Dynamical states, possibilities and propagation of stress signal

Abstract

The stress driven dynamics of Notch-Wnt-p53 cross-talk is subjected to a few possible dynamical states governed by simple fractal rules, and allowed to decide its own fate by choosing one of these states which are contributed from long range correlation with varied fluctuations due to active molecular interaction. The topological properties of the networks corresponding to these dynamical states have hierarchical features with assortive structure. The stress signal driven by nutlin and modulated by mediator GSK3 acts as anti-apoptotic signal in this system, whereas, the stress signal driven by Axin and modulated by GSK3 behaves as anti-apoptotic for a certain range of Axin and GSK3 interaction, and beyond which the signal acts as favor-apoptotic signal. However, this stress system prefers to stay in an active dynamical state whose counterpart complex network is closest to hierarchical topology with exhibited roles of few interacting hubs. During the propagation of stress signal, the system allows the propagator pathway to inherit all possible properties of the state to the receiver pathway/pathways with slight modifications, indicating efficient information processing and democratic sharing of responsibilities in the system via cross-talk. The increase in the number of cross-talk pathways in the system favors to establish self-organization.

Figure 1. The schematic diagram of Notch − Wnt − p53 cross-talk model.

Figure 2

Dynamical states of stress p53 driven by nutlin, and stress propagation: (A) dynamical states of p53 for different k₃₅ values, (B) complexity measurement characterized by calculated permutation entropy S_p53 values of the corresponding dynamical states. (C) Multifractal calcualations of the dynamical states: plots of F_s vs s, vs q and D_q vs q, (D) A_p53 as a function of k₃₅ for various values of k₃₉:…., (E) phase diagram in the parameter space (), where are the values of k₃₅ cut by horizontal line, and Δk₃₅ is the range of k₃₅ occupied by sustain oscillation, (F) schematic diagram of stress signal propagation, (G) topological properties of networks constructed from the time series of corresponding dynamical states: P(k), C(k), C_n(k), C_B(k), C_C(k) and C_E(k) as a function of degree k, (H) the propagated signal received by Notch and corresponding dynamical states, (I) permutation entropy (H_Notch) calculation of the dynamical states, (J) Multifractal measures of dynamical states of Notch: plots of F_s vs s, vs q and D_q vs q, (K) topological properties of the corresponding dynamical states: P(k), C(k), C_n(k), C_B(k), C_C(k) and C_E(k) as a function of degree k, (L) dynamical states of Axin due to propagated signal, and (M) corresponding permutation entropy (H_Axin) values, (N) Multifractal calculations, (O) topological properties of the networks constructed from the Axin dynamical states.

Figure 3

Dynamical states of stress p53 driven by Axin, and stress propagation: (A) dynamical states of p53 for different k₂₂ values, (B) permutation entropy S_p53 values of the corresponding dynamical states. (C) Multifractal calulations: plots of F_s vs s, vs q and D_q vs q, (D) A_p53 as a function of k₂₂ for various values of k₃₉:…., (E) phase diagram in the parameter space (), and Δk₂₂ is the range of k₂₂ occupied by sustain oscillation, (F) schematic diagram of stress signal propagation, (G) topological properties of networks of corresponding dynamical states: P(k), C(k), C_n(k), C_B(k), C_C(k) and C_E(k) as a function of degree k, (H) the propagated signal receied by Notch and corresponding dynamical states, (I) permutation entropy (H_Notch) calculations, (J) Multifractal measures, (K) topological properties of the corresponding dynamical states.

Figure 4. Cross-talk of pathways and properties.

(A) Dynamics of stress p53 triggered by nutlin (red), nutlin plus Wnt (blue), and nutlin plus Wnt plus Notch (maroon), (B) permutation entropy measures of these cross-talks, (C) corresponding multifractal measures: F_s vs s, H_q vs q, and D_q vs q plots, (D) A_p53 corresponding to the cross-talks, (E) topological properties of the corresponding networks: P(k), C(k), C_n(k), C_B(k), C_C(k) and C_E(k) as a function of degree k.