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On the universality of peptide computing

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Abstract

We present a simulation of Turing machines by peptide–antibody interactions. In contrast to an earlier simulation, this new technique simulates the computation steps automatically by the interaction between peptides and antibodies and does not rely on a “look-and-do” approach, in which the Turing machine program would be interpreted by an extraneous computing agent. We determine the resource requirements of the simulation. Towards a precise definition for peptide computing we construct a new theoretical model. We examine how the simulations presented in this paper fits this model. We also give conditions on the peptide computing model so that it can be simulated by a Turing machine.

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Notes

  1. One may doubt whether chemical stability in this strong sense can be achieved at all; for a more realistic model, it can be necessary to build fault-tolerance into the simulation and, hence, accept that, with some small probability, the simulation may not succeed.

  2. Under the assumption of “ideal” chemical reactions as mentioned above, this condition ensures that distinct cells can be distinguished and that antibodies can only bind to specific spots in specific cells. Many more such conditions are required in the proofs of both Theorems 1 and 2. Without them one can only show that the language accepted by the Turing machine \({{\mathcal M}}\) is contained in the language accepted by the peptide system simulating \({{\mathcal M}}\). We do not explicitly express all the conditions which are required in the proof sketches. This issue is, in part, addressed in Sect. 5. The general assumption in the two proof sketches is that all bindings are unique up to affinity and that there are no cross-reactions.

  3. Antibodies of types A a and \({A_{a,{\tt D}}}\) with \({{\tt D}\in\{{\tt L},{\tt R}\}}\) can be considered as equivalent for most purposes.

  4. To avoid look-and-do, we add epitopes for all j even though it would be sufficient to add only those with j = i.

  5. The number 20 below is the number of amino acids—abstractly an alphabet of any size with at least two elements would suffice.

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Authors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, London, ON, Canada, N6A 5B7

    M. Sakthi Balan & Helmut Jürgensen

  2. Institut für Informatik, Universität Potsdam, August-Bebel-Str. 89, 14482, Potsdam, Germany

    Helmut Jürgensen

Authors
  1. M. Sakthi Balan
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  2. Helmut Jürgensen
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Correspondence to M. Sakthi Balan.

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Sakthi Balan, M., Jürgensen, H. On the universality of peptide computing. Nat Comput 7, 71–94 (2008). https://doi.org/10.1007/s11047-007-9045-9

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  • DOI: https://doi.org/10.1007/s11047-007-9045-9

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