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Quantum-like interference effect in gene expression: glucose-lactose destructive interference

  • METHODOLOGY ARTICLE
  • Published:
Systems and Synthetic Biology

Abstract

In this note we illustrate on a few examples of cells and proteins behavior that microscopic biological systems can exhibit a complex probabilistic behavior which cannot be described by classical probabilistic dynamics. These examples support authors conjecture that behavior of microscopic biological systems can be described by quantum-like models, i.e., models inspired by quantum-mechanics. At the same time we do not couple quantum-like behavior with quantum physical processes in bio-systems. We present arguments that such a behavior can be induced by information complexity of even smallest bio-systems, their adaptivity to context changes. Although our examples of the quantum-like behavior are rather simple (lactose-glucose interference in E. coli growth, interference effect for differentiation of tooth stem cell induced by the presence of mesenchymal cell, interference in behavior of PrP C and PrP Sc prions), these examples may stimulate the interest in systems biology to quantum-like models of adaptive dynamics and lead to more complex examples of nonclassical probabilistic behavior in molecular biology.

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Notes

  1. For example, in applications to cognitive modelling, one need not worry whether the brain is too hot to perform real quantum physical computations.

  2. For instance, context dependence plays an important role in cognitive science and psychology. Therefore the quantum-like probability can be applicable here.

  3. Since the operon theory was proposed in 1956–1961 (Jacob and Monod 1961), the regulatory system of gene expression of lactose operon has been extensively studied and the molecular mechanism of it has been mostly elucidated including the catabolite repression phenomenon.

  4. The same effect, destructive interference, can be approached, by using, instead of mutant proteins, wild type prion protein, but after long time incubation.

  5. As was mentioned, in quantum physics by determining a slit which was passed by a photon we destroy the interference effect. It is not clear whether the same would happen in molecular biology.

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Authors and Affiliations

  1. International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, 35195, Växjö, Sweden

    Irina Basieva & Andrei Khrennikov

  2. Department of Information Sciences, Tokyo University of Science, Yamasaki 2641, Noda-shi, Chiba, 278-8510, Japan

    Masanori Ohya

  3. Department of Biological Science and Technology, Tokyo University of Science, Yamasaki 2641, Noda-shi, Chiba, 278-8510, Japan

    Ichiro Yamato

Authors
  1. Irina Basieva
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  2. Andrei Khrennikov
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  3. Masanori Ohya
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  4. Ichiro Yamato
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Corresponding author

Correspondence to Andrei Khrennikov.

Additional information

I. Basieva and A. Khrennikov were supported by the QBIC-grant (Tokyo University of Science); I. Basieva was also supported by the Swedish Institute.

Appendix: hyperbolic numbers

Appendix: hyperbolic numbers

The algebra of hyperbolic numbers G is a two dimensional real algebra with basis e 0 = 1 and e 1 = j, where j 2 = 1 (a two dimensional Clifford algebra). Elements of G have the form \(z=x + j y, \; x, y \in {\bf R}.\) We have z 1 + z 2 = (x 1 + x 2) + j(y 1 + y 2) and z 1 z 2 = (x 1 x 2 + y 1 y 2) + j(x 1 y 2 + x 2 y 1). This algebra is commutative. It is not a field - not every element has the inverse one. We introduce an involution in G by setting \(\bar{z} = x - j y.\) We set

$$ e^{j\theta}=\cosh\,\theta+ j \sinh\,\theta, \; \theta \in {\bf R }. $$

We remark that \(e^{j\theta_1} e^{j\theta_2}=e^{j(\theta_1+\theta_2)}, \overline{e^{j\theta}} =e^{-j\theta}.\) By operating with hyperbolic exponents we can proceed in the same way as in ordinary complex quantum mechanics (Khrennikov 2010).

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Basieva, I., Khrennikov, A., Ohya, M. et al. Quantum-like interference effect in gene expression: glucose-lactose destructive interference. Syst Synth Biol 5, 59–68 (2011). https://doi.org/10.1007/s11693-011-9081-8

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  • DOI: https://doi.org/10.1007/s11693-011-9081-8

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