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Sperm length is highly variable across species and many questions about its variation remain open. Although variation in body mass may affect sperm length evolution through its influence on multiple factors, the extent to which sperm length variation is linked to body mass remains elusive. Here, we use the Pareto multi-task evolution framework to investigate the relationship between sperm length and body mass across tetrapods. We find that tetrapods occupy a triangular Pareto front, indicating that trade-offs shape the evolution of sperm length in relation to body mass. By exploring the factors predicted to influence sperm length evolution, we find that sperm length evolution is mainly driven by sperm competition and clutch size, rather than by genome size. Moreover, the triangular Pareto front is maintained within endotherms, internal fertilizers, mammals and birds, suggesting similar evolutionary trade-offs within tetrapods. Finally, we demonstrate that the Pareto front is robust to phylogenetic dependencies and finite sampling bias. Our findings provide insights into the evolutionary mechanisms driving interspecific sperm length variation and highlight the importance of considering multiple trade-offs in optimizing reproductive traits.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Bacterial communities undergo collective behavioural switches upon producing and sensing diffusible signal molecules; a mechanism referred to as Quorum Sensing (QS). Exemplarily, biofilm organic matrices are built concertedly by bacteria in several environments. QS scope in bacterial ecology has been debated for over 20 years. Different perspectives counterpose the role of density reporter for populations to that of local environment diffusivity probe for individual cells. Here we devise a model system where tubes of different heights contain matrix-embedded producers and sensors. These tubes allow non-limiting signal diffusion from one open end, thereby showing that population spatial extension away from an open boundary can be a main critical factor in QS. Experimental data, successfully recapitulated by a comprehensive mathematical model, demonstrate how tube height can overtake the role of producer density in triggering sensor activation. The biotic degradation of the signal is found to play a major role and to be species-specific and entirely feedback-independent.

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The presence of knots has been observed in a small fraction of single-domain proteins and related to their thermodynamic and kinetic properties. The exchanging of identical structural elements, typical of domain-swapped proteins, makes such dimers suitable candidates to validate the possibility that mutual entanglement between chains may play a similar role for protein complexes. We suggest that such entanglement is captured by the linking number. This represents, for two closed curves, the number of times that each curve winds around the other. We show that closing the curves is not necessary, as a novel parameter G', termed Gaussian entanglement, is strongly correlated with the linking number. Based on 110 non redundant domain-swapped dimers, our analysis evidences a high fraction of chains with a significant intertwining, that is with |G'| > 1. We report that Nature promotes configurations with negative mutual entanglement and surprisingly, it seems to suppress intertwining in long protein dimers. Supported by numerical simulations of dimer dissociation, our results provide a novel topology-based classification of protein-swapped dimers together with some preliminary evidence of its impact on their physical and biological properties.

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The devising of efficient concerted rotation moves that modify only selected local portions of chain molecules is a long studied problem. Possible applications range from speeding the uncorrelated sampling of polymeric dense systems to loop reconstruction and structure refinement in protein modeling. Here, we propose and validate, on a few pedagogical examples, a novel numerical strategy that generalizes the notion of concerted rotation. The usage of the Denavit-Hartenberg parameters for chain description allows all possible choices for the subset of degrees of freedom to be modified in the move. They can be arbitrarily distributed along the chain and can be distanced between consecutive monomers as well. The efficiency of the methodology capitalizes on the inherent geometrical structure of the manifold defined by all chain configurations compatible with the fixed degrees of freedom. The chain portion to be moved is first opened along a direction chosen in the tangent space to the manifold, and then closed in the orthogonal space. As a consequence, in Monte Carlo simulations detailed balance is easily enforced without the need of using Jacobian reweighting. Moreover, the relative fluctuations of the degrees of freedom involved in the move can be easily tuned. We show different applications: the manifold of possible configurations is explored in a very efficient way for a protein fragment and for a cyclic molecule; the "local backbone volume", related to the volume spanned by the manifold, reproduces the mobility profile of all-α helical proteins; the refinement of small protein fragments with different secondary structures is addressed. The presented results suggest our methodology as a valuable exploration and sampling tool in the context of bio-molecular simulations.

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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.

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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/.

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Thermal denaturation of DNA is often studied with coarse-grained models in which native sequential base pairing is mimicked by the existence of attractive interactions only between monomers at the same position along strands (Poland and Scheraga models). Within this framework, the existence of a three-stranded DNA bound state in conditions where a duplex DNA would be in the denaturated state was recently predicted from a study of three directed polymer models on simplified hierarchical lattices (d>2) and in 1+1 dimensions. Such a phenomenon which is similar to the Efimov effect in nuclear physics was named Efimov-DNA. In this paper we study the melting of the three-stranded DNA on a Sierpinski gasket of dimensions d<2 by assigning extra weight factors to fork openings and closings, to induce a two-strand DNA melting. In such a context we can find again the existence of the Efimov-DNA-like state but quite surprisingly we discover also the presence of a different phase, to be called a mixed state, where the strands are pair-wise bound but without three chain contacts. Whereas the Efimov DNA turns out to be a crossover near melting, the mixed phase is a thermodynamic phase.

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The consequences of the boundary conditions (signal reflecting vs. signal adsorbing) on bacterial intercellular communication were addressed by a combined physics and microbiology approach. A predictive biophysical model was devised that considered system size, diffusion from given points, signal molecule decay and boundary properties. The theoretical predictions were tested with two experimental agarose-gel-based set-ups for reflecting or absorbing boundaries. N-acyl homoserine lactone (AHL) concentration profiles were measured using the Agrobacterium tumefaciens NTL4 bioassay and found to agree with model predictions. The half-life of AHL was estimated to be 7 days. The absorbing vs. reflecting nature of the boundaries drastically changed AHL concentration profiles. The effect of a single nonreflecting boundary side was equivalent to a 100-fold lower cell concentration. Results suggest that the kinetics of signal accumulation vs. signal removal and their threshold-mediated phenotypic consequences are directly linked to the properties of biofilm boundaries, stressing the relevance of the diffusion sensing component in bacterial communication.

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Repeats are frequently found in known protein sequences. The level of sequence conservation in tandem repeats correlates with their propensities to be intrinsically disordered. We employ a coarse-grained model of a protein with a two-letter amino acid alphabet, hydrophobic (H) and polar (P), to examine the sequence-structure relationship in the realm of repeated sequences. A fraction of repeated sequences comprises a distinct class of bad folders, whose folding temperatures are much lower than those of random sequences. Imperfection in sequence repetition improves the folding properties of the bad folders while deteriorating those of the good folders. Our results may explain why nature has utilized repeated sequences for their versatility and especially to design functional proteins that are intrinsically unstructured at physiological temperatures.

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