Toru Aonishi

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 Mukamels 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.

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.

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.

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.

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.

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 Greens 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 Greens function obtained in our study can be used to calculate response for any extracellular electric field.

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.

Estimation of Intracellular Calcium Ion Concentration by Nonlinear State Space Modeling and Expectation-Maximization Algorithm for Parameter Estimation

A calcium imaging method has superior ability in recording of spatial–temporal variations in ion concentration. However, it has two major problems. First, the imaging signals are very noisy. Second, the observation data are only the fluorescence intensities of Ca 2+ indicator dyes that provide indirect information about the Ca 2+ concentration. We develop a nonlinear state-space model for Ca imaging series involving Ca 2+ kinetics and a noisy fluorescence intensity pickup process. We devise recursive update algorithms for estimating the Ca 2+ concentration and Ca 2+ flux, and give the expectation-maximization algorithm for inferring model parameters.

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.The role of the Onsager reaction term (ORT) is not yet well understood in frustrated coupled oscillator systems, since the Thouless-Anderson-Palmer (TAP) and replica methods used to treat equilibrium systems cannot be directly applied to these non-equilibrium systems. In this paper, we consider two oscillator associative memory models, one with symmetric and one with asymmetric dilution of coupling. These two systems 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 systems have identical macroscopic properties, except for the acceleration effect caused by the ORT. This acceleration effect does not exist in any equilibrium system. PACS numbers: 87.10.+e, 05.90.+m, 05.45.-a, 89.70.+c Typeset using REVTEX 1 Coupled oscillators are of intrinsic interest in many branches of physics, chemistry and biology. Simple coupled-oscillator models involving uniform and global coupling have been investigated in some detail, and it has been found that they can be used to model many types of chemical reactions in solution [7]. However, in the modeling of more complicated phenomena (so-called complex systems), including those studied in the fields of neuronal systems, it is more natural (and perhaps necessary) to consider coupled oscillators with frustrated couplings. The Onsager reaction term (ORT), which describes the effective self-interaction, is of great importance in obtaining a physical understanding of frustrated random systems, because the presence of such an effective self-interaction is one of the characteristics that distinguish frustrated and non-frustrated systems of this types. In the case of an equilibrium system, we can rigorously evaluate the effect of the ORT using the high-temperature expansion of the free energy in the Thouless-Anderson-Palmer (TAP) framework [1,2], and/or using the replica method [3]. However, we cannot directly apply these systematic methods to non-equilibrium coupled-oscillator systems. For this reason, in order to evaluate the macroscopic quantities in such systems that include an ORT, a slightly heuristic method called the SCSNA (self-consistent signal to noise analysis) have been used [3]. The mathematical treatment of this method is similar to that of the cavity method [2]. While the SCSNA has proposed some interesting results, it is not sufficient to give a complete understanding of frustrated systems, and for this reason many theoretically fundamental questions remain in their study. In fact, even the existence of the type of self-interaction that can be described by the ORT is the subject of some debate [5,6]. In this paper, we discuss an effect of the ORT that exists only in frustrated globally coupled oscillator systems, and in particular cannot be found in equilibrium systems. In order to make this effect clear, it would be ideal for us to compare two frustrated systems that, with the exception of the different quantity of the ORT, have the same order parameter equations. In addition, it is desirable for these systems to have a clear correspondence with an equilibrium system, because the effects of the ORT are well understood in equilibrium systems. In consideration of the above-mentioned points, system of the form: dφi dt = ωi + N ∑ j 6=i Jij sin(φj − φi + βij + β0), (1) is ideal. In fact, such systems are well known as models of coupled oscillator systems [7,8]. Here, φi is the phase of the i th oscillator (with a total of N) and ωi represents its natural frequency. The natural frequencies are randomly distributed with a density represented by g(ω). We do not restrict g(ω) to a special case, e.g., a symmetric distribution with average 0. Also in Eq. 1, Jij and βij denote the amplitude of coupling from unit j to unit i and its delay, respectively. In the present study, we have selected the following two generalized Hebb learning rules with random dilutions [9] to determine Jij and βij : Kij = Jij exp(iβij) = cij cN p