Neurocomputing 44–46 (2002) 769–773www.elsevier.com/locate/neucom

Modeling frequency encoding in the cricketcercal sensory system

Sharon Crooka ;∗, John Millerb , Gwen Jacobsb

aDepartment of Mathematics and Statistics, University of Maine, Neville Hall 5752,Orono, ME 04469-5752, USA

bDepartment of Cell Biology and Neuroscience and Center for Computational Biology,Montana State University, Bozeman, MT 59717, USA

Abstract

The cercal sensory system of the cricket mediates the detection and analysis of low velocityair currents. Sensory stimuli are encoded as spatiotemporal patterns of activity within an a,erentmap that provides inputs to primary sensory interneurons. We have developed biophysicallybased interneuron models with synaptic inputs that are derived from a dynamic model of thea,erent map activity. Using these models, we have studied the possible mechanisms for thefrequency tuning of one type of interneuron in this system. Our results indicate that frequencypreferences are primarily due to the passive electrotonic structure of the dendritic arbor and thedynamic sensitivity of the spike initiation zone. c© 2002 Published by Elsevier Science B.V.

Keywords: Sensory system; Insect; Frequency; Activity pattern; Compartmental model

1. Introduction

The cercal sensory system of the cricket mediates the detection and analysis oflow velocity air currents in the animal’s immediate environment and functions asan extension of the auditory system for low frequency stimuli. The receptor organsare two antenna-like appendages called cerci, each covered with approximately 1000mechanosensory hairs. A single receptor neuron or a,erent is located at the base ofeach hair, and the terminals of these a,erents form monosynaptic excitatory connections

∗ Corresponding author. Tel.: +1-207-581-3919; fax: +1-207-581-3902.E-mail addresses: crook@math.umaine.edu (S. Crook), jpm@nervana.montana.edu (J. Miller),

gwen@nervana.montana.edu (G. Jacobs).

0925-2312/02/$ - see front matter c© 2002 Published by Elsevier Science B.V.PII: S0925 -2312(02)00470 -8

770 S. Crook et al. / Neurocomputing 44–46 (2002) 769–773

onto a set of local and projecting interneurons within the terminal ganglion. Theseinterneurons occur as mirror-symmetric pairs, and previous studies have characterizedthe frequency tuning properties of some of the pairs [7,9].

There are several biophysical mechanisms that could contribute to the frequencypreferences observed in the interneurons. One possible mechanism is the selectionof synaptic inputs from subclasses of a,erents having similar frequency sensitivities[6]. The passive membrane properties provide another possible mechanism by causinglow-pass Fltering of synaptic inputs. In this case, the preferred frequency range wouldbe a,ected by the cell morphology. In addition, there could be band-pass Fltering dueto the resonance caused by the active ionic channels in the dendrites and the spikeinitiation zone [2].

Sensory stimuli are encoded as spatiotemporal patterns of activity within an a,erentmap. We have developed biophysically based interneuron models with synaptic inputsthat are derived from a dynamic model of the a,erent map activity. Using these mod-els, we have studied the possible mechanisms for the frequency tuning of one type ofsensory interneuron in this system. The modeled interneurons included the pairs desig-nated as right and left 10–2 and right and left 10–3. These four directionally sensitiveinterneurons have indistinguishable stimulus intensity thresholds, operating ranges, andtemporal properties [7]. They also exhibit identical frequency tuning with peaks around15 Hz as shown in Fig. 1. Our modeling results indicate that the electrotonic structureof the dendritic arbor and the dynamic sensitivity of the spike initiation zone couldaccount for the frequency preferences for these cells with narrow-band low-frequencytuning.

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Frequency (Hz)

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Sti

mu

lus

/Re

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Interneuron Frequency Tuning

10-2 & 10-3

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Fig. 1. Coherence between white noise air current stimulus and spike response for several primary sensoryinterneurons in the cricket cercal system [Theunissen and Miller, unpublished data].

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2. Methods

The results described in this paper were derived from a database containing experi-mentally obtained anatomical and physiological data for identiFed neurons. All of theneurons in the database were stained and reconstructed in three dimensions and sub-sequently scaled and aligned to a common coordinate system. In previous research,anatomical and directional tuning characteristics of a,erents from this database wereused to construct a probabalistic representation of the spatial locations of di,erent a,er-ent types within the a,erent map [3]. For each receptor type, physiological data wereused to create a forward Wiener kernel representations of the input=output characteris-tics [8]. The derived Wiener kernels can be used to predict the spike train producedby an a,erent neuron when it is stimulated by an air current stimulus [1]. By com-bining these spatial and temporal representations, we are able to model the dynamicpattern of ensemble activity in the a,erent map for any particular air current stimulus.The direction of an air current stimulus is represented by the location of the increasedactivity within the a,erent map [4]; however, the frequency of an air current stimulusis represented by the temporal characteristics of the activity patterns.

Anatomical reconstructions and physiological data for primary sensory interneuronswere used to create biophysically based compartmental models of right and left 10–2 and right and left 10–3. The dynamic model of the a,erent map activity wasused to simulate the stimulus-dependent synaptic inputs to the interneuron models.We evaluated the performance of these models by comparing simulation results toexperimentally obtained results for various types of air current stimuli. We then usedthese models to examine the e,ects of morphology, passive membrane properties, andactive channels on frequency tuning.

3. Results

It is well known that the passive membrane structure of neurons functions as alow-pass Flter for synaptic inputs. This occurs due to the biophysical properties ofthe cell membrane which functions as a resistor and capacitor connected in parallel(see for example [5]). Current inputs arriving at low frequencies yield large voltageresponses, but high frequency inputs are attenuated or blocked. This phenomenon occursin the model interneurons and is demonstrated in Fig. 2. The coherence depicts thelinear correlation between an air current stimulus and the subthreshold voltage responseacross di,erent frequencies. The power of the response demonstrates that only thosestimuli with low frequency components will elicit enough of a voltage response toproduce action potentials in the presence of spike-producing ion channels.

Neurons can also exhibit band-pass Fltering properties or resonance; resonant neuronsproduce large responses when driven by inputs near their resonant frequencies andsmaller responses at other frequencies. This mechanism occurs due to the interactionsbetween active and passive membrane properties. For example, currents that activelyoppose changes in membrane voltage and also activate slowly relative to the membranetime constant will produce resonance [2].

772 S. Crook et al. / Neurocomputing 44–46 (2002) 769–773

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Normalized PowerCoherence

Fig. 2. The dashed curve depicts the coherence between white noise air current stimulus and voltage responsefor passive 10–2 interneuron model. The normalized power spectrum of the voltage response is shownas a solid curve. At intermediate frequencies, the stimulus=response coherence is signiFcant; however, theamplitude of the voltage response is too low to elicit spiking in the active membrane.

We added ion channels capable of eliciting action potentials to the spike initiationzone of our model interneurons. The particular ion channels involved are not known;thus, the model channels and their kinetic parameters were chosen to match the spikeshape and spiking characteristics observed in physiological experiments. The additionof these currents resulted in frequency tuning characteristics in the model that matchthe coherence analysis of experimental data as shown in Fig. 3.

Our results suggest that frequency preferences occur primarily due to the passiveelectrotonic structure of the dendritic arbor and the dynamic sensitivity of the spikeinitiation zone. However, it is certain that ion channels are present throughout thedendritic structure of these interneurons. The function of these channels is not known;they may amplify low frequency inputs or serve as modulators of cell behavior. Thesepossibilities will be the subject of future studies.

We have also initiated studies of the mechanisms contributing to the frequency se-lectivity of interneurons with broader tuning and higher frequency preferences such asright and left 9–2, right and left 9–3, and right and left 8–1 (see Fig. 1). Preliminarysimulations and theoretical studies suggest that the tuning in these cells can be partiallyexplained by dendritic structures with fewer branching structures and larger diametersthat are more electrotonically compact. This type of morphology causes less attenuationof higher frequencies. Since these interneurons do not respond to low frequency inputs,ion channels that resonate in the desired frequency range are also required. The cur-rents associated with these ion channels can create the band-pass Fltering e,ects seen

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Fig. 3. Coherence calculations for 10–2 interneuron model with active membrane are depicted by the dashedcurves. Coherence calculations based on experimental data are shown by the solid curves. For the model,ionic currents have been placed in the spike initiation zone only.

in the frequency responses of the interneurons. Further study of the functional signiF-cance of the structure of this system will also involve modeling interneuron behaviorfor synaptic inputs associated with naturalistic air current stimuli.

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[3] G.A. Jacobs, F.E. Theunissen, Functional organization of a neural map in the cricket cercal sensorysystem, J. Neurosci. 16 (1996) 769–784.

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[7] J.P. Miller, F.E. Theunissen, G.A. Jacobs, Representation of sensory information in the cricket cercalsensory system. I. Response properties of the primary interneurons, J. Neurophysiol. 66 (1991)1680–1689.

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[9] F.E. Theunissen, J.C. Roddey, S. StuLebeam, H. Clague, J.P. Miller, Information theoretic analysisof dynamical encoding by four identiFed primary sensory interneurons in the cricket cercal system,J. Neurophysiol. 75 (1996) 1345–1364.