Neuromechanical Model of fCO Sensory Inhibition
143
the AR configuration, the model does assist imposed flexion motions, but still
resists imposed extension motions, suggesting that the AR is demarcating which
joint motions are allowable in a context-dependent way. Finally, we discuss the
implications of our findings on how the animal nervous system may bring about
reflex reversal, as well as how these findings could be applied to robotic joint
control.
2 Methods
A simplification of our network structure is shown in Fig. 1. We constructed
our simulation in Animatlab 2 [6] based on the network layout for extension
presented in Fig. 1 of ref. [13]. In this layout, the E and I type non-spiking
interneurons (NSI) receive excitatory stimulus from six position sensory neurons (purple) and ten velocity neurons (orange), as well as delayed inhibitory
input from the velocity neurons mediated by a set of six spiking interneurons
(yellow). Of these neurons, half respond to fCO elongation (flexion) and half
to fCO relaxation (extension). As such, the sensory neurons can be split into
four major groupings: Flexion position, flexion velocity, extension position, and
extension velocity (Fig. 1). Each sensory neuron includes an arbitrary tonic noise
of 0.01 mV to create slight variance in the input signals of each grouping to the
NSI. To simplify our network construction, we elected to only model the slow
fibers of each muscle, and assumed each muscle would be activated by one slow
motorneuron (MN). The outputs from the NSI then synapse onto our slow MNs
(red) via graded neurotransmitter release.
The NSI were modeled as non-spiking leaky integrators [6]. As such, the
membrane voltage, V, of each NSI varies according to the differential equation:
C m
dV
dt
= I leak + I syn + I app
(1)
where
I leak = G m · (E r − V ),
(2)
I syn =
n
i=1
G(s, i) · (E s,i − V ),
(3)
and I app is an optional externally applied stimulus. Equations (2) and (3) define
the leak and synaptic currents, respectively. In these equations, V is the current membrane voltage, G m is the conductance of the cell membrane, C m is
the membrane capacitance, and E r is the resting potential of the neuron. The
instantaneous conductance of the i
th synapse models the graded release of neurotransmitter in nonspiking synapses, and is a piecewise-linear function of the
presynaptic neuron’s instantaneous membrane voltage, V pre :
G s,i = G max,i ·
⎧
⎨
⎩
1,
if V pre > E hi
Vpre−E lo
E hi −E lo
, if E lo ≤ V pre ≤ E hi
0,
if V pre < E lo
(4)
143
the AR configuration, the model does assist imposed flexion motions, but still
resists imposed extension motions, suggesting that the AR is demarcating which
joint motions are allowable in a context-dependent way. Finally, we discuss the
implications of our findings on how the animal nervous system may bring about
reflex reversal, as well as how these findings could be applied to robotic joint
control.
2 Methods
A simplification of our network structure is shown in Fig. 1. We constructed
our simulation in Animatlab 2 [6] based on the network layout for extension
presented in Fig. 1 of ref. [13]. In this layout, the E and I type non-spiking
interneurons (NSI) receive excitatory stimulus from six position sensory neurons (purple) and ten velocity neurons (orange), as well as delayed inhibitory
input from the velocity neurons mediated by a set of six spiking interneurons
(yellow). Of these neurons, half respond to fCO elongation (flexion) and half
to fCO relaxation (extension). As such, the sensory neurons can be split into
four major groupings: Flexion position, flexion velocity, extension position, and
extension velocity (Fig. 1). Each sensory neuron includes an arbitrary tonic noise
of 0.01 mV to create slight variance in the input signals of each grouping to the
NSI. To simplify our network construction, we elected to only model the slow
fibers of each muscle, and assumed each muscle would be activated by one slow
motorneuron (MN). The outputs from the NSI then synapse onto our slow MNs
(red) via graded neurotransmitter release.
The NSI were modeled as non-spiking leaky integrators [6]. As such, the
membrane voltage, V, of each NSI varies according to the differential equation:
C m
dV
dt
= I leak + I syn + I app
(1)
where
I leak = G m · (E r − V ),
(2)
I syn =
n
i=1
G(s, i) · (E s,i − V ),
(3)
and I app is an optional externally applied stimulus. Equations (2) and (3) define
the leak and synaptic currents, respectively. In these equations, V is the current membrane voltage, G m is the conductance of the cell membrane, C m is
the membrane capacitance, and E r is the resting potential of the neuron. The
instantaneous conductance of the i
th synapse models the graded release of neurotransmitter in nonspiking synapses, and is a piecewise-linear function of the
presynaptic neuron’s instantaneous membrane voltage, V pre :
G s,i = G max,i ·
⎧
⎨
⎩
1,
if V pre > E hi
Vpre−E lo
E hi −E lo
, if E lo ≤ V pre ≤ E hi
0,
if V pre < E lo
(4)