Publishing type：Research paper (scientific journal)   Publisher：Oxford University Press (OUP)  

Abstract

Characterizing phenotypes is a fundamental aspect of biological sciences, although it can be challenging due to various factors. For instance, the liverwort (Marchantia polymorpha), a model system for plant biology, exhibits morphological variability, making it difficult to identify and quantify distinct phenotypic features using objective measures. To address this issue, we utilized a deep learning-based image classifier that can handle plant images directly without manual extraction of phenotypic features, and analyzed pictures of M. polymorpha. This dioicous plant species exhibits morphological differences between male and female wild accessions at an early stage of gemmaling growth, although it remains elusive whether the differences are attributable to sex chromosomes. To isolate the effects of sex chromosomes from autosomal polymorphisms, we established a male and female set of recombinant inbred lines (RILs) from a set of male and female wild accessions. We then trained deep-learning models to classify the sexes of the RILs and the wild accessions. Our results showed that the trained classifiers accurately classified male and female gemmalings of wild accessions in the first week of growth, confirming the intuition of researchers in a reproducible and objective manner. In contrast, the RILs were less distinguishable, indicating that the differences between the parental wild accessions arose from autosomal variations. Furthermore, we validated our trained models by an “explainable AI” technique that highlights image regions relevant to the classification. Our findings demonstrate that the classifier-based approach provides a powerful tool for analyzing plant species that lack standardized phenotyping metrics.

DOI： 10.1093/pcp/pcad117

Publisher：Cold Spring Harbor Laboratory  

The cytoplasm is a complex, crowded environment that influences myriad cellular processes including protein folding and metabolic reactions. Recent studies have suggested that changes in the biophysical properties of the cytoplasm play a key role in cellular homeostasis and adaptation. However, it still remains unclear how cells control their cytoplasmic properties in response to environmental cues. Here, we used fission yeast spores as a model system of dormant cells to elucidate the mechanisms underlying regulation of the cytoplasmic properties. By tracking fluorescent tracer particles, we found that particle mobility decreased in spores compared to vegetative cells, and rapidly increased at the onset of dormancy breaking upon glucose addition. This cytoplasmic fluidization depended on glucose sensing via the cAMP-PKA pathway. PKA activation led to trehalose degradation through trehalase Ntp1, thereby increasing particle mobility as the amount of trehalose decreased. In contrast, the rapid cytoplasmic fluidization did not require de novo protein synthesis, cytoskeletal dynamics, or cell volume increase. Furthermore, the measurement of diffusion coefficients with tracer particles of different sizes suggests that the spore cytoplasm impedes the movement of larger protein complexes (40-150 nm) such as ribosomes, while allowing free diffusion of smaller molecules (-3 nm) such as second messengers and signaling proteins. Our experiments have thus uncovered a series of signaling events that enable cells to quickly fluidize the cytoplasm at the onset of dormancy breaking.

DOI： 10.1101/2023.09.27.559686

Publisher：Cold Spring Harbor Laboratory  

Cyclin-dependent kinase (CDK) plays an essential role in determining the temporal ordering of the cell cycle phases. However, despite significant progress in studying regulators of CDK, it remains elusive how they coordinately affect CDK activity at the single-cell level and how CDK controls the temporal order of cell cycle events. This could be due to the lack of tools to monitor CDK activity in living cells. Here, we elucidate the dynamics of CDK activity in fission yeast and mammalian cells by using a newly developed CDK activity biosensor, Eevee-spCDK, based on Forster Resonance Energy Transfer (FRET). Taking advantage of this system, we unravel the profile of CDK activity in vegetatively growing S. pombe cells. Thus, we detect a transient increase in S phase followed by a gradual increment during G2 phase. CDK activity then reaches its maximum in early M phase and rapidly decreases at mitotic exit. During G2 phase, CDK activity exhibits a biphasic pattern, i.e., an early slow increase and a late fast rise prior to the G2/M phase transition, as predicted from mathematical studies. Remarkably, although CDK activity does not necessarily correlate with cyclin levels, we find that it converges to the same level around mitotic onset in several mutant backgrounds, including pom1Δ cells and wee1 or cdc25 overexpressing cells. These data provide the first direct evidence that cells enter M phase when CDK activity reaches a high threshold, consistent with the quantitative model of cell cycle progression in fission yeast.

DOI： 10.1101/2023.03.26.534249

Language：English   Publishing type：Research paper (scientific journal)  

G-protein-coupled receptors (GPCRs) play an important role in sensing various extracellular stimuli, such as neurotransmitters, hormones, and tastants, and transducing the input information into the cell. While the human genome encodes more than 800 GPCR genes, only four Gα-proteins (Gαs, Gαi/o, Gαq/11, and Gα12/13) are known to couple with GPCRs. It remains unclear how such divergent GPCR information is translated into the downstream G-protein signaling dynamics. To answer this question, we report a live-cell fluorescence imaging system for monitoring GPCR downstream signaling dynamics. Genetically encoded biosensors for cAMP, Ca2+, RhoA, and ERK were selected as markers for GPCR downstream signaling, and were stably expressed in HeLa cells. GPCR was further transiently overexpressed in the cells. As a proof-of-concept, we visualized GPCR signaling dynamics of five dopamine receptors and 12 serotonin receptors, and found heterogeneity between GPCRs and between cells. Even when the same Gα proteins were known to be coupled, the patterns of dynamics in GPCR downstream signaling, including the signal strength and duration, were substantially distinct among GPCRs. These results suggest the importance of dynamical encoding in GPCR signaling.

DOI： 10.1042/BCJ20220021

PubMed

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

<title>Abstract</title>Cell tracking is one of the most critical tools for time-lapse image analysis to observe cell behavior and cell lineages over a long period of time. However, the accompanying graphical user interfaces are often difficult to use and do not incorporate seamless manual correction, data analysis tools, or simple training set design tools if it is machine learning based. In this paper, we introduce our cell tracking software “LIM Tracker”. This software has a conventional tracking function consisting of recognition processing and link processing, a sequential search-type tracking function based on pattern matching, and a manual tracking function. LIM Tracker enables the seamless use of these functions. In addition, the system incorporates a highly interactive and interlocking data visualization method, which displays analysis result in real time, making it possible to flexibly correct the data and reduce the burden of tracking work. Moreover, recognition functions with deep learning (DL) are also available, which can be used for a wide range of targets including stain-free images. LIM Tracker allows researchers to track living objects with good usability and high versatility for various targets. We present a tracking case study based on fluorescence microscopy images (NRK-52E/EKAREV-NLS cells or MCF-10A/H2B-iRFP-P2A-mScarlet-I-hGem-P2A-PIP-NLS-mNeonGreen cells) and phase contrast microscopy images (Glioblastoma-astrocytoma U373 cells). LIM Tracker is implemented as a plugin for ImageJ/Fiji. The software can be downloaded from <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://github.com/LIMT34/LIM-Tracker">https://github.com/LIMT34/LIM-Tracker</ext-link>.

DOI： 10.1038/s41598-022-06269-6

PubMed

Other Link： https://www.nature.com/articles/s41598-022-06269-6

Publishing type：Research paper (international conference proceedings)   Publisher：SCITEPRESS  

DOI： 10.5220/0010915700003124

Other Link： https://dblp.uni-trier.de/db/conf/visapp/visapp2022-1.html#FujiiMUKH22

Publishing type：Research paper (scientific journal)   Publisher：The Company of Biologists  

<title>ABSTRACT</title>
Near-infrared fluorescent protein (iRFP) is a bright and stable fluorescent protein with near-infrared excitation and emission maxima. Unlike the other conventional fluorescent proteins, iRFP requires biliverdin (BV) as a chromophore. Here, we report that phycocyanobilin (PCB) functions as a brighter chromophore for iRFP than BV, and that biosynthesis of PCB allows live-cell imaging with iRFP in the fission yeast Schizosaccharomyces pombe. We initially found that fission yeast cells did not produce BV and therefore did not show any iRFP fluorescence. The brightness of iRFP–PCB was higher than that of iRFP–BV both in vitro and in fission yeast. We introduced SynPCB2.1, a PCB biosynthesis system, into fission yeast, resulting in the brightest iRFP fluorescence. To make iRFP readily available in fission yeast, we developed an endogenous gene tagging system with iRFP and all-in-one integration plasmids carrying the iRFP-fused marker proteins together with SynPCB2.1. These tools not only enable the easy use of multiplexed live-cell imaging in fission yeast with a broader color palette, but also open the door to new opportunities for near-infrared fluorescence imaging in a wider range of living organisms.


This article has an associated First Person interview with the first author of the paper.

DOI： 10.1242/jcs.259315

Other Link： https://journals.biologists.com/jcs/article-pdf/doi/10.1242/jcs.259315/2125216/jcs259315.pdf

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

<jats:title>Abstract</jats:title><jats:p>Actomyosin contractility generated cooperatively by nonmuscle myosin II and actin filaments plays essential roles in a wide range of biological processes, such as cell motility, cytokinesis, and tissue morphogenesis. However, subcellular dynamics of actomyosin contractility underlying such processes remains elusive. Here, we demonstrate an optogenetic method to induce relaxation of actomyosin contractility at the subcellular level. The system, named OptoMYPT, combines a protein phosphatase 1c (PP1c)-binding domain of MYPT1 with an optogenetic dimerizer, so that it allows light-dependent recruitment of endogenous PP1c to the plasma membrane. Blue-light illumination is sufficient to induce dephosphorylation of myosin regulatory light chains and a decrease in actomyosin contractile force in mammalian cells and <jats:italic>Xenopus</jats:italic> embryos. The OptoMYPT system is further employed to understand the mechanics of actomyosin-based cortical tension and contractile ring tension during cytokinesis. We find that the relaxation of cortical tension at both poles by OptoMYPT accelerated the furrow ingression rate, revealing that the cortical tension substantially antagonizes constriction of the cleavage furrow. Based on these results, the OptoMYPT system provides opportunities to understand cellular and tissue mechanics.</jats:p>

DOI： 10.1038/s41467-021-27458-3

DOI： 10.1101/2021.04.19.440549

PubMed

Publishing type：Research paper (scientific journal)   Publisher：The Company of Biologists  

<title>ABSTRACT</title>
The extracellular signal-regulated kinase (ERK) pathway governs cell proliferation, differentiation and migration, and therefore plays key roles in various developmental and regenerative processes. Recent advances in genetically encoded fluorescent biosensors have unveiled hitherto unrecognized ERK activation dynamics in space and time and their functional importance mainly in cultured cells. However, ERK dynamics during embryonic development have still only been visualized in limited numbers of model organisms, and we are far from a sufficient understanding of the roles played by developmental ERK dynamics. In this Review, we first provide an overview of the biosensors used for visualization of ERK activity in live cells. Second, we highlight the applications of the biosensors to developmental studies of model organisms and discuss the current understanding of how ERK dynamics are encoded and decoded for cell fate decision-making.

DOI： 10.1242/dev.199767

Language：Japanese   Publisher：(公財)金原一郎記念医学医療振興財団  

＜文献概要＞細胞内情報伝達系の応答において,分子活性の時間的な変動や細胞内・個体内での分子局在の空間的な分布が重要であることがわかっている。しかし,このような複雑な応答と細胞外部環境との関係をいかに特徴づければよいだろうか。素朴に言えば,「時系列や空間分布に拡張された相関係数」のようなものが必要になるであろう。本稿では,情報理論を応用して前述の問題に対処しようとする近年の試みについて概観する。

Language：English   Publishing type：Research paper (scientific journal)  

Cells respond to a wide range of extracellular stimuli, and process the input information through an intracellular signaling system comprised of biochemical and biophysical reactions, including enzymatic and protein-protein interactions. It is essential to understand the molecular mechanisms underlying intracellular signal transduction in order to clarify not only physiological cellular functions but also pathological processes such as tumorigenesis. Fluorescent proteins have revolutionized the field of life science, and brought the study of intracellular signaling to the single-cell and subcellular levels. Much effort has been devoted to developing genetically encoded fluorescent biosensors based on fluorescent proteins, which enable us to visualize the spatiotemporal dynamics of cell signaling. In addition, optogenetic techniques for controlling intracellular signal transduction systems have been developed and applied in recent years by regulating intracellular signaling in a light-dependent manner. Here, we outline the principles of biosensors for probing intracellular signaling and the optogenetic tools for manipulating them.

DOI： 10.1007/978-981-15-8763-4_13

Scopus

PubMed

Language：English   Publishing type：Research paper (scientific journal)  

Collective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

DOI： 10.1038/s41598-021-83396-6

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PubMed

Publisher：Cold Spring Harbor Laboratory  

<title>Abstract</title>Domesticated plants and animals display tremendous diversity in various phenotypic traits and often this diversity is seen within the same species. Tomato (<italic>Solanum lycopersicum</italic>; Solanaceae) cultivars show wide variation in leaf morphology, but the influence of breeding efforts in sculpting this diversity is not known. Here, we demonstrate that a single nucleotide deletion in the homeobox motif of <italic>BIPINNATA</italic>, which is a <italic>BEL-LIKE HOMEODOMAIN</italic> gene, led to a highly complex leaf phenotype in an heirloom tomato, Silvery Fir Tree (SiFT). Additionally, a comparative gene network analysis revealed that reduced expression of the ortholog of <italic>WUSCHEL RELATED HOMEOBOX 1</italic> is also important for the narrow leaflet phenotype seen in SiFT. Phylogenetic and comparative genome analysis using whole-genome sequencing data suggests that the <italic>bip</italic> mutation in SiFT is likely a <italic>de novo</italic> mutation, instead of standing genetic variation. These results provide new insights into natural variation in phenotypic traits introduced into crops during improvement processes after domestication.

DOI： 10.1101/2020.09.08.287011

Publishing type：Research paper (scientific journal)   Publisher：American Chemical Society (ACS)  

DOI： 10.1021/acschembio.0c00477

Scopus

Publishing type：Research paper (scientific journal)  

DOI： 10.1074/jbc.RA119.007685

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PubMed

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Public Library of Science ({PLoS})  

Living tissues undergo deformation during morphogenesis. In this process, cells generate mechanical forces that drive the coordinated cell motion and shape changes. Recent advances in experimental and theoretical techniques have enabled in situ measurement of the mechanical forces, but the characterization of mechanical properties that determine how these forces quantitatively affect tissue deformation remains challenging, and this represents a major obstacle for the complete understanding of morphogenesis. Here, we proposed a non-invasive reverse-engineering approach for the estimation of the mechanical properties, by combining tissue mechanics modeling and statistical machine learning. Our strategy is to model the tissue as a continuum mechanical system and to use passive observations of spontaneous tissue deformation and force fields to statistically estimate the model parameters. This method was applied to the analysis of the collective migration of Madin-Darby canine kidney cells, and the tissue flow and force were simultaneously observed by the phase contrast imaging and traction force microscopy. We found that our monolayer elastic model, whose elastic moduli were reverse-engineered, enabled a long-term forecast of the traction force fields when given the tissue flow fields, indicating that the elasticity contributes to the evolution of the tissue stress. Furthermore, we investigated the tissues in which myosin was inhibited by blebbistatin treatment, and observed a several-fold reduction in the elastic moduli. The obtained results validate our framework, which paves the way to the estimation of mechanical properties of living tissues during morphogenesis.

DOI： 10.1371/journal.pcbi.1006029

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PubMed

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Nature Publishing Group  

Mathematical modeling and analysis of biochemical reaction networks are key routines in computational systems biology and biophysics
however, it remains difficult to choose the most valid model. Here, we propose a computational framework for data-driven and systematic inference of a nonlinear biochemical network model. The framework is based on the expectation-maximization algorithm combined with particle smoother and sparse regularization techniques. In this method, a "redundant" model consisting of an excessive number of nodes and regulatory paths is iteratively updated by eliminating unnecessary paths, resulting in an inference of the most likely model. Using artificial single-cell time-course data showing heterogeneous oscillatory behaviors, we demonstrated that this algorithm successfully inferred the true network without any prior knowledge of network topology or parameter values. Furthermore, we showed that both the regulatory paths among nodes and the optimal number of nodes in the network could be systematically determined. The method presented in this study provides a general framework for inferring a nonlinear biochemical network model from heterogeneous single-cell time-course data.

DOI： 10.1038/s41598-018-25064-w

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PubMed

Language：English   Publishing type：Research paper (scientific journal)  

The stress-activated protein kinases c-Jun N-terminal kinase (JNK) and p38 are important players in cell-fate decisions in response to environmental stress signals. Crosstalk signaling between JNK and p38 is emerging as an important regulatory mechanism in inflammatory and stress responses. However, it is unknown how this crosstalk affects signaling dynamics, cell-to-cell variation, and cellular responses at the single-cell level. We established a multiplexed live-cell imaging system based on kinase translocation reporters to simultaneously monitor JNK and p38 activities with high specificity and sensitivity at single-cell resolution. Various stresses activated JNK and p38 with various dynamics. In all cases, p38 suppressed JNK activity in a cross-inhibitory manner. We demonstrate that p38 antagonizes JNK through both transcriptional and post-translational mechanisms. This cross-inhibition generates cellular heterogeneity in JNK activity after stress exposure. Our data indicate that this heterogeneity in JNK activity plays a role in fractional killing in response to UV stress.

DOI： 10.1016/j.celrep.2018.08.020

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PubMed

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

Extracting a small number of relevant features for the task, i.e., feature selection, is often a crucial step in supervised learning problems. Sparse linear regression provides a fast and convenient option for feature selection, where regularization facilitates reducing the weight parameters of irrelevant features. However, the regularization also induces undesirable shrinkage in the weights of relevant features.
Here, we propose Bayesian masking (BM) in order to resolve the trade-off problem between sparsity and shrinkage. Our strategy is not to directly impose any regularization on the weights; instead, BM introduces binary latent variables, called masking variables, into a regression model to keep the sparsity; each feature and sample has a binary variable whose value determines if the feature is masked or not at the sample. We derive a variational Bayesian inference algorithm for the augmented model based on the factorized information criterion (FIC), a recently-proposed asymptotic approximation of the marginal log-likelihood. We analyze the one-dimensional estimators of Lasso, automatic relevance determination (ARD), and BM, and thus show the superiority of BM in terms of the sparsity-shrinkage trade-off. Finally, we confirm our theoretical analyses through experiments and, demonstrate that BM achieves higher feature selection accuracy compared with Lasso and ARD. (C) 2017 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.neucom.2016.12.080

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：CELL PRESS  

The biophysical framework of collective cell migration has been extensively investigated in recent years; however, it remains elusive how chemical inputs from neighboring cells are integrated to coordinate the collective movement. Here, we provide evidence that propagation waves of extracellular signal-related kinase (ERK) mitogen-activated protein kinase activation determine the direction of the collective cell migration. A wound-healing assay of Mardin-Darby canine kidney (MDCK) epithelial cells revealed two distinct types of ERK activation wave, a "tidal wave'' from the wound, and a self-organized "spontaneous wave'' in regions distant from the wound. In both cases, MDCK cells collectively migrated against the direction of the ERK activation wave. The inhibition of ERK activation propagation suppressed collective cell migration. An ERK activation wave spatiotemporally controlled actomyosin contraction and cell density. Furthermore, an optogenetic ERK activation wave reproduced the collective cell migration. These data provide new mechanistic insight into how cells sense the direction of collective cell migration.

DOI： 10.1016/j.devcel.2017.10.016

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PubMed

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Proceedings of the National Academy of Sciences  

Cell-cell signaling is subject to variability in the extracellular volume, cell number, and dilution that potentially increase uncertainty in the absolute concentrations of the extracellular signaling molecules. To direct cell aggregation, the social amoebae Dictyostelium discoideum collectively give rise to oscillations and waves of cyclic adenosine 3', 5'-monophosphate (cAMP) under a wide range of cell density. To date, the systems-level mechanism underlying the robustness is unclear. By using quantitative live-cell imaging, here we show that the magnitude of the cAMP relay response of individual cells is determined by fold change in the extracellular cAMP concentrations. The range of cell density and exogenous cAMP concentrations that support oscillations at the population level agrees well with conditions that support a large fold-change-dependent response at the singlecell level. Mathematical analysis suggests that invariance of the oscillations to density transformation is a natural outcome of combining secrete-and-sense systems with a fold-change detection mechanism.

DOI： 10.1073/pnas.1702181114

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Public Library of Science ({PLoS})  

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient D an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies.

DOI： 10.1371/journal.pone.0164674

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J-GLOBAL

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：JMLR.org  

Other Link： https://dblp.uni-trier.de/rec/conf/acml/2015

Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society ({APS})  

We propose a statistical machine-learning approach to derive low-dimensional models by integrating noisy time-series data from partial observation of high-dimensional systems, aiming to utilize quantitative data on biological phenomena in the cell. In particular, the method estimates a model from data at different values of a bifurcation parameter in order to characterize biological functions as bifurcation types that are insensitive to system details and experimental errors. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations and the learned systems are shown to robustly inherit the bifurcation types. DOI: 10.1103/PhysRevE.87.042716

DOI： 10.1103/PhysRevE.87.042716

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

All cells derive nutrition by absorbing some chemical and energy resources from the environment; these resources are used by the cells to reproduce the chemicals within them, which in turn leads to an increase in their volume. In this study we introduce a protocell model exhibiting catalytic reaction dynamics, energy metabolism, and cell growth. Results of extensive simulations of this model show the existence of four phases with regard to the rates of both the influx of resources and cell growth. These phases include an active phase with high influx and high growth rates, an inefficient phase with high influx but low growth rates, a quasistatic phase with low influx and low growth rates, and a death phase with negative growth rate. A mean field model well explains the transition among these phases as bifurcations. The statistical distribution of the active phase is characterized by a power law, and that of the inefficient phase is characterized by a nearly equilibrium distribution. We also discuss the relevance of the results of this study to distinct states in the existing cells.

DOI： 10.1103/PhysRevE.84.011927

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