Generalized Leaky Integrate-and-Fire Model Building blocks of models - - PowerPoint PPT Presentation

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Generalized Leaky Integrate-and-Fire Model Building blocks of models - - PowerPoint PPT Presentation

Mar 28, 2023 105 likes •444 views

Generalized Leaky Integrate-and-Fire Model Building blocks of models for cortical computation Stefan Mihalas Assistant Investigator Affiliate Assistant Professor Lecture plan 1. Motivation: why we study mouse cortex 2. Single neuron

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Generalized Leaky Integrate-and-Fire Model

Building blocks of models for cortical computation

Stefan Mihalas Assistant Investigator Affiliate Assistant Professor

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Lecture plan

1. Motivation: why we study mouse cortex 2. Single neuron models: From dynamical systems to hybrid systems 3. Generalized leaky integrate-and-fire model 4. Fitting GLIF models 5. Cell classification using GLIF models

alleninstitute.org | brain- map.org 2

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  • 1. Why study cortex?

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Herculano-Houzel (2012) PNAS

Cerebral cortex can vary in size

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Cerebral cortex can vary in size

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Perrenoud, 2012

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But the basic microstructure is very similar across areas

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Adult V1 Adult M1 Infant

Ramon y Cahal, 1911

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And across species

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Hill and Walsh, Nature 2005

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Cortical column computations

Hope:

  • Cortical columns implement canonical computations
  • The function of the cortex arises from a hierarchical
  • rganization of such computations

alleninstitute.org | brain- map.org 7

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Constructing minimalistic models which reproduce a desired function

Single neuron activity Activity in local circuits Mesoscopic models

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Long term goal: Integrate models across scales into a model of cortical computation in the mouse visual system

Single neuron activity Activity in local circuits Mesoscopic models

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In Vitro single neuron models

Single neuron activity Activity in local circuits Mesoscopic models

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  • 2. Why spiking models?
  • Time scale separation of the subthreshold vs spiking dynamics

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200 pA steps 20 mV 2 ms

  • 79 mV

slow fast

20 mV 400 ms

  • 78 mV

100 pA mean amplitude, 0.2 CV

slow fast

  • Spikes are stereotyped
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  • 3. Generalized Leaky Integrate and Fire Models

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V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC) membrane potential reset (R)

Θs(t)

threshold reset (R)

ΘV(t)

threshold adaptation (TA)

Corinne Teeter, Stefan Mihalas Mihalas and Niebur 2009

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V(t) Ie(t)

spike?

membrane potential reset (R)

Dynamics: between spikes Reset: if

Leaky Integrate and Fire Models

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V(t) Ie(t)

spike?

membrane potential reset (R)

Θs(t)

threshold reset (R)

Dynamics: between spikes Reset: if

LIF with reset rules

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SLIDE 15

V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC)

Dynamics: between spikes Reset: if

LIF with after-spike currents - optimization

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V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC)

Dynamics: between spikes Reset: if

LIF with after-spike currents

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V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC) membrane potential reset (R)

Θs(t)

threshold reset (R)

Dynamics: between spikes Reset: if

LIF with after-spike currents and voltage dependent threshold

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SLIDE 18

V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC) membrane potential reset (R)

Θs(t)

threshold reset (R)

LIF with after-spike currents and voltage dependent threshold

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SLIDE 19

V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC) membrane potential reset (R)

Θs(t)

threshold reset (R)

ΘV(t)

threshold adaptation (TA)

Dynamics: between spikes Reset: if

LIF with after-spike currents spiking and voltage dependent threshold

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V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC) membrane potential reset (R)

Θs(t)

threshold reset (R)

ΘV(t)

threshold adaptation (TA)

LIF with after-spike currents spiking and voltage dependent threshold

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  • 4. Allen Cell Types Database

alleninstitute.org | brain-map.org 2 1 Search and Filter Options Cell Positions in Common Coordinate Framework Summary of Cell Characteristics (Click for additional details)

Jim Berg, Hongkui Zeng

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Calb2-IRES-Cre Pvalb-2A-Flpo; Slc32a1-IRES-Cre Nos1-CreERT2 Vip-IRES-Cre Sst-IRES-Cre Ntsr1-Cre layer 6 Nr5a1-Cre layer 4 Cux2-CreERT2 layer 2/3/4 Scnn1a-Tg3-Cre layer 4 Rbp4-Cre layer 5 Rorb-IRES2-Cre layer 4 Slc17a6-IRES-Cre pan-excitatory

Excitatory neurons Inhibitory neurons

Gad2-IRES-Cre pan-inhibitory

Genetic Markers via Cre Lines

2 2 Julie Harris

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100 pA 20 mV 400 ms

  • 79 mV

200 pA steps 20 mV 2 ms

  • 79 mV

20 mV 400 ms

  • 78 mV

100 pA mean amplitude, 0.2 CV 20 mV 50 ms

  • 78 mV

Instantaneous threshold Adaptive threshold Subthreshold, Rheobase & Suprathreshold Naturalistic response

Electrophysiology Protocol

2 3

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V(t) Ie(t)

spike?

membrane potential reset (R)

Leaky Integrate and Fire Models - optimization

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V(t) Ie(t)

spike?

membrane potential reset (R)

Θs(t)

threshold reset (R)

LIF with reset rules - optimization

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LIF R ASC AT - optimization

V(t) Ie(t)

spike?

Ij(t) Ij(t)

after-spike currents (ASC) membrane potential reset (R)

Θs(t)

threshold reset (R)

ΘV(t)

threshold adaptation (TA)

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LIF R ASC AT – optimization Maximum likelihood based on internal noise (MLIN)

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LIF LIF- R LIF- ASC LIF- R- ASC LIF- R- ASC

  • TA

Training Data Test Data Explained Variance

Generalized Leaky Integrate and Fire Models

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Average explained variance

  • Glif 5: 75% - excitatory 84% for inhibitory
  • Biophysical perisomatic – 65%
  • Biophysical all-active – 69%

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Defining cell types based on models

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Single Cell Type Models Conclusion

  • A large diversity of neurons can be

characterized and modeled

  • GLIF models still outperform detailed biophysical
  • nes due to individual recording length limitation
  • Parameters in GLIF models can be used to

classify cell types

  • visit our website: http://www.brain-map.org/

alleninstitute.org | brain- map.org 3 2