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

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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


  1. 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 | PubMed ID:1763012 | HubMed [Allen-PNAS-88-1991]
  2. 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 | PubMed ID:11607249 | HubMed [Allen-PNAS-89-1992]

All Medline abstracts: PubMed | HubMed