Lectures 5,6,7

Ensembles of membrane proteins as statistical mixed-signal computers

Victor Eliashberg

Consulting professor, Stanford University, Department of Electrical Engineering

Slide 1

The brain has a very large but rather simple circuitryThe shown cerebellar network has ~1011 granule (Gr) cells and ~2.5 107 Purkinje (Pr) cells. There are around 105 synapses between T-shaped axons of Gr cells and the dendrites of a single Pr cell.

Cerebelum: N=2,5 107 * 105= 2.51012 B= 2.5 TB. Neocortex: N=1010 * 104= 1014 B= 100 TB.

Pr

Memory is stored in such matrices

LTM size:Slide 2

Simple “3-neuron” associative neural network (WTA.EXE)

Slide 3

DECODING

ENCODING

RANDOM CHOICE

Input long-term memory (ILTM)

Output long-term memory (OLTM)

addressing by content

retrieval

S21(I,j)

N1(j)

S21(i,j)

A functional model of the previous network [7],[8],[11]

(WTA.EXE)

(1)

(2)

(3)

(4)

(5)

Slide 4

Slide 5

Concept of a primitive E-machine

Slide 6

;s(i) > c

(α< .5)

Kandel experiments: molecules involved in STM in Aplysia (E.R. Kandel. In search of memory. 2006, p.233)

Slide 7

Computational machinery of a cell

Nucleus

Membrane proteins

Membrane

It took evolution much longer to create individual cells than to build systems containing many cells, including the human brain. Different cells differ by their shape and by the types of membrane proteins.

Nucleus

Membrane proteins

Membrane

18nm

3nm

Slide 8

Protein molecule as a probabilistic molecular machine (PMM)

i

Slide 9

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Slide 12

Ensemble of PMMs (EPMM)

E-states as occupation numbers

Slide 13

EPMM as a statistical mixed-signal computer

Slide 14

Ion channel as a PMM

Slide 15

Monte-Carlo simulation of patch clamp experiments

Slide 16

Two EPMM’s interacting via a) electrical and b) chemical messages

Slide 17

Spikes produced by an HH-like model with 5-state K+ and Na+ PMM’s. (EPMM.EXE)

Slide 18

The HH gate model

a) Potassium channel with 4 n-gates

b) Sodium channel with 3 m-gates and 1 h-gate

K+

Na+

Inside Outside

+

+

++

+

+

+

+

+

+

+

- -

Na+

K+

Cl -

Cl -

Membrane

uin ~ -64mV uout =0

~18 nm

~ 3nm

Slide 19

Reduced 5-state HH model for potassium channel

Slide 20

Reduced 8-state HH model for sodium channel

Slide 21

(1)

(2)

(3)

(4)

(5)

(6)

(7)

The HH mathematical model

NOTE. The HH mathematical model is an approximation of the HH gate model. It doesn’t follow rigorously from the HH gate model but does produce similar results Slide 22

(EPMM.EXE)

A model of sensitization and habituation in a pre-synaptic terminal

subunit of protein kinase A

Slide 23

A PMM implementation of a putative calcium channel with sensitization and habituation (not a viable biological hypothesis -- just to demonstrate the possibilities of the EPMM formalism)

Note. The PMM formalism allows one to naturally represent considerably more complex models.

This level of complexity is not available in traditional ANN models. Slide 24

Ionic currents and membrane potentials

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