Identifying critical transitions in complex diseases

Abstract

Mortality and the burden of diseases worldwide continue to reach substantial numbers with societal development and urbanization. In the face of decline in human health, early detection of complex diseases is indispensable, albeit challenging. In this review, we document the research carried out thus far on the appearance of complex diseases marked by a critical transition or a sudden shift from a healthy state to a disease state. The theory of resilience and critical slowing down can provide practical tools to forecast the onset of various fatal and perpetuating diseases. However, critical transitions in diseases across diverse temporal and spatial scales may not always be preceded by critical slowing down. In this backdrop, an in-depth study of the underlying molecular mechanisms provides dynamic network biomarkers that can forecast potential critical transitions. We have put together the theory of complex diseases and resilience, and have discussed the need for advanced research in developing early warning signals in the field of medicine and health care. We conclude the review with a few open questions and prospects for research in this emerging field.

Figure 1

Critical transition in the concentration of protein Cdc2-cyclin B: (a) Stochastic time series of the model represented in equation 1 a-b: with feedback strength $(v)=1.5$ (far from the tipping point), and (b) with $v=1$ (close to the tipping point). (c) Schematic potential landscapes representing stable states of the deterministic system: higher resilience of the Cdc2-cyclin B state when it is far from the tipping point, and (d) lower resilience close to a tipping point, when the system approaches a sudden shift from the lower stable state to the upper stable state. (e, f) Closer to a tipping point, on account of reduced resilience, the system has more memory for perturbation than when far from a tipping point, characterized by higher SD and AR-1. (e) All other parameters for the circuit are given in the mathematical model section.

Figure 2

Examples of circuits containing positive feedback loops: (a) Initiation of S-phase in eukaryote cell cycle. (b) Differentiation in ovaries of mammals. (c) Feedback in the two-component Cdc2-Cyclin B and Wee1 system. + sign denotes positive feedback.

Figure 3

Schematic representation of the functioning of DNB (Dynamical Network Biomarker): Disease progression in several diseases occur in three states, i.e., the normal state, the pre-disease state, and the disease state. The normal state and the disease state exhibit high resilience, while the pre-disease state shows lower resilience.

Figure 4

Critical transitions in protein Cdc2-Cyclin B and associated generic EWSs: (a) Transitions from a lower state to an upper stable state. Solid (cyan) lines indicate stable steady states, and dashed (red) lines indicate unstable steady states of the deterministic model. The black trajectory indicates stochastic time series. (b) Pre-transition stochastic time series (segment as indicated by the yellow boxed region in (a)). (c) Residual time series after applying a Gaussian filter (the orange curve in (b) is the trend used for filtering). (d and e) Generic EWSs calculated from the filtered time series after using a rolling window of $60\%$ of the data length: (d) variance and (e) AR-1. (f–i) Filtering bandwidth and rolling window chosen based on sensitivity analysis. (f) and (h) Contour plots showing the trends of generic EWSs variance and AR-1 respectively for different rolling-window sizes and filtering bandwidths as measured by the Kendall’s $\tau$ value. The triangles indicate the rolling-window size and bandwidth used to calculate the EWSs. (g and i) Frequency distributions of Kendall’s $\tau$ values corresponding to variance and AR-1, respectively.

Figure 5

The probability distribution of Kendall’s $\tau$ test statistic on a set of 1000 surrogate time series: Histograms depict the distribution of the test statistic for the surrogate time series (a) variance and (b) autocorrelation function at lag-1. Dashed (red) lines represent $5\%$ and $95\%$ confidence intervals. Solid (green) lines indicate the limit beyond which the Kendall’s $\tau$ of the surrogate data is higher than the statistic observed in the indicators of the original time series. As observed, trends for variance are significant, while AR-1 trends are not significant.

Figure 6

Stochastic potential landscapes and basin stability for feedback strength (v) obtained from the master equation (2): Stochastic potential for: (a) monostable low-density state for Cdc2-Cyclin B at $v=2$, (e) bistable high-density and low-density Cdc2-Cyclin B states for $v=0.9$, and (h) monostable high-density Cdc2-Cyclin B state at $v=0.4$. The blowup diagrams (a), (d), (f) and (i) represent magnified regions in potential wells. The color bar represents the negative logarithm of steady state probability [i.e., $-\text{log}(P_{\mathit{ss}})$]. (c, g and j) Pie diagrams representing basin stability of the system for feedback strengths $v=2$, 0.9, 0.4, respectively. The basin stability measure is calculated for percentages of ${10}^5$ simulations with random initial conditions reaching a particular steady state in a monostable or bistable region. Green and peach regions correspond to the percentage of simulations reaching upper and lower states, respectively. x and y denote Cdc2-Cyclin B complex and Wee 1, respectively.

Figure 7

MFPT with decrease in feedback strength (v): The red curve represents the MFPT calculated for Cdc2-Cyclin B system to switch from the upper state to the lower steady state under the influence of intrinsic noise. Similarly, the blue curve shows the MFPT to switch from the lower steady state to the upper state.