Effective implementation of [Formula: see text]-regularised compressed sensing with chaotic-amplitude-controlled coherent Ising machines.

Coherent Ising machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al., proposed a quantum-classical hybrid system to solve optimisation problems of [Formula: see text]-regularisation-based compressed sensing. In the hybrid system, the CIM was an open-loop system without an amplitude control feedback loop. In this case, the hybrid system is enhanced by using a closed-loop CIM to achieve chaotic behaviour around the target amplitude, which would enable escaping from local minima in the energy landscape. Both artificial and magnetic resonance image data were used for the testing of our proposed closed-loop system. Compared with the open-loop system, the results of this study demonstrate an improved degree of accuracy and a wider range of effectiveness.

Computational model predicts the neural mechanisms of prepulse inhibition in Drosophila larvae.

Prepulse inhibition (PPI) is a behavioural phenomenon in which a preceding weaker stimulus suppresses the startle response to a subsequent stimulus. The effect of PPI has been found to be reduced in psychiatric patients and is a promising neurophysiological indicator of psychiatric disorders. Because the neural circuit of the startle response has been identified at the cellular level, investigating the mechanism underlying PPI in Drosophila melanogaster larvae through experiment-based mathematical modelling can provide valuable insights. We recently identified PPI in Drosophila larvae and found that PPI was reduced in larvae mutated with the Centaurin gamma 1A (CenG1A) gene, which may be associated with autism. In this study, we used numerical simulations to investigate the neural mechanisms underlying PPI in Drosophila larvae. We adjusted the parameters of a previously developed Drosophila larvae computational model and demonstrated that the model could reproduce several behaviours, including PPI. An analysis of the temporal changes in neuronal activity when PPI occurs using our neural circuit model suggested that the activity of specific neurons triggered by prepulses has a considerable effect on PPI. Furthermore, we validated our speculations on PPI reduction in CenG1A mutants with simulations.

Dopamine Negatively Regulates Insulin Secretion Through Activation of D1-D2 Receptor Heteromer.

There is increasing evidence that dopamine (DA) functions as a negative regulator of glucose-stimulated insulin secretion; however, the underlying molecular mechanism remains unknown. Using total internal reflection fluorescence microscopy, we monitored insulin granule exocytosis in primary islet cells to dissect the effect of DA. We found that D1 receptor antagonists rescued the DA-mediated inhibition of glucose-stimulated calcium (Ca2+) flux, thereby suggesting a role of D1 in the DA-mediated inhibition of insulin secretion. Overexpression of D2, but not D1, alone exerted an inhibitory and toxic effect that abolished the glucose-stimulated Ca2+ influx and insulin secretion in ß-cells. Proximity ligation and Western blot assays revealed that D1 and D2 form heteromers in ß-cells. Treatment with a D1-D2 heteromer agonist, SKF83959, transiently inhibited glucose-induced Ca2+ influx and insulin granule exocytosis. Coexpression of D1 and D2 enabled ß-cells to bypass the toxic effect of D2 overexpression. DA transiently inhibited glucose-stimulated Ca2+ flux and insulin exocytosis by activating the D1-D2 heteromer. We conclude that D1 protects ß-cells from the harmful effects of DA by modulating D2 signaling. The finding will contribute to our understanding of the DA signaling in regulating insulin secretion and improve methods for preventing and treating diabetes.

Low computational-cost cell detection method for calcium imaging data.

The rapid progress of calcium imaging techniques has reached a point where the activity of thousands to tens of thousands of cells can be recorded simultaneously with single-cell resolution in a field-of-view (FOV) of about ten mm2. Consequently, there is a pressing need for developing automatic cell detection methods for large-scale image data. Several research groups have proposed automatic cell detection algorithms. Almost all algorithms can solve large-scale optimization problems for data, including hundreds of cells recorded from a conventional FOV at a resolution of 512 × 512 pixels, but the solution becomes more difficult as the data size increases beyond that. To handle large-scale data acquired with the latest large FOV microscopes, we propose a method called low computational cost cell detection (LCCD) that is based on filtering and thresholding. We compared LCCD with two other methods, constrained non-negative matrix factorization (CNMF) and Suite2P. We found that LCCD makes it possible to detect cells in artificial and actual data showing a high number density of cells within a shorter time and with an accuracy comparable to or better than those of CNMF and Suite2P. Moreover, LCCD succeeded in detecting more than 20,000 active cells from data acquired with the latest microscopy, called FASHIO-2PM, with a FOV of 3.0 mm × 3.0 mm.

Imaging data analysis using non-negative matrix factorization.

The rapid progress of imaging devices such as two-photon microscopes has made it possible to measure the activity of thousands to tens of thousands of cells at single-cell resolution in a wide field of view (FOV) data. However, it is not possible to manually identify thousands of cells in such wide FOV data. Several research groups have developed machine learning methods for automatically detecting cells from wide FOV data. Many of the recently proposed methods using dynamic activity information rather than static morphological information are based on non-negative matrix factorization (NMF). In this review, we outline cell-detection methods related to NMF. For the purpose of raising issues on NMF cell detection, we introduce our current development of a non-NMF method that is capable of detecting about 17,000 cells in ultra-wide FOV data.

Fast, cell-resolution, contiguous-wide two-photon imaging to reveal functional network architectures across multi-modal cortical areas.

Fast and wide field-of-view imaging with single-cell resolution, high signal-to-noise ratio, and no optical aberrations have the potential to inspire new avenues of investigations in biology. However, such imaging is challenging because of the inevitable tradeoffs among these parameters. Here, we overcome these tradeoffs by combining a resonant scanning system, a large objective with low magnification and high numerical aperture, and highly sensitive large-aperture photodetectors. The result is a practically aberration-free, fast-scanning high optical invariant two-photon microscopy (FASHIO-2PM) that enables calcium imaging from a large network composed of ∼16,000 neurons at 7.5 Hz from a 9 mm2 contiguous image plane, including more than 10 sensory-motor and higher-order areas of the cerebral cortex in awake mice. Network analysis based on single-cell activities revealed that the brain exhibits small-world rather than scale-free behavior. The FASHIO-2PM is expected to enable studies on biological dynamics by simultaneously monitoring macroscopic activities and their compositional elements.

Frequency-dependent entrainment of spontaneous Ca transients in the dendritic tufts of CA1 pyramidal cells in rat hippocampal slice preparations by weak AC electric field.

Neurons in the central nervous systems are exposed to endogenous oscillating electric fields and their activities are likely to be modified by those fields. We had previously investigated the effects of AC electric field by using a newly developed method to monitor local Ca transients in the dendrites of a neuronal population in acute rat hippocampal slices and reported that spontaneously occurring Ca transients in the tufts of the apical dendrites of CA1 pyramidal neurons become entrained to subthreshold AC electric fields. To further our understanding of the impact of AC fields on dendritic activities, in the present study we examined three questions: how does the extent of entrainment depend on the frequency of the applied field, how does the mean phase of the dendritic activities during field application depend on the frequency of the field, and whether the entrainment can be seen in the absence of synaptic transmission. We have found that, the extent of entrainment is significantly greater at a low frequency band (1-4 Hz) compared to a high frequency band (8-16 Hz), 0.688 ± 0.027 at 2 Hz compared to 0.087 ± 0.016 at 16 Hz in case of 7 mV/mm field strength, that the entrainment can be observed when synaptic transmission is pharmacologically blocked, and that the mean phase of the Ca transients during field stimulation at a low frequency band (1-4 Hz) stays constant. These results indicate that the electric fields with physiologically feasible frequencies and intensities can entrain activities of the dendrites in a frequency-dependent manner independent of synaptic transmission. AC electric fields during oscillatory brain activities might play a role in synchronizing neural activities by modulating dendritic activities.

White noise analysis for the correlation-type elementary motion detectors with half-wave rectifiers.

The motion detection mechanism of insects has been attracted attention of many researchers. Several motion-detection models have been proposed on the basis of insect visual system studies. Here, we examine two models, the Hassenstein-Reichardt (HR) model and the two-detector (2D) model. We analytically obtain the mean and variance of the stationary responses of the HR and the 2D models to white noise, and we derive the signal-to-fluctuation-noise ratio (SFNR) to evaluate encoding abilities of the two models. Especially when analyzing the 2D model, we calculate higher-order cumulants of a rectified Gaussian. The results show that the 2D model robustly works almost as well as the HR model in several sets of parameters estimated on the basis of experimental data.

Noise-robust recognition of wide-field motion direction and the underlying neural mechanisms in Drosophila melanogaster.

Appropriate and robust behavioral control in a noisy environment is important for the survival of most organisms. Understanding such robust behavioral control has been an attractive subject in neuroscience research. Here, we investigated the processing of wide-field motion with random dot noise at both the behavioral and neuronal level in Drosophila melanogaster. We measured the head yaw optomotor response (OMR) and the activity of motion-sensitive neurons, horizontal system (HS) cells, with in vivo whole-cell patch clamp recordings at various levels of noise intensity. We found that flies had a robust sensation of motion direction under noisy conditions, while membrane potential changes of HS cells were not correlated with behavioral responses. By applying signal classification theory to the distributions of HS cell responses, however, we found that motion direction under noise can be clearly discriminated by HS cells, and that this discrimination performance was quantitatively similar to that of OMR. Furthermore, we successfully reproduced HS cell activity in response to noisy motion stimuli with a local motion detector model including a spatial filter and threshold function. This study provides evidence for the physiological basis of noise-robust behavior in a tiny insect brain.

Weak sinusoidal electric fields entrain spontaneous Ca transients in the dendritic tufts of CA1 pyramidal cells in rat hippocampal slice preparations.

Neurons might interact via electric fields and this notion has been referred to as ephaptic interaction. It has been shown that various types of ion channels are distributed along the dendrites and are capable of supporting generation of dendritic spikes. We hypothesized that generation of dendritic spikes play important roles in the ephaptic interactions either by amplifying the impact of electric fields or by providing current source to generate electric fields. To test if dendritic activities can be modulated by electric fields, we developed a method to monitor local Ca-transients in the dendrites of a neuronal population in acute rat hippocampal slices by applying spinning-disk confocal microscopy and multi-cell dye loading technique. In a condition in which the dendrites of CA1 pyramidal neurons show spontaneous Ca-transients due to added 50 µM 4-aminopyridine to the bathing medium and adjusted extracellular potassium concentration, we examined the impact of sinusoidal electric fields on the Ca-transients. We have found that spontaneously occurring fast-Ca-transients in the tufts of the apical dendrites of CA1 pyramidal neurons can be blocked by applying 1 µM tetrodotoxin, and that the timing of the transients become entrained to sub-threshold 1-4 Hz electric fields with an intensity as weak as 0.84 mV/mm applied parallel to the somato-dendritic axis of the neurons. The extent of entrainment increases with intensity below 5 mV/mm, but does not increase further over the range of 5-20 mV/mm. These results suggest that population of pyramidal cells might be able to detect electric fields with biologically relevant intensity by modulating the timing of dendritic spikes.

Detecting cells using non-negative matrix factorization on calcium imaging data.

We propose a cell detection algorithm using non-negative matrix factorization (NMF) on Ca2+ imaging data. To apply NMF to Ca2+ imaging data, we use the bleaching line of the background fluorescence intensity as an a priori background constraint to make the NMF uniquely dissociate the background component from the image data. This constraint helps us to incorporate the effect of dye-bleaching and reduce the non-uniqueness of the solution. We demonstrate that in the case of noisy data, the NMF algorithm can detect cells more accurately than Mukamel's independent component analysis algorithm, a state-of-art method. We then apply the NMF algorithm to Ca2+ imaging data recorded on the local activities of subcellular structures of multiple cells in a wide area. We show that our method can decompose rapid transient components corresponding to somas and dendrites of many neurons, and furthermore, that it can decompose slow transient components probably corresponding to glial cells.

A novel behavioral strategy, continuous biased running, during chemotaxis in Drosophila larvae.

Animals collect and integrate information from their environment, and select an appropriate strategy to elicit a behavioral response. Here, we investigate the behavioral strategy employed by Drosophila larvae during chemotaxis toward a food source functioning as an attractive odor source. In larvae, sharp turns have been identified as the main strategy during locomotion to odorant sources, but the existence of runs orienting toward the direction of higher odor concentrations has not been described. In this study, we show the existence of such a successive orientation toward an odor source, which we term as biased running. Our behavioral analysis, which examines the relationship between larval rotational velocities and larval positions relative to an attractive odor source, brings out this newly found behavioral strategy. Additionally, theoretically estimated concentration gradients of chemoattractants between left and right olfactory organs were statistically correlated with rotational velocities during biased running. Finally, computer simulations demonstrated that biased running enhances navigation accuracy. Taken together, biased running is an effective behavioral strategy during chemotaxis, and this notion may provide a new insight on how animals can efficiently approach the odor source.

Cooperative integration and representation underlying bilateral network of fly motion-sensitive neurons.

How is binocular motion information integrated in the bilateral network of wide-field motion-sensitive neurons, called lobula plate tangential cells (LPTCs), in the visual system of flies? It is possible to construct an accurate model of this network because a complete picture of synaptic interactions has been experimentally identified. We investigated the cooperative behavior of the network of horizontal LPTCs underlying the integration of binocular motion information and the information representation in the bilateral LPTC network through numerical simulations on the network model. First, we qualitatively reproduced rotational motion-sensitive response of the H2 cell previously reported in vivo experiments and ascertained that it could be accounted for by the cooperative behavior of the bilateral network mainly via interhemispheric electrical coupling. We demonstrated that the response properties of single H1 and Hu cells, unlike H2 cells, are not influenced by motion stimuli in the contralateral visual hemi-field, but that the correlations between these cell activities are enhanced by the rotational motion stimulus. We next examined the whole population activity by performing principal component analysis (PCA) on the population activities of simulated LPTCs. We showed that the two orthogonal patterns of correlated population activities given by the first two principal components represent the rotational and translational motions, respectively, and similar to the H2 cell, rotational motion produces a stronger response in the network than does translational motion. Furthermore, we found that these population-coding properties are strongly influenced by the interhemispheric electrical coupling. Finally, to test the generality of our conclusions, we used a more simplified model and verified that the numerical results are not specific to the network model we constructed.

Optimal design for hetero-associative memory: hippocampal CA1 phase response curve and spike-timing-dependent plasticity.

Recently reported experimental findings suggest that the hippocampal CA1 network stores spatio-temporal spike patterns and retrieves temporally reversed and spread-out patterns. In this paper, we explore the idea that the properties of the neural interactions and the synaptic plasticity rule in the CA1 network enable it to function as a hetero-associative memory recalling such reversed and spread-out spike patterns. In line with Lengyel's speculation (Lengyel et al., 2005), we firstly derive optimally designed spike-timing-dependent plasticity (STDP) rules that are matched to neural interactions formalized in terms of phase response curves (PRCs) for performing the hetero-associative memory function. By maximizing object functions formulated in terms of mutual information for evaluating memory retrieval performance, we search for STDP window functions that are optimal for retrieval of normal and doubly spread-out patterns under the constraint that the PRCs are those of CA1 pyramidal neurons. The system, which can retrieve normal and doubly spread-out patterns, can also retrieve reversed patterns with the same quality. Finally, we demonstrate that purposely designed STDP window functions qualitatively conform to typical ones found in CA1 pyramidal neurons.

Higher-order spike triggered analysis of neural oscillators.

For the purpose of elucidating the neural coding process based on the neural excitability mechanism, researchers have recently investigated the relationship between neural dynamics and the spike triggered stimulus ensemble (STE). Ermentrout et al. analytically derived the relational equation between the phase response curve (PRC) and the spike triggered average (STA). The STA is the first cumulant of the STE. However, in order to understand the neural function as the encoder more explicitly, it is necessary to elucidate the relationship between the PRC and higher-order cumulants of the STE. In this paper, we give a general formulation to relate the PRC and the nth moment of the STE. By using this formulation, we derive a relational equation between the PRC and the spike triggered covariance (STC), which is the covariance of the STE. We show the effectiveness of the relational equation through numerical simulations and use the equation to identify the feature space of the rat hippocampal CA1 pyramidal neurons from their PRCs. Our result suggests that the hippocampal CA1 pyramidal neurons oscillating in the theta frequency range are commonly sensitive to inputs composed of theta and gamma frequency components.

Experience-dependent plasticity of the optomotor response in Drosophila melanogaster.

Experience in early life can affect the development of the nervous system. There is now evidence that experience-dependent plasticity exists in adult insects. To uncover the molecular basis of plasticity, an invertebrate model, such as Drosophila melanogaster, is a powerful tool, as many established genetic and molecular methods can be applied. To establish a model system in which behavioral plasticity can be examined, we investigated the optomotor response, a behavior common to most sight-reliant animals, in Drosophila and found that the response could be modified by the level of light during rearing. The angle turned by the head in response to a moving stimulus was used to quantify the response. Deprivation of light increased the response to low-contrast stimuli in wild-type Drosophila at 4 days after eclosion and this plastic change did not appear in rutabaga, a known mutant defective in short-term memory. In addition, the change was transient and was markedly decreased at 6 days after eclosion. Further, we found that Dark-flies, which have been kept in constant darkness for more than 50 years, showed a higher response to low-contrast stimuli even at 6 days after eclosion compared to wild type and this characteristic was not lost in Dark-flies placed in a normal light environment for 2 generations, suggesting that this high response has a hereditary nature. Thus, our model system can be used to examine how the environment affects behaviors.

Low-frequency dielectric dispersion of brain tissue due to electrically long neurites.

The dielectric properties of brain tissue are important for understanding how neural activity is related to local field potentials and electroencephalograms. It is known that the permittivity of brain tissue exhibits strong frequency dependence (dispersion) and that the permittivity is very large in the low-frequency region. However, little is known with regard to the cause of the large permittivity in the low-frequency region. Here, we postulate that the dielectric properties of brain tissue can be partially accounted for by assuming that neurites are of sufficient length to be "electrically long." To test this idea, we consider a model in which a neurite is treated as a long, narrow body, and it is subjected to a stimulus created by electrodes situated in the region external to it. With regard to this electric stimulus, the neurite can be treated as a passive cable. Assuming adequate symmetry so that the tissue packed with multiple cables is equivalent to an isolated system consisting of a single cable and a surrounding extracellular resistive medium, we analytically calculate the extracellular potential of the tissue in response to such an externally created alternating-current electric field using a Green's function that we obtained previously. Our results show that brain tissue modeled by such a cable existing within a purely resistive extracellular medium exhibits a large effective permittivity in the low-frequency region. Moreover, we obtain results suggesting that an extremely large low-frequency permittivity can coexist with weak low-pass filter characteristics in brain tissue.

Measurement of infinitesimal phase response curves from noisy real neurons.

We sought to measure infinitesimal phase response curves (iPRCs) from rat hippocampal CA1 pyramidal neurons. It is difficult to measure iPRCs from noisy neurons because of the dilemma that either the linearity or the signal-to-noise ratio of responses to external perturbations must be sacrificed. To overcome this difficulty, we used an iPRC measurement model formulated as the Langevin phase equation (LPE) to extract iPRCs in the Bayesian scheme. We then simultaneously verified the effectiveness of the measurement model and the reliability of the estimated iPRCs by demonstrating that LPEs with the estimated iPRCs could predict the stochastic behaviors of the same neurons, whose iPRCs had been measured, when they were perturbed by periodic stimulus currents. Our results suggest that the LPE is an effective model for real oscillating neurons and that many theoretical frameworks based on it may be applicable to real nerve systems.

Self-consistent signal-to-noise analysis of Hopfield model with unit replacement.

The Hopfield model has a storage capacity: the maximum number of memory patterns that can be stably stored. The memory state of this network model disappears if the number of embedded memory patterns is larger than 0.138N, where N is the system size. Recently, it has been shown in numerical simulations that the Hopfield model with a unit replacement process, in which a small number of old units are replaced with new ones at each learning step for embedding a new pattern, can stably retrieve recently embedded memory patterns even if an infinite number of patterns have been embedded. In this paper, we analyze the Hopfield model with the replacement process by utilizing self-consistent signal-to-noise analysis. We show that 3.21 is the minimum number of replaced units at each learning step that avoids an overload evoking disappearance of the memory state when embedding an infinite number of patterns. Furthermore, we show that the optimal number of replaced units at each learning step that maximizes the number of retrievable patterns is 6.95. These critical numbers of replaced units are independent of the system size N. Finally, we compare this model with the Hopfield model with the forgetting process.

Switch of encoding characteristics in single neurons by subthreshold and suprathreshold stimuli.

Spike-triggered analysis is a statistical method used to elucidate encoding properties in neural systems by estimating the statistical structure of input stimulus preceding spikes. A recent numerical study suggested that the profile of the spike-triggered average (STA) changes depending on whether the mean input stimuli are subthreshold or suprathreshold. Here we analytically verify the difference between subthreshold STA and suprathreshold STA by using the spike response model (SRM). We show by moment expansion that the suprathreshold STA is proportional to the first derivative of the response kernel, and that the subthreshold STA is expressed by a linear combination of the response kernel and its first derivative. We verify whether the analytical results obtained from the SRM can be applied to a multicompartment model with Hodgkin-Huxley type dynamics.