Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches.

Redundancy in biology may be explained by the need to optimize extreme searching processes, where one or few among many particles are requested to reach the target like in human fertilization. We show that non-Gaussian rare fluctuations in Brownian diffusion dominates such searches, introducing drastic corrections to the known Gaussian behavior. Our demonstration entails different physical systems and pinpoints the relevance of diversity within redundancy to boost fast targeting. We sketch an experimental context to test our results: polydisperse systems.

Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures.

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.

Vibrational entropy estimation can improve binding affinity prediction for non-obligatory protein complexes.

Predicting the binding affinity between protein monomers is of paramount importance for the understanding of thermodynamical and structural factors that guide the formation of a complex. Several numerical techniques have been developed for the calculation of binding affinities with different levels of accuracy. Approaches such as thermodynamic integration and Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodologies which account for well defined physical interactions offer good accuracy but are computationally demanding. Methods based on the statistical analysis of experimental structures are much cheaper but good performances have only been obtained throughout consensus energy functions based on many different molecular descriptors. In this study we investigate the importance of the contribution to the binding free energy of the entropic term due to the fluctuations around the equilibrium structures. This term, which we estimated employing an elastic network model, is usually neglected in most statistical approaches. Our method crucially relies on a novel calibration procedure of the elastic network force constant. The residue mobility profile is fitted to the one obtained through a short all-atom molecular dynamics simulation on a subset of residues only. Our results show how the proper consideration of vibrational entropic contributions can improve the quality of the prediction on a set of non-obligatory protein complexes whose binding affinity is known.

PASTA 2.0: an improved server for protein aggregation prediction.

The formation of amyloid aggregates upon protein misfolding is related to several devastating degenerative diseases. The propensities of different protein sequences to aggregate into amyloids, how they are enhanced by pathogenic mutations, the presence of aggregation hot spots stabilizing pathological interactions, the establishing of cross-amyloid interactions between co-aggregating proteins, all rely at the molecular level on the stability of the amyloid cross-beta structure. Our redesigned server, PASTA 2.0, provides a versatile platform where all of these different features can be easily predicted on a genomic scale given input sequences. The server provides other pieces of information, such as intrinsic disorder and secondary structure predictions, that complement the aggregation data. The PASTA 2.0 energy function evaluates the stability of putative cross-beta pairings between different sequence stretches. It was re-derived on a larger dataset of globular protein domains. The resulting algorithm was benchmarked on comprehensive peptide and protein test sets, leading to improved, state-of-the-art results with more amyloid forming regions correctly detected at high specificity. The PASTA 2.0 server can be accessed at http://protein.bio.unipd.it/pasta2/.

Native fold and docking pose discrimination by the same residue-based scoring function.

Structure prediction and quality assessment are crucial steps in modeling native protein conformations. Statistical potentials are widely used in related algorithms, with different parametrizations typically developed for different contexts such as folding protein monomers or docking protein complexes. Here, we describe BACH-SixthSense, a single residue-based statistical potential that can be successfully employed in both contexts. BACH-SixthSense shares the same approach as BACH, a knowledge-based potential originally developed to score monomeric protein structures. A term that penalizes steric clashes as well as the distinction between polar and apolar sidechain-sidechain contacts are crucial novel features of BACH-SixthSense. The performance of BACH-SixthSense in discriminating correctly the native structure among a competing set of decoys is significantly higher than other state-of-the-art scoring functions, that were specifically trained for a single context, for both monomeric proteins (QMEAN, Rosetta, RF_CB_SRS_OD, benchmarked on CASP targets) and protein dimers (IRAD, Rosetta, PIE*PISA, HADDOCK, FireDock, benchmarked on 14 CAPRI targets). The performance of BACH-SixthSense in recognizing near-native docking poses within CAPRI decoy sets is good as well.

Being heterogeneous is disadvantageous: Brownian non-Gaussian searches.

Diffusing diffusivity models, polymers in the grand canonical ensemble and polydisperse, and continuous-time random walks all exhibit stages of non-Gaussian diffusion. Is non-Gaussian targeting more efficient than Gaussian? We address this question, central to, e.g., diffusion-limited reactions and some biological processes, through a general approach that makes use of Jensen's inequality and that encompasses all these systems. In terms of customary mean first-passage time, we show that Gaussian searches are more effective than non-Gaussian ones. A companion paper argues that non-Gaussianity becomes instead highly more efficient in applications where only a small fraction of tracers is required to reach the target.

Statistical potentials from the Gaussian scaling behaviour of chain fragments buried within protein globules.

Knowledge-based approaches use the statistics collected from protein data-bank structures to estimate effective interaction potentials between amino acid pairs. Empirical relations are typically employed that are based on the crucial choice of a reference state associated to the null interaction case. Despite their significant effectiveness, the physical interpretation of knowledge-based potentials has been repeatedly questioned, with no consensus on the choice of the reference state. Here we use the fact that the Flory theorem, originally derived for chains in a dense polymer melt, holds also for chain fragments within the core of globular proteins, if the average over buried fragments collected from different non-redundant native structures is considered. After verifying that the ensuing Gaussian statistics, a hallmark of effectively non-interacting polymer chains, holds for a wide range of fragment lengths, although with significant deviations at short spatial scales, we use it to define a 'bona fide' reference state. Notably, despite the latter does depend on fragment length, deviations from it do not. This allows to estimate an effective interaction potential which is not biased by the presence of correlations due to the connectivity of the protein chain. We show how different sequence-independent effective statistical potentials can be derived using this approach by coarse-graining the protein representation at varying levels. The possibility of defining sequence-dependent potentials is explored.

Nanoparticles and Radioisotopes: A Long Story in a Nutshell.

The purpose of this narrative review was to assess the use of nanoparticles (NPs) to deliver radionuclides to targets, focusing on systems that have been tested in pre-clinical and, when available, clinical settings. A literature search was conducted in PubMed and Web of Science databases using the following terms: "radionuclides" AND "liposomes" or "PLGA nanoparticles" or "gold nanoparticles" or "iron oxide nanoparticles" or "silica nanoparticles" or "micelles" or "dendrimers". No filters were applied, apart from a minimum limit of 10 patients enrolled for clinical studies. Data from some significant studies from pre-clinical and clinical settings were retrieved, and we briefly describe the information available. All the selected seven classes of nanoparticles were highly tested in clinical trials, but they all present many drawbacks. Liposomes are the only ones that have been tested for clinical applications, though they have never been commercialized. In conclusion, the application of NPs for imaging has been the object of much interest over the years, albeit mainly in pre-clinical settings. Thus, we think that, based on the current state, radiolabeled NPs must be investigated longer before finding their place in nuclear medicine.

Fibril elongation mechanisms of HET-s prion-forming domain: topological evidence for growth polarity.

The prion-forming C-terminal domain of the fungal prion HET-s forms infectious amyloid fibrils at physiological pH. The conformational switch from the nonprion soluble form to the prion fibrillar form is believed to have a functional role, as HET-s in its prion form participates in a recognition process of different fungal strains. On the basis of the knowledge of the high-resolution structure of the prion forming domain HET-s(218-289) in its fibrillar form, we here present a numerical simulation of the fibril growth process, which emphasizes the role of the topological properties of the fibrillar structure. An accurate thermodynamic analysis of the way an intervening HET-s chain is recruited to the tip of the growing fibril suggests that elongation proceeds through a dock and lock mechanism. First, the chain docks onto the fibril by forming the longest ß-strands. Then, the re-arrangement in the fibrillar form of all the rest of the molecule takes place. Interestingly, we also predict that one side of the HET-s fibril is more suitable for sustaining its growth with respect to the other. The resulting strong polarity of fibril growth is a consequence of the complex topology of HET-s fibrillar structure, as the central loop of the intervening chain plays a crucially different role in favoring or not the attachment of the C-terminus tail to the fibril, depending on the growth side.

Exploring the universe of protein structures beyond the Protein Data Bank.

It is currently believed that the atlas of existing protein structures is faithfully represented in the Protein Data Bank. However, whether this atlas covers the full universe of all possible protein structures is still a highly debated issue. By using a sophisticated numerical approach, we performed an exhaustive exploration of the conformational space of a 60 amino acid polypeptide chain described with an accurate all-atom interaction potential. We generated a database of around 30,000 compact folds with at least of secondary structure corresponding to local minima of the potential energy. This ensemble plausibly represents the universe of protein folds of similar length; indeed, all the known folds are represented in the set with good accuracy. However, we discover that the known folds form a rather small subset, which cannot be reproduced by choosing random structures in the database. Rather, natural and possible folds differ by the contact order, on average significantly smaller in the former. This suggests the presence of an evolutionary bias, possibly related to kinetic accessibility, towards structures with shorter loops between contacting residues. Beside their conceptual relevance, the new structures open a range of practical applications such as the development of accurate structure prediction strategies, the optimization of force fields, and the identification and design of novel folds.

Polymers critical point originates Brownian non-Gaussian diffusion.

We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents γ and ν-depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase-concur to determine the potential divergency of a dynamic response, epitomized by the center-of-mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.

Amyloidogenic potential of transthyretin variants: insights from structural and computational analyses.

Human transthyretin (TTR) is an amyloidogenic protein whose mild amyloidogenicity is enhanced by many point mutations affecting considerably the amyloid disease phenotype. To ascertain whether the high amyloidogenic potential of TTR variants may be explained on the basis of the conformational change hypothesis, an aim of this work was to determine structural alterations for five amyloidogenic TTR variants crystallized under native and/or destabilizing (moderately acidic pH) conditions. While at acidic pH structural changes may be more significant because of a higher local protein flexibility, only limited alterations, possibly representing early events associated with protein destabilization, are generally induced by mutations. This study was also aimed at establishing to what extent wild-type TTR and its amyloidogenic variants are intrinsically prone to beta-aggregation. We report the results of a computational analysis predicting that wild-type TTR possesses a very high intrinsic beta-aggregation propensity which is on average not enhanced by amyloidogenic mutations. However, when located in beta-strands, most of these mutations are predicted to destabilize the native beta-structure. The analysis also shows that rat and murine TTR have a lower intrinsic beta-aggregation propensity and a similar native beta-structure stability compared with human TTR. This result is consistent with the lack of in vitro amyloidogenicity found for both murine and rat TTR. Collectively, the results of this study support the notion that the high amyloidogenic potential of human pathogenic TTR variants is determined by the destabilization of their native structures, rather than by a higher intrinsic beta-aggregation propensity.

REPETITA: detection and discrimination of the periodicity of protein solenoid repeats by discrete Fourier transform.

MOTIVATION: Proteins with solenoid repeats evolve more quickly than non-repetitive ones and their periodicity may be rapidly hidden at sequence level, while still evident in structure. In order to identify these repeats, we propose here a novel method based on a metric characterizing amino-acid properties (polarity, secondary structure, molecular volume, codon diversity, electric charge) using five previously derived numerical functions. RESULTS: The five spectra of the candidate sequences coding for structural repeats, obtained by Discrete Fourier Transform (DFT), show common features allowing determination of repeat periodicity with excellent results. Moreover it is possible to introduce a phase space parameterized by two quantities related to the Fourier spectra which allow for a clear distinction between a non-homologous set of globular proteins and proteins with solenoid repeats. The DFT method is shown to be competitive with other state of the art methods in the detection of solenoid structures, while improving its performance especially in the identification of periodicities, since it is able to recognize the actual repeat length in most cases. Moreover it highlights the relevance of local structural propensities in determining solenoid repeats. AVAILABILITY: A web tool implementing the algorithm presented in the article (REPETITA) is available with additional details on the data sets at the URL: http://protein.bio.unipd.it/repetita/.

Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding.

Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence of specific patterns adopted by protein sequences and structures to deal with backbone self-entanglement. A large scale analysis of the Protein Data Bank shows that loops significantly intertwined with another chain portion are typically closed by weakly bound amino acids. Why is this energetic frustration maintained? A possible picture is that entangled loops are formed only toward the end of the folding process to avoid kinetic traps. Consistently, these loops are more frequently found to be wrapped around a portion of the chain on their N-terminal side, the one translated earlier at the ribosome. Finally, these motifs are less abundant in natural native states than in simulated protein-like structures, yet they appear in 32% of proteins, which in some cases display an amazingly complex intertwining.

Inference of the solvation energy parameters of amino acids using maximum entropy approach.

We present a novel technique, based on the principle of maximum entropy, for deriving the solvation energy parameters of amino acids from the knowledge of the solvent accessible areas in experimentally determined native state structures as well as high quality decoys of proteins. We present the results of detailed studies and analyze the correlations of the solvation energy parameters with the standard hydrophobic scale. We study the ability of the inferred parameters to discriminate between the native state structures of proteins and their decoy conformations.

Signature of Pareto optimization in the Escherichia coli proteome.

Proteins have coevolved with cellular environments to improve or preserve their functions, maintaining at the same time the degree of hydrophobicity necessary to fold correctly and enough solubility to perform their biological roles. Here, we study the Escherichia coli proteome using a Pareto front analysis in the solubility-hydrophobicity space. The results indicate the existence of a Pareto optimal front, a triangle whose vertices correspond to archetypal proteins specialized in distinct tasks, such as regulatory processes, membrane transport, outer-membrane pore formation, catalysis, and binding. The vertices are further enriched with proteins that occupy different subcellular compartments, namely, cytoplasmic, inner membrane, outer membrane, and outer membrane bounded periplasmic space. The combination of various enriching features offers an interpretation of how bacteria use the physico-chemical properties of proteins, both to drive them into their final destination in the cell and to have their tasks accomplished.

The PASTA server for protein aggregation prediction.

Many different proteins aggregate into amyloid fibrils characterized by cross-beta structure. beta-strands contributed by distinct protein molecules are generally found in a parallel in-register alignment. Here, we describe the web server for a novel algorithm, prediction of amyloid structure aggregation (PASTA), to predict the most aggregation-prone portions and the corresponding beta-strand inter-molecular pairing for a given input sequence. PASTA was previously shown to yield results in excellent agreement with available experimental observations, when tested on both natively unfolded and structured proteins. The web server and downloadable source code are freely accessible from the URL: http://protein.cribi.unipd.it/pasta/.

Insight into the structure of amyloid fibrils from the analysis of globular proteins.

The conversion from soluble states into cross-beta fibrillar aggregates is a property shared by many different proteins and peptides and was hence conjectured to be a generic feature of polypeptide chains. Increasing evidence is now accumulating that such fibrillar assemblies are generally characterized by a parallel in-register alignment of beta-strands contributed by distinct protein molecules. Here we assume a universal mechanism is responsible for beta-structure formation and deduce sequence-specific interaction energies between pairs of protein fragments from a statistical analysis of the native folds of globular proteins. The derived fragment-fragment interaction was implemented within a novel algorithm, prediction of amyloid structure aggregation (PASTA), to investigate the role of sequence heterogeneity in driving specific aggregation into ordered self-propagating cross-beta structures. The algorithm predicts that the parallel in-register arrangement of sequence portions that participate in the fibril cross-beta core is favoured in most cases. However, the antiparallel arrangement is correctly discriminated when present in fibrils formed by short peptides. The predictions of the most aggregation-prone portions of initially unfolded polypeptide chains are also in excellent agreement with available experimental observations. These results corroborate the recent hypothesis that the amyloid structure is stabilised by the same physicochemical determinants as those operating in folded proteins. They also suggest that side chain-side chain interaction across neighbouring beta-strands is a key determinant of amyloid fibril formation and of their self-propagating ability.

Bacterial bioluminescence onset and quenching: a dynamical model for a quorum sensing-mediated property.

We present an effective dynamical model for the onset of bacterial bioluminescence, one of the most studied quorum sensing-mediated traits. Our model is built upon simple equations that describe the growth of the bacterial colony, the production and accumulation of autoinducer signal molecules, their sensing within bacterial cells, and the ensuing quorum activation mechanism that triggers bioluminescent emission. The model is directly tested to quantitatively reproduce the experimental distributions of photon emission times, previously measured for bacterial colonies of Vibrio jasicida, a luminescent bacterium belonging to the Harveyi clade, growing in a highly drying environment. A distinctive and novel feature of the proposed model is bioluminescence 'quenching' after a given time elapsed from activation. Using an advanced fitting procedure based on the simulated annealing algorithm, we are able to infer from the experimental observations the biochemical parameters used in the model. Such parameters are in good agreement with the literature data. As a further result, we find that, at least in our experimental conditions, light emission in bioluminescent bacteria appears to originate from a subtle balance between colony growth and quorum activation due to autoinducers diffusion, with the two phenomena occurring on the same time scale. This finding is consistent with a negative feedback mechanism previously reported for Vibrio harveyi.