1
$\begingroup$

I am student of Mathematics who is currently studying the utility of Algebraic Topology in the field of Neuroscience. In the paper I am reading (Reimann et al 2017) the authors explain that for several pairs of neurons they calculated the correlation of their spiking activity. Sometimes they also use the expression "correlation of connection", which I think refers to the correlation of spiking activity between two neurons (as the prior references). I am interested in understanding the following:

  1. How does one measure the correlation of a connection?
  2. I know the mathematical definition of correlation and have an intuitive understanding of it as a measurement of dependence. But in the case of neurons what is the actual interpretation for the correlation of a connection? Is it in the sense of synchronicity? Or something else?

Any insight will be appreciated. This is not my area of studies, so the most elementary observation might help. Thank you in advance.

Reimann, M. W., Nolte, M., Scolamiero, M., Turner, K., Perin, R., Chindemi, G., ... & Markram, H. (2017). Cliques of neurons bound into cavities provide a missing link between structure and function. Frontiers in computational neuroscience, 11, 48.

$\endgroup$
4
  • 1
    $\begingroup$ Can you provide a full citation? Titles aren't citations. Correlation of connection might refer to correlating the rows of a connectivity matrix for two nodes. Could also be anything else owing to non-native English speakers writing papers in English. $\endgroup$
    – Bryan Krause
    Jul 6 at 2:45
  • $\begingroup$ Yes, of course. This is the first time "correlation" is mentioned in the paper: "(...) we observed that pairwise correlations in neuronal activity increased with the number and dimension of the directed cliques to which a pair of neurons belongs (...)" Second reference: "We then calculated for each connected pair of neurons the correlation of their spiking activity and found a broad distribution of correlation coefficients (...)" $\endgroup$
    – Oscar
    Jul 6 at 10:28
  • $\begingroup$ Those are now quotes, but still not a citation :) $\endgroup$
    – Bryan Krause
    Jul 6 at 14:06
  • $\begingroup$ I edited to add what I meant by a citation. Hope it is now clear from my answer. $\endgroup$
    – Bryan Krause
    Jul 6 at 19:42
1
$\begingroup$

They write in the paper:

Correlations were calculated from histograms of the average spiking response (peri-stimulus time histogram, PSTH; bin size, 25 ms) to five seconds of thalamo-cortical input over 30 repetitions of a given input pattern

So, they count spikes in 25 ms bins for two neurons, resulting in two time vectors (one for each cell), and calculate the Pearson correlation between those vectors. A "connection" in this context is the same as an "edge" in graph theory; they're referring to a correlation between a pair of nodes (neurons). It's not really strictly correct to call it a "correlation of connection" but the meaning is still clear. More strictly you might call it "the spike count correlation of two connected neurons".

Generally, one would say that neurons that fire more spikes at the same time are functionally connected. That does not necessarily mean they are structurally connected, for example you could have a lot of functional connectivity between two (physically) unconnected neurons that share inputs. However, in this paper they are talking specifically about relationships between functional and structural connectivity. "Synchronicity" doesn't have any clear meaning without an operational definition, but firing rates on a time scale of 25 milliseconds aren't really all that synchronous from a neuron's perspective.

$\endgroup$
3
  • $\begingroup$ Thank you very much for your answer and patience :) The distinction you made between being functionally connected and structurally connected was very clear and explanatory. Indeed, the term "synchronicity" without any additional specifications is rather vague. Regarding your last statement, do you consider that choosing a time bin of 25 ms was not an adequate choice? $\endgroup$
    – Oscar
    Jul 7 at 14:11
  • $\begingroup$ @OuterSpace For counting and correlating spike counts I think 25 ms is just fine, it's just different than a timescale I would consider "synchronous". $\endgroup$
    – Bryan Krause
    Jul 7 at 14:15
  • $\begingroup$ Ok, got it. All understood, thank you once again. $\endgroup$
    – Oscar
    Jul 7 at 14:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.