# Julius B. Lucks/Bibliography/Allen-PNAS-88-1991

From OpenWetWare

Jump to navigationJump to search## Notes on [1]

- See also [2]
- pmid: 1763012
- design neural networks with computations achieved by single stationary state of the
**entire**reaction **REFERENCES 1-14:**different computational systems including digital computer, Fredkin logic gates, billiard ball collisions, cellular automata, etc.- "All living entities process information to varying degrees, and this can occur only by chemical means."
- (17-18) chemical mechanisms similar to electronics
- propose chemical reaction network that is hardware implementation of neural network
- (15-16) coupling bistable 'flip-flop' reactions, can build universal automata
- (19) - neural networks as a computational system
- (11-13) - neural networks basis collective computational systems: feedforward networks, Hopfield's networks
- propose a set of reactions that have two states, depending on the concentration of an input catalyst
- implementation wise, to create two chemical neurons and couple them, they would need to have two independent reaction systems that obeyed the same kinetics
- need n independent reaction systems to have n neurons
- seems very unlikely

- neurons communicate through activation or inhibition of another neurons catalyst that controls the state
- system of 4 chemical reactions - write down simple ODE's for kinetics
- conc of species A determines state of the neuron
- conservation constraint A_i + B_i = A_o
- conc of A and B evolve into a steady state determined by concentration of C - the chemical input parameter for the neuron
- tune the gain of the neuron (sharpness of the jump) with rate constants k_2 and k_3

- when couple, effect of other neurons on neuron i is encoded in C_i
- A_i and B_i can inhibit or activate production of C_j - couple neurons this way
- C_i can actually be the sum of many chemical entities

- A_i and B_i can inhibit or activate production of C_j - couple neurons this way
- goes through constructing logic gates out of neuron i, which operates on signals from neurons j and k
- AND - j and k activate C_i
- OR - ja and k activate C_i, but strongly
- A_j AND NOT A_k - j activates, k inhibits
- A_j NOR A_k - both inhibit
- plug in constants in the steady state concentration of C_i equation 6 to figure out if neuron i will fire

- autonomously oscillating catalyst can act as a clock
- all neurons updated at the same time based on current states before an impulse

- in this architecture, 4*(N+1) distinct chemical species required for N neurons
- each connection requires another distinct species
- compartmentalization would reduce the number of species required

- universal Turing machine - can do with clocked neural network of finite size and 2 infinite stacks

# References

- Hjelmfelt A, Weinberger ED, and Ross J.
*Chemical implementation of neural networks and Turing machines.*Proc Natl Acad Sci U S A. 1991 Dec 15;88(24):10983-7. DOI:10.1073/pnas.88.24.10983 | - Hjelmfelt A, Weinberger ED, and Ross J.
*Chemical implementation of finite-state machines.*Proc Natl Acad Sci U S A. 1992 Jan 1;89(1):383-7. DOI:10.1073/pnas.89.1.383 |