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 β-cells. Proximity ligation and Western blot assays revealed that D1 and D2 form heteromers in β-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 β-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 β-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.

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.

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.

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.

An analytic solution of the cable equation predicts frequency preference of a passive shunt-end cylindrical cable in response to extracellular oscillating electric fields

Under physiological and artificial conditions, the dendrites of neurons can be exposed to electric fields. Recent experimental studies suggested that the membrane resistivity of the distal apical dendrites of cortical and hippocampal pyramidal neurons may be significantly lower than that of the proximal dendrites and the soma. To understand the behavior of dendrites in time-varying extracellular electric fields, we analytically solved cable equations for finite cylindrical cables with and without a leak conductance attached to one end by employing the Green's function method. The solution for a cable with a leak at one end for direct-current step electric fields shows a reversal in polarization at the leaky end, as has been previously shown by employing the separation of variables method and Fourier series expansion. The solution for a cable with a leak at one end for alternating-current electric fields reveals that the leaky end shows frequency preference in the response amplitude. Our results predict that a passive dendrite with low resistivity at the distal end would show frequency preference in response to sinusoidal extracellular local field potentials. The Green's function obtained in our study can be used to calculate response for any extracellular electric field.

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.

Steep decrease in the specific membrane resistance in the apical dendrites of hippocampal CA1 pyramidal neurons

Specific membrane resistance (R(m)), distributed non-uniformly over the dendrite, has a substantial effect on neuronal information processing, since it is a major determinant in subthreshold-synaptic integration. From experimental data of dendritic excitatory postsynaptic potential (EPSP) spread, we previously reported that non-uniform R(m) distribution in hippocampal CA1 pyramidal neurons could be expressed as a step function. However, it remains unclear how steeply R(m) decreases. Here, we estimated the R(m) distribution using sigmoid function to evaluate the steepness of decrease in R(m). Simulations were performed to find the distribution which reproduced experimental voltage responses to extracellular electric field applied to CA1 slices, in contrast to the EPSP spread. Distribution estimated from the responses to electric field was a steep-sigmoid function, similar to that from the EPSP spread. R(m) in distal dendrite was estimated to be < or approximately 10(3.5) Omegacm(2) whereas that in proximal dendrite/soma was > or approximately 10(4.5) Omegacm(2). Our results not only supported previous studies, but, surprisingly, implied that R(m) decreases at a location more distal, and that distal dendrite was leakier, than previous estimates by other groups. Simulations satisfactorily reproduced the responses to two distinct perturbations, suggesting that steep decrease in R(m) is reliable. Our study suggests that the non-uniform R(m) distribution plays an important role in information processing for spatially segregated synaptic inputs.

MAP estimation algorithm for phase response curves based on analysis of the observation process

Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior.

Estimated distribution of specific membrane resistance in hippocampal CA1 pyramidal neuron

It has been suggested that dendritic membrane properties play an important role in a synaptic integration. In particular, the specific membrane resistance, one of membrane properties, has been reported to be non-uniformly distributed in a single neuron, although the spatial distribution of the specific membrane resistance is still unclear. To reveal its non-uniformity in dendrite, we estimated the spatial distribution of specific membrane resistance in a single neuron, based on voltage imaging data, observed optically in hippocampal CA1 slices. As the optically recorded data, we used bi-directional propagations of subthreshold excitatory postsynaptic potentials in dendrite, which were not be reproduced numerically with uniform-specific membrane resistance. By numerical simulations for multi-compartment models with non-uniformity of specific membrane resistance, we estimated that the distribution obeys a step function; the optically recorded data were consistently reproduced for the distribution with a steep decrease in the specific membrane resistance at the distal apical dendrite, which occurs 300-500 microm away from the soma. In the estimated distribution, the specific membrane resistance at the distal side is less than about 10(3) Omegacm(2), whereas the resistance at the proximal side is greater than about 10(4) Omegacm(2). This result implies that the specific membrane resistance decreases drastically at the distal apical dendrite in hippocampal CA1 pyramidal neuron.

Acceleration effect of coupled oscillator systems

We have developed a curved isochron clock (CIC) by modifying the radial isochron clock to provide a clean example of the acceleration (deceleration) effect. By analyzing a two-body system of coupled CICs, we determined that an unbalanced mutual interaction caused by curved isochron sets is the minimum mechanism needed for generating the acceleration (deceleration) effect in coupled oscillator systems. From this we can see that the Sakaguchi and Kuramoto (SK) model, which is a class of nonfrustrated mean field model, has an acceleration (deceleration) effect mechanism. To study frustrated coupled oscillator systems, we extended the SK model to two oscillator associative memory models, one with symmetric and the other with asymmetric dilution of coupling, which also have the minimum mechanism of the acceleration (deceleration) effect. We theoretically found that the Onsager reaction term (ORT), which is unique to frustrated systems, plays an important role in the acceleration (deceleration) effect. These two models are ideal for evaluating the effect of the ORT because, with the exception of the ORT, they have the same order parameter equations. We found that the two models have identical macroscopic properties, except for the acceleration effect caused by the ORT. By comparing the results of the two models, we can extract the effect of the ORT from only the rotation speeds of the oscillators.

Multibranch entrainment and slow evolution among branches in coupled oscillators

In globally coupled oscillators, it is believed that strong higher harmonics of coupling functions are essential for multibranch entrainment (MBE), in which there exist many stable states, whose number scales as approximately O(expN) (where N is the system size). The existence of MBE implies the nonergodicity of the system. Then, because this apparent breaking of ergodicity is caused by microscopic energy barriers, this seems to be in conflict with a basic principle of statistical physics. Using macroscopic dynamical theories, we demonstrate that there is no such ergodicity breaking, and such a system slowly evolves among branch states, jumping over microscopic energy barriers due to the influence of thermal noise. This phenomenon can be regarded as an example of slow dynamics driven by a perturbation along a neutrally stable manifold consisting of an infinite number of branch states.

Extension of dynamic link matching by introducing local linear maps

It is well known that dynamic link matching (DLM) is a flexible pattern matching model tolerant of deformation or nonlinear transformation. However, previous models cannot treat severely deformed data pattern in which local features do not have their counterparts in a template pattern. In this paper, we extend DLM by introducing local linear maps (LLM's). Our model has a reference vector and an LLM for each lattice point of a data pattern. The reference vector maps the lattice point into a template pattern and the LLM carries the information regarding how the local neighborhood is mapped. Our model transforms local features by LLM's in a data pattern and then matches them with their counterparts in a template pattern. Therefore, our model is adaptable to larger transformations. For simplicity, we restricted LLM's to rotations. Neighboring LLM's are diffusionally coupled with each other. The model is numerically demonstrated to be very flexible in dealing with deformation and rotation compared to previous models. The framework of our model can be easily extended to models with more general LLM's (expansion, contraction, and so on).

Deformation Theory of Dynamic Link Matching

Dynamic link matching is a self&hyphenorganizing topographic mapping between a template image and a data image. The mapping tends to be continuous, linking two points sharing similar local features, which, as a result, can lead to its deformation to some degree. In analyzing such deformation mathematically, we reduced the model equation to a phase equation, which enabled us to clarify the principles of the deformation process and the relationship between high&hyphendimensional models and low&hyphendimensional ones. We also elucidated the characteristics of the model in the context of the standard regularization theory.