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The Unconventionality of Nature: Biology, from Noise to Functional Randomness

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Unconventional Computation and Natural Computation (UCNC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9252))

Abstract

In biology, phenotypes’ variability stems from stochastic gene expression as well as from extrinsic fluctuations that are largely based on the contingency of developmental paths and on ecosystemic changes. Both forms of randomness constructively contribute to biological robustness, as resilience, far away from conventional computable dynamics, where elaboration and transmission of information are robust when they resist to noise. We first survey how fluctuations may be inserted in biochemical equations as probabilistic terms, in conjunction to diffusion or path integrals, and treated by statistical approaches to physics. Further work allows to better grasp the role of biological “resonance” (interactions between different levels of organization) and plasticity, in a highly unconventional frame that seems more suitable for biological processes. In contrast to physical conservation properties, thus symmetries, symmetry breaking is particularly relevant in biology; it provides another key component of biological historicity and of randomness as a source of diversity and, thus, of onto-phylogenetic stability and organization as these are also based on variation and adaptativity.

B. Bravi—This author’s work is supported by the Marie Curie Training Network NETADIS (FP7, grant 290038).

G. Longo—This author’s work is part of the project “Le lois des dieux, des hommes et de la nature” at IEA–Nantes.

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Notes

  1. 1.

    In this regard, Van Kampen critically claims an “indiscriminate application” of the Langevin approach for internal sources of stochasticity, the main reason being that fluctuations cannot be analyzed independently of the global evolution. From the mathematical point of view, in fact, the Eq. (3.2) is rigorously defined only if one specifies which integration rule is chosen (either the Itô or Stratonovich convention, as explained in Van Kampen 2007).

  2. 2.

    Almost ironically, Feynman (1948) notices in this regard: “There are, therefore, no fundamentally new results. However, there is a pleasure in recognizing old things from a new point of view”.

  3. 3.

    The intuition beyond can be traced back to E. Schrödinger’s words: “Incredibly small groups of atoms, much too small to display exact statistical laws, do play a dominating role in the very orderly and lawful events within a living organism”, What is Life (1944).

  4. 4.

    As a preliminary evidence, recent experiments (see Salman et al. 2012) suggest that the fitted curves for protein abundance resemble limit distributions of strongly correlated stochastic variables: this would reflect the spatial and temporal interdependence of processes regulating gene expression.

  5. 5.

    In these contexts, mean values analyses (or central limit theorems) are generally valid. However, in the complex case of second-order phase transitions, in thermodynamics, these analyses fail. For example, the transition between macroscopic order versus disorder in ferro-paramagnetic transitions, does not occur progressively but at a precise (critical) temperature. At that point, fluctuations at every scale dominate and this expresses a tendency to obtain magnetic alignments of every size. Moreover, some physical quantities become infinite, such as susceptibility to an external field. As a consequence of the dominating fluctuations, close or at the transition, mean value analyses fail (Longo et al. 2012b; Toulouse et al. 1977). This may be of interest for biological theoretizing, yet, in this case as well, the phase space is pre-given.

  6. 6.

    In reference to a previous footnote, this situation is closer to second order criticality than to the statistical “averaging out”.

  7. 7.

    Geodetics are usually derived by variational or equivalent methods that allow to write a Hamiltonian or extremize a Lagrangian functional that are given in terms of conservation properties.

  8. 8.

    Note that not only measurable phenotypes, as observables, may change, but pertinent parameters as well: air vibrations at audible frequencies were irrelevant before the formation of hears, in early vertebrates with a double jaw (Allin 1975).

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Acknowledgements

We thank Angelo Vulpiani for stimulating remarks on a preliminary draft and Peter Sollich for a careful reading of part of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, King’s College London, London, UK

    Barbara Bravi

  2. Centre Cavaillès, CNRS, École Normale Supérieure, Paris, France

    Giuseppe Longo

  3. Department of Integrative Physiology and Pathobiology, Tufts University, Boston, USA

    Giuseppe Longo

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  1. Barbara Bravi
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Correspondence to Barbara Bravi .

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  1. University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Auckland, Auckland, New Zealand

    Michael J. Dinneen

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Bravi, B., Longo, G. (2015). The Unconventionality of Nature: Biology, from Noise to Functional Randomness. In: Calude, C., Dinneen, M. (eds) Unconventional Computation and Natural Computation. UCNC 2015. Lecture Notes in Computer Science(), vol 9252. Springer, Cham. https://doi.org/10.1007/978-3-319-21819-9_1

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