A hierarchical multi-oscillator network orchestrates the Arabidopsis circadian system.

Short- and long-distance circadian communication is essential for integration of temporal information. However, a major challenge in plant biology is to decipher how individual clocks are interconnected to sustain rhythms in the whole plant. Here we show that the shoot apex is composed of an ensemble of coupled clocks that influence rhythms in roots. Live-imaging of single cells, desynchronization of dispersed protoplasts, and mathematical analysis using barycentric coordinates for high-dimensional space show a gradation in the strength of circadian communication in different tissues, with shoot apex clocks displaying the highest coupling. The increased synchrony confers robustness of morning and evening oscillations and particular capabilities for phase readjustments. Rhythms in roots are altered by shoot apex ablation and micrografting, suggesting that signals from the shoot apex are able to synchronize distal organs. Similarly to the mammalian suprachiasmatic nucleus, shoot apexes play a dominant role within the plant hierarchical circadian structure.

Earthquake alerting based on spatial geodetic data by spatiotemporal information transformation learning.

Alerting for imminent earthquakes is particularly challenging due to the high nonlinearity and nonstationarity of geodynamical phenomena. In this study, based on spatiotemporal information (STI) transformation for high-dimensional real-time data, we developed a model-free framework, i.e., real-time spatiotemporal information transformation learning (RSIT), for extending the nonlinear and nonstationary time series. Specifically, by transforming high-dimensional information of the global navigation satellite system into one-dimensional dynamics via the STI strategy, RSIT efficiently utilizes two criteria of the transformed one-dimensional dynamics, i.e., unpredictability and instability. Such two criteria contemporaneously signal a potential critical transition of the geodynamical system, thereby providing early-warning signals of possible upcoming earthquakes. RSIT explores both the spatial and temporal dynamics of real-world data on the basis of a solid theoretical background in nonlinear dynamics and delay-embedding theory. The effectiveness of RSIT was demonstrated on geodynamical data of recent earthquakes from a number of regions across at least 4 y and through further comparison with existing methods.

Infectious virus shedding duration reflects secretory IgA antibody response latency after SARS-CoV-2 infection.

Infectious virus shedding from individuals infected with severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) is used to estimate human-to-human transmission risk. Control of SARS-CoV-2 transmission requires identifying the immune correlates that protect infectious virus shedding. Mucosal immunity prevents infection by SARS-CoV-2, which replicates in the respiratory epithelium and spreads rapidly to other hosts. However, whether mucosal immunity prevents the shedding of the infectious virus in SARS-CoV-2-infected individuals is unknown. We examined the relationship between viral RNA shedding dynamics, duration of infectious virus shedding, and mucosal antibody responses during SARS-CoV-2 infection. Anti-spike secretory IgA antibodies (S-IgA) reduced viral RNA load and infectivity more than anti-spike IgG/IgA antibodies in infected nasopharyngeal samples. Compared with the IgG/IgA response, the anti-spike S-IgA post-infection responses affected the viral RNA shedding dynamics and predicted the duration of infectious virus shedding regardless of the immune history. These findings highlight the importance of anti-spike S-IgA responses in individuals infected with SARS-CoV-2 for preventing infectious virus shedding and SARS-CoV-2 transmission. Developing medical countermeasures to shorten S-IgA response time may help control human-to-human transmission of SARS-CoV-2 infection and prevent future respiratory virus pandemics.

Contrastively generative self-expression model for single-cell and spatial multimodal data.

Advances in single-cell multi-omics technology provide an unprecedented opportunity to fully understand cellular heterogeneity. However, integrating omics data from multiple modalities is challenging due to the individual characteristics of each measurement. Here, to solve such a problem, we propose a contrastive and generative deep self-expression model, called single-cell multimodal self-expressive integration (scMSI), which integrates the heterogeneous multimodal data into a unified manifold space. Specifically, scMSI first learns each omics-specific latent representation and self-expression relationship to consider the characteristics of different omics data by deep self-expressive generative model. Then, scMSI combines these omics-specific self-expression relations through contrastive learning. In such a way, scMSI provides a paradigm to integrate multiple omics data even with weak relation, which effectively achieves the representation learning and data integration into a unified framework. We demonstrate that scMSI provides a cohesive solution for a variety of analysis tasks, such as integration analysis, data denoising, batch correction and spatial domain detection. We have applied scMSI on various single-cell and spatial multimodal datasets to validate its high effectiveness and robustness in diverse data types and application scenarios.

Multiscale modeling of HBV infection integrating intra- and intercellular viral propagation to analyze extracellular viral markers.

Chronic infection with hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. Thus, quantifying and understanding the dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, such study requires repeated liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because liver biopsy is potentially morbid and not common during hepatitis B treatment. We here aimed to develop a noninvasive method for quantifying cccDNA in the liver using surrogate markers in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations, integrates experimental data from in vitro and in vivo investigations. By applying this model, we roughly predicted the amount and dynamics of intrahepatic cccDNA within a certain range using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The noninvasive quantification of cccDNA using our proposed method holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.

STAMarker: determining spatial domain-specific variable genes with saliency maps in deep learning.

Spatial transcriptomics characterizes gene expression profiles while retaining the information of the spatial context, providing an unprecedented opportunity to understand cellular systems. One of the essential tasks in such data analysis is to determine spatially variable genes (SVGs), which demonstrate spatial expression patterns. Existing methods only consider genes individually and fail to model the inter-dependence of genes. To this end, we present an analytic tool STAMarker for robustly determining spatial domain-specific SVGs with saliency maps in deep learning. STAMarker is a three-stage ensemble framework consisting of graph-attention autoencoders, multilayer perceptron (MLP) classifiers, and saliency map computation by the backpropagated gradient. We illustrate the effectiveness of STAMarker and compare it with serveral commonly used competing methods on various spatial transcriptomic data generated by different platforms. STAMarker considers all genes at once and is more robust when the dataset is very sparse. STAMarker could identify spatial domain-specific SVGs for characterizing spatial domains and enable in-depth analysis of the region of interest in the tissue section.

A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2.

The scientific community is focused on developing antiviral therapies to mitigate the impacts of the ongoing novel coronavirus disease 2019 (COVID-19) outbreak. This will be facilitated by improved understanding of viral dynamics within infected hosts. Here, using a mathematical model in combination with published viral load data, we compare within-host viral dynamics of SARS-CoV-2 with analogous dynamics of MERS-CoV and SARS-CoV. Our quantitative analyses using a mathematical model revealed that the within-host reproduction number at symptom onset of SARS-CoV-2 was statistically significantly larger than that of MERS-CoV and similar to that of SARS-CoV. In addition, the time from symptom onset to the viral load peak for SARS-CoV-2 infection was shorter than those of MERS-CoV and SARS-CoV. These findings suggest the difficulty of controlling SARS-CoV-2 infection by antivirals. We further used the viral dynamics model to predict the efficacy of potential antiviral drugs that have different modes of action. The efficacy was measured by the reduction in the viral load area under the curve (AUC). Our results indicate that therapies that block de novo infection or virus production are likely to be effective if and only if initiated before the viral load peak (which appears 2-3 days after symptom onset), but therapies that promote cytotoxicity of infected cells are likely to have effects with less sensitivity to the timing of treatment initiation. Furthermore, combining a therapy that promotes cytotoxicity and one that blocks de novo infection or virus production synergistically reduces the AUC with early treatment. Our unique modeling approach provides insights into the pathogenesis of SARS-CoV-2 and may be useful for development of antiviral therapies.

Monkey Prefrontal Single-Unit Activity Reflecting Category-Based Logical Thinking Process and Its Neural Network Model.

Category-based thinking is a fundamental form of logical thinking. Here, we aimed to investigate its neural process at the local circuit level in the prefrontal cortex (PFC). We recorded single-unit PFC activity while male monkeys (Macaca fuscata) performed a task in which the category and rule were prerequisites of logical thinking and the outcome contingency was its consequence. Different groups of neurons coded a single type of information discretely or multiple types in a transitional form. Results of time-by-time analysis of neuronal activity suggest an information flow from category-coding and rule-coding neurons to transitional intermediate neurons, and then to contingency-coding neurons. Category-coding, rule-coding, and contingency-coding neurons showed stable coding of information, whereas intermediate neurons showed dynamic coding, as if it integrated category and rule to derive contingency. A similar process was confirmed by using a spiking neural network model that consisted of subnetworks coding category and rule on the input layer and those coding contingency on the output layer, with a subnetwork for integration in the intermediate layer. These results suggest that category-based logical thinking is realized in the PFC by separated neural populations organized for working in a feedforward manner.SIGNIFICANCE STATEMENT To elucidate the neural process for logical thinking, we combined an in-depth analysis of single-unit activity data with a biologically plausible computational model. Results of time-by-time analysis of prefrontal neuronal activity suggest an information flow from category-coding and rule-coding neurons to transitional intermediate neurons, and then to contingency-coding neurons. Category-coding, rule-coding, and contingency-coding neurons showed stable coding, whereas intermediate neurons showed dynamic coding, as if they integrated category and rule to derive contingency. A spiking neural network model reproduced similar temporal changes of information as the recorded neuronal data. Our results suggest that the prefrontal cortex (PFC) is critically involved in category-based thought process, and this process may be produced by separated neural populations organized for working in a feedforward manner.

Maximal Memory Capacity Near the Edge of Chaos in Balanced Cortical E-I Networks.

We examine the efficiency of information processing in a balanced excitatory and inhibitory (E-I) network during the developmental critical period, when network plasticity is heightened. A multimodule network composed of E-I neurons was defined, and its dynamics were examined by regulating the balance between their activities. When adjusting E-I activity, both transitive chaotic synchronization with a high Lyapunov dimension and conventional chaos with a low Lyapunov dimension were found. In between, the edge of high-dimensional chaos was observed. To quantify the efficiency of information processing, we applied a short-term memory task in reservoir computing to the dynamics of our network. We found that memory capacity was maximized when optimal E-I balance was realized, underscoring both its vital role and vulnerability during critical periods of brain development.

Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model.

BACKGROUND: Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations. METHODS AND RESULTS: In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention. CONCLUSIONS: This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.

Estimation of timing of infection from longitudinal SARS-CoV-2 viral load data: mathematical modelling study.

BACKGROUND: Multiple waves of the COVID-19 epidemic have hit most countries by the end of 2021. Most of those waves are caused by emergence and importation of new variants. To prevent importation of new variants, combination of border control and contact tracing is essential. However, the timing of infection inferred by interview is influenced by recall bias and hinders the contact tracing process. METHODS: We propose a novel approach to infer the timing of infection, by employing a within-host model to capture viral load dynamics after the onset of symptoms. We applied this approach to ascertain secondary transmission which can trigger outbreaks. As a demonstration, the 12 initial reported cases in Singapore, which were considered as imported because of their recent travel history to Wuhan, were analyzed to assess whether they are truly imported. RESULTS: Our approach suggested that 6 cases were infected prior to the arrival in Singapore, whereas other 6 cases might have been secondary local infection. Three among the 6 potential secondary transmission cases revealed that they had contact history to previously confirmed cases. CONCLUSIONS: Contact trace combined with our approach using viral load data could be the key to mitigate the risk of importation of new variants by identifying cases as early as possible and inferring the timing of infection with high accuracy.

Mean-field analysis of Stuart-Landau oscillator networks with symmetric coupling and dynamical noise.

This paper presents analyses of networks composed of homogeneous Stuart-Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.

Detection of significant antiviral drug effects on COVID-19 with reasonable sample sizes in randomized controlled trials: A modeling study.

BACKGROUND: Development of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials. METHODS AND FINDINGS: A modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d-1 (95% CI: 1.06 to 1.27 d-1), 0.777 d-1 (0.716 to 0.838 d-1), and 0.450 d-1 (0.378 to 0.522 d-1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13,603 and 11,670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation. CONCLUSIONS: In this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model.

Electrical coupling controls dimensionality and chaotic firing of inferior olive neurons.

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum.

Randomly distributed embedding making short-term high-dimensional data predictable.

Future state prediction for nonlinear dynamical systems is a challenging task, particularly when only a few time series samples for high-dimensional variables are available from real-world systems. In this work, we propose a model-free framework, named randomly distributed embedding (RDE), to achieve accurate future state prediction based on short-term high-dimensional data. Specifically, from the observed data of high-dimensional variables, the RDE framework randomly generates a sufficient number of low-dimensional "nondelay embeddings" and maps each of them to a "delay embedding," which is constructed from the data of a to be predicted target variable. Any of these mappings can perform as a low-dimensional weak predictor for future state prediction, and all of such mappings generate a distribution of predicted future states. This distribution actually patches all pieces of association information from various embeddings unbiasedly or biasedly into the whole dynamics of the target variable, which after operated by appropriate estimation strategies, creates a stronger predictor for achieving prediction in a more reliable and robust form. Through applying the RDE framework to data from both representative models and real-world systems, we reveal that a high-dimension feature is no longer an obstacle but a source of information crucial to accurate prediction for short-term data, even under noise deterioration.

Forecasting wind power ramps with prediction coordinates.

To the best of our knowledge, the method of prediction coordinates is the only forecasting method in nonlinear time series analysis that explicitly uses the stochastic characteristics of a system with dynamical noise. Specifically, it generates multiple predictions to jointly infer the current states and dynamical noises. Recent findings based on hypothesis testing show that weather is nonlinear and stochastic and, therefore, so are renewable energy power outputs. This being the case, in this paper, we apply the method of prediction coordinates to forecast wind power ramps, which are rapid transitions in the wind power output that can deteriorate the quality of the electricity supply. First, the method of prediction coordinates is tested using numerical simulations. Then, we present an example of wind power ramp forecasting with empirical data. The results show that the method of prediction coordinates compares favorably with other methods, validating it as a reliable tool for forecasting transitions in nonlinear stochastic dynamics, particularly in the field of renewable energies.

Quantifying pluripotency landscape of cell differentiation from scRNA-seq data by continuous birth-death process.

Modeling cell differentiation from omics data is an essential problem in systems biology research. Although many algorithms have been established to analyze scRNA-seq data, approaches to infer the pseudo-time of cells or quantify their potency have not yet been satisfactorily solved. Here, we propose the Landscape of Differentiation Dynamics (LDD) method, which calculates cell potentials and constructs their differentiation landscape by a continuous birth-death process from scRNA-seq data. From the viewpoint of stochastic dynamics, we exploited the features of the differentiation process and quantified the differentiation landscape based on the source-sink diffusion process. In comparison with other scRNA-seq methods in seven benchmark datasets, we found that LDD could accurately and efficiently build the evolution tree of cells with pseudo-time, in particular quantifying their differentiation landscape in terms of potency. This study provides not only a computational tool to quantify cell potency or the Waddington potential landscape based on scRNA-seq data, but also novel insights to understand the cell differentiation process from a dynamic perspective.

Reliable target ligand detection by noise-induced receptor cluster formation.

Intracellular reactions are intrinsically stochastic. Nonetheless, cells can reliably respond to the changing environment by sensing their target molecules sensitively and specifically, even with the existence of abundant structurally-similar non-target molecules. The mechanism of how the cells can balance and achieve such different characteristics is not yet fully understood. In this work, we demonstrate that these characteristics can be attained by a ligand-induced stochastic cluster formation of receptors via the noise-induced symmetry breaking, in which the intrinsic stochasticity works to enhance sensitivity and specificity. We also show that the noise-induced cluster formation enables cells to detect the target ligand reliably by compensating the abundant non-target ligands in the environment. The proposed mechanism may lead to a deeper understanding of a biological function of the receptor clustering and provide an alternative candidate for the reliable ligand detection to the kinetic proofreading.

[Present and future perspectives of artificial intelligence: examples of mathematical approaches for analysis of disease dynamics].

Artificial intelligence (AI) has been applied widely in medicine. For example, deep neural network-based deep learning is particularly effective for pattern recognition in static medical images. Additionally, dynamic time series data are analysed ubiquitously in biology and medicine, as in the application of BCR-ABL International Scale time series data measured from CML patients treated with tyrosine-kinase inhibitors. Nonlinear data analyses, rather than conventional deep learning, can be more powerful for this type of dynamic disease information. Here, I introduce our mathematical approaches that are applicable for disease dynamics, such as dynamical network biomarkers (DNB) and randomly distributed embedding (RDE), as examples of nonlinear data analyses. I also discuss the availability of neuroinspired and neuromorphic hardware systems, which we are developing for potential use in next-generation AI.

Destabilization of Local Minima in Analog Spin Systems by Correction of Amplitude Heterogeneity.

The relaxation of binary spins to analog values has been the subject of much debate in the field of statistical physics, neural networks, and more recently quantum computing, notably because the benefits of using an analog state for finding lower energy spin configurations are usually offset by the negative impact of the improper mapping of the energy function that results from the relaxation. We show that it is possible to destabilize trapping sets of analog states that correspond to local minima of the binary spin Hamiltonian by extending the phase space to include error signals that correct amplitude inhomogeneity of the analog spin states and controlling the divergence of their velocity. Performance of the proposed analog spin system in finding lower energy states is competitive against state-of-the-art heuristics.