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

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
• 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

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1. Notes

2. Notes