Dimensional stacking Visualization of Conductance Space

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Dimensional stacking Visualization of Conductance
Space
Organization for Computational Neuroscience (CNS)
Workshop 2005

• Objective to provide a visualization of model
  neuron conductance space in order to reveal
  patterns in the underlying data and support
  biological inference.

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Introduction

• How can we visualize high dimensional neural
  parameter spaces?
• Repetitive problem for neuroscientists.
• How can we facilitate data access and information
  retrieval?

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Overview

• Data set
• Dimensional Stacking
• Projection finding
• Translucent Data Access
• Future Work
• Conclusion

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Data set Prinz et al. (2003) - an 8 dimensional
conductance space
68 1,679,616 single compartment models 6
conductance values for 8 currents
Like this...
...but in eight dimensions
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Data set 4 activity patterns
Neuron model from Prinz et al. 2003


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Data set

• Other recorded data
• Maxima and minima sequences
• resting potential for silent neurons
• spike frequency for spikers
• burst frequency
• burst duration
• duty cycle (burst duration/burst period)
• number of maxima per burst
• average spike frequency for non-periodic
• response properties for all models
• 2 different levels of constant current
• brief inputs at different times
• MySQL server hosts several relational database
  tables containing this data

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Data set questions

• What is the distribution of activity types
  throughout conductance space?
• Are all models of an activity type in one
  connected region in conductance space?
• Are there multiple distinct conductance level
  combinations that generate the same activity
  type?
• Are there connected boundaries between activity
  type regions and what can be said about them?
• How do you visualize activity type distribution
  in multi-dimensional conductance space?

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Dimensional Stacking

• introduced by LeBlanc, Ward, and Wittels
• data represent a function on tuples a
  (a1,...,an)
• 0 lt an lt D for some number D
• a base D number with n digits 1 dimension
• a a pair of base D numbers with n/2 digits ...

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Dimensional Stacking

• 8 conductances 8 independent parameters or
  dimensions that can take on 6 discrete values
  8 digit number in base 6
• need x and y value to plot in 2D
• Split the 8 digits into 2 base 6 numbers of 4
  digits
• X x1 63 x2 62 x3 61 x4 60 e.g.
• X Na 63 CaT 62 CaS 61 A 60
• 1679616 models/pixels 1296 X 1296 image

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Dimensional Stacking

• Each pixel 1 neuron
• Color activity type
• Position conductance values

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Dimensional Stacking structurex Na,CaT,CaS,A
y KCa,Kd,H,Leak
Kd 1
KCa 0
Na 1
CaT 3
Leak
H 0
Cas 0
A
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Dimensional Stacking

• Got lucky with default
• x Na,CaT,CaS,A
• y KCa,Kd,H,Leak
• Patterns instantly revealed
• KCa 0 and Na 0 mostly silent
• KCa 0 and Kd 0 mostly silent
• Distinct regions of spikers and bursters
• Tonic spikers mostly KCa 0
• Bursters mostly KCa gt 0

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Dimensional Stacking what do you get

• Immediate insight into the data structure
• Can fish for answers by changing parameter
  ordering and/or value to color mapping
• For a model that regulates its maximal
  conductances, you could trace an activity path
  along connected pixels e.g. during current
  injection experiments
• Answers to the previously posed questions
• Activity types are mostly contiguous in
  conductance space
• There are multiple distinct conductance level
  combinations that generate the same activity type.

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Projection Finding

• Permutation of conductances is variable
• x KCa, Kd, H, Leak y Na, CaT, CaS, A
• x Kd, KCa, H, Leak y Na, CaT, CaS, A
• 8! or 40,000 projections in all!
• Different projections reveal different patterns
  (or not)
• Most significant digit most significant
  conductance
• x KCa,Kd,H,Leak y Na,CaT,CaS,A
• General goal reveal connected regions of neuron
  models for the particular value you're looking at

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Projection Finding

• Simple algorithm for finding optimal projection
• visual complexity score of row/col variation
• score of 1 for each row, 0
  for each col
• breadth first search to minimize complexity score
• swaps parameters in permutation each iteration
• first local minima encountered is solution
• usualy only needs 10 steps
• effectively and rapidly finds informative
  projections

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Projection Finding Maxima per burst
Iteration 1
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Projection Finding
Iteration 2
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Projection Finding
Iteration 3
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Projection Finding
Iteration 4
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Projection Finding
Iteration 5
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Projection Finding
Iteration 5
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Demo

• mouse over coordinates
• data access
• color mapper
• click query
• permutations
• pan, zoom
• simulation

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Data Access

• Color mapper
• can query database and immediately see results
  visually
• customizable query / color map
• can highlight regions in a projection of neurons
  with desired properties
• Click through query
• customizable query can return result for any
  neuron model/pixel that you click on

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Data Access click through simulation
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Future Work

• More labels, map overlay of coordinates
• Extend mouse-over info
• Multivariate or continuous color mappings
• Finding Optimal Projections
• Many possible algorithms to try out including
  simulated annealing, clustering, linear
  programming
• simulated annealing
• Mixed initiative Artificial Intelligence
• selecting groups of pixels for model
  classification
• choosing heuristics
• More support for querying regions directly
• Select relevant dimensions, possible values
• Extending classifications
• Other visualization techniques
• 3D!
• Try it on other models, different of
  parameters.
• Release scheduled for September 2005

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Conclusion

• Dimensional stacking provides comprehensive yet
  immediate insight into a large data set
• In our conductance space, the three major
  activity types appear (tentatively) to be
  contiguous
• Can determine activity distribution throughout
  conductance space in a glance
• Can visually trace/predict path for changing
  activity patterns and voltage dependencies
• Transparent data access and custom queries for
  coloring allow quick inferencing
• Method for finding optimal permutations necessary