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A gap junction circuit enhances processing of coincident mechanosensory inputs.

Rabinowitch I, Chatzigeorgiou M, Schafer WR - Curr. Biol. (2013)

Bottom Line: Modeling approaches have been useful for understanding structurally and dynamically more complex electrical circuits.Therefore, we formulated a simple analytical model with minimal assumptions to obtain insight into the properties of the hub-and-spoke microcircuit motif.Thus, the hub-and-spoke architecture may implement an analog coincidence detector enabling distinct responses to distributed and localized patterns of sensory input.

View Article: PubMed Central - PubMed

Affiliation: Cell Biology Division, MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge CB2 0QH, UK.

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Hub-and-Spoke Circuit Model(A) Model of a hub-and-spoke circuit (see Supplemental Experimental Procedures). β1 and β2 are the relative transduction strengths of spokes 1 and 2 in the presence of sensory stimuli (lightning symbols). α1 and α2 are the relative coupling strengths of the gap junctions connecting spokes 1 and 2 to the hub (dotted lines).  and  are the steady-state membrane potentials of spoke 1 and the hub, respectively. Arrows indicate net direction of current flow, and the magnitude of  is represented schematically by the size of the gray bar.(B) When just one input is received in spoke 1 (lightning symbol), entailing an inactive spoke 2 (“2inactive”) implemented in the model by setting β2 = 0,  is expected to decrease in size, as illustrated by the shortened gray bar, since current now flows in the opposite direction from the hub to spoke 2 (arrows indicate net direction of current flow).(C) If an input is received in spoke 1 (lightning symbol) but spoke 2 is removed from the circuit altogether (“2ablated”), implemented by setting α2 = β2 = 0, then the model predicts less or no suppression of  compared to the “2inactive” condition, since current no longer leaves the hub (arrow indicates net direction of current flow).(D) Hub steady-state membrane potential, , for varying α1, α2 and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 7 in Supplemental Experimental Procedures) or an ablated spoke 2 (dashed lines; derived from Equation 10 in Supplemental Experimental Procedures). As the plot illustrates,  is expected to increase with larger α1 or smaller α2 (fainter lines) and is always smaller when spoke 2 is present compared to when it is ablated.(E) Spoke 1 steady-state membrane potential, , for varying α1, α2, and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 8 in Supplemental Experimental Procedures) or ablated spoke 2 (dashed lines; derived from Equation 11 in Supplemental Experimental Procedures). Spoke 1 membrane potential is expected to decrease with larger α1 and α2 (darker lines) and is always smaller when spoke 2 is present compared to when it is ablated.
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fig1: Hub-and-Spoke Circuit Model(A) Model of a hub-and-spoke circuit (see Supplemental Experimental Procedures). β1 and β2 are the relative transduction strengths of spokes 1 and 2 in the presence of sensory stimuli (lightning symbols). α1 and α2 are the relative coupling strengths of the gap junctions connecting spokes 1 and 2 to the hub (dotted lines). and are the steady-state membrane potentials of spoke 1 and the hub, respectively. Arrows indicate net direction of current flow, and the magnitude of is represented schematically by the size of the gray bar.(B) When just one input is received in spoke 1 (lightning symbol), entailing an inactive spoke 2 (“2inactive”) implemented in the model by setting β2 = 0, is expected to decrease in size, as illustrated by the shortened gray bar, since current now flows in the opposite direction from the hub to spoke 2 (arrows indicate net direction of current flow).(C) If an input is received in spoke 1 (lightning symbol) but spoke 2 is removed from the circuit altogether (“2ablated”), implemented by setting α2 = β2 = 0, then the model predicts less or no suppression of compared to the “2inactive” condition, since current no longer leaves the hub (arrow indicates net direction of current flow).(D) Hub steady-state membrane potential, , for varying α1, α2 and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 7 in Supplemental Experimental Procedures) or an ablated spoke 2 (dashed lines; derived from Equation 10 in Supplemental Experimental Procedures). As the plot illustrates, is expected to increase with larger α1 or smaller α2 (fainter lines) and is always smaller when spoke 2 is present compared to when it is ablated.(E) Spoke 1 steady-state membrane potential, , for varying α1, α2, and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 8 in Supplemental Experimental Procedures) or ablated spoke 2 (dashed lines; derived from Equation 11 in Supplemental Experimental Procedures). Spoke 1 membrane potential is expected to decrease with larger α1 and α2 (darker lines) and is always smaller when spoke 2 is present compared to when it is ablated.

Mentions: We formulated a model of a simplified hub-and-spoke circuit (Figure 1A; see also Supplemental Experimental Procedures available online) consisting of a hub interneuron connected to two spoke sensory neurons through electrical synapses (Figure 1A). Since the time course of sensory inputs is substantially slower than the neurons’ electrical time constants, and since C. elegans neurons are characterized by graded potentials rather than action potentials, we focused on the steady state rather than the dynamics of the circuit, reasoning that we could derive analytical expressions for the membrane potentials in each neuron of the model circuit. Based on previous findings [9], we assumed the gap junctions to be nonrectifying, and we assumed all neurons to be nonspiking and approximately isopotential, consistent with published electrophysiological data [12]. For simplicity, all cells were electrically passive with similar membrane resistance and capacitance. We derived the steady-state membrane potential in the hub interneuron and in the two spoke sensory neurons ( and ) in response to sensory stimulation in terms of five parameters (Figure 1A; Supplemental Experimental Procedures): the relative gap junction strengths of the two spoke connections (α1, α2 > 0), the sensory transduction strengths in the input neurons (β1, β2 > 0), and the receptor reversal potential (Etr > 0).


A gap junction circuit enhances processing of coincident mechanosensory inputs.

Rabinowitch I, Chatzigeorgiou M, Schafer WR - Curr. Biol. (2013)

Hub-and-Spoke Circuit Model(A) Model of a hub-and-spoke circuit (see Supplemental Experimental Procedures). β1 and β2 are the relative transduction strengths of spokes 1 and 2 in the presence of sensory stimuli (lightning symbols). α1 and α2 are the relative coupling strengths of the gap junctions connecting spokes 1 and 2 to the hub (dotted lines).  and  are the steady-state membrane potentials of spoke 1 and the hub, respectively. Arrows indicate net direction of current flow, and the magnitude of  is represented schematically by the size of the gray bar.(B) When just one input is received in spoke 1 (lightning symbol), entailing an inactive spoke 2 (“2inactive”) implemented in the model by setting β2 = 0,  is expected to decrease in size, as illustrated by the shortened gray bar, since current now flows in the opposite direction from the hub to spoke 2 (arrows indicate net direction of current flow).(C) If an input is received in spoke 1 (lightning symbol) but spoke 2 is removed from the circuit altogether (“2ablated”), implemented by setting α2 = β2 = 0, then the model predicts less or no suppression of  compared to the “2inactive” condition, since current no longer leaves the hub (arrow indicates net direction of current flow).(D) Hub steady-state membrane potential, , for varying α1, α2 and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 7 in Supplemental Experimental Procedures) or an ablated spoke 2 (dashed lines; derived from Equation 10 in Supplemental Experimental Procedures). As the plot illustrates,  is expected to increase with larger α1 or smaller α2 (fainter lines) and is always smaller when spoke 2 is present compared to when it is ablated.(E) Spoke 1 steady-state membrane potential, , for varying α1, α2, and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 8 in Supplemental Experimental Procedures) or ablated spoke 2 (dashed lines; derived from Equation 11 in Supplemental Experimental Procedures). Spoke 1 membrane potential is expected to decrease with larger α1 and α2 (darker lines) and is always smaller when spoke 2 is present compared to when it is ablated.
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fig1: Hub-and-Spoke Circuit Model(A) Model of a hub-and-spoke circuit (see Supplemental Experimental Procedures). β1 and β2 are the relative transduction strengths of spokes 1 and 2 in the presence of sensory stimuli (lightning symbols). α1 and α2 are the relative coupling strengths of the gap junctions connecting spokes 1 and 2 to the hub (dotted lines). and are the steady-state membrane potentials of spoke 1 and the hub, respectively. Arrows indicate net direction of current flow, and the magnitude of is represented schematically by the size of the gray bar.(B) When just one input is received in spoke 1 (lightning symbol), entailing an inactive spoke 2 (“2inactive”) implemented in the model by setting β2 = 0, is expected to decrease in size, as illustrated by the shortened gray bar, since current now flows in the opposite direction from the hub to spoke 2 (arrows indicate net direction of current flow).(C) If an input is received in spoke 1 (lightning symbol) but spoke 2 is removed from the circuit altogether (“2ablated”), implemented by setting α2 = β2 = 0, then the model predicts less or no suppression of compared to the “2inactive” condition, since current no longer leaves the hub (arrow indicates net direction of current flow).(D) Hub steady-state membrane potential, , for varying α1, α2 and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 7 in Supplemental Experimental Procedures) or an ablated spoke 2 (dashed lines; derived from Equation 10 in Supplemental Experimental Procedures). As the plot illustrates, is expected to increase with larger α1 or smaller α2 (fainter lines) and is always smaller when spoke 2 is present compared to when it is ablated.(E) Spoke 1 steady-state membrane potential, , for varying α1, α2, and β1 values for an inactive spoke 2 (continuous lines; derived from Equation 8 in Supplemental Experimental Procedures) or ablated spoke 2 (dashed lines; derived from Equation 11 in Supplemental Experimental Procedures). Spoke 1 membrane potential is expected to decrease with larger α1 and α2 (darker lines) and is always smaller when spoke 2 is present compared to when it is ablated.
Mentions: We formulated a model of a simplified hub-and-spoke circuit (Figure 1A; see also Supplemental Experimental Procedures available online) consisting of a hub interneuron connected to two spoke sensory neurons through electrical synapses (Figure 1A). Since the time course of sensory inputs is substantially slower than the neurons’ electrical time constants, and since C. elegans neurons are characterized by graded potentials rather than action potentials, we focused on the steady state rather than the dynamics of the circuit, reasoning that we could derive analytical expressions for the membrane potentials in each neuron of the model circuit. Based on previous findings [9], we assumed the gap junctions to be nonrectifying, and we assumed all neurons to be nonspiking and approximately isopotential, consistent with published electrophysiological data [12]. For simplicity, all cells were electrically passive with similar membrane resistance and capacitance. We derived the steady-state membrane potential in the hub interneuron and in the two spoke sensory neurons ( and ) in response to sensory stimulation in terms of five parameters (Figure 1A; Supplemental Experimental Procedures): the relative gap junction strengths of the two spoke connections (α1, α2 > 0), the sensory transduction strengths in the input neurons (β1, β2 > 0), and the receptor reversal potential (Etr > 0).

Bottom Line: Modeling approaches have been useful for understanding structurally and dynamically more complex electrical circuits.Therefore, we formulated a simple analytical model with minimal assumptions to obtain insight into the properties of the hub-and-spoke microcircuit motif.Thus, the hub-and-spoke architecture may implement an analog coincidence detector enabling distinct responses to distributed and localized patterns of sensory input.

View Article: PubMed Central - PubMed

Affiliation: Cell Biology Division, MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge CB2 0QH, UK.

Show MeSH
Related in: MedlinePlus