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N. S. Szczecinski et al.
2 Methods
2.1 Animal Experimental Methods
Recordings were taken from the tibial CS of the American cockroach (Periplaneta americana). Activities of axons of the receptors were monitored extracellularly and identified
by action potential amplitude and mechanical stimulation/ablation of the cuticular caps
[2]. Force waveforms were generated by an analog to digital interface (Spike 2, Cambridge Electronics), applied to the tibia via a probe linked to a DC motor and monitored
by strain gauges in the probe [4].
To aid in generating this model, we wished to test CS responses to ramp-and-hold
stimuli with different ramp rates but the same hold amplitude. For all stimuli, the hold
amplitude was 1.66 mN. The ramp durations tested were 0.125 s, 0.224 s, 0.456 s,
and 0.915 s. Each ramp-and-hold stimulus was applied to the tibia 11 times. For each
stimulus, the duration of the ramp phase was split into 20 bins. The number of spikes that
occurred in each bin was counted and used to calculate the mean afferent firing frequency
over that bin. Therefore, each “dataset” consisted of a single stimulus described by 20
time points and 20 frequency samples averaged from 11 repetitions of the stimulus. To
test the model response to naturalistic stimuli like the animal might experience during
walking, force waveforms obtained from freely walking insects were also applied [16].
2.2 Modeling Methods
Modeling Campaniform Sensilla Discharges. We wish to construct a dynamical
model that predicts the discharge (i.e. instantaneous firing frequency) of an afferent
nerve from a population of campaniform sensilla (CS) given a load stimulus applied
in that population’s preferred direction [5, 6]. The sensory discharge of such nerves is
known to reflect both the amplitude and rate of a load stimulus [2]. In addition, the sensory discharge adapts as a constant force is applied. Therefore, we choose to model the
sensory discharge as the sum of three terms: One proportional to the load stimulus; one
that adapts to the load over time; and a constant offset. We expect that rate-sensitivity
and hysteresis will emerge naturally from adaptation to stimuli.
We are not attempting to model the separate contribution of individual features in the
system, for example, the mechanical response of the CS to limb bending, the intrinsic
properties of the sensory or afferent neurons, or the processing performed by individual afferents in the nerve. At this stage, we wish to understand the phenomenological
relationship between the force applied to an insect’s leg and the rate-coded information
carried by the afferent nerves from the CS to the rest of the nervous system. We will refer
to these elements collectively as “the system.” Possible contributions of each component
of the system to the response are considered in the Discussion.
Conceptually, an adaptive response can be thought of as subtracting the long-term
history of the input from the input value itself. Thus, the response will reflect the input’s
rapid changes relative to its history, but will eventually return to zero if the input stops
changing and the history can “catch up”. Under certain assumptions, it can be shown that
such a system directly approximates the rate of change of the input [17]. But how should
N. S. Szczecinski et al.
2 Methods
2.1 Animal Experimental Methods
Recordings were taken from the tibial CS of the American cockroach (Periplaneta americana). Activities of axons of the receptors were monitored extracellularly and identified
by action potential amplitude and mechanical stimulation/ablation of the cuticular caps
[2]. Force waveforms were generated by an analog to digital interface (Spike 2, Cambridge Electronics), applied to the tibia via a probe linked to a DC motor and monitored
by strain gauges in the probe [4].
To aid in generating this model, we wished to test CS responses to ramp-and-hold
stimuli with different ramp rates but the same hold amplitude. For all stimuli, the hold
amplitude was 1.66 mN. The ramp durations tested were 0.125 s, 0.224 s, 0.456 s,
and 0.915 s. Each ramp-and-hold stimulus was applied to the tibia 11 times. For each
stimulus, the duration of the ramp phase was split into 20 bins. The number of spikes that
occurred in each bin was counted and used to calculate the mean afferent firing frequency
over that bin. Therefore, each “dataset” consisted of a single stimulus described by 20
time points and 20 frequency samples averaged from 11 repetitions of the stimulus. To
test the model response to naturalistic stimuli like the animal might experience during
walking, force waveforms obtained from freely walking insects were also applied [16].
2.2 Modeling Methods
Modeling Campaniform Sensilla Discharges. We wish to construct a dynamical
model that predicts the discharge (i.e. instantaneous firing frequency) of an afferent
nerve from a population of campaniform sensilla (CS) given a load stimulus applied
in that population’s preferred direction [5, 6]. The sensory discharge of such nerves is
known to reflect both the amplitude and rate of a load stimulus [2]. In addition, the sensory discharge adapts as a constant force is applied. Therefore, we choose to model the
sensory discharge as the sum of three terms: One proportional to the load stimulus; one
that adapts to the load over time; and a constant offset. We expect that rate-sensitivity
and hysteresis will emerge naturally from adaptation to stimuli.
We are not attempting to model the separate contribution of individual features in the
system, for example, the mechanical response of the CS to limb bending, the intrinsic
properties of the sensory or afferent neurons, or the processing performed by individual afferents in the nerve. At this stage, we wish to understand the phenomenological
relationship between the force applied to an insect’s leg and the rate-coded information
carried by the afferent nerves from the CS to the rest of the nervous system. We will refer
to these elements collectively as “the system.” Possible contributions of each component
of the system to the response are considered in the Discussion.
Conceptually, an adaptive response can be thought of as subtracting the long-term
history of the input from the input value itself. Thus, the response will reflect the input’s
rapid changes relative to its history, but will eventually return to zero if the input stops
changing and the history can “catch up”. Under certain assumptions, it can be shown that
such a system directly approximates the rate of change of the input [17]. But how should