Yuishi Iwasaki et al. (2003) International Worm Meeting "Statistical formulations for a partial neural circuit of C. elegans"

Yuishi Iwasaki, Sohei Gomi

[International Worm Meeting, 2003]

We present two statistical methods to analyze a partial neural circuit of C. elegans[1].Background: When behavior of C. elegans is studied from the neurobiological viewpoint, we usually focus on a partial neural circuit which is assumed to be closed. That is, only the associated neurons and their connectivity are taken into account. Influence of the remaining neurons of C. elegans is completely neglected. However, there is no guarantee that a result in the closed partial neural circuit is consistent with that in the whole (real) neural circuit since neural information processing is a highly non-linear phenomenon. Although laser ablation experiments of neurons have been performed on C. elegans to identify the associated neurons, this is still a problem in neural modeling.Methods and results: Firstly, all neurons are divided into two complementary groups. One is the neurons which are mainly associated with a certain behavior, and the other is the remaining neurons of C. elegans. Secondly, two popular frameworks in statistical physics are applied to evaluate influence of the remaining neurons on the associated neurons. In our methods, the influence is expressed by a stochastic variable. The structure of the ensemble for the stochastic variable is appropriately evaluated by the neural connectivity of C. elegans. In this way, the degree of freedom in the partial neural circuit, which consists of only the associated neurons, is effectively reduced. We apply the methods to predict the synaptic signs (excitatory or inhibitory) in the touch sensitivity circuit of C. elegans. We find that the influence of the remaining neurons on the touch sensitivity circuit is important to predict the synaptic signs.Database: The synaptic connectivity database[2] is used to determine the connectivity between neurons. This database is created from two memorial papers on the nervous system of C. elegans; Albertson and Thomson (1976), and White et al. (1986). All the chemical synapses and all the gap junctions are exactly listed in this database. Recently, this database is revised. We willingly explain the revised database in addition to the title work.[1] Y. Iwasaki and S. Gomi: submitted to J. theor. Biol; [2] K. Oshio et al.: Technical Report of CCEP, Keio Future, No.1, 1998.

Yuishi Iwasaki et al. (2002) Japanese Worm Meeting "Stochastic method to predict synaptic signs - in a partial neural network of C. elegans"

Sohei Gomi, Yuishi Iwasaki

[Japanese Worm Meeting, 2002]

The C. elegans has 302 neurons connected by about 8000 chemical synapses and about 900 gap junctions. In a computational study, reliable prediction of all synaptic signs in the whole neural network is impractical because of such a large number of the degree of freedom. Therefore, the prediction often focuses on a small partial neural network which is assumed to be closed. Only the associated neurons and their connectivity are taken into account, and influences from the remaining neurons are completely neglected. Since information processing in the neural network is a highly non-linear phenomenon, however, there is no guarantee that a result of the close partial neural network is consistent with that of the whole neural network. Motivated by these situations, we present an effective method to predict synaptic signs (excitatory or inhibitory synaptic connections) in a partial neural network. At first, neurons in a whole network are divided into two complementary groups. One is neurons in a given partial network which we concern, and the other is complement. Secondly, an influence from the complement is taken into account as an effective noise' to the concerned network so that the degree of freedom in the complement is reduced. This reduction follows an approach in statistical physics. In case of C. elegans, stochastic property of the effective noise' is evaluated from the neural connectivity. Thirdly, the synaptic signs are determined to satisfy some behavioral criteria in the model. We apply the presented method to neural network of C. elegans for touch-induced movement.

Yuishi Iwasaki et al. (2002) Japanese Worm Meeting "Stochastic method to predict synaptic signs in a partial neural network of C. elegans"

Yuishi Iwasaki, Sohei Gomi

[Japanese Worm Meeting, 2002]

The C. elegans has 302 neurons connected by about 8000 chemical synapses and about 900 gap junctions. In a computational study, reliable prediction of all synaptic signs in the whole neural network is impractical because of such a large number of the degree of freedom. Therefore, the prediction often focuses on a small partial neural network which is assumed to be closed. Only the associated neurons and their connectivity are taken into account, and influences from the remaining neurons are completely neglected. Since information processing in the neural network is a highly non-linear phenomenon, however, there is no guarantee that a result of the close partial neural network is consistent with that of the whole neural network. Motivated by these situations, we present an effective method to predict synaptic signs (excitatory or inhibitory synaptic connections) in a partial neural network. At first, neurons in a whole network are divided into two complementary groups. One is neurons in a given partial network which we concern, and the other is complement. Secondly, an influence from the complement is taken into account as an effective noise' to the concerned network so that the degree of freedom in the complement is reduced. This reduction follows an approach in statistical physics. In case of C. elegans, stochastic property of the effective noise' is evaluated from the neural connectivity. Thirdly, the synaptic signs are determined to satisfy some behavioral criteria in the model. We apply the presented method to neural network of C. elegans for touch-induced movement.

Ken-ichi Oshio et al. (2002) Japanese Worm Meeting "Revision of synaptic connectivity database"

Eizo Akiyama, Yuishi Iwasaki, Yuko Osana, Ken-ichi Oshio, Sohei Gomi, Satoru Morita, Kotaro Oka, Kazumi Omata

[Japanese Worm Meeting, 2002]

The synaptic connectivity of C. elegans is well known from observations of the somatic system by White et al. and those of the pharyngeal system by Albertson et al. So far, three databases were constructed for computational usage by Achacoso et al. and Durbin, and recently in WormBase. However, they lack some data such as those in tables of White's paper and those in figures of Albertson's book. Our database (K. Oshio, S. Morita, Y. Osana and K. Oka: Technical Report of CCEP, Keio Future No.1, 1998) includes all data described in White's paper and Albertson's book. Unfortunately, some mistakes were found in the database through private communications with John White who is the author of White's paper and with the users of the database. Thus we have been proceeding with the revision to make it perfect one. We are planning to complete the revision in September 2002. The database should be worthwhile not only for neurophysiological studies, but also for post-genomic interests mediating genomes and behavior.

Kiyoshi Kawamura et al. (2004) East Asia Worm Meeting "Anatomical Data of Synaptic Connectivity of C. elegans are Almost Perfectly Self-contained."

Satoru Morita, Kiyoshi Kawamura, Sohei Gomi, Yuishi Iwasaki, Yuko Osana, Kazumi Omata, Ken-ichi Oshio, Eizo Akiyama

[East Asia Worm Meeting, 2004]

The anatomical data of synaptic connectivity of C. elegans has been degitized for research with computers. The set of files are entitled 'The database of Synaptic Connectivity of C. elegans for Computaiton' and electronicaly delivered to request. The data files describe all items involved in the paper of Albertson and Thomson (1976) and that of White et al. (1986). The policy we empolyed on creating the data base was that diagrams and tables in the original paper can be reconstructed uniquely up to topology from the degitized data. Since our database is equivalent to the anatomical data, quality of the latter can be investigated on analysing the former by computer. It has been found that the anatomical data is almost perfectly self-contained except a few inconsistent descriptions such that the neuron class PDE sends 61 synapses to the class DVA while the latter receives only 36 synapses from the former. This is an exceptionally extreme case of inconsistency and number of erroneously described synaptic contacts are several hundred among eight thousand contacts. In addition, it has been found that several inconsistent description can be corrected from consideration of topological nature of processes in a three dimensional space, which is also suggested by the database.

Kotaro Oka et al. (2003) International Worm Meeting "Neuronal Circuit and Native Responses of C. elegans"

Kiyoshi Kawamura, Yasuhiro Funabashi, Sohei Gomi, Yuishi Iwasaki, Eizo Akiyama, Kotaro Oka, Ken-ichi Oshio, Satoru Morita, Kazumi Omata, Yuko Osana

[International Worm Meeting, 2003]

The ultimate goal of the present work is to determine pathways of neuronal signal from sensory neurons to motoneurons in occasion of native responses of C. elegans. The fundamental hypothesis is that the pathways consists of highly multiple synaptic connection among interneurons. The McCulloch-Pitts equation is employed to find out sequence of much synaptic connection from each sensory neuron. Although the McCulloch-Pitts equation cannot be used for simulation of propagation of neuronal signal without knowledge about physical parameters within it, it is useful for the present purpose. The point of the algorithm is ; (i) threshold of menbrain potential is replaced by an integer s which is independent of the neuron and (ii) the coupling coefficient between a pair of neurons is replaced with number of synapses between them. When a sensory neuron is always excited, a stationary distribution of excited neurons is realized. Excited neurons in the stationary state are connected to the sensory neuron by pathways which consist of synaptic connection of multiplicity larger than s. A neuron, which is connected with more than one excited neurons, is also excited when the sum of multiplicity of joined synapses are larger than s. A plan of the neuronal circuit is constructed from neurons, which are excited for s more than six, and synapses connecting them. Interneurons are classified into three groups. Three elementary motions of the worm are defined in terms of motoneurons which are simultaneously excited and its behavior in occasion of native responses is combination of such elementary motions. The number of synapses have been counted using the database constructed by our research group. It is translation from the sketch of neurons published by White et al.. into a digital form.

Yuishi Iwasaki (2005) International Worm Meeting "How to model and study a partial neural circuit of C. elegans?"

Yuishi Iwasaki

[International Worm Meeting, 2005]

In a numerical study of a partial neural circuit for a certain behavior, there are two general problems. (i) To simulate a certain behavior of a worm, we usually adopt only the neurons which are mainly associated with its behavior. The influence of the remaining neurons of C. elegans is completely neglected (closed circuit). However, the behavior is realized by the whole neural circuit with an external stimulation (open circuit). There is no guarantee that a numerical result in the closed partial neural circuit is consistent with that in the open circuit. This is a problem in neural modeling. (ii) To assign a behavioral criterion to the neural circuit, we usually analyze a stationary state of the neuron. That is, all the membrane potentials Vi(t) are dVi(t)/dt=0 in the neural circuit. However, it is not clear that the neuron is in a stationary state or not when a worm is moving. This is a problem in analyzing the neural circuit.To solve the former problem (i), a mathematical formulation has been proposed for the McCulloch-Pitts model (Iwasaki, Y. and Gomi, S. (2004). Bulletin of Mathematical Biology, 66, 727-743). The influence of the remaining neurons on the associated neurons is formulated as the external noise for a partial neural circuit. Since the neural connectivity of C. elegans has been completely determined, the stochastic property of the external noise is appropriately evaluated by the neural connectivity. Thus the degree of freedom is effectively reduced in neural modeling. However, the McCulloch-Pitts model is not the most suitable model to represent a real nervous system of C. elegans since the McCulloch-Pitts neuron is activated stepwisely. In this presentation, a mathematical formulation for a more physiologically adequate neural model is proposed. Furthermore, this formulation is applied to behavioral neural circuits of C. elegans. Considering the latter problem (ii), the dynamics of the neural circuit is analyzed. This work was supported by JSPS (No. RFTF-96I00102) and MEXT (No. 16740239).