFA performed tens of percent better than the best two-stage method.

Techniques for extracting single-trial activity patterns from large-scale neural recordings

Large, chronically implanted arrays of microelectrodes are an increasingly common tool for recording from primate cortex and can provide extracellular recordings from many (order of 100) neurons. While the desire for cortically based motor prostheses has helped drive their development, such arrays also offer great potential to advance basic neuroscience research. Here we discuss the utility of array recording for the study of neural dynamics. Neural activity often has dynamics beyond that driven directly by the stimulus. While governed by those dynamics, neural responses may nevertheless unfold differently for nominally identical trials, rendering many traditional analysis methods ineffective. We review recent studies - some employing simultaneous recording, some not - indicating that such variability is indeed present both during movement generation and during the preceding premotor computations. In such cases, large-scale simultaneous recordings have the potential to provide an unprecedented view of neural dynamics at the level of single trials. However, this enterprise will depend not only on techniques for simultaneous recording but also on the use and further development of analysis techniques that can appropriately reduce the dimensionality of the data, and allow visualization of single-trial neural behavior.

Predicting adaptive behavior in the environment from central nervous system dynamics

To generate adaptive behavior, the nervous system is coupled to the environment. The coupling constrains the dynamical properties that the nervous system and the environment must have relative to each other if adaptive behavior is to be produced. In previous computational studies, such constraints have been used to evolve controllers or artificial agents to perform a behavioral task in a given environment. Often, however, we already know the controller, the real nervous system, and its dynamics. Here we propose that the constraints can also be used to solve the inverse problem--to predict from the dynamics of the nervous system the environment to which they are adapted, and so reconstruct the production of the adaptive behavior by the entire coupled system. We illustrate how this can be done in the feeding system of the sea slug Aplysia. At the core of this system is a central pattern generator (CPG) that, with dynamics on both fast and slow time scales, integrates incoming sensory stimuli to produce ingestive and egestive motor programs. We run models embodying these CPG dynamics--in effect, autonomous Aplysia agents--in various feeding environments and analyze the performance of the entire system in a realistic feeding task. We find that the dynamics of the system are tuned for optimal performance in a narrow range of environments that correspond well to those that Aplysia encounter in the wild. In these environments, the slow CPG dynamics implement efficient ingestion of edible seaweed strips with minimal sensory information about them. The fast dynamics then implement a switch to a different behavioral mode in which the system ignores the sensory information completely and follows an internal "goal," emergent from the dynamics, to egest again a strip that proves to be inedible. Key predictions of this reconstruction are confirmed in real feeding animals.

Network mechanism for burst generation

We report on the mechanism of burst generation by populations of intrinsically spiking neurons, when a certain threshold in coupling strength is exceeded. These ensembles synchronize at relatively low coupling strength and lose synchronization at stronger coupling via spatiotemporal intermittency. The latter transition triggers fast repetitive spiking, which results in synchronized bursting. We present evidence that this mechanism is generic for various network topologies from regular to small-world and scale-free ones, different types of coupling and neuronal model.

Generation and reshaping of sequences in neural systems

The generation of informational sequences and their reorganization or reshaping is one of the most intriguing subjects for both neuroscience and the theory of autonomous intelligent systems. In spite of the diversity of sequential activities of sensory, motor, and cognitive neural systems, they have many similarities from the dynamical point of view. In this review we discus the ideas, models, and mathematical image of sequence generation and reshaping on different levels of the neural hierarchy, i.e., the role of a sensory network dynamics in the generation of a motor program (hunting swimming of marine mollusk Clione), olfactory dynamical coding, and sequential learning and decision making. Analysis of these phenomena is based on the winnerless competition principle. The considered models can be a basis for the design of biologically inspired autonomous intelligent systems.

Heteroclinic synchronization: ultrasubharmonic locking

According to the traditional view of synchronization, a weak periodic input is able to lock a nonlinear oscillator at a frequency close to that of the input (1:1 zone). If the forcing increases, it is possible to achieve synchronization at subharmonic bands also. Using a competitive dynamical system we show the inverse phenomenon: with a weak signal the 1:1 zone is narrow, but the synchronization of ultrasubharmonics is dominant. In the system's phase space, there exists a heteroclinic contour in the autonomous regime, which is the image of sequential dynamics. Under the action of a weak periodic forcing, in the vicinity of the contour a stable limit cycle with long period appears. This results in the locking of very low-frequency oscillations with the finite frequency of the forcing. We hypothesize that this phenomenon can be the origin for the synchronization of slow and fast brain rhythms.