SGC_exampleWorkflow

Example notebook for "time-nodal" spectral graph clustering of calcium imaging traces. Author: Julian Moran

🌱 Installation

pip install -r requirements.txt

Introduction

• Here I analyze a 135-neuron calcium imaging dataset for common patterns of activity

  • all 135 activity traces are collected from the same C. elegans whole-brain
  • all 135 traces have already been tracking-proofread and removed of motion, bleaching, and neighbor-invasion artifacts

• My goal is to find time windows in which "neuronal assemblies" manifest

  • that is to say, I am looking for instances when multiple neurons seem closely coordinated in their activity

• Spectral graph clustering (SGC) is an adjacency-matrix technique that leverages the graph Laplacian

• "Time nodal" graph clustering uses time-points as the nodes in the adjacency matrix

  • each node is a time point, for example t=135 during the calcium imaging video
  • each node is a 135-element array, where each element is the activity of a neuron during that time point
  • for a description of pre-processing steps, post-processing steps, and performance, see Molter 2018 (https://bmcbiol.biomedcentral.com/articles/10.1186/s12915-018-0606-4)

• While Molter 2018 provides a workable mathematical explanation...

  • the attached Jupyter notebook shows how to implement in Python many of the steps they describe
  • some of Molter 2018's post-processing steps have been ommitted; I was unable to follow them based on the paper's limited description

Notes on the data

• This particular C. elegans is an unc-13(s69) animal

  • meaning all chemical synaptic transmission between neurons has been perturbed; the animal is paralysed
  • meaning gap-junctional transmission remains intact; we expect to find patterns of coordinated neuroactivity with zero time-lag
  • therefore, we do not need to search for time-lagged patterns in this particular analysis

• Notably, in this animal, neuromodulatory transmission also remains intact

  • this can yield more complex patterns of activity between neurons
  • to further interrogate these relationships, more standard analysis techniques may be used, e.g. cross-correlation
  • to further interrogate these relationships, more tailored techniques may be used that evaluate for curve-transformation relationships

• Most neurons in this dataset are unnamed

  • as such, they receive a name of the format Na#, for example Na29
  • some pharyngeal and retrovesicular neurons have been identified with high-confidence and have been named accordingly

Conclusion

• Time-nodal SGC succeeds in elucidating novel neuronal assemblies in calcium imaging data
  • many of these are not easily discernible to the human eye by visually appraising the traces

• In this workflow, I constrained the time points that were included in the adjacency matrix (see Jupyter notebook)
  • the analysis may benefit from including all time points, as I found that the more time points I include, the more patterns this workflow reveals
  • graph-drawing code that depends on NetworkX must be reconfigured, as NetworkX throws errors when drawing >500 nodes in the graph