Why synaptic delay

For a general discussion of such delays, see Buonomano and Mauk and Buonomano Spike-based dynamic neuromorphic processors, such as the DYNAP-SE, cannot directly implement non-spiking neurons, such as the LN5 neuron in the cricket circuit, and flexible routing of such analog signals is problematic. Therefore, we approximate LN5 and PIR with an inhibitory—excitatory pair of dynamic synapses with different time constants, so that the sum of the two postsynaptic currents initially is inhibitory and subsequently becomes excitatory some time after presynaptic stimulation.

As its name implies, the subtractive inhibitory synapse type allows for combining excitation and inhibition dynamics by summing inhibitory and excitatory postsynaptic currents, as opposed to the shunting synapse type which inhibits the neuron using a different mechanism. This summation of postsynaptic currents is the central mechanism of the proposed disynaptic delay element. For the excitatory part, the slow synapse type is used, leaving the fast synapse type available for bias configuration and use for stimulation of the postsynaptic neuron; in this case, for the projection from AN1 to LN3.

The proposed disynaptic delay element can be modeled with Equation 3 , and the membrane potential resulting from presynaptic stimulation can be illustrated by solving Equation 1. Figure 2 shows a numerical simulation of the disynaptic delay element model for a 20 ms constant input current that represents the presynaptic stimulation, as in Figure 1. Figure 2. Simulation of the disynaptic delay element model. A Sum of inhibitory and excitatory postsynaptic currents from the delay element.

B Resulting postsynaptic neuron membrane potential. The neuron and synapse parameters are selected so that the membrane potential is comparable to the potential measured in the hardware, and should thus not be directly compared with biological potentials and threshold values.

Dynamic disynaptic elements of this type are expected to provide a delayed excitation that qualitatively matches the effect of PIR in the output of non-spiking delay neurons like the LN5.

Furthermore, we expect that the time delay and relative amplitude of inhibition and excitation can be configured, for example by modifying the synapse time constants and efficacies. The experimental results presented below demonstrate that this is indeed feasible, and that for some bias settings it is possible to control the time delay and delayed excitation amplitude with the synaptic efficacies only.

First, we aimed to mimic the post-inhibitory rebound in the cricket auditory circuit with a delay of about 20 ms. The time constant of the inhibitory synapse of the delay element was set so that the resulting inhibition of LN3 corresponded to the inhibition caused by LN5 in the cricket; that is, a couple of ms longer than the ms sound-pulse duration. The excitatory synapse was tuned so that the LN3 excitation lasts somewhat longer than that of the initial inhibition, approximately to the end of the corresponding PIR excitation of LN5 in the cricket.

The weight of the inhibitory synapse was set higher than that of the excitatory synapse, such that the sum of inhibition and excitation turned out negative, thus inhibiting the neuron for the duration of the delay.

For the excitatory synapse, the weight was set to yield a substantial excitation of the postsynaptic neuron following the inhibition, while not generating spikes without additional synaptic stimulation. In this manner, the effect of the non-spiking LN5 on LN3 is imitated with the summation of an inhibitory postsynaptic current and an excitatory postsynaptic current produced by two synapses on LN3.

Table 1. Given the large parameter space of a dynamic neuromorphic processor like the DYNAP-SE, we then explored different ways to simplify the configuration of the disynaptic delay elements for delays up to about ms. One identified possibility is to lower the constant injection current of the neurons receiving the delayed signal, to such an extent that the inhibition by the delay elements make the neuron reach its minimum membrane potential.

Furthermore, the amplitude of the post-inhibitory excitation, V max , is then controlled by the excitatory weight of the delay element, w exc , as well as by varying the number of presynaptic spikes stimulating the delay element. Table 2. For the purpose of characterization, the proposed disynaptic delay elements were implemented, in parallel, in one core of a DYNAP-SE neuromorphic processor; one delay element on each of the neurons in the core.

All of these neurons were then stimulated as described in section 2. To avoid oscilloscope and DYNAP-SE time synchronization issues, we analyzed the membrane potential measurements without reference to the precise timing of the presynaptic stimulation. The full duration at half minimum of the inhibition and the full duration at half maximum of the subsequent excitation, see Figure 2 , can be determined from membrane potential measurements without reference to the timing of presynaptic spikes.

These quantities are illustrated in Figure 3 , and allowed us to investigate the effect of different bias parameter settings on the disynaptic delay elements in a population of neurons in the DYNAP-SE. This way the bias parameter values of the delay elements could for example be tuned to imitate the behavior of the delay neuron LN5 in the cricket.

Further details on the experimental settings are described in section 2. Figure 3. A Postsynaptic membrane potential vs. B Distribution of the maximum measured membrane potential, V max , resulting from a presynaptic pulse. C Similarly, the distribution of the minimum measured membrane potential, V min.

The distributions in panels B—F were obtained via characterization of one DYNAP-SE core, comprising, in parallel, one disynaptic delay element on each of the neurons, with biases configured according to Table 1. For the implementation of the cricket auditory feature detection circuit, as described in section 2. Table 3. Table 4. Table 5. For the implementation of the inhibitory neuron, LN2, a single neuron on a reserved core was used. This neuron was set to receive the generated stimulation representing AN1 by assigning a synaptic connection of the fast excitatory type.

The bias parameter values from section 5. The parameter values of the fast excitatory synapse were then adjusted in order to model the behavior of LN2 as observed in the cricket. For the coincidence detecting neuron, LN3, the proposed delay elements were implemented according to the earlier description.

An excitatory connection of the fast type was added for LN3 to receive the projection from AN1. For the excitatory connection from LN3 to the feature detecting neuron LN4, a synapse of the fast type was used, and, for the inhibitory connection from LN2 to LN4, a synapse of the subtractive type was used.

Bias parameter values from section 5. For the fast inhibitory synapse, bias values from section 5. The bias parameters, time constant, threshold and weight, for both synapse types, were then hand-tuned in order to approximate the behavior of LN4 in one DYNAP-SE neuron, so as to make LN4 spike, thus signaling feature detection, for stimuli with IPIs of 20 ms, but not for IPIs of 0, 10, 30, 40, and 50 ms. We further investigated the possibility that a single neuron in the DYNAP-SE with multiple disynaptic delay elements can respond selectively to spatiotemporal spike patterns, which match the difference in the delay times resulting from device mismatch.

Specifically, we configured a neuron with two inputs via two different disynaptic delay elements. The input patterns consist of spike pairs, one spike for each delay element, with a variable spike-time interval.

Patterns with spike-time intervals that match the delay-time difference between the two delay elements should generate postsynaptic currents with coincident maxima, thus resulting in maximum excitation of the neuron. The neuron and delay elements were configured as described in section 2. The synapses were selected with an off-line Hebbian-like learning rule such that, for the spike patterns considered, the neuron responded selectively to spike patterns with intermediately long intervals, but not to spike patterns with shorter or longer intervals.

Spike patterns were generated as described in the next section, and the neuron was stimulated one hundred times with each pattern. Based on these experiments the average probability of the neuron to spike for each type of pattern was determined. More specifically, a custom module making use of the tools for configuration and monitoring provided by cAER was created and added to the framework.

Since these measurements only capture the neuron membrane potential, there is no information about the precise relative timing of spike-events in the resulting data. Because of this, the durations of inhibition and excitation of the delay elements were defined in terms of the FDHM as described above. For the extraction of the delay parameters defined in section 2. The stimulation cycle was given a duration of 0.

At the initial state of rest, the resting potential was automatically estimated for each neuron. The resting potential was subsequently subtracted from the measurement data, such that the resulting resting potentials are zero. The RT of the circuits between eye or ear or sites of tactile stimulation SOS and the index fingers were significantly shorter than that between eye or ear or the same SOS and the right or left big toes.

The greater the distance between the SOS and the brain the longer the RT of the response by a given effector organ. The overall signal speed OASS from the neck to the index finger was less than that from the neck to the big toe. Two EPPs are elicited, the second of which summates on the falling edge of the first.

As a result of two action potentials, a summated potential about 2 mV in amplitude occurs. If there were three presynaptic action potentials, and they occurred rapidly enough, the total potential would be about 3 mV, and so forth. Temporal summation is strictly a passive property of nerve cells. Special ionic conductive mechanisms are not needed to explain it.

The potentials summate because of the passive properties of the nerve cell membrane, specifically the ability of membranes to store charge. The membrane temporarily stores the charge of the first PSP and then the charge from the second PSP is added to it to produce a potential twice as large at first.

This process of temporal summation is very much dependent upon the duration of the synaptic potential. The temporal summation occurs when the presynaptic action potentials occur in quick succession. The time frame is dependent upon the passive properties of the membrane, specifically the time constant. Spatial summation. Now consider a motor neuron that receives two inputs.

Spatial summation in nerve cells occurs because of the space constant, the ability of a charge produced in one region of the cell to spread to other regions of the cell.

Whether a neuron fires in response to a synaptic input is dependent upon how many action potentials are being fired in any one afferent input, as well as how many individual afferent pathways are activated. The decision to fire also depends on the presence of inhibitory synaptic inputs. Artificially depolarizing the interneuron to initiate an action potential produces a transient hyperpolarization of the membrane potential of the motor neuron See Figure 6.

The time course of this hyperpolarization looks very similar to that of an EPSP, but it is reversed in sign. The synaptic potential in the motor neuron is called an inhibitory postsynaptic potential IPSP because it tends to move the membrane potential away from the threshold, thereby decreasing the probability of this neuron initiating an action potential. The membrane potential of the flexor motor neuron is about mV, so one might predict that the IPSP would be due to an increase in the permeability or the conductance of an ion whose equilibrium potential is more negative than mV.

One possibility is potassium. Potassium does mediate some inhibitory synaptic potentials in the central nervous system, but not at the particular synapse between a spinal interneuron and spinal motor neuron.

At this particular synapse, the IPSP is due to a selective increase in chloride permeability. Note that the equilibrium potential for chloride is about mV. The transmitter released by the spinal interneuron binds to a special class of ionotropic receptors which are normally closed, but open and become selectively permeable to chloride ions as a result of the binding of the transmitter. As a result of the increase in Cl - permeability, the membrane potential moves from its resting value of mV towards the Cl - equilibrium potential.

What about the transmitter substance that is released by the inhibitory interneuron in the spinal cord? The transmitter substance is glycine , an amino acid which is used frequently in the central nervous system as a transmitter that produces inhibitory actions. Don't have an account? Sign in via your Institution. You could not be signed in, please check and try again.

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