Figure 1
Schematic illustration of the dynamical features of disease progression from a normal state to a disease state through a pre-disease state.
(a) Deterioration progress of disease. (b) The normal state is a steady state or a minimum of a potential function, representing a relatively healthy stage. (c) The pre-disease state is situated immediately before the tipping point and is the limit of the normal state but with a lower recovery rate from small perturbations. At this stage, the system is sensitive to external stimuli and still reversible to the normal state when appropriately interfered with, but a small change in the parameters of the system may suffice to drive the system into collapse, which often implies a large phase transition to the disease state. (d) The disease state is the other stable state or a minimum of the potential function, where the disease has seriously deteriorated and thus the system is usually irreversible to the normal state. (e)–(g) The three states are schematically represented by a molecular network where the correlations and deviations of different species are described by the thickness of edges and the colors of nodes respectively. When the system approaches the pre-disease state, the deviations of (z1, z2, z3) increase drastically and the correlations among (z1, z2, z3) also increase drastically whereas their correlations with other nodes (z4, z5, z6) decrease drastically ((e) and (f)). We call (z1, z2, z3) as the dominant group or the DNB. (g) At the disease stage, the system settles down in another steady state, i.e., the disease state, with lowered deviations and correlations for the DNB. (h) Graphs show an example of the dynamical fluctuations of the molecular concentrations for the DNB in the pre-disease state, which dynamically change with strong temporal deviations but are closely (positively or negatively) correlated.
