A model of the basal ganglia in voluntary movement and postural reactions

A basal ganglia central pattern generator (CPG) is developed and its role in voluntary movements on the ground and postural reactions on a disturbed platform are studied and analysed by simulation. Biped dynamics and platform kinematics are utilised. The effects of agonist–antagonist muscular co-activation and joint stiffness are formulated. The implementation of the necessary counter-manoeuvres for maintaining balance and postural stability is studied. A control strategy, applicable to large systems, is formulated. The biped manoeuvres and transitions terminate in pre-specified intervals of time. Gravity is included and compensated for. Certain voluntary and postural adjustment strategies are the same but are initiated differently. Further experimental/computational research may identify the central nervous system and sensory paths that lead to the CPG. All actuator forces linearly evolve in time from their original values to their terminal values. There are no central continuous feedback loops present. Monitoring and sensing, however, are ongoing. The counter-manoeuvres are based on learned human-like voluntary movements that are triggered by the disturbance. The required central inputs to the musculoskeletal system are designed in the CPG. A functional structure for the CPG is proposed. The effect of certain disorders and malfunctions of the CPG are studied by simulation.     

SIGNIFICANT IMPROVEMENT OF QUALITY FOR LONG OLIGONUCLEOTIDES BY USING CONTROLLED PORE GLASS WITH LARGE PORES

A key factor influencing the quality of long oligonucleotides is the choice of controlled pore glass (CPG) which is used as a solid support during oligonucleotide synthesis. We studied the influence of CPG pore size on the quality of 75-mer oligonucleotides. Using electrophoresis and HPLC, we demonstrated failure modes that can occur at certain oligo lengths with 1000A pore size, and compared yield and purity of 75-mer oligos using 1000A and larger pore size CPG. We showed that oligonucleotides with much better quality are obtained using CPG with pore sizes of 1400A and larger. We also identified the key characteristics for CPG selection that lead to the best CPG performance.     

Significant improvement of quality for long oligonucleotides by using controlled pore glass with large pores

A key factor influencing the quality of long oligonucleotides is the choice of controlled pore glass (CPG) which is used as a solid support during oligonucleotide synthesis. We studied the influence of CPG pore size on the quality of 75-mer oligonucleotides. Using electrophoresis and HPLC, we demonstrated failure modes that can occur at certain oligo lengths with 1000A pore size, and compared yield and purity of 75-mer oligos using 1000A and larger pore size CPG. We showed that oligonucleotides with much better quality are obtained using CPG with pore sizes of 1400A and larger. We also identified the key characteristics for CPG selection that lead to the best CPG performance.     

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.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Resonance tuning in a neuro-musculo-skeletal model of the forearm

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior—such as resonance tuning—in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which—according to literature—is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.     

Cholinergic input is required during embryonic development to mediate proper assembly of spinal locomotor circuits

Rhythmic limb movements are controlled by pattern-generating neurons within the ventral spinal cord, but little is known about how these locomotor circuits are assembled during development. At early stages of embryogenesis, motor neurons are spontaneously active, releasing acetylcholine that triggers the depolarization of adjacent cells in the spinal cord. To investigate whether acetylcholine-driven activity is required for assembly of the central pattern-generating (CPG) circuit, we studied mice lacking the choline acetyltransferase (ChAT) enzyme. Our studies show that a rhythmically active spinal circuit forms in ChAT mutants, but the duration of each cycle period is elongated, and right-left and flexor-extensor coordination are abnormal. In contrast, blocking acetylcholine receptors after the locomotor network is wired does not affect right-left or flexor-extensor coordination. These findings suggest that the cholinergic neurotransmitter pathway is involved in configuring the CPG during a transient period of development.     

Hexapodal gaits and coupled nonlinear oscillator models

The general, model-independent features of different networks of six symmetrically coupled nonlinear oscillators are investigated. These networks are considered as possible models for locomotor central pattern generators (CPGs) in insects. Numerical experiments with a specific oscillator network model are briefly described. It is shown that some generic phase-locked oscillation-patterns for various systems of six symmetrically coupled nonlinear oscillators correspond to the common forward-walking gaits adopted by insects. It is also demonstrated that transitions observed in insect gaits can be modelled as standard symmetry-breaking bifurcations occurring in such systems. The present analysis, which leads to a natural classification of hexapodal gaits by symmetry and to natural sequences of gait bifurcations, relates observed gaits to the overall organizational structure of the underlying CPG. The implications of the present results for the development of simplified control systems for hexapodal walking robots are discussed.     

Topology selection by chaotic neurons of a pyloric central pattern generator

The pyloric Central Pattern Generator (CPG) in the lobster has an architecture in which every neuron receives at least one connection from another member of the CPG. We call this a "non-open" network topology. An "open" topology, where at least one neuron does not receive synapses from any other CPG member, is found neither in the pyloric nor in the gastric mill CPG. Here we investigate a possible reason for this topological structure using the ability to perform a biologically functional task as a measure of the efficacy of the network. When the CPG is composed of model neurons that exhibit regular membrane voltage oscillations, open topologies are as able to maximize this functionality as non-open topologies. When we replace these models by neurons which exhibit chaotic membrane voltage oscillations, the functional criterion selects non-open topologies. As isolated neurons from invertebrate CPGs are known in some cases to undergo chaotic oscillations, this suggests that there is a biological basis for the class of non-open network topologies that we observe.     

小球藻糖蛋白的分离、纯化和结构分析

采用柱层析分离纯化小球藻糖蛋白,并对其进行结构分析。结果表明,小球藻糖蛋白为白色粉末,产率为鲜藻的0．28％,易溶于水,分子量约为65,000Da,属O-连接方式,蛋白质含量为12．01％,糖链部分含有岩藻糖、阿拉伯糖、甘露糖、葡萄糖和半乳糖。     

Neuropeptide cycloprolylglycine is an endogenous positive modulator of AMPA receptors

We have previously shown that neuropeptide cycloprolylglycine (CPG) increases the content of brain-derived neurotrophic factor (BDNF) in the culture of neuronal cells under normal conditions and in pathology. This is the first study to show that CPG at a physiological concentration of 10^–6 M significantly enhances the transmembrane AMPA currents in rat cerebellar Purkinje cells. Thus, CPG is a positive endogenous modulator of AMPA receptors. It was assumed that the neuropsychotropic effects of CPG are implemented as a result of BDNF accumulation after the activation of AMPA receptors by this neuropeptide.     

Effects on hypothalamus when CPG is fed back to basal ganglia based on KIV model

The KIV model approximates the operation of the basic vertebrate forebrain together with the basal ganglia and motor systems. In KIV model, the hypothalamus and the basal ganglia which are two important parts in the midline forebrain are closely associated with the locomotion. The CPG model with time delay is established in this paper and the stability of this CPG model is discussed. The CPG output is treated as the proprioception and fed back to the basal ganglia. We focus on the effects on the hypothalamus and the basal ganglia when the time delay parameter a_d, the CPG amplitude parameter e and the CPG frequency parameter T_r are changed. Through analysis, we find that there exists optimum value of the parameters a_d or T_r which can make the synchronization of the hypothalamus optimum when the CPG is added into the basal ganglia. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.     

The relative efficiency of the Hardy-Weinberg equilibrium-likelihood and the conditional on parental genotype-likelihood methods for candidate-gene association studies.

Selecting a control group that is perfectly matched for ethnic ancestry with a group of affected individuals is a major problem in studying the association of a candidate gene with a disease. This problem can be avoided by a design that uses parental data in place of nonrelated controls. Schaid and Sommer presented two new methods for the statistical analysis using this approach: (1) a likelihood method (Hardy-Weinberg equilibrium [HWE] method), which rests on the assumption that HWE holds, and (2) a conditional likelihood method (conditional on parental genotype [CPG] method) appropriate when HWE is absent. Schaid and Sommer claimed that the CPG method can be more efficient than the HWE method, even when equilibrium holds. It can be shown, however that in the equilibrium situation the HWE method is always more efficient than the CPG method. For a dominant disease, the differences are slim. But for a recessive disease, the CPG method requires a much larger sample size to achieve a prescribed power than the HWE method. Additionally, we show how the relative risks for the various candidate-gene genotypes can be estimated without relying on iterative methods. For the CPG method, we represent an asymptotic power approximation that is sufficiently precise for planning the sample size of an association study.     

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN’s parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.     

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.     

Sensory feedback in CNN-based central pattern generators

Central Pattern Generators (CPGs) are a suitable paradigm to solve the problem of locomotion control in walking robots. CPGs are able to generate feed-forward signals to achieve a proper coordination among the robot legs. In literature they are often modelled as networks of coupled nonlinear systems. However the topic of feedback in these systems is rarely addressed. On the other hand feedback is essential for locomotion. In this paper the CPG for a hexapod robot is implemented through Cellular Neural Networks (CNNs). Feedback is included in the CPG controller by exploiting the dynamic properties of the CPG motor-neurons, such as synchronization issue and local bifurcations. These universal paradigms provide the essential issues to include sensory feedback in CPG architectures based on coupled nonlinear systems. Experiments on a dynamic model of a hexapod robot are presented to validate the approach introduced.     

An Approach for Adaptive Limbless Locomotion Using a CPG-Based Reflex Mechanism

Animals＇ free movement in natural environments has attracted many researchers to explore control methods for bio-inspired robots. This paper presents a novel reflex mechanism based on a Central Pattern Generator （CPG） for adaptive locomotion of limbless robots. First, inspired by the concept of reflex arc, the reflex mechanism is designed on a connectionist CPG model. Since the CPG model inspired by the spinal cord of lampreys is developed at the neuron level, it provides a possible natural solution for sensory reflex integration. Therefore, sensory neurons that bridge the external stimuli and the CPG model, together with the concept of reflex arc, are utilized for designing the sensory reflex mechanism. Then, a border reflex and a body reflex are further developed and applied on the ends and the middle part of a limbless robot, respectively. Finally, a ball hitting scenario and a corridor passing scenario are designed to verify the proposed method. Results of simulations and on-site experiments show the feasibility and effectiveness of the reflex mechanism in realizing fast response and adaptive limbless locomotion.     

On the definition of central pattern generator and its sensory control

A central pattern generator (CPG) is defined here as a neural network responsible for the production of the timing cues of a rhythmic motor output pattern in the isolated CNS. For the intact animal, model considerations show that this term is neither clearly delimited from the concept of a reflex chain nor from the concept of a pattern generator with functional principles different from those of the CPG. Therefore, it cannot be concluded from the existence of a CPG in the isolated nervous system that this CPG also provides the decisive timing cues in the intact animal. Consequences for the study of the neural basis of rhythmic movements are shown.     

Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator

The neuronal network underlying lamprey swimming has stimulated extensive modelling on different levels of abstraction. The lamprey swims with a burst frequency ranging from 0.3 to 8–10 Hz with a rostro-caudal lag between bursts in each segment along the spinal cord. The swimming motor pattern is characterized by a burst proportion that is independent of burst frequency and lasts around 30%–40% of the cycle duration. This also applies in preparations in which the reciprocal inhibition in the spinal cord between the left and right side is blocked. A network of coupled excitatory neurons producing hemisegmental oscillations may form the basis of the lamprey central pattern generator (CPG). Here we explored how such networks, in principle, could produce a large frequency range with a constant burst proportion. The computer simulations of the lamprey CPG use simplified, graded output units that could represent populations of neurons and that exhibit adaptation. We investigated the effect of an active modulation of the degree of adaptation of the CPG units to accomplish a constant burst proportion over the whole frequency range when, in addition, each hemisegment is assumed to be self-oscillatory. The degree of adaptation is increased with the degree of stimulation of the network. This will make the bursts terminate earlier at higher burst rates, allowing for a constant burst proportion. Without modulated adaptation the network operates in a limited range of swimming frequencies due to a progressive increase of burst duration with increasing background stimulation. By introducing a modulation of the adaptation, a broad burst frequency range can be produced. The reciprocal inhibition is thus not the primary burst terminating factor, as in many CPG models, and it is mainly responsible for producing alternation between the left and right sides. The results are compared with the Morris-Lecar oscillator model with parameters set to produce a type A and type B oscillator, in which the burst durations stay constant or increase, respectively, when the background stimulation is increased. Here as well, burst duration can be controlled by modulation of the slow variable in a similar way as above. When oscillatory hemisegmental networks are coupled together in a chain a phase lag is produced. The production of a phase lag in chains of such oscillators is compared with chains of Morris-Lecar relaxation oscillators. Models relating to the intact versus isolated spinal cord preparation are discussed, as well as the role of descending inhibition. Received: 1 April 1997 / Accepted in revised form: 20 March 1998