Binding characteristics of the doxepin E/Z-isomers to the histamine H1 receptor revealed by receptor-bound ligand analysis and molecular dynamics study.

Doxepin is an antihistamine and tricyclic antidepressant that binds to the histamine H1 receptor (H1R) with high affinity. Doxepin is an 85:15 mixture of the E- and Z-isomers. The Z-isomer is well known to be more effective than the E-isomer, whereas based on the crystal structure of the H1R/doxepin complex, the hydroxyl group of Thr1123.37 is close enough to form a hydrogen bond with the oxygen atom of the E-isomer. The detailed binding characteristics and reasons for the differences remain unclear. In this study, we analyzed doxepin isomers bound to the receptor following extraction from a purified H1R protein complexed with doxepin. The ratio of the E- and Z-isomers bound to wild-type (WT) H1R was 55:45, indicating that the Z-isomer was bound to WT H1R with an approximately 5.2-fold higher affinity than the E-isomer. For the T1123.37V mutant, the E/Z ratio was 89:11, indicating that both isomers have similar affinities. Free energy calculations using molecular dynamics (MD) simulations also reproduced the experimental results of the relative binding free energy differences between the isomers for WT and T1123.37V. Furthermore, MD simulations revealed that the hydroxyl group of T1123.37 did not form hydrogen bonds with the E-isomer, but with the adjacent residues in the binding pocket. Analysis of the receptor-bound doxepin and MD simulations suggested that the hydroxyl group of T1123.37 contributes to the formation of a chemical environment in the binding pocket, which is slightly more favorable for the Z-isomer without hydrogen bonding with doxepin.

Classification of the HCN isomerization reaction dynamics in Ar buffer gas via machine learning.

The effect of the presence of Ar on the isomerization reaction HCN ⇄ CNH is investigated via machine learning. After the potential energy surface function is developed based on the CCSD(T)/aug-cc-pVQZ level ab initio calculations, classical trajectory simulations are performed. Subsequently, with the aim of extracting insights into the reaction dynamics, the obtained reactivity, that is, whether the reaction occurs or not under a given initial condition, is learned as a function of the initial positions and momenta of all the atoms in the system. The prediction accuracy of the trained model is greater than 95%, indicating that machine learning captures the features of the phase space that affect reactivity. Machine learning models are shown to successfully reproduce reactivity boundaries without any prior knowledge of classical reaction dynamics theory. Subsequent analyses reveal that the Ar atom affects the reaction by displacing the effective saddle point. When the Ar atom is positioned close to the N atom (resp. the C atom), the saddle point shifts to the CNH (HCN) region, which disfavors the forward (backward) reaction. The results imply that analyses aided by machine learning are promising tools for enhancing the understanding of reaction dynamics.

CDK actively contributes to establishment of the stationary phase state in fission yeast.

Upon exhaustion of essential environmental nutrients, unicellular organisms cease cell division and enter stationary phase, a metabolically repressed state essential for cell survival in stressful environments. In the fission yeast Schizosaccharomyces pombe, cell size is reduced by cell division before entry into stationary phase; thus cyclin-dependent kinase (CDK) must actively contribute to stationary phase establishment. However, the contribution of CDK to stationary phase remains largely uncharacterized. Here, we examine the role of the sole S. pombe CDK, Cdc2, in the establishment of stationary phase. We show that in stationary phase, nuclear and chromosomal volumes and the nucleus-to-cell volume ratio are reduced, and sister chromatid separation and chromosome fluctuation are repressed. Furthermore, Cdc2 accumulates in the nucleolus. Most of these changes are induced by glucose depletion. Reduction in Cdc2 activity before and upon stationary phase entry alleviates the changes and shortens the survival time of stationary phase cells, whereas Cdc2 inhibition represses nucleolar Cdc2 accumulation and glucose depletion-induced nuclear volume reduction. These results demonstrate that CDK actively regulates stationary phase, both before and upon stationary phase entry.

Chiasmata and the kinetochore component Dam1 are crucial for elimination of erroneous chromosome attachments and centromere oscillation at meiosis I.

Establishment of proper chromosome attachments to the spindle requires elimination of erroneous attachments, but the mechanism of this process is not fully understood. During meiosis I, sister chromatids attach to the same spindle pole (mono-oriented attachment), whereas homologous chromosomes attach to opposite poles (bi-oriented attachment), resulting in homologous chromosome segregation. Here, we show that chiasmata that link homologous chromosomes and kinetochore component Dam1 are crucial for elimination of erroneous attachments and oscillation of centromeres between the spindle poles at meiosis I in fission yeast. In chiasma-forming cells, Mad2 and Aurora B kinase, which provides time for attachment correction and destabilizes erroneous attachments, respectively, caused elimination of bi-oriented attachments of sister chromatids, whereas in chiasma-lacking cells, they caused elimination of mono-oriented attachments. In chiasma-forming cells, in addition, homologous centromere oscillation was coordinated. Furthermore, Dam1 contributed to attachment elimination in both chiasma-forming and chiasma-lacking cells, and drove centromere oscillation. These results demonstrate that chiasmata alter attachment correction patterns by enabling error correction factors to eliminate bi-oriented attachment of sister chromatids, and suggest that Dam1 induces elimination of erroneous attachments. The coincidental contribution of chiasmata and Dam1 to centromere oscillation also suggests a potential link between centromere oscillation and attachment elimination.

Regression Analysis for Nucleation-Elongation Model of Supramolecular Assembly: How To Determine Nucleus Size.

Nucleation-elongation is known to give satisfactory descriptions of many supramolecular polymerization systems in thermal equilibrium. Its key feature is the necessity to form a "nucleus" consisting of a certain number of monomer units before being able to grow into a longer polymer chain. The size of the nucleus has significant implications for the understanding of the supramolecular polymerization mechanism. Here we investigate how experiments can give information on the nucleus size by regression analysis of various types of measurements. The measurements of free monomer concentrations, diffusion coefficients, and calorimetric response as functions of concentration or temperature are considered. The nucleation-elongation model with a general value for the nucleus size is used to provide mathematical expressions for these experimental observables. Numerical experiments are performed where experimental errors are simulated by computer-generated random numbers, and it is investigated whether least-squares fitting analyses can give the correct values of the nucleus size in the presence of experimental errors. It is recommended that the calorimetric measurements such as differential scanning calorimetry (DSC) or isothermal titration calorimetry (ITC) be performed under various conditions to correctly determine the nucleus size experimentally.

Control over differentiation of a metastable supramolecular assembly in one and two dimensions.

Molecular self-assembly under kinetic control is expected to yield nanostructures that are inaccessible through the spontaneous thermodynamic process. Moreover, time-dependent evolution, which is reminiscent of biomolecular systems, may occur under such out-of-equilibrium conditions, allowing the synthesis of supramolecular assemblies with enhanced complexities. Here we report on the capacity of a metastable porphyrin supramolecular assembly to differentiate into nanofibre and nanosheet structures. Mechanistic studies of the relationship between the molecular design and pathway complexity in the self-assembly unveiled the energy landscape that governs the unique kinetic behaviour. Based on this understanding, we could control the differentiation phenomena and achieve both one- and two-dimensional living supramolecular polymerization using an identical monomer. Furthermore, we found that the obtained nanostructures are electronically distinct, which illustrates the pathway-dependent material properties.

Recovering hidden dynamical modes from the generalized Langevin equation.

In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection.

On the environmental modes for the generalized Langevin equation.

The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.

Diversity in ATP concentrations in a single bacterial cell population revealed by quantitative single-cell imaging.

Recent advances in quantitative single-cell analysis revealed large diversity in gene expression levels between individual cells, which could affect the physiology and/or fate of each cell. In contrast, for most metabolites, the concentrations were only measureable as ensemble averages of many cells. In living cells, adenosine triphosphate (ATP) is a critically important metabolite that powers many intracellular reactions. Quantitative measurement of the absolute ATP concentration in individual cells has not been achieved because of the lack of reliable methods. In this study, we developed a new genetically-encoded ratiometric fluorescent ATP indicator "QUEEN", which is composed of a single circularly-permuted fluorescent protein and a bacterial ATP binding protein. Unlike previous FRET-based indicators, QUEEN was apparently insensitive to bacteria growth rate changes. Importantly, intracellular ATP concentrations of numbers of bacterial cells calculated from QUEEN fluorescence were almost equal to those from firefly luciferase assay. Thus, QUEEN is suitable for quantifying the absolute ATP concentration inside bacteria cells. Finally, we found that, even for a genetically-identical Escherichia coli cell population, absolute concentrations of intracellular ATP were significantly diverse between individual cells from the same culture, by imaging QUEEN signals from single cells.

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles.

Reactivity boundaries that divide the origin and destination of trajectories are of crucial importance to reveal the mechanism of reactions, which was recently found to exist robustly even at high energies for index 1 saddles [Phys. Rev. Lett. 105, 048304 (2010)]. Here we revisit the concept of the reactivity boundary and propose a more general definition that can involve a single reaction associated with a bottleneck composed of higher-index saddles and/or several saddle points with different indices, where the normal form theory, based on expansion around a single stationary point, does not work. We numerically demonstrate the reactivity boundary by using a reduced model system of the H(5)(+) cation where the proton exchange reaction takes place through a bottleneck composed of two index 2 saddle points and two index 1 saddle points. The cross section of the reactivity boundary in the reactant region of the phase space reveals which initial conditions are effective in making the reaction happen and thus sheds light on the reaction mechanism.

Reactivity boundaries to separate the fate of a chemical reaction associated with an index-two saddle.

Reactivity boundaries that divide the destination and the origin of trajectories are of crucial importance to reveal the mechanism of reactions. We investigate whether such reactivity boundaries can be extracted for higher index saddles in terms of a nonlinear canonical transformation successful for index-one saddles by using a model system with an index-two saddle. It is found that the true reactivity boundaries do not coincide with those extracted by the transformation taking into account a nonlinearity in the region of the saddle even for small perturbations, and the discrepancy is more pronounced for the less repulsive direction of the index-two saddle system. The present result indicates an importance of the global properties of the phase space to identify the reactivity boundaries, relevant to the question of what reactant and product are in phase space, for saddles with index more than one.

Numerical construction of estimators for single-molecule fluorescence measurements.

A novel scheme to estimate the values of the underlying physical quantity and those of any functions of the quantity from measured observable(s) contaminated with stochastic noise is presented for any arbitrary probability distribution. The constructed estimators can either maximize the unbiasedness (i.e., minimize the amount of the deviation of the expectation value from the true value buried in the measurement) or minimize the risk (the average deviation from the true value) depending on the relative priority of unbiasedness and risk in the data analysis. The performance of the constructed estimators is demonstrated with computer simulations of Förster-type resonance energy transfer (FRET) measurements and also with FRET experimental data of the agonist-binding domain of the GluA2 subunit of AMPA receptors with agonists chloro- and iodo-willardiines and with adenylate kinase both in the apo form and with substrates AMP-PNP and AMP. It is shown that the estimators constructed by the present method can quantify faithfully not only the physical quantity to be monitored but also the functions of that quantity for a wide range of values.

Why and how do systems react in thermally fluctuating environments?

Many chemical reactions, including those of biological importance, take place in thermally fluctuating environments. Compared to isolated systems, there arise markedly different features due to the effects of energy dissipation through friction and stochastic driving by random forces reflecting the fluctuation of the environment. Investigation of how robustly the system reacts under the influence of thermal fluctuation, and elucidating the role of thermal fluctuation in the reaction are significant subjects in the study of chemical reactions. In this article, we start with overviewing the generalized Langevin equation (GLE), which has long been used and continues to be a powerful tool to describe a system surrounded by a thermal environment. It has been also generalized further to treat a nonstationary environment, in which the conventional fluctuation-dissipation theorem no longer holds. Then, within the framework of the Langevin equation we present a method recently developed to extract a new reaction coordinate that is decoupled from all the other coordinates in the region of a rank-one saddle linking the reactant and the product. The reaction coordinate is buried in nonlinear couplings among the original coordinates under the influence of stochastic random force. It was ensured that the sign of this new reaction coordinate (= a nonlinear functional of the original coordinates, velocities, friction, and random force) at any instant is sufficient to determine in which region, the reactant or the product, the system finally arrives. We also discuss how one can extend the method to extract such a coordinate from the GLE framework in stationary and nonstationary environments, where memory effects exist in dynamics of the reaction.

Phase space geometry of dynamics passing through saddle coupled with spatial rotation.

Nonlinear reaction dynamics through a rank-one saddle is investigated for many-particle system with spatial rotation. Based on the recently developed theories of the phase space geometry in the saddle region, we present a theoretical framework to incorporate the spatial rotation which is dynamically coupled with the internal vibrational motions through centrifugal and Coriolis interactions. As an illustrative simple example, we apply it to isomerization reaction of HCN with some nonzero total angular momenta. It is found that no-return transition state (TS) and a set of impenetrable reaction boundaries to separate the "past" and "future" of trajectories can be identified analytically under rovibrational couplings. The three components of the angular momentum are found to have distinct effects on the migration of the "anchor" of the TS and the reaction boundaries through rovibrational couplings and anharmonicities in vibrational degrees of freedom. This method provides new insights in understanding the origin of a wide class of reactions with nonzero angular momentum.

Derivation of the generalized Langevin equation in nonstationary environments.

The generalized Langevin equation (GLE) is extended to the case of nonstationary bath. The derivation starts with the Hamiltonian equation of motion of the total system including the bath, without any assumption on the form of Hamiltonian or the distribution of the initial condition. Then the projection operator formulation is utilized to obtain a low-dimensional description of the system dynamics surrounded by the nonstationary bath modes. In contrast to the ordinary GLE, the mean force becomes a time-dependent function of the position and the velocity of the system. The friction kernel is found to depend on both the past and the current times, in contrast to the stationary case where it only depends on their difference. The fluctuation-dissipation theorem, which relates the statistical property of the random force to the friction kernel, is also derived for general nonstationary cases. The resulting equation of motion is as simple as the ordinary GLE, and is expected to give a powerful framework to analyze the dynamics of the system surrounded by a nonstationary bath.

Quantum reaction boundary to mediate reactions in laser fields.

Dynamics of passage over a saddle is investigated for a quantum system under the effect of time-dependent external field (laser pulse). We utilize the recently developed theories of nonlinear dynamics in the saddle region, and extend them to incorporate both time-dependence of the external field and quantum mechanical effects of the system. Anharmonic couplings and laser fields with any functional form of time dependence are explicitly taken into account. As the theory is based on the Weyl expression of quantum mechanics, interpretation is facilitated by the classical phase space picture, while no "classical approximation" is involved. We introduce a quantum reactivity operator to extract the reactive part of the system. In a model system with an optimally controlled laser field for the reaction, it is found that the boundary of the reaction in the phase space, extracted by the reactivity operator, is modulated with time by the effect of the laser field, to "catch" the system excited in the reactant region, and then to "release" it into the product region. This method provides new insights in understanding the origin of optimal control of chemical reactions by laser fields.

Dynamic reaction coordinate in thermally fluctuating environment in the framework of the multidimensional generalized Langevin equations.

A framework recently developed for the extraction of a dynamic reaction coordinate to mediate reactions buried in a multidimensional Langevin equation is extended to the generalized Langevin equations without a priori assumption of the forms of the potential (in general, nonlinearly coupled systems) and the friction kernel. The equation of motion with memory effect can be transformed into an equation without memory at the cost of an increase in the dimensionality of the system, and hence the theoretical framework developed for the (nonlinear) Langevin formulation can be generalized to the non-Markovian process with colored noise. It is found that the increased dimension can be physically interpreted as effective modes of the fluctuating environment. As an illustrative example, we apply this theory to a multidimensional generalized Langevin equation for motion on the Müller-Brown potential surface with an exponential friction kernel. Numerical simulations find a boundary between the highly reactive region and the less reactive region in the space of initial conditions. The location of the boundary is found to depend significantly on both the memory kernel and the nonlinear couplings. The theory extracts a reaction coordinate whose sign determines the fate of the reaction taking into account thermally fluctuating environments, memory effect, and nonlinearities. It is found that the location of the boundary of reactivity is satisfactorily reproduced as the zero of the statistical average of the new reaction coordinate, which is an analytical functional of both the original position coordinates and velocities of the system, and of the properties of the environment.

Robust existence of a reaction boundary to separate the fate of a chemical reaction.

Nonlinear dynamics around a rank-one saddle is investigated in a high energy regime above the reaction threshold. The transition state (TS) is considered as a surface of a "point of no return" through which all reactive trajectories pass only once in the process of climbing over the saddle before being captured in the product state. A no-return TS ceases to exist above a certain high energy regime. However, even at high energies where the no-return TS can no longer exist, it is shown that "an impenetrable barrier" in the phase space robustly persists, which acts as a boundary between reactive and nonreactive trajectories. This implies that we can yet predict the fate of reactions even when the no-return TS may not exist. As an example, we show the analysis of dynamical systems theory for a hydrogen atom in crossed electric and magnetic fields.

Hierarchy of reaction dynamics in a thermally fluctuating environment.

Nonlinear dynamics in the passage over a rank-one saddle is investigated as a function of temperature in the presence of stochastic, thermal fluctuation. The analyses are based on a framework we developed recently adopting a multidimensional underdamped Langevin equation (without any assumption for the form of the potential of mean force). The framework can in principle provide a single coordinate to enable us to predict the final destination of the reaction in a thermally fluctuating media. At each temperature, the preciseness or the error of the reaction coordinate is evaluated in capturing the true reaction dynamics at different levels of approximations. By using the Müller-Brown potential as an illustrative example, it is found that a hierarchy of dynamical structure exists in the region of a rank-one saddle, in which the crossing dynamics qualitatively changes as the temperature increases. We discuss the mechanism of how the reaction coordinate persists, which provides a boundary of the reaction to divide the phase space into the reactive and the nonreactive regions, even in the presence of thermal fluctuation.

Nonlinear dynamical effects on reaction rates in thermally fluctuating environments.

A framework to calculate the rate constants of condensed phase chemical reactions of manybody systems is presented without relying on the concept of transition state. The theory is based on a framework we developed recently adopting a multidimensional underdamped Langevin equation in the region of a rank-one saddle. The theory provides a reaction coordinate expressed as an analytical nonlinear functional of the position coordinates and velocities of the system (solute), the friction constants, and the random force of the environment (solvent). Up to moderately high temperature, the sign of the reaction coordinate can determine the final destination of the reaction in a thermally fluctuating media, irrespective of what values the other (nonreactive) coordinates may take. In this paper, it is shown that the reaction probability is analytically derived as the probability of the reaction coordinate being positive, and that the integration with the Boltzmann distribution of the initial conditions leads to the exact reaction rate constant when the local equilibrium holds and the quantum effect is negligible. Because of analytical nature of the theory taking into account all nonlinear effects and their combination with fluctuation and dissipation, the theory naturally provides us with the firm mathematical foundation of the origin of the reactivity of the reaction in a fluctuating media.