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.

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.

Comparison of particle image velocimetry and the underlying agents dynamics in collectively moving self propelled particles.

Collective migration of cells is a fundamental behavior in biology. For the quantitative understanding of collective cell migration, live-cell imaging techniques have been used using e.g., phase contrast or fluorescence images. Particle tracking velocimetry (PTV) is a common recipe to quantify cell motility with those image data. However, the precise tracking of cells is not always feasible. Particle image velocimetry (PIV) is an alternative to PTV, corresponding to Eulerian picture of fluid dynamics, which derives the average velocity vector of an aggregate of cells. However, the accuracy of PIV in capturing the underlying cell motility and what values of the parameters should be chosen is not necessarily well characterized, especially for cells that do not adhere to a viscous flow. Here, we investigate the accuracy of PIV by generating images of simulated cells by the Vicsek model using trajectory data of agents at different noise levels. It was found, using an alignment score, that the direction of the PIV vectors coincides with the direction of nearby agents with appropriate choices of PIV parameters. PIV is found to accurately measure the underlying motion of individual agents for a wide range of noise level, and its condition is 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.

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.

Raman imaging of rat nonalcoholic fatty liver tissues reveals distinct biomolecular states.

An essential challenge in diagnosing states of nonalcoholic fatty liver disease (NAFLD) is the early prediction of progression from nonalcoholic fatty liver (NAFL) to nonalcoholic steatohepatitis (NASH) before the disease progresses. Histological diagnoses of NAFLD rely on the appearance of anomalous tissue morphologies, and it is difficult to segment the biomolecular environment of the tissue through a conventional histopathological approach. Here, we show that hyperspectral Raman imaging provides diagnostic information on NAFLD in rats, as spectral changes among disease states can be detected before histological characteristics emerge. Our results demonstrate that Raman imaging of NAFLD can be a useful tool for histopathologists, offering biomolecular distinctions among tissue states that cannot be observed through standard histopathological means.

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.

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.

ERK MAP Kinase Signaling Regulates RAR Signaling to Confer Retinoid Resistance on Breast Cancer Cells.

Retinoic acid (RA) and its synthetic derivatives, retinoids, have been established as promising anticancer agents based on their ability to regulate cell proliferation and survival. Clinical trials, however, have revealed that cancer cells often acquire resistance to retinoid therapy. Therefore, elucidation of underlying mechanisms of retinoid resistance has been considered key to developing more effective use of retinoids in cancer treatment. In this study, we show that constitutive activation of ERK MAP kinase signaling, which is often caused by oncogenic mutations in RAS or RAF genes, suppresses RA receptor (RAR) signaling in breast cancer cells. We show that activation of the ERK pathway suppresses, whereas its inhibition promotes, RA-induced transcriptional activation of RAR and the resultant upregulation of RAR-target genes in breast cancer cells. Importantly, ERK inhibition potentiates the tumor-suppressive activity of RA in breast cancer cells. Moreover, we also reveal that suppression of RAR signaling and activation of ERK signaling are associated with poor prognoses in breast cancer patients and represent hallmarks of specific subtypes of breast cancers, such as basal-like, HER2-enriched and luminal B. These results indicate that ERK-dependent suppression of RAR activity underlies retinoid resistance and is associated with cancer subtypes and patient prognosis in breast cancers.

Modes of information flow in collective cohesion.

Pairwise interactions are fundamental drivers of collective behavior-responsible for group cohesion. The abiding question is how each individual influences the collective. However, time-delayed mutual information and transfer entropy, commonly used to quantify mutual influence in aggregated individuals, can result in misleading interpretations. Here, we show that these information measures have substantial pitfalls in measuring information flow between agents from their trajectories. We decompose the information measures into three distinct modes of information flow to expose the role of individual and group memory in collective behavior. It is found that decomposed information modes between a single pair of agents reveal the nature of mutual influence involving many-body nonadditive interactions without conditioning on additional agents. The pairwise decomposed modes of information flow facilitate an improved diagnosis of mutual influence in collectives.

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.

Transfer entropy dependent on distance among agents in quantifying leader-follower relationships.

Synchronized movement of (both unicellular and multicellular) systems can be observed almost everywhere. Understanding of how organisms are regulated to synchronized behavior is one of the challenging issues in the field of collective motion. It is hypothesized that one or a few agents in a group regulate(s) the dynamics of the whole collective, known as leader(s). The identification of the leader (influential) agent(s) is very crucial. This article reviews different mathematical models that represent different types of leadership. We focus on the improvement of the leader-follower classification problem. It was found using a simulation model that the use of interaction domain information significantly improves the leader-follower classification ability using both linear schemes and information-theoretic schemes for quantifying influence. This article also reviews different schemes that can be used to identify the interaction domain using the motion data of agents.

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.

Dependence of DNA length on binding affinity between TrpR and trpO of DNA.

We scrutinize the length dependency of the binding affinity of bacterial repressor TrpR protein to trpO (specific site) on DNA. A footprinting experiment shows that the longer the DNA length, the larger the affinity of TrpR to the specific site on DNA. This effect termed "antenna effect" might be interpreted as follows: longer DNA provides higher probability for TrpR to access to the specific site aided by one-dimensional diffusion along the nonspecific sites of DNA. We show that, however, the antenna effect cannot be explained while detailed balance holds among three kinetic states, that is, free protein/DNA, nonspecific complexes, and specific complex. We propose a working hypothesis that slow degree(s) of freedom in the system switch(es) different potentials of mean force causing transitions among the three states. This results in a deviation from detailed balance on the switching timescale. We then derive a simple reaction diffusion/binding model that describes the antenna effect on TrpR binding to its target operator. Possible scenarios for such slow degree(s) of freedom in TrpR-DNA complex are addressed.

Inferring domain of interactions among particles from ensemble of trajectories.

An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a "cutoff distance variable" which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain. It is shown that transfer entropy is superior for inferring the interaction radius compared to cross correlation, hence resulting in a higher performance for inferring the leader-follower relationship. The effects of noise size exerted from environment and the ratio of the numbers of leader and follower on the classification performance are also discussed.