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Stochastic dynamics and mean field approach in a system of three interacting species

100%
Valenti D., Spagnolo B.
|
EN
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied, by using Lotka-Volterra equations. A correlated dichotomous noise acts on the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of the three species. After analyzing the time behaviour of the three species in a single site, we consider a two-dimensional spatial domain, applying a mean field approach and obtaining the time behaviour of the first and second order moments for different multiplicative noise intensities. We find noise-induced oscillations of the three species with an anticorrelated behaviour of the two preys. Finally, we compare our results with those obtained by using a coupled map lattice (CML) model, finding a good qualitative agreement. However, some quantitative discrepancies appear, that can be explained as follows: i) different stationary values occur in the two approaches; ii) in the mean field formalism the interaction between sites is extended to the whole spatial domain, conversely in the CML model the species interaction is restricted to the nearest neighbors; iii) the dynamics of the CML model is faster since an unitary time step is considered.
2
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Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach

81%
Pizzolato N., Valenti D., Adorno D., Spagnolo B.
Open Physics
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2009
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vol. 7
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issue 3
541-548
EN
The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modelled therapies. We show how the patient response to the therapy changes when a high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a fraction of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.
3
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Monte Carlo analysis of polymer translocation with deterministic and noisy electric fields

61%
Valenti D., Denaro G., Adorno D., Pizzolato N., Zammito S., Spagnolo B.
Open Physics
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2012
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vol. 10
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issue 3
560-567
EN
Polymer translocation through the nanochannel is studied by means of a Monte Carlo approach, in the presence of a static or oscillating external electric voltage. The polymer is described as a chain molecule according to the two-dimensional “bond fluctuation model”. It moves through a piecewise linear channel, which mimics a nanopore in a biological membrane. The monomers of the chain interact with the walls of the channel, modelled as a reflecting barrier. We analyze the polymer dynamics, concentrating on the translocation time through the channel, when an external electric field is applied. By introducing a source of coloured noise, we analyze the effect of correlated random fluctuations on the polymer translocation dynamics.
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