Research Highlights

Computer Models of Neural Circuits

We are using computer simulations to study the dynamics of neural circuits. Although much is known about the inner workings of individual nerve cells, called neurons, the operational principles governing the dynamics of complex interconnected networks of neurons remain poorly understood. By simulating large, heterogeneous neural systems on modern digital computers, we hope to discover some of the operational principles that underlie the extraordinary processing power of biological computers. A better understanding of biological computation will likely contribute to the development of new technologies for treating neurological disease and may well lead to revolutionary advances in machine intelligence.

Understanding Information Processing in the Vertebrate Retina

Many of our studies to date have been directed toward understanding information processing in the vertebrate retina. The retina has many advantages as a target system for developing realistic computer models. The anatomy and physiology of the retina have been extensively studied, especially in comparison with many other parts of the central nervous system; the inputs and outputs of the retina can be well characterized; and the retina receives no major feedback projections from the brain, allowing it to be treated as a stand-alone circuit. Furthermore, we may reasonably expect that by understanding how the retina talks to the brain, we will gain fundamental insight into how the different parts of the brain talk to each other. The following results were obtained using a computer model of the cat retina that has allowed us to investigate the function of retinal circuitry at a level that would be very difficult with currently available experimental techniques.¹

Our most intriguing finding is that retinal neurons can encode visual information in rather surprising ways. The output of a neuron cannot be classified in conventional electrical engineering terms as either analog or digital, but rather it consists of something altogether different—a temporal sequence of impulses, or spikes. Because each spike is (to a first approximation) identical to every other spike, information can only be conveyed by the temporal pattern of impulses. Neuroscientists continue to debate how information is encoded within the temporal structure of neural spike trains, but there is widespread agreement that one very important variable is the firing rate. Figure 1 shows an example of how a typical neuron in our retinal model encodes the local intensity, or contrast, of a small stimulus as a transient increase in firing rate.

About 10 years ago, Wolf Singer’s laboratory in Germany reported that retinal neurons use the relative timing of spikes to encode global information about visual stimuli that is not conveyed by their local firing rates.^2,3,4 Using our retinal model, we were able to demonstrate a very similar phenomenon by examining the relative timing of spikes produced by neurons responding to either the same or to different objects (Figure 2). For retinal neurons activated by the same large object, their spike trains were strongly correlated, or phase locked, by a common underlying oscillation at a frequency of approximately 100 Hz. Pairs of retinal neurons activated by different objects, however, were not correlated because the phases of their underlying oscillations varied randomly with respect to each other. Thus, our retinal model captures the interesting property of biological neurons—their evoked oscillations in responses to appropriate large visual features are stimulus-specific and are only phase-locked between cells responding to the same contiguous object.

We used the retinal model to ask what information-stimulus-specific oscillations between retinal neurons might convey to the brain. To investigate this question, we were guided by two principles. (1) Because it only takes us a fraction of a second to form a visual impression, the information conveyed by stimulus-specific oscillations must be available on short, physiologically meaningful time scales—roughly a few hundred milliseconds. (2) Because the spatial convergence of retinal neurons onto target cells in the brain is rather low, with each target cell receiving input from only a few retinal neurons, the information conveyed by stimulus-specific oscillations must be available locally in the firing activity of a similarly small number of neighboring cells. We thus used the retinal model to quantify the information conveyed about the global properties of a stimulus—in this case, the total size of the object—by a 2 × 2 neighborhood of retinal output neurons in a few hundred milliseconds. At the same time, we were fortunate to receive data from Wolf Singer’s laboratory recorded from output neurons in the cat retina under similar experimental circumstances. These data allowed us to directly test the predictions of our retinal model.

The oscillations evoked by stimuli of various sizes in our retinal model were very similar to those measured from the cat retina (Figure 3). In both sets of data, small stimuli evoked little or no oscillatory response, whereas large stimuli evoked very large oscillations. Because our model is consistent with the known anatomy and physiology of the cat retina, it can provide a useful tool for investigating how information may be encoded by spike trains in the optic nerve.

Why Stimulus Size Matters

To determine the information content of both artificial and biological spike trains, we asked whether it was possible to determine if a group of neighboring cells was responding to a small or large object using their local firing activity alone (Figure 4). Our results are plotted as a percent correct, which was proportional to the fraction of trials on which the total size of the stimulus could be correctly inferred from the local firing activity. Random events were added to the model spike trains to ensure that the average number of spikes, or firing rate, did not change as a function of stimulus size. The only cue available from the local firing activity regarding the total size of the stimulus was therefore the amplitude of the synchronous oscillations. Our results showed that in 300 ms (using as few as 4 spike trains from a small 2 × 2 neighborhood), it was possible to achieve performance levels approaching 90% correct.

In related experiments, we showed that there was a tradeoff between the number of cells included in the analysis and the total time allowed for accomplishing the size discrimination task. Specifically, as more cells were included in the analysis, shorter time windows were required to achieve the same performance levels.
Why, one might ask, is it important for retinal neurons to convey information about stimulus size in their local firing activity? For a possible answer to this question, consider the frog retina, where Tachibanna’s laboratory in Japan has shown that there are specialized neurons, called dimming detectors, that exhibit strong synchronous oscillations when activated by a large dimming object but not when activated by a small dimming object.⁵ Considering that from a frog’s perspective, a small dimming spot might be a fly or other food source, whereas a large dimming spot is more likely to be a bird or other dangerous predator, one can quickly appreciate why size matters.

References

1. G.T. Kenyon, B. Moore, J. Jeffs, K.S. Denning, G.S. Stephens, B.J. Travis, J.S. George, J. Theiler, and D.W. Marshak, “A model of high frequency oscillatory potentials in retinal ganglion cells,” Visual Neuroscience (in press, 2003).
2. C.M. Gray, P. Konig, A.K. Engel, and W. Singer, “Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties,” Nature 338(6213), 334-337 (1989).
3. S. Neuenschwander, M. Castelo-Branco, and W. Singer, “Synchronous oscillations in the cat retina,” Vision Research 39(15), 2485-2497 (1999).
4. S. Neuenschwander and W. Singer, “Long-range synchronization of oscillatory light responses in the cat retina and lateral geniculate nucleus,” Nature 379(6567), 728-32 (1996).
5. H. Ishikane, A. Kawana, and M. Tachibana, “Short- and long-range synchronous activities in dimming detectors of the frog retina,” Visual Neuroscience 16(6), 1001-1014 (1999).

Acknowledgment

This work is supported by the LDRD program at LANL, by the Deployable Adaptive Processing Systems program funded by the DOE Office of Nuclear Nonproliferation, and by the DOE Office of Biomedical and Environmental Research.

G.T. Kenyon, G.J. Stephens, M.C. Flynn, J.S. George, J.M Galbraith (P-21), B.J. Travis (EES-2), J. Theiler (ISR-2)

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For more information, contact Garrett Kenyon at gkenyon@lanl.gov.

Figure 1. Responses of model ganglion cells to small spots. (a) Ganglion-cell output consists of discrete, uniform pulses. A relatively dim spot (top) produces a small increase in the firing rate, whereas a relatively bright spot (bottom) produces a large transient peak in the firing rate. (b) Peri-stimulus time histograms, giving the change in firing rate versus time, are plotted for various spot intensities (log₂ units). (c) Plot of peak (solid line) and plateau (long-short dashed line) firing rate as a function of spot intensity. Local inhibition prevents the plateau-firing rate from increasing significantly with stimulus intensity.

Figure 2. Stimulus-selective synchronization of ganglion cells. (a) Stimulus dimensions relative to the receptive field centers of individual ganglion cells. (b) Cross-correlation histograms computed during the plateau portion of the response between spike trains from pairs of ganglion cells at opposite ends of the same bar or at opposing tips of separate bars. All ganglion-cell pairs were separated by 7 diameters (bin size: 1 ms; scale: 100 ms, 0.5). Also, b₁ is the pair from the upper bar; b₂ is the pair from separate bars; and b₃ is the pair from the lower bar. Correlations were only significant for pairs from the same bar.

Figure 3. Multi-unit auto-correlograms and cross-correlograms reveal size-dependent high-frequency oscillations. (a) Auto-correlograms computed from multi-unit spike trains recorded from cat retina at the center-of-square spots of increasing size (data were re-plotted from Reference 3). Correlations are expressed as a fraction of the expected level due to chance. (b) Multi-unit cross-correlograms of artificial spike trains, generated by a Poisson process, containing four identically modulated units, each with a mean firing rate of 50 Hz. (c) Multi-unit cross-correlograms produced by an integrate-and-fire feedback circuit consistent with retinal anatomy. Multi-unit spike trains were recorded from a fixed 2 × 2 array of ganglion cells located at the center of each spot (intensity = -2). Poisson-distributed spikes were added to each train to maintain a constant mean firing rate of 50 Hz regardless of spot size.

Figure 4. Theoretically optimal performance on a size-discrimination task. Individual 200-ms segments of multi-unit spike-train data were obtained in response to spots of one of two sizes: (1) either an intermediate or small spot (top abscissa = 6.3º × 6.3º, bottom abscissa = 4 × 4) or (2) either a large or small spot (top abscissa = 9.8º × 9.8º, bottom abscissa = 6 × 6). The ordinate gives the maximum percentage of trials that could be classified correctly, assuming each binary possibility was equally likely a priori, based on the total energy in the single-trial power spectra between 75 and 95 Hz. All three data sets indicate that high-frequency oscillations within a small group of ganglion cells yield good single trial discrimination of stimulus size.