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Rhythmic gene expression can originate not only from the autonomous rhythm of clock genes but likely also from sleep-wake cycles. Jan and colleagues used a novel model-based approach to dissect these individual effects and found that both factors contribute to gene expression rhythms, varying in degree within and across tissues.
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Ritmo Circadiano , Sono , Sono/genética , Sono/fisiologia , Ritmo Circadiano/genética , Ritmo Circadiano/fisiologia , Humanos , Animais , Regulação da Expressão Gênica/genética , Relógios Circadianos/genética , Relógios Biológicos/genéticaRESUMO
The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. When substrates and enzymes are homogeneously distributed, the validity of the MM rate law can be easily assessed based on relative concentrations: the substrate is in large excess over the enzyme-substrate complex. However, the applicability of this conventional criterion remains unclear when species exhibit spatial heterogeneity, a prevailing scenario in biological systems. Here, we explore the MM rate law's applicability under spatial heterogeneity by using partial differential equations. In this study, molecules diffuse very slowly, allowing them to locally reach quasi-steady states. We find that the conventional criterion for the validity of the MM rate law cannot be readily extended to heterogeneous environments solely through spatial averages of molecular concentrations. That is, even when the conventional criterion for the spatial averages is satisfied, the MM rate law fails to capture the enzyme catalytic rate under spatial heterogeneity. In contrast, a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA), is accurate. Specifically, the tQSSA-based modified form, but not the original MM rate law, accurately predicts the drug clearance via cytochrome P450 enzymes and the ultrasensitive phosphorylation in heterogeneous environments. Our findings shed light on how to simplify spatiotemporal models for enzyme-catalyzed reactions in the right context, ensuring accurate conclusions and avoiding misinterpretations in in silico simulations.
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Enzimas , Cinética , Enzimas/metabolismo , Enzimas/química , Biologia Computacional/métodos , Modelos Químicos , Simulação por ComputadorRESUMO
BACKGROUND: The Dysfunctional Beliefs and Attitudes about Sleep Scale (DBAS-16) is a widely used self-report instrument for identifying sleep-related cognition. However, its length can be cumbersome in clinical practice. This study aims to develop a data-driven shortened version of the DBAS-16 that efficiently predicts the DBAS-16 total score among the general population. METHODS: We collected 1000 responses to the DBAS-16 from the general population through three separate surveys, each focusing on different aspects of insomnia severity and related factors. Using Exploratory Factor Analysis (EFA) on the survey responses, we grouped DBAS-16 items based on response pattern similarities. The most representative item from each group, showing the highest regression performance with eXtreme Gradient Boosting (XGBoost) in predicting the DBAS-16 total score, was selected to create a shortened version of the DBAS-16. RESULTS: Through EFA and XGBoost, we categorized the DBAS-16 items into six distinct groups. Selecting one item from each group, based on the highest coefficient of determination R2 values in predicting the DBAS-16 total score. After measuring the R2 values for all possible combinations of six items, items 4, 5, 7, 11, 13, and 15 were chosen, exhibiting the highest R2 value. Based on these six items, we developed the DBAS-6, a data-driven shortened version of the DBAS-16. The DBAS-6 exhibited outstanding predictive ability, achieving the highest R2 value of 0.90 for predicting the DBAS-16 total score, surpassing that of a previously developed shortened version. Notably, the DBAS-6 efficiently encapsulates the core aspects of the DBAS-16 and demonstrates robust predictive power over heterogeneous test data samples with distinct statistical characteristics from the training data. CONCLUSION: With its concise format and high predictive accuracy, the DBAS-6 offers a practical tool for assessing dysfunctional beliefs about sleep in clinical settings.
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Aprendizado de Máquina , Humanos , Masculino , Feminino , Inquéritos e Questionários , Pessoa de Meia-Idade , Adulto , Autorrelato , Distúrbios do Início e da Manutenção do Sono/psicologia , Distúrbios do Início e da Manutenção do Sono/diagnóstico , Reprodutibilidade dos Testes , Análise Fatorial , Psicometria , Sono/fisiologiaRESUMO
In mammals, CLOCK and BMAL1 proteins form a heterodimer that binds to E-box sequences and activates transcription of target genes, including Period (Per). Translated PER proteins then bind to the CLOCK-BMAL1 complex to inhibit its transcriptional activity. However, the molecular mechanism and the impact of this PER-dependent inhibition on the circadian clock oscillation remain elusive. We previously identified Ser38 and Ser42 in a DNA-binding domain of CLOCK as phosphorylation sites at the PER-dependent inhibition phase. In this study, knockout rescue experiments showed that nonphosphorylatable (Ala) mutations at these sites shortened circadian period, whereas their constitutive-phospho-mimetic (Asp) mutations completely abolished the circadian rhythms. Similarly, we found that nonphosphorylatable (Ala) and constitutive-phospho-mimetic (Glu) mutations at Ser78 in a DNA-binding domain of BMAL1 also shortened the circadian period and abolished the rhythms, respectively. The mathematical modeling predicted that these constitutive-phospho-mimetic mutations weaken the DNA binding of the CLOCK-BMAL1 complex and that the nonphosphorylatable mutations inhibit the PER-dependent displacement (reduction of DNA-binding ability) of the CLOCK-BMAL1 complex from DNA. Biochemical experiments supported the importance of these phosphorylation sites for displacement of the complex in the PER2-dependent inhibition. Our results provide direct evidence that phosphorylation of CLOCK-Ser38/Ser42 and BMAL1-Ser78 plays a crucial role in the PER-dependent inhibition and the determination of the circadian period.
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Fatores de Transcrição ARNTL , Proteínas CLOCK , Relógios Circadianos , Proteínas Circadianas Period , Animais , Humanos , Camundongos , Fatores de Transcrição ARNTL/metabolismo , Fatores de Transcrição ARNTL/genética , Fatores de Transcrição ARNTL/química , Relógios Circadianos/genética , Ritmo Circadiano/fisiologia , Ritmo Circadiano/genética , Proteínas CLOCK/metabolismo , Proteínas CLOCK/genética , DNA/metabolismo , Células HEK293 , Mutação , Células NIH 3T3 , Proteínas Circadianas Period/metabolismo , Proteínas Circadianas Period/genética , Fosforilação , Ligação Proteica , Domínios ProteicosRESUMO
BACKGROUND: Sleep and circadian rhythm disruptions are common in patients with mood disorders. The intricate relationship between these disruptions and mood has been investigated, but their causal dynamics remain unknown. METHODS: We analysed data from 139 patients (76 female, mean age = 23.5 ± 3.64 years) with mood disorders who participated in a prospective observational study in South Korea. The patients wore wearable devices to monitor sleep and engaged in smartphone-delivered ecological momentary assessment of mood symptoms. Using a mathematical model, we estimated their daily circadian phase based on sleep data. Subsequently, we obtained daily time series for sleep/circadian phase estimates and mood symptoms spanning >40,000 days. We analysed the causal relationship between the time series using transfer entropy, a non-linear causal inference method. FINDINGS: The transfer entropy analysis suggested causality from circadian phase disturbance to mood symptoms in both patients with MDD (n = 45) and BD type I (n = 35), as 66.7% and 85.7% of the patients with a large dataset (>600 days) showed causality, but not in patients with BD type II (n = 59). Surprisingly, no causal relationship was suggested between sleep phase disturbances and mood symptoms. INTERPRETATION: Our findings suggest that in patients with mood disorders, circadian phase disturbances directly precede mood symptoms. This underscores the potential of targeting circadian rhythms in digital medicine, such as sleep or light exposure interventions, to restore circadian phase and thereby manage mood disorders effectively. FUNDING: Institute for Basic Science, the Human Frontiers Science Program Organization, the National Research Foundation of Korea, and the Ministry of Health & Welfare of South Korea.
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Afeto , Transtorno Bipolar , Ritmo Circadiano , Transtorno Depressivo Maior , Sono , Dispositivos Eletrônicos Vestíveis , Humanos , Feminino , Masculino , Adulto , Transtorno Bipolar/fisiopatologia , Transtorno Bipolar/psicologia , Sono/fisiologia , Transtorno Depressivo Maior/fisiopatologia , Transtorno Depressivo Maior/psicologia , Adulto Jovem , República da Coreia , Estudos Prospectivos , SmartphoneRESUMO
High dimensionality and noise have limited the new biological insights that can be discovered in scRNA-seq data. While dimensionality reduction tools have been developed to extract biological signals from the data, they often require manual determination of signal dimension, introducing user bias. Furthermore, a common data preprocessing method, log normalization, can unintentionally distort signals in the data. Here, we develop scLENS, a dimensionality reduction tool that circumvents the long-standing issues of signal distortion and manual input. Specifically, we identify the primary cause of signal distortion during log normalization and effectively address it by uniformizing cell vector lengths with L2 normalization. Furthermore, we utilize random matrix theory-based noise filtering and a signal robustness test to enable data-driven determination of the threshold for signal dimensions. Our method outperforms 11 widely used dimensionality reduction tools and performs particularly well for challenging scRNA-seq datasets with high sparsity and variability. To facilitate the use of scLENS, we provide a user-friendly package that automates accurate signal detection of scRNA-seq data without manual time-consuming tuning.
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Algoritmos , RNA-Seq , Análise da Expressão Gênica de Célula Única , Animais , Humanos , Biologia Computacional/métodos , Análise de Dados , RNA Citoplasmático Pequeno/genética , RNA-Seq/métodos , Análise da Expressão Gênica de Célula Única/métodos , SoftwareRESUMO
BACKGROUND: The Insomnia Severity Index (ISI) is a widely used questionnaire with seven items for identifying the risk of insomnia disorder. Although the ISI is still short, more shortened versions are emerging for repeated monitoring in routine clinical settings. In this study, we aimed to develop a data-driven shortened version of the ISI that accurately predicts the severity level of insomnia disorder. METHODS: We collected a sample of 800 responses from the EMBRAIN survey system. Based on the responses, seven items were grouped based on the similarity of their response using exploratory factor analysis (EFA). The most representative item within each group was selected by using eXtreme Gradient Boosting (XGBoost). RESULTS: Based on the selected three key items, maintenance of sleep, interference with daily function, and concerns about sleep problems, we developed a data-driven shortened questionnaire of ISI, ISI-3 m (machine learning). ISI-3 m achieved the highest coefficient of determination ( R 2 = 0.910 ) for the ISI score prediction task and the accuracy of 0.965, precision of 0.841, and recall of 0.838 for the multiclass-classification task, outperforming four previous versions of the shortened ISI. CONCLUSION: As ISI-3 m is a highly accurate shortened version of the ISI, it allows clinicians to efficiently screen for insomnia and observe variations in the condition throughout the treatment process. Furthermore, the framework based on the combination of EFA and XGBoost developed in this study can be utilized to develop data-driven shortened versions of the other questionnaires.
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Aprendizado de Máquina , Índice de Gravidade de Doença , Distúrbios do Início e da Manutenção do Sono , Humanos , Distúrbios do Início e da Manutenção do Sono/diagnóstico , Distúrbios do Início e da Manutenção do Sono/epidemiologia , Masculino , Feminino , Pessoa de Meia-Idade , Adulto , Inquéritos e Questionários , Idoso , Psicometria , Reprodutibilidade dos TestesRESUMO
Target-mediated drug disposition (TMDD) is a phenomenon characterized by a drug's high-affinity binding to a target molecule, which significantly influences its pharmacokinetic profile within an organism. The comprehensive TMDD model delineates this interaction, yet it may become overly complex and computationally demanding in the absence of specific concentration data for the target or its complexes. Consequently, simplified TMDD models employing quasi-steady state approximations (QSSAs) have been introduced; however, the precise conditions under which these models yield accurate results require further elucidation. Here, we establish the validity of three simplified TMDD models: the Michaelis-Menten model reduced with the standard QSSA (mTMDD), the QSS model reduced with the total QSSA (qTMDD), and a first-order approximation of the total QSSA (pTMDD). Specifically, we find that mTMDD is applicable only when initial drug concentrations substantially exceed total target concentrations, while qTMDD can be used for all drug concentrations. Notably, pTMDD offers a simpler and faster alternative to qTMDD, with broader applicability than mTMDD. These findings are confirmed with antibody-drug conjugate real-world data. Our findings provide a framework for selecting appropriate simplified TMDD models while ensuring accuracy, potentially enhancing drug development and facilitating safer, more personalized treatments.
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Modelos Biológicos , Humanos , Biologia Computacional/métodos , Simulação por Computador , Preparações Farmacêuticas/metabolismo , Farmacocinética , Reprodutibilidade dos TestesRESUMO
All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman's law rather than the popular Fick's law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.
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Ultrasensitive transcriptional switches enable sharp transitions between transcriptional on and off states and are essential for cells to respond to environmental cues with high fidelity. However, conventional switches, which rely on direct repressor-DNA binding, are extremely noise-sensitive, leading to unintended changes in gene expression. Here, through model simulations and analysis, we discovered that an alternative design combining three indirect transcriptional repression mechanisms, sequestration, blocking, and displacement, can generate a noise-resilient ultrasensitive switch. Although sequestration alone can generate an ultrasensitive switch, it remains sensitive to noise because the unintended transcriptional state induced by noise persists for long periods. However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original transcriptional state. Because this transcriptional switch is effective in noisy cellular contexts, it goes beyond previous synthetic transcriptional switches, making it particularly valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in cells. Specifically, the concurrent use of seemingly redundant indirect repression mechanisms in diverse biological systems appears to be a strategy to achieve noise-resilience of ultrasensitive switches.
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Expressão GênicaRESUMO
Genetic oscillations are generated by delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay is distributed because it arises from a sequence of noisy processes, including transcription, translocation, translation, and folding. Because the delay determines repression timing and, therefore, oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. Here, we demonstrate that noisy delay can surprisingly denoise genetic oscillators. Specifically, moderate delay noise improves the signal-to-noise ratio and sharpens oscillation peaks, all without impacting period and amplitude. We show that this denoising phenomenon occurs in a variety of well-studied genetic oscillators, and we use queueing theory to uncover the universal mechanisms that produce it.
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The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces. We applied Density-PINNs to single-cell gene expression data from sixteen promoters regulated by unknown pathways in response to antibiotic stresses. We found that promoters with slower signaling initiation and transduction exhibit larger cell-to-cell heterogeneity in response intensity. However, this heterogeneity was greatly reduced when the response was regulated by slow and fast pathways together. This suggests a strategy for identifying effective signaling pathways for consistent cellular responses to disease treatments. Density-PINNs can also be applied to understand other time delay systems, including infectious diseases.
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Strong circadian (~24h) rhythms in heart rate (HR) are critical for flexible regulation of cardiac pacemaking function throughout the day. While this circadian flexibility in HR is sustained in diverse conditions, it declines with age, accompanied by reduced maximal HR performance. The intricate regulation of circadian HR involves the orchestration of the autonomic nervous system (ANS), circadian rhythms of body temperature (CRBT), and local circadian rhythmicity (LCR), which has not been fully understood. Here, we developed a mathematical model describing ANS, CRBT, and LCR in sinoatrial nodal cells (SANC) that accurately captures distinct circadian patterns in adult and aged mice. Our model underscores how the alliance among ANS, CRBT, and LCR achieves circadian flexibility to cover a wide range of firing rates in SANC, performance to achieve maximal firing rates, while preserving robustness to generate rhythmic firing patterns irrespective of external conditions. Specifically, while ANS dominates in promoting SANC flexibility and performance, CRBT and LCR act as primary and secondary boosters, respectively, to further enhance SANC flexibility and performance. Disruption of this alliance with age results in impaired SANC flexibility and performance, but not robustness. This unexpected outcome is primarily attributed to the age-related reduction in parasympathetic activities, which maintains SANC robustness while compromising flexibility. Our work sheds light on the critical alliance of ANS, CRBT, and LCR in regulating time-of-day cardiac pacemaking function and dysfunction, offering insights into novel therapeutic targets for the prevention and treatment of cardiac arrhythmias.
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Temperatura Corporal , Nó Sinoatrial , Animais , Camundongos , Nó Sinoatrial/fisiologia , Ritmo Circadiano , Frequência Cardíaca , Modelos TeóricosRESUMO
Sleep is a critical component of health and well-being but collecting and analyzing accurate longitudinal sleep data can be challenging, especially outside of laboratory settings. We propose a simple neural network model titled SOMNI (Sleep data restOration using Machine learning and Non-negative matrix factorIzation [NMF]) for imputing missing rest-activity data from actigraphy, which can enable clinicians to better handle missing data and monitor sleep-wake cycles of individuals with highly irregular sleep-wake patterns. The model consists of two hidden layers and uses NMF to capture hidden longitudinal sleep-wake patterns of individuals with disturbed sleep-wake cycles. Based on this, we develop two approaches: the individual approach imputes missing data based on the data from only one participant, while the global approach imputes missing data based on the data across multiple participants. Our models are tested with shift and non-shift workers' data from three independent hospitals. Both approaches can accurately impute missing data up to 24 hours of long dataset (>50 days) even for shift workers with extremely irregular sleep-wake patterns (AUCâ >â 0.86). On the other hand, for short dataset (~15 days), only the global model is accurate (AUCâ >â 0.77). Our approach can be used to help clinicians monitor sleep-wake cycles of patients with sleep disorders outside of laboratory settings without relying on sleep diaries, ultimately improving sleep health outcomes.
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Transtornos do Sono do Ritmo Circadiano , Dispositivos Eletrônicos Vestíveis , Humanos , Sono , Redes Neurais de Computação , Algoritmos , Descanso , ActigrafiaRESUMO
MOTIVATION: Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality. RESULTS: We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components. AVAILABILITY AND IMPLEMENTATION: Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.
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Algoritmos , Regulação da Expressão Gênica , Teorema de Bayes , Redes Reguladoras de Genes , Fatores de Transcrição/metabolismoRESUMO
BACKGROUND: Sleep disorders, such as obstructive sleep apnea (OSA), comorbid insomnia and sleep apnea (COMISA), and insomnia are common and can have serious health consequences. However, accurately diagnosing these conditions can be challenging as a result of the underrecognition of these diseases, the time-intensive nature of sleep monitoring necessary for a proper diagnosis, and patients' hesitancy to undergo demanding and costly overnight polysomnography tests. OBJECTIVE: We aim to develop a machine learning algorithm that can accurately predict the risk of OSA, COMISA, and insomnia with a simple set of questions, without the need for a polysomnography test. METHODS: We applied extreme gradient boosting to the data from 2 medical centers (n=4257 from Samsung Medical Center and n=365 from Ewha Womans University Medical Center Seoul Hospital). Features were selected based on feature importance calculated by the Shapley additive explanations (SHAP) method. We applied extreme gradient boosting using selected features to develop a simple questionnaire predicting sleep disorders (SLEEPS). The accuracy of the algorithm was evaluated using the area under the receiver operating characteristics curve. RESULTS: In total, 9 features were selected to construct SLEEPS. SLEEPS showed high accuracy, with an area under the receiver operating characteristics curve of greater than 0.897 for all 3 sleep disorders, and consistent performance across both sets of data. We found that the distinction between COMISA and OSA was critical for accurate prediction. A publicly accessible website was created based on the algorithm that provides predictions for the risk of the 3 sleep disorders and shows how the risk changes with changes in weight or age. CONCLUSIONS: SLEEPS has the potential to improve the diagnosis and treatment of sleep disorders by providing more accessibility and convenience. The creation of a publicly accessible website based on the algorithm provides a user-friendly tool for assessing the risk of OSA, COMISA, and insomnia.
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Síndromes da Apneia do Sono , Apneia Obstrutiva do Sono , Distúrbios do Início e da Manutenção do Sono , Transtornos do Sono-Vigília , Feminino , Humanos , Apneia Obstrutiva do Sono/diagnóstico , Aprendizado de Máquina , Transtornos do Sono-Vigília/diagnóstico , Fatores de RiscoRESUMO
The prevalence of artificial light exposure has enabled us to be active any time of the day or night, leading to the need for high alertness outside of traditional daytime hours. To address this need, we developed a personalized sleep intervention framework that analyzes real-world sleep-wake patterns obtained from wearable devices to maximize alertness during specific target periods. Our framework utilizes a mathematical model that tracks the dynamic sleep pressure and circadian rhythm based on the user's sleep history. In this way, the model accurately predicts real-time alertness, even for shift workers with complex sleep and work schedules (Nâ =â 71, tâ =â 13~21 days). This allowed us to discover a new sleep-wake pattern called the adaptive circadian split sleep, which incorporates a main sleep period and a late nap to enable high alertness during both work and non-work periods of shift workers. We further developed a mobile application that integrates this framework to recommend practical, personalized sleep schedules for individual users to maximize their alertness during a targeted activity time based on their desired sleep onset and available sleep duration. This can reduce the risk of errors for those who require high alertness during nontraditional activity times and improve the health and quality of life for those leading shift work-like lifestyles.
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Vigília , Dispositivos Eletrônicos Vestíveis , Humanos , Qualidade de Vida , Tolerância ao Trabalho Programado , Sono , Ritmo Circadiano , Modelos TeóricosRESUMO
To identify causation, model-free inference methods, such as Granger Causality, have been widely used due to their flexibility. However, they have difficulty distinguishing synchrony and indirect effects from direct causation, leading to false predictions. To overcome this, model-based inference methods that test the reproducibility of data with a specific mechanistic model to infer causality were developed. However, they can only be applied to systems described by a specific model, greatly limiting their applicability. Here, we address this limitation by deriving an easily testable condition for a general monotonic ODE model to reproduce time-series data. We built a user-friendly computational package, General ODE-Based Inference (GOBI), which is applicable to nearly any monotonic system with positive and negative regulations described by ODE. GOBI successfully inferred positive and negative regulations in various networks at both the molecular and population levels, unlike existing model-free methods. Thus, this accurate and broadly applicable inference method is a powerful tool for understanding complex dynamical systems.
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The circadian (â¼24h) clock is based on a negative-feedback loop centered around the PERIOD protein (PER), translated in the cytoplasm and then enters the nucleus to repress its own transcription at the right time of day. Such precise nucleus entry is mysterious because thousands of PER molecules transit through crowded cytoplasm and arrive at the perinucleus across several hours. To understand this, we developed a mathematical model describing the complex spatiotemporal dynamics of PER as a single random time delay. We find that the spatially coordinated bistable phosphoswitch of PER, which triggers the phosphorylation of accumulated PER at the perinucleus, leads to the synchronous and precise nuclear entry of PER. This leads to robust circadian rhythms even when PER arrival times are heterogeneous and perturbed due to changes in cell crowdedness, cell size, and transcriptional activator levels. This shows how the circadian clock compensates for spatiotemporal noise.
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The long-term behaviors of biochemical systems are often described by their steady states. Deriving these states directly for complex networks arising from real-world applications, however, is often challenging. Recent work has consequently focused on network-based approaches. Specifically, biochemical reaction networks are transformed into weakly reversible and deficiency zero generalized networks, which allows the derivation of their analytic steady states. Identifying this transformation, however, can be challenging for large and complex networks. In this paper, we address this difficulty by breaking the complex network into smaller independent subnetworks and then transforming the subnetworks to derive the analytic steady states of each subnetwork. We show that stitching these solutions together leads to the analytic steady states of the original network. To facilitate this process, we develop a user-friendly and publicly available package, COMPILES (COMPutIng anaLytic stEady States). With COMPILES, we can easily test the presence of bistability of a CRISPRi toggle switch model, which was previously investigated via tremendous number of numerical simulations and within a limited range of parameters. Furthermore, COMPILES can be used to identify absolute concentration robustness (ACR), the property of a system that maintains the concentration of particular species at a steady state regardless of any initial concentrations. Specifically, our approach completely identifies all the species with and without ACR in a complex insulin model. Our method provides an effective approach to analyzing and understanding complex biochemical systems.