A model of the intracellular response of an olfactory neuron in Caenorhabditis elegans to odor stimulation

Abstract

We developed a mathematical model of a hypothetical neuronal signal transduction pathway to better understand olfactory perception in Caenorhabditis elegans. This worm has only three pairs of olfactory receptor neurons. Intracellular Ca(2+) decreases in one pair of olfactory neurons in C. elegans, the AWC neurons, following application of an attractive odor and there is a transient increase in intracellular Ca(2+) following removal of odor. The magnitude of this increase is positively correlated with the duration of odor stimulation. Additionally, this Ca(2+) transient is induced by a cGMP second messenger system. We identified likely candidates for the signal transduction molecules functioning in this system based on available gene expression and physiological data from AWCs. Our model incorporated a G-protein-coupled odor receptor, a G-protein, a guanylate cyclase as the G-protein effector, and a single phosphodiesterase. Additionally, a cyclic-nucleotide-gated ion channel and a voltage-gated ion channel that mediated calcium influx were incorporated into the model. We posited that, upon odor stimulation, guanylate cyclase was suppressed by the G-protein and that, upon cessation of the stimulus, the G-protein-induced suppression ceased and cGMP synthesis was restored. A key element of our model was a Ca(2+)-dependent negative feedback loop that ensured that the calcium increases were transient. Two guanylate cyclase-activating proteins acted on the effector guanylate cyclase to negatively regulate cGMP signaling and the resulting calcium influx. Our model was able to closely replicate in silico three important features of the calcium dynamics of AWCs. Specifically, in our simulations, [Ca(2+)] increased rapidly and reached its peak within 10 s after the odor stimulus was removed, peak [Ca(2+)] increased with longer odor exposure, and [Ca(2+)] decreased during a second stimulus that closely followed an initial stimulus. However, application of random background signal ('noise') showed that certain components of the pathway were particularly sensitive to this noise.

Figure 1. The hypothetical scheme of signal transduction.

Reactions are classified into nine steps and numbered as reaction 1 thru 9. 1. Binding of an odor molecule to the receptor when odor stimulus is applied. Dissociation of an odor molecule from the receptor when odor stimulus is removed. 2. Activation of G-protein (Gα subunit) following the bind of odor molecule to the receptor. Inactivation of Gα subunit following an odor molecule dissociates from the receptor. 3. Inhibition of GCY by Gα. This process includes binding of GCY and Gα, GCY::GCAPa and Gα, and GCY::GCAPb and Gα. 4. Synthesis and decomposition of cGMP. These include cGMP synthesis by GCY, cGMP decomposition by PDE, and supply and removal of GTP by unknown process. 5. Binding of cGMP to the CNG channel, and changes in [Ca²⁺] and membrane potential via the CNG channel. 6. Changes in [Ca²⁺] and membrane potential via a voltage-gated channel (voltage-dependent calcium channel). 7. Change in [Ca²⁺] via a calcium extrusion mechanism (CaX). 8. Binding of calcium ions to the calcium buffer (CaM), and modulation of CaX and PDE. 9. Inactivation of GCAPs by calcium ions and feedback on GCY activity.

Figure 2. Change in [Ca²⁺].

The bars indicate periods of stimulation. A. Addition of stimulus. B. Removal of stimulus. Duration of stimulus was 1, 3, or 5 min. C. After removal of the first 5-min stimulus, a second 20-s stimulus was applied 10 or 30 s later. D, E, F. G-CaMP fluorescence associated with A, B, C, respectively. G, H, I. Membrane potential associated with A, B, C, respectively.

Figure 3. Changes in the nine components.

Changes in the components, indicated in each panel, from 10 s before the application of the stimulus for 1 (blue), 3 (red) and 5 min (green).

Figure 4. Changes in the components by addition of the second stimulus.

Changes in intracellular pathway components, indicated in each panel, by addition of the second stimulus after 10 s (red) and 30 s (green) after removal of the first stimulus for 5 min.

Figure 5. Changes in [Ca²⁺] by fluctuation of the equation parameters.

Changes in [Ca²⁺] when the equation parameters (indicated in each panel) include a random pulse train as described in Methods. The fluctuation of EC50_CNG, n_CNG and Ef_CaX produced large changes in [Ca²⁺]. Odor stimulus was given for 5 min and was removed at 10 s (right panel). The bar indicates the stimulus. Blue: no addition of fluctuation. Red, green, and magenta lines represent 30, 50, 100% magnitudes of the maximum pulse height of the noise, respectively.

Figure 6. Changes in [Ca²⁺] by fluctuation of the concentrations of substances.

Change in [Ca²⁺] when the concentrations of substances are determined using a random pulse train. Addition and removal of odor stimulus, and the colors of line are same as those in Fig. 5. The component is indicated in each panel. A. GTP, B. cGMP, C. CaM::Ca₄ where Ca₄ indicates four calcium ions.

Figure 7. Synergistic effects of pairs of noise inputs.

When pulse trains were added alongside different parameters or molecular concentrations, a synergistic increase in [Ca²⁺] fluctuations was observed. Noises were applied simultaneously to A) CaM::Ca₄ and K_{+1,PDE+CaM::Ca4} and B) K_{+1,CaM::Ca3+Ca} and K_+1,PDEactive. Bar indicates the maximal difference between [Ca²⁺] trace without noise and that with noise.