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N. S. Szczecinski et al.
Table 1. Model parameter descriptions and values.
Parameter
Description
Value
a
Adaptation term scale
1088
b
Proportional term scale
40.45
c
Constant offset
−52.84
d
Exponent in low-pass filter function, i.e. f (z) = z d
2.369
τ
Time constant for ˙
x
2.668 × 10 3
We wished to see if the model could capture the same characteristics without retuning
the model parameters. Figure 2 shows the model’s response to both a ramp-and-hold
stimulus and to a naturalistic stimulus. Figure 2A shows that the responses to the rampand-hold stimulus share several key characteristics: Both responses initially leap up to
a high value; both responses then continue to grow, but at a reduced and apparently
constant rate; both responses quickly adapt during the hold portion of the stimulus;
both responses are quickly eliminated during the downward ramp. The peak response
of the experimentally measured CS response is 25–30 Hz higher than that of the model.
However, the shape of both the rising phase and the relaxation phase qualitatively match,
suggesting that the model is capturing the underlying dynamics of the system. In addition,
the adaptation phases largely overlap, despite the model being tuned without any data
from the relaxation phase.
Figure 2B also shows that the responses to the naturalistic stimulus largely match
between the model and the animal, despite the dynamic nature of the stimulus and not
retuning the parameter values. The responses share several key characteristics: Both
responses are sensitive to the initial increase in the force; both responses are largely
constant between 10% and 40% of the stimulus duration, despite the dynamic nature
of the force’s rise; both responses slowly adapt, and then are silenced when the force
noticeably decreases at around 80% of the stimulus.
Figure 2C compares the model’s response to the two stimuli. As seen in the experimentally measured CS responses, the response to the ramp-and-hold stimulus increases
more rapidly, reaches a higher response frequency, and adapts more quickly than the
response to the naturalistic stimulus. The response to the naturalistic stimulus is persistent despite the dynamic nature of both the force stimulus and the model. These data
suggest that the CS are tuned to detect relevant sensory features during walking [4].
3.2 Emergent Properties of the Model
Our model reproduces the linear encoding of tonic force levels as well as the power law
reflection of the rate of force seen in insect CS [2]. Figure 3 shows data summarizing
simulation experiments in which the model was subjected to a ramp-and-hold stimulus
with a height A and a rise time T (i.e. u(t) = min(A · t/T , A)). Figure 3A shows that as
in the animal, the sensory discharge long after the hold phase begins (in our experiments,
9.5 s in accordance with [2]) is linearly correlated with the amplitude of the force, A.
N. S. Szczecinski et al.
Table 1. Model parameter descriptions and values.
Parameter
Description
Value
a
Adaptation term scale
1088
b
Proportional term scale
40.45
c
Constant offset
−52.84
d
Exponent in low-pass filter function, i.e. f (z) = z d
2.369
τ
Time constant for ˙
x
2.668 × 10 3
We wished to see if the model could capture the same characteristics without retuning
the model parameters. Figure 2 shows the model’s response to both a ramp-and-hold
stimulus and to a naturalistic stimulus. Figure 2A shows that the responses to the rampand-hold stimulus share several key characteristics: Both responses initially leap up to
a high value; both responses then continue to grow, but at a reduced and apparently
constant rate; both responses quickly adapt during the hold portion of the stimulus;
both responses are quickly eliminated during the downward ramp. The peak response
of the experimentally measured CS response is 25–30 Hz higher than that of the model.
However, the shape of both the rising phase and the relaxation phase qualitatively match,
suggesting that the model is capturing the underlying dynamics of the system. In addition,
the adaptation phases largely overlap, despite the model being tuned without any data
from the relaxation phase.
Figure 2B also shows that the responses to the naturalistic stimulus largely match
between the model and the animal, despite the dynamic nature of the stimulus and not
retuning the parameter values. The responses share several key characteristics: Both
responses are sensitive to the initial increase in the force; both responses are largely
constant between 10% and 40% of the stimulus duration, despite the dynamic nature
of the force’s rise; both responses slowly adapt, and then are silenced when the force
noticeably decreases at around 80% of the stimulus.
Figure 2C compares the model’s response to the two stimuli. As seen in the experimentally measured CS responses, the response to the ramp-and-hold stimulus increases
more rapidly, reaches a higher response frequency, and adapts more quickly than the
response to the naturalistic stimulus. The response to the naturalistic stimulus is persistent despite the dynamic nature of both the force stimulus and the model. These data
suggest that the CS are tuned to detect relevant sensory features during walking [4].
3.2 Emergent Properties of the Model
Our model reproduces the linear encoding of tonic force levels as well as the power law
reflection of the rate of force seen in insect CS [2]. Figure 3 shows data summarizing
simulation experiments in which the model was subjected to a ramp-and-hold stimulus
with a height A and a rise time T (i.e. u(t) = min(A · t/T , A)). Figure 3A shows that as
in the animal, the sensory discharge long after the hold phase begins (in our experiments,
9.5 s in accordance with [2]) is linearly correlated with the amplitude of the force, A.