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On Two Quantum Approaches to Adaptive Mutations in Bacteria On two quantum approaches to adaptive mutations in bacteria. Vasily Ogryzko* INSERM, CNRS UMR 8126, Universite Paris Sud XI Institut Gustave Roussy, Villejuif, France Key words: Adaptive mutations, quantum mechanics, measurement, decoherence, Lamarck [email protected] http://sites.google.com/site/vasilyogryzko/ ABSTRACT approach. The positive role of environmentally induced decoherence (EID) on both steps of the The phenomenon of adaptive mutations has been adaptation process in the framework of the Q-cell attracting attention of biologists for several approach is emphasized. A starving bacterial cell is decades as challenging the basic premise of the proposed to be in an einselected state. The Central Dogma of Molecular Biology. Two intracellular dynamics in this state has a unitary approaches, based on the quantum theoretical character and is proposed to be interpreted as principles (QMAMs - Quantum Models of ‘exponential growth in imaginary time’, Adaptive Mutations) have been proposed in analogously to the commonly considered order to explain this phenomenon. In the present ‘diffusion’ interpretation of the Schroedinger work, they are termed Q-cell and Q-genome equation. Addition of a substrate leads to Wick approaches and are compared using ‘fluctuation rotation and a switch from ‘imaginary time’ trapping’ mechanism as a general framework. reproduction to a ‘real time’ reproduction regime. Notions of R-error and D-error are introduced, Due to the variations at the genomic level (such as and it is argued that the ‘fluctuation trapping base tautomery), the starving cell has to be model’ can be considered as a QMAM only if it represented as a superposition of different employs a correlation between the R- and D- components, all ‘reproducing in imaginary time’. errors. It is shown that the model of McFadden & Any addition of a selective substrate, allowing only Al-Khalili (1999) cannot qualify as a QMAM, as it one of these components to amplify, will cause corresponds to the 'D-error only' model. Further, Wick rotation and amplification of this component, the paper compares how the Q-cell and Q-genome thus justifying the occurrence of the R-D-error approaches can justify the R-D-error correlation, correlation. Further ramifications of the proposed focusing on the advantages of the Q-cell ideas for evolutionary theory are discussed. 1. Introduction way unexpected from the classical view of the world. That is, an individual object can behave in The exorcism of teleology from the natural sciences is some sense as a population of objects (so called widely considered to be the main legacy of Darwinism ‘quantum parallelism’). This suggested to the (Dennet, 1996). According to the Darwinian paradigm, present author that if the quantum principles are the adaptation of life to its surroundings does not taken into account in the explanation of biological involve any ‘foresight’ and can be explained as the adaptation, the logic that inexorably links natural result of a random search through a succession of selection to populational thinking might break heritable variations and selection. The essential claim down. This could return an individual living of Darwinism that an adaptive value of a heritable organism to the 'driver’s seat' of biological variation cannot be directly anticipated by an organism evolution, as the adaptive evolution could be and can be proven only via selection on the understood as a result of 'selection in the populational level is supported by the Central Dogma population of virtual states' of an individual of molecular biology (Crick, 1970). This widely organism (Ogryzko, 1994; Ogryzko, 1997; accepted framework for understanding the mechanisms Ogryzko, 2007; Ogryzko, 2008b). The most of gene expression forbids the transfer of sequential important difference of this concept from regular information from proteins to nucleic acids, erecting a Darwinian mechanism is the inability to separate border between genotype and phenotype and thus variations from selection (borrowing terminology separating heritable variations from selection. from probability theory, in this case the sampling space depends on the conditions of observation, The notion that an individual organism cannot adapt i.e. the state of environment) (Ogryzko, 1997; directly to its environment by changing its genome has Ogryzko, 2008b). Other approaches have also been challenged in the last two decades with the implicated quantum theory in the phenomenon of discovery that the emergence of some mutations in adaptive mutations (Goswami & Todd, 1997; microorganisms depends on their phenotypic McFadden & Al-Khalili, 1999). consequences, i.e., they appear mostly when they are needed for the cell to grow (Cairns et al., 1988; Foster, Despite continuous efforts to explain the 2000; Hall, 1991; Roth et al., 2006). This phenomenon of adaptive mutations by special ‘phenomenon of adaptive mutations’ is more in molecular mechanisms (such as a transient accordance with the views of Lamarck (Lamarck, hypermutable state (Foster, 1998; Hall, 1991), and 1809), who believed that individual organisms have transient gene amplification (Pettersson ME, enough plasticity to contribute directly into the 2005; Roth et al., 2006)), their validity has been evolutionary process. questioned (Seger et al., 2003; Stumpf et al., 2007). Thus, the phenomenon is still very poorly From the physical point of view, life can be considered understood, keeping the chances that the deeper as a particular case of condensed matter (Anderson & understanding of the physics of Life, and quantum Stein, 1987). Bearing with the fact that quantum principles in particular, would be relevant in the mechanics (quantum field theory, in particular) is explanation of this biological phenomenon. In any indispensable for understanding the physics of case, I feel that the study of the Quantum Models condensed matter, many authors, most notably of Adaptive Mutations (QMAMs) has the Schroedinger (Schroedinger, 1944), have suggested potential to develop into a field in its own right that quantum principles have to play a role in the inner and become relevant due to the coming of age of workings of life. An additional reason to believe that quantum information theory and nanotechnology quantum theory will be required, is the ongoing (Nalwa, 2004; Nielsen & Chuang, 2000). Progress progress of ‘omics-‘ and ‘nano-’ technologies in in these fields could ultimately result in the biological sciences, which will eventually lead to a realization of quantum self-reproducing automata. recognition of the limits to how much can be observed The question whether such devices will be able to concerning an individual biological object (e.g., a 'cheat' the Central Dogma of molecular biology single cell) (Ogryzko, 2008a; Ogryzko, 2009). A and evolve in Lamarckian, rather than Darwinian, natural language to take these limits into account could fashion presents an independent interest, be the formalism of quantum theory. regardless of whether the regular 'earth' organisms are 'quantum self-reproducing automata' or not. Intriguingly, in quantum theory, the notions of Also, I hope that the concept of quantum 'ensemble' and 'individual' are interrelated in a subtle adaptation (Ogryzko, 1997), wherein, unlike the because quantum mechanics is a fundamental Darwinian adaptation scheme, the ‘variation’ and theory for description of physical reality, any ‘selection’ steps cannot be separated, could provide a explanation of adaptive mutations (even based on bridge between the physicalist world-view and the ‘straight’ molecular biology) could eventually be notion of values (Ogryzko, 1994), pertinent in described at the fundamental quantum mechanical understanding the phenomenon of intentionality level, whatever the cost and complexity of this (Brentano, 1973; Chalmers, 2002; Stapp, 1999), one of exercise might entail. What sets the QMAMs the crucial subjects of the philosophy of mind. apart is their reliance on characteristic features of the quantum mechanical description of the world, The approach of Goswami starts with introducing the such as entanglement or coherence (Horodecki et concept of consciousness in the description of the cell al., 1996; Ono & Fujikawa, 1998). (Goswami & Todd, 1997), and thus merits a separate discussion outside of the scope of this paper. Here I Both my and McFadden's approaches use the will compare my approach (Ogryzko, 1994; Ogryzko, same general scheme to account for the main 1997; Ogryzko, 2007; Ogryzko, 2008b) with the observation (Figure 1), which will be called approach of McFadden (and Al-Khalili) (McFadden & 'fluctuation trapping' (McFadden & Al-Khalili, Al-Khalili, 1999), which appeared later in the same 2001; Ogryzko, 2007; Ogryzko, 2008b). (a) The journal and then in a book (McFadden, 2000). I system under consideration fluctuates reversibly introduce language of R-error and D-error for the between different states (W and M). In the description of adaptive mutations and show that the absence of the selective substrate (e.g. lactose), first model of McFadden (McFadden & Al-Khalili, the M and W states are indistinguishable by the 1999) cannot be considered as a QMAM. I further environment, and this situation is stable, i.e., not introduce the hypothesis of ‘R-D-error correlation’ and changing with time. (b) The fluctuating state is compare how my and McFadden's approaches fare in destabilized by the application of the selective the context of this hypothesis. I further argue that substrate (lactose),
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