An encompassed representation of timescale hierarchies in first-order reaction network.

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

On-the-fly Raman microscopy guaranteeing the accuracy of discrimination.

Accelerating the measurement for discrimination of samples, such as classification of cell phenotype, is crucial when faced with significant time and cost constraints. Spontaneous Raman microscopy offers label-free, rich chemical information but suffers from long acquisition time due to extremely small scattering cross-sections. One possible approach to accelerate the measurement is by measuring necessary parts with a suitable number of illumination points. However, how to design these points during measurement remains a challenge. To address this, we developed an imaging technique based on a reinforcement learning in machine learning (ML). This ML approach adaptively feeds back "optimal" illumination pattern during the measurement to detect the existence of specific characteristics of interest, allowing faster measurements while guaranteeing discrimination accuracy. Using a set of Raman images of human follicular thyroid and follicular thyroid carcinoma cells, we showed that our technique requires 3,333 to 31,683 times smaller number of illuminations for discriminating the phenotypes than raster scanning. To quantitatively evaluate the number of illuminations depending on the requisite discrimination accuracy, we prepared a set of polymer bead mixture samples to model anomalous and normal tissues. We then applied a home-built programmable-illumination microscope equipped with our algorithm, and confirmed that the system can discriminate the sample conditions with 104 to 4,350 times smaller number of illuminations compared to standard point illumination Raman microscopy. The proposed algorithm can be applied to other types of microscopy that can control measurement condition on the fly, offering an approach for the acceleration of accurate measurements in various applications including medical diagnosis.

Multi-armed bandit algorithm for sequential experiments of molecular properties with dynamic feature selection.

Sequential optimization is one of the promising approaches in identifying the optimal candidate(s) (molecules, reactants, drugs, etc.) with desired properties (reaction yield, selectivity, efficacy, etc.) from a large set of potential candidates, while minimizing the number of experiments required. However, the high dimensionality of the feature space (e.g., molecular descriptors) makes it often difficult to utilize the relevant features during the process of updating the set of candidates to be examined. In this article, we developed a new sequential optimization algorithm for molecular problems based on reinforcement learning, multi-armed linear bandit framework, and online, dynamic feature selections in which relevant molecular descriptors are updated along with the experiments. We also designed a stopping condition aimed to guarantee the reliability of the chosen candidate from the dataset pool. The developed algorithm was examined by comparing with Bayesian optimization (BO), using two synthetic datasets and two real datasets in which one dataset includes hydration free energy of molecules and another one includes a free energy difference between enantiomer products in chemical reaction. We found that the dynamic feature selection in representing the desired properties along the experiments provides a better performance (e.g., time required to find the best candidate and stop the experiment) as the overall trend and that our multi-armed linear bandit approach with a dynamic feature selection scheme outperforms the standard BO with fixed feature variables. The comparison of our algorithm to BO with dynamic feature selection is also addressed.

Correction for Extrinsic Background in Raman Hyperspectral Images.

Raman hyperspectral microscopy is a valuable tool in biological and biomedical imaging. Because Raman scattering is often weak in comparison to other phenomena, prevalent spectral fluctuations and contaminations have brought advancements in analytical and chemometric methods for Raman spectra. These chemometric advances have been key contributors to the applicability of Raman imaging to biological systems. As studies increase in scale, spectral contamination from extrinsic background, intensity from sources such as the optical components that are extrinsic to the sample of interest, has become an emerging issue. Although existing baseline correction schemes often reduce intrinsic background such as autofluorescence originating from the sample of interest, extrinsic background is not explicitly considered, and these methods often fail to reduce its effects. Here, we show that extrinsic background can significantly affect a classification model using Raman images, yielding misleadingly high accuracies in the distinction of benign and malignant samples of follicular thyroid cell lines. To mitigate its effects, we develop extrinsic background correction (EBC) and demonstrate its use in combination with existing methods on Raman hyperspectral images. EBC isolates regions containing the smallest amounts of sample materials that retain extrinsic contributions that are specific to the device or environment. We perform classification both with and without the use of EBC, and we find that EBC retains biological characteristics in the spectra while significantly reducing extrinsic background. As the methodology used in EBC is not specific to Raman spectra, correction of extrinsic effects in other types of hyperspectral and grayscale images is also possible.

Geometrical analysis identified morphological features of hydrogel-induced cancer stem cells in synovial sarcoma model cells.

Cancer stem cells (CSCs) has been a key target to cure cancer patients completely. Although many CSC markers have been identified, they are frequently cancer type-specific and those expressions are occasionally variable, which becomes an obstacle to elucidate the characteristics of the CSCs. Here we scrutinized the relationship between stemness elevation and geometrical features of single cells. The PAMPS hydrogel was utilized to create the CSCs from mouse myoblast C2C12 and its synovial sarcoma model cells. qRT-PCR analysis confirmed the significant increase in expression levels of Sox2, Nanog, and Oct3/4 on the PAMPS gel, which was higher in the synovial sarcoma model cells. Of note, the morphological heterogeneity was appeared on the PAMPS gel, mainly including flat spreading, elongated spindle, and small round cells, and the Sox2 expression was highest in the small round cells. To examine the role of morphological differences in the elevation of stemness, over 6,400 cells were segmented along with the Sox2 intensity, and 12 geometrical features were extracted at single cell level. A nonlinear mapping of the geometrical features by using uniform manifold approximation and projection (UMAP) clearly revealed the existence of relationship between morphological differences and the stemness elevation, especially for C2C12 and its synovial sarcoma model on the PAMPS gel in which the small round cells possess relatively high Sox2 expression on the PAMPS gel, which supports the strong relationship between morphological changes and the stemness elevation. Taken together, these geometrical features can be useful for morphological profiling of CSCs to classify and distinguish them for understanding of their role in disease progression and drug discovery.

Lipid droplet accumulation and adipophilin expression in follicular thyroid carcinoma.

Follicular neoplasms of the thyroid include follicular thyroid carcinoma (FTC) and follicular thyroid adenoma (FTA). However, the differences in cytological findings between FTC and FTA remain undetermined. Here, we aimed to evaluate the accumulation of lipid droplets (LDs) and the expression of adipophilin (perilipin 2/ADRP/ADFP), a known LD marker, in cultured FTC cells. We also immunohistochemically compared adipophilin expression in the FTC and FTA of resected human thyroid tissues. Cultured FTC (FTC-133 and RO82W-1) possessed increased populations of LDs compared to thyroid follicular epithelial (Nthy-ori 3-1) cells. In vitro treatment with phosphatidylinositol-3-kinase (PI3K)/Akt/mammalian target of rapamycin (mTOR) signaling inhibitors (LY294002, MK2206, and rapamycin) in FTC-133 cells downregulated the PI3K/Akt/mTOR/sterol regulatory element-binding protein 1 (SREBP1) signaling pathway, resulting in a significant reduction in LD accumulation. SREBP1 is a master transcription factor that controls lipid metabolism. Fluorescence immunocytochemistry revealed adipophilin expression in the LDs of FTC-133 cells. Immunohistochemical analysis of surgically resected human thyroid tissues revealed significantly increased expression of adipophilin in FTC compared with FTA and adjacent non-tumorous thyroid epithelia. Taken together, LDs and adipophilin were abundant in cultured FTC; the evaluation of adipophilin expression can help distinguish FTC from FTA in surgical specimens.

Differentiability of cell types enhanced by detrending a non-homogeneous pattern in a line-illumination Raman microscope.

A line illumination Raman microscope extracts the underlying spatial and spectral information of a sample, typically a few hundred times faster than raster scanning. This makes it possible to measure a wide range of biological samples such as cells and tissues - that only allow modest intensity illumination to prevent potential damage - within feasible time frame. However, a non-uniform intensity distribution of laser line illumination may induce some artifacts in the data and lower the accuracy of machine learning models trained to predict sample class membership. Here, using cancerous and normal human thyroid follicular epithelial cell lines, FTC-133 and Nthy-ori 3-1 lines, whose Raman spectral difference is not so large, we show that the standard pre-processing of spectral analyses widely used for raster scanning microscopes introduced some artifacts. To address this issue, we proposed a detrending scheme based on random forest regression, a nonparametric model-free machine learning algorithm, combined with a position-dependent wavenumber calibration scheme along the illumination line. It was shown that the detrending scheme minimizes the artifactual biases arising from non-uniform laser sources and significantly enhances the differentiability of the sample states, i.e., cancerous or normal epithelial cells, compared to the standard pre-processing scheme.

NMR spectrum prediction for dynamic molecules by machine learning: A case study of trefoil knot molecule.

Nuclear magnetic resonance (NMR) spectroscopy is one of the indispensable techniques in chemistry because it enables us to obtain accurate information on the chemical, electronic, and dynamic properties of molecules. Computational simulation of the NMR spectra requires time-consuming density functional theory (DFT) calculations for an ensemble of molecular conformations. For large flexible molecules, it is considered too high-cost since it requires time-averaging of the instantaneous chemical shifts of each nuclear spin across the conformational space of molecules for NMR timescales. Here, we present a Gaussian process/deep kernel learning-based machine learning (ML) method for enabling us to predict, average in time, and analyze the instantaneous chemical shifts of conformations in the molecular dynamics trajectory. We demonstrate the use of the method by computing the averaged 1H and 13C chemical shifts of each nuclear spin of a trefoil knot molecule consisting of 24 para-connected benzene rings (240 atoms). By training ML model with the chemical shift data obtained from DFT calculations, we predicted chemical shifts for each conformation during dynamics. We were able to observe the merging of the time-averaged chemical shifts of each nuclear spin in a singlet 1H NMR peak and two 13C NMR peaks for the knot molecule, in agreement with experimental measurements. The unique feature of the presented method is the use of the learned low-dimensional deep kernel representation of local spin environments for comparing and analyzing the local chemical environment histories of spins during dynamics. It allowed us to identify two groups of protons in the knot molecule, which implies that the observed singlet 1H NMR peak could be composed of the contributions from protons with two distinct local chemical environments.

Phase space geometry of isolated to condensed chemical reactions.

The complexity of gas and condensed phase chemical reactions has generally been uncovered either approximately through transition state theories or exactly through (analytic or computational) integration of trajectories. These approaches can be improved by recognizing that the dynamics and associated geometric structures exist in phase space, ensuring that the propagator is symplectic as in velocity-Verlet integrators and by extending the space of dividing surfaces to optimize the rate variationally, respectively. The dividing surface can be analytically or variationally optimized in phase space, not just over configuration space, to obtain more accurate rates. Thus, a phase space perspective is of primary importance in creating a deeper understanding of the geometric structure of chemical reactions. A key contribution from dynamical systems theory is the generalization of the transition state (TS) in terms of the normally hyperbolic invariant manifold (NHIM) whose geometric phase-space structure persists under perturbation. The NHIM can be regarded as an anchor of a dividing surface in phase space and it gives rise to an exact non-recrossing TS theory rate in reactions that are dominated by a single bottleneck. Here, we review recent advances of phase space geometrical structures of particular relevance to chemical reactions in the condensed phase. We also provide conjectures on the promise of these techniques toward the design and control of chemical reactions.

An information-theoretic approach to infer the underlying interaction domain among elements from finite length trajectories in a noisy environment.

Transfer entropy in information theory was recently demonstrated [Basak et al., Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. Therefore, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to the noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes the identification of the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy difficult. A measure to quantify the degree of strong convexity at the coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of the global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change in transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories.

FRET monitoring of a nonribosomal peptide synthetase.

Nonribosomal peptide synthetases (NRPSs) are multidomain enzyme templates for the synthesis of bioactive peptides. Large-scale conformational changes during peptide assembly are obvious from crystal structures, yet their dynamics and coupling to catalysis are poorly understood. We have designed an NRPS FRET sensor to monitor, in solution and in real time, the adoption of the productive transfer conformation between phenylalanine-binding adenylation (A) and peptidyl-carrier-protein domains of gramicidin synthetase I from Aneurinibacillus migulanus. The presence of ligands, substrates or intermediates induced a distinct fluorescence resonance energy transfer (FRET) readout, which was pinpointed to the population of specific conformations or, in two cases, mixtures of conformations. A pyrophosphate switch and lysine charge sensors control the domain alternation of the A domain. The phenylalanine-thioester and phenylalanine-AMP products constitute a mechanism of product inhibition and release that is involved in ordered assembly-line peptide biosynthesis. Our results represent insights from solution measurements into the conformational dynamics of the catalytic cycle of NRPSs.

Effects of non-equilibrium angle fluctuation on F1-ATPase kinetics induced by temperature increase.

F1-ATPase (F1) is an efficient rotary protein motor, whose reactivity is modulated by the rotary angle to utilize thermal fluctuation. In order to elucidate how its kinetics are affected by the change in the fluctuation, we have extended the reaction-diffusion formalism [R. Watanabe et al., Biophys. J., 2013, 105, 2385] applicable to a wider range of temperatures based on experimental data analysis of F1 derived from thermophilic Bacillus under high ATP concentration conditions. Our simulation shows that the rotary angle distribution manifests a stronger non-equilibrium feature as the temperature increases, because ATP hydrolysis and Pi release are more accelerated compared with the timescale of rotary angle relaxation. This effect causes the rate coefficient obtained from dwell time fitting to deviate from the Arrhenius relation in Pi release, which has been assumed in the previous activation thermodynamic quantities estimation using linear Arrhenius fitting. Larger negative correlation is also found between hydrolysis and Pi release waiting time in a catalytic dwell with the increase in temperature. This loss of independence between the two successive reactions at the catalytic dwell sheds doubt on the conventional dwell time fitting to obtain rate coefficients with a double exponential function at temperatures higher than 65 °C, which is close to the physiological temperature of the thermophilic Bacillus.

Deciphering hierarchical features in the energy landscape of adenylate kinase folding/unfolding.

Hierarchical features of the energy landscape of the folding/unfolding behavior of adenylate kinase, including its dependence on denaturant concentration, are elucidated in terms of single-molecule fluorescence resonance energy transfer (smFRET) measurements in which the proteins are encapsulated in a lipid vesicle. The core in constructing the energy landscape from single-molecule time-series across different denaturant concentrations is the application of rate-distortion theory (RDT), which naturally considers the effects of measurement noise and sampling error, in combination with change-point detection and the quantification of the FRET efficiency-dependent photobleaching behavior. Energy landscapes are constructed as a function of observation time scale, revealing multiple partially folded conformations at small time scales that are situated in a superbasin. As the time scale increases, these denatured states merge into a single basin, demonstrating the coarse-graining of the energy landscape as observation time increases. Because the photobleaching time scale is dependent on the conformational state of the protein, possible nonequilibrium features are discussed, and a statistical test for violation of the detailed balance condition is developed based on the state sequences arising from the RDT framework.

Extracting Subcellular Fibrillar Alignment with Error Estimation: Application to Microtubules.

The order and orientation of cortical microtubule (CMT) arrays and their dynamics play an essential role in plant morphogenesis. To extract detailed CMT alignment structures in an objective, local, and accurate way, we propose an error-based extraction method that applies to general fluorescence intensity data on three-dimensional cell surfaces. Building on previous techniques to quantify alignments, our method can determine the statistical error for specific local regions, or the minimal scales of local regions for a desired accuracy goal. After validating our method with synthetic images with known alignments, we demonstrate the ability of our method to quantify subcellular CMT alignments on images with microtubules marked with green fluorescent protein in various cell types. Our method could also be applied to detect alignment structures in other fibrillar elements, such as actin filaments, cellulose, and collagen.

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.

Kinetic Analysis for the Multistep Profiles of Organic Reactions: Significance of the Conformational Entropy on the Rate Constants of the Claisen Rearrangement.

The significance of kinetic analysis as a tool for understanding the reactivity and selectivity of organic reactions has recently been recognized. However, conventional simulation approaches that solve rate equations numerically are not amenable to multistep reaction profiles consisting of fast and slow elementary steps. Herein, we present an efficient and robust approach for evaluating the overall rate constants of multistep reactions via the recursive contraction of the rate equations to give the overall rate constants for the products and byproducts. This new method was applied to the Claisen rearrangement of allyl vinyl ether, as well as a substituted allyl vinyl ether. Notably, the profiles of these reactions contained 23 and 84 local minima, and 66 and 278 transition states, respectively. The overall rate constant for the Claisen rearrangement of allyl vinyl ether was consistent with the experimental value. The selectivity of the Claisen rearrangement reaction has also been assessed using a substituted allyl vinyl ether. The results of this study showed that the conformational entropy in these flexible chain molecules had a substantial impact on the overall rate constants. This new method could therefore be used to estimate the overall rate constants of various other organic reactions involving flexible molecules.

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.

Subdomain dynamics enable chemical chain reactions in non-ribosomal peptide synthetases.

Many peptide-derived natural products are produced by non-ribosomal peptide synthetases (NRPSs) in an assembly-line fashion. Each amino acid is coupled to a designated peptidyl carrier protein (PCP) through two distinct reactions catalysed sequentially by the single active site of the adenylation domain (A-domain). Accumulating evidence suggests that large-amplitude structural changes occur in different NRPS states; yet how these molecular machines orchestrate such biochemical sequences has remained elusive. Here, using single-molecule Förster resonance energy transfer, we show that the A-domain of gramicidin S synthetase I adopts structurally extended and functionally obligatory conformations for alternating between adenylation and thioester-formation structures during enzymatic cycles. Complementary biochemical, computational and small-angle X-ray scattering studies reveal interconversion among these three conformations as intrinsic and hierarchical where intra-A-domain organizations propagate to remodel inter-A-PCP didomain configurations during catalysis. The tight kinetic coupling between structural transitions and enzymatic transformations is quantified, and how the gramicidin S synthetase I A-domain utilizes its inherent conformational dynamics to drive directional biosynthesis with a flexibly linked PCP domain is revealed.

Aggregated markov model using time series of single molecule dwell times with minimum excessive information.

Statistics of the dwell times, the stationary state distributions (SSDs), are often studied to infer the underlying kinetics from a single molecule finite-level time series. However, it is well known that the underlying kinetic scheme, a hidden Markov model (HMM), cannot be identified uniquely from the SSDs because some features of the underlying HMM are hidden by finite-level measurements. Here, we quantify the amount of excessive information in a given HMM that is not warranted by the measured SSDs and extract the HMM with minimum excessive information as the most objective representation of the data. The method is applied to a single molecule enzymatic turnover experiment, and the origin of dynamic disorder is discussed in terms of the network properties of the HMM.

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.