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Quantum biology and human carcinogenesis
BioSystems 178 (2019) 16–24
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Quantum biology and human carcinogenesis
T
Michael Bordonaro Geisinger Commonwealth School of Medicine, 525 Pine Street, Scranton, PA 18509, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Cancer Quantum mechanics Density matrix Decoherence Adaptive mutation Wnt signaling
Quantum-mediated effects have been observed in biological systems. We have previously discussed basis-dependent quantum selection as a mechanism for directed adaptive mutation, a process in which selective pressure specifically induces mutation in those genes involved in the adaptive response. Tumor progression in cancer easily lends itself to the adaptive evolutionary perspective, as the Darwinian combination of heritable variations together with selection of the better proliferating variants are believed to play a major role in multistep carcinogenesis. Adaptive mutation may play a role in carcinogenesis; accordingly, we propose that the principles of quantum biology are involved in directed adaptive mutation processes that promote tumor formation. In this paper, we discuss the intersection between quantum mechanics, biology, adaptive evolution, and cancer, and present general models by which adaptive mutation may influence neoplastic initiation and progression. As a potential theoretical and experimental model, we use colorectal cancer. Our model of “quantum cancer” suggests experiments to evaluate directed adaptive mutation in tumorigenesis, and may have important implications for cancer therapeutics.
1. Directed adaptive mutation: a quantum phenomenon? In this paper, biological mutations are defined as “Darwinian” when they are random, independent of selection pressure. While this definition likely describes most mutations, adaptive mutation may also contribute to genetic variability in changing environments. In adaptive mutation the genetic change does not exist prior to the selective pressure; instead, the presence and type of selection influences the frequency and character of the mutation event. Evidence for adaptive mutation exists for both bacteria and yeast, and possibly for prostate cancer cells; researchers believe that adaptive mutation contributes to the evolution of microbial pathogenesis, cancer, and drug resistance, and may become a focus of novel therapeutic interventions (Bielas et al., 2006; Cairns et al., 1988; Cairns and Foster, 1991; Foster, 2007; Foster and Cairns, 1992; Hall, 1990, 1991a, 1991b, 1992a, 1992b, 1995, 1997, 1998a, 1998b, 1999, 2003; Hara et al., 2005; Karpinets and Foy, 2004, 2005; Karpinets et al., 2006; Kugelberg et al., 2006; Rosenberg, 2001). Thus, this manuscript evaluates the possibility of directed adaptive mutation in carcinogenesis. We distinguish between three types of mutation: (a) random (Darwinian) mutations that are independent of selective pressure; (b) undirected adaptive mutations, which arise when selective pressure induces a general increase in the mutation rate; and (c) directed adaptive mutations, which arise when selective pressures induce targeted mutations that specifically influence the adaptive response. In this paper, we focus on directed adaptive
mutation, mediated by quantum mechanical effects, as a potential factor contributing to carcinogenesis. Similarities exist between adaptive mutation in bacteria or yeast and processes that contribute to the development of cancer. This is particularly true with respect to the evolution of mutation-driven cancer “virulence” during neoplastic progression, as well as the development of resistance to therapy (Hara et al., 2005; Karpinets and Foy, 2004, 2005; Karpinets et al., 2006). While certain cancers exhibit an increase in the frequency of random mutations of several orders of magnitude compared to normal tissue (Bielas et al., 2006), there are examples of human cancers that do not exhibit an increased mutation rate (Hall, 1995). Of interest is the possible role played by adaptive mutation in the development of resistance to the androgen receptor antagonist bicalutamide in prostate cancer cells (Hara et al., 2005). Here, the undirected “mutator phenotype” mechanism has been invoked, with evidence that LNCap prostate cancer cells respond to a bicalutamide challenge by upregulating expression of error-prone DNA polymerases, while downregulating expression of mismatch repair (MMR) proteins, resulting in an overall increased mutation rate (Hara et al., 2005). Several hypotheses have been postulated to explain undirected adaptive mutation. These include: replication and recombination systems, slow repair of mismatched bases, mutagenic transcription, and gene amplification/duplication (reviewed in Rosenberg, 2001). The most cited potential mechanism for undirected adaptive mutation is induction of a transient hypermutagenic “mutator
E-mail address: [email protected]. https://doi.org/10.1016/j.biosystems.2019.01.010 Received 13 December 2018; Received in revised form 21 January 2019; Accepted 25 January 2019 Available online 26 January 2019 0303-2647/ © 2019 Elsevier B.V. All rights reserved.
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labels. Thus, in a theoretical matrix containing ten rows and ten columns, the diagonal elements would be those describing the contents of, e.g., cell of row 1, column 1; cell of row 2, column 2…reaching the cell of row 10, column 10; forming a diagonal set of states. All the other possible cell states (e.g., cell of row x, column not-x) would describe the off-diagonal elements. The diagonal terms correlate with the probability of finding the system in a particular basis state. In contrast, the off-diagonal terms describe interference between different basis states. Thus, the presence of off-diagonal terms means that the system is in superposition relative to the chosen basis (Bordonaro and Ogrzko, 2013). With respect to the density matrix, decoherence refers to disappearance of the off-diagonal terms as the system becomes irreversibly linked to the environment. Given that the states of the system that survive decoherence are the preferred basis states, decoherence must be a basis-dependent phenomenon. For example, a diagonal density matrix can always be described in a different basis, and, if so, off-diagonal terms will reappear, as the original preferred states are represented in the new basis. Therefore, in this new basis, we will observe interference between states (i.e., superposition) and these off-diagonal terms will naturally disappear via the coevolution of the system with its environment (i.e., decoherence). This is of direct relevance to the biological situation of adaption, since a change in basis is analogous to a change in the environment. These events – change in basis, generation of off-diagonal terms in the cellular density matrix, decoherence via coupling to the environment, followed by “collapse” to a defined observed state – can describe the process of a cell’s adaption to a novel environment (Bordonaro and Ogrzko, 2013). Thus, this form of quantum selection is termed “basis-dependent selection” since the preferred states of the system, and the presence or absence of superposition (off-diagonal terms of the density matrix), are dependent upon the chosen basis. The process described above is analogous to the concept of “fluctuation well trapping,” in which a specific quantum state is “captured” or “fixed” through an irreversible interaction with the environment (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013). First, assume that a cell can be in states A1 or A2; each state represents the phenotypic consequences of particular gene sequences. In environment B1, the two states A1 and A2 cannot be distinguished; however, the state of the cell can be represented as a superposition of A1/A2 in anticipation of a change to a new environment B2. In other words, in environment B1 the state of the cell can be viewed as “fluctuating” between the two alternative states A1 or A2. However, in the new environment B2, cell states A1 and A2 can be distinguished, since B2 allows for cells in state A2 to proliferate and undergo clonal cell expansion, while cells in state A1 remain quiescent. The change from a quiescent cell in environment B1 to clonal expansion in environment B2 represents an irreversible change that “traps” cell state A2. Therefore, if several cells were originally in environment B1, after the switch to environment B2 an increasing number of cells with state A2 will be observed, as these are the cells whose state is “trapped” or “fixed” through clonal expansion. If, after the change in environment, cells can be in either state A1 or A2 and if only those cells in state A2 grow, then over time, only cell colonies characterized as state A2 will be observed. There is an essential difference between this scheme and regular Darwinian selection. In adaptive mutation, selection is implicated at two different steps in two different time scales (shorter and longer). First, in our model, selection acts to generate the “virtual population” i.e., the spectrum of different alternatives (i.e., elements of the new basis), that are allowed in the new environment. Second, selection also results in choosing certain “best fit” elements out of this virtual population. The first step corresponds to the shorter time scale, and the second step to the longer time scale, although as we shall see the two steps are in fact inseparable. One way to formalize the interplay between these two modes of selection is the notion of “self-reproduction in imaginary time” (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013). In this description, the two steps of selection process are present,
phenotype,” in which the mutation frequency is increased by up to several orders of magnitude (Foster, 2007; Hall, 1991a; Kugelberg et al., 2006). In contrast, directed adaptive mutation is a process in which selective pressure specifically induces mutation in those genes whose products are responsible for mediating the adaptive response. We propose that directed adaptive mutation is component of the cell’s ability to adapt to a changing environment. This form of targeted adaptive mutation would not be associated with a generalized increase in the mutation rate, and therefore would not exhibit the mutator phenotype. Therefore, alternative mechanisms need to be hypothesized and evaluated to explain directed adaptive mutation. We have proposed a general model of directed adaptive mutation (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013) which is summarized as follows. A directed mutation that enables, e.g., cell growth will occur only (a) in an environment suitable for cell growth, and (b) only after exposure to that specific environment. The same growth-promoting mutation would not occur in an environment that promotes, e.g., cellular quiescence or apoptosis. Therefore, each specific microenvironment would be correlated with a specific set of potential cell states (e.g., wild-type or mutant DNA sequences). These mutations do not occur randomly; instead, the cellular microenvironment selects the possible spectrum of cell states possible in that environment. Subsequently, an irreversible change in the state of the cell (e.g., proliferation or death) establishes the mutant state as that which is observed, “fixing” the cell state as an observable. According to our model, quantum coherence contributes to the development of directed adaptive mutations through a process we call “basisdependent (quantum) selection.” 2. Quantum biology and adaptive mutation: density matrix and fluctuation well trapping Quantum mechanisms may mediate directed adaptive mutation (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013), and may play a role in directed evolution (Melkikh and Khrennikov, 2016). In our basis-dependent model of directed adaptive mutation, biological quantum superposition is context-dependent, and exists only during the change of environmental conditions. Since there is no requirement to maintain quantum coherence for some arbitrary period, past criticisms (Seife, 2000; Tegmark, 2000) of quantum biology (e.g., “biological systems are too warm and complex to maintain quantum coherence”) are not relevant for the specific model proposed here. Further, regardless of how the problem of coherence vs. decoherence is approached in our hypothesis, we note that quantum coherent effects have been observed in biological systems, including systems at room temperature (reviewed in Lambert et al., 2013). However, the role of quantum effects in adaptive mutation has not been established. We will summarize the arguments, made in greater detail previously (Bordonaro and Ogrzko, 2013) for basis-dependent selection, before considering cell death and neoplasia from a quantum biological perspective. The density matrix formalism can be utilized to apply quantum mechanical principles to biological states. The density operator description is most appropriate for biological systems, since such systems are large and complex; further, their environment cannot be exactly controlled, as compared to prepared pure quantum states involving, e.g., individual photons, electrons, protons, neutrons, etc. A density matrix describing a physical system, such as a cell state, can be envisioned, for the sake of simple illustration for the “layman,” as a table with a matching number of rows and columns. The basis of a density matrix represents the alternative states of the system represented by the matrix, and these states label the rows and columns of the density matrix table. The cells of the table can be divided into two categories. First, we term “diagonal elements” those cells in which the labels of the rows and columns are the same. Second, off-diagonal elements” describe those elements in which the rows and columns have different 17
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Fig. 1. Differences between random “Darwninian” (A) and quantum-mediated directed adaptive (B) mutation. (A) Mutations are random and typically pre-exist selective pressure. Cells with different DNA sequences at the relevant allele may have different survival rates in varying environments, which “selects” the most “fit” cell-sequence configuration by favoring its replication. In the figure shown, the “black” cell containing a mutated version of the relevant gene is more able to survive in the particular environment, increasing the frequency of cells containing this DNA sequence. (B) In a quantum-mediated adaptive mutation event, the possible outcomes are directly influenced by the environment. An Operator “X” working on the state space of the system selects possibilities “X” or “not X” as possible outcomes, and the actual outcome of X vs. not X is random. Similarly, a different Operator, “Y,” selects “Y” or “not Y” as possible outcomes and the Y/not Y outcome can be random. Here, “X” and “Y” may represent different gene mutations, and “not X” and “not Y” represent the respective wild-types. Operators are measurables of the system such as proliferation or apoptosis in particular environments. Therefore, in (A), randomness occurs from the beginning of the process, in that the mutational choices for the possible outcomes is random, but the choice of outcome (growth or not) is selected by the environment. In (B), the mutational choice of outcome (X or Y) is selected by the environment, and the outcome of X/not X or Y/not Y is random.
mutation rate, but rather the idea is that the environment determines the potential state space of gene variants (and cell phenotypes) and only those are subject to decoherence and measurement (however defined).
now in the form of an opposition between reproduction in imaginary time versus reproduction in real time. A quiescent cell is described as reproducing in imaginary time, since at this shorter time scale one can neglect exchange with the environment; hence, the intracellular dynamics can be approximated by unitary evolution. Reproduction in real time (e.g., after an adaptive mutation) corresponds to a longer time scale; thus, the switch from the starving cell state to the reproducing cell state can be described as Wick rotation, from imaginary time to real time (which are orthogonal to each other). The nonseparability between the two time scales is manifested by the fact that the conditions of measurement (i.e., what happens in real time) determine how one must represent the state of the cell before the measurement, i.e., while it is “reproducing in imaginary time” Namely, the change to different environmental conditions will lead to the same state of the quiescent cell expanded in a different basis. The basis-dependent superposition is observed as a definitive mutation after a change in the microenvironment allows mutant cells to undergo an irreversible change; e.g., proliferation or apoptosis. The difference between this scheme (described by operator formalism) and Darwinian mutation, is shown in Fig. 1. To summarize, as per basis-dependent selection: the practical manifestation of gene sequence variants is dependent upon the environment. Therefore, we assume an environment in which cells can grow if they have gene variant “X” – a variant that would require mutation (e.g. from base tautomerism due to proton tunneling). In any other environment, cells with gene variant X would not grow. Importantly, many other gene variants would be irrelevant to cell growth in this environment. Cells with gene variant X will be observed only if those cells survive and proliferate. Therefore, cells with X, generated by quantum effects at the gene sequence will be observed, and observed only in the “permissive” environment. If the gene variant does not occur, the cell would not proliferate. The environment “traps” the gene variant – hence, “fluctuation well trapping” – through the physical manifestation of the survival and proliferation of the cell that has that variant. With respect other possible variants, they may not be observed if those variants do not contribute to cell survival. All possible gene variants and consequent cell states reproduce in imaginary time (Bordonaro and Ogrzko, 2013). But only those gene variants that confer an adaptive advantage in a given environment are observed; as reproduction in real time. Otherwise, such cells would not be observed and we would not be able to isolate DNA from the cell with the relevant mutation. The mutation is directed because the production of the adaptive mutation is not due to a non-specific increase in the
3. Base tautomerism A simple example of how quantum mechanical effects can be manifested in adaptive mutation is through base tautomerism (superposition of base isomers), which result in base substitution mutation. For example, given a change in basis (a change in the cellular microenvironment), the density matrix of a cell can contain off-diagonal terms representing interference between cell states in which keto or enol forms of guanine are at a given position in a gene sequence. Enol guanine can base-pair with thymine (or uracil in RNA transcription), introducing mutation. The same principle can occur with, e.g., amino and imino forms of cytosine, with the imino form base-pairing with adenine. If we assume that the mutant gene sequence in question codes for a product that allows for the cell to proliferate in the relevant environmental conditions, adaptive mutants G > A and C > T will be observed. This hypothesis is supported by W.G. Cooper’s analysis of T4 bacteriophage mutation data (Cooper, 2009, 2011; 2012). Cooper identified G and C bases as particularly sensitive to proton tunneling, resulting in a lowest-energy state consisting of a linear combination (i.e., superposition) of G-C isomers (Cooper, 2009, 2011; 2012). PCR analysis, which has been used to probe DNA quantum superposition in vitro (Bieberich, 2000), also supports our proposed mechanism. A study of the effects of primer-template mismatch determined that G-T and C-A mismatches minimally affect PCR amplification efficiency; other types of base pair mismatch diminish amplification to a far greater extent (Stadhouders et al., 2010). This suggests that base tautomerism allows G-T and C-A mismatches to be sufficiently energetically stable to not significantly diminish amplification efficiency. PCR amplification in vitro is analogous to DNA replication and RNA transcription in vivo; Successful PCR amplification is a “potential well” “capturing” base tautomerism (enol G and imino C) that results from the linear combination of G-C isomers (Cooper, 2009, 2011; 2012). These mismatches will result in the G > A and C > T base substitutions that are consistent with our hypothesis (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013) and which were identified by Cooper (Cooper, 2009, 2011; 2012). Importantly, these G > A and C > T base substitutions are represented among mutations leading to colorectal cancer, as will 18
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formalism, the change in environment due to wounding is analogous to a basis transformation. Thus, the old preferred states of the cell before wounding can be expressed in terms of the new basis (post-wounding cell environment), resulting in the appearance of off-diagonal terms. These off-diagonal terms, representing interference between states in the new basis, may include superposition of states leading to uncontrolled cell growth. Decoherence will eliminate these off-diagonal terms, leaving a new set of preferred states for the new basis, including cell states characterized by gene sequence mutations allowing for growth in the absence of contact inhibition (i.e., post-wounding). Fluctuation well trapping will result in the observation of cell growth of those cells containing the appropriate pro-proliferative mutation, as described above. Another issue relevant for oncology is programmed cell death. Although adaptive mutation has traditionally been invoked to explain cell proliferation, we extend the scope of the fluctuation trapping model, applying it to mutations that cause cell death as well (Bordonaro and Ogrzko, 2013). Our main argument is that, like proliferation, cell death is also an irreversible process. Therefore, the mutations that favor cell death could also be a subject of fluctuation well trapping in appropriate environmental conditions. Then, like quantum measurement and adaptation, apoptosis and other cell-death decisions can be also described by operator formalism (Fig. 1). Accordingly, quantum biology predicts that, like mutations beneficial for cell growth, the rate of mutations or epigenetic alterations leading to apoptosis and other forms of cell death can be affected by environmental changes. There are obvious implications for cancer in this scenario, since apoptosis often results from the imbalance in cell cycle regulation that accompanies cancer development. In addition, many anticancer drugs work by inducing apoptosis (and other forms of cell death).
be discussed in Section 5. The generalized theory of basis-dependent selection environment (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013) involves more than just base tautomerism, and extends to all correlations of altered gene expression and associated cellular phenotypes that are constrained by the environment. However, we stress that the findings of Cooper (2009; 2011; 2012) and Brieberich (2000) clearly establish a physical mechanism for the generation of gene variants underlying basis-dependent selection (i.e., proton tunneling leading to superposition of isomers, resulting in mutation via base tautomerism). Therefore, even if other proposed mechanisms require validation, already established mechanisms would minimally provide the physical basis for the proposed hypothetical mechanism. 4. Carcinogenesis and mutation, general considerations Cancer can be understood as an adaptation process. It therefore comes as no surprise that the “Darwinian” mechanism (i.e., natural selection of randomly generated mutations) has been applied to the description of tumor progression (Nowak et al., 2002; Gatenby and Vincent, 2003; Kimmel, 2010). However, the possibility of adaptive mutation in carcinogenesis should also be considered. It has long been established that multiple mutations contribute to the development of cancer. This notion was first formulated in Knudson’s “two hit hypothesis” (Knudson, 1971), and later it has been argued that the typical cancer contains at least four (Loeb, 1991) or five (Stein, 1991) driver gene mutations facilitating tumor growth. Moreover, a significant portion of human cancers likely contain more than nine relevant driver mutations (Hollstein et al., 1991). The usual expectation is that these mutations and their selection occur in a consecutive manner. However, it has never experimentally confirmed whether two pertinent values: (a) the levels of “fitness” increase, caused by the mutation, and (b) the costs of selection, required for the “adaptive” changes to be fixed in the heterogeneous population of cancer cells, match the reality met in the confines of a host organism. Thus, a potential problem with multistep carcinogenesis is that the odds that all the multiple mutations will occur in the same lineage is low, and in theory, tumors should never be detected (Hall, 1995; Loeb, 1991; Stein, 1991). Of course, an additional factor that could be at work in multistep carcinogenesis is enhanced mutation rates, i.e., the early mutations that occur in human cancers result in a mutator phenotype (Loeb, 1991; Jackson and Loeb, 1998). However, there are examples of human cancers that do not exhibit an increased mutation rate (reviewed in Hall, 1995). The strict Darwinian scheme of multistep carcinogenesis may be putting too many requirements on the possible mutation rates, selection pressures and cell generation numbers required to explain tumor appearance and subsequent progression. On the other hand, quantum selectionism proposes more subtle links between cell variability and selection conditions (Fig. 1), and does not pose such strict constraints on the values of these parameters. With respect to basis-dependent selection and fluctuation welltrapping, one intriguing potential model to explore is the effect of wounding on tumor promotion. For example, there is an association between wounding and the mobilization of hair stem cells in carcinogenesis (Wong and Reiter, 2011). One simple model whereby wounding can induce cancer would be through the loss of contact inhibition, which would normally repress uncontrolled cell growth and prevent the amplification of certain virtual pro-proliferative mutations. Assuming a “quantum selectionist” mechanism for mutation generation, wounding would remove the constraint of contact inhibition, allowing for the amplification of mutations through the clonal expansion of cells possessing the relevant mutation (Fig. 2). In relation to the model discussed in Section 2, the loss of contact inhibition due to wounding represents the shift from an environment not permissive for cell growth (E1) to one that allows for cell growth in the presence of the appropriate cell state (E2). Using the density matrix
5. Colorectal cancer as a model We consider colorectal cancer as a particularly useful model for the analysis of the adaptive mutation-cancer paradigm, since this disease is predominantly derived from well characterized mutations in defined cell signaling pathways. In addition, both neoplasia and prevention are influenced by specific changes in the cellular environment, such as diet (reviewed in Bordonaro et al., 2008; Lazarova and Bordonaro, 2012). Most cases of colorectal cancer are initiated by mutations in the Wnt signaling pathway, resulting in deregulated Wnt activity (Korinek et al., 1997). The most common Wnt pathway mutation is of the APC gene. Truncated APC proteins are no longer capable of efficiently repressing the levels of transcriptionally active beta-catenin, resulting in deregulated Wnt signaling. Thus, inappropriate constitutive Wnt signaling, within a specific range of transcriptional activity, results in neoplasia (Albuquerque et al., 2002; Korinek et al., 1997). Many mutations in APC have been characterized. A typical spectrum of APC mutations (point mutations, deletions, and insertions) was observed in The Netherlands Cohort Study (Luchtenborg et al., 2004); a total of 978 mutations were detected in 665 sporadic CRC patients. Of these gene abnormalities, 833 were point mutations, 126 were deletions, and 19 were insertions. Among the point mutations, the large majority were transitions, with G > A and C > T being particularly well represented; this is consistent with the quantum mechanical analysis of T4 bacteriophage mutation data (Cooper, 2009, 2011, 2012), and fits with a basis-dependent quantum selection method influencing base tautomerism (Bordonaro and Ogrzko, 2013). An interesting and useful feature of APC mutations is the broad spectrum of the phenotypic consequences that they can have. Mutations resulting in very high levels of Wnt activity induce programmed cell death rather than uncontrolled proliferation, while APC mutations that result in moderate levels of Wnt activity drive proliferation and neoplastic transformation (Albuquerque et al., 2002). Further, treatment of Wnt positive neoplastic cells with histone deacetylase inhibitors such as butyrate, a breakdown product of dietary fiber, hyperactivate Wnt 19
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Fig. 2. Contact inhibition and the amplification of virtual mutants in cancer. (A) An example of general carcinogenesis induced by an environmental trigger such as loss of contact inhibition. At left, there is a wild-type cell “WT” and three examples of cells with virtual mutations associated with the ability for continuous, uncontrolled proliferation. With maintenance of contact inhibition (top), the mutations cannot be amplified, since the environment will not allow clonal expansion. However, with wounding, wound healing, and the loss of contact inhibition (bottom), clonal expansion can occur, resulting in amplification of mutations allowing uncontrolled growth. Neoplasia results, and this can be viewed as an “adaptive mutation” to the wound environment. (B) For large bowel neoplasia, there can be several virtual mutations of the APC gene, one of which (black filled circle) results in a moderate level of Wnt signaling consistent with uncontrolled proliferation. Thus, mutation can be amplified via clonal expansion of the cellular microenvironment allows for proliferation of cells containing this mutation. Examples can include inflammatory bowel disease, dietary changes, mutations in other signaling pathways, etc. Only in particular environmental contexts are specific pro-proliferative virtual mutations amplified and observed; “induced” or adaptive mutation leading to carcinogenesis.
density matrix formalism (Fig. 4), analogous to our general model of directed adaptive mutation as a quantum biological phenomenon (Bordonaro and Ogrzko, 2013). cancer well trapping model. (A) In Environment 1 (Basis 1), no cell growth is possible regardless of the mutational state of the relevant gene; here represented by APC. The environment therefore cannot distinguish between the wild-type and mutant APC states, which, with their associated cell types, can remain in superposition in this basis. The “mutation well” is irrelevant in this environment. (B) A change to Environment 2 (Basis 2) produces a situation that allows outgrowth of “black” cells containing the “correct” APC mutation that allows cell growth. The environment therefore allows us to distinguish different APC gene sequences and their associated states. Cells that randomly happen to have their DNA sequence in the correct APC format will grow, amplifying and fixing the mutation/mutated cell phenotype. In other cells, the APC gene (and cell phenotype) will remain in superposition and each time the gene sequence/phenotype is in the “correct” configuration, this configuration will be “trapped” in the “mutation well” by cell outgrowth and amplification/fixation of the mutation/ mutated cell phenotype. Building upon Fig. 4, and using a density matrix model for illustration, we start with a situation in which the colonic cells exhibit a set of preferred states in one given environment E0; thus we have a diagonalized matrix (mixture of states with no superposition:
activity and induce apoptosis (Bordonaro et al., 1999, 2007; Lazarova et al., 2004). Therefore, definite correlations have been documented between the type of APC mutation, levels of Wnt activity, environmental factors, and the physiological outcome for the colonic cell (Lazarova and Bordonaro, 2012). The “just right” hypothesis of APC mutation in colorectal cancer (Albuquerque et al., 2002) is particularly intriguing considering the possibilities for adaptive mutation in neoplasia. This hypothesis starts with the fact that there is a spectrum of possible mutation states (including deletion) for the two APC alleles of a given cell. Each set of APC sequence combinations is associated with associated phenotypic outcomes in specific potential cellular microenvironments. The neoplastic “read-out” of “just right” mutation is deregulated cell proliferation, fixing the mutations as the adaptive response through clonal expansion of the cell containing the mutations. Quantum-mediated adaptive mutation is particularly relevant for explaining the “just right” distribution of the mutation hit of the second APC allele. Thus, in our model, the characteristics of the original APC mutation contributes to the overall cell state that influence the induction of the “correct” mutation of the second allele. A related example considers the role of tyrosine 654 phosphorylation of beta-catenin on Wnt signaling and intestinal tumorigenesis (van Veelen et al., 2011). Activation of receptor tyrosine kinases (RTKs) by overexpression, mutation, or growth factor release in the cellular microenvironment results in tyrosine 654 phosphorylation of beta-catenin, enhancing Wnt signaling and potentiating intestinal tumorigenesis (van Veelen et al., 2011). Importantly, tyrosine 654 phosphorylation of beta-catenin can synergize with APC mutation to enhance intestinal tumorigenesis; this likely occurs by increasing Wnt activity within the range of pro-proliferative levels of Wnt signaling. Therefore, the presence of activated RTKs, in the context of a cellular milieu favoring cell growth as an adaptive outcome, may favor (or “induce”) specific sets of pro-proliferative APC mutations, above and beyond what would be expected from random Darwinian processes. However, in another cellular microenvironment, one in which uncontrolled growth is not an optimal adaptive outcome for cell, the presence of activated RTKs would not favor pro-proliferative APC mutations, but may favor genetic changes correlated to, e.g., quiescence or apoptosis. Therefore, quantum-mediated APC mutation can be viewed as analogous to fluctuation well trapping (Fig. 3). We can also represent the process of quantum-mediated adaptive APC mutation using the
ρ= 1/2 |Σ1 > < Σ1 | + 1/2 |Σ2 > < Σ2 | = 1/2
(10 01)
The preferred states here can represent APC gene sequences and associated cell phenotypes (e.g., normal regulation of Wnt signaling and normal regulation of cell proliferation). If the cells are placed in a pro-proliferative and carcinogenic environment E1, then the old preferred states have to be written in the basis of this new environment; thus:
( )
ρ= 1/ √2 |Ψ > < Ψ | = 1/2 1 1 1 1
We now have off-diagonal terms representing superpositions, as the cells are exploring the state space in this new environment. We can consider these off-diagonal terms to be superpositions of APC gene variant states (physically generated e.g., by quantum proton tunneling leading to base tautomerism) and correlated states of the cell. Decoherence then eliminates the off-diagonal terms, thus: 20
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Fig. 3. A cancer well trapping model. (A) In Environment 1 (Basis 1), no cell growth is possible regardless of the mutational state of the relevant gene; here represented by APC. The environment therefore cannot distinguish between the wildtype and mutant APC states, which, with their associated cell types, can remain in superposition in this basis. The “mutation well” is irrelevant in this environment. (B) A change to Environment 2 (Basis 2) produces a situation that allows outgrowth of “black” cells containing the “correct” APC mutation that allows cell growth. The environment therefore allows us to distinguish different APC gene sequences and their associated states. Cells that randomly happen to have their DNA sequence in the correct APC format will grow, amplifying and fixing the mutation/mutated cell phenotype. In other cells, the APC gene (and cell phenotype) will remain in superposition and each time the gene sequence/phenotype is in the “correct” configuration, this configuration will be “trapped” in the “mutation well” by cell outgrowth and amplification/fixation of the mutation/mutated cell phenotype.
Fig. 4. Basis-dependent selection of APC mutations. (A) Top left. Colonic cell in environment E0 represented by a diagonal density matrix showing preferred cell states with particular DNA sequences (D). E0 can be considered an environment that does not promote either cell growth or cell death. Right. To describe the adaption of the cell to new environment E1, we represent the same state shown in top left in the basis of preferred state of environment E1 (top right) or E2 (bottom right). E1 is an environment that promotes cell growth, while E2 is an environment that promotes cell death. Note that representing the original state in the new basis for E1 or for E2 results in off-diagonal terms in the cellular density matrix, which represent interference between basis states. For E1, the old states are written in terms of the cell growth basis, with terms representing cell states with APC gene sequences that may be associated with cell growth (AGn). For E2, the old states can be written in terms of the cell death basis, with terms representing cell states with APC gene sequences that may be associated with cell death (ADn). Despite the fact that the original state can be represented in a new basis, it remains stable as long as the cell is in E0. (B) Top and bottom. After the cell is placed in the new environment E1 or E2, decoherence results in the disappearance of the off-diagonal terms. We are left with the preferred states of the new basis for E1 (cell growth) or E2 (cell death). (C) The collapse (reduction) chooses one of the states (far right). This can lead to uncontrolled cell growth resulting from an APC mutation characterized by moderate levels of Wnt signaling (|Ψ >) in E1 or an APC mutation resulting in apoptosis due to extremely high levels of Wnt signaling in E2 (|Φ >).
ρ= 1/2 |Ψ1 > < Ψ1 | + 1/2 |Ψ2 > < Ψ2 | = 1/2
(10 01)
Decoherence would lead to a mixed state, with pro-apoptotic APC gene variants:
So, in the new environment E1 we have new preferred states of the APC gene, which can be compatible with unregulated Wnt signaling and cell growth. After “measurement” we have one observed state, which can be a neoplastic cell with a growth-inducing APC gene variant:
ρ= 1 |Ψ > < Ψ | =
ρ= 1/2 |Φ1 > < Φ1 | + 1/2 |Φ2 > < Φ2 | = 1/2
(10 01)
Finally, in the end, we observe an apoptotic cell with an APC gene variant and Wnt signaling consistent with apoptosis:
ρ= 1|Φ > < Φ| =
(10 00)
(10 00)
The broad spectrum of various APC mutations, observed in colon cancer, and the variety of documented outcomes from their interaction with different environmental (or intracellular conditions), may prove to be a fertile resource for experimental systems used to detect the appearance of mutations in a directed/adaptive fashion, causing either cell proliferation or apoptosis. We would like to emphasize a crucial
What if the cells was placed in environment E2 instead, an environnement more conducive to apoptosis? We would then write the original preferred basis states in the new basis thus:
( )
ρ= 1/ √2 |Φ > < Φ| = 1/2 1 1 1 1
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same mutation occurs in a context that cannot lead to cell proliferation (e.g., absence of growth factor/ligand). If the frequency of the mutation is higher in the first instance, this would suggest a contribution of directed adaptive mutation. Potential experimental scenarios involving colorectal cancer could focus on APC mutation (first constraint) and alterations in the environment (second constraint; e.g., presence of HDACis, chemotherapeutic agents, cell crowding/growth factor depletion, etc.) that would change the adaptive fitness of varying APC gene sequence-Wnt signaling correlations. One could then evaluate the frequencies of different forms of APC sequence alterations according to “Darwinian” or adaptive mutation models, using the general scheme described above. Second, for apoptosis-inducing mutations, the technical challenge is to determine their frequency, given that the cells are not expected to survive, i.e., cannot be selected for further analysis. Here, one can take advantage of the fact that dead cells lyse and release their DNA to the supernatant. Therefore, one should be able to measure the rate of appearance of such mutations by quantitative PCR (specific for the mutation) by analyzing DNA purified from the conditioned cell medium. In parallel, one could also measure the presence of such mutations in the DNA of remaining living cells. By adding the two frequencies together, one can estimate the overall frequency of mutations in one type of environmental conditions (those that trap mutations causing cell death, e.g., B2). The next step would be to compare this mutation frequency with the value obtained in the same manner from the same cells, but in the environmental conditions (e.g., B1) that do not favor pro-apoptotic mutations. If the fluctuation trapping paradigm holds for pro-apoptotic mutations, one would expect the mutation frequency to be higher in the former set of environmental conditions, as compared to the latter set of conditions that reflect the baseline of random mutation. With respect to the evaluation of pro-proliferative vs. pro-apoptotic mutations associated with cancer, a starting point would be APC mutations, which can influence Wnt signaling, depending upon context, to a degree consistent with either proliferation or apoptosis Albuquerque et al., 2002; Bordonaro et al., 2008). Environmental conditions influencing the neoplastic process in conjunction with mutation include, but are not limited to: dietary factors (such as butyrate), autocrine and/or paracrine growth factors, inflammation, contact inhibition or the lack thereof, exposure to carcinogens, and changes in gene expression due to genetic and/or epigenetic changes of other genes, in the relevant cell or in surrounding cells. With its potential to change dramatically our view on cancer, it is intriguing to ask what new possibilities Quantum Biology would suggest for cancer management? For example, given the more direct connection between environment and genetic changes than is granted by the Darwinian perspective, could there be more possibilities to modulate and affect the outcomes of cellular “proliferation or quiescence or death” decisions? Could, for example, by choosing a “correct” environment, cells be more directly guided towards less tumorigenic outcomes? Could in other words, mutations leading to cancer be prevented by modulating the environment? Or, if these mutations have already happened, could we force these cells to undergo apoptosis by inducing additional mutations or other changes? To the extent that adaptive mutation plays a role in mammalian cell physiology and in carcinogenesis (which needs to be empirically determined), altering cell phenotype through such mechanisms would be a rapid and direct approach to achieve therapeutic objectives, in addition to the slower processes involving selection of pre-existing random mutations. An estimation of the relative quantitative contribution of adaptive mutation mechanism would be essential to predict the efficacy of such approaches. The new perspective brought by the adaptive mutations mechanism could also force us to reevaluate certain drug-based therapeutic anticancer strategies. The fluctuation well trapping model requires that cells have sufficient time to explore the space of possibilities (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013). Thus, to prevent such a
point. Spontaneous, random mutations that occur independently of changes in the environment and selective pressures (“Darwinian”) will always remain an important source of genetic variation contributing to carcinogenesis. What we propose is that in addition to standard, classical mechanisms, adaptive mutation may also play a role, particularly in those cases in which a mutation can cause a radical alteration in cell fate in a rapidly changing environment. Therefore, a combination of “Darwinian” and adaptive mutation may contribute to the highly complex and multi-variable nature of biological systems. To summarize: the APC example underscores the utility of colorectal cancer as a model system for consideration of adaptive mutation in neoplasia. Notably, the same concepts can be eventually applied to virtually any other cancer characterized by well-defined mutations that allow adaptive advantages in certain cellular microenvironments. It is likely that as we learn more about neoplasia, and the heterogeneity of cell types within the tumor, as well as the role of selective pressures in initiation, progression, and metastasis, other examples similar to the APC model will come to our attention. Therefore, the task is to understand: first, whether the adaptive mutations phenomenon exists; and second, what could be its quantitative contribution, compared to the standard Darwinian mechanism. 6. Experimental approaches and implications for prevention/ treatment In this section, we will describe some potential experimental models to test the predictions of Quantum Biology in the field of oncology. They mostly concern the evaluation of adaptive mutations in the context of cell proliferation or apoptosis. We will describe a general experimental scheme to accomplish this task. First, by performing a fluctuation test (reviewed in Rosenberg, 2001), it should be possible to determine whether a genetic variation A was generated in the cell population before the application of selective conditions B1. If a deviation from the Luria-Delbruck distribution is observed, the next task is to rule out as a mechanism increased mutational variability (e.g., mutator phenotype) due to the stress induced by selection condition B1. The cells should be left for a prescribed amount of time in a condition B2 that does not allow proliferation even if the mutation A has occurred. The accumulation of the mutation A in these conditions can be monitored directly by DNA extraction, PCR analysis, and sequencing. Second, like the basis-dependent selection and welltrapping scheme outlined in Section 2, we can formalize an experimental approach in terms of two conditions that constrain cell growth. The first constraint (“A”) is associated with the state of a gene (or an epigenetic variation) that we would like to follow; and it is lifted when a mutation occurs (A1 transforms to A2) and thus cells start to proliferate. The second condition (“B”) corresponds to the state of the cell environment that constraints the cell growth regardless of whether the constraint A is lifted or not. We assume that environment B1 will not allow cell growth regardless of the cell state, while environment B2 will allow growth of state A2. Thus, only one combination of states A and B (namely, A2 + B2) can lead to cell proliferation. A general model to evaluate basis-dependent selection in non-neoplastic, non-human mammalian cells, using proliferation of mouse embryonic fibroblast cells, was previously outlined (Bordonaro et al., 2014). How one can apply this experimental design more specifically to the oncology context and do so in a manner generally applicable to different cell states, including apoptosis? We will therefore briefly review what could be done for two types of relevant mutations in human cancer cells: proliferation-inducing and cell death-inducing mutations. First, the mutation that corresponds to the transition from A1 to A2 could be an activation of an oncogene or inactivation of a tumor suppressor gene, and it would allow for cell proliferation in certain conditions, but not in others. The state of environment B2 could be presence of some exogenous factor, such as a growth factor and/or cell signaling ligand. This scenario can be compared to that in which the 22
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mechanism from occurring, it would be important to use cytotoxic methods to kill cells quickly. This is because drugs that induce cell-cycle arrest or other, slower-acting anti-cancer cell treatments would be more conducive to counter-productive adaptive mutation for resistance. Further, many preventative approaches, including some dietary interventions, are relatively slow-acting and, therefore, would likely be more prone to the appearance of adaptive mutations for resistance. Conversely, using adaptive mutation through the fluctuation well trapping model to promote clinically favorable mutations (e.g., ones causing differentiation and/or apoptosis) is better achieved through longerduration treatments and exposures that would allow cells to explore the adaptive possibilities. This is a “double-edged sword” in that the same conditions that allow for “negative” adaptive mutation would also be best for “positive,” clinically helpful, adaptive mutation. This balance between positive vs. negative adaptive mutation underscores the importance of selecting the proper environments and treatment regimens to irreversibly trap the helpful outcomes, without creating the context in which cellular exploration of clinically negative outcomes is favored.
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7. Conclusion There is an urgent need to understand whether directed adaptive mutation plays a role in carcinogenesis as well as in the development of resistance to anticancer therapies. This can have significant implications for cancer prevention and treatment. In fact, the directed adaptive mutation paradigm may be particularly relevant for cancer, a disease characterized by correlations between environmental factors, genetic changes in defined signaling pathways, and fundamental phenotypic outcomes. In addition to theory, we present a general outline of experiments to observe adaptive mutation events in mammalian cells, and further describe how these approaches could be applied to human cancer. Potential discoveries derived from such experiments will lead to methodologically more challenging biophysical studies aimed at directly identifying quantum mechanical processes involved in adaptive mutation and tumorigenesis. Ultimately, this knowledge can be used to more effectively prevent, diagnose, and/or treat cancer and other human disorders. Funding This work was supported by The Geisinger Commonwealth School of Medicine. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Acknowledgements Dr. Vasily Ogryzko made important contributions to the ideas underlying this work; unfortunately, Dr. Ogryzko passed away while this manuscript was in its earliest draft phases. The completed manuscript is dedicated to his memory. References Albuquerque, C., Breukel, C., van der Luijt, Fidalgo P., Lage, P., Slors, F.G.M., Leitao, C.N., Fodde, R., Smits, R., 2002. The just-right signaling model: APC somatic mutations are selected based on a special level of activation of the beta-catenin signaling cascade. Hum. Mol. Genet. 11, 1549–1560. Bieberich, E., 2000. Probing quantum coherence in a biological system by means of DNA amplification. Biosystems 57, 109–124. Bielas, J.H., Loeb, K.R., Rubin, B.P., True, L.D., Loeb, L.A., 2006. Human cancers express a mutator phenotype. Proc. Natl. Acad. Sci. U. S. A. 103, 18238–18242. Bordonaro, M., Ogrzko, V., 2013. Quantum Biology at the cellular level-elements of the research program. Biosystems 112, 11–30. Bordonaro, M., Mariadason, J.M., Aslam, F., Heerdt, B.G., Augenlicht, L.H., 1999. Butyrate-induced apoptotic cascade in colonic carcinoma cells: modulation of the beta-catenin-Tcf pathway and concordance with effects if sulindac and trichostatin A but not curcumin. Cell Growth Differ. 11, 713–720. Bordonaro, M., Lazarova, D.L., Sartorelli, A.C., 2007. The activation of beta-catenin by Wnt signaling mediates the effects of histone deacetylase inhibitors. Exp. Cell Res.
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Contents lists available at ScienceDirect
BioSystems journal homepage: www.elsevier.com/locate/biosystems
Quantum biology and human carcinogenesis
T
Michael Bordonaro Geisinger Commonwealth School of Medicine, 525 Pine Street, Scranton, PA 18509, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Cancer Quantum mechanics Density matrix Decoherence Adaptive mutation Wnt signaling
Quantum-mediated effects have been observed in biological systems. We have previously discussed basis-dependent quantum selection as a mechanism for directed adaptive mutation, a process in which selective pressure specifically induces mutation in those genes involved in the adaptive response. Tumor progression in cancer easily lends itself to the adaptive evolutionary perspective, as the Darwinian combination of heritable variations together with selection of the better proliferating variants are believed to play a major role in multistep carcinogenesis. Adaptive mutation may play a role in carcinogenesis; accordingly, we propose that the principles of quantum biology are involved in directed adaptive mutation processes that promote tumor formation. In this paper, we discuss the intersection between quantum mechanics, biology, adaptive evolution, and cancer, and present general models by which adaptive mutation may influence neoplastic initiation and progression. As a potential theoretical and experimental model, we use colorectal cancer. Our model of “quantum cancer” suggests experiments to evaluate directed adaptive mutation in tumorigenesis, and may have important implications for cancer therapeutics.
1. Directed adaptive mutation: a quantum phenomenon? In this paper, biological mutations are defined as “Darwinian” when they are random, independent of selection pressure. While this definition likely describes most mutations, adaptive mutation may also contribute to genetic variability in changing environments. In adaptive mutation the genetic change does not exist prior to the selective pressure; instead, the presence and type of selection influences the frequency and character of the mutation event. Evidence for adaptive mutation exists for both bacteria and yeast, and possibly for prostate cancer cells; researchers believe that adaptive mutation contributes to the evolution of microbial pathogenesis, cancer, and drug resistance, and may become a focus of novel therapeutic interventions (Bielas et al., 2006; Cairns et al., 1988; Cairns and Foster, 1991; Foster, 2007; Foster and Cairns, 1992; Hall, 1990, 1991a, 1991b, 1992a, 1992b, 1995, 1997, 1998a, 1998b, 1999, 2003; Hara et al., 2005; Karpinets and Foy, 2004, 2005; Karpinets et al., 2006; Kugelberg et al., 2006; Rosenberg, 2001). Thus, this manuscript evaluates the possibility of directed adaptive mutation in carcinogenesis. We distinguish between three types of mutation: (a) random (Darwinian) mutations that are independent of selective pressure; (b) undirected adaptive mutations, which arise when selective pressure induces a general increase in the mutation rate; and (c) directed adaptive mutations, which arise when selective pressures induce targeted mutations that specifically influence the adaptive response. In this paper, we focus on directed adaptive
mutation, mediated by quantum mechanical effects, as a potential factor contributing to carcinogenesis. Similarities exist between adaptive mutation in bacteria or yeast and processes that contribute to the development of cancer. This is particularly true with respect to the evolution of mutation-driven cancer “virulence” during neoplastic progression, as well as the development of resistance to therapy (Hara et al., 2005; Karpinets and Foy, 2004, 2005; Karpinets et al., 2006). While certain cancers exhibit an increase in the frequency of random mutations of several orders of magnitude compared to normal tissue (Bielas et al., 2006), there are examples of human cancers that do not exhibit an increased mutation rate (Hall, 1995). Of interest is the possible role played by adaptive mutation in the development of resistance to the androgen receptor antagonist bicalutamide in prostate cancer cells (Hara et al., 2005). Here, the undirected “mutator phenotype” mechanism has been invoked, with evidence that LNCap prostate cancer cells respond to a bicalutamide challenge by upregulating expression of error-prone DNA polymerases, while downregulating expression of mismatch repair (MMR) proteins, resulting in an overall increased mutation rate (Hara et al., 2005). Several hypotheses have been postulated to explain undirected adaptive mutation. These include: replication and recombination systems, slow repair of mismatched bases, mutagenic transcription, and gene amplification/duplication (reviewed in Rosenberg, 2001). The most cited potential mechanism for undirected adaptive mutation is induction of a transient hypermutagenic “mutator
E-mail address: [email protected]. https://doi.org/10.1016/j.biosystems.2019.01.010 Received 13 December 2018; Received in revised form 21 January 2019; Accepted 25 January 2019 Available online 26 January 2019 0303-2647/ © 2019 Elsevier B.V. All rights reserved.
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labels. Thus, in a theoretical matrix containing ten rows and ten columns, the diagonal elements would be those describing the contents of, e.g., cell of row 1, column 1; cell of row 2, column 2…reaching the cell of row 10, column 10; forming a diagonal set of states. All the other possible cell states (e.g., cell of row x, column not-x) would describe the off-diagonal elements. The diagonal terms correlate with the probability of finding the system in a particular basis state. In contrast, the off-diagonal terms describe interference between different basis states. Thus, the presence of off-diagonal terms means that the system is in superposition relative to the chosen basis (Bordonaro and Ogrzko, 2013). With respect to the density matrix, decoherence refers to disappearance of the off-diagonal terms as the system becomes irreversibly linked to the environment. Given that the states of the system that survive decoherence are the preferred basis states, decoherence must be a basis-dependent phenomenon. For example, a diagonal density matrix can always be described in a different basis, and, if so, off-diagonal terms will reappear, as the original preferred states are represented in the new basis. Therefore, in this new basis, we will observe interference between states (i.e., superposition) and these off-diagonal terms will naturally disappear via the coevolution of the system with its environment (i.e., decoherence). This is of direct relevance to the biological situation of adaption, since a change in basis is analogous to a change in the environment. These events – change in basis, generation of off-diagonal terms in the cellular density matrix, decoherence via coupling to the environment, followed by “collapse” to a defined observed state – can describe the process of a cell’s adaption to a novel environment (Bordonaro and Ogrzko, 2013). Thus, this form of quantum selection is termed “basis-dependent selection” since the preferred states of the system, and the presence or absence of superposition (off-diagonal terms of the density matrix), are dependent upon the chosen basis. The process described above is analogous to the concept of “fluctuation well trapping,” in which a specific quantum state is “captured” or “fixed” through an irreversible interaction with the environment (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013). First, assume that a cell can be in states A1 or A2; each state represents the phenotypic consequences of particular gene sequences. In environment B1, the two states A1 and A2 cannot be distinguished; however, the state of the cell can be represented as a superposition of A1/A2 in anticipation of a change to a new environment B2. In other words, in environment B1 the state of the cell can be viewed as “fluctuating” between the two alternative states A1 or A2. However, in the new environment B2, cell states A1 and A2 can be distinguished, since B2 allows for cells in state A2 to proliferate and undergo clonal cell expansion, while cells in state A1 remain quiescent. The change from a quiescent cell in environment B1 to clonal expansion in environment B2 represents an irreversible change that “traps” cell state A2. Therefore, if several cells were originally in environment B1, after the switch to environment B2 an increasing number of cells with state A2 will be observed, as these are the cells whose state is “trapped” or “fixed” through clonal expansion. If, after the change in environment, cells can be in either state A1 or A2 and if only those cells in state A2 grow, then over time, only cell colonies characterized as state A2 will be observed. There is an essential difference between this scheme and regular Darwinian selection. In adaptive mutation, selection is implicated at two different steps in two different time scales (shorter and longer). First, in our model, selection acts to generate the “virtual population” i.e., the spectrum of different alternatives (i.e., elements of the new basis), that are allowed in the new environment. Second, selection also results in choosing certain “best fit” elements out of this virtual population. The first step corresponds to the shorter time scale, and the second step to the longer time scale, although as we shall see the two steps are in fact inseparable. One way to formalize the interplay between these two modes of selection is the notion of “self-reproduction in imaginary time” (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013). In this description, the two steps of selection process are present,
phenotype,” in which the mutation frequency is increased by up to several orders of magnitude (Foster, 2007; Hall, 1991a; Kugelberg et al., 2006). In contrast, directed adaptive mutation is a process in which selective pressure specifically induces mutation in those genes whose products are responsible for mediating the adaptive response. We propose that directed adaptive mutation is component of the cell’s ability to adapt to a changing environment. This form of targeted adaptive mutation would not be associated with a generalized increase in the mutation rate, and therefore would not exhibit the mutator phenotype. Therefore, alternative mechanisms need to be hypothesized and evaluated to explain directed adaptive mutation. We have proposed a general model of directed adaptive mutation (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013) which is summarized as follows. A directed mutation that enables, e.g., cell growth will occur only (a) in an environment suitable for cell growth, and (b) only after exposure to that specific environment. The same growth-promoting mutation would not occur in an environment that promotes, e.g., cellular quiescence or apoptosis. Therefore, each specific microenvironment would be correlated with a specific set of potential cell states (e.g., wild-type or mutant DNA sequences). These mutations do not occur randomly; instead, the cellular microenvironment selects the possible spectrum of cell states possible in that environment. Subsequently, an irreversible change in the state of the cell (e.g., proliferation or death) establishes the mutant state as that which is observed, “fixing” the cell state as an observable. According to our model, quantum coherence contributes to the development of directed adaptive mutations through a process we call “basisdependent (quantum) selection.” 2. Quantum biology and adaptive mutation: density matrix and fluctuation well trapping Quantum mechanisms may mediate directed adaptive mutation (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013), and may play a role in directed evolution (Melkikh and Khrennikov, 2016). In our basis-dependent model of directed adaptive mutation, biological quantum superposition is context-dependent, and exists only during the change of environmental conditions. Since there is no requirement to maintain quantum coherence for some arbitrary period, past criticisms (Seife, 2000; Tegmark, 2000) of quantum biology (e.g., “biological systems are too warm and complex to maintain quantum coherence”) are not relevant for the specific model proposed here. Further, regardless of how the problem of coherence vs. decoherence is approached in our hypothesis, we note that quantum coherent effects have been observed in biological systems, including systems at room temperature (reviewed in Lambert et al., 2013). However, the role of quantum effects in adaptive mutation has not been established. We will summarize the arguments, made in greater detail previously (Bordonaro and Ogrzko, 2013) for basis-dependent selection, before considering cell death and neoplasia from a quantum biological perspective. The density matrix formalism can be utilized to apply quantum mechanical principles to biological states. The density operator description is most appropriate for biological systems, since such systems are large and complex; further, their environment cannot be exactly controlled, as compared to prepared pure quantum states involving, e.g., individual photons, electrons, protons, neutrons, etc. A density matrix describing a physical system, such as a cell state, can be envisioned, for the sake of simple illustration for the “layman,” as a table with a matching number of rows and columns. The basis of a density matrix represents the alternative states of the system represented by the matrix, and these states label the rows and columns of the density matrix table. The cells of the table can be divided into two categories. First, we term “diagonal elements” those cells in which the labels of the rows and columns are the same. Second, off-diagonal elements” describe those elements in which the rows and columns have different 17
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Fig. 1. Differences between random “Darwninian” (A) and quantum-mediated directed adaptive (B) mutation. (A) Mutations are random and typically pre-exist selective pressure. Cells with different DNA sequences at the relevant allele may have different survival rates in varying environments, which “selects” the most “fit” cell-sequence configuration by favoring its replication. In the figure shown, the “black” cell containing a mutated version of the relevant gene is more able to survive in the particular environment, increasing the frequency of cells containing this DNA sequence. (B) In a quantum-mediated adaptive mutation event, the possible outcomes are directly influenced by the environment. An Operator “X” working on the state space of the system selects possibilities “X” or “not X” as possible outcomes, and the actual outcome of X vs. not X is random. Similarly, a different Operator, “Y,” selects “Y” or “not Y” as possible outcomes and the Y/not Y outcome can be random. Here, “X” and “Y” may represent different gene mutations, and “not X” and “not Y” represent the respective wild-types. Operators are measurables of the system such as proliferation or apoptosis in particular environments. Therefore, in (A), randomness occurs from the beginning of the process, in that the mutational choices for the possible outcomes is random, but the choice of outcome (growth or not) is selected by the environment. In (B), the mutational choice of outcome (X or Y) is selected by the environment, and the outcome of X/not X or Y/not Y is random.
mutation rate, but rather the idea is that the environment determines the potential state space of gene variants (and cell phenotypes) and only those are subject to decoherence and measurement (however defined).
now in the form of an opposition between reproduction in imaginary time versus reproduction in real time. A quiescent cell is described as reproducing in imaginary time, since at this shorter time scale one can neglect exchange with the environment; hence, the intracellular dynamics can be approximated by unitary evolution. Reproduction in real time (e.g., after an adaptive mutation) corresponds to a longer time scale; thus, the switch from the starving cell state to the reproducing cell state can be described as Wick rotation, from imaginary time to real time (which are orthogonal to each other). The nonseparability between the two time scales is manifested by the fact that the conditions of measurement (i.e., what happens in real time) determine how one must represent the state of the cell before the measurement, i.e., while it is “reproducing in imaginary time” Namely, the change to different environmental conditions will lead to the same state of the quiescent cell expanded in a different basis. The basis-dependent superposition is observed as a definitive mutation after a change in the microenvironment allows mutant cells to undergo an irreversible change; e.g., proliferation or apoptosis. The difference between this scheme (described by operator formalism) and Darwinian mutation, is shown in Fig. 1. To summarize, as per basis-dependent selection: the practical manifestation of gene sequence variants is dependent upon the environment. Therefore, we assume an environment in which cells can grow if they have gene variant “X” – a variant that would require mutation (e.g. from base tautomerism due to proton tunneling). In any other environment, cells with gene variant X would not grow. Importantly, many other gene variants would be irrelevant to cell growth in this environment. Cells with gene variant X will be observed only if those cells survive and proliferate. Therefore, cells with X, generated by quantum effects at the gene sequence will be observed, and observed only in the “permissive” environment. If the gene variant does not occur, the cell would not proliferate. The environment “traps” the gene variant – hence, “fluctuation well trapping” – through the physical manifestation of the survival and proliferation of the cell that has that variant. With respect other possible variants, they may not be observed if those variants do not contribute to cell survival. All possible gene variants and consequent cell states reproduce in imaginary time (Bordonaro and Ogrzko, 2013). But only those gene variants that confer an adaptive advantage in a given environment are observed; as reproduction in real time. Otherwise, such cells would not be observed and we would not be able to isolate DNA from the cell with the relevant mutation. The mutation is directed because the production of the adaptive mutation is not due to a non-specific increase in the
3. Base tautomerism A simple example of how quantum mechanical effects can be manifested in adaptive mutation is through base tautomerism (superposition of base isomers), which result in base substitution mutation. For example, given a change in basis (a change in the cellular microenvironment), the density matrix of a cell can contain off-diagonal terms representing interference between cell states in which keto or enol forms of guanine are at a given position in a gene sequence. Enol guanine can base-pair with thymine (or uracil in RNA transcription), introducing mutation. The same principle can occur with, e.g., amino and imino forms of cytosine, with the imino form base-pairing with adenine. If we assume that the mutant gene sequence in question codes for a product that allows for the cell to proliferate in the relevant environmental conditions, adaptive mutants G > A and C > T will be observed. This hypothesis is supported by W.G. Cooper’s analysis of T4 bacteriophage mutation data (Cooper, 2009, 2011; 2012). Cooper identified G and C bases as particularly sensitive to proton tunneling, resulting in a lowest-energy state consisting of a linear combination (i.e., superposition) of G-C isomers (Cooper, 2009, 2011; 2012). PCR analysis, which has been used to probe DNA quantum superposition in vitro (Bieberich, 2000), also supports our proposed mechanism. A study of the effects of primer-template mismatch determined that G-T and C-A mismatches minimally affect PCR amplification efficiency; other types of base pair mismatch diminish amplification to a far greater extent (Stadhouders et al., 2010). This suggests that base tautomerism allows G-T and C-A mismatches to be sufficiently energetically stable to not significantly diminish amplification efficiency. PCR amplification in vitro is analogous to DNA replication and RNA transcription in vivo; Successful PCR amplification is a “potential well” “capturing” base tautomerism (enol G and imino C) that results from the linear combination of G-C isomers (Cooper, 2009, 2011; 2012). These mismatches will result in the G > A and C > T base substitutions that are consistent with our hypothesis (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013) and which were identified by Cooper (Cooper, 2009, 2011; 2012). Importantly, these G > A and C > T base substitutions are represented among mutations leading to colorectal cancer, as will 18
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formalism, the change in environment due to wounding is analogous to a basis transformation. Thus, the old preferred states of the cell before wounding can be expressed in terms of the new basis (post-wounding cell environment), resulting in the appearance of off-diagonal terms. These off-diagonal terms, representing interference between states in the new basis, may include superposition of states leading to uncontrolled cell growth. Decoherence will eliminate these off-diagonal terms, leaving a new set of preferred states for the new basis, including cell states characterized by gene sequence mutations allowing for growth in the absence of contact inhibition (i.e., post-wounding). Fluctuation well trapping will result in the observation of cell growth of those cells containing the appropriate pro-proliferative mutation, as described above. Another issue relevant for oncology is programmed cell death. Although adaptive mutation has traditionally been invoked to explain cell proliferation, we extend the scope of the fluctuation trapping model, applying it to mutations that cause cell death as well (Bordonaro and Ogrzko, 2013). Our main argument is that, like proliferation, cell death is also an irreversible process. Therefore, the mutations that favor cell death could also be a subject of fluctuation well trapping in appropriate environmental conditions. Then, like quantum measurement and adaptation, apoptosis and other cell-death decisions can be also described by operator formalism (Fig. 1). Accordingly, quantum biology predicts that, like mutations beneficial for cell growth, the rate of mutations or epigenetic alterations leading to apoptosis and other forms of cell death can be affected by environmental changes. There are obvious implications for cancer in this scenario, since apoptosis often results from the imbalance in cell cycle regulation that accompanies cancer development. In addition, many anticancer drugs work by inducing apoptosis (and other forms of cell death).
be discussed in Section 5. The generalized theory of basis-dependent selection environment (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013) involves more than just base tautomerism, and extends to all correlations of altered gene expression and associated cellular phenotypes that are constrained by the environment. However, we stress that the findings of Cooper (2009; 2011; 2012) and Brieberich (2000) clearly establish a physical mechanism for the generation of gene variants underlying basis-dependent selection (i.e., proton tunneling leading to superposition of isomers, resulting in mutation via base tautomerism). Therefore, even if other proposed mechanisms require validation, already established mechanisms would minimally provide the physical basis for the proposed hypothetical mechanism. 4. Carcinogenesis and mutation, general considerations Cancer can be understood as an adaptation process. It therefore comes as no surprise that the “Darwinian” mechanism (i.e., natural selection of randomly generated mutations) has been applied to the description of tumor progression (Nowak et al., 2002; Gatenby and Vincent, 2003; Kimmel, 2010). However, the possibility of adaptive mutation in carcinogenesis should also be considered. It has long been established that multiple mutations contribute to the development of cancer. This notion was first formulated in Knudson’s “two hit hypothesis” (Knudson, 1971), and later it has been argued that the typical cancer contains at least four (Loeb, 1991) or five (Stein, 1991) driver gene mutations facilitating tumor growth. Moreover, a significant portion of human cancers likely contain more than nine relevant driver mutations (Hollstein et al., 1991). The usual expectation is that these mutations and their selection occur in a consecutive manner. However, it has never experimentally confirmed whether two pertinent values: (a) the levels of “fitness” increase, caused by the mutation, and (b) the costs of selection, required for the “adaptive” changes to be fixed in the heterogeneous population of cancer cells, match the reality met in the confines of a host organism. Thus, a potential problem with multistep carcinogenesis is that the odds that all the multiple mutations will occur in the same lineage is low, and in theory, tumors should never be detected (Hall, 1995; Loeb, 1991; Stein, 1991). Of course, an additional factor that could be at work in multistep carcinogenesis is enhanced mutation rates, i.e., the early mutations that occur in human cancers result in a mutator phenotype (Loeb, 1991; Jackson and Loeb, 1998). However, there are examples of human cancers that do not exhibit an increased mutation rate (reviewed in Hall, 1995). The strict Darwinian scheme of multistep carcinogenesis may be putting too many requirements on the possible mutation rates, selection pressures and cell generation numbers required to explain tumor appearance and subsequent progression. On the other hand, quantum selectionism proposes more subtle links between cell variability and selection conditions (Fig. 1), and does not pose such strict constraints on the values of these parameters. With respect to basis-dependent selection and fluctuation welltrapping, one intriguing potential model to explore is the effect of wounding on tumor promotion. For example, there is an association between wounding and the mobilization of hair stem cells in carcinogenesis (Wong and Reiter, 2011). One simple model whereby wounding can induce cancer would be through the loss of contact inhibition, which would normally repress uncontrolled cell growth and prevent the amplification of certain virtual pro-proliferative mutations. Assuming a “quantum selectionist” mechanism for mutation generation, wounding would remove the constraint of contact inhibition, allowing for the amplification of mutations through the clonal expansion of cells possessing the relevant mutation (Fig. 2). In relation to the model discussed in Section 2, the loss of contact inhibition due to wounding represents the shift from an environment not permissive for cell growth (E1) to one that allows for cell growth in the presence of the appropriate cell state (E2). Using the density matrix
5. Colorectal cancer as a model We consider colorectal cancer as a particularly useful model for the analysis of the adaptive mutation-cancer paradigm, since this disease is predominantly derived from well characterized mutations in defined cell signaling pathways. In addition, both neoplasia and prevention are influenced by specific changes in the cellular environment, such as diet (reviewed in Bordonaro et al., 2008; Lazarova and Bordonaro, 2012). Most cases of colorectal cancer are initiated by mutations in the Wnt signaling pathway, resulting in deregulated Wnt activity (Korinek et al., 1997). The most common Wnt pathway mutation is of the APC gene. Truncated APC proteins are no longer capable of efficiently repressing the levels of transcriptionally active beta-catenin, resulting in deregulated Wnt signaling. Thus, inappropriate constitutive Wnt signaling, within a specific range of transcriptional activity, results in neoplasia (Albuquerque et al., 2002; Korinek et al., 1997). Many mutations in APC have been characterized. A typical spectrum of APC mutations (point mutations, deletions, and insertions) was observed in The Netherlands Cohort Study (Luchtenborg et al., 2004); a total of 978 mutations were detected in 665 sporadic CRC patients. Of these gene abnormalities, 833 were point mutations, 126 were deletions, and 19 were insertions. Among the point mutations, the large majority were transitions, with G > A and C > T being particularly well represented; this is consistent with the quantum mechanical analysis of T4 bacteriophage mutation data (Cooper, 2009, 2011, 2012), and fits with a basis-dependent quantum selection method influencing base tautomerism (Bordonaro and Ogrzko, 2013). An interesting and useful feature of APC mutations is the broad spectrum of the phenotypic consequences that they can have. Mutations resulting in very high levels of Wnt activity induce programmed cell death rather than uncontrolled proliferation, while APC mutations that result in moderate levels of Wnt activity drive proliferation and neoplastic transformation (Albuquerque et al., 2002). Further, treatment of Wnt positive neoplastic cells with histone deacetylase inhibitors such as butyrate, a breakdown product of dietary fiber, hyperactivate Wnt 19
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Fig. 2. Contact inhibition and the amplification of virtual mutants in cancer. (A) An example of general carcinogenesis induced by an environmental trigger such as loss of contact inhibition. At left, there is a wild-type cell “WT” and three examples of cells with virtual mutations associated with the ability for continuous, uncontrolled proliferation. With maintenance of contact inhibition (top), the mutations cannot be amplified, since the environment will not allow clonal expansion. However, with wounding, wound healing, and the loss of contact inhibition (bottom), clonal expansion can occur, resulting in amplification of mutations allowing uncontrolled growth. Neoplasia results, and this can be viewed as an “adaptive mutation” to the wound environment. (B) For large bowel neoplasia, there can be several virtual mutations of the APC gene, one of which (black filled circle) results in a moderate level of Wnt signaling consistent with uncontrolled proliferation. Thus, mutation can be amplified via clonal expansion of the cellular microenvironment allows for proliferation of cells containing this mutation. Examples can include inflammatory bowel disease, dietary changes, mutations in other signaling pathways, etc. Only in particular environmental contexts are specific pro-proliferative virtual mutations amplified and observed; “induced” or adaptive mutation leading to carcinogenesis.
density matrix formalism (Fig. 4), analogous to our general model of directed adaptive mutation as a quantum biological phenomenon (Bordonaro and Ogrzko, 2013). cancer well trapping model. (A) In Environment 1 (Basis 1), no cell growth is possible regardless of the mutational state of the relevant gene; here represented by APC. The environment therefore cannot distinguish between the wild-type and mutant APC states, which, with their associated cell types, can remain in superposition in this basis. The “mutation well” is irrelevant in this environment. (B) A change to Environment 2 (Basis 2) produces a situation that allows outgrowth of “black” cells containing the “correct” APC mutation that allows cell growth. The environment therefore allows us to distinguish different APC gene sequences and their associated states. Cells that randomly happen to have their DNA sequence in the correct APC format will grow, amplifying and fixing the mutation/mutated cell phenotype. In other cells, the APC gene (and cell phenotype) will remain in superposition and each time the gene sequence/phenotype is in the “correct” configuration, this configuration will be “trapped” in the “mutation well” by cell outgrowth and amplification/fixation of the mutation/ mutated cell phenotype. Building upon Fig. 4, and using a density matrix model for illustration, we start with a situation in which the colonic cells exhibit a set of preferred states in one given environment E0; thus we have a diagonalized matrix (mixture of states with no superposition:
activity and induce apoptosis (Bordonaro et al., 1999, 2007; Lazarova et al., 2004). Therefore, definite correlations have been documented between the type of APC mutation, levels of Wnt activity, environmental factors, and the physiological outcome for the colonic cell (Lazarova and Bordonaro, 2012). The “just right” hypothesis of APC mutation in colorectal cancer (Albuquerque et al., 2002) is particularly intriguing considering the possibilities for adaptive mutation in neoplasia. This hypothesis starts with the fact that there is a spectrum of possible mutation states (including deletion) for the two APC alleles of a given cell. Each set of APC sequence combinations is associated with associated phenotypic outcomes in specific potential cellular microenvironments. The neoplastic “read-out” of “just right” mutation is deregulated cell proliferation, fixing the mutations as the adaptive response through clonal expansion of the cell containing the mutations. Quantum-mediated adaptive mutation is particularly relevant for explaining the “just right” distribution of the mutation hit of the second APC allele. Thus, in our model, the characteristics of the original APC mutation contributes to the overall cell state that influence the induction of the “correct” mutation of the second allele. A related example considers the role of tyrosine 654 phosphorylation of beta-catenin on Wnt signaling and intestinal tumorigenesis (van Veelen et al., 2011). Activation of receptor tyrosine kinases (RTKs) by overexpression, mutation, or growth factor release in the cellular microenvironment results in tyrosine 654 phosphorylation of beta-catenin, enhancing Wnt signaling and potentiating intestinal tumorigenesis (van Veelen et al., 2011). Importantly, tyrosine 654 phosphorylation of beta-catenin can synergize with APC mutation to enhance intestinal tumorigenesis; this likely occurs by increasing Wnt activity within the range of pro-proliferative levels of Wnt signaling. Therefore, the presence of activated RTKs, in the context of a cellular milieu favoring cell growth as an adaptive outcome, may favor (or “induce”) specific sets of pro-proliferative APC mutations, above and beyond what would be expected from random Darwinian processes. However, in another cellular microenvironment, one in which uncontrolled growth is not an optimal adaptive outcome for cell, the presence of activated RTKs would not favor pro-proliferative APC mutations, but may favor genetic changes correlated to, e.g., quiescence or apoptosis. Therefore, quantum-mediated APC mutation can be viewed as analogous to fluctuation well trapping (Fig. 3). We can also represent the process of quantum-mediated adaptive APC mutation using the
ρ= 1/2 |Σ1 > < Σ1 | + 1/2 |Σ2 > < Σ2 | = 1/2
(10 01)
The preferred states here can represent APC gene sequences and associated cell phenotypes (e.g., normal regulation of Wnt signaling and normal regulation of cell proliferation). If the cells are placed in a pro-proliferative and carcinogenic environment E1, then the old preferred states have to be written in the basis of this new environment; thus:
( )
ρ= 1/ √2 |Ψ > < Ψ | = 1/2 1 1 1 1
We now have off-diagonal terms representing superpositions, as the cells are exploring the state space in this new environment. We can consider these off-diagonal terms to be superpositions of APC gene variant states (physically generated e.g., by quantum proton tunneling leading to base tautomerism) and correlated states of the cell. Decoherence then eliminates the off-diagonal terms, thus: 20
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Fig. 3. A cancer well trapping model. (A) In Environment 1 (Basis 1), no cell growth is possible regardless of the mutational state of the relevant gene; here represented by APC. The environment therefore cannot distinguish between the wildtype and mutant APC states, which, with their associated cell types, can remain in superposition in this basis. The “mutation well” is irrelevant in this environment. (B) A change to Environment 2 (Basis 2) produces a situation that allows outgrowth of “black” cells containing the “correct” APC mutation that allows cell growth. The environment therefore allows us to distinguish different APC gene sequences and their associated states. Cells that randomly happen to have their DNA sequence in the correct APC format will grow, amplifying and fixing the mutation/mutated cell phenotype. In other cells, the APC gene (and cell phenotype) will remain in superposition and each time the gene sequence/phenotype is in the “correct” configuration, this configuration will be “trapped” in the “mutation well” by cell outgrowth and amplification/fixation of the mutation/mutated cell phenotype.
Fig. 4. Basis-dependent selection of APC mutations. (A) Top left. Colonic cell in environment E0 represented by a diagonal density matrix showing preferred cell states with particular DNA sequences (D). E0 can be considered an environment that does not promote either cell growth or cell death. Right. To describe the adaption of the cell to new environment E1, we represent the same state shown in top left in the basis of preferred state of environment E1 (top right) or E2 (bottom right). E1 is an environment that promotes cell growth, while E2 is an environment that promotes cell death. Note that representing the original state in the new basis for E1 or for E2 results in off-diagonal terms in the cellular density matrix, which represent interference between basis states. For E1, the old states are written in terms of the cell growth basis, with terms representing cell states with APC gene sequences that may be associated with cell growth (AGn). For E2, the old states can be written in terms of the cell death basis, with terms representing cell states with APC gene sequences that may be associated with cell death (ADn). Despite the fact that the original state can be represented in a new basis, it remains stable as long as the cell is in E0. (B) Top and bottom. After the cell is placed in the new environment E1 or E2, decoherence results in the disappearance of the off-diagonal terms. We are left with the preferred states of the new basis for E1 (cell growth) or E2 (cell death). (C) The collapse (reduction) chooses one of the states (far right). This can lead to uncontrolled cell growth resulting from an APC mutation characterized by moderate levels of Wnt signaling (|Ψ >) in E1 or an APC mutation resulting in apoptosis due to extremely high levels of Wnt signaling in E2 (|Φ >).
ρ= 1/2 |Ψ1 > < Ψ1 | + 1/2 |Ψ2 > < Ψ2 | = 1/2
(10 01)
Decoherence would lead to a mixed state, with pro-apoptotic APC gene variants:
So, in the new environment E1 we have new preferred states of the APC gene, which can be compatible with unregulated Wnt signaling and cell growth. After “measurement” we have one observed state, which can be a neoplastic cell with a growth-inducing APC gene variant:
ρ= 1 |Ψ > < Ψ | =
ρ= 1/2 |Φ1 > < Φ1 | + 1/2 |Φ2 > < Φ2 | = 1/2
(10 01)
Finally, in the end, we observe an apoptotic cell with an APC gene variant and Wnt signaling consistent with apoptosis:
ρ= 1|Φ > < Φ| =
(10 00)
(10 00)
The broad spectrum of various APC mutations, observed in colon cancer, and the variety of documented outcomes from their interaction with different environmental (or intracellular conditions), may prove to be a fertile resource for experimental systems used to detect the appearance of mutations in a directed/adaptive fashion, causing either cell proliferation or apoptosis. We would like to emphasize a crucial
What if the cells was placed in environment E2 instead, an environnement more conducive to apoptosis? We would then write the original preferred basis states in the new basis thus:
( )
ρ= 1/ √2 |Φ > < Φ| = 1/2 1 1 1 1
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same mutation occurs in a context that cannot lead to cell proliferation (e.g., absence of growth factor/ligand). If the frequency of the mutation is higher in the first instance, this would suggest a contribution of directed adaptive mutation. Potential experimental scenarios involving colorectal cancer could focus on APC mutation (first constraint) and alterations in the environment (second constraint; e.g., presence of HDACis, chemotherapeutic agents, cell crowding/growth factor depletion, etc.) that would change the adaptive fitness of varying APC gene sequence-Wnt signaling correlations. One could then evaluate the frequencies of different forms of APC sequence alterations according to “Darwinian” or adaptive mutation models, using the general scheme described above. Second, for apoptosis-inducing mutations, the technical challenge is to determine their frequency, given that the cells are not expected to survive, i.e., cannot be selected for further analysis. Here, one can take advantage of the fact that dead cells lyse and release their DNA to the supernatant. Therefore, one should be able to measure the rate of appearance of such mutations by quantitative PCR (specific for the mutation) by analyzing DNA purified from the conditioned cell medium. In parallel, one could also measure the presence of such mutations in the DNA of remaining living cells. By adding the two frequencies together, one can estimate the overall frequency of mutations in one type of environmental conditions (those that trap mutations causing cell death, e.g., B2). The next step would be to compare this mutation frequency with the value obtained in the same manner from the same cells, but in the environmental conditions (e.g., B1) that do not favor pro-apoptotic mutations. If the fluctuation trapping paradigm holds for pro-apoptotic mutations, one would expect the mutation frequency to be higher in the former set of environmental conditions, as compared to the latter set of conditions that reflect the baseline of random mutation. With respect to the evaluation of pro-proliferative vs. pro-apoptotic mutations associated with cancer, a starting point would be APC mutations, which can influence Wnt signaling, depending upon context, to a degree consistent with either proliferation or apoptosis Albuquerque et al., 2002; Bordonaro et al., 2008). Environmental conditions influencing the neoplastic process in conjunction with mutation include, but are not limited to: dietary factors (such as butyrate), autocrine and/or paracrine growth factors, inflammation, contact inhibition or the lack thereof, exposure to carcinogens, and changes in gene expression due to genetic and/or epigenetic changes of other genes, in the relevant cell or in surrounding cells. With its potential to change dramatically our view on cancer, it is intriguing to ask what new possibilities Quantum Biology would suggest for cancer management? For example, given the more direct connection between environment and genetic changes than is granted by the Darwinian perspective, could there be more possibilities to modulate and affect the outcomes of cellular “proliferation or quiescence or death” decisions? Could, for example, by choosing a “correct” environment, cells be more directly guided towards less tumorigenic outcomes? Could in other words, mutations leading to cancer be prevented by modulating the environment? Or, if these mutations have already happened, could we force these cells to undergo apoptosis by inducing additional mutations or other changes? To the extent that adaptive mutation plays a role in mammalian cell physiology and in carcinogenesis (which needs to be empirically determined), altering cell phenotype through such mechanisms would be a rapid and direct approach to achieve therapeutic objectives, in addition to the slower processes involving selection of pre-existing random mutations. An estimation of the relative quantitative contribution of adaptive mutation mechanism would be essential to predict the efficacy of such approaches. The new perspective brought by the adaptive mutations mechanism could also force us to reevaluate certain drug-based therapeutic anticancer strategies. The fluctuation well trapping model requires that cells have sufficient time to explore the space of possibilities (Ogryzko, 1997, 2008; Bordonaro and Ogrzko, 2013). Thus, to prevent such a
point. Spontaneous, random mutations that occur independently of changes in the environment and selective pressures (“Darwinian”) will always remain an important source of genetic variation contributing to carcinogenesis. What we propose is that in addition to standard, classical mechanisms, adaptive mutation may also play a role, particularly in those cases in which a mutation can cause a radical alteration in cell fate in a rapidly changing environment. Therefore, a combination of “Darwinian” and adaptive mutation may contribute to the highly complex and multi-variable nature of biological systems. To summarize: the APC example underscores the utility of colorectal cancer as a model system for consideration of adaptive mutation in neoplasia. Notably, the same concepts can be eventually applied to virtually any other cancer characterized by well-defined mutations that allow adaptive advantages in certain cellular microenvironments. It is likely that as we learn more about neoplasia, and the heterogeneity of cell types within the tumor, as well as the role of selective pressures in initiation, progression, and metastasis, other examples similar to the APC model will come to our attention. Therefore, the task is to understand: first, whether the adaptive mutations phenomenon exists; and second, what could be its quantitative contribution, compared to the standard Darwinian mechanism. 6. Experimental approaches and implications for prevention/ treatment In this section, we will describe some potential experimental models to test the predictions of Quantum Biology in the field of oncology. They mostly concern the evaluation of adaptive mutations in the context of cell proliferation or apoptosis. We will describe a general experimental scheme to accomplish this task. First, by performing a fluctuation test (reviewed in Rosenberg, 2001), it should be possible to determine whether a genetic variation A was generated in the cell population before the application of selective conditions B1. If a deviation from the Luria-Delbruck distribution is observed, the next task is to rule out as a mechanism increased mutational variability (e.g., mutator phenotype) due to the stress induced by selection condition B1. The cells should be left for a prescribed amount of time in a condition B2 that does not allow proliferation even if the mutation A has occurred. The accumulation of the mutation A in these conditions can be monitored directly by DNA extraction, PCR analysis, and sequencing. Second, like the basis-dependent selection and welltrapping scheme outlined in Section 2, we can formalize an experimental approach in terms of two conditions that constrain cell growth. The first constraint (“A”) is associated with the state of a gene (or an epigenetic variation) that we would like to follow; and it is lifted when a mutation occurs (A1 transforms to A2) and thus cells start to proliferate. The second condition (“B”) corresponds to the state of the cell environment that constraints the cell growth regardless of whether the constraint A is lifted or not. We assume that environment B1 will not allow cell growth regardless of the cell state, while environment B2 will allow growth of state A2. Thus, only one combination of states A and B (namely, A2 + B2) can lead to cell proliferation. A general model to evaluate basis-dependent selection in non-neoplastic, non-human mammalian cells, using proliferation of mouse embryonic fibroblast cells, was previously outlined (Bordonaro et al., 2014). How one can apply this experimental design more specifically to the oncology context and do so in a manner generally applicable to different cell states, including apoptosis? We will therefore briefly review what could be done for two types of relevant mutations in human cancer cells: proliferation-inducing and cell death-inducing mutations. First, the mutation that corresponds to the transition from A1 to A2 could be an activation of an oncogene or inactivation of a tumor suppressor gene, and it would allow for cell proliferation in certain conditions, but not in others. The state of environment B2 could be presence of some exogenous factor, such as a growth factor and/or cell signaling ligand. This scenario can be compared to that in which the 22
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mechanism from occurring, it would be important to use cytotoxic methods to kill cells quickly. This is because drugs that induce cell-cycle arrest or other, slower-acting anti-cancer cell treatments would be more conducive to counter-productive adaptive mutation for resistance. Further, many preventative approaches, including some dietary interventions, are relatively slow-acting and, therefore, would likely be more prone to the appearance of adaptive mutations for resistance. Conversely, using adaptive mutation through the fluctuation well trapping model to promote clinically favorable mutations (e.g., ones causing differentiation and/or apoptosis) is better achieved through longerduration treatments and exposures that would allow cells to explore the adaptive possibilities. This is a “double-edged sword” in that the same conditions that allow for “negative” adaptive mutation would also be best for “positive,” clinically helpful, adaptive mutation. This balance between positive vs. negative adaptive mutation underscores the importance of selecting the proper environments and treatment regimens to irreversibly trap the helpful outcomes, without creating the context in which cellular exploration of clinically negative outcomes is favored.
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7. Conclusion There is an urgent need to understand whether directed adaptive mutation plays a role in carcinogenesis as well as in the development of resistance to anticancer therapies. This can have significant implications for cancer prevention and treatment. In fact, the directed adaptive mutation paradigm may be particularly relevant for cancer, a disease characterized by correlations between environmental factors, genetic changes in defined signaling pathways, and fundamental phenotypic outcomes. In addition to theory, we present a general outline of experiments to observe adaptive mutation events in mammalian cells, and further describe how these approaches could be applied to human cancer. Potential discoveries derived from such experiments will lead to methodologically more challenging biophysical studies aimed at directly identifying quantum mechanical processes involved in adaptive mutation and tumorigenesis. Ultimately, this knowledge can be used to more effectively prevent, diagnose, and/or treat cancer and other human disorders. Funding This work was supported by The Geisinger Commonwealth School of Medicine. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Acknowledgements Dr. Vasily Ogryzko made important contributions to the ideas underlying this work; unfortunately, Dr. Ogryzko passed away while this manuscript was in its earliest draft phases. The completed manuscript is dedicated to his memory. References Albuquerque, C., Breukel, C., van der Luijt, Fidalgo P., Lage, P., Slors, F.G.M., Leitao, C.N., Fodde, R., Smits, R., 2002. The just-right signaling model: APC somatic mutations are selected based on a special level of activation of the beta-catenin signaling cascade. Hum. Mol. Genet. 11, 1549–1560. Bieberich, E., 2000. Probing quantum coherence in a biological system by means of DNA amplification. Biosystems 57, 109–124. Bielas, J.H., Loeb, K.R., Rubin, B.P., True, L.D., Loeb, L.A., 2006. Human cancers express a mutator phenotype. Proc. Natl. Acad. Sci. U. S. A. 103, 18238–18242. Bordonaro, M., Ogrzko, V., 2013. Quantum Biology at the cellular level-elements of the research program. Biosystems 112, 11–30. Bordonaro, M., Mariadason, J.M., Aslam, F., Heerdt, B.G., Augenlicht, L.H., 1999. Butyrate-induced apoptotic cascade in colonic carcinoma cells: modulation of the beta-catenin-Tcf pathway and concordance with effects if sulindac and trichostatin A but not curcumin. Cell Growth Differ. 11, 713–720. Bordonaro, M., Lazarova, D.L., Sartorelli, A.C., 2007. The activation of beta-catenin by Wnt signaling mediates the effects of histone deacetylase inhibitors. Exp. Cell Res.
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