Mechanism and Experimental Observability of Global Switching Between Reactive and Nonreactive Coordinates at High Total Energies.

We present a mechanism of global reaction coordinate switching, namely, a phenomenon in which the reaction coordinate dynamically switches to another coordinate as the total energy of the system increases. The mechanism is based on global changes in the underlying phase space geometry caused by a switching of dominant unstable modes from the original reactive mode to another nonreactive mode in systems with more than 2 degrees of freedom. We demonstrate an experimental observability to detect a reaction coordinate switching in an ionization reaction of a hydrogen atom in crossed electric and magnetic fields. For this reaction, the reaction coordinate is a coordinate along which electrons escape and its switching changes the escaping direction from the direction of the electric field to that of the magnetic field and, thus, the switching can be detected experimentally by measuring the angle-resolved momentum distribution of escaping electrons.

Local-heterogeneous responses and transient dynamics of cage breaking and formation in colloidal fluids.

Quantifying the interactions in dense colloidal fluids requires a properly designed order parameter. We present a modified bond-orientational order parameter, ψ̄6, to avoid problems of the original definition of bond-orientational order parameter. The original bond-orientational order parameter can change discontinuously in time but our modified order parameter is free from the discontinuity and, thus, it is a suitable measure to quantify the dynamics of the bond-orientational ordering of the local surroundings. Here we analyze ψ̄6 in a dense driven monodisperse quasi-two-dimensional colloidal fluids where a single particle is optically trapped at the center. The perturbation by the trapped and driven particle alters the structure and dynamics of the neighboring particles. This perturbation disturbs the flow and causes spatial and temporal distortion of the bond-orientational configuration surrounding each particle. We investigate spatio-temporal behavior of ψ̄6 by a Wavelet transform that provides a time-frequency representation of the time series of ψ̄6. It is found that particles that have high power in frequencies corresponding to the inverse of the timescale of perturbation undergo distortions of their packing configurations that result in cage breaking and formation dynamics. To gain insight into the dynamic structure of cage breaking and formation of bond-orientational ordering, we compare the cage breaking and formation dynamics with the underlying dynamical structure identified by Lagrangian Coherent Structures (LCSs) estimated from the finite-time Lyapunov exponent (FTLE) field. The LCSs are moving separatrices that effectively divide the flow into distinct regions with different dynamical behavior. It is shown that the spatial distribution of the FTLE field and the power of particles in the wavelet transform have positive correlation, implying that LCSs provide a dynamic structure that dominates the dynamics of cage breaking and formation of the colloidal fluids.

Influence of SigB inactivation on Corynebacterium glutamicum protein secretion.

The non-essential Corynebacterium glutamicum sigma factor, sigB, modulates global gene expression during the transition from exponential growth to the stationary phase. Utilizing a signal peptide derived from C. glutamicum R CgR_0949, a sigB disruption mutant able to secrete 3- to 5-fold more green fluorescence protein (GFP) and α-amylase than the wild type strain was isolated. The signal peptide selectively enabled the mutant to produce greater amounts of both proteins, which were in turn secreted in culture medium in greater quantities than previously acknowledged. A peak GFP productivity of 2.8 g/l was attained, representing the highest GFP productivity reported in C. glutamicum to date. CgR_0949 signal sequence length (30 residues), type (Tat) or the target protein identity (GFP or α-amylase) had no measurable effect on the magnitude of the protein accumulation and consequent secretion. It therefore follows that actual experimentation remains the fastest way to identify suitable signal sequences in C. glutamicum. More secretion studies may reveal even greater secretion productivity by C. glutamicum and consequently present an attractive avenue to further enhance the utility of C. glutamicum as an industrial workhorse.

Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series.

We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ~3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.

Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems.

Normally hyperbolic invariant manifolds (NHIMs) are well-known organizing centers of the dynamics in the phase space of a nonlinear system. Locating such manifolds in systems far from symmetric or integrable, however, has been an outstanding challenge. Here, we develop an automated detection method for codimension-one NHIMs in autonomous dynamical systems. Our method utilizes Stationary Lagrangian Coherent Structures (SLCSs), which are hypersurfaces satisfying one of the necessary conditions of a hyperbolic LCS, and are also quasi-invariant in a well-defined sense. Computing SLCSs provides a quick way to uncover NHIMs with high accuracy. As an illustration, we use SLCSs to locate two-dimensional stable and unstable manifolds of hyperbolic periodic orbits in the classic ABC flow, a three-dimensional solution of the steady Euler equations.

Reproducing the Reaction Route Map on the Shape Space from Its Quotient by the Complete Nuclear Permutation-Inversion Group.

This study develops an algorithm to reproduce reaction route maps (RRMs) in the shape space from the outputs of potential search algorithms. To demonstrate the algorithm, global reaction route mapping is utilized as a potential search algorithm, but the proposed algorithm should work with other potential search algorithms in principle. The proposed algorithm does not require any encoding of the molecular configurations and is thus applicable to complicated realistic molecules for which efficient encoding is not readily available. We show that subgraphs of an RRM mapped to each other by the action of the symmetry group are isomorphic and also provide an algorithm to compute the set of feasible transformations in the sense of Longuet-Higgins. We demonstrate the proposed algorithm in toy models and in more realistic molecules. Finally, we remark on absolute rate theory from our perspective.

Characterizing Reaction Route Map of Realistic Molecular Reactions Based on Weight Rank Clique Filtration of Persistent Homology.

A reaction route map (RRM) constructed using the GRRM program is a collection of elementary reaction pathways, each of which comprises two equilibrium (EQ) geometries and one transition state (TS) geometry connected by an intrinsic reaction coordinate (IRC). An RRM can be mathematically represented by a graph with weights assigned to both vertices, corresponding to EQs, and edges, corresponding to TSs, representing the corresponding energies. In this study, we propose a method to extract topological descriptors of a weighted graph representing an RRM based on persistent homology (PH). The work of Mirth et al. [ J. Chem. Phys. 2021, 154, 114114], in which PH analysis was applied to the (3N - 6)-dimensional potential energy surface of an N atomic system, is related to the present method, but our method is practically applicable to realistic molecular reactions. Numerical assessments revealed that our method can extract the same information as the method proposed by Mirth et al. for the 0-th and 1-st PHs, except for the death of the 1-st PH. In addition, the information obtained from the 0-th PH corresponds to the analysis using the disconnectivity graph. The results of this study suggest that the descriptors obtained using the proposed method accurately reflect the characteristics of the chemical reactions and/or physicochemical properties of the system.

Dynamical switching of a reaction coordinate to carry the system through to a different product state at high energies.

Questions of how the nature of a reaction coordinate that dominates the reaction ceases to exist and whether some new features emerge as an increase of total energy of systems are investigated for many degrees of freedom Hamiltonian systems. As a model system, a hydrogen atom in crossed electric and magnetic fields is scrutinized. It is shown that, when the total energy increases, the reaction coordinate no longer dominates the reaction as did at the lower energies. In turn, a new reaction coordinate emerges, connecting totally different reactant and product states. Furthermore, depending on which parts of the phase space the system traverses through the saddle, the system nonuniformly experiences the switching of the reaction coordinate leading to the different product state. The universal mechanism of the cessation and the switching of the reaction coordinate at high energy regimes above the saddle is investigated.

High yield secretion of heterologous proteins in Corynebacterium glutamicum using its own Tat-type signal sequence.

Efficient protein secretion, the basis of large-scale production of many compounds central to the biotechnology industry, is achieved by signal peptide and propeptide optimization in addition to optimizing host factors affecting heterologous protein production. Here, we fused green fluorescent protein (GFP) to the recently identified Tat-type secretory signal peptide of CgR0949 to demonstrate a high-yield protein secretion system of Corynebacterium glutamicum. The resultant secretion vector facilitated effective secretion of active-form GFP (20 mg l(-1)) into C. glutamicum culture medium. The expression of GFP was enhanced 2.9-fold using the Shine-Dalgarno sequence of triosephosphate isomerase in the secretion vector. Moreover, GFP drastically accumulated in the culture supernatant upon addition of calcium chloride even though Ca(2+) addition did neither enhanced the transcription of gfp nor resulted in the accumulation of cytosolic GFP. Active-form GFP concentration reached 1.8 g l(-1) after 48-h incubation in a jar fermentor. Likewise, α-amylase accumulation in C. glutamicum cultures was also enhanced by Ca(2+) addition, suggesting that Ca(2+) may affect general protein secretion in C. glutamicum.

Development of a rapid process monitoring method for dry-coated tableting process by using near-infrared spectroscopy.

A nondestructive transmittance near-infrared (NIR) method for detecting off-centered cores in dry-coated (DC) tablets was developed as a monitoring system in the DC tableting process. Caffeine anhydrate was used as a core active pharmaceutical ingredient (API), and DC tablets were made by the direct compression method. NIR spectra were obtained from these intact DC tablets using the transmittance method. The reference assay was performed with HPLC. Calibration models were generated by partial least squares (PLS) regression and principal component regression (PCR) utilizing external validations. Hierarchical cluster analysis (HCA) of the results confirmed that NIR spectroscopy correctly detected off-centered cores in DC tablets. We formulated and used the Centering Index (CI) to evaluate the precision of core alignment and generated an NIR calibration model that could correctly predict this index. The principal component (PC) 1 loading vector of the final calibration model indicated that it could specifically detect the misalignment of tablet cores. The model also had good linearity and accuracy. The CIs of unknown sample tablets predicted by the final calibration model and those calculated through the HPLC analysis were closely parallel with each other. These results demonstrate the validity of the final calibration model and the utility of the transmittance NIR spectroscopic method developed in this study as a monitoring system in DC tableting process.

Cytochrome P450 monooxygenases involved in anthracene metabolism by the white-rot basidiomycete Phanerochaete chrysosporium.

Cytochrome P450 monooxygenases (P450s) involved in anthracene metabolism by the white-rot basidiomycete Phanerochaete chrysosporium were identified by comprehensive screening of both catalytic potentials and transcriptomic profiling. Functional screening of P. chrysosporium P450s (PcCYPs) revealed that 14 PcCYP species catalyze stepwise conversion of anthracene to anthraquinone via intermediate formation of anthrone. Moreover, transcriptomic profiling explored using a complementary DNA microarray system demonstrated that 12 PcCYPs are up-regulated in response to exogenous addition of anthracene. Among the up-regulated PcCYPs, five species showed catalytic activity against anthracene. Based upon both catalytic and transcriptional properties, these five species are most likely to play major roles in anthracene metabolic processes in vivo. Thus, the combination of functional screening and a microarray system may provide a novel strategy for obtaining a thorough understanding of the catalytic functions and biological impacts of PcCYPs.

How does a choice of Markov partition affect the resultant symbolic dynamics?

The mutual relationship among Markov partitions is investigated for one-dimensional piecewise monotonic map. It is shown that if a Markov partition is regarded as a map-refinement of the other Markov partition, that is, a concept we newly introduce in this article, one can uniquely translate a set of symbolic sequences by one Markov partition to those by the other or vice versa. However, the set of symbolic sequences constructed using Markov partitions is not necessarily translated with each other if there exists no map-refinement relation among them. By using a roof map we demonstrate how the resultant symbolic sequences depend on the choice of Markov partitions.

Exploring remnants of invariants buried in a deep potential well in chemical reactions.

We revisit the concept of "remnant of invariant manifolds" originally discussed by Shirts and Reinhardt in a two degrees of freedom Henon-Heiles system [J. Chem. Phys. 77, 5204 (1982)]. This is regarded as the remnants of a destroyed invariant manifold that can dominate the transport in phase space even at high energy regions where most of all tori vanish. We present a novel technique to extract such remnants of invariants from a sea of chaos in highly nonlinear coupled molecular systems in terms of the canonical perturbation theory based on Lie transforms. As an illustrative example we demonstrate in HCN isomerization reaction that the conventional procedure based on a finite order truncation of the coordinate transformation prevent us from detecting remnants of invariants. However, our technique correctly captures the underlying remnants of invariants that shed light on the energetics of chemical reaction, that is, how the reactive mode acquires (releases) energy from (to) the other vibrational mode in order to overcome the potential barrier (to be trapped in the potential well). We also found the qualitative difference between the two potential wells, HCN and CNH, which coincides with the nearest neighbor level spacing distribution of the vibrational quantum states within the wells.

Probing remnants of invariants to mediate energy exchange in highly chaotic many-dimensional systems.

A technique is presented to scrutinize a piece of remnants of invariants [R. B. Shirts and W. P. Reinhardt, J. Chem. Phys. 77, 15 (1982)] buried in chaos in many degrees of freedom (DOF) dynamical systems in terms of canonical perturbation theory based on Lie transforms. The transformed canonical variables are often evaluated by the truncation of the coordinate transformation at a finite order in the original Hamiltonian system. However, the truncation of canonical variables gives rise to a loss of the symplectic property of the system. This results in apparent abrupt fluctuation of the action integrals, which yields a misinterpretation. We demonstrate, in a three-DOF Hamiltonian system of HCN isomerization reaction, that our technique can detect remnants of invariants buried in the potential well even at energies higher than the potential barrier, although the conventional truncation scheme fails to do so. This technique makes it possible to shed light on the physical insight into how the reactive mode exchanges its energy with the other modes and through which resonance the energy exchange takes place in reacting systems.

Spectral-clustering approach to Lagrangian vortex detection.

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.

Deciphering Time Scale Hierarchy in Reaction Networks.

Markovian dynamics on complex reaction networks are one of the most intriguing subjects in a wide range of research fields including chemical reactions, biological physics, and ecology. To represent the global kinetics from one node (corresponding to a basin on an energy landscape) to another requires information on multiple pathways that directly or indirectly connect these two nodes through the entire network. In this paper we present a scheme to extract a hierarchical set of global transition states (TSs) over a discrete-time Markov chain derived from first-order rate equations. The TSs can naturally take into account the multiple pathways connecting any pair of nodes. We also propose a new type of disconnectivity graph (DG) to capture the hierarchical organization of different time scales of reactions that can capture changes in the network due to changes in the time scale of observation. The crux is the introduction of the minimum conductance cut (MCC) in graph clustering, corresponding to the dividing surface across the network having the "smallest" transition probability between two disjoint subnetworks (superbasins on the energy landscape) in the network. We present a new combinatorial search algorithm for finding this MCC. We apply our method to a reaction network of Claisen rearrangement of allyl vinyl ether that consists of 23 nodes and 66 links (saddles on the energy landscape) connecting them. We compare the kinetic properties of our DG to those of the transition matrix of the rate equations and show that our graph can properly reveal the hierarchical organization of time scales in a network.

Microscopic description of the equality between violation of fluctuation-dissipation relation and energy dissipation.

In systems far from equilibrium, the fluctuation-dissipation relation is violated due to the lack of detailed balance. Recently, for a class of Langevin equations, it has been proved that this violation is related to energy dissipation as an equality [Phys. Rev. Lett. 95, 130602 (2005)]. We provide a microscopic description of this equality by studying a nonequilibrium colloidal system on the basis of classical mechanics with some physical assumptions.

Fungal cytochrome P450s catalyzing hydroxylation of substituted toluenes to form their hydroxymethyl derivatives.

The degradation of a series of nitroaromatic compounds by the lignin-degrading fungus Phanerochaete chrysosporium was examined. From 4-nitrotoluene (4-NT), several metabolic intermediates were identified. Initially, 4-NT was converted to 4-nitrobenzyl alcohol (4-NBA), followed by the oxidation reactions to form 4-nitrobenzaldehyde and 4-nitrobenzoic acid, albeit slowly. Exogenously added 4-nitrobenzaldehyde and 4-nitrobenzoic acid were predominantly reduced to 4-NBA. The fungal formation of 4-NBA was inhibited by piperonyl butoxide, a cytochrome P450 inhibitor, suggesting the involvement of cytochrome P450 in the hydroxylation of the methyl group. Similarly, 2-, and 3-nitrotoluenes and 4-chlorotoluene were converted to the corresponding arylalcohols by P. chrysosporium. On the other hand, toluene and 4-methoxytoluene were not converted. Thus, P. chrysosporium possesses an alkyl hydroxylation activity against aromatic compounds substituted with a strong electron-withdrawing group.

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.

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.