A quantum probability explanation for violations of ‘rational’ decision theory

Two experimental tasks in psychology, the two-stage gambling game and the Prisoner''s Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger''s equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making.     

AN EXTENDED TRANSITION PROBABILITY MODEL OF THE VARIABILITY OF CELL GENERATION TIMES

The transition probability model of variability of cell generation times is extended so that the rate constant for the transition from the A-state to the B-phase of the cell cycle depends on time which a particular cell has already spent in the A-state. A specific time dependence of this rate constant is introduced. It is determined by the value of one constant which is then an additional parameter of the model. The corresponding cell population kinetics are calculated and compared to existing experimental evidence. The model accounts satisfactorily for the generation time distribution function and for the shortening of the G₁ phase of binucleate cells. The time dependence of the transition probability is related to the cell kinetics of an hypothetical cell constituent. A possible relationship is proposed between the chemical parameters within the cell and the parameters of the cell population kinetics.     

Coincidence detectors and two-pulse visual temporal integration: new theoretical results and comparison with data

Exact predictions for two-pulse visual temporal integration data are derived from the Bouman-van der Velden quantum coincidence model for threshold vision. The predictions of the model start with complete summation for superposed pulses, then pass to a transition zone of partial integration, and finally reach the level of probability summation for pulses presented with large interstimulus intervals. From our results we can clearly reject the assumption of constant integration times with the basic model. We thus generalize the coincidence model to allow for variable integration times, derive the corresponding predictions for two-pulse integration data, and compare these predictions to published data currently available. It is shown that detectors of low order of coincidence generally underestimate the actual reduction of threshold intensity (or equivalently the corresponding increase of the detection probability) for two pulses as compared to the singlepulse performance.     

Isotopic effects in the electronic spectra of tryptophan

Summary. No influence of isotopic substitution in deuterium-substituted tryptophan on the florescence excitation spectrum has previously been found out. Here, the isotopic effects of electronic excitation of deuterium-substituted tryptophan were experimentally and theoretically analyzed for first time. It was shown a short-wave shift of the UV-absorption maximum at 220 nm corresponding to the 360 cal/mol and short-wave shift for fluorescence spectrum corresponding to the 210 cal/mol. To account for this effect, the quantum chemical calculations of the geometric and electron structure, frequencies of normal vibrations and transition energies have been performed. The isotopic effects originate from the zero-point energies of ground and excited states. It was found that isotopic shifts depend on the position of isotope in the molecule and kind of transition. So, it can be utilized in the analysis of proteins structure and complexation.     

Quantum chemical studies of the catalytic mechanism of N-terminal nucleophile hydrolase

Modeling of the catalytic mechanism of penicillin acylase, a member of the N-terminal nucleophile hydrolase superfamily, is for the first time conducted at ab initio quantum chemistry level. The uniqueness of this family of enzymes is that their active site lacks His and Asp (Glu) residues, comprising together with a serine residue the classical catalytic triad. The current investigation confirms that the amino group of the N-terminal serine residue in N-terminal hydrolases is capable of activating its own hydroxyl group. Using the MP2/RHF method with the 6−31+G** basis set, stationary points on the potential energy surface of the considered molecular system were located, corresponding to local minima (complexes of reagents, products, intermediate) and to saddle points (transition states). It turned out that the stage of acyl-serine formation proceeds via two transition states; the first one, which separates reagents from the so-called tetrahedral intermediate, has the highest relative energy (30 kcal/mol). In contrast to recently proposed empiric suggestions, we have found that participation of a bridging water molecule in proton shuttling is not necessary for the catalysis. The quantum chemical calculations showed a crucial role of a specific solvation in decreasing the activation barrier of the reaction by approximately 10 kcal/mol. Published in Russion in Biokhimiya, 2007, Vol. 72, No. 5, pp. 615–621.     

生物光子发射的半经典理论

生物光子发射（ＰＥ）方法是揭示生命活动的一种非损伤方法。由于机理不清,仅获有限的认同。根据Ｄｉｃｋｅ近似,顾樵曾经提出ＰＥ的全量子理论。然而,Ｄｉｃｋｅ近似不适合生物系统。本文在不引入Ｄｉｃｋｅ近似的前提下,利用量子化学和半径典辐射理论研究了ＰＥ的全同粒子模型。结果表明,全同粒子会成相干态,其中超辐射态的光子发射几率是粒子数的平方和三次方的线性函数。本文结论成功地解了细胞分裂和细胞癌变等生命活动的ＰＥ现象和外界因素对ＰＥ现象的影响。     

On atomic nuclear fusion processes at low temperatures. Enhancement of potential barrier transmission probability due to the so-called barrier anti-Zeno effect

It is known that in quantum mechanics the observation of an experiment may in some cases change the results of this experiment. In particular, this occurs for the so-called Zeno effect. It is shown that, unlike the standard Zeno effect for which observation reduces its probability, for a particle that penetrates a potential barrier the opposite situation (called the barrier anti-Zeno effect) can occur, i.e., observation can considerably increase the probability of barrier penetration. The possibility of utilizing the barrier anti-Zeno effect for explaining the paradoxical results of experiments on “cold nuclear fusion” that have been observed in various, including biological, systems is discussed. (According to the experimentalists who performed such studies, in these systems energy release that cannot be explained by any chemical processes, as well as changes of the isotope and even elemental composition of the studied substance, occur).     

Evaluation of catalytic free energies in genetically modified proteins

A combination of the empirical valence bond method and a free energy perturbation approach is used to simulate the activity of genetically modified enzymes. The simulations reproduce in a semiquantitative way the observed effects of mutations on the activity and binding free energies of trypsin and subtilisin. This suggests that we are approaching a stage of quantitative structure-function correlation of enzymes. The analysis of the calculations points towards the electrostatic energy of the reacting system as the key factor in enzyme catalysis. The changes in the charges of the reacting system and the corresponding changes in "solvation" free energy (generalized here as the interaction between the charges and the given microenvironment) are emphasized. It is argued that a reliable evaluation of these changes might be sufficient for correlating structure and catalysis. The use of free energy perturbation methods and thermodynamic cycles for evaluation of solvation energies and reactivity is discussed, pointing out our early contributions. The apparent elaborated nature of our treatment is clarified, explaining that such a treatment is essential for consistent calculations of chemical reactions in polar environments. The problems associated with seemingly more rigorous quantum mechanical methods are discussed, emphasizing the inconsistency associated with using gas phase charge distributions. The importance of dynamic aspects is examined by evaluating the autocorrelation of the protein "reaction field" on the reacting substrate. It is found that, at least in the present case, dynamic effects are not important. The nature of the catalytic free energy is considered, arguing that the protein provides preoriented dipoles (polarized to stabilize the transition state charge distribution) and small reorganization energy, thus reducing the activation free energy. The corresponding catalytic free energy is related to the folding free energy, which is being invested in aligning the active site dipoles.     

QM/MM modeling the Ras-GAP catalyzed hydrolysis of guanosine triphosphate

The mechanism of the hydrolysis reaction of guanosine triphosphate (GTP) by the protein complex Ras-GAP (p21(ras) - p120(GAP)) has been modeled by the quantum mechanical-molecular mechanical (QM/MM) and ab initio quantum calculations. Initial geometry configurations have been prompted by atomic coordinates of a structural analog (PDBID:1WQ1). It is shown that the minimum energy reaction path is consistent with an assumption of two-step chemical transformations. At the first stage, a unified motion of Arg789 of GAP, Gln61, Thr35 of Ras, and the lytic water molecule results in a substantial spatial separation of the gamma-phosphate group of GTP from the rest of the molecule (GDP). This phase of hydrolysis process proceeds through the low-barrier transition state TS1. At the second stage, Gln61 abstracts and releases protons within the subsystem including Gln61, the lytic water molecule and the gamma-phosphate group of GTP through the corresponding transition state TS2. Direct quantum calculations show that, in this particular environment, the reaction GTP + H(2)O --> GDP + H(2)PO(4) (-) can proceed with reasonable activation barriers of less than 15 kcal/mol at every stage. This conclusion leads to a better understanding of the anticatalytic effect of cancer-causing mutations of Ras, which has been debated in recent years.     

New theoretical treatment of ion resonance phenomena

Despite experimental evidence supporting ICR-like interactions in biological systems, to date there is no reasonable theoretical explanation for this phenomenon. The parametric resonance approach introduced by Lednev has enjoyed limited success in predicting the response as a function of the ratio of AC magnetic intensity to that of the DC field, explaining the results in terms of magnetically induced changes in the transition probability of calcium binding states. In the present work, we derive an expression for the velocity of a damped ion with arbitrary q/m under the influence of the Lorentz force. Series solutions to the differential equations reveal transient responses as well as resonance-like terms. One fascinating result is that the expressions for ionic drift velocity include a somewhat similar Bessel function dependence as was previously obtained for the transition probability in parametric resonance. However, in the present work, not only is there an explicit effect due to damping, but the previous Bessel dependence now occurs as a subset of a more general solution, including not only the magnetic field AC/DC ratio as an independent variable, but also the ratio of the cyclotronic frequency Omega to the applied AC frequency omega. In effect, this removes the necessity to explain the ICR interaction as stemming from ion-protein binding sites. We hypothesize that the selectively enhanced drift velocity predicted in this model can explain ICR-like phenomena as resulting from increased interaction probabilities in the vicinity of ion channel gates.     

pH dependent unfolding characteristics of DLC8 dimer: Residue level details from NMR

Environment dependence of folding and unfolding of a protein is central to its function. In the same vein, knowledge of pH dependence of stability and folding/unfolding is crucial for many biophysical equilibrium and kinetic studies designed to understand protein folding mechanisms. In the present study we investigated the guanidine induced unfolding transition of dynein light chain protein (DLC8), a cargo adaptor of the dynein complex in the pH range 7-10. It is observed that while the protein remains a dimer in the entire pH range, its stability is somewhat reduced at alkaline pH. Global unfolding features monitored using fluorescence spectroscopy revealed that the unfolding transition of DLC8 at pH 7 is best described by a three-state model, whereas, that at pH 10 is best described by a two-state model. Chemical shift perturbations due to pH change provided insights into the corresponding residue level structural perturbations in the DLC8 dimer. Likewise, backbone (15)N relaxation measurements threw light on the corresponding motional changes in the dimeric protein. These observations have been rationalized on the basis of expected changes with increasing pH in the protonation states of the titratable residues on the structure of the protein. These, in turn provide an explanation for the change from three-state to two-state guanidine induced unfolding transition as the pH is increased from 7 to 10. All these results exemplify and highlight the role of environment vis-à-vis the sequence and structure of a given protein in dictating its folding/unfolding characteristics.     

The regulation of the oxidative processes in the tissues of Muridae like rodents caught in the Chernobyl accident zone

The results of the investigations of the radioactive contamination consequences on the lipid peroxidation (LPO) processes in organs and tissues of wild rodents which were caught in the Chernobyl NPP accident 30-km zone during 1986-1993 are generalized. The behaviors of the technogenic contamination effect on dynamic of changes of the LPO physico-chemical regulatory system parameters and the generalized parameters of the phospholipid composition in organs of the different radioresistance wild rodents are revealed in dependence on the radioactive contamination level and the duration of the radiation factor exposure. Different sensitivity of the LPO regulatory system parameters in wild rodent tissues to the radioactive contamination of their environment and the unequal ability to normalization of the antioxidant status and the energy exchange in tissues result in the change of the scale and character of interrelations between the reciprocal parameters in norm and have an influence on the development of qualitatively new subpopulations of wild rodents due to the transition of the cell regulatory system to the another level of the function.     

Code dependent conservation of the physico-chemical properties in amino acid substitutions

The frequency of amino acid replacements in families of typical proteins has been elegantly analyzed by Argyle (1980) showing that the most frequent replacements involve a conservation of the amino acid chemical properties. The cyclic arrangement of the twenty amino acids resulting from the most frequent replacements has been described as an amino acid chemical ring. In this work, a novel amino acid replacement frequency ring is proposed, for which a conservation of over 90% of the most general physico-chemical properties can be deduced. The amino acid chemical similarity ring is also analyzed in terms of the genetic code base probability changes, showing that the discrepancy that exists between the standard deviation value of the amino acid replacement frequency matrix and its respective ideal value is almost equal to that deduced from the corresponding base codon replacement probability matrices. These differences are finally evaluated and discussed in terms of the restrictions imposed by the structure of the genetic code and the physico-chemical dissimilarities between some codons of amino acids which are chemically similar.     

Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or “site.” Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment–proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment–protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna–Mathews–Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.     

Non-equilibrium thermodynamics of marginal- and conditional-open chemical systems

Every open chemical system treated in this paper is restricted to the case involving a sequence of monomolecular reactions. Various kinds of probability distribution governing it are introduced according to the situations in which it is placed. The chemical system subject to marginal distribution is given the term marginal-open system MO. The open chemical system ō discussed by Nicolis and Babloyantz can be regarded as the limiting system of MO. For an open chemical system, itself in contact with an external reservoir of finite volume, the probability distribution conditioned on the marginal distribution for the external reservoir in an arbitrarily fixed state is more appropriate. Such an open chemical system is called a conditional-open system CO. However, in the case of the external reservoir of infinite volume, although it is not certainly trivial, another conditional probability distribution has to be proposed; it is derived on the hypothesis that the probability distribution for an arbitrary total number of molecules in the open chemical system is known. The open chemical system so specified is called conditional-open system $\text{C}\text{O}\text{?}$. It is shown that for each system $\text{MO, CO}\text{and}\text{C}\text{O}\text{?}$ the change of entropy starting from the steady state provides a Liapunov function under some conditions and that the steady state is asymptotically stable. The relation of the entropy change to non-equilibrium fluctuations of chemical components in each system is discussed in comparison with that in the corresponding open chemical system ō, for which the steady state surely exists and is always stable. It is shown that the concept of $\text{C}\text{O}\text{?}$ is useful for investigating the phenomenon of steady-state coupling.     

The hive bee to forager transition in honeybee colonies: the double repressor hypothesis

In summer, the honeybee (Apis mellifera) worker population consists of two temporal castes, a hive bee group performing a multitude of tasks including nursing inside the nest, and a forager group specialized on collecting nectar, pollen, water and propolis. Elucidation of the regulatory mechanisms responsible for the hive bee to forager transition holds a prominent position within present day sociobiology. Here we suggest a new explanation dubbed the "double repressor hypothesis" aimed to account for the substantial amount of empirical data in this field. This is the first time where both the regular transition and starvation-induced precocious transition are explained within the same regulatory framework. We suggest that the transition is under regulatory control by an internal and an external repressor of the allatoregulatory central nervous system, where these two repressors modulate a positive regulatory feedback loop involving juvenile hormone (JH) and the lipoprotein vitellogenin. The concepts of age-neutrality, fixed and variable response thresholds and reinforcement are integral parts of our explanation, and in addition they are given explicit physiological content. The hypothesis is represented by a differential equations model at the level of the individual bee, and by a discrete individual-based colony model. The two models generate predictions in accordance with empirical data concerning the cumulative probability of becoming a forager, mean age at onset of foraging, reversal of foragers, time window of reversal, relationship between JH titre and onset of foraging, relative representations of genotypic groups, and effects of forager depletion and confinement.     

Identification and characterization of the slowly exchanging pH-dependent conformational rearrangement in KcsA

Gating of ion channels is strictly regulated by physiological conditions as well as intra/extracellular ligands. To understand the underlying structures mediating ion channel gating, we investigated the pH-dependent gating of the K(+) channel KcsA under near-physiological conditions, using solution-state NMR. In a series of (1)H(15)N-TROSY HSQC (transverse relaxation optimized spectroscopy-heteronuclear single quantum coherence) spectra measured at various pH values, significant chemical shift changes were detected between pH 3.9 and 5.2, reflecting a conformational rearrangement associated with the gating. The pH-dependent chemical shift changes were mainly observed for the resonances from the residues near the intracellular helix bundle, which has been considered to form the primary gate in the K(+) channel, as well as the intracellular extension of the inner helix. The substitution of His-25 by Ala abolished this pH-dependent conformational rearrangement, indicating that the residue serves as a "pH-sensor" for the channel. Although the electrophysiological open probability of KcsA is less than 10%, the conformations of the intracellular helix bundle between the acidic and neutral conditions seem to be remarkably different. This supports the recently proposed "dual gating" properties of the K(+) channel, in which the activation-coupled inactivation at the selectivity filter determines the channel open probability of the channel. Indeed, a pH-dependent chemical shift change was also observed for the signal from the Trp-67 indole, which is involved in a hydrogen bond network related to the activation-coupled inactivation. The slow kinetic parameter obtained for the intracellular bundle seems to fit better into the time scale for burst duration than very fast fluctuations within a burst period, indicating the existence of another gating element with faster kinetic properties.