The main theories of biodiversity either neglect species interactions or assume that species interact randomly with each other. However, recent empirical work has revealed that ecological networks are highly structured, and the lack of a theory that takes into account the structure of interactions precludes further assessment of the implications of such network patterns for biodiversity. Here we use a combination of analytical and empirical approaches to quantify the influence of network architecture on the number of coexisting species. As a case study we consider mutualistic networks between plants and their animal pollinators or seed dispersers. These networks have been found to be highly nested, with the more specialist species interacting only with proper subsets of the species that interact with the more generalist. We show that nestedness reduces effective interspecific competition and enhances the number of coexisting species. Furthermore, we show that a nested network will naturally emerge if new species are more likely to enter the community where they have minimal competitive load. Nested networks seem to occur in many biological and social contexts, suggesting that our results are relevant in a wide range of fields.

We have sequenced the genome of the intracellular symbiont Buchnera aphidicola from the aphid Baizongia pistacea. This strain diverged 80 -150 million years ago from the common ancestor of two previously sequenced Buchnera strains. Here, a field-collected, nonclonal sample of insects was used as source material for laboratory procedures. As a consequence, the genome assembly unveiled intrapopulational variation, consisting of Ϸ1,200 polymorphic sites. Comparison of the 618-kb (kbp) genome with the two other Buchnera genomes revealed a nearly perfect gene-order conservation, indicating that the onset of genomic stasis coincided closely with establishment of the symbiosis with aphids, Ϸ200 million years ago. Extensive genome reduction also predates the synchronous diversification of Buchnera and its host; but, at a slower rate, gene loss continues among the extant lineages. A computational study of protein folding predicts that proteins in Buchnera, as well as proteins of other intracellular bacteria, are generally characterized by smaller folding efficiency compared with proteins of free living bacteria. These and other degenerative genomic features are discussed in light of compensatory processes and theoretical predictions on the long-term evolutionary fate of symbionts like Buchnera.

Chromatin is of major relevance for gene expression, cell division, and differentiation. Here, we determined the landscape of Arabidopsis thaliana chromatin states using 16 features, including DNA sequence, CG methylation, histone variants, and modifications. The combinatorial complexity of chromatin can be reduced to nine states that describe chromatin with high resolution and robustness. Each chromatin state has a strong propensity to associate with a subset of other states defining a discrete number of chromatin motifs. These topographical relationships revealed that an intergenic state, characterized by H3K27me3 and slightly enriched in activation marks, physically separates the canonical Polycomb chromatin and two heterochromatin states from the rest of the euchromatin domains. Genomic elements are distinguished by specific chromatin states: four states span genes from transcriptional start sites (TSS) to termination sites and two contain regulatory regions upstream of TSS. Polycomb regions and the rest of the euchromatin can be connected by two major chromatin paths. Sequential chromatin immunoprecipitation experiments demonstrated the occurrence of H3K27me3 and H3K4me3 in the same chromatin fiber, within a two to three nucleosome size range. Our data provide insight into the Arabidopsis genome topography and the establishment of gene expression patterns, specification of DNA replication origins, and definition of chromatin domains.

We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.

The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.

We study numerically a lattice model of semiflexible homopolymers with nearest neighbor attraction and energetic preference for straight joints between bonded monomers. For this we use a new Monte Carlo algorithm, the 'Pruned-Enriched Rosenbluth Method' (PERM). It is very efficient both for relatively open configurations at high temperatures, and for compact and frozen-in low-T states. This allows us to study in detail the phase diagram as a function of nn attraction ǫ and stiffness x. It shows a θ-collapse line with a transition from open coils (small ǫ) to molten compact globules (large ǫ), and a freezing transition toward a state with orientational global order (large stiffness x). Qualitatively this is similar to a recently studied mean field theory (S. Doniach, T. Garel and H. Orland (1996), J. Chem. Phys. 105 (4), 1601), but there are important differences in details. In contrast to the mean field theory and to naive expectations, the θ-temperature increases with stiffness x. The freezing temperature increases even faster, and reaches the θ-line at a finite value of x. For even stiffer chains, the freezing transition takes place directly, without the formation of an intermediate globular state. Although being in conflict with mean field theory, the latter had been conjectured already by Doniach et al. on the basis of heuristic arguments and of low statistics Monte Carlo simulations.Finally, we discuss the relevance of the present model as a very crude model for protein folding.

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 introduce the torsional network model (TNM), an elastic network model whose degrees of freedom are the torsion angles of the protein backbone. Normal modes of the TNM displace backbone atoms including C maintaining their covalent geometry. For many proteins, low frequency TNM modes are localized in torsion space yet collective in Cartesian space, reminiscent of hinge motions. A smaller number of TNM modes than anisotropic network model modes are enough to represent experimentally observed conformation changes. We observed significant correlation between the contribution of each normal mode to equilibrium fluctuations and to conformation changes, and defined the excess correlation with respect to a simple neutral model. The stronger this excess correlation, the lower the predicted free energy barrier of the conformation change and the fewer modes contribute to the change. DOI: 10.1103/PhysRevLett.104.228103 PACS numbers: 87.14.et Protein flexibility is essential for function, allowing structural rearrangements to propagate in allosteric regulation [1], and it is believed to play an important role in protein structure evolution [2]. A proper description of flexibility would be highly desirable both for improving computational drug design through flexible protein-ligand docking [3] and for refining homology models of protein structures [4]. Nevertheless, this is a very challenging task because of the very long time scales involved in functional motions and the lack of a computationally manageable, yet detailed enough statistical mechanical model of proteins. In this context, normal mode analysis [5] (NMA) provides a simple analytical description of the thermal dynamics of proteins in their native state. Normal modes calculations require an effective free energy function and a native structure that is placed at a local minimum of this energy function. However, energy minimization through the effective energy functions adopted in molecular dynamics can drive the native structure several Å away from the experimental one. An alternative approach, proposed by Tirion [6] and followed by several authors [7][8][9][10], consists in adopting as a starting point the experimentally known native structure and designing an effective free energy function that places such a structure at the absolute minimum. Such an approach, called the elastic network model (ENM), is analogous to GO models, which describe the statistical mechanics of protein folding using as only input the experimentally known native structure. Despite their simplicity, GO models are sometimes superior to more realistic but more complicated models in predicting protein folding kinetics [11]. Similarly, low frequency ENM normal modes, describing collective fluctuations in the native state, have highly significant overlap with experimentally observed conformation changes [12][13][14][15] and with evolutionary deformations of protein structures [16]. The success of ENMs indicates that a lot of information about protein flexibility is contained in the topology...