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Pre-validation of the Purkinje cell before model submission

Introduction

This document shows specific capabilities of the GENESIS 3 publication system for automated model validation and electronic model publication of single neurons. The examples used in this document include the neuron model developed in [4], [3] and studied in [5], the comparative extension of these studies in [1] and finally the theoretical study of the model in [2].

What is included?

Single neuron models can be validated by analysis of their morphological and mathematical structure. Static checks include soundness checks on the morphology such as range checks on dendritic lengths and number of branch points, passive cable parameters, maximal channel conductances and channel kinetics. Behaviour checks are implemented with simulations that apply common experimental paradigms to the neuron model. Simulations for parameter searches are not included.

From [4]

Static model checks:
- Morphology validation: are all the branches connected via an electric pathway?
- Cable discretization validation:
  - Are the constraints to electrotonic length met?
  - Are all electrotonic compartments of similar lengths?
- Equations for different membrane and synaptic channel types and their kinetics? Are these common equations or new ones?
- Model parameter values: are all parameter values in the physiological range?
  - Passive parameters: capacitance, axial and membrane resistance, resulting membrane time constant?
  - Channel maximal conductances and channel densities?
  - Channel time constants?
  - Concentration value time constants?
Dynamic response to specific protocols:
- Current injection (fig 5, 0.2nA, 0.4nA, 0.6nA, 0.8nA) and current clamp (fig 3, 0.5nA, 1nA, 2nA, 3nA).
- Current injection with sodium blocker (TTX): 1nA, 0.1nA
- Current injection with Ca²⁺ blocker (Co²⁺, Cd²⁺): 4nA, 3.5nA, 3nA, 2.5nA, 2nA, 1nA
- Fig10: False color representation of membrane potential and Ca²⁺ concentration in the complete model during a 2.0nA current injection.
- Fig 11: model variable plots during somatic and dendritic spikes, 2nA current injection.
- Fig 12: complicated
- Fig 13: Simulation of voltage clamp steps: -100mV, +40mV, -40mV.
Dynamic response to additional common protocols:
- Voltage clamp with various blockers.

From [3]

Comparison of model parameters to model of [4]. Report of changes and differences.
Application of validation procedures of [4].
Static validation of new model parameters.
- Passive structure of spines.
- For each of the following synapses:
  - Locations (visualization).
  - Maximal synaptic conductance.
  - Reversal Potentials.
  - Other (nernst equations, Mg blocking?).
- Parallel fiber synapses.
- Climbing fiber synapse locations.
- Stellate cell synapses.
- Basket cell synapses.
Selected figures:
- Figure 1: climbing fiber response characterization in vitro.
- Figure 3: climbing fiber response characterization in vitro, active vs passive model.
- Figure 6: asynchronous excitation alone, 5Hz, 3Hz, 1Hz, 0.5Hz, 0.1Hz.
- Figure 7: 8 simulations with asynchronous excitation 100Hz, 60Hz, 40Hz, 30Hz, 26Hz, 24Hz, 22Hz, 20Hz and with inhibition 1Hz.
- Figure 8, left panel (right is experimental data): unclear what the simulations were, to be reconstructed.
- Figure 9
  - Panel A: inhibition 0Hz, 7 simulations. Inhibition 0.5Hz, 6 slow + 22 fast firing. Inhibition 1.0Hz, 7 slow + 22 fast firing. Inhibition 1.5Hz, 6 slow + 14 fast firing. Inhibition 2.0Hz, 10 slow + 12 fast firing.
  - Panel B is model PM10
  - Panel C: excitation 10.4Hz and inhibition 0.5Hz, excitation 23.5Hz and inhibition 1Hz, excitation 37Hz and inhibition 1.5Hz, excitation 50Hz and inhibition 2Hz.
- Figure 10: inhibition always 1Hz, excitation (1) 21Hz at 1nS, (2) 30Hz at 0.7nS, (3) 60Hz at 0.35nS, (4) 210Hz at 0.1nS. Simulation runs until 1600 events have been collected.

From [5]

Comparison of base model parameters to model of [3].
Application of validation procedures of [4].
Checks on changed parameters
- Passive soma.
Selected figures:
- Figure 1
  - Twice the same set of simulations.
  - 9 different stimulation protocols: unitary synaptic stimulation applied to 8 different branchlets individually and to the 8 same branches simultaneously.
  - Passive model.
  - Active model.
- Figure 2: 10 data points, averaged over 40 simulation runs (events), 4 different model variations.
- Figure 3: Detail of two selected simulations.
- Figure 4: one selected simulation, false color images of the dendrite.
- Figure 5: 200 simulations, distributed, proximal and distal stimulation.

From [1]

Comparison of base model parameters to model of [3].
Application of validation procedures of [4].
This study applies 4 different stimulation protocols to 9 different reconstructed PC cell morphologies. Stimulation protocols are static dendritic voltage clamp, static somatic voltage clamp, dynamic somatic voltage clamp, unitary synaptic stimulation.

From [2]

Comparison of base model parameters to model of [3].
Application of validation procedures of [4].
The simulations explore the response of the Purkinje cell to normal in-vivo conditions (poissonian synaptic background activity) over a wide ranges of different parameters.

Benchmarking

Introduction

Queries to the system for static model checks must be configured. These checks complete ’instantly’ (< 1s).
For simple simulations benchmarking on a passive and an active version of the Purkinje cell has been done. Details related to the stimulation protocol or simulation such as an active model with a passive soma or addition of a single synapse for unitary synaptic stimulation are currently ignored.
Simulation construction time for an active version of the purkinje cell model is about 4 seconds and for a passive version 0.5 seconds. All simulations were run on a 2 CPU 8 core intel 64bit at 1.60GHz with 6MB level 2 cache. The simulations were neither run in parallel nor multi-threaded. All simulations of the Purkinje cell model were run with each of the 1474 spines explicitly modeled with two compartments.
Estimates for more complicated analysis with results from many simulations such as figure 10 in [3] are acquired by extrapolation of the estimates of the previous item.

Results

From [4]
- Static model checks: complete instantly.
- Parameter search is not included.
- Dynamic response to specific protocols:
  - Current injection (fig 5, 4 simulations of 0.5s, 36s run-time each) and current clamp (fig 3, 4 simulations of 1s, 72s run-time each).
  - Current injection with sodium blocker (TTX), fig 9A, 2 simulations of 1s, 72s run-time each.
  - Current injection with Ca²⁺ blocker (Co²⁺, Cd²⁺), fig 9B, 6 simulations of 1.2s, 86s run-time each.
  - Fig 11: model variable plots, 2nA current injection, one simulation of 1s, 72s run-time.
  - Fig 13: Simulation of voltage clamp steps: -100mV, +40mV, -40mV, 3 simulations of 0.2s, 15s run-time each.
- Total run-time of [4] is 144s + 288s + 144s + 516s + 72s + 45s = 1209s.
From [3]
- Comparison of model parameters to model of [4]. Report of changes and differences.
- Application of validation procedures of [4].
- Static validation of new model parameters completes instantly.
- Selected figures:
  - Figure 1: climbing fiber response characterization in vitro, 3 simulations of 0.15s, 13s run-time each.
  - Figure 3: climbing fiber response characterization in vitro, active vs passive model, 2 simulations of 0.15s with 13s run-time each, active model, passive model 2.5s run-time.
  - Figure 6: asynchronous excitation alone, 5Hz, 3Hz, 1Hz, 0.5Hz, 0.1Hz, 5 simulations of 50ms, each 7s run-time.
  - Figure 7: 8 simulations with asynchronous excitation 100Hz, 60Hz, 40Hz, 30Hz, 26Hz, 24Hz, 22Hz, 20Hz and with inhibition 1Hz, simulations of 50ms, each 7s run-time.
  - Figure 8, left panel (right is experimental data): unclear what the simulations were, to be reconstructed. We assume 24Hz excitation, 1Hz inhibition, about 100s simulation, about 7100s run-timewhy again 100s?.
  - Figure 9
    - Panel A: inhibition 0Hz, 7 simulations. Inhibition 0.5Hz, 6 slow + 22 fast firing. Inhibition 1.0Hz, 7 slow + 22 fast firing. Inhibition 1.5Hz, 6 slow + 14 fast firing. Inhibition 2.0Hz, 10 slow + 12 fast firing. Total is 7 + 6 + 22 + 7 + 22 + 6 + 14 + 10 + 12 = 106 simulations. Assuming a minimum of 100 events per simulation and a total average firing frequency of 100Hz gives about 7200s run-time per simulation.
    - Panel B is model PM10, this model is not included in this report.
    - Panel C: excitation 10.4Hz and inhibition 0.5Hz, excitation 23.5Hz and inhibition 1Hz, excitation 37Hz and inhibition 1.5Hz, excitation 50Hz and inhibition 2Hz. Each simulation of 800s has a run-time of 800 * 68s run-time = 54400s (15hours). Total of 4 simulations.
- Total run-time of [3] is 39s + 31s + 35s + 56s + 7100s + 763200s + 217600s = 988061s (274.46 hours).
From [5]
- Comparison of base model parameters to model of [3].
- Application of validation procedures of [4].
- Checks on changed parameters
  - Passive soma.
- Selected figures:
  - Figure 1
    - Twice the same set of simulations.
    - 9 different stimulation protocols: unitary synaptic stimulation applied to 8 different branchlets individually and to the 8 same branches simultaneously. Simultaneously asynchronous excitation of 28Hz and inhibition of 1Hz.
    - Passive model, 9 simultaneously of 50ms, each 1.5s run-time.
    - Active model, 9 simulations of 50ms, each 7s run-time.
  - Figure 2: 10 data points, averaged over 40 simulation runs (events), 4 different model variations. 10 x 40 x 4 simulations, each 7s run-time. 11200s total run-time (3 hours).
  - Figure 5: 200 simulations, distributed, proximal and distal stimulation. 600 simulations total, each 7s run-time. Total of 4200s run-time.
- Total run-time of [5] is 76.5s + 11200s + 4200s = 15476.5s (4.3 hours).
From [1]
- static dendritic voltage clamp
  - fish1: simulation construction time takes about 2s, a simulation of 0.5s takes about 5.5s run-time for each of the 2187 simulations.
  - gp_pc1: simulation construction time takes about 1s, a simulation of 0.5s takes about 4s run-time for each of the 2066 simulations.
  - gp_pc2: simulation construction time takes about 1s, a simulation of 0.5s takes about 3s run-time for each of the 1520 simulations.
  - gp_pc3: simulation construction time takes about 1s, a simulation of 0.5s takes about 3s run-time for each of the 1381 simulations.
  - rat_pc1: simulation construction time takes about 2.5s, a simulation of 0.5s takes about 8s run-time for each of the 3885 simulations.
  - rat_pc2: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 5s run-time for each of the 2331 simulations.
  - rat_pc3: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 5.5s run-time for each of the 2671 simulations.
  - turtle1: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 6s run-time for each of the 2554 simulations.
  - turtle2: simulation construction time takes about 3.5s, a simulation 0.5s takes about 11s run-time for each of the 4507 simulations.
  - turtle3: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 4.5s run-time for each of the 1991 simulations.
  - Total of 12028.5s + 8264s + 4560s + 4143s + 31080s + 11655s + 14690.5s + 15324s + 49577s + 8959.5s = 160281.5s (44.5 hours).
- static somatic voltage clamp: due to the high volume output of these simulations, they are strictly I/O bound. For simplicity and because they have a marginal contribution to the total run time for this study we assume that the I/O can be ignored.
  - fish1: simulation construction time takes about 2s, a simulation of 0.5s takes about 5.5s run-time.
  - gp_pc1: simulation construction time takes about 1s, a simulation of 0.5s takes about 4s run-time.
  - gp_pc2: simulation construction time takes about 1s, a simulation of 0.5s takes about 3s run-time.
  - gp_pc3: simulation construction time takes about 1s, a simulation of 0.5s takes about 3s run-time.
  - rat_pc1: simulation construction time takes about 2.5s, a simulation of 0.5s takes about 8s run-time.
  - rat_pc2: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 5s run-time.
  - rat_pc3: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 5.5s run-time.
  - turtle1: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 6s run-time.
  - turtle2: simulation construction time takes about 3.5s, a simulation 0.5s takes about 11s run-time.
  - turtle3: simulation construction time takes about 1.5s, a simulation of 0.5s takes about 4.5s run-time.
  - Total of 5.5s + 4s + 3s + 3s + 8s + 5s + 5.5s + 6s + 11s + 4.5s = 55.5s.
- dynamic somatic voltage clamp: CPU load is the same as for static somatic voltage clamp (55.5s).
- unitary synaptic stimulation: CPU load is the same as for static dendritic voltage clamp (160281.5s, 44.5 hours).
- Total run-time of [1] is 160281.5s + 55.5s + 55.5s + 160281.5s = 320674s (89 hours).
From [2]
- A simulation of 400s had a run-time of about 25h.
- A total of 1355 simulations were run.
- This makes for a total CPU-time of 33875 hours (1411 days).

Conclusion

Table with the total run-times for each of the publications (chronological order).
[4] [3] [5] [1] [2]
1209 seconds 274.46 hours 4.3 hours 89 hours 33875 hours
Different publications can use very different stimulation protocols. Consequently there is a great variation between the run-times of different publications.

References

[1] James M. Bower, Hugo Cornelis, and Rachael Wilcox. Comparative evolutionary computational analysis of cerebellar purkinje cell structure and function. In Nineteenth Annual Computational Neuroscience Meeting CNS*2009 July 2009., 2009.

[2] Allan D. Coop, Hugo Cornelis, and Fidel Santamaria. Using mutual information to quantify the contribution of dendritic excitability to information processing in a purkinje cell model. Frontiers in Computational Neuroscience, 2009.

[3] E De Schutter and J M Bower. An active membrane model of the cerebellar purkinje cell II. simulation of synaptic responses. Journal of Nerurophysiology, 71:401–419, 1994.

[4] E De Schutter and JM Bower. An active membrane model of the cerebellar purkinje cell I. Simulation of current clamp in slice. Journal of Nerurophysiology, 71:375–400, 1994.

[5] Erik De Schutter and J.M. Bower. Simulated responses of cerebellar Purkinje cells are independent of the dentritic location of granule cell synaptic inputs. Proceedings of the National Academy of Sciences USA, 91:4736–4740, 1994.