A new mechanism leading to scale-free networks is proposed in this Letter. It is shown that, in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Assigning a quenched fitness value x i to every vertex, and drawing links among vertices with a probability depending on the fitnesses of the two involved sites, gives rise to what we call a good-get-richer mechanism, in which sites with larger fitness are more likely to become hubs (i.e., to be highly connected).

The aggregation of proteins is central to many aspects of daily life, including food processing, blood coagulation, eye cataract formation disease and prion-related neurodegenerative infections [1][2][3][4][5] . However, the physical mechanisms responsible for amyloidosis-the irreversible fibril formation of various proteins that is linked to disorders such as Alzheimer's, Creutzfeldt-Jakob and Huntington's diseases-have not yet been fully elucidated [6][7][8][9] . Here, we show that different stages of amyloid aggregation can be examined by performing a statistical polymer physics analysis of single-molecule atomic force microscopy images of heat-denatured b-lactoglobulin fibrils. The atomic force microscopy analysis, supported by theoretical arguments, reveals that the fibrils have a multistranded helical shape with twisted ribbon-like structures. Our results also indicate a possible general model for amyloid fibril assembly and illustrate the potential of this approach for investigating fibrillar systems.Protein self-assembly is a wide-ranging phenomenon and is of great importance in several areas of science. The reversible formation of fibrils from globular proteins is a phenomenon occurring naturally, in vivo, for proteins such as actin and tubulin 10,11 . Other well-known examples of protein fibrillation include the irreversible amyloid fibril formation of various proteins implicated in neurological disorders such as Alzheimer's, Creutzfeldt-Jakob or Huntington's diseases. Typically, these fibrils have long, unbranched, and often twisted structures that are a few nanometres in diameter 1,8 . However, many peptides and proteins, including many globular food proteins that are used as gelling agents, foaming agents or emulsifiers, can also form amyloid-like structures in vitro. Such structures can possess desirable mechanical properties and can be used to create useful textures and structures 12,13 .An example of a fibril formation of globular proteins is provided by the fine-stranded heat-set gels formed by heating solutions of various globular food proteins such as ovalbumin, bovine serum albumin 12 and b-lactoglobulin 13 . b-Lactoglobulin has been particularly well studied, because it represents both a relevant model system and a major whey protein of interest to the food industry [14][15][16][17][18][19][20][21][22] .Despite the fact that the individual parameters controlling the aggregation of globular proteins into amyloid fibrils have been well identified, the driving force for such an aggregation process still remains obscure. Studies devoted to the characterization of fibril structures based on light, neutrons and X-ray scattering methods, being bulk techniques, have only provided an average ensemble picture of the fibrils 23 . Single-molecule techniques such as atomic force microscopy (AFM) and transmission electron microscopy (TEM) have recently emerged to probe amyloid fibrils at the molecular level [24][25][26][27] . Nevertheless, so far, a fully comprehensive picture of the aggregation behaviour...

ParABS systems facilitate chromosome segregation and plasmid partitioning in bacteria and archaea. ParB protein binds centromeric parS DNA sequences and spreads to flanking DNA. We show that ParB is an enzyme that hydrolyzes cytidine triphosphate (CTP) to cytidine diphosphate (CDP). parS DNA stimulates cooperative CTP binding by ParB and CTP hydrolysis. A nucleotide cocrystal structure elucidates the catalytic center of the dimerization-dependent ParB CTPase. Single-molecule imaging and biochemical assays recapitulate features of ParB spreading from parS in the presence but not absence of CTP. These findings suggest that centromeres assemble by self-loading of ParB DNA sliding clamps at parS. ParB CTPase is not related to known nucleotide hydrolases and might be a promising target for developing new classes of antibiotics.

Hsp70-Hsp40-NEF and possibly Hsp100 are the only known molecular chaperones that can use the energy of ATP to convert stably pre-aggregated polypeptides into natively refolded proteins. However, the kinetic parameters and ATP costs have remained elusive because refolding reactions have only been successful with a molar excess of chaperones over their polypeptide substrates. Here we describe a stable, misfolded luciferase species that can be efficiently renatured by substoichiometric amounts of bacterial Hsp70-Hsp40-NEF. The reactivation rates increased with substrate concentration and followed saturation kinetics, thus allowing the determination of apparent V(max)' and K(m)' values for a chaperone-mediated renaturation reaction for the first time. Under the in vitro conditions used, one Hsp70 molecule consumed five ATPs to effectively unfold a single misfolded protein into an intermediate that, upon chaperone dissociation, spontaneously refolded to the native state, a process with an ATP cost a thousand times lower than expected for protein degradation and resynthesis.

The kinetics of biomolecular isomerization processes, such as protein folding, is governed by a free-energy surface of high dimensionality and complexity. As an alternative to projections into one or two dimensions, the free-energy surface can be mapped into a weighted network where nodes and links are configurations and direct transitions among them, respectively. In this work, the free-energy basins and barriers of the alanine dipeptide are determined quantitatively using an algorithm to partition the network into clusters (i.e., states) according to the equilibrium transitions sampled by molecular dynamics. The network-based approach allows for the analysis of the thermodynamics and kinetics of biomolecule isomerization without reliance on arbitrarily chosen order parameters. Moreover, it is shown on low-dimensional models, which can be treated analytically, as well as for the alanine dipeptide, that the broad-tailed weight distribution observed in their networks originates from freeenergy basins with mainly enthalpic character. Energy landscape theory provides a framework for the description of the thermodynamics and kinetics of complex systems. Since the publication of the seminal ideas almost 40 years ago (1), the energy landscape paradigm has been successfully applied to the study of a broad range of systems (2, 3). The potential energy function of a multibody system such as a protein is a multidimensional and often very complex surface. At nonzero temperature, entropic contributions become relevant, and therefore the free-energy landscape governs the thermodynamics and kinetics. A common way to investigate and display the free energy involved in biomolecular isomerization and protein folding is to study it as a function of one or more order parameters, i.e., suitably chosen macroscopic quantities that distinguish the different states of the system (4). States are associated with local free-energy minima of the projected landscape. The depth of the minima is considered proportional to the stability of the states associated to them, and the barriers between different minima indicate activation energies between states. Due to the complexity of the process and the large number of degrees of freedom involved, order parameters are often arbitrarily chosen. Moreover, using free-energy projections for the study of the kinetics requires knowledge of a good reaction coordinate for the isomerization process, which is a difficult and unsolved problem (5-11). For this reason, new approaches based on graph theory have been explored for the analysis of free-energy landscapes. Recently, Krivov and Karplus introduced a method based on the disconnectivity graphs (DGs) for analyzing the unprojected free-energy surface of short peptides using an equilibrium molecular dynamics (MD) trajectory (12). They have developed the free-energy DG approach by exploiting an isomorphism between the total rate between two free-energy minima (considering all possible pathways) and the maximum flow through a network with capacitated edges, ...

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The enthalpically favoured hydration of hydrophobic entities, termed hydrophobic hydration, impacts the phase behaviour of numerous amphiphiles in water. Here, we show experimental evidence that hydrophobic hydration is strongly determined by the mean energetics of the aqueous medium. We investigate the aggregation and collapse of an amphiphilic polymer, poly-N-isopropyl acrylamide (PNiPAM), in aqueous solutions containing small amounts of alcohol and find that the thermodynamic characteristics defining the phase transitions of PNiPAM evolve relative to the solvent composition at which the excess mixing enthalpy of the water/alcohol mixtures becomes minimal. Such correlation between solvent energetics and solution thermodynamics extends to other mixtures containing neutral organic solutes that are considered as kosmotropes to induce a strengthening of the hydrogen bonded water network. This denotes the energetics of water as a key parameter controlling the phase behaviour of PNiPAM and identifies the excess mixing enthalpy of water/kosmotrope mixtures as a gauge of the kosmotropic effect on hydrophobic assemblies.

Hsp70s are highly conserved ATPase molecular chaperones mediating the correct folding of de novo synthesized proteins, the translocation of proteins across membranes, the disassembly of some native protein oligomers, and the active unfolding and disassembly of stress-induced protein aggregates. Here, we bring thermodynamic arguments and biochemical evidences for a unifying mechanism named entropic pulling, based on entropy loss due to excluded-volume effects, by which Hsp70 molecules can convert the energy of ATP hydrolysis into a force capable of accelerating the local unfolding of various protein substrates and, thus, perform disparate cellular functions. By means of entropic pulling, individual Hsp70 molecules can accelerate unfolding and pulling of translocating polypeptides into mitochondria in the absence of a molecular fulcrum, thus settling former contradictions between the power-stroke and the Brownian ratchet models for Hsp70-mediated protein translocation across membranes. Moreover, in a very different context devoid of membrane and components of the import pore, the same physical principles apply to the forceful unfolding, solubilization, and assisted native refolding of stable protein aggregates by individual Hsp70 molecules, thus providing a mechanism for Hsp70-mediated protein disaggregation.H sp70 is a central component of the chaperone network in the cell with disparate cellular functions. Associated with the ribosome, Hsp70s foster proper de novo protein folding. In the cytoplasm, Hsp70s mediate the deoligomerization and recycling of native protein complexes (1, 2) and control key functions in evolution, cell morphogenesis (2), and apoptosis (3), often in association with Hsp90 (4). Hsp70 also serves as the central translocation motor in the posttranslational import of cytoplasmic proteins into mitochondria (5), chloroplasts (6, 7), and the endoplasmic reticulum (8). Moreover, Hsp70s can actively unfold, solubilize, and reactivate already formed, stable protein aggregates (9, 10) and may participate in targeting proteins to the degradation pathway (11, 12). Existing Models for Hsp70-Mediated Protein Translocation into MitochondriaThe translocation of proteins across the mitochondrial membrane, through the translocase of the outer membrane (TOM) and translocase of the inner membrane (TIM) translocation pores, is mediated by the presequence translocase-associated motor (PAM) complex consisting of matrix-localized Hsp70 (mtHsp70), membrane-associated J domain-containing proteins (three identified so far, PAM16͞Tim16, PAM18͞Tim14, and Mdj2) (13-19) and the nucleotide exchange factor Mge1. In the ATP-bound state, mtHsp70 is in the open (unlocked) state, which is as yet unbound to the translocating protein substrate, whereas mtHsp70 is found anchored to the mitochondrial import channel by way of its transient association with the mitochondrial peripheral inner-membrane protein Tim44. In the ADP-bound state, mtHsp70 is tightly bound (locked) onto the incoming polypeptide and is not associated to the m...