Apicomplexans pulling the strings: manipulation of the host cell cytoskeleton dynamics

Invasive stages of apicomplexan parasites require a host cell to survive, proliferate and advance to the next life cycle stage. Once invasion is achieved, apicomplexans interact closely with the host cell cytoskeleton, but in many cases the different species have evolved distinct mechanisms and pathways to modulate the structural organization of cytoskeletal filaments. The host cell cytoskeleton is a complex network, largely, but not exclusively, composed of microtubules, actin microfilaments and intermediate filaments, all of which are modulated by associated proteins, and it is involved in diverse functions including maintenance of cell morphology and mechanical support, migration, signal transduction, nutrient uptake, membrane and organelle trafficking and cell division. The ability of apicomplexans to modulate the cytoskeleton to their own advantage is clearly beneficial. We here review different aspects of the interactions of apicomplexans with the three main cytoskeletal filament types, provide information on the currently known parasite effector proteins and respective host cell targets involved, and how these interactions modulate the host cell physiology. Some of these findings could provide novel targets that could be exploited for the development of preventive and/or therapeutic strategies.

Besnoitia besnoiti and Toxoplasma gondii: two apicomplexan strategies to manipulate the host cell centrosome and Golgi apparatus

Besnoitia besnoiti and Toxoplasma gondii are two closely related parasites that interact with the host cell microtubule cytoskeleton during host cell invasion. Here we studied the relationship between the ability of these parasites to invade and to recruit the host cell centrosome and the Golgi apparatus. We observed that T. gondii recruits the host cell centrosome towards the parasitophorous vacuole (PV), whereas B. besnoiti does not. Notably, both parasites recruit the host Golgi apparatus to the PV but its organization is affected in different ways. We also investigated the impact of depleting and over-expressing the host centrosomal protein TBCCD1, involved in centrosome positioning and Golgi apparatus integrity, on the ability of these parasites to invade and replicate. Toxoplasma gondii replication rate decreases in cells over-expressing TBCCD1 but not in TBCCD1-depleted cells; while for B. besnoiti no differences were found. However, B. besnoiti promotes a reorganization of the Golgi ribbon previously fragmented by TBCCD1 depletion. These results suggest that successful establishment of PVs in the host cell requires modulation of the Golgi apparatus which probably involves modifications in microtubule cytoskeleton organization and dynamics. These differences in how T. gondii and B. besnoiti interact with their host cells may indicate different evolutionary paths.

Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg'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, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.