Lectures 5,6,7 Ensembles of membrane proteins as statistical mixed-signal computers
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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
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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 circuitry. - PowerPoint PPT Presentation
Transcript of Lectures 5,6,7 Ensembles of membrane proteins as statistical mixed-signal computers
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)
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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
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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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