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

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 quantummechanics. 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.Keywords Quantum-like interference Á Nonclassical probabilistic behavior Á Lactose-glucose interference Á E. coli growth Á Differentiation of tooth stem cell Á Mesenchymal cell Á Interference of PrP C and PrP Sc prions

The use of action functionals within the quantum-like paradigm

“…Where the term "quantum feature"has more traction, so to speak, is in the area where quantum probability (in decision making) is employed. In that same area do we …nd the di¢ cult concept of 'context' (Khrennikov (2010)). Quantum features occur also in the use of Fisher information in economics and …nance.…”

“…Although we do not discuss such an interpretation in this paper (see for instance, Khrennikov, 2010;Haven, 2008), it needs to be indicated that if we were to formulate a 'preference for information'function then such device would be intimately related to the notion of probability as it is expressed in (14) above. This is quite di¤erent from the interpretation Ma (2010) gives to preferences for information, where such preferences can be unrelated to the probability measure assigned to an event.…”

“…Central to this paradigm is the notion that the wave function, the central object in quantum mechanics, has an information based character. The quantum-like paradigm has now been the main topic of several monographs and many papers (see for example, Basieva et al, 2010;Khrennikov, 2010Khrennikov, , 2015Haven & Khrennikov, 2013;Piotrowski & S÷ adkowski, 2003Piotrowski & S÷ adkowski, , 2004Asano et al , 2011Asano et al , , 2015Busemeyer & Bruza, 2012;Plotnitsky, 2009Plotnitsky, , 2014Dzhafarov et al, 2015;Dzhafarov & Kujala, 2012Baaquie, 2004Baaquie, , 2013Baaquie, , 2014Yukalov & Sornette, 2011Hawkins & Frieden, 2004Hawkins et al, 2010;Aerts et al, 2013 and other work). A key paper which started, to a large extend, the quantum-like paradigm is by Khrennikov (1999).…”

A model of epigenetic evolution based on theory of open quantum systems

“…2 In particular, in Basieva et al (2011) we demonstrated that one of the basic laws of classical probability theory, the law of total probability, is violated by well known experimental data, e.g., Inada et al (1996), on functioning of the lac-operon in E. coli bacteria. This violation can be interpreted as an interference effect which is similar to interference of probabilities in the two slit experiment with photons.…”

“…In this paper we use the quantum-like (QL) paradigm by which the formalism of QM can applied to describe measurements and information processes even outside of quantum physics, in particular, in biology (Khrennikov 2006;Accardi et al 2008). In a series of papers (Basieva et al 2011;Asano et al 2012a, b) we elaborated a QL model of a cell processing information in accordance with the laws of quantum information theory, cf. also Wanke et al (2009).…”