Establishment of the estimation method of the neural network using CMA-ES for elucidating the neural mechanism of a silkworm moth brain
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1
The University of Tokyo, Graduate School of Information Science and Technology, Japan
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2
The University of Tokyo, Research Center for Advanced Science and Technology, Japan
In this research, we developed the scheme to estimate the neural circuit with biophysically detailed model. CMA-ES, a kind of evolutionary computation, was used for fitting the model to the data acquired from the physiological experiment. We used this method to understand the neural mechanism of the premotor area of silkworm moth (Bombyx mori) which generates the behavioral commands of the odor-source searching behavior. The odor-source searching behavior is one of the typical behaviors of animals that have high adaptability and robustness towards the environment. To investigate this behavior, we observed silkworm moths. Male silkworm moths show an especially remarkable zigzag searching locomotion initiated by a lump of sex pheromone as they navigate through the plume of pheromone [1]. Our purpose is to make a model of the neural networks which control the odor-source searching behavior of silkworm moths. Previous works have partially revealed the neural mechanisms of the odor-source searching behavior of silkworm moths. Firstly, the flip-flop response of the group I/II descending neurons corresponds to the locomotion [2]. Secondly, the premotor center that generates the flip-flop pattern is identified as Lateral Accessary Lobe – Ventral Protocerebrum (LAL-VPC). Thirdly, physiological and morphological records at the single-cell level in that region were obtained and stored in the database [4]. However, the detailed network model is not yet to be known because of how complicated the neural network is. This level of complexity makes it hard to determine the model by hand-tuning. In addition, it is also difficult to estimate the activity parameters of the each cell alone [5]. There are previous works of research that tackled this problem by using restricted Artificial Neural Network model and intended to replicate the behavior [6]. However, the expression ability of the model was limited compared to a real neural circuit. Moreover this method could only tell us a map from input to output, so was not suitable for the detailed investigation of the effect of the neural factors such as the morphology, the membrane properties of the cells, the connectivity of the network and the physical positions of the connections. Thus, we included these detailed information. We employed an estimation method
which can treat these factors as the evaluation parameters. With the increase in complexity of the model, the computational complexity is increased. In order to overcome this difficulty, we executed the simulation in the hierarchically parallelized environment. The estimated parameters will be used to investigate the effect of the aforementioned elements.
For achieving our purpose, we used the multi-compartment model to represent the morphology of the cells, and the evolutionary computation to estimate the parameters. The simulation was executed on a supercomputer to tackle the problem of the complexity of the model. We built the multi-compartment model in NEURON K+ simulator [7]. Hodgkin-Huxley type model with the Ca2+, the Ca2+-activated K+ channel, and the A-current channel [8] was calculated in each compartment. To estimate the parameters, the evolutionary computation called Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [9] was used. The input (in this case, pheromonal stimulus) and the output (the flip-flop response of the descending neurons) were fixed and the internal parameters were searched. The evaluation parameters were the activity factors of the firing model and the cellular connections. The evaluation was carried out by measuring the difference between the actual and the estimated response of the output cell in each generation. This will be the first method estimating neural circuits with biophysically detailed model. Because of the good compatibility to the highly parallelized computation, we used CMA-ES. Combining these methods allows us to quantitatively evaluate the target value which has been estimated empirically or by hand-tuning.
In the preliminary simulation, we verified the effectiveness of this approach by solving the simplified problem. Concretely, the single-compartment model was used to represent the morphology of the cells, and the number of cells in the network was reduced. After that, the input and the output signals were fixed, and whether the method could estimate the connection parameters or not was investigated (fig. a). The number of cells in the network was 6, and the Excitatory-Inhibitory ratio was 2:1. The network was fully connected, and the connection weight and delay were used as the evaluation parameters. The dimension of parameter space was 72. The hyper-parameter was set as followings; the number of gene was 4096, the number of the selected elites was 64, and the number of generation was 55. To simulate a cell with the single-compartment model, the activity parameters were fitted to the measured data in
terms of the maximum firing rate and the attenuation factor. We showed one example of the target function and a result of estimation (fig. b, c). We got the expected results about the activity curve. The shape of arch, and increasing and decreasing pattern were fairly fitted to the target data.
In the future, we are going to estimate the real LAL-VPC network with single and morphological multi-compartment model. Specifically, we are interested in the property of the neural circuit which generates flip-flop neural activity in response to the stochastic pheromonal input. The more parameters are used, the worse the convergence and the calculation time of the estimation are. As a countermeasure for this difficulty, we will extend our method based on the technique called CMA-TWEANN [10]. In this study, we are estimating the brain of silkworm moth, but our method can be generalized. Therefore, if the input and the output are defined, this method can be applied to the estimation of the neural networks of any other species (even humans).
Acknowledgements
This research used computational resources of the K computer and other computers of the HPCI system provided by the AICS and Nagoya university through the HPCI System Research (Project ID: hp150074, hp160187)．
References
[1] Kanzaki R, Shibuya T (1992) Long-lasting excitation of protocer-ebral bilateral neurons in the pheromone-processing pathways of the male moth Bombyx mori. Brain Res 587:211-215. [2] Kanzaki R, Mishima T. 1996. Pheromone-triggered ’flipflopping’ neural signals correlated with activities of neck motor neurons of a male moth, Bombyx mori. Zool Sci 13:79 – 87. [3] Mishima T, Kanzaki R. 1999. Physiological and morphological characterization of olfactory descending interneurons of the male silkworm moth, Bombyx mori. J Comp Physiol A 184:143–160. [4] Iwano, M. et al. Neurons associated with the flip-flop activity in the lateral accessory lobe and ventral protocerebrum of the silkworm moth brain. J. Comp. Neurol. 518, 366– 388 (2010). [5]Goto, Akihiko, Tomoki Kazawa, Daisuke Miyamoto, Masashi Tabuchi and Ryohei Kanzaki. “Examination of stimulus pattern and neuronal morphology for efficient biophysical property estimation of neurons in the silkmoth antennal lobe.” International Congress of Neuroethology. 29 July 2014. [6] Nishikawa, I., et al. "Estimation of the neural circuit for the command generation in the premotor center of an insect brain." Computer Sciences and Convergence Information Technology (ICCIT), 2011 6th International Conference on. IEEE, 2011. [7] Miyamoto, Daisuke, Tomoki Kazawa, and Ryohei Kanzaki. "Neural circuit simulation of hodgkin-huxley type neurons toward peta scale computers." High Performance Computing, Networking, Storage and Analysis (SCC), 2012 SC Companion:. IEEE, 2012. [8] Hana Belmabrouk, Thomas Nowotny, Jean-Pierre Rospars, and Dominique Martinez. Interaction of cellular and network mechanisms for efficient pheromone coding in moths. Vol. 108, No. 49, 2011. [9] Nikolaus Hansen and Andreas Ostermeier. Convergence properties of evolution strategies with the derandomized covariance matrix adaptation: The (μ/μ I , λ)-CMA-ES. Eufit, Vol. 97, pp. 650–654, 1997. [10] Moriguchi, Hirotaka, and Shinichi Honiden. "CMA-TWEANN: efficient optimization of neural networks via self-adaptation and seamless augmentation." Proceedings of the 14th annual conference on Genetic and evolutionary computation. ACM, 2012.
Keywords:
CMA-ES,
Multi-compartment,
Parallel Computing,
insect,
phromone,
odor-source searching behavior
Conference:
Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016.
Presentation Type:
Poster
Topic:
Computational neuroscience
Citation:
Fukuda
T,
Kazawa
T and
Kanzaki
R
(2016). Establishment of the estimation method of the neural network using CMA-ES for elucidating the neural mechanism of a silkworm moth brain.
Front. Neuroinform.
Conference Abstract:
Neuroinformatics 2016.
doi: 10.3389/conf.fninf.2016.20.00085
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Received:
31 May 2016;
Published Online:
18 Jul 2016.