3) Surrogate Responses

Transcription

1 1) Introducton Vsual neurophysology has benefted greatly for many years through the use of smple, controlled stmul lke bars and gratngs. One common characterzaton of the responses elcted by these stmul s a tme-varyng Posson process wth a relatve refractory perod (Berry and Mester, 1998). However, recent studes have argued for the necessty of studyng the vsual system usng more natural stmul (Feld, 1987; Dan et al., 1996; Vnje and Gallant, ). In ths study, we recorded the responses of solated neurons to naturalstc tme-varyng moves n all layers of strate cortex of anesthetzed cats. We quantfed the responses n terms of relablty n spke counts and spke tmes, and compared the neuronal responses to surrogate data generated usng a tmevaryng Posson process wth a relatve refractory perod.

2 ) Stmul We presented the anmals wth repeated presentatons of short natural tme-varyng move clps wth frame rates of 5-3 Hz. The moves (64 x 48 pxels) were postoned at the center of a gamma corrected montor screen ( ), occupyng 3º x 4º of vsual angle (.5º/pxel). All moves were presented monochromatcally.

3 A 3) Surrogate Responses 1 3 a4s5n5g5c1s ISI hstogram 16 Free frng rate, q(t), for cell a4s5n5g5c1s Frequency B Interval (ms) a4s5n5g5c1s Recovery functon, w(t) 1 Free Rate Probablty Tme (ms) Tme (ms) The surrogate responses were generated usng the method of Berry and Mester (1998). Brefly, the ISI hstogram from the data (A) was used to obtan the recovery functon (B). The probablty of free frng was computed by placng the recovery functon wherever there was a spke and averagng the resultng probablty functon across repettons. The free frng rate (q(t), shown n red on the rght) was then obtaned by dvdng the frng rate (r(t), shown n blue on the rght) by the probablty of free frng. The free frng rate was then used to generate surrogate spke trans. In ths study, we wanted to test the hypothess that the neuronal response can be modeled usng a tme-varyng Posson process changng at the rate of the stmulus, so we computed the recovery functon and the frng rate at a resoluton of. ms and the free frng rate at the resoluton of a move frame. 1 sets of surrogate spke trans were generated for each cell.

4 4) Neuronal Responses Repettons a4s5n5g5c1s R = Rate (Hz) 5 Repettons PSTH & Free frng rate, q(t), for cell a4s5n5g5c1s Surrogate Spke Trans for cell a4s5n5g5c1s Tme (ms) x 1 The rasters of a neuron n response to 1 repettons of a 3 second move are shown above. The PSTH (calculated at. ms resoluton) and the free rate (calculated at the frame rate ~35 ms) are shown n the mddle. The bottom raster plot shows a set of surrogate spke trans generated at. ms resoluton usng the free rate.

5 5) Spke Count Varablty Repettons a4s5n5g5c1s R = a4s5n5g5c1s x 1 4 Fano Factors Tme (ms) The response of one cell s llustrated n the raster plot on top and the Fano Factors (FF = Varance/Mean spke counts) for each move frame are plotted below. Frames wth mean spke counts smaller than 1 (MSC<1) are plotted n gray whle the rest are plotted n black. Frames wth Fano Factors lower than 95% of the surrogates are plotted n blue (for MSC<1) and red (for MSC 1). The green ponts and bars llustrate the mean and standard devaton of the FF of the surrogate spke trans. x 1 4

6 6) Spke Count Varablty The mean spke counts for each move frame n one cell are plotted aganst the varance of the spke counts. The color scheme s the same as the prevous slde. The dagonal lne ndcate a Fano Factor of 1, whch descrbes a Posson process. The scalloped lnes ndcate the mnmum varance obtanable wth nteger spke counts (de Ruyter van Stevennck et al., 1997).

7 7) Spke Count Varablty Data from 3 cells Fano Factors Varance Data from 3 cells Mean spke count Mean spke count The spke count varablty for the 3 cells n our database are shown above. The wndows wth FF lower than 95% of the surrogates are hghlghted n blue and red (n = 19). We found 19.9% of the wndows (4715/365) had FF< 1. As the FF appeared to be unstable when the MSC<1, we excluded those wndows from further analyss. 16.4% of the remanng wndows (85/518) had FF<1. We found at least one such wndow n 71.9% of the cells (3/3). The FF and the mean spke count n these wndows were negatvely correlated (Pearson r=-., p<.1). However, only 1.7% of these wndows (9/518, shown n red) n 1.9% of the cells (7/3) had FF lower than 95% of the surrogates. Ths suggests that most of the spke count varablty can be accounted for wth a Posson process wth a relatve refractory perod.

8 8) Spke Tme Varablty We used a measure we called Temporal Relablty Entropy (TR-Entropy) to quantfy the spke tme varablty n our data. Brefly, each frame was dvded nto n bns and the bns were ranked n ascendng order of spke counts for each repetton. Bns wth the same spke counts were assgned the mean rank. The probablty of gettng a rank n bn j, P(r,j ), was then used to compute the TR-Entropy usng the followng equaton: =(n 1) j= n E = P(r, j )logp(r, j ) =1 j=1 The entropy would be hgh f spke tmes were randomly dstrbuted wthn a frame and low f they were concentrated n a few bns across repettons. In ths study, we used n=1 for all the analyss. The same calculaton was appled to the surrogate spke trans, whch then allowed us to compute the percentage of surrogates wth hgher entropy as well as the z-score of the data compared to the surrogates.

9 9) Spke Tme Varablty 1 a4s5n5g5c1s R = 1 Repettons a4s5n5g5c1s x 1 4 Entropy Tme (ms) x 1 4 The TR-entropy for each move frame n one cell are plotted wth the same color scheme as before. The frames where the TR-entropy of the data was lower than 95% of the surrogates are plotted n blue for frames wth MSC<1 and red for frames wth MSC 1.

10 1) Spke Tme Varablty 5 Data from 3 cells Data from 3 cells 1 3 Entropy Z!Score!5!1!15! Number of Frames ! Frame Number x 1 4 1! Percent of surrogates wth hgher Entropes The z-score of the TR-entropy of each of the frames n 3 cells are shown on the left. The hstogram of the percent of surrogates wth hgher TR-entropy are shown on the rght. The frames wth entropes lower than 95% percentage of the surrogates are hghlghted n blue (for MSC<1) and red (for MSC 1). We found 45.6% of the frames wth MSC>1 (n=36/ 518) had entropes lower than 95% of the surrogates. We found at least one such wndow n 78.1% of our cells (5/3).

11 11) Count vs Tme Varablty 8 Spke!tme versus spke!count varablty 6 Fano Z!Score 4!!4!5!!15!1!5 5 Entropy Z!Score The TR-entropy z-scores are plotted aganst the FF z-scores for the wndows wth MSC 1 and FF<1 (n=85). The two values are postvely correlated (Pearson r =.4, Spearman r =.6, p <.1 for both), ndcatng that wndows wth hgher spke tme precson tended to have lower spke count varablty.

12 1) Count vs Tme Varablty To understand how spke tme varablty can nfluence spke count relablty, we modeled the response of a neuron n a wndow of m ms, as a successon of m ndependent Bernoull trals, each havng a frng probablty p. The response to n repettons of the same stmulus, s then gven by n bnary tme seres of m samples. Each sample value, s j (sample n tral j) could ether be 1 (spke) or (no spke). The probablty for a spke n s j s determned solely by the tme-varyng frng probablty p, whch s dentcal across trals. The number of spkes n each tme seres, as well as the mean and varance, s gven by: Spke count Mean Varance N j = s j N j = p j Var(N j ) j = p.(1 p ) p (1 p ) ( p p ) p FF(p) = = =1 p ( p ) p It follows that the Fano Factor would be: FF can also be wrtten as: FF(p) =1 1 m. p p. m ( p ) =1 M(p). 1 C(p) where M(p) s the mean value of p, and C(p) s a measure of the correlaton between the probablty functon p, and a flat probablty dstrbuton: C( p) = p m. p Thus, for a gven mean probablty of frng n a wndow, M(p), FF(p) wll be at ts maxmum when p s unform, and at ts mnmum when p s zero everywhere except for a sngle bn.

13 13) Summary We recorded from 3 well solated sngle unts n the strate cortex of 1 anesthetzed cats. We found spke count varablty lower than that predcted from a Posson process wth a relatve refractory perod n 1.9% of our cells, and n 1.7% of the wndows wth a mean spke count of at least 1. We found spke tme varablty lower than predcted n 78.1% of our cells, and n 45.6% of the wndows wth a mean spke count of at least 1. We found spke count varablty to be sgnfcantly correlated wth spke tme varablty (r =.4, p<.1) for wndows wth a mean spke count of at least 1 and Fano Factors less than 1. We show analytcally usng a Bernoull process that non-unform spke probablty functons wthn a wndow lead to low spke count varablty.

14 14) Conclusons Our results show that neurons n prmary vsual cortex can respond wth hghly reproducble spke counts and spke tmes when stmulated wth natural stmul. The wndows wth low varablty n spke counts could be accounted for usng a non-unform Posson process wth a relatve refractory perod that was changng at the frame rate, but we found a hgh number of wndows wth lower spke tme varablty than predcted. Our results suggest that a tmevaryng Posson process wth a relatve refractory perod s a poor characterzaton of the neuronal response under natural stmulaton. References 1. Berry, M. J., nd & Mester, M. Refractorness and neural precson. J Neurosc 18, -11 (1998).. Dan, Y., Atck, J. J. & Red, R. C. Effcent codng of natural scenes n the lateral genculate nucleus: expermental test of a computatonal theory. J Neurosc 16, (1996). 3. Feld, D. J. Relatons between the statstcs of natural mages and the response propertes of cortcal cells. J Opt Soc Am [A] 4, (1987). 4. Vnje, W. E. & Gallant, J. L. Sparse codng and decorrelaton n prmary vsual cortex durng natural vson. Scence 87, (). 5. de Ruyter van Stevennck, R. R., Lewen, G. D., Strong, S. P., Koberle, R. & Balek, W. Reproducblty and varablty n neural spke trans. Scence 75, (1997). Acknowledgements Ths work was supported by the Natonal Eye Insttute. Baker, J. L. was supported by the Koprva Fellowshp.