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In fact, relying solely on the above SNDSM still cannot sort solutions in the same grade set, we call these solutions undetermined solutions (USs), and we further rank them according to the single congestion degree (SCD). Fig 6 shows the example of SCD. Define the ultra-optimized solution for each solution in US set, whose rank of each objective is immediately lower than the solution, for instance q' is the ultra-optimized solution of q. The boundary consisting of those ultra-optimized solutions are called ultra-optimized boundary, namely A'. SCD is proposed to measure the closeness between a solution and its ultra-optimized solution. Intuitively, SCD is the perimeter of the rectangle in Fig 6, which is composed of the solution point (i.e. q) and its ultra-optimized solution point (i.e. q') on the ultra-optimized boundary. For a solution in US set, the less SCD means more optimal, and result in lower ranking.
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study
| 99.94 |
Tumble operation. A unit length random direction, say vector Δ(i) ∈ [−1,1], is generated for each bacterium and this defines the direction of movement after a move. The update of bacteria is mainly according to Eq 13. Q(i,t+1,k)=Q(i,t,k)+H(t,k)Δ(i)Δ(i)TΔ(i),(13) where Q(i,t,k) is the code of the kth position of bacterial i at iteration t, H(t, k) is the step size of direction for position k, which is generated randomly.
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| 99.75 |
Swim operation. If the better solution is found in tumble operation, H(t, k) is updated in the generated direction, as shown in Eq 14, and continue to create bacteria until no better ones are found. H(t+1,k)=min{MSE(i)−MSEbestMSEmax−MSEminH(t,k),ME(i)−MEbestMEmax−MEminH(t,k)},(14) where MSEbest is the best MSE value found so far and MEbest is the best ME value.
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| 99.7 |
In reproduction operation, half of the optimal bacteria reproduce their offspring. Specially, we rank each bacterium according to PBM and half of bacteria with poor ranking reproduce. Assuming that every component in bacteria is independent with each other, and follow the Gaussian distribution, the reproduction operation presented as follows: Qt+1=ηnormσt+μt,(15) ηnorm=−2lnη1cos(2πη2),(16) where η1 and η2 are the uniformly distributed random number in interval [0, 1], the formula generating ηnorm is called BOX-Muller formula, μt, σt are the mean and standard deviation of the element in each position of the bacteria generated in iteration t and before.
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study
| 99.94 |
In traditional BFOA, the elimination-dispersal probability for each bacterium solution is equal . However, that will lose potential Pareto optimal solutions, consequently IBFOA sets elimination-dispersal probability mainly according to the PBM ranks of bacterium, shown as follows: Si=RiRmaxPed,(17) where Rmax is the maximum rank according to PBM, Ri is the rank of bacterium i, Ped is the basic elimination-dispersal probability.
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| 90.2 |
The application of the proposed model in solving a real world business valuation problem by determining the community structure in NG is presented in this section. Performance assessment is made in terms of forecast accuracy, running time for optimal solutions and domain knowledge extraction.
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| 99.9 |
We collected data on 13 typical Chinese RFID listed companies, and their main business areas covered are: tags and packaging, reading and writing equipment, system integration and software development. This data set contains samples of these companies from 1997 to 2014. Removing invalid samples, and 155 short-term (one-year-ahead forecast) samples, 142 medium-term (two-year-ahead forecast) samples and 129 long-term (three-year-ahead forecast) samples were obtained. We scaled the collecting data into interval [1, 5].
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other
| 98.75 |
We compared the performance of our method with several existing methods: RMs, support vector machine (SVM), NNs, NSGAII and SPEA2, which are two highly competitive algorithms for bi-objective optimization. We adopted 4 most commonly used RMs: multiple curvilinear regression with the kernel function of y = axb (RM1), y=1a+be−x (RM2), y = a+bx+cx2 (RM3), and y = a+bx+cx2+dx3 (RM4). Three kinds of NNs were adopted: back propagation NN (BPNN), general regression NN (GRNN), and radial basis function (RBF) NN. The reasons for selecting these NNs to present a contrast is that: BPNN is the most widely used NN, GRNN has the ability to converge to the underlying functions of the data with only few training samples available and needs relatively small knowledge to turn the parameter, and RBFNN has the characteristics of best approximation and global optimal performance.
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| 100.0 |
IBFOA, NSGAII and SPEA2 were adopted to find the community and further forecast the net profit. The proposed IBFOA was implemented in VB. SVM, NNs, and RMs aimed at optimizing MSE and were achieved in Matlab with the default setting. NSGAII and SPEA2 were also designed in Matlab environment according to the codes provided in and , respectively. The population size of NSGAII and SPEA2 were 20 and both ran 100 iterations.
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| 99.9 |
In IBFOA, initiated β and ε between -8.25~8.25, initiated θ between 0~1, set elimination-dispersal probability (Ped) to be 0.9, and the population size to be 20, IBFOA was run 100 iterations. In ROA models, risk-free interest rate r was replaced by the bank’s benchmark interest rate, which was selected as 3.5%, σ was set to be 40%.
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| 52.06 |
Three types of experiments were carried out: short-term, middle-term, and long-term test. In each test, randomly selected 100 samples as training samples and others as testing samples. The ME, MSE of profit forecast and ∆V are shown in Tables 2–4, respectively, where AV1 and UB1 represent average value (AV) and upper bound (UB) of ME and MSE in short-term test, AV2 and UB2 indicate that in medium-term test, and AV3 and UB3 mean that value of long-term test. Fig 7 shows the radar chart of average value of ME and MSE in different terms for various bi-objective algorithms.
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| 100.0 |
As can be seen from Tables 2–4, whether in the test of net profit forecast or company value evaluation, our IBFOA demonstrates superior performances, namely MSE, ME and ∆V are the smallest. Those show that using IBFOA to optimize BPF and clustering NG with BPF are good at predicting the profit of company and ECMM is expert in evaluating the business value.
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| 99.75 |
In Fig 7, the solutions of IBFOA densely distribute in the internal and optimal area of the radar chart, while the solutions of NSGAII and SPEA2 uniformly disperse in the outer edge of the chart. Therefore, the solutions of IBFOA are more Pareto optimal than those of NSGAII and SPEA2, in other words, NSGAII and SPEA2 are dominated by IBFOA, and those mean that the proposed IBFOA contributes to promoting the convergence of the algorithm as well as maintaining the diversity of the population.
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| 85.25 |
By the mechanism of IBFOA, we can obtain its time complexity O(n2), where n is the length of bacterium solution, as shown in Fig 5. Table 5 shows the running time of various models for each experiment. In Table 5, compared with other models, although our IBFOA takes a little more time, its high precision offsets this deficiency.
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| 99.94 |
We run IBFOA 100 iterations on the collected dataset to acquire the optimal offsets of the edge weight in NG, and then calculate the weights of nodes. Specifically, in Fig 3, for any evaluation factor node Ii, its weight is the sum of the absolute value of weight dij and its offset βij, that is, ∑j|βij+dij|, similarly, for any classification node Zij, its weight is ∑k|αijk+εijk|. Then nodes are sorted in descending order of their weights, and top 10 nodes of each type are displayed in Table 6.
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| 99.94 |
As can be seen from Table 6, factors significantly affecting the profitability of companies are net profit growth rate, revenue growth rate, producer price index, interest rate, etc. Although some factors, such as general index of total wages, total retail sales of social consumer goods, current asset turnover, and so on, are not listed as the key evaluation factors, some of their classification nodes have a significant impact on profitability. This shows that the NG based method can not only depict which factors have an effect on the profitability of companies, but also can describe the specific impact of each value of factors, for example, “GDP, grade 5” in Table 6 indicates if the GDP factor value is 5, it has an important impact on profitability.
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study
| 99.9 |
The valuation of the company is the basis for determining the relevant negotiating parameters when venture capitalist and entrepreneur negotiate the deal. A reliable valuation model helps to provide the basic standard for the measurement of the company’s fair market value as well as determining its price. In this study, combing CM method and ROA, a novel business valuation model for RFID companies is proposed. Compared with the existing methods, the proposed technique is distinctive in the following aspects:
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| 99.7 |
Firstly, unlike the current RM or NN based forecast methods, our method is based on NG. Moreover, we calculate the credibility of a node belonging to each community of NG, and then cluster the network based on the credibility. That is different from the traditional CM methods, which cluster the network directly using the network structure.
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| 99.9 |
Secondly, different from current BM which adopts rigid and fixed function expressions, in this study, the flexible BM is developed to calculate the clustering credibility, that is, adopt GPF to approximate BPF and use IBFOA to optimize the parameters of BPF.
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other
| 99.8 |
Thirdly, dissimilar to general single objective BFOA, IBFOA is bi-objective algorithm, which uses PBM to evaluate the reliability of forecast model. In the proposed PBM, SNDSM and SCD are adopted to rank the solutions, which can keep the diversity of the solutions without the cost of delaying the algorithm convergence.
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| 99.8 |
Finally, in IBFOA, new solutions are generated mainly through integrating the merits of existing solutions, and that spurs further search along the optimal direction so as to promote the convergence of the algorithm. Simultaneously, the parameters of the algorithm are adaptively adjusted according to the performance of IBFOA to further improve its efficiency.
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other
| 99.9 |
Simulation results of RFID companies show that the proposed model demonstrates higher accuracy and reliability compared with other models. Future research will focus on the further improvement of the proposed model of NG. Although the experiment results show NG structure in this paper is appropriate, we cannot prove that it is optimal. So an optimal NG structure for business valuation is hoped to be given in future studies.
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other
| 99.9 |
Eastern meditation techniques are a common integral part in everyday life as a means to alleviate working stress, and fostering an attentive mind. One main aim is to enable meditation practitioners to lead a more conscientious style of life. Besides Hindu meditation techniques as different styles of Yoga, Buddhist and Taoist meditation such as Qigong experiences an increasing number of practitioners in the Western hemisphere. Qigong comprises several techniques applied in Traditional Chinese Medicine (TCM) to strengthen physical and mental health. Qigong is commonly divided into static and dynamic forms. Static forms contain meditational techniques whereas dynamic forms afford bodily movements as a tool to direct practitioners’ attention (Tsang et al., 2002; Shinnick, 2006). Research on meditative Qigong practice demonstrates beneficial effects on health (for an overview see Ng and Tsang, 2009). A beneficial influence of Qigong practice on the cardiovascular system, i.e., on blood pressure (Xu, 1994; Lee et al., 2003; Cheung et al., 2005), and electrocardiographic parameters (Lee et al., 2000, 2003) was investigated. Furthermore, Qigong meditation lead to changes in breathing frequency (Sun, 1988). Positive effects of Qigong practice on mental health could be demonstrated in major depression (Tsang et al., 2003; Wang C.W. et al., 2013; Wang F. et al., 2013; Yeung et al., 2013; Yin and Dishman, 2014; Liu et al., 2015; Martinez et al., 2015), anxiety disorders (Lee et al., 2004a,b; Abbott and Lavretsky, 2013; Chan et al., 2013), post-traumatic disorders (Grodin et al., 2008; Kim et al., 2013), in the burnout syndrome (Stenlund et al., 2009, 2012), and in tinnitus (Biesinger et al., 2010). In several studies, a stress alleviating and relaxing effect in healthy subjects (Lee et al., 2005; Posadzki et al., 2010; Terjestam et al., 2010; Glei et al., 2012; Sousa et al., 2012; Hwang et al., 2013; Shim, 2014; Wang et al., 2014) was shown.
|
review
| 99.9 |
An essential research question is how the beneficial effects of Qigong meditation on physical and mental health are mediated by neurophysiological processes. Several studies applying electroencephalography (EEG) and fMRI demonstrated changes in brain activity induced by Qigong meditation. Most studies report increases in theta and alpha activity after Qigong meditation. The first studies on the effect of Qigong meditation on electrical brain activity reported alpha activity predominantly in the anterior brain regions (Wallace, 1970). More differentiated results of effects of meditational Qigong techniques on EEG activity are shown dependent on expertise level. Shifts in alpha activation were observed from posterior to anterior regions during Qigong meditation (Zhang et al., 1988a,b; Jang et al., 2004; Qin et al., 2009). Yang et al. (1994) obtained effects of Zhanzhuang Qigong on brain activity. After 1 year of practice, the alpha activity of the right frontal and right temporal regions increased significantly. The beta index of the right frontal and right temporal regions decreased significantly. A synchronization of brain activity was shown. The effects did not occur after half a year of regular Qigong meditation practice. Therefore, it was assumed to be a gradually adjusting process.
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review
| 99.4 |
Psychophysiological states of wakefulness and arousal as measured in terms of activation of particular EEG frequency bands are commonly correlated with distinct self-reported experiences of the Qigong state in regular meditators. Mostly, an increase of alpha activity is related to an experience of relaxation and increased well-being. An increase of EEG frontal theta activity is correlated to a self-report of mindfulness, an attentive state which is one of the main aims to reach in Buddhist meditation techniques (for an overview see Tomasino et al., 2014). How are changes in brain activity induced by Qigong meditation correlated to the reported psychophysiological states of relaxation, attentiveness, and attentional processing? In a recent study, EEG alpha-2 activity in posterior right parietal Brodmann areas 5, 7, 31, and 40 during Qigong meditation was demonstrated (Faber et al., 2012). The authors argue that the found patterns of brain activation reflect self-reference, attention and input-centered processing in Qigong meditation. Pan et al. (1994) identified frontal mid-line theta rhythm during the concentrative Qigong state compared to the state of mind reached by non-concentrative Qigong engagement. Shim (2012) found theta activity centering around the frontal lobe parts in Qigong masters and decreased alpha activity compared to beginners. The authors argue that Qigong experts maintained more deeply internalized and relaxed theta activity in the frontal lobe, which reflects an attentive mind. Qigong masters show efficiency in keeping a relaxed and attentive mind around central midline. Lee et al. (1997) investigated effects of ChunDoSunBup Qi-training on brain activity. The Qi-training consisted of acoustic exercises, bodily motion, and meditation. Increases in alpha activity in ChunDoSunBup Qi-training were observed in the occipital regions in eyes-open conditions. The increase in occipital alpha activity was correlated with less self-reported state anxiety. The authors argue that in ChunDoSunBup Qi-training activity of the occipital cortex is reduced and the thalamus is influenced.
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review
| 99.75 |
On a more structural level, Lehmann et al. (2012) showed reduced functional connectivity between cortical sources in Qigong meditation and reduced functional interdependence between brain regions. These results were interpreted to be a correlate of the reported subjective experience of non-involvement, detachment and letting go, as well as of all-oneness and dissolution of ego borders during Qigong meditation. Cheng et al. (2010) showed an effect of Qigong meditation on prefrontal activity. Practitioners showed in comparison to non-practitioners a significant decrease in deoxyhemoglobin levels suggesting an increase in prefrontal activation during Qigong meditation. Two fMRI studies report changes in brain activity under the state of Qigong during pain exposure in Qigong masters correlating with reduced pain sensation (Chan et al., 2006; Yu et al., 2007). Functional activation in the SII-insula region and other brain areas was reported, whereas a functional suppression under the state of Qigong meditation was observed. Thus, the found functional suppression in brain regions may be responsible for the reduced pain sensation in Qigong masters under the Qigong state.
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study
| 99.44 |
To our knowledge, there are no systematical studies reported in the Western hemisphere on effects on brain activity of dynamic Qigong techniques that afford bodily movement. For instance, the Health Qigong technique Wu Qin Xi comprises a consecutive sequence of complex movement configurations. These configurations are symbolic exposures of five animals (tiger, deer, bear, monkey, bird) with each movement sequence performed for several minutes. Practitioners are requested to focus on breathing when performing the movement sequences. According to theoretical assumptions of TCM, Wu Qin Xi is an intervention to strengthen especially physical health in general (for an overview see Yang and Wu, 2011). Only a few studies have been reported in the Western hemisphere on the dynamic Qigong technique Wu Qin Xi on physical health. Positive effects of Wu Qin Xi training are reported on lumbar spinal disease (Yeom et al., 2013; You et al., 2013, 2014; Zhang et al., 2014), blood lipid levels and the antioxidant enzyme activities (Chen, 2011). To date, no studies have been reported in the Western hemisphere on effects of Wu Qin Xi on neurophysiological parameters.
|
review
| 99.9 |
In previous experimental studies conducted in our working group, increases in midline fronto-central theta and shifts in alpha activity from posterior to anterior regions over the whole scalp after physical training of the dynamic Qigong technique Wu Qin Xi were observed (Henz et al., 2013, 2014, 2015; Henz and Schöllhorn, 2015). From a qualitative point of view, the found brain activation patterns were in line with findings of studies conducted with meditational (static) Qigong. As in studies on meditational Qigong, increases in fronto-central theta and posterior alpha activity were obtained. Thus, a relaxing effect in sense of an evidence-based approach can be stated for the dynamic Qigong technique Wu Qin Xi.
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study
| 100.0 |
As dynamic Qigong affords series of complex bodily movements, practitioners have to invest high effort and attention to learn the new movements. One benefit of that is that directing attention toward the movement execution and kinaesthetic sensations is intended to result in a centered state of internalized concentration. This mechanism plays a key role in mind-body therapies such as dynamic Qigong to draw the attention away from the everyday mind flow to reach an attentive state (for an overview, see Schmalzl et al., 2014).
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review
| 99.8 |
In the present study, we tested whether the beneficial effects of physical practice of dynamic Qigong on EEG brain activity can be reached by practicing the dynamic Qigong technique Wu Qin Xi mentally. From a theoretical point of view, this question is relevant because a large number of brain mapping studies have shown that the same neural areas are activated during either physical or mental simulation of motor actions. The rationale behind is that mental practice with motor content engages areas of the brain that govern movement execution (for an overview see Cicinelli et al., 2006; Sharma and Baron, 2013). This was not only demonstrated for cortical areas such as the supplementary area, the premotor cortex, and the primary motor cortex, but also for subcortical areas such as the basal ganglia and the cerebellum (Lotze et al., 1999; Jeannerod, 2001; Lafleur et al., 2002; Munzert et al., 2008). From a practical point of view, mental Qigong practice becomes relevant for the everyday practitioner in situations when the physical practice of Qigong is impracticable. I.e., when waiting at the train station surrounded by many other passengers it is not possible to practice dynamical Qigong physically due to a limited physical space. Further, this research question is relevant for designs of Qigong courses for elderly persons or patients with bodily impairments. Especially at the beginners’ stage, the movement sequences are practiced many times with several hours of practicing physically leading to increased physical tiredness. Here, the research question arises whether intervals of mental practice sessions would have the same effect on EEG brain activity as a merely physical Qigong practice. Finally, mental Qigong practice becomes relevant especially in persons who do not have the possibility to engage in Qigong training physically, either on the short-term, or on the long-term perspective. For instance, in stroke patients who have a low capability to move or in patients with chronically relapsing diseases of the musculoskeletal system mental practice of Wu Qin Xi would be a suitable therapeutic intervention. In achievement sports, when athletes experience phases of immobility due to sports concussions, mental practice of Wu Qin Xi Qigong would be an appropriate alternative to physical training.
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study
| 99.94 |
Recent research has shown that mental practice in the form of motor imagery causes comparable patterns of brain activation as physical training of the same movement. From this, we suppose that mental practice of the dynamic Qigong technique Wu Qin Xi leads to comparable effects in EEG brain activation as in physical Qigong training. More precisely, in line with the findings of previous studies on Qigong meditation, and on the dynamic Qigong technique Wu Qin Xi on EEG brain activity we hypothesize an increase in EEG midline fronto-central theta and posterior alpha activity when practicing the dynamic Qigong technique Wu Qin Xi mentally.
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study
| 100.0 |
Twenty-five subjects (mean age 27.9 years, SD = 2.91; age range: 19–47; 12 males, 13 females) volunteered in this study. Subjects were recruited from the Qigong workshops at the Institute of Sports Science of the University of Mainz and from sports science courses. Inclusion criteria for the study were participation in a Qigong workshop (30 h of lessons) and at least 1 h practice per week for 1 year. Regular Qigong practice was assessed prior to the experiment by a questionnaire. The subjects were all healthy, and had no current diseases or a history of neurological impairments or intake of medication that may have affected EEG recordings. All subjects were naïve as to the purpose of the current study. All subjects gave written informed consent. The experimental procedures were approved by the local ethics committee at the Johannes Gutenberg University of Mainz, Germany. All experimental procedures were carried out in accordance with the Declaration of Helsinki.
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study
| 100.0 |
The subjects were sat comfortably in a dimly-lit isolated room. At each measurement time point, participants began with a resting condition. Spontaneous EEG of the subject was recorded for 2 min for eyes-open, and 2 min for eyes-closed conditions. Then, they were required to perform a 30-min training session. The experiment contained three training conditions: Participants were required to perform the dynamic Qigong technique Wu Qin Xi (five animals) physically, and mentally in a within-subjects design. In the mental training condition, subjects were asked to perform the movement sequence mentally from the ego-perspective with imagination of kinaesthetic and visual cues. Further, they were required to apply the same breathing technique in the mental practice condition as in physical training. Additionally, a control condition was tested where subjects were presented a video showing practitioners performing the Qigong exercise Wu Qin Xi. All participants were familiar with mental practice of the Qigong technique Wu Qin Xi. Experimental conditions were randomized. All training sessions, and the control session were performed with eyes-open. EEG data were obtained during the four resting conditions: (1) pretraining rest, (2) post-Qigong training rest, (3) post-mental Qigong training rest, (4) post-video control rest, which were then used for subsequent analyses.
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study
| 100.0 |
Electroencephalography was recorded through the Micromed Brain quick amplifier and Micromed Brainspy software (Micromed, Venice, Italy). Recordings were taken from nineteen electrodes (Fp1, Fp2, F3, F7, Fz, F4, F8, C3, Cz, C4, T3, T4, P3, P7, Pz, P4, P8, O1, O2) placed according to the Int. Ten to twenty systems with reference to the nose. All electrode impedances were kept at 10 kΩ or below. The EEG signals were continuously recorded and digitized at a sampling rate of 256 Hz. The EEG signal was amplified with a fixed time constant of 0.3 s with a Butterworth second order high-pass filter at 0.5 Hz, and a low-pass filter at 120 Hz (frequency range: 0.5–120 Hz). Electrooculography (EOG) was monitored placed at the medial upper and lateral orbital rim of the right eye (time constant: 0.3 s; high-pass filter: 0.1 Hz; low-pass filter: 120 Hz; frequency range: 0.5–120 Hz).
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study
| 99.94 |
The spontaneous EEG was recorded for 2 min with eyes-closed, and 2 min eyes-open conditions. Subsequent analyses were performed separately for eyes-closed, and eyes-open conditions. The EEG and EOG signals were visually scored and portions of the data that contained aberrant eye movements, muscle movements of artifacts were removed. The EEG was analyzed and Discrete Fast Fourier Transform was used to obtain the mean power amplitudes in theta (4–7.5 Hz), low-frequency alpha-1 (8–10 Hz), high-frequency alpha-2 (10–12.5 Hz), beta (13–30 Hz), and gamma (30–40 Hz) bands. The ranges of high- and low-frequency alpha bands were defined according to previous studies by Aeschbach et al. (1999) and Cantero et al. (2002).
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study
| 100.0 |
A statistical comparison of power of theta, alpha-1, alpha-2, beta, and gamma bands was calculated by repeated-measure analyses of variance (ANOVA) including the within-subject factors as training condition (physical Qigong training, mental Qigong training, video control, baseline rest), condition (eyes-open, eyes-closed), and location (Frontal, Central, Temporal, Parietal, Occipital), followed by Bonferroni corrected post hoc tests for further comparisons. ηP2 was calculated to obtain effect sizes. Effects were considered to be statistically significant when the p-values were less or equal than 0.05. All data are expressed as the mean ± S.E.
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study
| 100.0 |
Figure 1 shows the mean power spectra for the theta, alpha-1, alpha-2, beta, and gamma band. The ANOVA of theta responses revealed significant differences for training, F(3,72) = 3.77, p = 0.014, ηP2 = 0.13. Post hoc comparisons showed that the spontaneous EEG theta power was significantly increased after physical and mental Qigong training compared to the video control condition, p = 0.03, and baseline rest, p = 0.01. No significant difference was obtained between physical and mental Qigong practice. The ANOVA of theta responses revealed highly significant differences between conditions (eyes-open, eyes-closed), F(1,24) = 8.92, p = 0.006, ηP2 = 0.27. The ANOVA of theta responses revealed significant results for training × condition, F(3,72) = 3.95, p = 0.012, ηP2 = 0.14. Post hoc comparisons showed that in mental practice theta activity was decreased in the eyes-closed condition compared to physical training, p = 0.007, video control, p = 0.021, and baseline rest, p = 0.015. The ANOVA of theta responses revealed significant differences between locations, F(4,96) = 3.41, p = 0.015, ηP2 = 0.12. Post hoc comparisons showed that spontaneous EEG theta power was increased at frontal, p = 0.017, central, p = 0.009, parietal electrodes, p = 0.021, and occipital electrodes, p = 0.007.
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study
| 100.0 |
Spontaneous electroencephalogram (EEG) brain activity at baseline rest, after the video control condition, and after physical and mental Qigong training. Increased theta and alpha-1 power was obtained after physical and mental Qigong practice. Alpha-2 power was increased after physical Qigong training in the eyes-open condition. In mental Qigong practice, theta power was decreased in the eyes-closed condition.
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study
| 100.0 |
The ANOVA of alpha-1 responses revealed highly significant differences for training, F(3,72) = 4.34, p = 0.007, ηP2 = 0.15. Post hoc comparisons showed that the spontaneous EEG alpha-1 power was significantly increased after physical and mental Qigong training compared to the control condition, p < 0.01 each, and baseline rest, p < 0.01 each. No significant difference was obtained between physical and mental Qigong practice. The ANOVA of alpha-1 responses revealed highly significant differences between experimental conditions (eyes-open, eyes-closed), F(1,24) = 14.088, p = 0.001, ηP2 = 0.370. The ANOVA of alpha-1 responses revealed no significant results for the factor training × condition. The ANOVA of alpha-1 responses revealed significant differences between locations, F(4,96) = 4.437, p = 0.002, ηP2 = 0.156. Post hoc comparisons showed that spontaneous EEG alpha-1 power was higher at central, and parietal electrodes than that of frontal, p < 0.05 each, temporal, p < 0.05 each, and occipital electrodes, p < 0.05 each.
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study
| 100.0 |
The ANOVA of alpha-2 responses revealed significant differences for training, F(3,72) = 3.30, p = 0.025, ηP2 = 0.12. Post hoc comparisons showed that the spontaneous EEG alpha-2 power was significantly higher after physical Qigong training compared to mental practice, p = 0.03, video control, p = 0.02, and baseline rest, p = 0.01. No difference was obtained between mental practice, video control, and baseline rest. The ANOVA of alpha-2 responses revealed highly significant differences between experimental conditions (eyes-open, eyes-closed), F(1,24) = 13.38, p = 0.012, ηP2 = 0.36. The ANOVA of alpha-2 responses revealed no significant results for training × condition. The ANOVA of alpha-2 responses revealed significant differences between locations, F(4,96) = 3.93, p = 0.005, ηP2 = 0.14. Post hoc comparisons showed that the spontaneous EEG alpha-2 power at central, and parietal electrodes was higher than that of frontal, p < 0.05 each, temporal, p < 0.05 each, and occipital electrodes, p < 0.05 each.
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study
| 100.0 |
The ANOVA of beta responses revealed significant differences for training, F(3,72) = 3.02, p = 0.033, ηP2 = 0.11. Post hoc comparisons showed that the spontaneous EEG beta power was increased in the video control condition, compared to mental practice, p = 0.04, physical training, p = 0.02, and resting baseline, p = 0.03. Significant differences were found between experimental conditions (eyes-open, eyes-closed), F(1,24) = 4.66, p = 0.041, ηP2 = 0.16. The ANOVA of beta responses revealed significant results for training × condition, F(3,72) = 3.17, p = 0.030, ηP2 = 0.12. The ANOVA of beta responses revealed significant differences between locations, F(4,96) = 2.74, p = 0.033, ηP2 = 0.10. Post hoc comparisons showed that the spontaneous EEG beta power at central electrodes was higher than that of frontal, p = 0.03, temporal, p = 0.04, parietal, p = 0.04, and occipital electrodes, p = 0.03.
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study
| 100.0 |
The ANOVA of gamma responses revealed significant differences for training, F(3,72) = 3.43, p = 0.022, ηP2 = 0.13. Post hoc comparisons showed that the spontaneous EEG gamma power was increased in the video control condition, than in mental, p = 0.03, and physical Qigong practice, p = 0.02, and at baseline rest, p = 0.04. Significant differences were found for experimental conditions (eyes-open, eyes-closed), F(1,24) = 5.45, p = 0.028, ηP2 = 0.19. The ANOVA of gamma responses revealed significant results for training × condition, F(3,72) = 3.04, p = 0.034, ηP2 = 0.11. Post hoc comparisons showed that gamma activity was increased in the video control condition in eyes-open compared to eyes-closed condition, p = 0.031. The ANOVA of gamma responses revealed significant differences between locations, F(4,96) = 2.83, p = 0.029, ηP2 = 0.11. Post hoc comparisons showed that spontaneous EEG gamma power at temporal electrodes was increased compared to frontal, p = 0.02, central, p = 0.03, parietal, p = 0.03, and occipital electrodes, p = 0.03.
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study
| 100.0 |
The literature includes several previous investigations on effects of Qigong meditation on EEG brain activity. Most studies report an increase in EEG frontal theta and shift of alpha activity from posterior to anterior regions during and after Qigong meditation. In the present study, we demonstrate an increase of midline fronto-central theta and posterior alpha-1 and alpha-2 activity after practice of the dynamic Qigong technique Wu Qin Xi. The finding of increases in midline fronto-central theta and shifts in alpha-1 and alpha-2 activity from posterior to anterior regions after physical training of the dynamic Qigong technique Wu Qin Xi was replicated (Henz et al., 2013, 2014, 2015; Henz and Schöllhorn, 2015). Further, our results mirror the findings of previous studies of effects on EEG brain activity after Qigong meditation demonstrating a shift of EEG activity from posterior to anterior regions (Zhang et al., 1988a,b; Yang et al., 1994; Litscher et al., 2001; Jang et al., 2004; Tei et al., 2006a,b, 2009; Qin et al., 2009; Faber et al., 2012). Therefore, a comparable effect for dynamic Qigong on EEG brain activity as found in studies on meditational Qigong can be stated. Training of the dynamic Qigong technique Wu Qin Xi induces a relaxed and attentive mind as indicated by an increase in midline fronto-central theta and shifts in alpha activity from posterior to anterior regions. In conclusion, a relaxing effect of the dynamic Qigong technique Wu Qin Xi in sense of an evidence-based approach can be stated. Our results indicate that the dynamic Qigong technique Wu Qin Xi induces a centered state of mind that has to be distinguished from mind-wandering. Empirical evidence is shown that frontal EEG theta activity is activated in attentional processes and correlates negatively with the default mode network in resting state (Scheeringa et al., 2008).
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| 99.94 |
The highlighted finding of this study is that mental practice of the dynamic Qigong technique Wu Qin Xi causes significant modulations of EEG brain activity. Practicing the dynamic Qigong technique Wu Qin Xi mentally results in increased fronto-central midline theta activity and increases in alpha-1power in the same intensity as in physical training in eyes open-conditions. Therefore, mental practice of the dynamic Qigong technique Wu Qin Xi has the same effect on EEG brain activity as physical training considering the eyes-open condition.
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| 100.0 |
In the present study, the training by condition interaction with respect to changes in the theta band was replicated. In a previous study, it was shown that after training of the dynamic Qigong technique Wu Qin Xi theta activity was increased in eyes-open conditions whereas in the eyes-closed condition theta activity was diminished (Henz et al., 2013). In the current study, the same pattern of results with a training × condition interaction was demonstrated. Our results are in line with a study conducted by Aftanas and Golocheikine (2001) who examined EEG brain activity in meditation in eyes-open and eyes-closed conditions. Depending on eyes-open and eyes-closed conditions, different patterns of anterior and midline theta activity occurred. The authors argue that the obtained theta activity reflects internalized attentional processes during meditation that are dependent on eyes-open and eyes-closed states.
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| 100.0 |
The found patterns of brain activations are partially in line with our hypotheses. Our speculation was that based on findings from EEG studies on motor imagery (i.e., Jeannerod, 2006) nearly same effects on EEG brain activity would occur in mental as well as in physical training of the Qigong technique Wu Qin Xi. Having a closer look at theta activity, a decrease in mental practice in the eyes-closed condition compared to physical training, and the remaining conditions was observed. Therefore, our results indicate different underlying cognitive and neurophysiological processes in mental and physical Wu Qin Xi Qigong training. We hypothesized that different attentional processes during mental and physical Wu Qin Xi Qigong training play an essential part that lead to the obtained brain activation patterns. In previous studies on Qigong meditation, frontal and central midline theta activity was associated with internalized attentional processes. For instance, frontal mid-line theta rhythm during the concentrative Qigong state compared to the state of mind reached by non-concentrative Qigong meditation was shown by Pan et al. (1994). In the same manner, Shim (2012) demonstrated frontal theta activity after Qigong meditation in experienced practitioners. In previous studies on Qigong meditation, spontaneous resting EEG was measured with eyes-open. Therefore, no comparison between eyes-open and eyes-closed resting state EEG after Qigong meditation was done although this might allow insights into the underlying attentional processes. For instance, recent studies revealed an association between theta power and switching of involuntary attention from internally directed attention specific to the eyes-closed state to externally directed attention specific to the eyes-open state (Boytsova and Danko, 2009). Specific for meditational states, Aftanas and Golocheikine (2001) demonstrated effects of eyes-open resting state, and eyes-closed resting state on EEG theta activity as a correlate for internalized attentional processes.
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| 99.94 |
One line of argumentation to explain the obtained results for modulations of theta activity dependent on eyes-open and eyes-closed state could be that practicing Qigong physically requires the subjects to strongly direct their attention to the performance of the complex movement sequences and the resulting kinaesthetic sensations as it is conceptualized in mind-body therapies such as Qigong. One main aim is to draw the attention away from the everyday mind flow to reach an attentive state (for an overview, see Schmalzl et al., 2014). As a consequence, a state of deep relaxation is reached in physical training mirroring in increased theta activity in eyes-open as well as eyes-closed conditions.
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review
| 99.56 |
In physical Wu Qin Xi training, many details of the complex movement sequences have to be considered during movement performance, which might lead to a strong internalized attentional processing. From studies on the role of attentional focus during movement performance it is known that an external focus of attention alleviates movement performance, and therefore requires less effort, whereas an internal focus of attention requires more attentional demands. For instance, it has been shown that movement performance benefits from an external focus of attention in gymnastics (Abdollahipour et al., 2015). Several recent studies have provided evidence that movement efficiency, or the physical effort exerted to produce a given performance level or outcome, is also enhanced by an external focus (Zachry et al., 2005; Marchant et al., 2009). Benefits of directing external focus have been found to result in more effective motor performance than those inducing an internal focus by directing attention to the body movements themselves (Totsika and Wulf, 2003; Wulf et al., 2003, 2009; Wulf, 2007). It is argued that focusing on the intended movement effect facilitates the utilization of unconscious or automatic processes, resulting in greater movement ease or fluidity (Wulf et al., 2001; Wulf and Lewthwaite, 2010). Conversely, focusing on one’s own movements leads to a more conscious type of control, thereby constraining the motor system and disrupting automatic control processes (Wulf et al., 2001). It has been shown that relative to an internal focus, an external focus reduces attentional demands and results in the utilization of fast reflexive (automatic) feedback loops (Wulf et al., 2001). Transferring these findings on the physical performance of dynamic Qigong technique Wu Qin Xi, induction of internalized attention might be best reached with an attentional demanding complex motor task as in the movement sequences of Wu Qin Xi.
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review
| 98.75 |
From this point of view, an important question arises: does an internal focus of attention during Qigong practice lead to a more demanding type of movement control, and therefore binds more attention which finally results in increased EEG theta and alpha activity? Especially in non-expert practitioners, demanding monitoring processes of movement performance during Qigong practice could result in enhanced stress reduction mirrored by increased EEG theta and alpha activity. We argue that one underlying cognitive mechanism is a working memory load which results from increased motor affordances. From a neurophysiological point of view, frontal theta power has been found to increase with working memory load (Gevins et al., 1997; Krause et al., 2000; Jensen and Tesche, 2002; Onton et al., 2005). Challenging working memory finally results in a loss of a merely executive action control due to limited capacity. Subsequently, practitioners’ attention is drawn away from cognitive engagement in everyday thoughts by a demanding monitoring process. Additionally, a loss of cognitive action control toward a state of non-focusing and non-involvement on the everyday mind flow is one of the main aims in Eastern meditation techniques. Especially in Buddhism-related meditation traditions a mindfulness state is reached by sustained attention on the body. Activations in midline fronto-central lobe structures associated with attentional processes possibly confirm the fundamental role of mindfulness shared by many Buddhist meditations (for an overview see Tomasino et al., 2014). The finding of increased theta activity after physical Qigong training in eyes-closed conditions in our study indicates that internalized attention might be reached more easily when attention and breathing behavior is guided by movements in Qigong training.
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study
| 88.25 |
A second line of argumentation is that breathing behavior in physical practice underlies a tighter regulation and a stronger forcing due to a coupling to the movement sequences of Wu Qin Xi than in mental practice. The breathing technique is strongly determined in the movement sequences of Wu Qin Xi, which might lead to the observed increase in low frequencies in the EEG in physical training due to a strong reinforcement by the movement sequences. Recent EEG studies have shown that abdominal breathing techniques lead to increased frontal theta activity (e.g., Yu et al., 2011; Chervin et al., 2012; Park and Park, 2012). Considering breathing as a meditation technique, it was observed that Shaolin Dan Tian Breathing increases EEG frontal theta activity (Chan et al., 2011). The authors argue that the observed increase in frontal theta activity in Shaolin Dan Tian Breathing is a correlate for an attentive mind. Further, several studies have shown that abdominal breathing enhances EEG alpha activity. For instance, Arambula et al. (2001) demonstrated increases in EEG alpha activity in abdominal breathing techniques. Increased alpha band activity with decreased theta band activity was achieved by abdominal breathing during Zen practice (Arita, 2012). Comparing alpha-1 and alpha-2 activity Fumoto et al. (2004) showed increases in alpha-1 activity with disappearance of alpha-2 activity in voluntary abdominal breathing. Therefore, a stronger reinforcement of breathing behavior by movement performance in physical training would be a suitable interpretation for the obtained pattern of EEG brain activity. This might explain a diminished theta activity in mental practice in the eyes-closed condition compared to physical training.
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study
| 99.8 |
A third line of argumentation considers the role of visual processing during mental practice. Dimitriadis et al. (2015) showed modulations in theta activity as a correlate for mental workload in visual processing. Transferring these findings on mental practice of Wu Qin Xi, the decreased theta activity in eyes-closed conditions might reflect attentional demands of visual processing of the movement sequence.
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study
| 99.94 |
To our knowledge, the present study is the first one that compares effects of mental and physical dynamic Qigong training on EEG brain activity in eyes-open and eyes-closed conditions. From this, we supposed that mental practice of the dynamic Qigong technique Wu Qin Xi leads to comparable effects in EEG brain activation than in physical Qigong training. Having a closer look at theta activity in mental practice, a centering around the central areas compared to activation of a broader range of locations after physical training in eyes-open conditions was obtained. From this, we conclude different attentional processes in mental and physical Wu Qin Xi Qigong training.
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study
| 100.0 |
The results of our study have important implications for the design of interventions applying the dynamic Qigong technique Wu Qin Xi. Especially in clinical populations who display reduced spontaneous alpha activity as in stress mediated diseases like burnout (see van Luitjelaar et al., 2010), but as well as in anxiety, depression, and bipolar disorders a strong induction of alpha activity by Qigong practice is essential for the therapeutic success of the intervention. With the results of the current study we showed that physical as well as mental training of the Qigong technique Wu Qin Xi lead to significant increases in low frequencies in spontaneous EEG. Therefore, mental practice of Wu Qin Xi is a suitable alternative therapeutic as to physical dynamic Qigong training.
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study
| 99.94 |
In the present study, we tested whether the beneficial effects of physical practice of the dynamic Qigong technique on EEG brain activity can be reached by practicing Wu Qin Xi mentally. This research question becomes relevant for the everyday practitioner in situations when the physical practice of Qigong is impracticable. Further, this research question is relevant for designs of Qigong courses for elderly persons or patients with bodily impairments. Especially at the beginners’ stage, the movement sequences are practiced many times with several hours of practicing physically leading to increased physical tiredness. Here, the research question arises whether intervals of mental practice sessions would have the same effect on EEG brain activity as a merely physical Qigong practice.
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| 99.94 |
Secondly, mental Qigong practice becomes relevant especially in persons who do not have the possibility to engage in Qigong training physically, either on the short-term, or on the long-term perspective. For instance, in stroke patients who have a low capability to move, mental training of the Qigong technique Wu Qin Xi would be an appropriate intervention to induce low frequencies in EEG brain activity and especially stimulate the Mu wave activity in the motor and premotor areas. Recent research has shown that mental practice in the form of motor imagery causes comparable patterns of brain activation as physical training of the movement. The rationale behind is that mental practice with motor content engages areas of the brain that govern movement execution (for an overview see Cicinelli et al., 2006; Sharma and Baron, 2013). Increases in alpha power are reported during mental practice of swimming movements (Beyer et al., 1990). In the same line, changes in EEG alpha oscillations in mental practice of volleyball serves were observed (Stecklow et al., 2010). Transient activations of the M1 area during mental practice are reported (Jeannerod, 1994, 2006; Pfurtscheller et al., 1997; Romero et al., 2000; Munzert et al., 2009). More precisely, inhibition of a movement leads to synchronization in alpha activity whereas preparation, execution and imagery lead to a de-synchronization in sensorimotor areas in the alpha and beta bands (Neuper et al., 2005; Neuper and Pfurtscheller, 2010). In a recent study, it was shown that these specific neuronal circuits are built with increasing experience with a motor task (Nakata et al., 2010). Reiterated engagement of motor areas as in mental Wu Qin Xi training is intended to influence brain plasticity phenomena, improving functional outcomes (Cramer et al., 2011; Dimyan and Cohen, 2011; Moisello et al., 2013). Recently, the rehabilitative potential of motor imagery was shown contributing to significantly better motor functional outcomes in sub-acute stroke patients with severe motor impairments (Pichiorri et al., 2015). Further, in patients with chronically relapsing diseases of the musculoskeletal system mental practice of Wu Qin Xi would be a suitable therapeutic intervention. Finally, in achievement sports, when athletes experience phases of immobility due to sports concussions, mental practice of Wu Qin Xi Qigong would be an appropriate alternative to physical training.
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review
| 99.9 |
Further research is needed to clarify whether regular mental practice enhances neuroplasticity as shown for physical training of the dynamic Qigong technique Wu Qin Xi (Henz et al., 2013) or in meditational Qigong. From studies on the role of expertise level in Qigong practice it was demonstrated that development of a frequency-specific brain excitability is a long-term process. For instance, Shim (2012) demonstrated theta activity centering around the frontal lobe parts (Fp1, Fp2, Fz, F4) in Qigong masters and decreased alpha activity compared to beginners. The authors argue that Qigong experts maintained more deeply internalized and relaxed theta activity in the frontal lobe which reflects an attentive mind. Therefore it is argued that Qigong masters show efficiency in keeping a relaxed and attentive mind around central midline. One further interesting question is whether the same effects would be expected for mental training of the Qigong technique Wu Qin Xi in clinical populations with reduced alpha oscillations at resting baseline (see Basar et al., 2012).
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review
| 98.75 |
Purkinje cells (PCs) are the final common collector of the whole neuronal activity generated in the granular and molecular layer of the cerebellar cortex (Eccles et al., 1967; Ramón y Cajal, 1995). A complex structural and functional organization allows PCs to elaborate the largest synaptic input of the brain, amounting to over 200,000 synapses in rodents (Korbo et al., 1993). PCs are characterized by active dendrites (Llinás and Sugimori, 1980a,b) endowed with different types of voltage-dependent channels. Several experiments and models have been developed with the aim to explain how PCs integrate synaptic inputs (De Schutter and Bower, 1994a,b; Rapp et al., 1994; Roth and Häusser, 2001; Brunel et al., 2004; Santamaria and Bower, 2005; Steuber et al., 2007; Masoli et al., 2015), but the role of voltage-dependent currents in local computation has not been fully clarified. PCs have recently been proposed to react to input bursts by generating a burst-pause response (BPR), which has been correlated with animal behavior (Cao et al., 2012; Herzfeld et al., 2015). While the intervention of inhibitory molecular layer interneurons (molecular layer interneurons; Barmack and Yakhnitsa, 2008; Bower, 2010; Grasselli et al., 2016) has been proposed to regulate the pause, the role played by dendritic properties in BPR generation remained unclear.
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review
| 99.7 |
BPRs are thought to reflect a stereotyped PC response to bursting granular layer inputs. The granule cells generate brief spike bursts in vitro (D’Angelo et al., 1995; Nieus et al., 2006) and in vivo (Chadderton et al., 2004; van Beugen et al., 2013; Powell et al., 2015) in response to bursts in the mossy fibers (Rancz et al., 2007). These granule cell bursts are finely regulated by GoC inhibition (Mapelli et al., 2009; Nieus et al., 2014) generating specific patterns in the number and timing of spikes (D’Angelo and De Zeeuw, 2009; Arleo et al., 2010). The granule cell bursts are then conveyed to molecular layer activating PCs and molecular layer interneurons, which in turn generate feed-forward inhibition on PCs (Santamaria et al., 2007; Rieubland et al., 2014; Zhang and Südhof, 2016). Therefore, granule cells and molecular layer interneuron set-up complex spatio-temporal patterns of activity generating PC responses that have been classified as type I, II and III (De Zeeuw et al., 2011) and are differentiated depending on Zebrin positive or negative (Z+ or Z−) PCs in different cerebellar areas (Zhou et al., 2014, 2015).
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review
| 93.9 |
Since synaptic activity patterns impinging on PCs are not fully known and since monitoring the PC dendritic response is challenging, a first insight into the way PCs respond to their inputs can be obtained using in silico simulations. Here we have faced the issue by exploiting a detailed PC model (Masoli et al., 2015) that was extended with excitatory and inhibitory synapses. This model is auto-rhythmic and its electroresponsiveness has been validated against a large set of biological experiments providing an ideal substrate to explore how intrinsic electroresponsiveness is modulated by synaptic inputs. Simulations with this PC model allowed us to face a set of questions. Does the PC model generate BPR in response to synaptic inputs? Is BPR different in Z+ and Z− PC models? Is BPR affected by the specific location of inputs on dendritic branches, as in the case of ascending axons (aa) vs. parallel fiber inputs (Sims and Hartell, 2005, 2006; Walter et al., 2009)? Is BPR different when inputs are randomly distributed rather than concentrated in limited sub-regions? What is the impact on BPR of the number of spikes and of the intensity of inhibition in the input burst? What are the mechanisms of BPR (intrinsic electroresponsiveness or synaptic inhibition) and what is the role of voltage-dependent ionic channels? Can BPR be modulated by synaptic plasticity? Simulations can provide a coherent mechanistic hypothesis on this broad range of questions that would be otherwise be hard to achieve.
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| 100.0 |
The simulations showed that, for a broad set of activity regimens, PCs generate BPRs modulated by the excitatory/inhibitory balance and by synaptic plasticity. The underlying BPR mechanism reflects modulation of intrinsic pacemaking by Ca/KCa currents generated in the dendritic compartment and transmitted to the soma and axon initial segment (AIS) through the internal resistance. Therefore, BPR emerges as a relevant coding strategy for PCs that could be modulated by spatio-temporal granule cell spike patterns and synaptic inhibition and plasticity, generating the specific outputs to be transmitted to DCN.
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study
| 100.0 |
The present synaptic PC model is based on the recent PC model of intrinsic electroresponsiveness by Masoli et al. (2015), which in turn derives its morphology from Rapp et al. (1994). The present model updates in several respects the previous active model by De Schutter and Bower (1994a,b) by incorporating a completely new set of ionic channels, by dislocating the action potential generation mechanism in the AIS and axon, by using dynamic synapses and by exploiting a wide set or recent experimental evidences for validation. The model by Masoli et al. (2015) (available on ModelDB), which was built to reproduce PC responses to current injections in vitro and in vivo, is extended here by connecting excitatory and inhibitory synapses on the dendrites and by evaluating a large set of combinations in the input space. As a further update to account for recent in vivo data, the maximum conductance of some ionic channels (soma HCN1 = 0.001 mS/cm2; soma Kv3.4 = 0.0515 mS/cm2; AIS Nav1.6 = 0.8 mS/cm2) was adjusted to raise the average frequency from 35 Hz to 40 Hz in the Z+ PC model (Zhou et al., 2014). The Z− differed Z+ models only for the presence of TRPC channels. TRPC channels are cationic channels generating a tonic depolarizing current, which, once placed in Z− PCs, raised background frequency to around 90 Hz (dendrite TRPC = 4.18e−6 mS/cm2). All simulations were performed at 37° with fixed time step (0.025 ms) and were run using NEURON multisplit (Python 2.7; NEURON 7.5; Hines et al., 2007, 2009) to exploit the eight-core processor of an AMD FX 8350 with 16 GB RAM and an AMD Ryzen 1800x 8 cores/16 threads with 32 GB RAM. The data were analyzed with custom python and MATLAB scripts.
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study
| 100.0 |
PCs are endowed with hundred thousand spines (O’Brien and Unwin, 2006), each one receiving a single contact from an aa or a parallel fibers (pf) synapse (Walter et al., 2009). While spines may be critical to implement local biochemical processing during synaptic transmission, they have been suggested to generate linear attenuation with little impact on the overall synaptic excitation process (Ly et al., 2016). Therefore, spines were not reconstructed in the model and excitatory synapses were placed directly on the dendrites. The dendrites were divided into three orders of branching [branch I, composed by 105 sections with diameters between 3.5 μm and 9 μm; branch II, composed by 1111 sections with diameters between 1.2 μm and 3.5 μm; branch III, composed by 383 sections with a diameter between 0 μm and 1.2 μm] receiving specific synaptic inputs. Concerning excitatory synapses (Figure 1A), branch II received only pf synapses and branch III received only aa synapses (Santamaria et al., 2007; Lu et al., 2009; Bower, 2010). Branch I should have received a cf input (Kaneko et al., 2011; Zhang et al., 2015) but this was not used here (not shown). Concerning inhibitory synapses (Figure 1A), these were distributed only on branches I and II for a total of 221 sections, since branches III were experimentally reported not to have inhibitory synapses (Lu et al., 2009; Bower, 2010). Inhibitory synapses on branches I and II were made identical, although those on section I may have a different control (He et al., 2015). The inhibitory BC synapses on the soma and AIS (Iwakura et al., 2012; Blot and Barbour, 2014; Kole et al., 2015) were not used here (not shown).
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| 100.0 |
Synaptic activation of the Purkinje cell (PC) neuron model. (A) The localization of synapses on PC model dendrites. The dendritic tree receives 1111 excitatory AMPA-type synapses from parallel fibers (pfs; red dots) and 383 from ascending axons (aa; blue dots). The aa are locate on more distal dendritic branches than pf synapses. The GABA-A-type synapses from stellate cells (SCs) were distributed over 1332 dendrites (green dots). (B) Unitary EPSCs and IPSCs recorded from the soma. The bars (same colors as in (A) indicate the dendritic localization. The EPSPs recorded from the soma show increasing electrotonic filtering moving farther away from soma (Roth and Häusser, 2001). (C) Unitary EPSCs elicited in the dendrite using a random stimulation pattern (black ticks) and recorded from the PC model soma. The dotted line represents the experimental result (Dittman et al., 2000).
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| 100.0 |
The excitatory and inhibitory synapses were built according to Nieus et al. (2006, 2014) following a modified Tsodyks and Markram formalism (Tsodyks et al., 1998). Model EPSCs and IPSCs were adapted to reproduce unitary synaptic currents recorded from PCs at 37°.
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study
| 99.94 |
The glutamatergic AMPA receptor-mediated EPSC model was derived from granule cells and the maximum synaptic conductance was balanced to reproduce a single pf EPSC (Barbour, 1993; Isope and Barbour, 2002). Release probability was adapted to account for pair-pulse facilitation (Zhang et al., 2015). The aa synapses were made with identical physiological properties as the pf synapses (Walter et al., 2009). The AMPA synapse parameters were: release probability = 0.13, τREC = 35.1 ms, τfacil = 54 ms, τI = 6 ms, Gmax of 2800 pS, reversal potential = 0 mV. The model as a whole faithfully reproduced the response to random pf stimulations (Dittman et al., 2000). The number of synapses was adjusted to imitate experimental observations of pf bursts that elicited excitatory 250 Hz spike burst in the PC soma (Walter and Khodakhah, 2006).
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study
| 100.0 |
The gabaergic GABA-A receptor-mediated synaptic mechanism was derived from granule cells and modified by maintaining the alpha1 subunit but deleting the alpha6 subunit (absent in PCs). The value for the fitting were taken from Zhang et al. (2015) to account for in vivo recording from stellate cell (SC) in the range P35–P42 to better match the mature PC. The GABA-A synapse parameters were: release probability = 0.35, τREC = 15 ms, τfacil = 4 ms, τI = 1 ms and a Gmax = 1200 pS, reversal potential = −60 mV. The number of synapses was adjusted to imitate experimental observations of multiple SC that elicited background inhibitory activity at 1.5 Hz and single SC bursts up to 150 Hz (Zhang et al., 2015).
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study
| 100.0 |
This protocol was constructed to investigate the BPR. The fundamental patterns were designed by combining a pf/aa bursts with a SC burst (De Zeeuw et al., 2011; van Beugen et al., 2013; Valera et al., 2016). In a first design, excitatory synapses were randomly distributed over 100 dendrites, both from aa or pf. This allowed to obtain a 250 Hz PC burst as in Walter et al. (2009). The inhibitory burst was composed by three spikes with a 7 ms interspike interval (ISI). Inhibitory synapses were distributed over 25 dendrites and delayed by 4 ms with respect to the excitatory burst to account or synaptic delays along the afferent neuronal chain (granule cell to SC to PC; see also Ramakrishnan et al., 2016). Variants to this pattern were used to reproduce type I, II and III responses (De Zeeuw et al., 2011; Valera et al., 2016), to evaluate the impact of synaptic inhibition, to selectively activate aa rather than pf synapses, to change the intensity or frequency or duration of the bursts, to modify synaptic parameters like release probability and maximum conductance, to restrict pf/aa activity to specific dendritic sectors.
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study
| 100.0 |
The model response was recorded either in voltage clamp or in current-clamp at the soma, and the voltage-dependent ionic conductances were modified in some cases to test their impact on BPR generation. The membrane voltage, the calcium concentration, the ionic currents from each model section were recorded and saved in a nested MATLAB file. The model response properties were analyzed using MATLAB routines (MathWorks, Natick, MA, USA) and custom made Python scripts, using data recorded during each simulations. Each simulation data file contained information about the membrane voltage, ionic channels and synaptic currents recorded in specific location throughout the models.
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study
| 100.0 |
Biophysical analysis of the model was carried out according to standard theory (Jack et al., 1975). The model electrotonic properties were analyzed using NEURON functions yielding the input impedance, Zin, for each model section and the corresponding signal attenuation between e.g., a dendritic sections and the soma, A = Vdend/Vsoma. This allowed to determine the electrotonic distance L = ln(A). This definition coincided with the more classical one (L = anatomical distance/length constant) defined when a neuron can be reduced through the 3/2 power branching rule to an equivalent cylinder. The NEURON definition proves particularly useful since PCs do not follow the 3/2 power branching rule (Hines and Carnevale, 2001; Hines et al., 2007, 2009).
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study
| 100.0 |
Since the PC was continuously pacing and input bursts were applied randomly with respect to ongoing spike discharge, repeated PC responses to the inputs differed one from each other. This behavior was represented using raster plots and peri-stimulus time histograms (PSTH), that were constructed using MATLAB routines and were subsequently analyzed to extract the average properties of PC responses.
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study
| 99.94 |
The impact of cortical input patterns, conveyed through pf, granule cell aa and stellate cells (SC), on PC spike firing was investigated using detailed PC models differentiated into Z+ and Z− types (Masoli et al., 2015). These models differ for the expression of depolarizing TRPC-like channels in the terminal dendrites, resulting in higher background SS activity in Z− than Z+ PCs (around 90 Hz vs. 45 Hz). Both models were endowed with excitatory and inhibitory synapses, which were located according to anatomical measurements. This, combined with the filtering properties of dendrites, caused the expected EPSP electrotonic decay from synapses to soma (Roth and Häusser, 2001). The synaptic models were endowed with dynamic mechanisms (Tsodyks and Markram, 1997; Nieus et al., 2006, 2014; Figures 1A,B) allowing to adapt neurotransmission to arbitrary spike patterns (Dittman et al., 2000; Figure 1C).
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| 100.0 |
A first question was whether the PC model was able to generate BPRs following activation of excitatory and inhibitory synapses (Cao et al., 2012; Herzfeld et al., 2015) and whether BPRs were different between Z+ and Z− PCs. The PC responses to input bursts generated by Granule cells (Rancz et al., 2007; van Beugen et al., 2013; Powell et al., 2015; Wilms and Häusser, 2015; Delvendahl and Hallermann, 2016) were tested in Z+ and Z− PC models in three stereotyped functional cases corresponding to the definitions of type I, type II and type III responses reported in vivo (De Zeeuw et al., 2011). Type I responses were driven by pure Granule cell excitatory inputs (100 synapses), type II responses were driven by both granule cell excitatory inputs (100 synapses) and SCs inhibitory inputs (25 synapses), type III responses were driven by SC inhibitory inputs only (25 synapses; Figure 2). In all cases, molecular layer interneuron inhibition was delayed by 4 ms to account for delays accumulated along the synaptic chain (Eccles et al., 1967; Ramakrishnan et al., 2016). In this set of simulations, a random distribution of active synapses was used and maintained the same with all the different stimulation patterns (Figure 2A).
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| 100.0 |
Burst/Pause responses (BPR) in the PC model (A) Distribution of the excitatory and inhibitory synapses used for the simulation. The synapses were distributed randomly in the specific dendritic branches. (B) Type I, II, III responses in the Z+ and Z− PC models. Type I responses were elicited by a 500 Hz—10 spikes burst in 100 pfs. This elicited a ~250 Hz burst, that was followed by a pause in Z+ but not in Z− PC models. Type II responses were elicited by a 500 Hz—10 spikes burst in 100 pfs followed by a 130 Hz—three spikes burst in 25 SCs. This elicited a ~250 Hz burst, that was followed by a pause in Z+ but not in Z− PC models. The pause occurred in the Z− model only when the number of SC synapses was increased to 100. Type III responses were elicited by a 130 Hz—three spikes burst in either 25 SCs. This elicited a pause in Z+ but not in Z− PC models. The pause occurred in the Z− model only when the number of SC synapses was increased from 25 to 100. The Z− behaved similarly to Z+ model when the Z− was equalized to Z+ basal firing rate with somatic injection of a constant negative current. (C) Left, Sensitivity of the burst to the number of inhibitory synapses. The interspike interval (ISI) for each spike is reported. Increasing the number of inhibitory synapses does not change the burst but generates progressively longer pauses with a sharper burst/pause transition. Right, using the example with 25 SC synapses for comparison, the impact of ascending axons (aa) stimulation is evaluated. When aa are made identical to pf synapses, there is no clear pause generation. However, this occurs when the aa synapses are potentiated by increasing their postsynaptic maximum conductance and presynaptic release probability (Sims and Hartell, 2005, 2006) demonstrating “functional equivalence” with pf synapses (Walter et al., 2009) in BPR.
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| 100.0 |
In Type I responses, a brief pf burst elicited a PC burst terminating in close coincidence with the stimuli (average frequency of 260 Hz) followed by a pause, configuring a typical BPR. The pause between the last spike of the burst and the first spikes when SS activity restarted showed an ISI of 50.46 ± 25.6 ms. Type II responses showed a similar BPR as type I, with the pause showing an average ISI of 48.2 ± 20.4 ms (Steuber et al., 2007). Type III responses showed just the pause, with an ISI of 27.4 ± 3.7 ms. Thus, with this stimulation pattern, BPRs were determined by intrinsic properties of Z+ PCs and were accentuated by molecular layer interneurons.
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In the Z− model, a 10-pulses/500 Hz pf burst generated a PC burst like in the Z+ model type I and type II responses. However, the Z− model was almost unable to generate any pauses, in either type I, II or III responses. This difference with the Z+ model was reduced by raising synaptic inhibition from 25 to 100 molecular layer interneuron synapses, which allowed pauses to emerge in the type I and type II responses (see Figure 2C). Therefore, the Z− PC model showed reduced ability to generate intrinsic BPR, in which the pauses were markedly dependent on the amount of molecular layer interneuron inhibition. It should be noted that the reduced ability of Z− PC models to generate intrinsic BPRs was likely to be related to the high basal firing rate, since Z− became similar to Z+ BPR when the basal firing rate was equalized with somatic injection of a constant negative current (Figure 2B).
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Modulation of BPR was investigated in detail in Z+ PC type II responses, in which BPR was the most pronounced. Increasing the strength of inhibition did not change the burst but prolonged the pause. Moreover, responses to aa synapses were differentiated by considering their specific location on distal dendrites. The aa generated weaker BPR than pf probably because of their longer electrotonic distance from soma (see also Figure 6A). However, the aa and pf BPR became very similar when aa transmission strength was increase, reproducing the functional equivalence of transmission along these two transmission lines (Sims and Hartell, 2005, 2006; Walter et al., 2009).
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General mechanisms of BPR. (A) The electrical circuit provides a schematic representation of the compartmentalization of the PC model, highlighting the axon initial segment (AIS), soma and dendrites. Membrane potential in the main nodes (VAIS, Vsoma, Vdend) depends on current flow along the internal resistances (Rsoma-AIS, Rdend-soma) and through the membrane of each compartment (including leakage resistances and voltage-dependent ionic channels). Traces on the left show the BPR (enhanced for the purpose of clarity by increasing KCa by 50%) along with the current flowing through the AIS membrane (the action potential current threshold is indicated) and the AIS Na channel states (open, closed, inactivated and blocked). Traces on the bottom show the current flowing through internal resistances from dendrites to soma and AIS. The action potential current threshold is indicated by dotted lines (see “Materials and Methods” Section for details). (B) Effect of ionic channel knock-out from the PC model on BPR. Left, voltage traces. Right, corresponding percent change of the ratio between pause and basal ISI in the different conditions.
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Sensitivity of PC responses to differences in input spike patterns. (A) Type I BPRs were elicited using different input frequencies and burst durations. Left, the relationship between output bursts length and the duration of input burst at 100 Hz, 200 Hz, 500 Hz. A linear fitting is superimposed (R2 = 0.996, p(F) < 10−6). Right, the relationship between the burst/pause ratio (duration of burst by duration of pause) and the duration of input burst at 100 Hz, 200 Hz, 500 Hz. A linear fitting is superimposed (R2 = 0.96, p(F) < 10−4). Bottom, PC burst transmission across the 8th Ranvier node for input burst at 100 Hz, 200 Hz, 500 Hz. (B) Continuous spike frequency modulation was elicited using input spike trains with different frequencies and number of pf synapses.
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Sensitivity of BPR to synaptic parameters. (A) Type II BPRs were elicited by 500 Hz-10 spikes bursts using different release probabilities, p. By increasing p, the EPSCs trains changed progressively from facilitation to depression. The raster plots obtained over repeated trails reveal an increased precision of spike emission by increasing release probability, but this cannot be detected in the peri-stimulus time histograms (PSTH). (B) The CV of the ISI measured from raster plots shows a decrease both for the burst and pause by increasing p. Decaying exponential fitting is superimposed (bursts, R2 = 0.98, p(F) < 10−6; pause, R2 = 0.996, p(F) < 10−6). The histograms show the changes caused by a ±30% change in AMPA maximum conductance.
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Sensitivity of BPR to dendritic localization. (A) Type II BPRs were elicited by 500 Hz—10 spikes pf or aa bursts in four different dendritic sectors, labeled I to IV. SC synapses were activated by 130 Hz—three spikes trains and were located in the same sectors. In all cases the number of pf or aa and SC synapses was the same as in the case of random synapses distribution. Left, distribution of active pf synapses. The raster plots and PSTH reveal that BPRs are different in the four sectors, mostly due to a different duration of the pause. Right, effect of activation of aa synapses in the same sectors and with the same inhibitory synapses. Note that the raster plots and PSTH look similar to those of pf except for sector I, in which the pause is longer. (B) Different localization of inhibitory synapses has a marginal effect on BPRs elicited by pf synapse (almost the same happened for aa synapses, not shown).
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The BPRs mechanism was analyzed by tracking transmembrane currents and intracellular axial currents in different cellular compartments using the Z+ PC type I model, in which the intrinsic ability to generate BPRs was evident (Figure 3A). In the PC model, APs arise from the AIS (Masoli et al., 2015) and, not surprisingly, the pause is characterized by a protracted decrease of the AIS transmembrane current (IAIS; Jack et al., 1975). In fact, this makes the pause appearing as an interruption of pacemaking. Pacemaking in PCs is sustained by the persistent Na currents generated mostly in AIS and by Ca currents generated mostly in the dendrites and transmitted to the AIS through the internal resistance (Llinás and Sugimori, 1980a,b), providing two candidate mechanisms for pause generation.
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Na currents in the AIS may be inactivated during the burst and then take time to recover, reducing the depolarizing drive. However, there was no remarkable inactivation of Na currents during the bursts that might prevent reactivation of the pacemaker. Therefore, this first mechanism could be excluded.
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Ca channel activation and the consequent Ca entry into the dendrites may activate KCa currents overtaking inward currents and generating a protracted repolarizing drive. Actually, the current transmitted from the dendrite to soma (Idend-soma) and from soma to AIS (Isoma-AIS) was reduced during the pause compared to pacemaking regime. Therefore, reduced depolarizing current transmission from the somato-dendritic compartment to AIS appears as the main responsible of the pause.
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The ionic nature of the mechanism was confirmed by specific manipulations of the Ca/KCa ionic mechanisms. When either dendritic KCa conductances or Ca conductances were set to zero, the BPR was altered with a marginal reduction of burst duration (from 0% to −16.7%) but a much more dramatic reduction of the pause (from −20% to −80%) (Figure 3B). It should be noted that all Ca channels proved critical for BPR, especially Cav2.1 and Cav3.1 (Cav3.2 switch-off blocked pacemaking; Masoli et al., 2015) as well as all KCa channels, including KCa1.1, KCa2.2, KCa3.1.
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These observations show that making BPRs is an intrinsic property of the PC model, which depends on the generation of large KCa currents in the dendrites. In Z− PCs, the mechanism were the same as in Z+ PCs except that TRP channels injected a constant inward current through the dendrites counterbalancing KCa and making the pause more difficult to elicit (not shown).
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A central issue in cerebellar physiology is how PCs transform signals coming from granule cells into specific outputs. The spike patterns emitted by granule cells in response to punctuate stimulation consist of short bursts composed of spikes with variable number and ISI (Chadderton et al., 2004; Rancz et al., 2007; D’Angelo and De Zeeuw, 2009). We have therefore used the PC model to simulate the impact on BPR of stereotyped patterns composed by a fixed number of pulses at different frequencies. Concerning burst length, the PC model showed an almost linear input/output relationship at frequencies ranging from 100 Hz to 500 Hz (Figure 4A, left). The pause also showed a slight dependency on the length of the input burst and this eventually caused the burst/pause ratio to reliably report the duration of the input burst (Figure 4A, right). There are two additional noteworthy properties. First, the linearity of burst and burst/pause coding was maintained almost independently from the input frequency. Secondly, the Ranvier nodes in the PC axon filtered the highest frequencies (Masoli et al., 2015) so that the burst was more reliably transmitted at the lower input frequencies (Figure 4A, bottom).
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Another modality of granule cell response, largely investigated in the vestibulo-cerebellum, is to generate spike trains in response to prolonged mossy fiber inputs (Arenz et al., 2008). When such stimuli were used, the PC model followed the input frequency (Figure 4B, left), although the frequency dependence was rather weak (as also noted for the BPR in Figure 4A). However, there was a steep relationship between the output frequency and the number of active synapses (Figure 4B, right). Therefore, the PC model was more efficient in detecting the intensity of the granule cell input rather than the frequency at individual synapses.
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The recoding of input into output spike patterns in PCs is thought to depend on how long-term synaptic plasticity modifies PC synaptic responsiveness. While classical pf-PC LTD has postsynaptic expression and simply causes a scale-down of postsynaptic currents, a presynaptic change in release probability (P) would modify neurotransmission dynamics (Tsodyks and Markram, 1997; Nieus et al., 2006). These can shift from the typical short-term facilitation at low P to short-term depression at high P. These changes can therefore differentially affect the PC BPR.
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At different P values (range 0.1 and 0.9), the overall response pattern in PC output bursts did not change remarkably. In all cases, the output spikes followed the input spikes quite closely during the burst, then one or two extra spikes were generated and the pause occurred. However, at a closer inspection of raster plots, the precision of action potential emission changed. By increasing P (from P = 0.13 to P = 0.91) the PC model responses were characterized by a greater precision, with decreased variability in burst spike pattern and pause length (see also Figure 2C). Increased precision derived from the decreased paired pulse ratio (A2/A1, where A1 and A2 are the amplitudes of the first and second response in a pair). In this way, the first EPSP in the train became more precisely aligned with the input burst leading to a repeatable spike generation independent from the relative phase of background firing activity (see also Figure 8 below). Therefore, the highest precision was obtained when the pf-PC synapse expressed presynaptic pf-PC LTP. This suggests that release probability controls fine regulation of spike timing on millisecond scale.
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The mechanisms differentiating BPRs among dendritic sectors. In these simulations on a Z+ PC model, type II BPRs were elicited by 500 Hz—10 spikes pf bursts in dendritic sectors I and II and SC synapses were activated by 130 Hz—three spikes trains in the corresponding pf sectors (see Figure 6A). (A) Local generation of minimal EPSPs in one of the terminal compartments of dendritic sectors I (~140 μm from soma) and II (~270 μm from soma). Note the larger and faster EPSP in sector II than I. In the same dendritic compartments, Zin is about twice as large in sector II than I at 10, 100 and 500 Hz. Correspondingly, attenuation follows different profiles in sector I and II. (B) Local currents in one of the terminal compartments of sectors I and II. Note that, in sector 2, the EPSPs trigger a local Ca spike along with a strong activation of Ca currents (Cav3.1, Cav3.2, Cav3.3, Cav2.1) and KCa currents (KCa1.1, KCa 2.2, KCa3.1) and a large [Ca2+]i increase. In sector I, the depolarization is too weak to activate the Ca spike so that ionic currents and [Ca2+]i changes are correspondingly much smaller.
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Spatio-temporal evolution of BPRs in the dendrites. The figure extends the description of the simulations shown in Figures 6, 7. For simplicity, only the currents showing the largest changes are shown (Cav3.3, Cav2.1, KCa 2.2) along with [Ca2+]i. Note the log scale (all parameters are made positive) to account for large variations on the ordinate. (A) Spatial profile of ionic currents and [Ca2+]i changes. Note the larger extension of dendritic activation when stimuli are delivered to sector II than I. Synaptic stimuli are given either in sector I and II. The color scale shows relative values for Vm (−80; 40 mV), [Ca2+]i (4.5*10−8; 3*10−7 M/l), ICav3.3 (−1*10−9; 0 mA/cm2), ICav2.1 (−0.001; 0 mA/cm2), IKCav2.2 (0; 1*10−5 mA/cm2). (B) Temporal profile of ionic currents and [Ca2+]i changes taken from five different compartments indicated by colors (see the legend on top). Although the synaptic stimulus is given only in sector I or II, there is a progressive invasion of neighboring dendritic regions that can lead to full-blown Ca spikes and large ionic current activation outside the stimulated sector (e.g., arrows). These dynamic changes are more marked when stimuli are delivered to sector II than I.
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In the case of a postsynaptic change in synaptic conductance G (−30% to 30% with respect to control), the only remarkable effect was a reduction in burst spikes precision when G was reduced, while no appreciable changes were observe in pause precision. The spike precision decrease at low G was likely related to a greater influence of previous spikes on burst initiation. Therefore, in the present conditions, precision could be more effectively tuned by P than G.
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The PC shows complex branching (Nedelescu and Abdelhack, 2013) and active electroresponsiveness in the dendrites, so that the specific location of afferent synapses may influence the response pattern. The model was exploited to redirect to specific dendritic sectors (numbered I–IV) the same stimuli that were used before for synapses randomly distributed over the whole dendritic tree (see Figures 1–6).
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The PC response was different depending on the stimulated sector (Figure 6A). When excitatory pf and inhibitory stimulations were delivered to dendritic sector I or IV, the PC BPRs were similar to those obtained using a random distribution of synapses. However, when excitatory stimulation was delivered to sector II or III, the pause was much longer than usual (over 250 ms in the Z+ model). When aa was substituted to pf stimulation, the responses were similar except for sector I, which showed a longer pause with aa then pf stimulation (the reason of this will be explained below). The difference between sectors was poorly sensitive to the location of inhibition, and BPRs did not change remarkably when inhibition was moved to sectors different from the one that was excited by pf synapses (Figure 6B). Similar response properties were observed in the Z− model, although pauses were shorter (data not shown).
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In order to understand the mechanism differentiating responses among dendritic sectors, we compared sector I to sector II, which showed a remarkably different pause lengths. The impact of dendritic structure was considered first (Figure 7A). The local currents generated by synaptic activation (that were identical in the two sectors) caused a stronger depolarization in sector II than sector I. This reflected the different Zin, that was about twice as large for sector II than sector I. Accordingly, this determined different voltage attenuation profiles, so that sector I depolarization started from a higher level and then decayed over a longer distance while approaching the soma. It should be noted that, in these simulations, we used single-synapse stimuli causing small depolarizations from a hyperpolarized membrane potential, so that voltage-dependent currents were not remarkably activated.
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Then we considered the activation of voltage-dependent currents in the dendrites (Anwar et al., 2014) by delivering the appropriate multisynaptic stimulation pattern to the PC model in pacemaking regime. The higher synaptic depolarization in sector II than in sector I resulted in a stronger voltage-dependent activation of Ca channels in the former than in the latter (Figure 7B). In sector II, LVA currents amplified the EPSPs leading membrane potential to raise enough to activate also the HVA currents, thus causing a regenerative calcium spike. Consequently, a large raise in intracellular calcium activated the KCa system. This effect eventually influenced the spike-generating mechanisms in the AIS and regulated the pause, that was longer in sector II than sector I.
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While sector I phenomena remained almost locally confined, the voltage-dependent effects initiated in sector II rapidly spread to neighboring sectors and eventually to the whole dendrite (Figure 8B). Full-blown calcium spikes appeared with some delay in a region close to sector II, involving LVA followed by HVA calcium channel activation causing a large [Ca2+]i raise and eventually KCa activation and the pause. Therefore, also dendritic sectors that are not activated synaptically can generate a local [Ca2+]i increase and take part to control the BPR pause.
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The analysis of Figures 7, 8 shows that voltage-dependent channels in sector II (but not sector I) cross the activation threshold, so that a local Ca spike is activated bringing about a remarkable KCa channels activation and a long pause. In sector II, Ca spikes and threshold crossing could be prevented by down-tuning the synaptic input. Indeed, when the number of pf synapses was increased progressively from 50 to 100, a sharp threshold in Ca spike activation was observed around 70–80 synapses. Interestingly, with sub-threshold responses the BPR of sector II became almost the same as for sector I (Figure 9).
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Threshold effects in dendritic sectors. In these simulations on the Z+ PC model, type II BPRs were elicited by 500 Hz—10 spikes pf bursts in dendritic sectors II and SC synapses were activated by 130 Hz—three spikes trains in the same sector. The number of active pf synapse was increased from 50 to 100. Traces on the left show membrane potential in a compartment of sector II. The dendritic response remained sub-threshold until around 70 synapses and then jumped steeply over-threshold generating Ca spike at 80 synapses. The plot on the right shows the amplitude of the dendritic depolarization as a function of the number of activated synapses.
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When sector I and II were activated together, different behaviors appeared depending on the intensity of dendritic activation. Below Ca spike threshold, the conjoint BPR showed a burst enhancement but the pause was almost the same as in the two sectors alone (Figure 10). Conversely, when sector II Ca spike was supra-threshold, BPRs were dominated by the pause (Figure 10). The BPR burst became shorter and smaller and the pause longer and deeper than in any one of the two sectors activated alone. This was likely to reflect boosting of KCa current activation due to the conjoint action of the two sectors.
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