We study the temporal correlations in the atmospheric variability by 14 meteorological stations around the globe, the variations of the daily maximum temperatures from their average values. We apply several methods that can systematically overcome possible nonstationarities in the data. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, approximately decays C͑s͒ ϳ s 2g , with roughly the same exponent g Х 0.7 for all stations considered. The range of this universal persistence law seems to exceed one decade, and is possibly even larger than the range of the temperature series considered. [S0031-9007(98)06602-2]

With the aim to study the relationship between protein sequences and their native structures, we adopt vectorial representations for both sequence and structure. The structural representation is based on the Principal Eigenvector of the fold's contact matrix (PE). As recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence is represented through a Hydrophobicity Profile (HP), using a generalized hydrophobicity scale that we obtain from the principal eigenvector of a residue-residue interaction matrix and denote it as interactivity scale. Using this novel scale, we define the optimal HP of a protein fold, and predict, by means of stability arguments, that it is strongly correlated with the PE of the fold's contact matrix. This prediction is confirmed through an evolutionary analysis, which shows that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N -dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call Vectorial Protein Space. In this way, we define a unified framework for sequence to sequence, sequence to structure, and structure to structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences with sequences and sequences with structures.

We study the impact of mutations (changes in amino acid sequence) on the thermodynamics of simple protein-like heteropolymers consisting of N monomers, representing the amino acid sequence. The sequence is designed to fold into its native conformation on a cubic lattice. It is found that quite a large fraction, between one half and one third of the substitutions, which we call 'cold errors', make important contributions to the dynamics of the folding process, increasing folding times typically by a factor of two, the altered chain still folding into the native structure. Few mutations ('hot errors'), have quite dramatic effects, leading to protein misfolding. Our analysis reveals that mutations affect primarily the energetics of the native conformation and to a much lesser extent the ensemble of unfolded conformations, corroborating the utility of the "energy gap" concept for the analysis of folding properties of protein-like heteropolymers.

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We stimulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves (1) the structure of the ground state, (2) its thermodynamic stability and (3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space-sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than 1). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with the biological data.

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The electromagnetic response of the fullerene C60 in the energy range 0