Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

The coupling between electron transfer and Protein/Solvent Dynamics in Photosynthetic Reaction Centers: Spectroscopic Studies in Amorphous Matrices

We investigated at the molecular level protein/solvent interactions and their relevance in protein function through the use of amorphous matrices at room temperature. As a model protein, we used the bacterial photosynthetic reaction center (RC) of Rhodobacter sphaeroides, a pigment protein complex which catalyzes the light-induced charge separation initiating the conversion of solar into chemical energy. The thermal fluctuations of the RC and its dielectric conformational relaxation following photoexcitation have been probed by analyzing the recombination kinetics of the primary charge-separated (P+QA-) state, using time resolved optical and EPR spectroscopies. We have shown that the RC dynamics coupled to this electron transfer process can be progressively inhibited at room temperature by decreasing the water content of RC films or of RC-trehalose glassy matrices. Extensive dehydration of the amorphous matrices inhibits RC relaxation and interconversion among conformational substates to an extent comparable to that attained at cryogenic temperatures in water-glycerol samples. An isopiestic method has been developed to finely tune the hydration level of the system. We have combined FTIR spectral analysis of the combination and association bands of residual water with differential light-minus-dark FTIR and high-field EPR spectroscopy to gain information on thermodynamics of water sorption, and on structure/dynamics of the residual water molecules, of protein residues and of RC cofactors. The following main conclusions were reached: (i) the RC dynamics is slaved to that of the hydration shell; (ii) in dehydrated trehalose glasses inhibition of protein dynamics is most likely mediated by residual water molecules simultaneously bound to protein residues and sugar molecules at the protein-matrix interface; (iii) the local environment of cofactors is not involved in the conformational dynamics which stabilizes the P+QA-; (iv) this conformational relaxation appears to be rather delocalized over several aminoacidic residues as well as water molecules weakly hydrogen-bonded to the RC.