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The noncomputability of immune reaction complexity: Algorithmic information gaps under effective constraints.
Emmanuel Pio Pastore1, Francesco De Rango2
1Department of Biology, Ecology and Earth Science, University of Calabria, 87036 Rende, Italy; Department of Health Sciences, University of Genoa, 16132 Genoa, Italy.
Bio Systems
|July 13, 2026
Summary
Adaptive immune responses face informational challenges in generating valid molecular actions. This study introduces the Normalized Advice Quantile (NAQ) to quantify response difficulty, aiding in understanding immune system complexity.
Area of Science:
- Immunology
- Information Theory
- Computational Biology
Background:
- Adaptive immune responses require complex decision-making under strict biological constraints.
- Understanding the informational basis of immune recognition and execution is crucial.
Purpose of the Study:
- To quantify the informational difficulty of generating valid immune responses.
- To develop a scale-free measure for comparing response complexity.
Main Methods:
- Representing immune challenges (x) and potential responses (r) using a validity predicate V(x,r).
- Defining minimum feasible realizer complexity M(x) as the shortest description of a valid response.
- Introducing Normalized Advice Quantile (NAQ) as the percentile rank of M(x) within a reference pool.
Main Results:
- The Exact Realizer Identity establishes a relationship between minimum advice and M(x).
- Feature maps decompose response complexity into specification and realization costs.
- Computability separations and resource-bounded variants were derived.
Conclusions:
- NAQ provides a scale-free measure of relative immune response difficulty.
- The framework links informational complexity to advice and memory requirements in biological systems.
- Empirical NAQ can be approximated using code-length proxies.
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