Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Mould and yeast identification in archival settings: preliminary results on the use of traditional methods and molecular biology options in Portuguese archives

This project was developed to fully assess the indoor air quality in archives and libraries from a fungal flora point of view. It uses classical methodologies such as traditional culture media – for the viable fungi – and modern molecular biology protocols, especially relevant to assess the non-viable fraction of the biological contaminants. Denaturing high-performance liquid chromatography (DHPLC) has emerged as an alternative to denaturing gradient gel electrophoresis (DGGE) and has already been applied to the study of a few bacterial communities. We propose the application of DHPLC to the study of fungal colonization on paper-based archive materials. This technology allows for the identification of each component of a mixture of fungi based on their genetic variation. In a highly complex mixture of microbial DNA this method can be used simply to study the population dynamics, and it also allows for sample fraction collection, which can, in many cases, be immediately sequenced, circumventing the need for cloning. Some examples of the methodological application are shown. Also applied is fragment length analysis for the study of mixed Candida samples. Both of these methods can later be applied in various fields, such as clinical and sand sample analysis. So far, the environmental analyses have been extremely useful to determine potentially pathogenic/toxinogenic fungi such as Stachybotrys sp., Aspergillus niger, Aspergillus fumigatus, and Fusarium sp. This work will hopefully lead to more accurate evaluation of environmental conditions for both human health and the preservation of documents.

Potential pathogenic fungi assessment through molecular biology in cork industry

Portugal has been the world leader in the cork sector in terms of exports, employing ten thousands of workers. In this working activity, the permanent contact with cork may lead to the exposure to fungi, raising concerns as potential occupational hazards in cork industry. The application of molecular tools is crucial in this setting, since fungal species with faster growth rates may hide other species with clinical relevance, such as species belonging to P. glabrum and A. fumigatus complexes. A study was developed aiming at assessing fungal contamination due to Aspergillus fumigatus complex and Penicillium glabrum complex by molecular methods in three cork industries in the outskirt of Lisbon city.

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.