Mimicking Collective Firing Patterns of Hundreds of Connected Neurons using a Single-Neuron Experiment

The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission unachievable. In addition, as a result of the enormous number of required measurements, the estimated network parameters would differ from the original ones. Here we present a versatile experimental technique, which enables the study of recurrent neural networks activity while being capable of dictating the network connectivity and synaptic strengths. This method is based on the observation that the response of neurons depends solely on their recent stimulations, a short-term memory. It allows a long-term scheme of stimulation and recording of a single neuron, to mimic simultaneous activity measurements of neurons in a recurrent network. Utilization of this technique demonstrates the spontaneous emergence of cooperative synchronous oscillations, in particular the coexistence of fast Gamma and slow Delta oscillations, and opens the horizon for the experimental study of other cooperative phenomena within large-scale neural networks.

SnapshotNo. -An integer denoting the currently mimicked snapshot.

Load connectivity to Edges and initial conditions to
StimulationsData. StimulationsData(n,m) indicates a stimulation to neuron n at snapshot number StimulationsData(n,m).
Insert to Queue1 all the neurons that are stimulated at SnapshotNo.=1, according to the initial conditions (the maximal random integer is 1, i.e. the stimulation time equals ).

For each neuron n in Queue1:
-The mimicking neuron is stimulated M times, with the M corresponding last inter-stimulation intervals of neuron n, from StimulationsData(n).
-Another stimulation is given after the appropriate inter-stimulationinterval. This stimulation will be also the first stimulation for the next mimicking process.
-If the stimulation results in an evoked spike: Add the row Edges(n) to Queue2, without repetitions.
-Replace the minimal value of StimulationsData(n) with SnapshotNo..

Appendix B
Experimental scheme: Discrete time, sub-threshold connections (e.g. Figure 5B): This scheme is similar to the scheme presented in Appendix A, but also incorporates sub-threshold synaptic connections.
All synaptic connections are sub-threshold, and typically the number of postsynaptic connections per neuron, K, is between 10 and 50. Kmin denotes the minimal number of simultaneous sub-threshold stimulations that can result in an evoked spike, typically between 2 and 5. During the procedure if the number of pre-synaptic neurons that fired in the previous snapshot is above Kmin, the stimulation is above-threshold.
Above-threshold stimulation has a strength of -800 mV, with a duration of 200 μs.
The strength of a sub-threshold stimulation is in the range of [-200, -500] mV with a duration of 200 μs. The memory of the stimulations accounts also for sub-threshold stimulations, where typically M=8. Initial conditions of stimulations are generated randomly similar to the first scheme, with additional below-threshold stimulations.
The strength of the sub-threshold stimulation was -300 mV. The mimicking neuron had fc=2.1 Hz, and was given 1000 pre-scheme stimulations with a rate of 2fc to reach the intermittent phase.
The mimicking scheme is done using the following procedure: SnapshotNo. -An integer denoting the currently mimicked snapshot.
1. As in Appendix A.

For each neuron n in Queue1:
If Counter1(n)>=Kmin, the stimulation is above-threshold: -The mimicking neuron is stimulated M times, with the M corresponding inter-stimulation-intervals.
-Above-threshold stimulation is given after the appropriate inter-stimulation-interval. This stimulation will be also the first stimulation for the next mimicking process. Clear Counter1, move Counter2 into Counter1 and Clear Counter2.

Appendix C
Experimental scheme: Continues time, above-threshold connections (e.g. Figure   5C): A continuous time version of Appendix A. The continuity of this scheme is limited by the machine cycle, 20 μs in our implementation. All synaptic connections are abovethreshold, where typically K=2 and M=3. For each connection,  was chosen randomly from [min, max], where typically min is between 8 and 12 ms and max is between 12 and 20 ms. Initial conditions are constructed by choosing M random delays using exponential distribution with a rate of 2fc.
In Figure 5C, the values are N=500, K=2, Fnoise=0.5 Hz, M=3, min=8 and max=12 ms. The mimicking neuron had fc=3 Hz, and was given 700 pre-scheme stimulations with rate of 2fc to reach the intermittent phase.
The mimicking scheme is done using the following procedure:

Variables:
StimulationsData -A N×30 matrix that holds the stimulation times.

T -Mimicked time.
Counter -A 1×N array of zeros.

Load connectivity to Edges and initial conditions to StimulationsData.
Assign T=0. 6 2. Find a neuron n such that StimulationsData(n,Counter(n)) is minimal but also greater than T. If no neuron is found -go to clause 4.

The mimicking neuron is stimulated M times, with the M
corresponding inter-stimulation-intervals of n (taken from

StimulationsData).
Another stimulation is given. This stimulation will be also the first stimulation for the next mimicking process.
If the stimulations results in an evoked spike: For each neuron j from the row Edges(n), add the sum of the spike's time and neuron j's delay to

Generate noise in StimulationsData:
A stimulation every 0.1 ms with a probability of 10 -4* Fnoise to each neuron.

Appendix D
Experimental scheme: Continuous time, Sub-Threshold connections (e.g. Figure   6): A continuous time version of Appendix B. In the end of each mimicking process, if the last stimulation results in an evoked spike, a weak stimulations will be given to each one of the post synaptic neurons of the mimicked neuron. If two weak stimulations arrive with a short lime-lag between them, they will be merged to one strong stimulation. The procedure could be generalized to account for stricter temporal summations, where more than two weak stimulations are required to fall within a short time window in order to yield a spike (Kmin can be defined similarly to Appendix B)the current implementation requires only two stimulations. The program advances in segments of time with the size of SegmentLength, such that neurons whose current segment does not contain any above-threshold stimulations will not be mimicked at the In Figure 6, the values are N=350, K=13, NoiseNum=3, SegmentLength=4.5 ms, LookBack=3.5 s, MinGap=5.5 ms, min=6 ms and max=10 ms. The mimicking neuron had fc=4.2 Hz, and was given 700 pre-scheme stimulations with a rate of 2fc to reach the intermittent phase.
The mimicking scheme is done using the following procedure: Parameters: N -Number of neurons. SegmentLength -The time segment in which the program advances, has to be smaller than the minimal neuronal response latency.
NoiseNum -The number of random neurons stimulated at every segment.
LookBack -The length of the mimicking sequence.
MinGap -The maximal time-lag between two weak stimulations which results in one merged supra-threshold stimulation.
Edges -N×K matrix, containing information of nodal connections and their delays.
The delays are randomly chosen in the range [min, max].

Variables:
StimulationsData -A data structure that holds the times of weak and strong stimulations.
SegmentIndex -An index indicating the current segment (the time step being mimicked).
IsStimulated -N×m matrix, the first index indicates a neuron in the network and the second index indicates a Segment Index. IsStimulated(i,SegmentIndex)=1 means that the neuron is stimulated above-threshold at the segment Index SegmentIndex, otherwise it is not.
Next -a FIFO with the neurons that should be stimulated at the current segment.
1. Load connectivity to Edges and initial condition to StimulationsData and IsStimulated.
Generate random above-threshold stimulations according to