The Effects of Environmental Disturbances on Tumor Growth

Wang, Ning Xing; Zhang, Xiao Miao; Han, Xiao

doi:10.1007/s13538-012-0082-1

Cited by 6 publications

(3 citation statements)

References 29 publications

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“…One motivation for the development of this model was to propose a mathematical framework within which we can understand resistance to treatment under the Frank-Rosner paradigm of drug resistance [ 5 ]. While most previous work on tumor growth modeling [ 25 – 33 ] has largely focused on the deterministic growth of tumors for mean values, heterogeneity and variability are key factors in understanding the development of tumors [ 5 , 34 , 35 ]. It has been observed that cancerous cells have greater variability in growth rate than do normal cells [ 36 ], confirming that there is merit to the assumption that growth rate is driven by a random process.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations

et al. 2015

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There has been increasing awareness in the wider biological community of the role of clonal phenotypic heterogeneity in playing key roles in phenomena such as cellular bet-hedging and decision making, as in the case of the phage-λ lysis/lysogeny and B. Subtilis competence/vegetative pathways. Here, we report on the effect of stochasticity in growth rate, cellular memory/intermittency, and its relation to phenotypic heterogeneity. We first present a linear stochastic differential model with finite auto-correlation time, where a randomly fluctuating growth rate with a negative average is shown to result in exponential growth for sufficiently large fluctuations in growth rate. We then present a non-linear stochastic self-regulation model where the loss of coherent self-regulation and an increase in noise can induce a shift from bounded to unbounded growth. An important consequence of these models is that while the average change in phenotype may not differ for various parameter sets, the variance of the resulting distributions may considerably change. This demonstrates the necessity of understanding the influence of variance and heterogeneity within seemingly identical clonal populations, while providing a mechanism for varying functional consequences of such heterogeneity. Our results highlight the importance of a paradigm shift from a deterministic to a probabilistic view of clonality in understanding selection as an optimization problem on noise-driven processes, resulting in a wide range of biological implications, from robustness to environmental stress to the development of drug resistance.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations

et al. 2015

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“…Many systems in nature or laboratories are nonlinear and involve stochastic processes due to intrinsic variability, heterogeneity, or uncertainty in a system [1][2][3][4][5][6][7][8]. An interesting consequence of the complex interaction in these nonlinear systems is the ability to self-regulate [1,2,9], leading to the formation of an attractor; a set of states, invariant under the dynamics, towards which neighboring trajectories asymptotically approach following the dynamical evolution.…”

Section: Introductionmentioning

confidence: 99%

Novel mapping in non-equilibrium stochastic processes

Heseltine¹,

Kim²

2016

J. Phys. A: Math. Theor.

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We investigate the time-evolution of a non-equilibrium system in view of the change in information and provide a novel mapping relation which quantifies the change in information far from equilibrium and the proximity of a nonequilibrium state to the attractor. Specifically, we utilize a nonlinear stochastic model where the stochastic noise plays the role of incoherent regulation of the dynamical variable x and analytically compute the rate of change in information (information velocity) from the time-dependent probability distribution function. From this, we quantify the total change in information in terms of information length  and the associated action  , where  represents the distance that the system travels in the fluctuation-based, statistical metric space parameterized by time. As the initial probability density function's mean position (μ) is decreased from the final equilibrium value * m (the carrying capacity),  and  increase monotonically with interesting power-law mapping relations. In comparison, as μ is increased from , *  m and  increase slowly until they level off to a constant value. This manifests the proximity of the state to the attractor caused by a strong correlation for large μ through large fluctuations. Our proposed mapping relation provides a new way of understanding the progression of the complexity in non-equilibrium system in view of information change and the structure of underlying attractor.

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“…This concept has been generalized to non-equilibrium systems [36][37][38][39][40][41][42][43], including the utilization for controlling systems to minimize entropy production [38,40,42], the measurement of the statistical distance in experiments to validate theoretical predictions [41], etc. However, some of these works rely on the equilibrium distribution Equation (2) that is valid only in or near equilibrium while many important phenomena in nature and laboratories are often far from equilibrium with strong fluctuations, variability, heterogeneity, or stochasticity [44][45][46][47][48][49][50][51][52]. Far from equilibrium, there is no (infinite-capacity) heat bath that can maintain the system at a certain temperature, or constant fluctuation level.…”

Section: Introductionmentioning

confidence: 99%

Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

Kim

2021

Entropy

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Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate Γ=dLdt and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, L is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.

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The Effects of Environmental Disturbances on Tumor Growth

Cited by 6 publications

References 29 publications

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations

Novel mapping in non-equilibrium stochastic processes

Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

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