Metabolic networks evolve towards states of maximum entropy production

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles.     

Quantum-like model of brain's functioning: decision making from decoherence

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex.     

Electronic excited states and excitation transfer kinetics in the Fenna-Matthews-Olson protein of the photosynthetic bacterium Prosthecochloris aestuarii at low temperatures

The molecular structure-function relationship of the Fenna-Matthews-Olson light-harvesting complex of the photosynthetic green bacterium Prosthecochloris aestuarii has been investigated. It has been assumed that the electronic excited states responsible for the function (transfer of electronic excitation energy) result from the dipole-dipole interactions between the bacteriochlorophyll molecules bound to the polypeptide chain of the complex at a specific three-dimensional geometry. The molecular structure-electronic excited states relationship has been addressed on the basis of simultaneous simulations of several spectroscopic observations. Current electronic excited state models for the Fenna-Matthews-Olson complex have generally been based on obtaining an optimal match between the information contents of the optical steady-state spectra and the bacteriochlorophyll organization. Recent kinetic and spectral information gathered from ultrafast time-resolved measurements have not yet been used effectively for further refinement of the excited state models and for quantification of the relation between the excited states and the energy transfer processes. In this study, we have searched for a model that not only can explain the key features of several steady-state spectra but also the temporal and spectral evolution observed in a recent absorption difference experiment and we have discussed the implications of this model for equilibration of the electronic excitation energy in systems at low temperatures. Received: 12 June 1998 / Revised version: 19 October 1998 / Accepted: 30 November 1998     

Entropy involved in fidelity of DNA replication

Information has an entropic character which can be analyzed within the framework of the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. Here, we introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.     

A quantum chemical investigation of the electronic structure of thionine

We have examined the electronic and molecular structure of 3,7-diaminophenothiazin-5-ium dye (thionine) in the electronic ground state and in the lowest excited states. The electronic structure was calculated using a combination of density functional theory and multi-reference configuration interaction (DFT/MRCI). Equilibrium geometries were optimized employing (time-dependent) density functional theory (B3LYP functional) combined with the TZVP basis set. Solvent effects were estimated using the COSMO model and micro-hydration with up to five explicit water molecules. Our calculated electronic energies are in good agreement with experimental data. We find the lowest excited singlet and triplet states at the ground state geometry to be of π→π* (S(1), S(2), T(1), T(2)) and n→π* (S(3), T(3)) character. This order changes when the molecular structure in the electronically excited states is relaxed. Geometry relaxation has almost no effect on the energy of the S(1) and T(1) states (~0.02 eV). The relaxation effects on the energies of S(2) and T(2) are moderate (0.14-0.20 eV). The very small emission energy results in a very low fluorescence rate. While we were not able to locate the energetic minimum of the S(3) state, we found a non-planar minimum for the T(3) state with an energy which is very close to the energy of the S(1) minimum in the gas phase (0.04 eV above). When hydration effects are taken into account, the n→π* states S(3) and T(3) are strongly blueshifted (0.33 and 0.46 eV), while the π→π* states are only slightly affected (<0.06 eV).     

Evolution of the major histocompatibility complex: independent origin of nonclassical class I genes in different groups of mammals

The class I major histocompatibility complex genes are composed of classical and nonclassical genes, the latter being largely nonfunctional. To understand the evolutionary relationships of the two groups of class I genes, a phylogenetic analysis of DNA sequences was conducted using 45 genes from six mammalian and one avian species. The results indicate that nonclassical genes in one species are more closely related to classical genes from the same species than to nonclassical genes from a species belonging to a different order or family. This indicates that the differentiation of classical and nonclassical genes occurs rather rapidly in the genome. Classical genes are apparently duplicated with a high frequency in the evolutionary process, and many of the duplicated genes seem to degenerate into nonclassical genes as a result of deleterious mutation. The nonclassical Qa genes in the mouse have sequences homologous to regulatory sequences involved in the universal expression of classical class I genes, but they have accumulated numerous nucleotide substitutions in these sequences. The pattern of nucleotide substitution in nonclassical genes is different from that in classical genes. In nonclassical genes, the rate of nonsynonymous substitution is higher in the antigen recognition site than in other gene regions, as is true of classical genes. However, unlike the case of classical genes, the nonsynonymous rate does not always exceed the synonymous rate in the antigen recognition site. Nonclassical proteins further differ from classical proteins in having amino acid replacements in conserved antigen recognition site positions. These observations are consistent with the hypothesis that nonclassical genes have originated from classical genes but have lost classical class I function because of deleterious mutation.     

Activation process of [NiFe] hydrogenase elucidated by high-resolution X-ray analyses: conversion of the ready to the unready state

Hydrogenases catalyze oxidoreduction of molecular hydrogen and have potential applications for utilizing dihydrogen as an energy source. [NiFe] hydrogenase has two different oxidized states, Ni-A (unready, exhibits a lag phase in reductive activation) and Ni-B (ready). We have succeeded in converting Ni-B to Ni-A with the use of Na2S and O2 and determining the high-resolution crystal structures of both states. Ni-B possesses a monatomic nonprotein bridging ligand at the Ni-Fe active site, whereas Ni-A has a diatomic species. The terminal atom of the bridging species of Ni-A occupies a similar position as C of the exogenous CO in the CO complex (inhibited state). The common features of the enzyme structures at the unready (Ni-A) and inhibited (CO complex) states are proposed. These findings provide useful information on the design of new systems of biomimetic dihydrogen production and fuel cell devices.     

How O2 binds to heme: reasons for rapid binding and spin inversion

We have used density functional methods to calculate fully relaxed potential energy curves of the seven lowest electronic states during the binding of O(2) to a realistic model of ferrous deoxyheme. Beyond a Fe-O distance of approximately 2.5 A, we find a broad crossing region with five electronic states within 15 kJ/mol. The almost parallel surfaces strongly facilitate spin inversion, which is necessary in the reaction of O(2) with heme (deoxyheme is a quintet and O(2) a triplet, whereas oxyheme is a singlet). Thus, despite a small spin-orbit coupling in heme, the transition probability approaches unity. Using reasonable parameters, we estimate a transition probability of 0.06-1, which is at least 15 times larger than for the nonbiological Fe-O(+) system. Spin crossing is anticipated between the singlet ground state of bound oxyheme, the triplet and septet dissociation states, and a quintet intermediate state. The fact that the quintet state is close in energy to the dissociation couple is of biological importance, because it explains how both spin states of O(2) may bind to heme, thereby increasing the overall efficiency of oxygen binding. The activation barrier is estimated to be <15 kJ/mol based on our results and M?ssbauer experiments. Our results indicate that both the activation energy and the spin-transition probability are tuned by the porphyrin as well as by the choice of the proximal heme ligand, which is a histidine in the globins. Together, they may accelerate O(2) binding to iron by approximately 10(11) compared with the Fe-O(+) system. A similar near degeneracy between spin states is observed in a ferric deoxyheme model with the histidine ligand hydrogen bonded to a carboxylate group, i.e. a model of heme peroxidases, which bind H(2)O(2) in this oxidation state.     

Molecular dipole effects on tuning electron transfer in a porphine–quinone complex: a DFT and TDDFT study

The effect of a strong electric field generated by molecular dipoles on the ground state electronic structure and the Q and B states as well as the lowest charge transfer (CT) excited state of porphine–2,5-dimethyl-1,4-benzoquinone (PQ) complex has been investigated theoretically. Density functional theory DFT and time-dependent DFT (TDDFT) with the BH&HLYP hybrid functional have been applied in these calculations. The molecular dipole effect was generated by imposing one or two helical homopeptides consisting of eight α-aminoisobutyric acid residues (Aib₈) close to the PQ complex. The molecular dipoles in a close proximity to the PQ complex expose it to an electric field of the order of magnitude of 10⁹ V/m. The presence of the ambient molecular dipoles affects mainly the energy of the lowest CT state and barely the energies of the Q and B states. The molecular dipoles affect the energies of the excited states in a similar way as an external electrostatic field. Hence, the electric field induced by the molecular dipoles of the helical peptides could be used analogously to the external electrostatic field to control electron transfer (ET) in the PQ complex.     

Thermodynamics of the interaction of insulin with its receptor.

Insulin binding to its cellular receptors is markedly dependent on the temperature. The thermodynamic parameters for the reaction of insulin with the high affinity state of its receptor have been evaluated with equilibrium studies at multiple temperatures between 5 degrees and 37 degrees C. The thermodynamics of the insulin-receptor interaction is not classical. The van't Hoff plot is not linear. Both the enthalpy and entropy changes, due to the formation of the hormone . receptor complex, decrease markedly with temperature, corresponding to a large heat capacity change of -766 cal/(mol deg) at 25 degrees C. The reaction is endothermic and entropically driven at low temperature and exothermic and enthalpically driven at higher temperature. This thermodynamic behavior is suggestive of a hydrophobic reaction and supports Blundell's concept that the loss of non-polar surface residues in the formation of the hormone . receptor complex is an important driving force of the reaction. Alternatively, this nonclassical behavior may indicate that the reaction of insulin with its receptor involves more than one step.     

Miscibility, chain packing, and hydration of 1-palmitoyl-2-oleoyl phosphatidylcholine and other lipids in surface phases.

The miscibility of 1-palmitoyl-2-oleoyl phosphatidylcholine with triolein, 1,2-diolein, 1,3-diolein, 1(3)-monoolein, oleyl alcohol, methyl oleate, oleic acid, and oleyl cyanide (18:1 lipids) was studied at the argon-water interface. The isothermal phase diagrams for the mixtures at 24 degrees were characterized by two compositional regions. At the limit of miscibility with lower mol fractions of 18:1 lipid, the surface pressure was composition-independent, but above a mixture-specific stoichiometry, surface pressure at the limit of miscibility was composition-dependent. From the two-dimensional phase rule, it was determined that at low mol fractions of 18:1 lipids, the surface consisted of phospholipid and a preferred packing array or complex of phospholipid and 18:1 lipid, whereas, above the stoichiometry of the complex, the surface phase consisted of complex and excess 18:1 lipids. In both regions of the phase diagram, mixing along the phase boundary was apparently ideal allowing application of an equation of state described earlier (J. M. Smaby and H. L. Brockman, 1984, Biochemistry, 23:3312-3316). From such analysis, apparent partial molecular areas and hydrations for phospholipid, complex, and 18:1 lipid were obtained. Comparison of these calculated parameters for the complexed and uncomplexed states shows that the aliphatic moieties behave independently of polar head group. The transition of each 18:1 chain to the complexed state involves the loss of about one interfacial water molecule and its corresponding area. For 18:1 lipids with more than one chain another two water molecules per additional chain are present in both states but contribute little to molecular area.(ABSTRACT TRUNCATED AT 250 WORDS)     

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

In this note we illustrate on a few examples of cells and proteins behavior that microscopic biological systems can exhibit a complex probabilistic behavior which cannot be described by classical probabilistic dynamics. These examples support authors conjecture that behavior of microscopic biological systems can be described by quantum-like models, i.e., models inspired by quantum-mechanics. At the same time we do not couple quantum-like behavior with quantum physical processes in bio-systems. We present arguments that such a behavior can be induced by information complexity of even smallest bio-systems, their adaptivity to context changes. Although our examples of the quantum-like behavior are rather simple (lactose-glucose interference in E. coli growth, interference effect for differentiation of tooth stem cell induced by the presence of mesenchymal cell, interference in behavior of PrP(C) and PrP(Sc) prions), these examples may stimulate the interest in systems biology to quantum-like models of adaptive dynamics and lead to more complex examples of nonclassical probabilistic behavior in molecular biology.     

Binding free energy calculation with QM/MM hybrid methods for Abl-Kinase inhibitor

We report a Quantum mechanics/Molecular Mechanics–Poisson-Boltzmann/ Surface Area (QM/MM-PB/SA) method to calculate the binding free energy of c-Abl human tyrosine kinase by combining the QM and MM principles where the ligand is treated quantum mechanically and the rest of the receptor by classical molecular mechanics. To study the role of entropy and the flexibility of the protein ligand complex in a solvated environment, molecular dynamics calculations are performed using a hybrid QM/MM approach. This work shows that the results of the QM/MM approach are strongly correlated with the binding affinity. The QM/MM interaction energy in our reported study confirms the importance of electronic and polarization contributions, which are often neglected in classical MM-PB/SA calculations. Moreover, a comparison of semi-empirical methods like DFTB-SCC, PM3, MNDO, MNDO-PDDG, and PDDG-PM3 is also performed. The results of the study show that the implementation of a DFTB-SCC semi-empirical Hamiltonian that is derived from DFT gives better results than other methods. We have performed such studies using the AMBER molecular dynamic package for the first time. The calculated binding free energy is also in agreement with the experimentally determined binding affinity for c-Abl tyrosine kinase complex with Imatinib.