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Register a new userCo-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response
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Added by
Anna Ochab-Marcinek
Publication date
2006
fields
Biology
and research's language is
English
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We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together.
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We study a Langevin equation derived from the Michaelis-Menten (MM) phenomenological scheme for catalysis accompanying a spontaneous replication of molecules, which may serve as a simple model of cell-mediated immune surveillance against cancer. We examine how two different and statistically independent sources of noise - dichotomous multiplicative noise and additive Gaussian white noise - influence the populations extinction time. This quantity is identified as the mean first passage time of the system across the zero population state. We observe the effects of resonant activation (RA) and noise-enhanced stability (NES) and we report the evidence for competitive co-occurrence of both phenomena in a given regime of noise parameters. We discuss the statistics of first passage times in this regime and the role of different pseudo-potential profiles on the RA and NES phenomena. The RA/NES coexistence region brings an interesting interpretation for the growth kinetics of cancer cells population, as the NES effect enhancing the stability of the tumoral state becomes strongly reduced by the RA phenomenon.
Increasing number in global COVID-19 cases demands for mathematical model to analyze the interaction between the virus dynamics and the response of innate and adaptive immunity. Here, based on the assumption of a weak and delayed response of the innate and adaptive immunity in SARS-CoV-2 infection, we constructed a mathematical model to describe the dynamic processes of immune system. Integrating theoretical results with clinical COVID-19 patients data, we classified the COVID-19 development processes into three typical modes of immune responses, correlated with the clinical classification of mild & moderate, severe and critical patients. We found that the immune efficacy (the ability of host to clear virus and kill infected cells) and the lymphocyte supply (the abundance and pool of naive T and B cell) play important roles in the dynamic process and determine the clinical outcome, especially for the severe and critical patients. Furthermore, we put forward possible treatment strategies for the three typical modes of immune response. We hope our results can help to understand the dynamical mechanism of the immune response against SARS-CoV-2 infection, and to be useful for the treatment strategies and vaccine design.
A small portion of a tissue defines a microstate in gene expression space. Mutations, epigenetic events or external factors cause microstate displacements which are modeled by combining small independent gene expression variations and large Levy jumps, resulting from the collective variations of a set of genes. The risk of cancer in a tissue is estimated as the microstate probability to transit from the normal to the tumor region in gene expression space. The formula coming from the contribution of large Levy jumps seems to provide a qualitatively correct description of the lifetime risk of cancer, and reveals an interesting connection between the risk and the way the tissue is protected against infections.
In the last decades, the interest to understand the connection between brain and body has grown notably. For example, in psychoneuroimmunology many studies associate stress, arising from many different sources and situations, to changes in the immune system from the medical or immunological point of view as well as from the biochemical one. In this paper we identify important behaviours of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end we develop a differential equation model with two equations for infection level and immune system, which integrates the effects of stress as an additional parameter. We are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a burn-out or stable sick state for extremely high stress. The mechanism between the different dynamics is controlled by two saddle-node in cycle (SNIC) bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing before eventually reaching a burn-out state.
Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. in 2015 for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we head back to the stochastic model and calculate the probability that the T cells all get exhausted during the treatment. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.
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