The GFNL has worked in two main subjects: reaction-diffusion systems with symmetries and chaos in dissipative systems like Josephson junctions. Lately, its main research interest is the study of breathers, localised nonlinear oscillations in discrete lattices, which appear in an incredible variety of systems, both Hamiltonian, like crystals, and dissipative, like Josephson junction arrays.
The GFNL is an associate node of a Research Training Network, Localisation by Nonlinearity, and Energy Transfer, in Crystals, Biomolecules and Josephson Arrays (LOCNET). The leader of the Network is Prof. Robert Mackay at the University of Warwick, UK, and the Spanish main node is the Department of Theory and Simulation of Complex Systems at the University of Zaragoza, Spain. The LOCNET is a four years project of intense research in the subject, split in fifteen different tasks, being the Sevilla node, involved in some of them: breathers in disordered systems, breathers in Josephson junction arrays, breathers in biomolecules and breather mobility. One of the GFNL members is leader of the task 6, Disorder and Nonlinearity, with special application to DNA.
An important application of breathers in disordered systems and biomolecules is the description of the phenomena occurring in DNA. By means of studying different nonlinear models describing DNA dynamics, we aim to contribute, using both analytical and numerical methods, to decipher the mechanisms that determine the melting and the initiation of the transcription bubble, related with the phenomena of energy localization in DNA sequences.
The knowledge of the genome is of great importance and establishes the starting point to investigate the basic mechanisms that lead to its expression, but it is not enough. It is essential to understand the regulation of its expression, particularly how many times a certain gene is read and how fast is expressed.
Only very recently, simplified DNA dynamical models have been proposed in order to understand and explain biological processes such as the initiation of the transcription, the transcription itself and the melting. These models are necessarily nonlinear; their postulation, resolution and the interpretation of their solutions implies cooperation between the worlds of physics and biology. A primary aspect of the regulation is the initiation of the transcription, that is, the formation of the "transcription bubbles". A mechanism that has been proposed is the localization of energy in the DNA sequences, there are at least two possible origins: (i) the inhomogeneity of the DNA double strands, which constitute the genetic code. From the physical point of view they can be described as disordered systems. In these systems the localization of energy can take place, which is known as "Anderson localization"; (ii) the nonlinearity due to the nature of the interactions and the discreteness (discrete breathers). It is of fundamental importance to determine which of the two mechanisms is dominant, and under which circumstances, in nonlinear and inhomogeneous systems as those conformed by the DNA sequences. Do both mechanism cooperate in energy localization, or do they compete, and the simultaneous presence of nonlinearity and disorder limits the formation of localized excitations? The advances that may result from these studies, together with the experimental contributions made by other research groups, would determine the formulation of new dynamical models for the DNA sequence. It will improve both the predictability and knowledge of mechanisms inherent to basic processes of life.