The document describes ongoing efforts to optimize a computational model of a CA1 pyramidal neuron. The model integrates synaptic and cellular interactions using the EONS/NEURON framework. The optimization aims to accurately reproduce various experimental data through tuning of channel conductances and other biophysical parameters. Several approaches are explored, including varying temperature effects, comparing different CA1 models, and deconvolving EPSCs to model presynaptic mechanisms. Future plans include using evolutionary optimization techniques and additional experimental objectives to further refine the model.

1. Optimization and Validation of a CA1 Pyramidal
Cell Model with Glutaminergic Synapses
EONS – Elementary Objects of the
Nervous System – Modeling at the
synaptic level
NEURON Simulation Environment –
Compartmental modeling of the neuron

2. The Ideal Model
•Accurate - reproduces observed data precisely
•Global (not ad hoc) – model interpolates and
extrapolates to data or situations beyond what
was originally used to describe the model
•Interpretable – describes causal relationships in
the system to answer scientific questions of how
mechanistic processes give rise to function

3. Strategy - a reductionist and integrative
approach
• A parametric model describes the large scale interactions of a
system’s elementary components.
• EONS/NEURON framework integrates cellular and synaptic interactions at
the molecular level
All elementary models were optimized using a large number of
experimental results with multiple levels of complexity
However, no optimization had yet been conducted for the entire
framework.

4. Experimental Protocol
Room temperature: 25-27C
EPSC voltage clamp: -80mV
EPSP current clamp: -246.3pA
20uM picrotoxin to block inhibitory
GABAA channels

5. Results – Initial vs current efforts

6. Optimization Objectives
• Accurate dendritic integration of synaptic inputs to the soma
• Spatial summation
• Temporal summation
• Spiking behavior – Threshold, AP amplitude and half-width
• After-potentials
• Fast AHP
• After depolarization
• Medium AHP
• Slow AHP
• Synaptic nonlinearities
• Presynaptic nonlinearities
• NT release and residual calcium hypothesis
• NMDA/AMPA
• Paired pulse facilitation and depression

7. Summary of optimization efforts
• Synapse placement
• Experimental evidence through immunogold staining (Megias 2001)
• Synapse count
• Do we need to accurately replicate the number of active synapses present in the
experimental setup?
• Effects of temperature
• Parts of the model is generated at room temperature (25C) while other parts at body
temperature (37C).
• How big of a role does temperature play in the results?
• How to model temperature dependency?

8. Summary of optimization efforts
•Explored multiple CA1 models
• Jarsky 2005
• Inherited from Sushmita
• Limited variety of channel types
• Experimental validation: backpropagation (Golding 2001)
• Very low spike threshold (-62mV)
• Migliore 2004
• Inherited from Sushmita
• Limited variety of channel types
• Validation data only exists for elementary models
• Spikes prematurely due to dendritic spikes
CA1 Channel Types Source: The Hippocampus Book

9. • Multiple CA1 models, continued…
• Poirazi-Mel 2003/2013
• Comprehensive variety of channels.
• Validated prediction: Spatial summation, validated by Losonczy 2006
• Validation: Spike train attenuation
• Validation: Backpropagation attenuation
• Low spike threshold (-57mV)?
• Q10 temperature dependence in most biophysics components
Summary of optimization efforts
Ca2+ ICaR

10. Summary of optimization efforts
• Hand tuned channel conductances of Poirazi 2013 to
optimize spike threshold and amplitude, and after-
potentials
• Evolutionary Optimization of conductances - planned
• NMDA-8 model – temporal nonlinearities
• Optimization of parameters to EMOO with multiple objectives
• Presynaptic mechanisms – temporal nonlinearities
• Deconvolution of EPSC
• P/Q Calcium Channel
• Diffusion model - planned
• NT Release model - planned

11. Synapse placement
Distribution of synapses imaged through immunogold
staining of synapses. (Megias 2001)
6.9 : 2.3 : 0.04 ratio distribution for
Distal : medial : proximal radiatum, respectively.
For 30 synapses, 22:7:1 synapse count in the
distal:medial:proximal radiatum, respectively.
• Exact synapse placement may not matter
• Distance-dependent conductance scaling
(Magee and Cook, 2000) shows increased
conductance as a function of distance from the
soma that compensates for distance
attenuation.

12. Synapse count
• Reduction of many synapses to a few strong ones?
• Valid if dendritic spikes are generated or not generated appropriately
• Synapses sum sigmoidally as shown by Losonczy et al. 2006
• Sigmoidal summation is due to strong local depolarization
causing dendritic spikes. Thus at subthresholds, synaptic
scaling would be similar to linear summation of synapses.

13. Forward Propagating Dendritic Spikes: in vivo/in vitro
• Strong synchronous input
• Dendritic spikes can be generated with ~50 synapses spread over 100µm and
activated within 3msec. (Gasparini 2004)
• Conjectured to only occur in slow wave sleep by Poirazi and Mel, 2011
• Schaffer Collateral stimulation is very synchronous, but does it activate
enough synapses to elicit dendritic spikes?

14. CA Pyramidal Cell Model – Poirazi 2013

15. Spatial Summation
•Sigmoidal nonlinear
summation within
branch
•Linear summation
between branches
Sidiropoulou et al. “Inside the brain of a neuron” 2006

16. Mechanisms of Sigmoidal Summation
Characteristics
• Multiple inputs in ‘within branch’ oblique
dendrites generates sodium spikes due to
strong local depolarization
• Between branch inputs insufficient to
generate sodium spike
Losonczy, A, Magee, J, “Integrative Properties of Radial Oblique Dendrites in Hippocampal CA1 Pyramidal Neurons” 2006

17. Temperature
• Varied temperature conditions in data
• Room temp ~ 24C
• Body temp – 37C
• Influences
• Spike threshold
• Resting potential
• Rise and fall rates of channel currents
• Afterpotentials
• Conductance
• Modeling in active channels
• Voltage dependency
• Boltzmann equations (Ca2+ channels, and Ka)
• Q10 temperature coefficient (some K+ channels)
• Time dependency – Q10 (only Ka)

18. Poirazi CA1 model - 34°C
95AMPA/60NMDA

19. Poirazi CA1 model - 25°C
95AMPA/60NMDA

20. Poirazi CA1 model - 34°C
Increased input strength
to spiking
105AMPA/71NMDA

21. Temperature on CA1 Pyramidal Neuron – in
vitro
Source: Vitro, Thompson, Temperature Dependence of Intrinsic Membrane Properties and Synaptic Potentials in Hippocampal CA1 Neurons, 1985

22. Temp on Voltage Dependency - Model
• Boltzmann equations describe the activation and inactivation steady state
voltage dependencies of active channels.
Po=P(open), Pc=P(closed)
W=potential, zeE=potential(p(0.5)),
K=Boltzmann constant, T=temp in kelvin
-100 -80 -60 -40 -20 0 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Voltage(mV)
ProbabilityOpen
VDCC Type-T
0°C
25°C
50°C
-100 -80 -60 -40 -20 0 20
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
x 10
-5
Voltage(mV)Current(nA)
I-V VDCC Type-T
0°C
25°C
50°C

23. Modeling temp with Q10 - Model
•Modeled with Q10 coefficients
• For voltage dependency
• q10*exp((1e-3)*zettax*(v-vhalfx)*kT))
• For time dependency
• qt=q10^((Celsius-24)/10)
• Taun=betn(v)/(qt*a0n*1+a))

24. Temp modeling - which channels?
• Boltzmann voltage dependency
• cal
• calH
• can
• car
• cat
• hha-Hodgkin Huxley Na+ channels, only in s attenuation system
• kadist, kaprox
• Q10 voltage dependency
• Kct
• kdBG
• km
• Q10 time dependency
• kadist, kaprox
• No temperature dependency
• pas
• Na+, Nap+
• Kdr
• Kd
• Kap
• kahp
• h

25. Spike Threshold and Resting Potential
• According to "The Hippocampus Book," the action potential threshold
of CA1 pyramidal cells is -45mV (pg 165).
• 20mV subthreshold window on experimental cell at 24°C (Shane’s
data)
• Resting membrane potential @ 27°C -60.0±7.4 n=14 (Thompson
1985)
• Spike threshold higher in dendrites than soma

26. Optimizing Channel Conductances –
Experimental Limitations - Examples
• To measure ion channel density, drugs are used to block all but the
one ion channel. It's uncertain if all the necessary drugs are used to
block all but that one channel. (Catterall, 1995)
• Experience-dependent dendritic plasticity shows distribution of K+
channel concentrates change with experience (Makara, Magee, 2009)
• It's unknown if the CA1 pyramidal neuron is the strong
backpropagating or weak backpropagating type. (Golding, 2001)
Weak Propagating
Strong Propagating

27. Optimizing Channel Conductances - Strategy
• Na+ conductance: spike amplitude
• Na+/K+ permeability ratio: spike threshold and
afterdepolarization potential time course and
amplitude
• Ca2+ T-type and R-type conductance:
afterdepolarization potential time course and
amplitude
• Hyperpolarization current conductance: passive
channel pulls potential to resting. Attenuates
subthreshold temporal summation and strengthens
EPSP repolarization at potentials approaching spike
threshold.
• Ca2+ dependent K+ conductance: After
hyperpolarization potential amplitude

28. Optimizing Channel Conductances –
Preliminary Results

29. Optimizing Channel Conductances –
Future Plans
• Optimization with EMOO
• Objective: I-V plots
• Objective: Effects of blocking various channels on synaptic
summation(Cash and Yuste 1999)
• In thin branches
• In apical trunk

30. Optimizing Channel Conductances –
Future Plans – cellular temporal nonlinearities
• Objective: Effects of blocking Na+ and K+ on temporal summation
(Margulis et al. 1998)
• Objective: Effects of blocking Ih on temporal summation (Magee
2000)
Margulis, Tang 1998. “Temporal Integration Can Readily Switch Between Sublinear and Supralinear Summation”
Magee J, 2000, “Dendritic Integration of Excitatory Synaptic Input,” Nature Reviews

31. • Objective (if able to obtain data) – Use two photon microscopy to
perform dual somato-dendritic recordings with glutamate uncaging as
the input.
• Optimize afterpotentials
• Florescent imaging to match model morphology with experimental
• Glutamate uncaging to know synapse location which will be useful to optimize
the non-uniform channel conductances
Optimizing Channel Conductances –
Future Plans

32. NMDA-R Model – 15 states
It was not possible to optimize the AMPA/NMDAR ratio to match the EPSP shape. NMDAR
persistently appeared much slower than the experimental data.
A revisit to the NMDAR-15 model reveals that it is indeed much slower than experimental data.

33. NMDA-R Model – 8 states
• Fixed slowness problem as AMPAR/NMDAR ratio can be optimized to
a count of 80/55, in range of physiological recordings (Takumi et al.,
1999; Matsuzaki et al., 2001).
• However, problems with desensitization

34. NMDA-R Optimization with EMOO
• Optimization to additional objectives that account for desensitization.
• Objective: Paired pulse
• Objective: Long step input

35. Temporal Nonlinearities – quantifying the disparity
Interval(ms) Experimental(V2/V1) Simulation(V2/V1)
56ms .68(to AP threshold), 1.27(to ADP peak) 0.22
84ms .80 .57

36. Presynaptic contribution to nonlinearities
• According to Song 2007, presynaptic mechanisms account for an
overwhelming majority of the temporal nonlinearities
• Residual Calcium Hypothesis
• To test this, I deconvolved the EPSC to extract the presynaptic
nonlinearities in addition to a smaller component of AMPA
nonlinearities. This provided an impulse amplitude that corresponds
to the NT release strength.

37. EPSC Deconvolution Results
Subthreshold NRMSE = 10%
Temporal nonlinearities
significantly restored
• Reasons?
• Presynaptic nonlinearities
• No NMDA with overly strong
desensitization

38. EPSC Deconvolution Results – A longer
timespan

39. Presynaptic mechanisms - Planned
• P/Q VDCC (Bischofberger 2002) - implemented
• Ca2+ Diffusion model (Sikora 2005) – prior model
• NT release model (Nadkarni et al 2010) - planned

40. PQ VDCC EONS Implementation
Activation Curve IV Curve