A reduced (stereo-chemical) model is employed to study kinetic aspects of globular protein folding process, by Monte Carlo simulation. Nonextensive statistical approach is used: transition probability p i j between configurations i → j is given by p i j =[1 +(1 - q)ΔGi j/kB T ]1/(1-q), where q is the nonextensive (Tsallis) parameter. The system model consists of a chain of 27 beads immerse in its solvent; the beads represent the sequence of amino acids along the chain by means of a 10-letter stereo-chemical alphabet; a syntax (rule) to design the amino acid sequence for any given 3D structure is embedded in the model. The study focuses mainly kinetic aspects of the folding problem related with the protein folding time, represented in this work by the concept of first passage time (FPT). Many distinct proteins, whose native structures are represented here by compact self avoiding (CSA) configurations, were employed in our analysis, although our results are presented exclusively for one representative protein, for which a rich statistics was achieved. Our results reveal that there is a specific combinations of value for the nonextensive parameter q and temperature T, which gives the smallest estimated folding characteristic time (t). Additionally, for q = 1.1, (t) stays almost invariable in the range 0.9 < T < 1.3, slightly oscillating about its average value <img border=0 width=32 height=32 src="../../../../../../../img/revistas/bjp/v39n2a/a16txt01.gif" align=absmiddle > or = 27 ±σ, where σ = 2 is the standard deviation. This behavior is explained by comparing the distribution of the folding times for the Boltzmann statistics (q → 1), with respect to the nonextensive statistics for q = 1.1, which shows that the effect of the nonextensive parameter q is to cut off the larger folding times present in the original (q → 1) distribution. The distribution of natural logarithm of the folding times for Boltzmann statistics is a triple peaked Gaussian, while, for q = 1.1 (Tsallis), it is a double peaked Gaussian, suggesting that a log-normal process with two characteristic times replaced the original process with three characteristic times. Finally we comment on the physical meaning of the present results, as well its significance in the near future works.

Globular proteins are produced as a linear chain of aminoacids in water solution in the cell and, in the same aqueous environment, fold into their respective unique and functional native structures. In spite of this, many theoretical studies have tried to explain the folding process in vacuum, but in this paper we adopt an alternative point of view: the folding problem of heteropolymers is analyzed from the solvent perspective. The thermodynamics of the folding process is discussed for a non homogeneous system composed by the chain and solvent together; hydrophobic effects, modulated by the polar/nonpolar attributes of the residue sequence and by its corresponding steric specificities, are proposed as basic ingredients for the mechanisms of the folding process. These ideas are incorporated in both lattice and off-lattice models and treated by Monte Carlo simulations. Configurational and thermodynamical results are compared with properties of real proteins. The results suggest that the folding problem of small globular protein can be considered as a process in which the mechanism to reach the native structure and the requirements for the globule stability are uncoupled.

O fenômeno da difusão epidêmica é considerado tanto no aspecto temporal quanto geográfico. A dinâmica populacional é descrita através da simulação Monte Carlo e a idéia de conectividade é utilizada na construção da analogia entre o fenômeno epidêmico e o da percolação, envolvendo coordenadas espaciais. O modelo estudado considera uma população idealizada, disposta em uma rede bidimensional e o mecanismo de espalhamento da doença, essencialmente estocástico, processa-se através de contatos efetivos entre vizinhos adjacentes. Vários graus de vizinhança e de heterogeneidade espacial, envolvendo diferentes concentrações de imunes e susceptíveis, foram considerados. Uma generalização do conceito de percolação é utilizada como instrumento de medida, possibilitando a identificação do estado, ou fase epidêmica, no aspecto geográfico. Os resultados obtidos permitem associações à vários conceitos da Epidemiologia (imunidade de massa, processo e estado epidêmico) através de uma visão ampla, envolvendo explicitamente as dimensões espaciais. Alguns resultados numéricos encontrados incluem: (i)- determinação da duração do processo epidêmico em função da distribuição espacial inicial de indivíduos infectados, (ii)- efeito do "escudo topológico", na redução da difusão epidêmica.

The phenomenon of epidemic spread is studied, considering equally the temporal and the geographic features. The populational dynamics is described through the Monte Carlo simulation, and the idea of connectivity is used to build an analogy between percolation and the epidemic phenomenum including spatial coordinates. The model considers an idealized population distributed in a bidimentional net, and the illness spread mechanism, essentially stochastic, is processed through effective contacts between the adjacent populational neighbours. Many degrees of neighbourhood were used, as well as several degrees of spatial heterogeneity, including different immune and susceptible concentrations. A generalized concept of percolation is used as a measurement instrument, making possible the identification of an epidemic state, or phase, in a geographic feature. The results allow many concepts of Epidemiology to be taken into consideration (as mass immunity, epidemic process and state) through a wider point of view, involving explicitly the spatial dimensions. Some numeric results include: (i)- the determination of the duration of the epidemic process as a function of the initial spatial distribution of infected individuals (ii)- the effect of the "topological shield" in the reduction of the epidemic spread.