Lectures 5,6,7 Ensembles of membrane proteins as statistical mixed-signal computers

1. 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

2. The brain has a very large but rather simple circuitry The 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. Pr Memory is stored in such matrices Slide 2 LTM size: Cerebelum: N=2,5 107 * 105= 2.51012 B= 2.5 TB. Neocortex: N=1010 * 104= 1014 B= 100 TB.

3. addressing by content DECODING S21(I,j) S21(i,j) Input long-term memory (ILTM) N1(j) RANDOM CHOICE Output long-term memory (OLTM) ENCODING retrieval Simple “3-neuron” associative neural network (WTA.EXE) Slide 3

4. A functional model of the previous network[7],[8],[11] (WTA.EXE) (1) (2) (3) (4) (5) Slide 4

5. Concept of a primitive E-machine Slide 5

6. s(i) > c ; Slide 6 (α< .5)

7. Kandel experiments: molecules involved in STM in Aplysia (E.R. Kandel. In search of memory. 2006, p.233) Slide 7

8. Computational machinery of a cell Membrane proteins Membrane proteins Membrane Membrane Nucleus Nucleus 3nm 18nm 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. Slide 8

9. Protein molecule as a probabilistic molecular machine (PMM) i Slide 9

10. Slide 10

11. Slide 11

12. Slide 12

13. Ensemble of PMMs (EPMM) E-states as occupation numbers Slide 13

14. EPMM as a statistical mixed-signal computer Slide 14

15. Ion channel as a PMM Slide 15

16. Monte-Carlo simulation of patch clamp experiments Slide 16

17. Two EPMM’s interacting via a) electrical and b) chemical messages Slide 17

18. Spikes produced by an HH-like model with 5-state K+ and Na+ PMM’s. (EPMM.EXE) Slide 18

19. The HH gate model Inside Outside ~18 nm Na+ + Na+ + + + + + Cl - Cl - - - K+ + + K+ + + + uin ~ -64mV uout =0 a) Potassium channel with 4 n-gates b) Sodium channel with 3 m-gates and 1 h-gate ~ 3nm Membrane Slide 19

20. Reduced 5-state HH model for potassium channel Slide 20

21. Reduced 8-state HH model for sodium channel Slide 21

22. The HH mathematical model (1) (2) (3) (4) (5) (6) (7) (EPMM.EXE) 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

23. subunit of protein kinase A A model of sensitization and habituation in a pre-synaptic terminal Slide 23

24. 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

25. Ionic currents and membrane potentials Slide 25

26. Slide 26

27. Slide 27

28. Slide 28

29. Slide 29

30. Slide 29