Neuronal Circuitry: Signal Synchronization

The general idea for synchronization is to allow a signal with arbitrary timing to accumulate, while using a signal with known timing to synchronize the resulting spike propagation. An example of a known signal is a theta modulation that is used throughout a system (or throughout connected circuitry) at a given frequency with region-specific phases.

Place cell activity may be used to accumulate depolarization in cells of the synchronization population. The depolarization may be allowed to saturate at a known level. That level must be below threshold, so that a certain degree of theta modulation is necessary to achieve spiking.

A stable level of saturation is not always easily obtained with dynamic components, since the arrival of input can cause depolarization ripples. These ripples may be minimized if the neuronal dynamics are modulated by depolarization, such that membrane responses are slower at greater depolarization. Smoothing of the ripples may also be achieved by noise or population effects. Population effects can involve probabilistic timing shifts in groups of cells undergoing the input saturation, which must then cooperate to cause population or target spiking.

Any phase of a synchronization signal (such as theta) may be used to elicit synchronized spiking. The phase at which spiking is achieved depends on the signal amplitude that must combine with the (saturated) input to reach threshold. A steep section of the synchronization signal can achieve greater timing precision than a flat section when the depolarization through accumulated input can vary slightly. Further spikking during the high portions of the synchronization signal can then be avoided with an AHP.

A combination of synchronization circuitry may further improve timing precision. Consecutive stages may be used such that spiking frequency is divided more than once, e.g. a gamma frequency modulation could be used for initial synchronization and a theta frequency modulation for further synchronization. Serial chaining of multiple synchronization circuits at the same synchronization signal frequency may improve timing if the EPSPs received from a prior synchronization stage are relatively slow and relatively flat. Multiple populations may apply signal synchronization in parallel, which can then be combined.

The principles:

The circuitry investigated at this time seeks to control the time at which threshold is reached in order to achieve precise synchronization. With a largely unpredictable input signal, the ideal functional system then has the following features:

• The arbitrary input signal is constrained between accumulated potential values of Th - A and Th - delta, where Th is the threshold, A is some interval greater than delta and delta is a small offset.
• A step-function synchronization signal has an amplitude of Th-delta and width sufficient to allow the EPSP and membrane capacitance rise times to add the synchronization signal to the accumulated input potential and reach threshold. This synchronization signal should not reach threshold without the presence of at least a minimum accumulated input potential.

(optimal-thresholded-signal-synchronization.fig)

The optimal step-function synchronization signal is not achievable through synaptic inputs to a neuronal circuit, since the characteristic timing of its EPSP and the membrane capacitance limit the rate of depolarization that is achievable. Two approaches seek to approximate the optimal synchronizing behaviour described above:

1. Constraints on synchronization signal: Arbitrary levels of accumulated potential due to the information signal are permitted within the specified range from Th - A to Th - delta. If the synchronization signal cannot be a step function, a short EPSP may be used (which may necessitate that the interval from Th - A to Th - delta is adequately small). The precision is then given by the time from the onset of the synchronization EPSP to its maximum amplitude. While such a short EPSP does not explicitly reflect a recorded field potential such as that reflected by theta modulation of membrane potentials, it can be generated at synapses that receive spikes at theta frequency. This is demonstrated in the model newtmaze.short-sync-signal-high-precision.ccm.gz. Alternatively, the precision can be specified as an initial section in the rising portion of a longer EPSP (such as theta modulation of membrane potentials). It is then guaranteed that any accumulated potential above a specific minimum will cause spiking between the onset of the synchronization EPSP and the end of the chosen initial section. When this alternative is used, one must deal with the network behaviour in the cases where accumulated potential at some cells is below the specified minimum. Perhaps inhibitory synaptic input must commence shortly after the end of the initial section of each synchronization signal, to suppress spiking of cells that did not spike during the permitted interval.

   

2. Constraints on accumulated potential of information signal: The EPSP of the synchronization signal may rise gradually, by mandating a dependence on the amplitude of the synchronization signal (and therefore also the accumulated potential) at which threshold can be reached. The maximal amplitude of theta modulation of membrane potential may be chosen as the necessary amplitude of the synchronization signal. The accumulated potential due to the information signal must then be constrained within a specific range. That range, and the time-offset from the required amplitude of the synchronization signal that it represents, determines the precision. This may be a plausible approach where much is known about the information signal, such as in the case of place cell input at a given rate. This is demonstrated in the model newtmaze.full-theta-full-input-precision.ccm.gz. Again, an initial section of the synchronization signal may be used, by specifying the necessary amplitude as the amplitude of the synchronization signal at the end of that section. In this case, the network behaviour in for cells with accumulated potential below the desired level must be dealt with as above.