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With networks of more than two neurons different connectivity schemes are studied. Firstly lines of neurons are considered, with each neuron connected to those either side of it. Rings of neurons are similar to lines but the end neurons are connected to each other. Mexican hat coupling introduces the idea that coupling between neurons may vary with the distance between them. |
Neurons in a Line
Firstly a line of three neurons was studied, and the timing difference between each pair of neurons studied. By doing this it was possible to see that the adjacent neurons (those with a connection between them) were always more synchronised than the non-adjacent ones. This suggested some wavelike behvaiour, specifically that the first neuron in the line firing an action potential would cause the second to do so immediately afterwards, followed by the third.
Typical Spiking Propagation: Right to Left in a System of 5 Neurons
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A similar process was undertaken looking at the synchronisation between pairs of neurons in larger systems, and the same trend observed. The spiking starts at one of the outermost neurons in the vast majority of cases and propagates from one end of the line to the other. In the rare cases when the first neuron to spike is inside the line, the spikes propagate symmetrically to the outsides.
If you look at the amplitude of the spikes a quite different trend can be observed. The neurons amplitude synchronise with the corresponding neuron at the other end of the line; the system tends towards symmetric amplitude synchronisation. However this trend is only observed in systems with an odd number of neurons, those with an even number are amplitude synchronised from the start.
Neurons in a Ring
When the neurons are arranged in a ring the temporal spike synchronisation is stronger betweeen adjacent neurons than symmetric ones. This suggests that, in a similar way to neurons in a line, there may be some propagation of spikes through the system.
There is a difference, however, in the amplitude synchronisation between the neurons. In a system of four neurons in a ring there is an intermittant stage between non-synchronised and synchronised behaviour during which the neurons synchronise completely in adjacent pairs. As the systems get larger (5 or more neurons) the requirement for these pairs to be adjaent is relaxed and often non-adjacent neurons synchronise in pairs before complete synchronisation.
Mexican Hat Coupling
The mexican hat wavelet is introduced in order to give some physiological description of the decay in coupling between neurons with distance. It means that neurons close to each other are excitatory, and those further away inhibit each other. This inhibition tends to zero as the distance between them increases. The neurons are arranged in a line.
For a 5 neurons system of this type the neurons completely synchronise with each other, with the exception of the central neuron which is anti-synchronised with the others. This means it fires actions potentions half a phase out from the other neurons.
Much larger systems (more than 10 neurons) are very different; each neuron anti-synchronises with those neurons it is adjacent to. Effectively the system is synchronised into two groups, with group membership alternating along the line.
For networks of sizes 6-10 neurons there is again synchronisation in two groups, but membership of the groups is not stable with neurons swaping between the two .
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