Keywords

Searching for Significance of Repeating Spike Patterns

I met George for the first time in 1969 at the Second Intensive Study Program organized by Francis O. Schmitt in Boulder Colorado. I was a very young faculty at the Hebrew University of Jerusalem and was invited as such to attend the program. At the registration, there were several bins each with a range of participant names. After getting my badge and program, a young person approached me and with a kind smile asked “how did you like that?” pointing to the registration desk stating “Abeles to Goy.” At first, I did not get what was the punch. But, after a short pause I got it. “GOY” is the Hebrew word for a non-Jewish believer and also has a connotation of a simple minded person. That was George who was recruited to help with the organization of the program. His presence, the young physicist who moved into “wet” neurophysiology but used very sophisticated analysis tools, was evident throughout the workshop.

His kind and friendly attitude spanned our entire encounters. Back in Jerusalem, I started to record form auditory cortex using advanced spike sorting techniques for isolating in parallel several spike trains (Abeles and Goldstein 1977). I used extensively the analysis methods devised by Don Perkel and George to quantitatively study the dynamic firing properties of single neurons and pairs of neurons (Perkel et al. 1967a,b; Gerstein and Perkel 1969). However, I felt there is room for studying more complex interactions. Looking at the literature, the only thing I found was their “snowflake” method for studying 3-fold interactions (Perkel et al. 1975).

When measuring times of 3 spikes, say at t 1, t 2, t 3, there are 3 intervals to be considered: (t 2 − t 1), (t 3 − t 2), and (t 1 − t 3). However, they are not independent as: (t 2 − t 1) + (t 3 − t 2) + (t 1 − t 3) = 0. They found an elegant way to present the 3 intervals on a plane by using the Einthoven’s Triangle (used in medicine to present the activity vector of the electrocardiogram). If the maximal allowed delay was some fixed value, the dots fall within a hexagonal area looking similar to a “snowflake.” This display provided a qualitative impression of the relations among the 3 spike trains. I could convert this display into a quantitative one by tessellating the area with triangular bins, counting the number of points that fell in each bin, and finding various ways of normalization (Abeles 1983).

While studying the 3-fold correlations with this method, I encountered several cases in which 1 or 2 bins stood up with a lot of counts. Such cases represented a situation where 3 spikes were repeating again and again with almost precisely the same intervals (see Abeles (1982 Chapter 6)). While searching the literature for such phenomena, I found the impressive work of Dayhoff and Gerstein (see also Chap. 5 this Volume). They looked on intervals between successive spikes within a spike train as “characters” and searched for “words” that repeated many times.

George was interested in my way of quantifying the “snowflakes,” while I was interested in his method of finding repeating structures within a spike train. So, I paid him a visit in Philadelphia to discuss these issues. I felt this to be very useful and asked whether he would host me for a sabbatical. George agreed and very kindly offered to supplement my somewhat inadequate university salary from his grant money.

George was also very kind in helping us to find a house to rent at Haverford just outside Philadelphia. We (my spouse, two little daughters, and me) spent a wonderful year there. My main interest was to find a way for detecting complex spatio-temporal patterns that repeat many times. I had numerous discussions with George in which we examined several alternatives. But, they all seem too cumbersome to implement with the computing power available at the time.

One morning George came up with the following analogy: Suppose we represent the spike times of a neuron as holes along a line in a punched paper tape. If we recorded several neurons in parallel, their spiking times would be represented as holes along parallel lines. Take two copies of such a punched paper tape and slide them past each other. Any repeated patterns of holes will show up at some point of sliding. I coded this magnificently simple idea in Fortran and added ways to estimate what might be found by chance. When data was analyzed this way, it often showed a significant excess of repeating spatio-temporal firing patterns (Abeles and Gerstein 1988). This algorithm serves me for detecting such patterns to this very day (although the Fortran was replaced by C and now by Matlab).

A couple of years later, in an international workshop in Jerusalem, I presented my synfire chain model and the results on repeated spatio-temporal patterns. As supporting evidence, I showed the number of patterns found in surrogate spike trains that were very close to the estimated chance occurrence. At the end of my talk, van Essen said:

  • – Can you show the table for the surrogate data?

  • I showed it.

  • – The numbers you found are too close to the expected, and this cannot be true.

  • I was stunned! A famous scientist accuses me, a young and unknown researcher, of faking data. It took me a while to recover and then.

  • – Here the expected was 39 patterns and I found 38. I assume that had I found 31 you would be happier.

  • – Ah hah.

  • – But the probability of finding 31 when the expected is 39 is much smaller than the probability of finding 38 when 39 is expected.

  • – Silence.

A somewhat similar case arose many years later in an international workshop in France where both George and I participated. The organizers scheduled a talk by Roger Lemon to immediately follow mine, without warning me of what is coming. After giving my talk about repeated spatio-temporal patterns in recordings from the cortex of behaving monkeys, Roger described his very elegant experiments on recording pyramidal tract neurons in monkeys performing a precision motor task. In these data, he searched for repeating spatio-temporal patterns and found many with a high number of repetitions. This number was much higher than expected based on surrogate trains generated with Poisson statistics. However, Roger claimed, the spike trains are not Poissonian. When using the appropriate Gamma distribution of inter-spike intervals (ISI), the number of patterns found was much larger than the number in the experimental data. All my “friends” were happily grinning. The fallacy of these results was immediately clear to me. But now, being more mature, I did not want to offend him publicly. So I suggested we discuss his findings over lunch. At lunch, I told him that he showed an expected number of ≈ 100 patterns, while in the data there were only 35. The probability of finding 35 or less when 100 is expected is well below 10−13. (Note: I do not recall the exact numbers, but the principle of the above description is correct). Thus, if the surrogates were appropriate, there should be some special mechanism that avoids the repetition of any firing patterns that were already generated.

The moral of these two incidences is: Do not mess with statistics and probabilities unless you have a profound grasp of these issues.

Following that talk, George told me you gave a hell of a lecture. Maybe I am taking an unjustified credit, but following this incident, George took enhanced interest in synfire chains and the precisely repeating spatio-temporal patterns. One of the first studies he made was to find what would be the appropriate statistics to use for surrogate spike trains (Gerstein 2004), followed by work on how to decompose complex patterns into sub-patterns and several works with Markus Diesmann, Sonja Grün, and their students on how to detect repeated patterns in massively parallel spike trains (see also Chap. 14 in this Volume).

For me, the most illuminating conclusion that emerged from these studies was that if multiple synfire chains were embedded in a small cortical volume you would need to record from at least 200 neurons in parallel to detect such synfire activities. Recording from over 100 neurons in parallel is now available, and getting to over 200 is coming. However, such recordings are now either spread over a too large of area or have a too low time resolution. Yet the time that such recordings will be possible from a small volume of cortical tissue is fast approaching. Only then it will be possible to establish or refute the synfire chain model.