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Monosynaptic inference via finely-timed spikes

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Abstract

Observations of finely-timed spike relationships in population recordings have been used to support partial reconstruction of neural microcircuit diagrams. In this approach, fine-timescale components of paired spike train interactions are isolated and subsequently attributed to synaptic parameters. Recent perturbation studies strengthen the case for such an inference, yet the complete set of measurements needed to calibrate statistical models is unavailable. To address this gap, we study features of pairwise spiking in a large-scale in vivo dataset where presynaptic neurons were explicitly decoupled from network activity by juxtacellular stimulation. We then construct biophysical models of paired spike trains to reproduce the observed phenomenology of in vivo monosynaptic interactions, including both fine-timescale spike-spike correlations and firing irregularity. A key characteristic of these models is that the paired neurons are coupled by rapidly-fluctuating background inputs. We quantify a monosynapse’s causal effect by comparing the postsynaptic train with its counterfactual, when the monosynapse is removed. Subsequently, we develop statistical techniques for estimating this causal effect from the pre- and post-synaptic spike trains. A particular focus is the justification and application of a nonparametric separation of timescale principle to implement synaptic inference. Using simulated data generated from the biophysical models, we characterize the regimes in which the estimators accurately identify the monosynaptic effect. A secondary goal is to initiate a critical exploration of neurostatistical assumptions in terms of biophysical mechanisms, particularly with regards to the challenging but arguably fundamental issue of fast, unobservable nonstationarities in background dynamics.

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Notes

  1. To be explicit about the subtlety in the setting here: in fact, we will model E[μ(t)] as time-invariant (Eq. (4)). Thus, for an observer that does not know μ(t), the spike probabilities are time-invariant. On the other hand, for an observer that knows μ(t), the spike probabilities are not time-invariant.

  2. No constraints are placed on the probability distribution of N(B) itself, and this is the source of robustness to nonstationarity, broadly defined. This conditional modeling framework for modeling temporal structure in spike trains is motivated and developed from several points of view in prior work (Amarasingham et al. 2012; Amarasingham et al. 2015; Harrison et al. 2015; Harrison et al. 2013). See Amarasingham et al. (2012) for a thorough introductory exposition. As an example, if B is conditionally a homogeneous Bernoulli process, conditioned on R, then Eq. (7) is satisfied. (The homogeneous Benoulli process approximates the homogeneous Poisson process in discrete time.) But the model is far broader than this. For example, N(B) can be deterministic and Eq. (7) can still be valid (cf., Section A.2 of Amarasingham et al. (2011)).

  3. For intuition, a canonical example can be constructed by generating two distinct independent, background spike trains B1 and B2, which are conditionally uniform, conditioned on N(B1) and N(B2), and superposing a homogeneous Bernoulli process synchronously (with appropriate lag) onto both trains (see Amarasingham et al, 2012, for example, for examples based on Cox processes for the background.)

  4. Note that i) these jitter perturbations are distorted slightly via the role of the interval positions, ii) those distortions are necessary (Platkiewicz et al. 2017), and also iii) such tests can in principle be performed analytically, without surrogate-generation.

  5. Since R is in fact observable, this is a potential observation rather than an assumption.

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Acknowledgments

We thank G. Buzsáki for providing advice and inspiring our work on this problem, and T. Evans, M. Regnaud, and H. Rotstein for advice and comments. This work was supported by NIMH R01-MH102840 (A.A.), DOD ARO W911NF-15-1-0426 (A.A. and J.P.), PSC-CUNY 68521-00 46 (A.A.), and NIMH K99 MH118423 (S.M.). We warmly acknowledge the hospitality of the Initiative for Theoretical Sciences (ITS) at the CUNY Graduate Center.

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    1. Department of Mathematics, The City College of New York, The City University of New York, New York, NY, 10031, USA

      Jonathan Platkiewicz & Asohan Amarasingham

    2. Department of Biology, The Graduate Center, The City University of New York, New York, NY, 10016, USA

      Zachary Saccomano & Asohan Amarasingham

    3. Neuroscience Institute, New York University, New York, NY, 10016, USA

      Sam McKenzie

    4. School of Neuroscience, Virginia Tech, Blacksburg, VA, 24060, USA

      Daniel English

    5. Departments of Computer Science and Psychology, The Graduate Center, The City University of New York, New York, NY, 10016, USA

      Asohan Amarasingham

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    Platkiewicz, J., Saccomano, Z., McKenzie, S. et al. Monosynaptic inference via finely-timed spikes. J Comput Neurosci 49, 131–157 (2021). https://doi.org/10.1007/s10827-020-00770-5

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