A quantum mechanical model of adaptive mutation

Advantages of two quantum programming platforms in quantum computing and quantum chemistry

Quantum computing is at the forefront of technological advancement and has the potential to revolutionize various fields, including quantum chemistry. Choosing an appropriate quantum programming language becomes critical as quantum education and research increase. In this paper, we comprehensively compare two leading quantum programming languages, Qiskit and PennyLane, focusing on their suitability for teaching and research. We delve into their basic and advanced usage, examine their learning curves, and evaluate their capabilities in quantum computing experiments. We also demonstrate using a quantum programming language to build a half adder and a machine learning model. Our study reveals that each language has distinct advantages. While PennyLane excels in research applications due to its flexibility to adjust parameters in detail and access multiple sources of real quantum devices, Qiskit stands out in education because of its web-based graphical user interface and smaller code size. The codes and the dataset used in the studies are available at https://github.com/wangpeihua1231/quantum-programming-platform .

A Metric for the Entropic Purpose of a System

Purpose in systems is considered to be beyond the purview of science since it is thought to be intrinsically personal. However, just as Claude Shannon was able to define an impersonal measure of information, so we formally define the (impersonal) 'entropic purpose' of an information system (using the theoretical apparatus of Quantitative Geometrical Thermodynamics) as the line integral of an entropic "purposive" Lagrangian defined in hyperbolic space across the complex temporal plane. We verify that this Lagrangian is well-formed: it has the appropriate variational (Euler-Lagrange) behaviour. We also discuss the teleological characteristics of such variational behaviour (featuring both thermodynamically reversible and irreversible temporal measures), so that a "Principle of Least (entropic) Purpose" can be adduced for any information-producing system. We show that entropic purpose is (approximately) identified with the information created by the system: an empirically measurable quantity. Exploiting the relationship between the entropy production of a system and its energy Hamiltonian, we also show how Landauer's principle also applies to the creation of information; any purposive system that creates information will also dissipate energy. Finally, we discuss how 'entropic purpose' might be applied in artificial intelligence contexts (where degrees of system 'aliveness' need to be assessed), and in cybersecurity (where this metric for 'entropic purpose' might be exploited to help distinguish between people and bots).

Understanding cancer from a biophysical, developmental and systems biology perspective using the landscapes-attractor model

Biophysical, developmental and systems-biology considerations enable deeper understanding why cancer is life threatening despite intensive research. Here we use two metaphors. Both conceive the cell genome and the encoded molecular system as an interacting gene regulatory network (GRN). According to Waddington's epigenetic (quasi-potential)-landscape, an instrumental tool in ontogenetics, individual interaction patterns ( = expression profiles) within this GRN represent possible cell states with different stabilities. Network interactions with low stability are represented on peaks. Unstable interactions strive towards regions with higher stability located at lower altitude in valleys termed attractors that correspond to stable cell phenotypes. Cancer cells are seen as GRNs adopting aberrant semi-stable attractor states (cancer attractor). In the second metaphor, Wright's phylogenetic fitness (adaptive) landscape, each genome ( = GRN) is assigned a specific position in the landscape according to its structure and reproductive fitness in the specific environment. High elevation signifies high fitness and low altitude low fitness. Selection ensures that mutant GRNs evolve and move from valleys to peaks. The genetic flexibility is highlighted in the fitness landscape, while non-genetic flexibility is captured in the quasi-potential landscape. These models resolve several inconsistencies that have puzzled cancer researchers, such as the fact that phenotypes generated by non-genetic mechanisms coexist in a single tumor with phenotypes caused by mutations and they mitigate conflicts between cancer theories that claim cancer is caused by mutation (somatic mutation theory) or by disruption of tissue architecture (tissue organization field theory). Nevertheless, spontaneous mutations play key roles in cancer. Remarkable, fundamental natural laws such as the second law of thermodynamics and quantum mechanics state that mutations are inevitable events. The good side of this is that without mutational variability in DNA, evolutionary development would not have occurred, but its bad side is that the occurrence of cancer is essentially inevitable. In summary, both landscapes together fully describe the behavior of cancer under normal and stressful conditions such as chemotherapy. Thus, the landscapes-attractor model fully describes cancer cell behavior and offers new perspectives for future treatment.

Tunnelling of electrons via the neighboring atom

As compared to the intuitive process that the electron emits straight to the continuum from its parent ion, there is an alternative route that the electron may transfer to and be trapped by a neighboring ionic core before the eventual release. Here, we demonstrate that electron tunnelling via the neighboring atomic core is a pronounced process in light-induced tunnelling ionization of molecules by absorbing multiple near-infrared photons. We devised a site-resolved tunnelling experiment using an Ar-Kr+ ion as a prototype system to track the electron tunnelling dynamics from the Ar atom towards the neighboring Kr+ by monitoring its transverse momentum distribution, which is temporally captured into the resonant excited states of the Ar-Kr+ before its eventual releasing. The influence of the Coulomb potential of neighboring ionic cores promises new insights into the understanding and controlling of tunnelling dynamics in complex molecules or environment.

Environment assisted quantum model for studying RNA-DNA-error correlation created due to the base tautomery

The adaptive mutation phenomenon has been drawing the attention of biologists for several decades in evolutionist community. In this study, we propose a quantum mechanical model of adaptive mutation based on the implications of the theory of open quantum systems. We survey a new framework that explain how random point mutations can be stabilized and directed to be adapted with the stresses introduced by the environments according to the microscopic rules dictated by constraints of quantum mechanics. We consider a pair of entangled qubits consist of DNA and mRNA pair, each coupled to a distinct reservoir for analyzing the spreed of entanglement using time-dependent perturbation theory. The reservoirs are physical demonstrations of the cytoplasm and nucleoplasm and surrounding environments of mRNA and DNA, respectively. Our predictions confirm the role of the environmental-assisted quantum progression of adaptive mutations. Computing the concurrence as a measure that determines to what extent the bipartite DNA-mRNA can be correlated through entanglement, is given. Preventing the entanglement loss is crucial for controlling unfavorable point mutations under environmental influences. We explore which physical parameters may affect the preservation of entanglement between DNA and mRNA pair systems, despite the destructive role of interaction with the environments.

Darwin's agential materials: evolutionary implications of multiscale competency in developmental biology

A critical aspect of evolution is the layer of developmental physiology that operates between the genotype and the anatomical phenotype. While much work has addressed the evolution of developmental mechanisms and the evolvability of specific genetic architectures with emergent complexity, one aspect has not been sufficiently explored: the implications of morphogenetic problem-solving competencies for the evolutionary process itself. The cells that evolution works with are not passive components: rather, they have numerous capabilities for behavior because they derive from ancestral unicellular organisms with rich repertoires. In multicellular organisms, these capabilities must be tamed, and can be exploited, by the evolutionary process. Specifically, biological structures have a multiscale competency architecture where cells, tissues, and organs exhibit regulative plasticity-the ability to adjust to perturbations such as external injury or internal modifications and still accomplish specific adaptive tasks across metabolic, transcriptional, physiological, and anatomical problem spaces. Here, I review examples illustrating how physiological circuits guiding cellular collective behavior impart computational properties to the agential material that serves as substrate for the evolutionary process. I then explore the ways in which the collective intelligence of cells during morphogenesis affect evolution, providing a new perspective on the evolutionary search process. This key feature of the physiological software of life helps explain the remarkable speed and robustness of biological evolution, and sheds new light on the relationship between genomes and functional anatomical phenotypes.

UVC radiation intensity dependence of pathogen decontamination rate: semiclassical theory and experiment

A semiclassical (light classical and molecule quantum) model describing the dependence of DNA/RNA dimerization rate as function of the ultraviolet C (UVC) radiation's intensity is proposed. Particularly, a nonlinear model is developed based on the Raman-like processes in quantum optics. The main result of the theory shows that the process of dimerization in the DNA/RNA depends strongly on the UVC light's intensity, thus proving a possible quantum microscopical mechanism of the interaction of UV light with the DNA. To corroborate the theoretical findings, we realize some experiments, by which want to investigate how the inactivation rate of the yeast colonies depends on the intensity of the UVC irradiation. The experimental results evidence a nonlinear decreasing of the residual yeast colonies as a function of the intensity in the irradiation process. The possibilities to optimize the intensity of UVC radiation in the considered decontamination equipment by using metamaterials are studied. The application of such equipment in disinfection of fluids (air, water, droplets, etc.), as well for the SARS-CoV-2-infected aerosols, is discussed.

A Quantum Vaccinomics Approach Based on Protein-Protein Interactions

Vaccines are the most effective preventive intervention to reduce the impact of infectious diseases worldwide. In particular, tick-borne diseases represent a growing burden for human and animal health worldwide and vaccines are the most effective and environmentally sound approach for the control of vector infestations and pathogen transmission. However, the development of effective vaccines for the control of tick-borne diseases with combined vector-derived and pathogen-derived antigens is one of the limitations for the development of effective vaccine formulations. Quantum biology arise from findings suggesting that living cells operate under non-trivial features of quantum mechanics, which has been proposed to be involved in DNA mutation biological process. Then, the electronic structure of the molecular interactions behind peptide immunogenicity led to quantum immunology and based on the definition of the photon as a quantum of light, the immune protective epitopes were proposed as the immunological quantum. Recently, a quantum vaccinomics approach was proposed based on the characterization of the immunological quantum to further advance the design of more effective and safe vaccines. In this chapter, we describe methods of the quantum vaccinomics approach based on proteins with key functions in cell interactome and regulome of vector-host-pathogen interactions for the identification by yeast two-hybrid screen and the characterization by in vitro protein-protein interactions and musical scores of protein interacting domains, and the characterization of conserved protective epitopes in protein interacting domains. These results can then be used for the design and production of chimeric protective antigens.

Vaccinomics: a future avenue for vaccine development against emerging pathogens

INTRODUCTION

Vaccines are a major achievement in medical sciences, but the development of more effective vaccines against infectious diseases is essential for prevention and control of emerging pathogens worldwide. The application of omics technologies has advanced vaccinology through the characterization of host-vector-pathogen molecular interactions and the identification of candidate protective antigens. However, major challenges such as host immunity, pathogen and environmental factors, vaccine efficacy and safety need to be addressed. Vaccinomics provides a platform to address these challenges and improve vaccine efficacy and safety.

AREAS COVERED

In this review, we summarize current information on vaccinomics and propose quantum vaccinomics approaches to further advance vaccine development through the identification and combination of antigen protective epitopes, the immunological quantum. The COVID-19 pandemic caused by SARS-CoV-2 is an example of emerging infectious diseases with global impact on human health.

EXPERT OPINION

Vaccines are required for the effective and environmentally sustainable intervention for the control of emerging infectious diseases worldwide. Recent advances in vaccinomics provide a platform to address challenges in improving vaccine efficacy and implementation. As proposed here, quantum vaccinomics will contribute to vaccine development, efficacy, and safety by facilitating antigen combinations to target pathogen infection and transmission in emerging infectious diseases.

A quantum mechanical approach to random X chromosome inactivation

<abstract> <p>The X chromosome inactivation is an essential mechanism in mammals' development, that despite having been investigated for 60 years, many questions about its choice process have yet to be fully answered. Therefore, a theoretical model was proposed here for the first time in an attempt to explain this puzzling phenomenon through a quantum mechanical approach. Based on previous data, this work theoretically demonstrates how a shared delocalized proton at a key base pair position could explain the random, instantaneous, and mutually exclusive nature of the choice process in X chromosome inactivation. The main purpose of this work is to contribute to a comprehensive understanding of the X inactivation mechanism with a model proposal that can complement the existent ones, along with introducing a quantum mechanical approach that could be applied to other cell differentiation mechanisms.</p> </abstract>

Protein-DNA target search relies on quantum walk

Protein-DNA interactions play a fundamental role in all life systems. A critical issue of such interactions is given by the strategy of protein search for specific targets on DNA. The mechanisms by which the protein are able to find relatively small cognate sequences, typically 15-20 base pairs (bps) for repressors, and 4-6 bps for restriction enzymes among the millions of bp of non-specific chromosomal DNA have hardly engaged researchers for decades. Recent experimental studies have generated new insights on the basic processes of protein-DNA interactions evidencing the underlying complex dynamic phenomena involved, which combine three-dimensional and one-dimensional motion along the DNA chain. It has been demonstrated that protein molecules have an extraordinary ability to find the target very quickly on the DNA chain, in some cases, with two orders of magnitude faster than the diffusion limit. This unique property of protein-DNA search mechanism is known as facilitated diffusion. Several theoretical mechanisms have been suggested to describe the origin of facilitated diffusion. However, none of such models currently has the ability to fully describe the protein search strategy. In this paper, we suggest that the ability of proteins to identify consensus sequences on DNA is based on the entanglement of π-π electrons between DNA nucleotides and protein amino acids. The π-π entanglement is based on Quantum Walk (QW), through Coin-position entanglement (CPE). First, the protein identifies a dimer belonging to the consensus sequence, and localize a π on such dimer, hence, the other π electron scans the DNA chain until the sequence is identified. Focusing on the example of recognition of consensus sequences of EcoRV or EcoRI, we will describe the quantum features of QW on protein-DNA complexes during the search strategy, such as walker quadratic spreading on a coherent superposition of different vertices and environment-supported long-time survival probability of the walker. We will employ both discrete- or continuous-time versions of QW. Biased and unbiased classical Random Walk (CRW) have been used for a long time to describe the Protein-DNA search strategy. QW, the quantum version of CRW, has been widely studied for its applications in quantum information applications. In our biological application, the walker (the protein) resides at a vertex in a graph (the DNA structural topology). Differently to CRW, where the walker moves randomly, the quantum walker can hop along the edges in the graph to reach other vertices entering coherently a superposition across different vertices spreading quadratically faster than CRW analogous evidencing the typical speed up features of the QW. When applied to a protein-DNA target search problem, QW gives the possibility to achieve the experimental diffusional motion of proteins over diffusion classical limits experienced along DNA chains exploiting quantum features such as CPE and long-time survival probability supported by the environment. In turn, we come to the conclusion that, under quantum picture, the protein search strategy does not distinguish between one-dimensional (1D) and three-dimensional (3D) cases.

Quantum aspects of evolution: a contribution towards evolutionary explorations of genotype networks via quantum walks

Quantum biology seeks to explain biological phenomena via quantum mechanisms, such as enzyme reaction rates via tunnelling and photosynthesis energy efficiency via coherent superposition of states. However, less effort has been devoted to study the role of quantum mechanisms in biological evolution. In this paper, we used transcription factor networks with two and four different phenotypes, and used classical random walks (CRW) and quantum walks (QW) to compare network search behaviour and efficiency at finding novel phenotypes between CRW and QW. In the network with two phenotypes, at temporal scales comparable to decoherence time TD, QW are as efficient as CRW at finding new phenotypes. In the case of the network with four phenotypes, the QW had a higher probability of mutating to a novel phenotype than the CRW, regardless of the number of mutational steps (i.e. 1, 2 or 3) away from the new phenotype. Before quantum decoherence, the QW probabilities become higher turning the QW effectively more efficient than CRW at finding novel phenotypes under different starting conditions. Thus, our results warrant further exploration of the QW under more realistic network scenarios (i.e. larger genotype networks) in both closed and open systems (e.g. by considering Lindblad terms).

Reflexivity, coding and quantum biology

Biological systems are fundamentally computational in that they process information in an apparently purposeful fashion rather than just transferring bits of it in a purely syntactical manner. Biological information, such has genetic information stored in DNA sequences, has semantic content. It carries meaning that is defined by the molecular context of its cellular environment. Information processing in biological systems displays an inherent reflexivity, a tendency for the computational information-processing to be "about" the behaviour of the molecules that participate in the computational process. This is most evident in the operation of the genetic code, where the specificity of the reactions catalysed by the aminoacyl-tRNA synthetase (aaRS) enzymes is required to be self-sustaining. A cell's suite of aaRS enzymes completes a reflexively autocatalytic set of molecular components capable of making themselves through the operation of the code. This set requires the existence of a body of reflexive information to be stored in an organism's genome. The genetic code is a reflexively self-organised mapping of the chemical properties of amino acid sidechains onto codon "tokens". It is a highly evolved symbolic system of chemical self-description. Although molecular biological coding is generally portrayed in terms of classical bit-transfer events, various biochemical events explicitly require quantum coherence for their occurrence. Whether the implicit transfer of quantum information, qbits, is indicative of wide-ranging quantum computation in living systems is currently the subject of extensive investigation and speculation in the field of Quantum Biology.

A quantum mechanical approach towards the calculation of transition probabilities between DNA codons

The role of quantum tunneling in altering the structure of nucleotides to each other and causing a mutational event in DNA has been a topic of debate for years. Here, we introduce a new quantum mechanical approach for analyzing a typical point-mutation in DNA strands. Assuming each codon as a base state, a superposition of codon states could provide a physical description for a set of codons encoding the same amino acid and there are transition amplitudes between them. We choose the amino acids Phe and Ile as our understudy bio-systems which are encoded by two and three codons, respectively. We treat them as large quantum systems and use double- and triple-well potential models to study the fundamental behaviors of them in interaction with a harmonic environment. We use the perturbation theory to calculate the transition probabilities between the codons which encoding the same amino acid and determine the transition rates of some point mutations. Moreover, we evaluate the quantum biological channel capacity for these transitions to show that the channel capacity depends on the system-environment interaction via the dissipation factor Γ. The obtained results demonstrate that the tunneling rate is under the control of capacity of the corresponding biological channel. In other words, the reduction in quantum channel capacity prevents the quantum tunneling rate to be increased.

The origins of quantum biology

Quantum biology is usually considered to be a new discipline, arising from recent research that suggests that biological phenomena such as photosynthesis, enzyme catalysis, avian navigation or olfaction may not only operate within the bounds of classical physics but also make use of a number of the non-trivial features of quantum mechanics, such as coherence, tunnelling and, perhaps, entanglement. However, although the most significant findings have emerged in the past two decades, the roots of quantum biology go much deeper-to the quantum pioneers of the early twentieth century. We will argue that some of the insights provided by these pioneering physicists remain relevant to our understanding of quantum biology today.

Sub-picosecond proton tunnelling in deformed DNA hydrogen bonds under an asymmetric double-oscillator model

We present a model of proton tunnelling across DNA hydrogen bonds, compute the characteristic tunnelling time (CTT) from donor to acceptor and discuss its biological implications. The model is a double oscillator characterised by three geometry parameters describing planar deformations of the H bond, and a symmetry parameter representing the energy ratio between ground states in the individual oscillators. We discover that some values of the symmetry parameter lead to CTTs which are up to 40 orders of magnitude smaller than a previous model predicted. Indeed, if the symmetry parameter is sufficiently far from its extremal values of 1 or 0, then the proton's CTT under any physically realistic planar deformation is guaranteed to be below one picosecond, which is a biologically relevant time-scale. This supports theories of links between proton tunnelling and biological processes such as spontaneous mutation.

Quantum effects in biology: golden rule in enzymes, olfaction, photosynthesis and magnetodetection

Despite certain quantum concepts, such as superposition states, entanglement, 'spooky action at a distance' and tunnelling through insulating walls, being somewhat counterintuitive, they are no doubt extremely useful constructs in theoretical and experimental physics. More uncertain, however, is whether or not these concepts are fundamental to biology and living processes. Of course, at the fundamental level all things are quantum, because all things are built from the quantized states and rules that govern atoms. But when does the quantum mechanical toolkit become the best tool for the job? This review looks at four areas of 'quantum effects in biology'. These are biosystems that are very diverse in detail but possess some commonality. They are all (i) effects in biology: rates of a signal (or information) that can be calculated from a form of the 'golden rule' and (ii) they are all protein-pigment (or ligand) complex systems. It is shown, beginning with the rate equation, that all these systems may contain some degree of quantumeffect, and where experimental evidence is available, it is explored to determine how the quantum analysis aids in understanding of the process.

A biophysical approach to cancer dynamics: Quantum chaos and energy turbulence

Cancer is a term used to define a collective set of rapidly evolving cells with immortalized replication, altered epimetabolomes and patterns of longevity. Identifying a common signaling cascade to target all cancers has been a major obstacle in medicine. A quantum dynamic framework has been established to explain mutation theory, biological energy landscapes, cell communication patterns and the cancer interactome under the influence of quantum chaos. Quantum tunneling in mutagenesis, vacuum energy field dynamics, and cytoskeletal networks in tumor morphogenesis have revealed the applicability for description of cancer dynamics, which is discussed with a brief account of endogenous hallucinogens, bioelectromagnetism and water fluctuations. A holistic model of mathematical oncology has been provided to identify key signaling pathways required for the phenotypic reprogramming of cancer through an epigenetic landscape. The paper will also serve as a mathematical guide to understand the cancer interactome by interlinking theoretical and experimental oncology. A multi-dimensional model of quantum evolution by adaptive selection has been established for cancer biology.

Quantum dynamics of a hole migration through DNA: A single strand DNA model

A model predicting the behavior of a hole acting on the DNA strand was investigated. The hole-DNA interaction on the basis of a quantum-classical, non-linear DNA single strand model was described. The fact that a DNA molecule is formed by a furanose ring as its sugar, phosphate group and bases was taken into consideration. Based on the model, results were obtained for the probability of a hole location on the DNA base sequences, such as GTTGGG, GATGTGGG, GTTGTTGGG as well as on the sugar-phosphate groups mated with them.

Nontrivial quantum and quantum-like effects in biosystems: Unsolved questions and paradoxes

Non-trivial quantum effects in biological systems are analyzed. Some unresolved issues and paradoxes related to quantum effects (Levinthal's paradox, the paradox of speed, and mechanisms of evolution) are addressed. It is concluded that the existence of non-trivial quantum effects is necessary for the functioning of living systems. In particular, it is demonstrated that classical mechanics cannot explain the stable work of the cell and any over-cell structures. The need for quantum effects is generated also by combinatorial problems of evolution. Their solution requires a priori information about the states of the evolving system, but within the framework of the classical theory it is not possible to explain mechanisms of its storage consistently. We also present essentials of so called quantum-like paradigm: sufficiently complex bio-systems process information by violating the laws of classical probability and information theory. Therefore the mathematical apparatus of quantum theory may have fruitful applications to describe behavior of bio-systems: from cells to brains, ecosystems and social systems. In quantum-like information biology it is not presumed that quantum information bio-processing is resulted from quantum physical processes in living organisms. Special experiments to test the role of quantum mechanics in living systems are suggested. This requires a detailed study of living systems on the level of individual atoms and molecules. Such monitoring of living systems in vivo can allow the identification of the real potentials of interaction between biologically important molecules.

Neuroreceptor activation by vibration-assisted tunneling

G protein-coupled receptors (GPCRs) constitute a large family of receptor proteins that sense molecular signals on the exterior of a cell and activate signal transduction pathways within the cell. Modeling how an agonist activates such a receptor is fundamental for an understanding of a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as a model for the mechanism by which olfactory GPCRs are activated by a bound agonist. We apply this hyothesis to GPCRs within the mammalian nervous system using quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a particular IET spectral aspect both amongst each other and with the serotonin molecule: a peak whose intensity scales with the known agonist potencies. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its deuterated isotopologues; we also provide theoretical predictions for comparison to experiment. If validated our theory may provide new avenues for guided drug design and elevate methods of in silico potency/activity prediction.

Basis for a neuronal version of Grover's quantum algorithm

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N^1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca²⁺ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca²⁺-induced Ca²⁺ release and the search (or signaling) velocity of Ca²⁺ wave propagation. As chemical processes, such as the duration of Ca²⁺ mobilization, become rate-limiting over interstore distances, Ca²⁺ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca²⁺ diffusion coefficient, D^1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca²⁺ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.

Toward topological descriptions of the therapeutic process: part 3. Two new metaphors based on quantum superposition, wave function "collapse," and conic sections

INTRODUCTION

Quantum theoretical discourse has previously illustrated (1) the therapeutic process as three-way macro-entanglement (between patient, practitioner, and remedy, called PPR entanglement), and (2) depicted the Vital Force (Vf) as a quantized spinning gyroscope. Combining the two via semiotic geometry leads to a topological description of the patient's journey to cure. In this present article, two new metaphors for the homeopathic therapeutic encounter are described, based on (1) a quantum mechanical model of adaptive mutation (QMAM), and (2) the illuminated geometric patterns generated by a light source attached to a spinning gyroscope.

METHODS

(1) QMAM demonstrates how quantum superposition between DNA and mutant adaptations could arise and how environmental pressure "collapses" the DNA wave function to a particular state. In QMAM for the therapeutic process, isolation helps induce coherence between patient, practitioner, and remedy, generating a quantum-like superposition of patient "unwell" and "well" states. (2) The light beam from a precessing gyroscope sweeps out an ellipse, which becomes circular, the faster the gyroscope spins on its axis and the less it precesses. Ellipses have two foci that, as a metaphor for the state of a patient's Vf, are seen to represent the patient's "unwell" and "well" states.

RESULTS

Superposition of the patient's "unwell" and "well" states generated by the QMAM metaphor can "collapse" to the cured state, following decoherence at the end of therapeutic process. Similarly, the curative therapeutic process may be thought to "spin up" the patient's Vf, so the precessing ellipse's foci (i.e., the patient's "unwell" and "well" states) merge into a "circular" curative state.

CONCLUSIONS

The two new metaphors may be seen as equivalent and semiotic simplifications of the previous more complex topological description of the patient's "journey to cure."

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

We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.

Quantum information and the problem of mechanisms of biological evolution

One of the most important conditions for replication in early evolution is the de facto elimination of the conformational degrees of freedom of the replicators, the mechanisms of which remain unclear. In addition, realistic evolutionary timescales can be established based only on partially directed evolution, further complicating this issue. A division of the various evolutionary theories into two classes has been proposed based on the presence or absence of a priori information about the evolving system. A priori information plays a key role in solving problems in evolution. Here, a model of partially directed evolution, based on the learning automata theory, which includes a priori information about the fitness space, is proposed. A potential repository of such prior information is the states of biologically important molecules. Thus, the need for extended evolutionary synthesis is discussed. Experiments to test the hypothesis of partially directed evolution are proposed.

On genetic information uncertainty and the mutator phenotype in cancer

Recent evidence supports the existence of a mutator phenotype in cancer cells, although the mechanistic basis remains unknown. In this paper, it is shown that this enhanced genetic instability is generated by an amplified measurement uncertainty on genetic information during DNA replication. At baseline, an inherent measurement uncertainty implies an imprecision of the recognition, replication and transfer genetic information, and forms the basis for an intrinsic genetic instability in all biological cells. Genetic information is contained in the sequence of DNA bases, each existing due to proton tunnelling, as a coherent superposition of quantum states composed of both the canonical and rare tautomeric forms until decoherence by interaction with DNA polymerase. The result of such a quantum measurement process may be interpreted classically as akin to a Bernoulli trial, whose outcome X is random and can be either of two possibilities, depending on whether the proton is tunnelled (X=1) or not (X=0). This inherent quantum uncertainty is represented by a binary entropy function and quantified in terms of Shannon information entropy H(X)=-P(X=1)log(2)P(X=1)-P(X=0)log(2)P(X=0). Enhanced genetic instability may either be directly derived from amplified uncertainty induced by increases in quantum and thermodynamic fluctuation, or indirectly arise from the loss of natural uncertainty reduction mechanisms.

The molecular clock in terms of quantum information processing of coherent states, entanglement and replication of evolutionarily selected decohered isomers

Evolutionary pressures have selected quantum uncertainty limits -ΔxΔp ( x ) ≥ 1/2ħ-to operate on metastable amino DNA protons. This introduces a probability of molecular clock arrangement, keto-amino → enol-imine, where product protons are entangled and participate in coupled quantum oscillation at frequencies of ∼ 10(13) s(-1). The ket "seen by" the transcriptase, reading a coherent enol-imine G'-state, is |φ >= α| + + > +β|+- > +γ|-+ > +δ|-->. The transcriptase implements its measurement and generates an output qubit of observable genetic specificity information in an interval Δt ≪ 10(-13) s. These quantum measurements can specify the relative distribution of coherent G'-C' states at time of measurement. The ensuing quantum entanglement between coherent protons and transcriptase units is utilized as a resource to generate proper decoherence and introduce selected time-dependent substitutions, ts, and deletions, td. Topal-Fresco ts are G'202 → T, G'002 → C, *G020(0) → A and *C202(2) → T, whereas td are exhibited at coherent *A-*T sites. Variation in clock 'tic-rate' is a consequence of clock introduction of initiation codons - UUG, CUG, AUG, GUG - and stop codons, UAA, UAG, UGA. Using approximate quantum methods for times t < ∼ 100 y, the probability, P(t), of keto-amino → enolimine arrangement is P ( ρ )(t) = 1/2(γ ( ρ )/ħ)(2) t (2) where γ ( ρ ) is the energy shift. This introduces a quantum Darwinian evolution model which provides insight into biological consequences of coherent states populating human genes, including inherited (CAG)( n ) repeat tracts.

Speculation on quantum mechanics and the operation of life giving catalysts

The origin of life necessitated the formation of catalytic functionalities in order to realize a number of those capable of supporting reactions that led to the proliferation of biologically accessible molecules and the formation of a proto-metabolic network. Here, the discussion of the significance of quantum behavior on biological systems is extended from recent hypotheses exploring brain function and DNA mutation to include origins of life considerations in light of the concept of quantum decoherence and the transition from the quantum to the classical. Current understandings of quantum systems indicate that in the context of catalysis, substrate-catalyst interaction may be considered as a quantum measurement problem. Exploration of catalytic functionality necessary for life's emergence may have been accommodated by quantum searches within metal sulfide compartments, where catalyst and substrate wave function interaction may allow for quantum based searches of catalytic phase space. Considering the degree of entanglement experienced by catalytic and non catalytic outcomes of superimposed states, quantum contributions are postulated to have played an important role in the operation of efficient catalysts that would provide for the kinetic basis for the emergence of life.

Evidence for transcriptase quantum processing implies entanglement and decoherence of superposition proton states

Evidence requiring transcriptase quantum processing is identified and elementary quantum methods are used to qualitatively describe origins and consequences of time-dependent coherent proton states populating informational DNA base pair sites in T4 phage, designated by G-C-->G'-C', G-C-->*G-*C and AT-->*A-*T. Coherent states at these 'point' DNA lesions are introduced as consequences of hydrogen bond arrangement, keto-amino-->enol-imine, where product protons are shared between two sets of indistinguishable electron lone-pairs, and thus, participate in coupled quantum oscillations at frequencies of approximately 10(13) s(-1). This quantum mixing of proton energy states introduces stability enhancements of approximately 0.25-7 kcal/mole. Transcriptase genetic specificity is determined by hydrogen bond components contributing to the formation of complementary interstrand hydrogen bonds which, in these cases, is variable due to coupled quantum oscillations of coherent enol-imine protons. The transcriptase deciphers and executes genetic specificity instructions by implementing measurements on superposition proton states at G'-C', *G-*C and *A-*T sites in an interval Deltat<<10(-13) s. After initiation of transcriptase measurement, model calculations indicate proton decoherence time, tau(D), satisfies the relation Deltat<tau(D)<10(-13)s. Decohered states participate in Topal-Fresco replication to introduce substitutions G'-->T, G'-->C, *C-->T and *G-->A. Measurements of 37 degrees C lifetimes of the keto-amino DNA hydrogen bond indicate a range of approximately 3200-68,000 yrs. Arguments are presented that quantum uncertainty limits on amino protons may drive the keto-amino-->enol-imine arrangement. Data imply that natural selection at the quantum level has generated effective schemes (a) for introducing superposition proton states--at rates appropriate for DNA evolution--in decoherence-free subspaces and (b) for creating entanglement states that augment (i) transcriptase quantum processing and (ii) efficient decoherence for accurate Topal-Fresco replication.

Cardiac cell: a biological laser?

We present a new concept of cardiac cells based on an analogy with lasers, practical implementations of quantum resonators. In this concept, each cardiac cell comprises a network of independent nodes, characterised by a set of discrete energy levels and certain transition probabilities between them. Interaction between the nodes is given by threshold-limited energy transfer, leading to quantum-like behaviour of the whole network. We propose that in cardiomyocytes, during each excitation-contraction coupling cycle, stochastic calcium release and the unitary properties of ionic channels constitute an analogue to laser active medium prone to "population inversion" and "spontaneous emission" phenomena. This medium, when powered by an incoming threshold-reaching voltage discharge in the form of an action potential, responds to the calcium influx through L-type calcium channels by stimulated emission of Ca2+ ions in a coherent, synchronised and amplified release process known as calcium-induced calcium release. In parallel, phosphorylation-stimulated molecular amplification in protein cascades adds tuneable features to the cells. In this framework, the heart can be viewed as a coherent network of synchronously firing cardiomyocytes behaving as pulsed laser-like amplifiers, coupled to pulse-generating pacemaker master-oscillators. The concept brings a new viewpoint on cardiac diseases as possible alterations of "cell lasing" properties.

Reconstruction of DNA sequences using genetic algorithms and cellular automata: towards mutation prediction?

Change of DNA sequence that fuels evolution is, to a certain extent, a deterministic process because mutagenesis does not occur in an absolutely random manner. So far, it has not been possible to decipher the rules that govern DNA sequence evolution due to the extreme complexity of the entire process. In our attempt to approach this issue we focus solely on the mechanisms of mutagenesis and deliberately disregard the role of natural selection. Hence, in this analysis, evolution refers to the accumulation of genetic alterations that originate from mutations and are transmitted through generations without being subjected to natural selection. We have developed a software tool that allows modelling of a DNA sequence as a one-dimensional cellular automaton (CA) with four states per cell which correspond to the four DNA bases, i.e. A, C, T and G. The four states are represented by numbers of the quaternary number system. Moreover, we have developed genetic algorithms (GAs) in order to determine the rules of CA evolution that simulate the DNA evolution process. Linear evolution rules were considered and square matrices were used to represent them. If DNA sequences of different evolution steps are available, our approach allows the determination of the underlying evolution rule(s). Conversely, once the evolution rules are deciphered, our tool may reconstruct the DNA sequence in any previous evolution step for which the exact sequence information was unknown. The developed tool may be used to test various parameters that could influence evolution. We describe a paradigm relying on the assumption that mutagenesis is governed by a near-neighbour-dependent mechanism. Based on the satisfactory performance of our system in the deliberately simplified example, we propose that our approach could offer a starting point for future attempts to understand the mechanisms that govern evolution. The developed software is open-source and has a user-friendly graphical input interface.

Uncertainty principle of genetic information in a living cell

Background

Formal description of a cell's genetic information should provide the number of DNA molecules in that cell and their complete nucleotide sequences. We pose the formal problem: can the genome sequence forming the genotype of a given living cell be known with absolute certainty so that the cell's behaviour (phenotype) can be correlated to that genetic information? To answer this question, we propose a series of thought experiments.

Results

We show that the genome sequence of any actual living cell cannot physically be known with absolute certainty, independently of the method used. There is an associated uncertainty, in terms of base pairs, equal to or greater than μs (where μ is the mutation rate of the cell type and s is the cell's genome size).

Conclusion

This finding establishes an "uncertainty principle" in genetics for the first time, and its analogy with the Heisenberg uncertainty principle in physics is discussed. The genetic information that makes living cells work is thus better represented by a probabilistic model rather than as a completely defined object.

The complementarity model of brain–body relationship

We introduce the complementarity concept to understand mind-body relations and the question why the biopsychosocial model has in fact been praised, but not integrated into medicine. By complementarity, we mean that two incompatible descriptions have to be used to describe something in full. The complementarity model states that the physical and the mental side of the human organism are two complementary notions. This contradicts the prevailing materialist notion that mental and psychological processes are emergent properties of an organism. The complementarity model also has consequences for a further understanding of biological processes. Complementarity is a defining property of quantum systems proper. Such systems exhibit correlated properties that result in coordinated behavior without signal transfer or interaction. This is termed EPR-correlation or entanglement. Weak quantum theory, a generalized version of quantum mechanics proper, predicts entanglement also for macroscopic systems, provided a local and a global observable are complementary. Thus, complementarity could be the key to understanding holistically correlated behavior on different levels of systemic complexity.

Does quantum mechanics play a non-trivial role in life?

There have been many claims that quantum mechanics plays a key role in the origin and/or operation of biological organisms, beyond merely providing the basis for the shapes and sizes of biological molecules and their chemical affinities. These range from Schrödinger's suggestion that quantum fluctuations produce mutations, to Hameroff and Penrose's conjecture that quantum coherence in microtubules is linked to consciousness. I review some of these claims in this paper, and discuss the serious problem of decoherence. I advance some further conjectures about quantum information processing in bio-systems. Some possible experiments are suggested.

An algorithm for the study of DNA sequence evolution based on the genetic code

Recent studies of the quantum-mechanical processes in the DNA molecule have seriously challenged the principle that mutations occur randomly. The proton tunneling mechanism causes tautomeric transitions in base pairs resulting in mutations during DNA replication. The meticulous study of the quantum-mechanical phenomena in DNA may reveal that the process of mutagenesis is not completely random. We are still far away from a complete quantum-mechanical model of DNA sequence mutagenesis because of the complexity of the processes and the complex three-dimensional structure of the molecule. In this paper we have developed a quantum-mechanical description of DNA evolution and, following its outline, we have constructed a classical model for DNA evolution assuming that some aspects of the quantum-mechanical processes have influenced the determination of the genetic code. Conversely, our model assumes that the genetic code provides information about the quantum-mechanical mechanisms of mutagenesis, as the current code is the product of an evolutionary process that tries to minimize the spurious consequences of mutagenesis. Based on this model we develop an algorithm that can be used to study the accumulation of mutations in a DNA sequence. The algorithm has a user-friendly interface and the user can change key parameters in order to study relevant hypotheses.

A cellular automaton model for the study of DNA sequence evolution

Cellular automata are introduced as a model for DNA structure, function and evolution. DNA is modeled as a one-dimensional cellular automaton with four states per cell. These states are the four DNA bases A, C, T and G. The four states are represented by numbers of the quaternary number system. Linear evolution rules, represented by square matrices, are considered. Based on this model a simulator of DNA evolution is developed and simulation results are presented. This simulator has a user-friendly input interface and can be used for the study of DNA evolution.

Patient-practitioner-remedy (PPR) entanglement. Part 1: a qualitative, non-local metaphor for homeopathy based on quantum theory

A metaphor for homeopathy is developed in which the potentised medicine, the patient, and the practitioner are seen as forming a non-local therapeutically 'entangled' triad, qualitatively described in terms of the transactional interpretation of quantum mechanics.