Metastasis Models: Thermodynamics and Complexity.

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.

Protein surface roughness accounts for binding free energy of Plasmepsin II-ligand complexes.

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; SDerror  = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.

Unravelling the relationship between protein sequence and low-complexity regions entropies: Interactome implications.

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.