Mechanisms Underlying the Recruitment of Inhibitory Interneurons in Fictive Swimming in Developing Xenopus laevis Tadpoles.

Developing spinal circuits generate patterned motor outputs while many neurons with high membrane resistances are still maturing. In the spinal cord of hatchling frog tadpoles of unknown sex, we found that the firing reliability in swimming of inhibitory interneurons with commissural and ipsilateral ascending axons was negatively correlated with their cellular membrane resistance. Further analyses showed that neurons with higher resistances had outward rectifying properties, low firing thresholds, and little delay in firing evoked by current injections. Input synaptic currents these neurons received during swimming, either compound, unitary current amplitudes, or unitary synaptic current numbers, were scaled with their membrane resistances, but their own synaptic outputs were correlated with membrane resistances of their postsynaptic partners. Analyses of neuronal dendritic and axonal lengths and their activities in swimming and cellular input resistances did not reveal a clear correlation pattern. Incorporating these electrical and synaptic properties into a computer swimming model produced robust swimming rhythms, whereas randomizing input synaptic strengths led to the breakdown of swimming rhythms, coupled with less synchronized spiking in the inhibitory interneurons. We conclude that the recruitment of these developing interneurons in swimming can be predicted by cellular input resistances, but the order is opposite to the motor-strength-based recruitment scheme depicted by Henneman's size principle. This form of recruitment/integration order in development before the emergence of refined motor control is progressive potentially with neuronal acquisition of mature electrical and synaptic properties, among which the scaling of input synaptic strengths with cellular input resistance plays a critical role.SIGNIFICANCE STATEMENT The mechanisms on how interneurons are recruited to participate in circuit function in developing neuronal systems are rarely investigated. In 2-d-old frog tadpole spinal cord, we found the recruitment of inhibitory interneurons in swimming is inversely correlated with cellular input resistances, opposite to the motor-strength-based recruitment order depicted by Henneman's size principle. Further analyses showed the amplitude of synaptic inputs that neurons received during swimming was inversely correlated with cellular input resistances. Randomizing/reversing the relation between input synaptic strengths and membrane resistances in modeling broke down swimming rhythms. Therefore, the recruitment or integration of these interneurons is conditional on the acquisition of several electrical and synaptic properties including the scaling of input synaptic strengths with cellular input resistances.

From decision to action: Detailed modelling of frog tadpoles reveals neuronal mechanisms of decision-making and reproduces unpredictable swimming movements in response to sensory signals.

How does the brain process sensory stimuli, and decide whether to initiate locomotor behaviour? To investigate this question we develop two whole body computer models of a tadpole. The "Central Nervous System" (CNS) model uses evidence from whole-cell recording to define 2300 neurons in 12 classes to study how sensory signals from the skin initiate and stop swimming. In response to skin stimulation, it generates realistic sensory pathway spiking and shows how hindbrain sensory memory populations on each side can compete to initiate reticulospinal neuron firing and start swimming. The 3-D "Virtual Tadpole" (VT) biomechanical model with realistic muscle innervation, body flexion, body-water interaction, and movement is then used to evaluate if motor nerve outputs from the CNS model can produce swimming-like movements in a volume of "water". We find that the whole tadpole VT model generates reliable and realistic swimming. Combining these two models opens new perspectives for experiments.

The decision to move: response times, neuronal circuits and sensory memory in a simple vertebrate.

All animals use sensory systems to monitor external events and have to decide whether to move. Response times are long and variable compared to reflexes, and fast escape movements. The complexity of adult vertebrate brains makes it difficult to trace the neuronal circuits underlying basic decisions to move. To simplify the problem, we investigate the nervous system and responses of hatchling frog tadpoles which swim when their skin is stimulated. Studying the neuron-by-neuron pathway from sensory to hindbrain neurons, where the decision to swim is made, has revealed two simple pathways generating excitation which sums to threshold in these neurons to initiate swimming. The direct pathway leads to short, and reliable delays like an escape response. The other includes a population of sensory processing neurons which extend firing to introduce noise and delay into responses. These neurons provide a brief, sensory memory of the stimulus, that allows tadpoles to integrate stimuli occurring within a second or so of each other. We relate these findings to other studies and conclude that sensory memory makes a fundamental contribution to simple decisions and is present in the brainstem of a basic vertebrate at a surprisingly early stage in development.

A simple decision to move in response to touch reveals basic sensory memory and mechanisms for variable response times.

KEY POINTS: Short-term working memory and decision-making are usually studied in the cerebral cortex; in many models of simple decision making, sensory signals build slowly and noisily to threshold to initiate a motor response after long, variable delays. When touched, hatchling frog tadpoles decide whether to swim; we define the long and variable delays to swimming and use whole-cell recordings to uncover the neurons and processes responsible. Firing in sensory and sensory pathway neurons is short latency, and too brief and invariant to explain these delays, while recordings from hindbrain reticulospinal neurons controlling swimming reveal a prolonged and variable build-up of synaptic excitation which can reach firing threshold and initiate swimming. We propose this excitation provides a sensory memory of the stimulus and may be generated by small reverberatory hindbrain networks. Our results uncover fundamental network mechanisms that allow animals to remember brief sensory stimuli and delay simple motor decisions. ABSTRACT: Many motor responses to sensory input, like locomotion or eye movements, are much slower than reflexes. Can simpler animals provide fundamental answers about the cellular mechanisms for motor decisions? Can we observe the 'accumulation' of excitation to threshold proposed to underlie decision making elsewhere? We explore how somatosensory touch stimulation leads to the decision to swim in hatchling Xenopus tadpoles. Delays measured to swimming in behaving and immobilised tadpoles are long and variable. Activity in their extensively studied sensory and sensory pathway neurons is too short-lived to explain these response delays. Instead, whole-cell recordings from the hindbrain reticulospinal neurons that drive swimming show that these receive prolonged, variable synaptic excitation lasting for nearly a second following a brief stimulus. They fire and initiate swimming when this excitation reaches threshold. Analysis of the summation of excitation requires us to propose extended firing in currently undefined presynaptic hindbrain neurons. Simple models show that a small excitatory recurrent-network inserted in the sensory pathway can mimic this process. We suggest that such a network may generate slow, variable summation of excitation to threshold. This excitation provides a simple memory of the sensory stimulus. It allows temporal and spatial integration of sensory inputs and explains the long, variable delays to swimming. The process resembles the 'accumulation' of excitation proposed for cortical circuits in mammals. We conclude that fundamental elements of sensory memory and decision making are present in the brainstem at a surprisingly early stage in development.

A Network Model of Local Field Potential Activity in Essential Tremor and the Impact of Deep Brain Stimulation.

Essential tremor (ET), a movement disorder characterised by an uncontrollable shaking of the affected body part, is often professed to be the most common movement disorder, affecting up to one percent of adults over 40 years of age. The precise cause of ET is unknown, however pathological oscillations of a network of a number of brain regions are implicated in leading to the disorder. Deep brain stimulation (DBS) is a clinical therapy used to alleviate the symptoms of a number of movement disorders. DBS involves the surgical implantation of electrodes into specific nuclei in the brain. For ET the targeted region is the ventralis intermedius (Vim) nucleus of the thalamus. Though DBS is effective for treating ET, the mechanism through which the therapeutic effect is obtained is not understood. To elucidate the mechanism underlying the pathological network activity and the effect of DBS on such activity, we take a computational modelling approach combined with electrophysiological data. The pathological brain activity was recorded intra-operatively via implanted DBS electrodes, whilst simultaneously recording muscle activity of the affected limbs. We modelled the network hypothesised to underlie ET using the Wilson-Cowan approach. The modelled network exhibited oscillatory behaviour within the tremor frequency range, as did our electrophysiological data. By applying a DBS-like input we suppressed these oscillations. This study shows that the dynamics of the ET network support oscillations at the tremor frequency and the application of a DBS-like input disrupts this activity, which could be one mechanism underlying the therapeutic benefit.

The generation of antiphase oscillations and synchrony by a rebound-based vertebrate central pattern generator.

Many neural circuits are capable of generating multiple stereotyped outputs after different sensory inputs or neuromodulation. We have previously identified the central pattern generator (CPG) for Xenopus tadpole swimming that involves antiphase oscillations of activity between the left and right sides. Here we analyze the cellular basis for spontaneous left-right motor synchrony characterized by simultaneous bursting on both sides at twice the swimming frequency. Spontaneous synchrony bouts are rare in most tadpoles, and they instantly emerge from and switch back to swimming, most frequently within the first second after skin stimulation. Analyses show that only neurons that are active during swimming fire action potentials in synchrony, suggesting both output patterns derive from the same neural circuit. The firing of excitatory descending interneurons (dINs) leads that of other types of neurons in synchrony as it does in swimming. During synchrony, the time window between phasic excitation and inhibition is 7.9 ± 1 ms, shorter than that in swimming (41 ± 2.3 ms). The occasional, extra midcycle firing of dINs during swimming may initiate synchrony, and mismatches of timing in the left and right activity can switch synchrony back to swimming. Computer modeling supports these findings by showing that the same neural network, in which reciprocal inhibition mediates rebound firing, can generate both swimming and synchrony without circuit reconfiguration. Modeling also shows that lengthening the time window between phasic excitation and inhibition by increasing dIN synaptic/conduction delay can improve the stability of synchrony.

Can simple rules control development of a pioneer vertebrate neuronal network generating behavior?

How do the pioneer networks in the axial core of the vertebrate nervous system first develop? Fundamental to understanding any full-scale neuronal network is knowledge of the constituent neurons, their properties, synaptic interconnections, and normal activity. Our novel strategy uses basic developmental rules to generate model networks that retain individual neuron and synapse resolution and are capable of reproducing correct, whole animal responses. We apply our developmental strategy to young Xenopus tadpoles, whose brainstem and spinal cord share a core vertebrate plan, but at a tractable complexity. Following detailed anatomical and physiological measurements to complete a descriptive library of each type of spinal neuron, we build models of their axon growth controlled by simple chemical gradients and physical barriers. By adding dendrites and allowing probabilistic formation of synaptic connections, we reconstruct network connectivity among up to 2000 neurons. When the resulting "network" is populated by model neurons and synapses, with properties based on physiology, it can respond to sensory stimulation by mimicking tadpole swimming behavior. This functioning model represents the most complete reconstruction of a vertebrate neuronal network that can reproduce the complex, rhythmic behavior of a whole animal. The findings validate our novel developmental strategy for generating realistic networks with individual neuron- and synapse-level resolution. We use it to demonstrate how early functional neuronal connectivity and behavior may in life result from simple developmental "rules," which lay out a scaffold for the vertebrate CNS without specific neuron-to-neuron recognition.

Spatiotemporal visualization of deep brain stimulation-induced effects in the subthalamic nucleus.

Deep brain stimulation (DBS) is a successful surgical therapy used to treat the disabling symptoms of movement disorders such as Parkinson's disease. It involves the chronic stimulation of disorder-specific nuclei. However, the mechanisms that lead to clinical improvements remain unclear. Consequently, this slows the optimization of present-day DBS therapy and hinders its future development and application. We used a computational model to calculate the distribution of electric potential induced by DBS and study the effect of stimulation on the spiking activity of a subthalamic nucleus (STN) projection neuron. We previously showed that such a model can reveal detailed spatial effects of stimulation in the vicinity of the electrode. However, this multi-compartmental STN neuron model can fire in either a burst or tonic mode and, in this study, we hypothesized that the firing mode of the cell will have a major impact on the DBS-induced effects. Our simulations showed that the bursting model exhibits behaviour observed in studies of high-frequency stimulation of STN neurons, such as the presence of a silent period at stimulation offset and frequency-dependent stimulation effects. We validated the model by simulating the clinical parameter settings used for a Parkinsonian patient and showed, in a patient-specific anatomical model, that the region of affected tissue is consistent with clinical observations of the optimal DBS site. Our results demonstrated a method of quantitatively assessing neuronal changes induced by DBS, to maximize therapeutic benefit and minimize unwanted side effects.

A computational model of familiarity detection for natural pictures, abstract images, and random patterns: Combination of deep learning and anti-Hebbian training.

We present a neural network model for familiarity recognition of different types of images in the perirhinal cortex (the FaRe model). The model is designed as a two-stage system. At the first stage, the parameters of an image are extracted by a pretrained deep learning convolutional neural network. At the second stage, a two-layer feed forward neural network with anti-Hebbian learning is used to make the decision about the familiarity of the image. FaRe model simulations demonstrate high capacity of familiarity recognition memory for natural pictures and low capacity for both abstract images and random patterns. These findings are in agreement with psychological experiments.

A simple method defines 3D morphology and axon projections of filled neurons in a small CNS volume: Steps toward understanding functional network circuitry.

BACKGROUND: Fundamental to understanding neuronal network function is defining neuron morphology, location, properties, and synaptic connectivity in the nervous system. A significant challenge is to reconstruct individual neuron morphology and connections at a whole CNS scale and bring together functional and anatomical data to understand the whole network. NEW METHOD: We used a PC controlled micropositioner to hold a fixed whole mount of Xenopus tadpole CNS and replace the stage on a standard microscope. This allowed direct recording in 3D coordinates of features and axon projections of one or two neurons dye-filled during whole-cell recording to study synaptic connections. Neuron reconstructions were normalised relative to the ventral longitudinal axis of the nervous system. Coordinate data were stored as simple text files. RESULTS: Reconstructions were at 1 µm resolution, capturing axon lengths in mm. The output files were converted to SWC format and visualised in 3D reconstruction software NeuRomantic. Coordinate data are tractable, allowing correction for histological artefacts. Through normalisation across multiple specimens we could infer features of network connectivity of mapped neurons of different types. COMPARISON WITH EXISTING METHODS: Unlike other methods using fluorescent markers and utilising large-scale imaging, our method allows direct acquisition of 3D data on neurons whose properties and synaptic connections have been studied using whole-cell recording. CONCLUSIONS: This method can be used to reconstruct neuron 3D morphology and follow axon projections in the CNS. After normalisation to a common CNS framework, inferences on network connectivity at a whole nervous system scale contribute to network modelling to understand CNS function.

A Population Model of Deep Brain Stimulation in Movement Disorders From Circuits to Cells.

For more than 30 years, deep brain stimulation (DBS) has been used to target the symptoms of a number of neurological disorders and in particular movement disorders such as Parkinson's disease (PD) and essential tremor (ET). It is known that the loss of dopaminergic neurons in the substantia nigra leads to PD, while the exact impact of this on the brain dynamics is not fully understood, the presence of beta-band oscillatory activity is thought to be pathological. The cause of ET, however, remains uncertain, however pathological oscillations in the thalamocortical-cerebellar network have been linked to tremor. Both of these movement disorders are treated with DBS, which entails the surgical implantation of electrodes into a patient's brain. While DBS leads to an improvement in symptoms for many patients, the mechanisms underlying this improvement is not clearly understood, and computational modeling has been used extensively to improve this. Many of the models used to study DBS and its effect on the human brain have mainly utilized single neuron and single axon biophysical models. We have previously shown in separate models however, that the use of population models can shed much light on the mechanisms of the underlying pathological neural activity in PD and ET in turn, and on the mechanisms underlying DBS. Together, this work suggested that the dynamics of the cerebellar-basal ganglia thalamocortical network support oscillations at frequency range relevant to movement disorders. Here, we propose a new combined model of this network and present new results that demonstrate that both Parkinsonian oscillations in the beta band and oscillations in the tremor frequency range arise from the dynamics of such a network. We find regions in the parameter space demonstrating the different dynamics and go on to examine the transition from one oscillatory regime to another as well as the impact of DBS on these different types of pathological activity. This work will allow us to better understand the changes in brain activity induced by DBS, and allow us to optimize this clinical therapy, particularly in terms of target selection and parameter setting.

Visual perception of ambiguous figures: synchronization based neural models.

We develop and study two neural network models of perceptual alternations. Both models have a star-like architecture of connections with a central element connected to a set of peripheral elements. A particular perception is simulated in terms of partial synchronization between the central element and some sub-group of peripheral elements. The first model is constructed from phase oscillators and the mechanism of perceptual alternations is based on chaotic intermittency under fixed parameter values. Similar to experimental evidence, the distribution of times between perceptual alternations is represented by the gamma distribution. The second model is built of spiking neurons of the Hodgkin-Huxley type. The mechanism of perceptual alternations is based on plasticity of inhibitory synapses which increases the inhibition from the central unit to the neural assembly representing the current percept. As a result another perception is formed. Simulations show that the second model is in good agreement with behavioural data on switching times between percepts of ambiguous figures and with experimental results on binocular rivalry of two and four percepts.

Stochasticity and functionality of neural systems: mathematical modelling of axon growth in the spinal cord of tadpole.

In this paper we study a simple mathematical model of axon growth in the spinal cord of tadpole. Axon development is described by a system of three difference equations (the dorso-ventral and longitudinal coordinates of the growth cone and the growth angle) with stochastic components. We find optimal parameter values by fitting the model to experimentally measured characteristics of the axon and using the quadratic cost function. The fitted model generates axons for different neuron types in both ascending and descending directions which are similar to the experimentally measured axons. Studying the model of axon growth we have found the analytical solution for dynamics of the variance of the dorso-ventral coordinate and the variance of the growth angle. Formulas provide conditions for the case when the increase of the variance is limited and the analytical expression for the saturation level. It is remarkable that optimal parameters always satisfy the condition of limited variance increase. Taking into account experimental data on distribution of neuronal cell bodies along the spinal cord and dorso-ventral distribution of dendrites we generate a biologically realistic architecture of the whole tadpole spinal cord. Preliminary study of the electrophysiological properties of the model with Morris-Lecar neurons shows that the model can generate electrical activity corresponding to the experimentally observed swimming pattern activity of the tadpole in a broad range of parameter values.

Winner-take-all in a phase oscillator system with adaptation.

We consider a system of generalized phase oscillators with a central element and radial connections. In contrast to conventional phase oscillators of the Kuramoto type, the dynamic variables in our system include not only the phase of each oscillator but also the natural frequency of the central oscillator, and the connection strengths from the peripheral oscillators to the central oscillator. With appropriate parameter values the system demonstrates winner-take-all behavior in terms of the competition between peripheral oscillators for the synchronization with the central oscillator. Conditions for the winner-take-all regime are derived for stationary and non-stationary types of system dynamics. Bifurcation analysis of the transition from stationary to non-stationary winner-take-all dynamics is presented. A new bifurcation type called a Saddle Node on Invariant Torus (SNIT) bifurcation was observed and is described in detail. Computer simulations of the system allow an optimal choice of parameters for winner-take-all implementation.

Bifurcations of Limit Cycles in a Reduced Model of the Xenopus Tadpole Central Pattern Generator.

We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These synchronous episodes are rarely recorded and have no identified behavioural purpose. However, metamorphosing tadpoles require both anti-phase and in-phase oscillations for swimming locomotion. Previous models have shown the ability to generate biologically realistic patterns of synchrony and swimming oscillations in tadpoles, but a mathematical description of how these oscillations appear is still missing. We define a simplified model that incorporates the key operating principles of tadpole locomotion. The model generates the various outputs seen in experimental recordings, including swimming and synchrony. To study the model, we perform detailed one- and two-parameter bifurcation analysis. This reveals the critical boundaries that separate different dynamical regimes and demonstrates the existence of parameter regions of bi-stable swimming and synchrony. We show that swimming is stable in a significantly larger range of parameters, and can be initiated more robustly, than synchrony. Our results can explain the appearance of long-lasting synchrony bouts seen in experiments at the start of a swimming episode.

Structural and functional properties of a probabilistic model of neuronal connectivity in a simple locomotor network.

Although, in most animals, brain connectivity varies between individuals, behaviour is often similar across a species. What fundamental structural properties are shared across individual networks that define this behaviour? We describe a probabilistic model of connectivity in the hatchling Xenopus tadpole spinal cord which, when combined with a spiking model, reliably produces rhythmic activity corresponding to swimming. The probabilistic model allows calculation of structural characteristics that reflect common network properties, independent of individual network realisations. We use the structural characteristics to study examples of neuronal dynamics, in the complete network and various sub-networks, and this allows us to explain the basis for key experimental findings, and make predictions for experiments. We also study how structural and functional features differ between detailed anatomical connectomes and those generated by our new, simpler, model (meta-model).

Metastable states, phase transitions, and persistent neural activity.

A new mathematical model to describe the spiking rate of a neural population is derived, which considers both the mean and the variance of the activity. Bifurcation analysis identifies a critical interval of parameter values in which the standard bistability regime coexists with an additional third attractor corresponding to the metastable state of bounded mean activity and high variance. To understand the structure of spatio-temporal activity in the metastable state, we study a simple discrete-time model of binary elements with random noise locally coupled on the grid, which produces rich dynamics including metastability. A critical value of the noise amplitude is identified; in the vicinity of this value the system is flexible and can easily generate transitions between UP and DOWN metastable states, either autonomously or in response to a control process. These metastable states and phase transitions provide a proper basis for the modelling of persistent neural activity reported in many experimental studies.

Reaction times in visual search can be explained by a simple model of neural synchronization.

We present an oscillatory neural network model that can account for reaction times in visual search experiments. The model consists of a central oscillator that represents the central executive of the attention system and a number of peripheral oscillators that represent objects in the display. The oscillators are described as generalized Kuramoto type oscillators with adapted parameters. An object is considered as being included in the focus of attention if the oscillator associated with this object is in-phase with the central oscillator. The probability for an object to be included in the focus of attention is determined by its saliency that is described in formal terms as the strength of the connection from the peripheral oscillator to the central oscillator. By computer simulations it is shown that the model can reproduce reaction times in visual search tasks of various complexities. The dependence of the reaction time on the number of items in the display is represented by linear functions of different steepness which is in agreement with biological evidence.

Advanced correlation grid: Analysis and visualisation of functional connectivity among multiple spike trains.

BACKGROUND: This study analyses multiple spike trains (MST) data, defines its functional connectivity and subsequently visualises an accurate diagram of connections. This is a challenging problem. For example, it is difficult to distinguish the common input and the direct functional connection of two spike trains. NEW METHOD: The new method presented in this paper is based on the traditional pairwise cross-correlation function (CCF) and a new combination of statistical techniques. First, the CCF is used to create the Advanced Correlation Grid (ACG) correlation where both the significant peak of the CCF and the corresponding time delay are used for detailed analysis of connectivity. Second, these two features of functional connectivity are used to classify connections. Finally, the visualization technique is used to represent the topology of functional connections. RESULTS: Examples are presented in the paper to demonstrate the new Advanced Correlation Grid method and to show how it enables discrimination between (i) influence from one spike train to another through an intermediate spike train and (ii) influence from one common spike train to another pair of analysed spike trains. COMPARISON WITH EXISTING METHODS: The ACG method enables scientists to automatically distinguish between direct connections from spurious connections such as common source connection and indirect connection whereas existing methods require in-depth analysis to identify such connections. CONCLUSIONS: The ACG is a new and effective method for studying functional connectivity of multiple spike trains. This method can identify accurately all the direct connections and can distinguish common source and indirect connections automatically.

Studying the role of axon fasciculation during development in a computational model of the Xenopus tadpole spinal cord.

During nervous system development growing axons can interact with each other, for example by adhering together in order to produce bundles (fasciculation). How does such axon-axon interaction affect the resulting axonal trajectories, and what are the possible benefits of this process in terms of network function? In this paper we study these questions by adapting an existing computational model of the development of neurons in the Xenopus tadpole spinal cord to include interactions between axons. We demonstrate that even relatively weak attraction causes bundles to appear, while if axons weakly repulse each other their trajectories diverge such that they fill the available space. We show how fasciculation can help to ensure axons grow in the correct location for proper network formation when normal growth barriers contain gaps, and use a functional spiking model to show that fasciculation allows the network to generate reliable swimming behaviour even when overall synapse counts are artificially lowered. Although we study fasciculation in one particular organism, our approach to modelling axon growth is general and can be widely applied to study other nervous systems.