Cross-correlation for Distinguishing Models of Direction Selective Complex Cells

Pamela M. Baker¹ and Wyeth Bair

Dept. Physiology, Anatomy and Genetics, Univ of Oxford, Oxford UK
¹ pamela(dot)baker(at)dpag(dot)ox(dot)ac(dot)uk

Summary

Direction selectivity is a fundamental physiological property in V1 in the macaque, yet crucial questions of how DS receptive fields in V1 are built remain unanswered. Two fundamental issues that remain unresolved are the stage of the thalamocortical network where the DS time delay arises, and the nature of the nonlinear interaction, i.e. is it facilitatory or suppressive? We built a set of network models of the early visual system with populations of spiking LGN and V1 orientation tuned simple cells and DS complex cells connected by physiologically realistic synapses (Troyer et al. 1998). We built models that differed in placement of the DS time delay and sign of the DS nonlinear interaction, and then examined how these models could be distinguished using cross-correlation analysis (Baker and Bair 2010).

Models

We have developed 4 population models that implement different circuits and mechanisms for generating direction selective V1 complex cells. We show that these models can generate well-tuned DS complex cells, and that the different models can be discriminated using CCG analysis:

• DS_Post_Fac - A model with a postsynaptic DS time delay, and facilitatory nonlinear DS interaction.
• DS_Post_Sup - A model with a postsynaptic DS time delay, and suppressive nonlinear DS interaction.
• DS_Pre_Fac - A model with a presynaptic DS time delay, and facilitatory nonlinear DS interaction.
• DS_Pre_Sup - A model with a presynaptic DS time delay, and suppressive nonlinear DS interaction.

Visual Stimulus

To perform cross-correlation analysis, any stimulus that drives spiking activity in the network should be sufficient. We used drifting sine wave gratings to generate spike trains from non-DS simple cells and DS complex cells that were used to create CCGs. Our study showed that varying stimulus parameters such as direction and temporal frequency can be crucial for revealing features in the CCG. To view an example stimulus, click the button below to launch the iModel stimulus viewer. Then click Play or scroll through frames manually to see the drifting grating stimulus.

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Model Results

We tested 4 different models for the generating DS complex cells (see 'Models' below), using simple drifting grating stimuli while varying direction and temporal frequency. We recorded the spiking responses of EX units, that provide the sole input to the DS population, and the spikes from the DS complex units themselves. To examine these results, click the following button to launch the Results browser:

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1) Tuning of DS neurons

The following results for each of the 4 DS models we developed can be examined by choosing the desired model in the selection box at the top of the Results browser window.

• In the plot browser, select the DS unit (DS DC channel). This shows the narrow tuning curve we obtained for these models. Compare with the EX unit tuning curve (EX F1 channel). The EX cell inputs respond well at 0 and 180 degrees.

• Also compare TF tuning at preferred and anti-preferred directions. In the plot browser, select the TF data set and the DS unit (DS DC channel). This is TF tuning at the preferred direction.

• Compare with the DS unit tuning curve at the anti-preferred direction (TF_Opp data file). DS units respond equally well at both directions for low TFs. Experimental studies from V1 DS cells have shown that they also exhibit this temporal frequency dependence of direction selectivity.

2) Location of DS time delay can be revealed in the CCG

Cross-correlation of spike trains from a non-DS EX cell input and the postsynaptic DS cell can reveal where in the network the DS time delay originates. Our models differ in the location of the DS delay (presynaptic to the DS neuron or postsynaptic, on the DS neuron itself), and this differene can be observed in the CCG.

• Choose the postsynaptic delay model with a facilitatory DS interaction (DS_Post_Fac), and look at the CCG_dir data set. Look at the Preferred Dir trace. Note that there is a peak in the CCG at approximately 30 ms.

• Compare with the CCGs obtained at the oreferred direction for the presynaptic delay model with a facilitatory DS mechanism (DS_Pre_Fac). The peak in the CCG obtained in this model occurs at a far shorter time-to-peak, even though this EX input to the DS neuron is the 'delayed' input.

3) The appearance of CCG features is stimulus direction dependent

Characteristic features in CCGs between EX inputs and recipient DS units depend on the sign of the DS interaction (facilitatory or suppressive) and stimulus direction in both pre- and postsynaptic delay models.

• Choose the postsynaptic delay model with a suppressive DS interaction (DS_Post_Sup), and look at the CCG_dir data set. There is a dip in the CCG when the stimulus drifts in the anti-preferred direction (select Anti-Preferred Dir in the plot window), but no connection can be seen in the CCG when a preferred direction stimulus is used to generate spike trains (Preferred Dir in the plot window).

• Now compare with the postsynaptic delay model with facilatatory DS interaction (DS_Post_Fac). Now there is a large peak in the CCG (CCG_Dir data set) with a preferred direction stimulus, but there is no peak visible for the anti-preferred direction stimulus.

• Similarly for the presynaptic delay models with facilitatory (DS_Pre_Fac) and suppressive (DS_Pre_Sup) interactions. For the suppressive model, only the anti-preferred direction stimulus can reveal the dip characteristic of a suppressive DS connection. The facilitatory interaction generates a much stronger peak for the preferred direction stimulus, while the anti-preferred direction stimulus only generates an attenutated peak in the CCG.

References

• Baker PM, Bair W (2010) Cross-correlation analysis reveals circuits and mechanisms underlying direction selectivity. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00332

• Troyer TW, Krukowski AE, Priebe NJ, Miller KD (1998) Contrast-invariant orientation tuning in cat visual cortex: thalamocortical input tuning and correlation-based intracortical connectivity. J Neurosci 18:5908--5927.