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Computations in living organisms modeled by marked graphs.

John M Myers1, Hadi Madjid2

  • 1John A. Paulson School of Engineering and Applied Sciences (Retired), Harvard University, 29 Oxford St., Cambridge, Massachusetts, 02108, USA. jmartmyers@gmail.com.

Bulletin of Mathematical Biology
|July 25, 2025
PubMed
Summary

Living organisms perform computations that change unpredictably. Using marked graph mathematics, we show how to preserve organism integrity during these computational changes, illustrated by slime mold behavior.

Keywords:
Live and safe markingsMarked graphsSlime moldUnpredictable changes.

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Area of Science:

  • Computational Biology
  • Theoretical Biology
  • Biophysics

Background:

  • Biological processes, including DNA replication and cognitive functions, can be viewed as computations.
  • Previous work (Madjid and Myers, 2005) established that linking quantum calculations to evidence involves revision-prone guesswork.
  • This suggests biological computations are subject to continuous, unpredictable structural changes.

Purpose of the Study:

  • To address how biological computations can change while maintaining organismal integrity.
  • To propose a mathematical framework for understanding and preserving the integrity of dynamic biological computations.

Main Methods:

  • Utilizing the mathematics of marked graphs to represent computations as networks of logical operations.
  • Representing sequences of computational changes using sequences of marked graphs with live and safe markings.
  • Defining "preserving integrity" as maintaining liveness and safety throughout the sequence of marked graphs.

Main Results:

  • Demonstrated that liveness and safety in marked graphs can be preserved during sequences of changes, representing computational integrity.
  • Provided a specific example of a slime mold amoeba integrating into a filament without disrupting ongoing computation.
  • Showcased an alternative interpretation of marked graph sequences as representing the integration of a thought fragment into a human thought chain.

Conclusions:

  • Marked graph mathematics provides a robust framework for modeling and ensuring the integrity of dynamic biological computations.
  • The framework is applicable to diverse biological phenomena, from cellular processes to cognitive functions.
  • The mathematical model allows for different interpretations, highlighting the abstract nature of computation in living systems.