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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]

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]

The thermodynamic formalism of nonequilibrium systems together with the theory of complex systems and systems biology offer an appropriate theoretical framework to explain the complexity observed at the macroscopic level in physiological phenomena. In turn, they allow the establishment of an appropriate conceptual and operational framework to address the study of phenomena such as the emergence and evolution of cancer.This chapter is organized as follows: In Subheading 1, an integrated vision of these disciplines is offered for the characterization of the emergence and evolution of cancer, seen as a nonlinear dynamic system, temporally and spatially self-organized out of thermodynamic equilibrium. The development of the various mathematical models and different techniques and approaches used in the characterization of cancer metastasis is presented in Subheading 2. Subheading 3 is devoted to the time course of cancer metastasis, with particular emphasis on the epithelial-mesenchymal transition (EMT henceforth) as well as chronotherapeutic treatments. In Subheading 4, models of the spatial evolution of cancer metastasis are presented. Finally, in Subheading 5, some conclusions and remarks are presented., (© 2024. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

Low-complexity regions are sub-sequences of biased composition in a protein sequence. The influence of these regions over protein evolution, specific functions and highly interactive capacities is well known. Although protein sequence entropy has been largely studied, its relationship with low-complexity regions and the subsequent effects on protein function remains unclear. In this work we propose a theoretical and empirical model integrating the sequence entropy with local complexity parameters. Our results indicate that the protein sequence entropy is related with the protein length, the entropies inside and outside the low-complexity regions as well as their number and average size. We found a small but significant increment in the sequence entropy of hubs proteins. In agreement with our theoretical model, this increment is highly dependent of the balance between the increment of protein length and average size of the low-complexity regions. Finally, our models and proteins analysis provide evidence supporting that modifications in the average size is more relevant in hubs proteins than changes in the number of low-complexity regions., (Copyright © 2015 Elsevier Ltd. All rights reserved.)