The functional role of different neural activation profiles during precision grip: An artificial neural network approach

A dynamic and recurrent artificial neural network was used to investigate the functional properties of firing patterns observed in the primary motor (M1) and the primary somatosensory (S1) cortex of the behaving monkey during control of precision grip force. In the behaving monkey it was found that neurons in M1 and in S1 increase their firing activity with increasing grip force, as do the intrinsic and extrinsic hand muscles implicated in the task. However, some neurons also decreased their activity as a function of increasing force. The functional implication of these latter neurons is not clear and has not been elucidated so far. In order to explore their functional implication, we therefore simulated patterns of neural activity in artificial neural networks that represent cortical, spinal and afferent neural populations and tested whether particular activity profiles would emerge as a function of the input and of the connectivity of these networks. The functional implication of units with emergent or imposed decreasing activity was then explored.Decreasing patterns of activity in M1 units did not emerge from the networks. However, the same networks generated decreasing activity if imposed as target patterns. As indicated by the emerging weight space, M1 projection units with decreasing patterns are functionally less involved in driving alpha motoneurons than units with increasing profiles. Furthermore, these units did not provide significant fusimotor drive, whereas those with increasing profiles did. Fusimotor drive was a function of the (imposed) form of muscle spindle afferent activity: with gamma (fusimotor) drive, muscle spindle afferents provided signals other than muscle length (as observed experimentally). The network solutions thus predict a functional dichotomy between increasing and decreasing M1 neurons: the former primarily drive alpha and gamma motoneurons, the latter only weakly alpha motoneurons.     

Dynamic Neural Network Models of the Premotoneuronal Circuitry Controlling Wrist Movements in Primates

Dynamic recurrent neural networks were derived to simulate neuronal populations generating bidirectional wrist movements in the monkey. The models incorporate anatomical connections of cortical and rubral neurons, muscle afferents, segmental interneurons and motoneurons; they also incorporate the response profiles of four populations of neurons observed in behaving monkeys. The networks were derived by gradient descent algorithms to generate the eight characteristic patterns of motor unit activations observed during alternating flexion-extension wrist movements. The resulting model generated the appropriate input-output transforms and developed connection strengths resembling those in physiological pathways. We found that this network could be further trained to simulate additional tasks, such as experimentally observed reflex responses to limb perturbations that stretched or shortened the active muscles, and scaling of response amplitudes in proportion to inputs. In the final comprehensive network, motor units are driven by the combined activity of cortical, rubral, spinal and afferent units during step tracking and perturbations.The model displayed many emergent properties corresponding to physiological characteristics. The resulting neural network provides a working model of premotoneuronal circuitry and elucidates the neural mechanisms controlling motoneuron activity. It also predicts several features to be experimentally tested, for example the consequences of eliminating inhibitory connections in cortex and red nucleus. It also reveals that co-contraction can be achieved by simultaneous activation of the flexor and extensor circuits without invoking features specific to co-contraction.     

Learning with slight forgetting optimizes sensorimotor transformation in redundant motor systems

Recent theoretical studies have proposed that the redundant motor system in humans achieves well-organized stereotypical movements by minimizing motor effort cost and motor error. However, it is unclear how this optimization process is implemented in the brain, presumably because conventional schemes have assumed a priori that the brain somehow constructs the optimal motor command, and largely ignored the underlying trial-by-trial learning process. In contrast, recent studies focusing on the trial-by-trial modification of motor commands based on error information suggested that forgetting (i.e., memory decay), which is usually considered as an inconvenient factor in motor learning, plays an important role in minimizing the motor effort cost. Here, we examine whether trial-by-trial error-feedback learning with slight forgetting could minimize the motor effort and error in a highly redundant neural network for sensorimotor transformation and whether it could predict the stereotypical activation patterns observed in primary motor cortex (M1) neurons. First, using a simple linear neural network model, we theoretically demonstrated that: 1) this algorithm consistently leads the neural network to converge at a unique optimal state; 2) the biomechanical properties of the musculoskeletal system necessarily determine the distribution of the preferred directions (PD; the direction in which the neuron is maximally active) of M1 neurons; and 3) the bias of the PDs is steadily formed during the minimization of the motor effort. Furthermore, using a non-linear network model with realistic musculoskeletal data, we demonstrated numerically that this algorithm could consistently reproduce the PD distribution observed in various motor tasks, including two-dimensional isometric torque production, two-dimensional reaching, and even three-dimensional reaching tasks. These results may suggest that slight forgetting in the sensorimotor transformation network is responsible for solving the redundancy problem in motor control.     

Simulating vestibular compensation using recurrent back-propagation

Vestibular compensation is simulated as learning in a dynamic neural network model of the horizontal vestibulo-ocular reflex (VOR). The bilateral, three-layered VOR model consists of nonlinear units representing horizontal canal afferents, vestibular nuclei (VN) neurons and eye muscle motoneurons. Dynamic processing takes place via commissural connections that link the VN bilaterally. The intact network is trained, using recurrent back-propagation, to produce the VOR with velocity storage integration. Compensation is simulated by removing vestibular afferent input from one side and retraining the network. The time course of simulated compensation matches that observed experimentally. The behavior of model VN neurons in the compensated network also matches real data, but only if connections at the motoneurons, as well as at the VN, are allowed to be plastic. The dynamic properties of real VN neurons in compensated and normal animals are found to differ when tested with sinusoidal but not with step stimuli. The model reproduces these conflicting data, and suggests that the disagreement may be due to VN neuron nonlinearity.     

Gap junctional communication among motor and other neurons shapes patterns of neural activity and synaptic connectivity during development

We are studying the functional roles of neuronal gap junctional coupling during development, using motor neurons and their synapses with muscle fibers as a model system. At neuromuscular synapses, several studies have shown that the relative pattern of activity among motor inputs competing for innervation of the same target muscle fiber determines how patterns of innervation are sculpted during the first weeks after birth. We asked whether gap junctional coupling among motor neurons modulates the relative timing of motor neuron activity in awake, behaving neonatal mice. We found that the activity of motor neurons innervating the same muscle is temporally correlated perinatally, during the same period that gap junction-mediated electrical and dye coupling are present. In vivo blockade of gap junctions abolished temporal correlations in motor neuron activity, without changing overall motor behavior, motor neuron activity patterns or firing frequency. Together with preliminary studies in mice lacking gap junction protein Cx40, our data suggest that developmentally regulated gap junctional coupling among motor and other neurons affects the activity in nascent neural circuits and thus in turn affects synaptic connectivity. Dynamic monitoring of dye coupling can be used to explore this possibility in normal mice and in mice lacking gap junction proteins during embryonic and neonatal development.     

Monitoring Performance Degradation of Cerebellar Functions Using Computational Neuroscience Methods: Implications on Neurological Diseases

Neurodegeneration is a major cause of human disease. Within the cerebellum, neuronal degeneration and/or dysfunction has been associated with many diseases, including several forms of cerebellar ataxia, since normal cerebellar function is paramount for proper motor coordination, balance, and motor learning. The cerebellum represents a well-established neural circuit. Determining the effects of neuronal loss is of great importance for understanding the fundamental workings of the cerebellum and disease-associated dysfunctions. This paper presents computational modeling of cerebellar function in relation to neurodegeneration either affecting a specific cerebellar cell type, such as granule cells or Purkinje cells, or more generally affecting cerebellar cells and the implications on effects in relation to performance degradation throughout the progression of cell death. The results of the models show that the overall number of cells, as a percentage of the total cell number in the model, of a particular type and, primarily, their proximity to the circuit output, and not the neuronal convergence due to the relative number of cells of a particular type, is the main indicator of the gravity of the functional deficit caused by the degradation of that cell type. Specifically, the greater the percentage loss of neurons of a specific type and the closer proximity of those cells to the deep cerebellar neurons, the greater the deficit caused by the neuronal cell loss. These findings contribute to the understanding of the functional consequences of neurodegeneration and the functional importance of specific connectivity within a neuronal circuit.     

Cholinergic sensitivity as an index of the functional differences in cortical neurons in young and old rabbits]

Acetylcholine-sensitivity of motor cortex neurons was studied in the young and old rabbits. Muscarinic-type excitation in the neurons of old animals was revealed twice less frequently compared to the young ones. The age-related fall in the number of cholinoceptive neurons may be due to general decrease of neuronal activation in the motor cortex during aging. Changes in functional properties of motor cortex neurons with age may have a result that firing rate of movement related neurons becomes insufficient for the effective control of motor function.     

Tracking Plasticity: Effects of Long-Term Rehearsal in Expert Dancers Encoding Music to Movement

Our knowledge of neural plasticity suggests that neural networks show adaptation to environmental and intrinsic change. In particular, studies investigating the neuroplastic changes associated with learning and practicing motor tasks have shown that practicing such tasks results in an increase in neural activation in several specific brain regions. However, studies comparing experts and non-experts suggest that experts employ less neuronal activation than non-experts when performing a familiar motor task. Here, we aimed to determine the long-term changes in neural networks associated with learning a new dance in professional ballet dancers over 34 weeks. Subjects visualized dance movements to music while undergoing fMRI scanning at four time points over 34-weeks. Results demonstrated that initial learning and performance at seven weeks led to increases in activation in cortical regions during visualization compared to the first week. However, at 34 weeks, the cortical networks showed reduced activation compared to week seven. Specifically, motor learning and performance over the 34 weeks showed the typical inverted-U-shaped function of learning. Further, our result demonstrate that learning of a motor sequence of dance movements to music in the real world can be visualized by expert dancers using fMRI and capture highly significant modeled fits of the brain network variance of BOLD signals from early learning to expert level performance.     

瞳孔光反应系统的空间分布式神经网络模型

为模拟刺激光空间分布变化引起瞳孔反应的实验现象,本文建立了空间分布式神经网络瞳孔模型。它是在瞳孔双通道模型基础上,借鉴Ｃａｎｎｏｎ－Ｒｏｂｉｎｓｏｎ的Ｏｃｕｌｏｍｏｔｏｒ模型的双层网络结构和视网膜的镶嵌式特点,经空间延括而成。空间各部位信号经第一层神经元处理得到对应各部位的线性ＤＣ和非线性ＡＣ输出,在第二层神经元进行空间综合,再经第三层神经元复合去控制效应器官虹膜肌的反应。该分布式部位机制模型能解释多种瞳孔实验现象。     

Neuromodulation and flexibility in Central Pattern Generator networks

Central Pattern Generator (CPG) networks, which organize rhythmic movements, have long served as models for neural network organization. Modulatory inputs are essential components of CPG function: neuromodulators set the parameters of CPG neurons and synapses to render the networks functional. Each modulator acts on the network by many effects which may oppose one another; this may serve to stabilize the modulated state. Neuromodulators also determine the active neuronal composition in the CPG, which varies with state changes such as locomotor speed. The pattern of gene expression which determines the electrophysiological personality of each CPG neuron is also under modulatory control. It is not possible to model the function of neural networks without including the actions of neuromodulators.     

Unsupervised learning and temporal context to recall complex robot trajectories

An unsupervised neural network is proposed to learn and recall complex robot trajectories. Two cases are considered: (i) A single trajectory in which a particular arm configuration (state) may occur more than once, and (ii) trajectories sharing states with each other. Ambiguities occur in both cases during recall of such trajectories. The proposed model consists of two groups of synaptic weights trained by competitive and Hebbian learning laws. They are responsible for encoding spatial and temporal features of the input sequences, respectively. Three mechanisms allow the network to deal with repeated or shared states: local and global context units, neurons disabled from learning, and redundancy. The network reproduces the current and the next state of the learned sequences and is able to resolve ambiguities. The model was simulated over various sets of robot trajectories in order to evaluate learning and recall, trajectory sampling effects and robustness.     

A dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories

As a dynamical model for motor cortical activity during hand movement we consider an artificial neural network that consists of extensively interconnected neuron-like units and performs the neuronal population vector operations. Local geometrical parameters of a desired curve are introduced into the network as an external input. The output of the model is a time-dependent direction and length of the neuronal population vector which is calculated as a sum of the activity of directionally tuned neurons in the ensemble. The main feature of the model is that dynamical behavior of the neuronal population vector is the result of connections between directionally tuned neurons rather than being imposed externally. The dynamics is governed by a system of coupled nonlinear differential equations. Connections between neurons are assigned in the simplest and most common way so as to fulfill basic requirements stemming from experimental findings concerning the directional tuning of individual neurons and the stabilization of the neuronal population vector, as well as from previous theoretical studies. The dynamical behavior of the model reveals a close similarity with the experimentally observed dynamics of the neuronal population vector. Specifically, in the framework of the model it is possible to describe a geometrical curve in terms of the time series of the population vector. A correlation between the dynamical behavior of the direction and the length of the population vector entails a dependence of the neural velocity on the curvature of the tracing trajectory that corresponds well to the experimentally measured covariation between tangential velocity and curvature in drawing tasks.On leave of absencefrom the Institute of Molecular Genetics, Russian Academy of Sciences, Moscow, Russia.     

Maturation of rhythmic neural network: role of central modulatory inputs.

Modulatory systems are well known for their roles in tuning the cellular and synaptic properties in the adult neuronal networks, and play a major role in the control of the flexibility of functional outputs. However far less is known concerning their role in the maturation of neural networks during the development. In this review, using the stomatogastric nervous system of lobster, we will show that the neuromodulatory system exerts a powerful influence on developing neural networks. In the adult the number of both motor target neurons and their modulatory neurons is restricted to tens of identifiable cells. They are therefore well characterized in terms of cellular, synaptic and morphological properties. In the embryo, these target cells and their neuromodulatory population are already present from mid-embryonic life. However, the motor output generated by the system is quite different: while in the embryo all the target neurons are organized into a single network generating unique motor pattern, in the adult this population splits into two distinct networks generating separate patterns. This ontogenetic partitioning does not rely on progressive acquisition of adult properties but rather on a switch between two possible network operations. Indeed, adult networks are present early in the embryonic life but their expression is repressed by central modulatory neurons. Moreover, embryonic networks can be revealed in the adult system again by altering modulatory influences. Therefore, independently of the developmental age, two potential network phenotypes co-exist within the same neuronal architecture: when one is expressed, the other one is hidden and vice versa. These transitions do not necessarily need dramatic changes such as growth/retraction of processes, acquisition of new intra-membrane proteins etc. but rather, as shown by modelling studies, it may simply rely on a subtle tuning of pre-existing intercellular electrical coupling. This in turn suggests that progressive ontogenetic alteration may not take place at the level of the target network but rather at the level of modulatory input neurons.     

Estimating the dimensionality of the manifold underlying multi-electrode neural recordings

It is generally accepted that the number of neurons in a given brain area far exceeds the number of neurons needed to carry any specific function controlled by that area. For example, motor areas of the human brain contain tens of millions of neurons that control the activation of tens or at most hundreds of muscles. This massive redundancy implies the covariation of many neurons, which constrains the population activity to a low-dimensional manifold within the space of all possible patterns of neural activity. To gain a conceptual understanding of the complexity of the neural activity within a manifold, it is useful to estimate its dimensionality, which quantifies the number of degrees of freedom required to describe the observed population activity without significant information loss. While there are many algorithms for dimensionality estimation, we do not know which are well suited for analyzing neural activity. The objective of this study was to evaluate the efficacy of several representative algorithms for estimating the dimensionality of linearly and nonlinearly embedded data. We generated synthetic neural recordings with known intrinsic dimensionality and used them to test the algorithms’ accuracy and robustness. We emulated some of the important challenges associated with experimental data by adding noise, altering the nature of the embedding of the low-dimensional manifold within the high-dimensional recordings, varying the dimensionality of the manifold, and limiting the amount of available data. We demonstrated that linear algorithms overestimate the dimensionality of nonlinear, noise-free data. In cases of high noise, most algorithms overestimated the dimensionality. We thus developed a denoising algorithm based on deep learning, the “Joint Autoencoder”, which significantly improved subsequent dimensionality estimation. Critically, we found that all algorithms failed when the intrinsic dimensionality was high (above 20) or when the amount of data used for estimation was low. Based on the challenges we observed, we formulated a pipeline for estimating the dimensionality of experimental neural data.     

Systems principle for separating out neuron groups as relatively independent working units

The respiratory center has been studied as an example of the neural center organization. This organization is presented by a number of cellular populations, each of them consisting of several neuronal groups (components of the populations) of various types. These groups are considered as relatively autonomic sets of various neuronal categories, where 1-5 large efferent (phase) neurons are present as a central link. Analyzing the spatial arrangement and functional interrelations of the neurons in the group, it is possible to conclude that the groups revealed (respirons) are functional units of neuronal activity. Applying the theory of functional system (P. K. Anokhin) for analyzing connections between the neurons in the group and the afferent impulsation that gets into action sphere of the group, it is possible to formulate certain criteria on integrity and a relative functional independence of the neuronal groups as working units of neuronal activity, in which the reticular component of the groups as widely represented in all parts of the CNS, a suggestion is made that the respirons are the natural invariant of the structure when the cerebral function is reorganized.     

Distinct Neuronal Lineages of the Ascidian Embryo Revealed by Expression of a Sodium Channel Gene

The ascidian larva contains tubular neural tissue, one of the prominent anatomical features of the chordates. The cell-cleavage pattern and cell maps of the nervous system have been described in the ascidian larva in great detail. Cell types in the neural tube, however, have not yet been defined due to the lack of a suitable molecular marker. In the present work, we identified neuronal cells in the caudal neural tube of theHalocynthiaembryo by utilizing a voltage-gated Na⁺channel gene, TuNa I, as a molecular marker. Microinjection of a lineage tracer revealed that TuNa I-positive neurons in the brain and in the trunk epidermis are derived from the a-line of the eight-cell embryo, which includes cell fates to epidermal and neural tissue. On the other hand, TuNa I-positive cells in the more caudal part of the neural tissue were not stained by microinjection into the a-line. These neurons are derived from the A-line, which contains fates of notochord and muscle, but not of epidermis. Electron microscopic observation confirmed that A-line-derived neurons consist of motor neurons innervating the dorsal and ventral muscle cells. Isolated A-line blastomeres have active membrane excitability distinct from those of the a-line-derived neuronal cells after culture under cleavage arrest, suggesting that the A-line gives rise to a neuronal cell distinct from that of the a-lineage. TuNa I expression in the a-line requires signals from another cell lineage, whereas that in the A-line occurs without tight cell contact. Thus, there are at least two distinct neuronal lineages with distinct cellular behaviors in the ascidian larva: the a-line gives rise to numerous neuronal cells, including sensory cells, controlled by a mechanism similar to vertebrate neural induction, whereas A-line cells give rise to motor neurons and ependymal cells in the caudal neural tube that develop in close association with the notochord or muscle lineage, but not with the epidermal lineage.     

Associative neural network model for the generation of temporal patterns. Theory and application to central pattern generators.

Cyclic patterns of motor neuron activity are involved in the production of many rhythmic movements, such as walking, swimming, and scratching. These movements are controlled by neural circuits referred to as central pattern generators (CPGs). Some of these circuits function in the absence of both internal pacemakers and external feedback. We describe an associative neural network model whose dynamic behavior is similar to that of CPGs. The theory predicts the strength of all possible connections between pairs of neurons on the basis of the outputs of the CPG. It also allows the mean operating levels of the neurons to be deduced from the measured synaptic strengths between the pairs of neurons. We apply our theory to the CPG controlling escape swimming in the mollusk Tritonia diomedea. The basic rhythmic behavior is shown to be consistent with a simplified model that approximates neurons as threshold units and slow synaptic responses as elementary time delays. The model we describe may have relevance to other fixed action behaviors, as well as to the learning, recall, and recognition of temporally ordered information.     

Hebbian learning in parallel and modular memories

Many cognitive and sensorimotor functions in the brain involve parallel and modular memory subsystems that are adapted by activity-dependent Hebbian synaptic plasticity. This is in contrast to the multilayer perceptron model of supervised learning where sensory information is presumed to be integrated by a common pool of hidden units through backpropagation learning. Here we show that Hebbian learning in parallel and modular memories is more advantageous than backpropagation learning in lumped memories in two respects: it is computationally much more efficient and structurally much simpler to implement with biological neurons. Accordingly, we propose a more biologically relevant neural network model, called a tree-like perceptron, which is a simple modification of the multilayer perceptron model to account for the general neural architecture, neuronal specificity, and synaptic learning rule in the brain. The model features a parallel and modular architecture in which adaptation of the input-to-hidden connection follows either a Hebbian or anti-Hebbian rule depending on whether the hidden units are excitatory or inhibitory, respectively. The proposed parallel and modular architecture and implicit interplay between the types of synaptic plasticity and neuronal specificity are exhibited by some neocortical and cerebellar systems. Received: 13 October 1996 / Accepted in revised form: 16 October 1997     

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.