A point process model for the parabigeminal nucleus as a recursive estimator
The parabigemial nucleus (PBN) is a satellite of the superior colliculus (SC), the midbrain saccadic oculomotor control center. PBN neurons fire action potentials at a rate proportional to the retinal position error (RPE) of attended visual targets, whether stationary or moving. The tuning functions of PBN neurons are usually not Gaussian, but are better described by an exponentially decaying sigmoid function. Recently, using periodically blinking moving targets, it has been discovered that PBN activity continues to predict the unseen (virtual) target?s trajectory, as inferred from kinetic information before the target disappears. The sigmoidal tuning function is maintained during target-off phases, except that its dynamic range shrinks somewhat. Such predictive neural events are critical for behavior, but are not well understood, either from the physiological or computational standpoint.
This is study is focused on the encoding problem, attempting to understand the computational mechanism for the predictive neuronal activity in the PBN by building statistical models that can be tested against real spike train data.
The point process theoretical framework that we used treats the spike train as a non-homogeneous poisson process, enabling us to relate various possible factors, such as auto-regressive self-firing history and predicted virtual target positions, to the logarithm of conditional intensity of spiking probability at each discrete time bin via a linear model.
We assume that the PBN has full knowledge of the dynamics of the visual target and the eye movements made by the animal. As a consequence, when the target is momentarily turned off, the animal will assume its continual existence and predict the virtual target?s position using a Kalman filter. The mean of the virtual target positions predicted by the Kalman filter lies very close to the ?true? target position, whether visible or not. The variance of the prediction is near zero when the target is on, grows linearly with time after the target is turned off, and suddenly drops back to near zero when the target is turned back on. We have also incorporated the temporal evolution of the sigmoid tuning function dynamic range during a complete duty cycle by modulating its parameters as functions of the variance of the Kalman filter prediction.
The results of this modeling were evaluated with a K-S plot constructed according to the time rescaling theorem, as well as an auto-correlation scatter plot of the consecutive rescaled inter-spike intervals. The curve falls mainly within the 95% confidence intervals, and the auto-correlation scatter plot is spread basically evenly on the unit square area. These observations suggest the model provides a satisfactory fit for the data presented.
Our model has successfully captured the characteristics of PBN spike trains related to the encoding of extrapolated positions of virtual targets, and thus provided a plausible explanation for the origin of predictive activity, and how this internal representation of the external world is reflected in neural spike trains.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). A point process model for the parabigeminal nucleus as a recursive estimator.
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.014
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Received:
29 Jan 2009;
Published Online:
29 Jan 2009.