On the existence of potential landscape in the evolution of complex systems

Ao, Ping; Kwon, Chulan; Qian, Hong

doi:10.1002/cplx.20171

Cited by 82 publications

(92 citation statements)

References 23 publications

(54 reference statements)

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“…A vivid and graphical description of the dynamical system is an adaptive landscape, which can depict the robustness of these attractors and the transition between the attractors intuitively [56]. Recent progress allows us to construct the adaptive landscape based on the endogenous molecular-cellular network [55,57].…”

Section: Quantitative Analysis Of the Endogenous Molecular -Cellular mentioning

confidence: 99%

Quantitative implementation of the endogenous molecular–cellular network hypothesis in hepatocellular carcinoma

Wang

Zhu

et al. 2014

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One contribution of 10 to a Theme Issue 'Computational cell biology: from the past to the future'. A quantitative hypothesis for cancer genesis and progression-the endogenous molecular-cellular network hypothesis, intended to include both genetic and epigenetic causes of cancer-has been proposed recently. Using this hypothesis, here we address the molecular basis for maintaining normal liver and hepatocellular carcinoma (HCC), and the potential strategy to cure or relieve HCC. First, we elaborate the basic assumptions of the hypothesis and establish a core working network of HCC according to the hypothesis. Second, we quantify the working network by a nonlinear dynamical system. We show that the working network reproduces the main known features of normal liver and HCC at both the modular and molecular levels. Lastly, the validated working network reveals that (i) specific positive feedback loops are responsible for the maintenance of normal liver and HCC; (ii) inhibiting proliferation and inflammation-related positive feedback loops and simultaneously inducing a liver-specific positive feedback loop is predicated as a potential strategy to cure or relieve HCC; and (iii) the genesis and regression of HCC are asymmetric. In light of the characteristic properties of the nonlinear dynamical system, we demonstrate that positive feedback loops must exist as a simple and general molecular basis for the maintenance of heritable phenotypes, such as normal liver and HCC, and regulating the positive feedback loops directly or indirectly provides potential strategies to cure or relieve HCC.

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Section: Quantitative Analysis Of the Endogenous Molecular -Cellular mentioning

confidence: 99%

Quantitative implementation of the endogenous molecular–cellular network hypothesis in hepatocellular carcinoma

Wang

Zhu

et al. 2014

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“…These two conditions can be realized only in high dimensions (not possible in one dimension). Unusual results were reported for the dynamics with the combination of these * ckwon@mju.ac.kr † jdnoh@uos.ac.kr ‡ hgpark@kias.re.kr two conditions [21][22][23]. In particular it was found that the zero mass limit and the over-damping limit are different in reducing the Kramers equation to the FokkerPlanck equation.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium fluctuations for linear diffusion dynamics

2011

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We present the theoretical study on non-equilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We consider a general situation in which NEQ is caused by two conditions: (i) drift force not derivable from a potential function and (ii) diffusion matrix not proportional to the unit matrix, implying non-identical and correlated multi-dimensional noise. The former is a well-known NEQ source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources. We develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy, work, and heat. The NEQ fluctuation theorems are reproduced successfully. We also find the time-dependent probability distribution function exactly as well as the NEQ work production distribution P (W) in terms of solutions of nonlinear differential equations. In addition, we compute low-order cumulants of the NEQ work production explicitly. In two dimensions, we carry out numerical simulations to check out our analytic results and also to get P (W). We find an interesting dynamic phase transition in the exponential tail shape of P (W), associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.

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“…which in general may depend on the system under study 15,26 . The change of a can have dramatic consequences for the long-term behaviour of systems (Supplementary Figs S1-S4 and Supplementary Note 1).…”

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Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

et al. 2013

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Intrinsically noisy mechanisms drive most physical, biological and economic phenomena. Frequently, the system's state influences the driving noise intensity (multiplicative feedback). These phenomena are often modelled using stochastic differential equations, which can be interpreted according to various conventions (for example, Itô calculus and Stratonovich calculus), leading to qualitatively different solutions. Thus, a stochastic differential equationconvention pair must be determined from the available experimental data before being able to predict the system's behaviour under new conditions. Here we experimentally demonstrate that the convention for a given system may vary with the operational conditions: we show that a noisy electric circuit shifts from obeying Stratonovich calculus to obeying Itô calculus. We track such a transition to the underlying dynamics of the system and, in particular, to the ratio between the driving noise correlation time and the feedback delay time. We discuss possible implications of our conclusions, supported by numerics, for biology and economics.

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On the existence of potential landscape in the evolution of complex systems

Cited by 82 publications

References 23 publications

Quantitative implementation of the endogenous molecular–cellular network hypothesis in hepatocellular carcinoma

Quantitative implementation of the endogenous molecular–cellular network hypothesis in hepatocellular carcinoma

Nonequilibrium fluctuations for linear diffusion dynamics

Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

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