Iwasaki, Yuishi (2009) International Worm Meeting "Analysis of noise robustness in neural circuit of C. elegans."

Iwasaki, Yuishi

[International Worm Meeting, 2009]

Is a worm''s behavior, which seems to be random walk, deterministic or not? Noise or fluctuation sometimes plays an important role to organize decision or choice behavior. Neurons in C. elegans are believed to be non-spiking and communicate by graded synaptic transmission. In this meaning, the nervous system of C. elegans is not a "digital" control system but an "analogue" control system which seems to be sensitive to noise. In general, noises (fluctuations) are classified into two types. One is external noises for individuals such as environmental noises. For examples, concentration fluctuation in chemicals for chemotaxis and thermal fluctuation for thermotaxis. The other is internal noises in living organisms. For examples, fluctuation in a neuron''s membrane potential and noise in synaptic transmission. To analyze the noise robustness in neural circuit of C. elegans, simulation is carried out using a stochastic differential equation, so-called Langevin equation. As a neural circuit to simulate the dynamics, I focus on that of chemotaxis in this work. The number of chemical synapses and gap junctions is determined from the two databases of the neural connectivity (Oshio et al., 2003; Chen et al., 2006). I analyze the response of the neural circuit against the noises. If the additive noises are supposed to be uncorrelated each other, the law of large numbers naively says that the influence of the noises decreases as the number of connected neurons (elements) increases. In C. elegans, however, the number of connected neurons for a given neuron is not so large since the total number of neurons in the whole nervous system is 302. Therefore the influence of the noises does not sufficiently vanish. This work was supported by MEXT No. 20115004.

Iwasaki Yuishi (2007) International Worm Meeting "Numerical study of habituation to touch stimulation and synaptic plasticity."

Iwasaki Yuishi

[International Worm Meeting, 2007]

C. elegans escapes backward in response to anterior touch. As touch stimuli are given at regular intervals, however, the escape distance becomes shorter. This is the habituation to touch stimulation. From experimental results of habituation after ablation of neurons, it is reported that some operated animals habituate rapidly than intact animals (J. Neurobiol., 46 (2001) 29). In the rapid habituation, AVD interneurons play an important role. To understand the fundamental nature of a neural circuit for learning in C. elegans, we numerically study the habituation to touch stimulation and synaptic plasticity. Since the neural connectivity of C. elegans is determined, behavior and learning can be discussed from the viewpoint of neural circuit. To simulate the electrical signals in the neural circuit, a well-known conductance-based model is adopted. We mainly consider the neurons which are associated with touch-induced movement. However the remaining neurons of C. elegans are not neglected completely. The influence of the remaining neurons on the associated neurons is taken into account by the dynamical mean-field theory (Int. Congress Series, 1291 (2006) 125). This influence is important to simulate a ''behavior'' in a small neural circuit. The number of chemical synapses and gap junctions is determined from the database of the neural connectivity (Tech. Rep. CCeP, 2003; http://www.bio.keio.ac.jp/ccep). For other parameters in the neural model, the same values in the paper (J. Neurosci., 16 (1996) 4017) are used. The functional synaptic signs (excitatory or inhibitory) of the chemical synapses are determined to satisfy the touch-induced movement (Bull. Math. Biol., 66 (2004) 727). To simulate ''habituation'' in the neural circuit, the conductance values of the chemical synapses are changed in this study. This synaptic plasticity is due to the rapid habituation to tap stimulation in eat-4</I> which decreases the ratio of synaptic vesicle fusion (J. Neurosci., 20 (2000) 4337). On the other hand, the conductance values of the gap junctions are not changed. According to the above mentioned neural modeling, we study the electrical signals in the intact and the neurons ablated touch sensitivity circuits. This work was supported by JSPS (No. RFTF-96I00102) and MEXT (No. 16740239).

Iwasaki, Yuishi et al. (2011) International Worm Meeting "Neuronal modeling toward quantitative understanding of nervous system of C. elegans."

Sakata, Kazumi, Kuramochi, Masahiro, Shingai, Ryuzo, Oda, Shigekazu, Iino, Yuichi, Iwasaki, Yuishi

[International Worm Meeting, 2011]

Our aim is to construct a neural model which quantitatively reproduces the experimental data and reliably predicts the neuronal dynamics in C. elegans. C. elegans shows various behaviors such as chemotaxis and thermotaxis. To understand these behaviors from the neurobiological viewpoint, the neuronal activity needs to be measured. The calcium imaging is a popular technique to visualize the neuronal activity. Since no evidence of Na+ current has been found in C. elegans, Ca2+ current is a key issue to the nervous system. Here quantity to be measured in the calcium imaging is not the intracellular Ca2+ concentration itself but the fluorescence intensity. In addition to the membrane potential, therefore, our model includes the concentrations of Ca2+, Ca2+-buffering protein, fluorescent protein and Ca2+-binding proteins as dynamical variables [Kuramochi & Iwasaki, 2010]. These concentrations are determined by chemical reaction equations. As ion channels, K+ channel, Ca2+ channel and SK channel are considered. A calcium pumping mechanism which carries Ca2+ out of the cell across the membrane is also considered. The fluorescence intensity is calculated from the concentration of Ca2+-binding fluorescent protein. The membrane potential and the fluorescence intensity are the observable variables which are comparable with the experimental data in C. elegans. On the basis of the neuronal model, we carry out computational studies on the nervous system of C. elegans. Firstly, we study the electrical properties of a single neuron (ASE chemosensory neurons) and find that our results agree well with the experimental data [Goodman et al., 1998]. Secondly, we study a neural circuit for NaCl chemotaxis [Iino & Yoshida, 2009]. In C. elegans, the main chemosensory neurons for NaCl are ASEL/R. Here ASEL/R neurons exhibit the left/right asymmetric activities [Suzuki et al., 2008]. In this work, the asymmetric stimulations are considered. The responses of the membrane potential, the Ca2+ concentration and the fluorescence intensity to the NaCl stimulus are simulated. We find that the neuronal activity measured by the fluorescence intensity shows quantitatively different behavior from that measured by the membrane potential. The difference comes from the threshold dynamics of Ca2+ current.

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).

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"

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.

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.

Yamazoe, Akiko et al. (2011) International Worm Meeting "Worms maintain their response to the repulsive odor 2-nonanone during avoidance behavior."

Yamazoe, Akiko, Kimura, Kotaro, Iwasaki, Yuishi

[International Worm Meeting, 2011]

Animals can maintain their behavioral response to environmental stimuli even under unstable environmental conditions and during various animal movements. To investigate neural mechanisms for such robust behavioral responses, it is necessary to quantitatively analyze the time-course changes in the correlation between the stimulus and behavioral response. For this, we quantitatively analyzed stimulus as well as behavior of worms' avoidance response to repulsive odor 2-nonanone. When animals migrate away from a source of repulsive signal, their avoidance response is likely weakened. In a previous study, however, we have shown that worms exhibited a constant average velocity of avoidance from 2-nonanone for 10 min (Kimura et al., J. Neurosci., 2010), suggesting a neural mechanism for such constant avoidance. In addition to the quantitative analysis of avoidance response to 2-nonanone (Yamazoe & Kimura, CeNeuro, 2010), we recently developed a technique to measure the concentration of 2-nonanone at specific spatial and temporal points of gas phase in the assay plate. By using a highly sensitive gas chromatograph, we observed a clear gradient of 2-nonanone, of which concentration increased with time. Based on this measured gradient of 2-nonanone, we determined the 2-nonanone concentration that each worm experienced during the avoidance assay (Cworm) and observed the following: (1) During the first 2 min of the assay worms did not initiate avoidance response and migrated randomly, and Cworm increased continuously up to the order of mM at 2 min. (2) After 2 min, worms started to migrate farther away from the odor source, and Cworm was maintained around the concentration, despite increase in the concentration gradient. (3) Cworm decreased effectively during runs, while it increased and decreased largely during pirouettes. (4) When compared between the early and late phases of the assay, the maximum dCworm/dt in each run decreased several fold along with the avoidance behavior, even though the orientation directions did not change considerably; that is, even when the gradient of 2-nonanone became shallower, the accuracy of worm orientation appeared maintained. These results suggest that worms may increase sensitivity to dC/dt during exposure to a certain concentration of 2-nonanone. We are currently conducting computer simulation to test this hypothesis. Further analysis may help us uncover the mechanism of maintaining proper behavioral responses.

Usuyama, Mamoru et al. (2013) International Worm Meeting "A computational model of the intracellular signaling pathway for odor receptor neuron in C. elegans."

Iwasaki, Yuishi, Usuyama, Mamoru, Ushida, Chisato, Shingai, Ryuzo

[International Worm Meeting, 2013]

Caenorhabditis elegans has only three pairs of olfactory receptor neurons, and AWC neurons are known to a pair of them. AWC neurons can respond to odor stimulus, and these responses are reported. In AWC neurons, intracellular [Ca2+] decrease is induced by attractive odor application, and [Ca2+] transiently increase by odor stimulus removal. The magnitude of this increase is positively corrected with time length of stimulation. AWCs can sense attractive odor, and using cGMP as a second messenger for intracellular signaling. But, how odor stimulus controls cGMP synthesis is unclear. In this study, we developed hypothetical model of olfactory signal transduction pathway to better understanding for olfaction in C. elegans. We indentified likely candidates of components for signal transduction, using available gene expression and physiological data from AWCs. We assume that, odor stimulus inhibit cGMP synthesis, owing to suppression of guanylate cyclase by G-protein signaling. In addition, we assumed Ca2+ dependant negative feedback loop to enhance the cGMP synthesis. These assumptions were necessary to replicate major features of the calcium dynamics in AWCs. AWC neurons indicated [Ca2+] fluctuation in decreasing phase of transient excitation. But, our model could not generate these fluctuations. So, to examine which component was related with generating of these fluctuations, adding random signal into the model pathway. Adding noise into model components, fluctuations were closely related with activity of phosphodiestelase and inflow/outflow of calcium ion and its buffering. Kinetic parameter for activity of guanylate cyclase was not effective to fluctuations in our model.

Usuyama, Mamoru et al. (2015) International Worm Meeting "Ca2+ dependent negative feedback loop in AWC olfactory neurons: from mathematical viewpoint."

Usuyama, Mamoru, Ishihara, Takeshi, Iwasaki, Yuishi, Kuge, Sayuri, Teramoto, Takayuki

[International Worm Meeting, 2015]

AWC receptor neurons show inhibitory response for odor stimulus and transient excitement for odor removal. This means that AWC neurons have mechanism which suppresses neural activity by external stimulation and activates by removal of the stimulation. AWC neurons change [Ca2+] via cGMP as second messenger. However, how AWC neurons change [cGMP] by stimulation is still unclear. In order to reproduce odor response in AWC neurons, we propose the negative feedback system to control [cGMP] in stimulation. The mathematical model consists of biochemical reactions and ionic transports through ion channels. Each biochemical molecules in the model, such as Ca2+, cGMP and so on, give concentrations and reaction rate constants to describe the intracellular biochemical reactions. The model is designed to easily mimic genetic assay such as gene over expression and its knock out experiments. We consider the two experimental features of odor response: (1) Peak [Ca2+] of off-response was linearly increased with duration of stimulus. (2)[Ca2+] was quickly decreased when neurons receive stimulus. Our previous work suggests that two or more Ca2+ dependent negative feedback loops for controlling cGMP production is necessary to reproduce odor responses in AWC (Usuyama, et. al 2012). In our study, however, further speculations in signaling pathway and parameter search show that only one negative feedback loop is enough to reproduce such experimental features. In addition to the experimental features, we consider the response of AWC neurons to successive stepwise stimulation. And we report "neural response" to odor stimulus in "wild type" and "mutant" in sillco, such as peak value and time constants of [Ca2+] change.