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From the perspectives of the thermodynamics of irreversible processes and the theory of complex systems, a characterization of longevity and aging and their relationships with the emergence and evolution of cancer was carried out. It was found that: (1) the rate of entropy production could be used as an index of the robustness, plasticity, and aggressiveness of cancer, as well as a measure of biological age; (2) the aging process, as well as the evolution of cancer, goes through what we call a "biological phase transition"; (3) the process of metastasis, which occurs during the epithelial–mesenchymal transition (EMT), appears to be a phase transition that is far from thermodynamic equilibrium and exhibits Shilnikov chaos-like dynamic behavior, which guarantees the robustness of the process and, in turn, its unpredictability; (4) as the ferroptosis process progresses, the complexity of the dynamics that are associated with the emergence and evolution of cancer decreases. The theoretical framework that was developed in this study could contribute to a better understanding of the biophysical and chemical phenomena of longevity and aging and their relationships with cancer. [ABSTRACT FROM AUTHOR]

A non-autonomous model was developed for vascular tumor growth and cancer metastasis under periodic perturbations that simulate chronotherapy. It was found that for a critical amplitude and a perturbation frequency of twice the autonomous frequency in vascular growth, less complex and therefore less robust states are reached and the tumor population decreases. In metastasis, similar results were found for a perturbation frequency equal to the autonomous frequency. In metastasis, similar behaviors occur, for a perturbation's frequency equal to the fundamental frequency of system. [ABSTRACT FROM AUTHOR]

A non-autonomous model for the regulation of apoptosis by p53 is proposed as a model for cancer chronotherapy. A perturbation is introduced that simulates damage caused to DNA in a periodic regime. To characterize the resulting system dynamics, the techniques used were stroboscopic analysis, Poincare section and power spectrum. The complexity of the time series was determined using the LZ index. Periodic and quasi-periodic dynamics were obtained as the control parameters were varied. The less complex states are those corresponding to higher values of the amplitude which indicates a strict control of the dose is required on periodic treatments. [ABSTRACT FROM AUTHOR]

The calculation of absolute binding affinities for protein-inhibitor complexes remains as one of the main challenges in computational structure-based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high-resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x-ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave-one-out cross-validation showed that our model reproduced accurately the absolute binding free energies for our training set ( R2 = 0.76; <|error|> =0.55 kcal/mol; SD error = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article. [ABSTRACT FROM AUTHOR]

Dynamics resulting from periodic perturbations in oscillating chemical reaction, as theoretical models of chronotherapy techniques are studied. Replication reactions and fluctuations take place in these models giving rise to new species with autocatalitic properties. Oscillating chemical reaction models due to Hanusse (H) with three intermediaries and Bourceanu (E[SUB1], E[SUB2], E[SUB3])) with four, five and six intermediaries, respectively, are taken for this study and are manipulated numerically using a Gear algorithm. The bifurcation diagrams are obtained applying non-linear dynamic techniques such as, power spectrum, stroboscopic method, Lyapunov exponents and correlation dimension D[SUB2]. The dynamics of Hanusse and Bourceanu perturbed models are very similar. The main dynamic behaviours observed after perturbation are quasiperiodicity, entrainment, some Arnold tongues and situations without chemical meaning. Chaos is not observed. This study contributes to understand theoretical and practical aspects of the chronotherapy techniques. [ABSTRACT FROM AUTHOR]

The article examines thermodynamic properties concerned with analyzing the stability of a complex system via the Lyapunov function. The thermodynamic point of view shows that the rate of entropy production is a function of Lyapunov in the linear region. A bifurcation point within the entropy production rate as a result of autocatalysis is examined.

El artículo discurre sobre la ecuación de Gompertz, la cual se utiliza en la descripción del crecimiento de tumores y en el uso de terapias. Los autores comentan sobre la importancia de la ecuación en el estudio de las características fractales de los tumores. También se provee una serie de ecuaciones ejemplares.

Cancer cells diagnose is essentially made from the hystopathological image of the cell pattern and based on this, studies have been made to characterize this morphology using its fractal dimension and its relation with the prognosis. The results show that in a same location the fractal dimension of neoplasic tissues is greater than that of healthy tissues. A mathematical model was developed from these results to predict the cancer's growth using its fractal dimension. The model was used to relate the aggressiveness of cervical cancer with the age of the patients showing that the growth rate decreases with the age, similarly to what was obtained from clinical studies. [ABSTRACT FROM AUTHOR]

In the present work, we propose a discrete model to the characterization of heart rate variability (HRV) complexity in the aging process of healthy subjects. We apply the Shannon entropy on the basis of an alternative way to probability calculation and to define a new index taking into consideration the transition probability that is related to the physiological complexity of the system. Our results suggest that in the aging process the capability response decreases according to the reduction of the physiological complexity. In the oldest group, an alternative mechanism emerges to compensate for this lack of capability; however, this effect does not increase the physiological complexity. Concomitantly, we provide some physiological explanation for our results. [ABSTRACT FROM AUTHOR]

It was made an analysis of the pattern dynamics of zinc electrodeposition at two constant current values (3,0 and 10,3 mA). The experimental results show damped oscillations in fractal dimension that converge to a constant value of D0 ≅ 1.7. In fact, we found a similar phenomenology in a simulated DLA (Diffusion Limited Aggregation) growth process. The mesoscopic model proposed allows us to get a better insight of the pattern formation dynamic morphogenesis. In this sense, this stochastic formalism makes possible not only to reproduce but also to understand the observed physical complexity. An important characteristic of the formalism developed here is that a discrete equation is obtained. This equation allows us to reproduce the phenomenological results obtained. These results support the hypothesis that the observed complexity of patterns is related with its multifractal nature. [ABSTRACT FROM AUTHOR]

El artículo discurre sobre el proceso de la glicólisis del cáncer. Los autores comentan sobre las características únicas de las células tumorales, conocidas como glicólisis o el efecto Warburg. También se considera el impacto de la glicólisis en el ciclo de ácidos tricarboxílicos o la cadena de transporte electrónica.