Theory of early warning signals of disease emergenceand leading indicators of elimination

Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of critical transitions. A key problem is the development of theory relating the dynamical processes of transmission to observable phenomena. In this paper, we consider compartmental susceptible-infectious-susceptible (SIS) and susceptible-infectious-recovered (SIR) models that are slowly forced through a critical transition. We derive expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination. We validated these expressions using individual-based simulations. We further showed that moving-window estimates of these quantities may be used for anticipating critical transitions in infectious disease systems. Although leading indicators of elimination were highly predictive, we found the approach to emergence to be much more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.

Identifying critical state of complex diseases by single-sample Kullback-Leibler divergence

Background

Developing effective strategies for signaling the pre-disease state of complex diseases, a state with high susceptibility before the disease onset or deterioration, is urgently needed because such state usually followed by a catastrophic transition into a worse stage of disease. However, it is a challenging task to identify such pre-disease state or tipping point in clinics, where only one single sample is available and thus results in the failure of most statistic approaches.

Methods

In this study, we presented a single-sample-based computational method to detect the early-warning signal of critical transition during the progression of complex diseases. Specifically, given a set of reference samples which were regarded as background, a novel index called single-sample Kullback–Leibler divergence (sKLD), was proposed to explore and quantify the disturbance on the background caused by a case sample. The pre-disease state is then signaled by the significant change of sKLD.

Results

The novel algorithm was developed and applied to both numerical simulation and real datasets, including lung squamous cell carcinoma, lung adenocarcinoma, stomach adenocarcinoma, thyroid carcinoma, colon adenocarcinoma, and acute lung injury. The successful identification of pre-disease states and the corresponding dynamical network biomarkers for all six datasets validated the effectiveness and accuracy of our method.

Conclusions

The proposed method effectively explores and quantifies the disturbance on the background caused by a case sample, and thus characterizes the criticality of a biological system. Our method not only identifies the critical state or tipping point at a single sample level, but also provides the sKLD-signaling markers for further practical application. It is therefore of great potential in personalized pre-disease diagnosis.

Detecting the tipping points in a three-state model of complex diseases by temporal differential networks

Background

The progression of complex diseases, such as diabetes and cancer, is generally a nonlinear process with three stages, i.e., normal state, pre-disease state, and disease state, where the pre-disease state is a critical state or tipping point immediately preceding the disease state. Traditional biomarkers aim to identify a disease state by exploiting the information of differential expressions for the observed molecules, but may fail to detect a pre-disease state because there are generally little significant differences between the normal and pre-disease states. Thus, it is challenging to signal the pre-disease state, which actually implies the disease prediction.

Methods

In this work, by exploiting the information of differential associations among the observed molecules between the normal and pre-disease states, we propose a temporal differential network based computational method to accurately signal the pre-disease state or predict the occurrence of severe disease. The theoretical foundation of this work is the quantification of the critical state using dynamical network biomarkers.

Results

Considering that there is one stationary Markov process before reaching the tipping point, a novel index, inconsistency score (I-score), is proposed to quantitatively measure the change of the stationary processes from the normal state so as to detect the onset of pre-disease state. In other words, a drastic increase of I-score implies the high inconsistency with the preceding stable state and thus signals the upcoming critical transition. This approach is applied to the simulated and real datasets of three diseases, which demonstrates the effectiveness of our method for predicting the deterioration into disease states. Both functional analysis and pathway enrichment also validate the computational results from the perspectives of both molecules and networks.

Conclusions

At the molecular network level, this method provides a computational way of unravelling the underlying mechanism of the dynamical progression when a biological system is near the tipping point, and thus detecting the early-warning signal of the imminent critical transition, which may help to achieve timely intervention. Moreover, the rewiring of differential networks effectively extracts discriminatively interpretable features, and systematically demonstrates the dynamical change of a biological system.

Electronic supplementary material

The online version of this article (doi:10.1186/s12967-017-1320-7) contains supplementary material, which is available to authorized users.

Leading indicators of mosquito-borne disease elimination

Mosquito-borne diseases contribute significantly to the global disease burden. High-profile elimination campaigns are currently underway for many parasites, e.g., Plasmodium spp., the causal agent of malaria. Sustaining momentum near the end of elimination programs is often difficult to achieve and consequently quantitative tools that enable monitoring the effectiveness of elimination activities after the initial reduction of cases has occurred are needed. Documenting progress in vector-borne disease elimination is a potentially important application for the theory of critical transitions. Non-parametric approaches that are independent of model-fitting would advance infectious disease forecasting significantly. In this paper, we consider compartmental Ross-McDonald models that are slowly forced through a critical transition through gradually deployed control measures. We derive expressions for the behavior of candidate indicators, including the autocorrelation coefficient, variance, and coefficient of variation in the number of human cases during the approach to elimination. We conducted a simulation study to test the performance of each summary statistic as an early warning system of mosquito-borne disease elimination. Variance and coefficient of variation were highly predictive of elimination but autocorrelation performed poorly as an indicator in some control contexts. Our results suggest that tipping points (bifurcations) in mosquito-borne infectious disease systems may be foreshadowed by characteristic temporal patterns of disease prevalence.

Forecasting infectious disease emergence subject to seasonal forcing

BACKGROUND

Despite high vaccination coverage, many childhood infections pose a growing threat to human populations. Accurate disease forecasting would be of tremendous value to public health. Forecasting disease emergence using early warning signals (EWS) is possible in non-seasonal models of infectious diseases. Here, we assessed whether EWS also anticipate disease emergence in seasonal models.

METHODS

We simulated the dynamics of an immunizing infectious pathogen approaching the tipping point to disease endemicity. To explore the effect of seasonality on the reliability of early warning statistics, we varied the amplitude of fluctuations around the average transmission. We proposed and analyzed two new early warning signals based on the wavelet spectrum. We measured the reliability of the early warning signals depending on the strength of their trend preceding the tipping point and then calculated the Area Under the Curve (AUC) statistic.

RESULTS

Early warning signals were reliable when disease transmission was subject to seasonal forcing. Wavelet-based early warning signals were as reliable as other conventional early warning signals. We found that removing seasonal trends, prior to analysis, did not improve early warning statistics uniformly.

CONCLUSIONS

Early warning signals anticipate the onset of critical transitions for infectious diseases which are subject to seasonal forcing. Wavelet-based early warning statistics can also be used to forecast infectious disease.

scGET: Predicting Cell Fate Transition During Early Embryonic Development by Single-cell Graph Entropy

During early embryonic development, cell fate commitment represents a critical transition or "tipping point" of embryonic differentiation, at which there is a drastic and qualitative shift of the cell populations. In this study, we presented a computational approach, scGET, to explore the gene-gene associations based on single-cell RNA sequencing (scRNA-seq) data for critical transition prediction. Specifically, by transforming the gene expression data to the local network entropy, the single-cell graph entropy (SGE) value quantitatively characterizes the stability and criticality of gene regulatory networks among cell populations and thus can be employed to detect the critical signal of cell fate or lineage commitment at the single-cell level. Being applied to five scRNA-seq datasets of embryonic differentiation, scGET accurately predicts all the impending cell fate transitions. After identifying the "dark genes" that are non-differentially expressed genes but sensitive to the SGE value, the underlying signaling mechanisms were revealed, suggesting that the synergy of dark genes and their downstream targets may play a key role in various cell development processes.The application in all five datasets demonstrates the effectiveness of scGET in analyzing scRNA-seq data from a network perspective and its potential to track the dynamics of cell differentiation. The source code of scGET is accessible at https://github.com/zhongjiayuna/scGET_Project.

Cerebrospinal fluid protein dynamic driver network: At the crossroads of brain tumorigenesis

To get a better understanding of the ongoing in situ environmental changes preceding the brain tumorigenesis, we assessed cerebrospinal fluid (CSF) proteome profile changes in a glioma rat model in which brain tumor invariably developed after a single in utero exposure to the neurocarcinogen ethylnitrosourea (ENU). Computationally, the CSF proteome profile dynamics during the tumorigenesis can be modeled as non-smooth or even abrupt state changes. Such brain tumor environment transition analysis, correlating the CSF composition changes with the development of early cellular hyperplasia, can reveal the pathogenesis process at network level during a time before the image detection of the tumors. In our controlled rat model study, matched ENU- and saline-exposed rats' CSF proteomics changes were quantified at approximately 30, 60, 90, 120, 150 days of age (P30, P60, P90, P120, P150). We applied our transition-based network entropy (TNE) method to compute the CSF proteome changes in the ENU rat model and test the hypothesis of the critical transition state prior to impending hyperplasia. Our analysis identified a dynamic driver network (DDN) of CSF proteins related with the emerging tumorigenesis progressing from the non-hyperplasia state. The DDN associated leading network CSF proteins can allow the early detection of such dynamics before the catastrophic shift to the clear clinical landmarks in gliomas. Future characterization of the critical transition state (P60) during the brain tumor progression may reveal the underlying pathophysiology to device novel therapeutics preventing tumor formation. More detailed method and information are accessible through our website at http://translationalmedicine.stanford.edu.

Identifying the critical states and dynamic network biomarkers of cancers based on network entropy

Background

There are sudden deterioration phenomena during the progression of many complex diseases, including most cancers; that is, the biological system may go through a critical transition from one stable state (the normal state) to another (the disease state). It is of great importance to predict this critical transition or the so-called pre-disease state so that patients can receive appropriate and timely medical care. In practice, however, this critical transition is usually difficult to identify due to the high nonlinearity and complexity of biological systems.

Methods

In this study, we employed a model-free computational method, local network entropy (LNE), to identify the critical transition/pre-disease states of complex diseases. From a network perspective, this method effectively explores the key associations among biomolecules and captures their dynamic abnormalities.

Results

Based on LNE, the pre-disease states of ten cancers were successfully detected. Two types of new prognostic biomarkers, optimistic LNE (O-LNE) and pessimistic LNE (P-LNE) biomarkers, were identified, enabling identification of the pre-disease state and evaluation of prognosis. In addition, LNE helps to find “dark genes” with nondifferential gene expression but differential LNE values.

Conclusions

The proposed method effectively identified the critical transition states of complex diseases at the single-sample level. Our study not only identified the critical transition states of ten cancers but also provides two types of new prognostic biomarkers, O-LNE and P-LNE biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12967-022-03445-0.

Heteroskedasticity as a leading indicator of desertification in spatially explicit data

Regime shifts are abrupt transitions between alternate ecosystem states including desertification in arid regions due to drought or overgrazing. Regime shifts may be preceded by statistical anomalies such as increased autocorrelation, indicating declining resilience and warning of an impending shift. Tests for conditional heteroskedasticity, a type of clustered variance, have proven powerful leading indicators for regime shifts in time series data, but an analogous indicator for spatial data has not been evaluated. A spatial analog for conditional heteroskedasticity might be especially useful in arid environments where spatial interactions are critical in structuring ecosystem pattern and process. We tested the efficacy of a test for spatial heteroskedasticity as a leading indicator of regime shifts with simulated data from spatially extended vegetation models with regular and scale-free patterning. These models simulate shifts from extensive vegetative cover to bare, desert-like conditions. The magnitude of spatial heteroskedasticity increased consistently as the modeled systems approached a regime shift from vegetated to desert state. Relative spatial autocorrelation, spatial heteroskedasticity increased earlier and more consistently. We conclude that tests for spatial heteroskedasticity can contribute to the growing toolbox of early warning indicators for regime shifts analyzed with spatially explicit data.

Identifying pre-outbreak signals of hand, foot and mouth disease based on landscape dynamic network marker

Background

The high incidence, seasonal pattern and frequent outbreaks of hand, foot and mouth disease (HFMD) represent a threat for billions of children around the world. Detecting pre-outbreak signals of HFMD facilitates the timely implementation of appropriate control measures. However, real-time prediction of HFMD outbreaks is usually challenging because of its complexity intertwining both biological systems and social systems.

Results

By mining the dynamical information from city networks and horizontal high-dimensional data, we developed the landscape dynamic network marker (L-DNM) method to detect pre-outbreak signals prior to the catastrophic transition into HFMD outbreaks. In addition, we set up multi-level early warnings to achieve the purpose of distinguishing the outbreak scale. Specifically, we collected the historical information of clinic visits caused by HFMD infection between years 2009 and 2018 respectively from public records of Tokyo, Hokkaido, and Osaka, Japan. When applied to the city networks we modelled, our method successfully identified pre-outbreak signals in an average 5 weeks ahead of the HFMD outbreak. Moreover, from the performance comparisons with other methods, it is seen that the L-DNM based system performs better when given only the records of clinic visits.

Conclusions

The study on the dynamical changes of clinic visits in local district networks reveals the dynamic or landscapes of HFMD spread at the network level. Moreover, the results of this study can be used as quantitative references for disease control during the HFMD outbreak seasons.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-020-05709-w.

Dynamics of sleep: Exploring critical transitions and early warning signals

BACKGROUND AND OBJECTIVES

In standard practice, sleep is classified into distinct stages by human observers according to specific rules as for instance specified in the AASM manual. We here show proof of principle for a conceptualization of sleep stages as attractor states in a nonlinear dynamical system in order to develop new empirical criteria for sleep stages.

METHODS

EEG (single channel) of two healthy sleeping participants was used to demonstrate this conceptualization. Firstly, distinct EEG epochs were selected, both detected by a MLR classifier and through manual scoring. Secondly, change point analysis was used to identify abrupt changes in the EEG signal. Thirdly, these detected change points were evaluated on whether they were preceded by early warning signals.

RESULTS

Multiple change points were identified in the EEG signal, mostly in interplay with N2. The dynamics before these changes revealed, for a part of the change points, indicators of generic early warning signals, characteristic of complex systems (e.g., ecosystems, climate, epileptic seizures, global finance systems).

CONCLUSIONS

The sketched new framework for studying critical transitions in sleep EEG might benefit the understanding of individual and pathological differences in the dynamics of sleep stage transitions. Formalising sleep as a nonlinear dynamical system can be useful for definitions of sleep quality, i.e. stability and accessibility of an equilibrium state, and disrupted sleep, i.e. constant shifting between instable sleep states.

Characterization of lacustrine harmful algal blooms using multiple biomarkers: Historical processes, driving synergy, and ecological shifts

Harmful algal blooms (HABs) producing toxic metabolites are increasingly threatening environmental and human health worldwide. Unfortunately, long-term process and mechanism triggering HABs remain largely unclear due to the scarcity of temporal monitoring. Retrospective analysis of sedimentary biomarkers using up-to-date chromatography and mass spectrometry techniques provide a potential means to reconstruct the past occurrence of HABs. By combining aliphatic hydrocarbons, photosynthetic pigments, and cyanotoxins, we quantified herein century-long changes in abundance, composition, and variability of phototrophs, particularly toxigenic algal blooms, in China's third largest freshwater Lake Taihu. Our multi-proxy limnological reconstruction revealed an abrupt ecological shift in the 1980s characterized by elevated primary production, Microcystis-dominated cyanobacterial blooms, and exponential microcystin production, in response to nutrient enrichment, climate change, and trophic cascades. The empirical results from ordination analysis and generalized additive models support climate warming and eutrophication synergy through nutrient recycling and their feedback through buoyant cyanobacterial proliferation, which sustain bloom-forming potential and further promote the occurrence of increasingly-toxic cyanotoxins (e.g., microcystin-LR) in Lake Taihu. Moreover, temporal variability of the lake ecosystem quantified using variance and rate of change metrics rose continuously after state change, indicating increased ecological vulnerability and declined resilience following blooms and warming. With the persistent legacy effects of lake eutrophication, nutrient reduction efforts mitigating toxic HABs probably be overwhelmed by climate change effects, emphasizing the need for more aggressive and integrated environmental strategies.

Regime shifts in shallow lake ecosystems along an urban-rural gradient in central China

Due to differential exploitation pressure, ecosystems along the urban to rural gradients often exhibit different status in ecological structure and function. This can be challenging for lake restoration, given the relative strengths, magnitudes and speed of the exploitation. In this paper, we reconstructed the ecological changes over the past century and identified the regime shifts based on subfossil aquatic biota (chironomid records) in three shallow lakes (Shahu, Yanxi and Futou Lake) along an urban-rural gradient in the Yangtze floodplain, China. Our results illustrated the differences among lakes in trajectories, timing of critical transition and current ecological status. Eutrophic chironomid taxa increased markedly and replaced macrophyte-related taxa in urban Shahu Lake and suburban Yanxi Lake, indicated by the shift from a stable, vegetation-dominated state to an alternative, algal-dominated state in 1963 CE and 1975 CE respectively. The ecological regime in rural Futou Lake transited around 1980 CE but it is still in a relatively clear water state with abundant macrophytes due to anthropogenic hydrological controls. The greatest variance of chironomid compositional changes in both Shahu and Yanxi Lake was captured by anthropogenic pollutants, and analyses show that when these pressures are high they may be further amplified by climate warming. Responses along the urban-rural gradient are exemplified by urban Shahu Lake having shifted to a fragile regime with weak resistance and resilience, while rural Futou Lake has stabilized in a new regime with improved ecological resilience. Suburban Yanxi Lake is still moving toward a new state, and as such is unstable, because the types and magnitudes of external stressors are changing with urbanization in the city. It is suggested that active and precise management strategies for lakes should be established along the urban-rural gradient given their distinct development trajectories, drivers and current status.

Sediment DNA Records the Critical Transition of Bacterial Communities in the Arid Lake

It is necessary to predict the critical transition of lake ecosystems due to their abrupt, non-linear effects on social-economic systems. Given the promising application of paleolimnological archives to tracking the historical changes of lake ecosystems, it is speculated that they can also record the lake's critical transition. We studied Lake Dali-Nor in the arid region of Inner Mongolia because of the profound shrinking the lake experienced between the 1300 s and the 1600 s. We reconstructed the succession of bacterial communities from a 140-cm-long sediment core at 4-cm intervals and detected the critical transition. Our results showed that the historical trajectory of bacterial communities from the 1200 s to the 2010s was divided into two alternative states: state1 from 1200 to 1300 s and state2 from 1400 to 2010s. Furthermore, in the late 1300 s, the appearance of a tipping point and critical slowing down implied the existence of a critical transition. By using a multi-decadal time series from the sedimentary core, with general Lotka-Volterra model simulations, local stability analysis found that bacterial communities were the most unstable as they approached the critical transition, suggesting that the collapse of stability triggers the community shift from an equilibrium state to another state. Furthermore, the most unstable community harbored the strongest antagonistic and mutualistic interactions, which may imply the detrimental role of interaction strength on community stability. Collectively, our study showed that sediment DNA can be used to detect the critical transition of lake ecosystems.

System Biology Approach in Investigating Epithelial-Mesenchymal Transition (EMT)

Epithelial-mesenchymal transition (EMT) is a trans-differentiating and reversible process that leads to dramatic cell phenotypic changes, enabling epithelial cells in acquiring mesenchymal phenotypes and behaviors. EMT plays a crucial role during embryogenesis, and occurs in several para-physiologic and pathological conditions, as during fibrosis or cancer development. EMT displays some hallmarks of critical transitions, as a sudden change in the overall configuration of a system in correspondence of specific tipping point around which a "catastrophic bifurcation" happens. The transition occurs when external conditions breach specific thresholds. This definition helps in highlighting two main aspects: (1) the change involves the overall system, rather than single, discrete components; (2) cues from the microenvironment play an irreplaceable role in triggering the transition. This evidence implies that critical transition should be ascertained focusing the investigation at the system level (rather than investigating only molecular parameters) in a well-defined context, as the transition is strictly dependent on the microenvironment in which it occurs. Therefore, we need a systems biology approach to investigate EMT across the Waddington-like epigenetic landscape wherein the participation of both internal and external cues can be studied to follow the extent and the main characteristics of the phenotypic transition. Herein, we suggest a set of systems parameters (motility, invasiveness) altogether with specific molecular/histological markers to identify those critical observables, which can be integrated into a comprehensive mechanistic model.

Complex relationship between the diversity and stability of chironomid assemblages in the recent sediments of two large alpine lakes in SW China

There is no doubt that the diversity and stability of freshwater ecosystems have suffered dramatic changes as a result of intensified human activities. However, the relationship between community diversity and stability is still debated. In this study, we used biological and geochemical records from the recent sediments of two lakes to test the hypothesis that different aspects of the diversity of the chironomid community have different relationships with community stability. Yangzong Lake (YZ) and Chenghai Lake (CH) are large and deep alpine lakes in SW China. We conducted a multi-proxy study of the sedimentary records spanning the last 200 years from the two lakes. Our focus was on subfossil chironomid remains, but analyses of chemical elements, total organic carbon (TOC) and total nitrogen (TN) were also conducted. The principal results are as follows: 1) Both nutrient and chironomid assemblages underwent a critical transition in 1990 at YZ and in 1998 at CH. 2) The response of species richness varied between the two lakes, but the trends of their respective β diversity indices are consistent, despite the fact that the contributors to β diversity are different. 3) The stability of the chironomid communities has decreased in both lakes since the mid-20th century. 4) The relationship between diversity and stability varies in relation to the type of diversity. Overall, our results emphasize the importance of considering the complex nature of diversity and stability when studying community assemblages.

Identifying the critical state of cancers by single-sample Markov flow entropy

Background

The progression of complex diseases sometimes undergoes a drastic critical transition, at which the biological system abruptly shifts from a relatively healthy state (before-transition stage) to a disease state (after-transition stage). Searching for such a critical transition or critical state is crucial to provide timely and effective scientific treatment to patients. However, in most conditions where only a small sample size of clinical data is available, resulting in failure when detecting the critical states of complex diseases, particularly only single-sample data.

Methods

In this study, different from traditional methods that require multiple samples at each time, a model-free computational method, single-sample Markov flow entropy (sMFE), provides a solution to the identification problem of critical states/pre-disease states of complex diseases, solely based on a single-sample. Our proposed method was employed to characterize the dynamic changes of complex diseases from the perspective of network entropy.

Results

The proposed approach was verified by unmistakably identifying the critical state just before the occurrence of disease deterioration for four tumor datasets from The Cancer Genome Atlas (TCGA) database. In addition, two new prognostic biomarkers, optimistic sMFE (O-sMFE) and pessimistic sMFE (P-sMFE) biomarkers, were identified by our method and enable the prognosis evaluation of tumors.

Conclusions

The proposed method has shown its capability to accurately detect pre-disease states of four cancers and provide two novel prognostic biomarkers, O-sMFE and P-sMFE biomarkers, to facilitate the personalized prognosis of patients. This is a remarkable achievement that could have a major impact on the diagnosis and treatment of complex diseases.