Large-scale experiments and integration of published data (1) have provided maps of several biological networks such as metabolic networks (2, 3), protein-protein (4, 5) and protein-DNA interactions (6, 7), etc. Although incomplete and, perhaps, inaccurate (8-11), these maps became a focal point of a search for the general principles that govern the organization of molecular networks (12-16). Important statistical characteristics of such networks include power-law distribution (P(k) ϳ k Ϫ␥ ) (e.g., refs. 16 and 17) or a similar distribution of the node degree k (i.e., the number of edges of a node); the small-world property (11, 13, 16) (i.e., a high clustering coefficient and a small shortest path between every pair of nodes); anticorrelation in the node degree of connected nodes (15) (i.e., highly interacting nodes tend to be connected to low-interacting ones); and other properties.These properties become evident when hundreds or thousands of molecules and their interactions are studied together. Recently discovered motifs (7, 18) that consist of three to four nodes constitute the other end of the spectrum. Large-scale characteristics are usually attributed to massive evolutionary processes that shape the network (6, 14), whereas many small-scale motifs represent feedback and feed-forward loops in cellular regulation (18,19). However, most important biological processes such as signal transduction, cell-fate regulation, transcription, and translation involve more than four but much fewer than hundreds of proteins. Most relevant processes in biological networks correspond to the mesoscale (5-25 genes͞proteins). Meso-scale properties of biological networks have been mostly elusive because of computational difficulties in enumerating midsize subnetworks (e.g., a network of 1,000 nodes contains 1 ϫ 10 23 possible 10-node sets).Here, we present an in-depth exploration of molecular networks on the meso-scale level. We focused on multibody interactions and searched for sets of proteins having many more interactions among themselves than with the rest of the network (clusters). We have developed several algorithms to find such clusters in an arbitrary network. We analyzed a yeast network of protein-protein interactions (20) and found Ͼ50 known and previously uncharacterized protein clusters. We analyzed functional annotation of these clusters and found that most of identified clusters correspond to either of the two types of cellular modules: protein complexes or functional modules (see Discussion). Protein complexes are groups of proteins that interact with each other at the same time and place, forming a single multimolecular machine. Examples of identified protein complexes include several large transcription factor complexes, the anaphase-promoting complex, RNA splicing and polyadenylation machinery, protein export and transport complexes, etc. Functional modules, in contrast, consist of proteins that participate in a particular cellular process while binding each other at a different time and place (different con...

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zerotemperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe "defect". In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically "blinking" metastable states.PACS Numbers: 64.60.My, 05.50.+q, 75.40.Gb What happens when an Ising ferromagnet, with spins endowed with Glauber dynamics [1], is suddenly cooled from high temperature to zero temperature (T = 0)? A first expectation is that the system should coarsen [2] and eventually reach the ground state. However, even the simple Ising ferromagnet admits a large number of metastable states with respect to Glauber spin-flip dynamics. Therefore at zero temperature the system could get stuck forever in one of these states.In this Letter, we present evidence that the behavior of such a kinetic Ising model is richer than either of these scenarios. While the ground state is always reached in one dimension, there appears to be a non-zero probability that the square lattice system freezes into a "stripe" phase, at least for equal initial concentrations of ↑ and ↓ spins [3]. The relaxation is governed by two distinct time scales, the larger of which stems from a long-lived diagonal stripe "defect". On hypercubic lattices (d ≥ 3), the probability to reach the ground state vanishes in the thermodynamic limit and the system ends up wandering forever on an iso-energy subset of connected metastable states. Again, the relaxation seems to be characterized by at least two time scales. It bears emphasizing that these long-time anomalies require that the limit T → 0 is taken before the thermodynamic limitWe can easily appreciate the peculiarities of zerotemperature dynamics for odd-coordinated lattices, such as the honeycomb lattice. Here any connected cluster in which each spin has at least 2 aligned neighbors is energetically stable in a sea of opposite spins. For any initial state, a sufficiently large system will have many such stable defects. Because the number of such metastable states generally scales exponentially with the total number of spins N , the system necessarily freezes into one of these states. However, on even-coordinated lattices the number of metastable states grows as a slower, stretched exponential function of N , and they affect the asymptotic relaxation in much more subtle way.We therefore study the homogeneous Ising model, with Hamiltonian H = −J ij σ i σ j , where σ i = ±1 and the sum is over all nearest-neighbor pairs of sites ij . We assume initially uncorrelated spins, with σ j (t = 0) = ±1 equiprobably, which evolve by zero-temperature Glauber dynamics [1]...

We investigate the final state of zero-temperature Ising ferromagnets which are endowed with single-spin flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the system either reaches a frozen stripe state with probability ≈ 1/3 or the ground state with probability ≈ 2/3. In greater than two dimensions, the probability to reach the ground state or a frozen state rapidly vanishes as the system size increases and the system wanders forever in an iso-energy set of metastable states. An external magnetic field changes the situation drastically -in two dimensions the favorable ground state is always reached, while in three dimensions the field must exceed a threshold value to reach the ground state. For small but non-zero temperature, relaxation to the final state first proceeds by the formation of very long-lived metastable states, similar to the zero-temperature case, before equilibrium is reached.

Homology-driven proteomics is a major tool to characterize proteomes of organisms with unsequenced genomes. This paper addresses practical aspects of automated homology-driven protein identifications by LC-MS/MS on a hybrid LTQ Orbitrap mass spectrometer. All essential software elements supporting the presented pipeline are either hosted at the publicly accessible web server, or are available for free download.