Search results for: Chaotic folding

Authors: Paola Lecca, Lorenzo Dematte

Abstract:

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.

Keywords: Reaction-diffusion systems, Fick's law, stochastic simulation algorithm.

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Authors: J.Partanen

Abstract:

Complexity, as a theoretical background has made it easier to understand and explain the features and dynamic behavior of various complex systems. As the common theoretical background has confirmed, borrowing the terminology for design from the natural sciences has helped to control and understand urban complexity. Phenomena like self-organization, evolution and adaptation are appropriate to describe the formerly inaccessible characteristics of the complex environment in unpredictable bottomup systems. Increased computing capacity has been a key element in capturing the chaotic nature of these systems. A paradigm shift in urban planning and architectural design has forced us to give up the illusion of total control in urban environment, and consequently to seek for novel methods for steering the development. New methods using dynamic modeling have offered a real option for more thorough understanding of complexity and urban processes. At best new approaches may renew the design processes so that we get a better grip on the complex world via more flexible processes, support urban environmental diversity and respond to our needs beyond basic welfare by liberating ourselves from the standardized minimalism. A complex system and its features are as such beyond human ethics. Self-organization or evolution is either good or bad. Their mechanisms are by nature devoid of reason. They are common in urban dynamics in both natural processes and gas. They are features of a complex system, and they cannot be prevented. Yet their dynamics can be studied and supported. The paradigm of complexity and new design approaches has been criticized for a lack of humanity and morality, but the ethical implications of scientific or computational design processes have not been much discussed. It is important to distinguish the (unexciting) ethics of the theory and tools from the ethics of computer aided processes based on ethical decisions. Urban planning and architecture cannot be based on the survival of the fittest; however, the natural dynamics of the system cannot be impeded on grounds of being “non-human". In this paper the ethical challenges of using the dynamic models are contemplated in light of a few examples of new architecture and dynamic urban models and literature. It is suggested that ethical challenges in computational design processes could be reframed under the concepts of responsibility and transparency.

Keywords: urban planning, architecture, dynamic modeling, ethics, complexity theory.

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