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Eukaryotic cells are characterized by a stiff nucleus whose effect in modeling the collective behavior of cell aggregates is usually underestimated. However, increasing experimental evidence links nuclear modifications with phenotypic transition, like the one between epithelial and mesenchymal states. In this work, we explore the effect of short-range repulsive forces in the non-equilibrium dynamics of the self-propelled Voronoi model. We show that the competition between steric repulsions (representing nuclear/cellular compressibility) and Vertex interactions (mimicking cell-cell adhesion/interaction and cytoskeleton organization) generate a variety of non-equilibrium phase transitions from Motility-Induced Phase Separation to mesenchymal-like phases up to disordered confluent configurations. Notably, we found that tuning the nucleus's effective size/compressibility provides an additional way to cross the boundary between the different possible phases in line with experimental observations., Comment: 11 pages, 4 figures

Asymmetric partition of fate determinants during cell division is a hallmark of cell differentiation. Recent works suggested that such a mechanism is hijacked by cancer cells to increase both their phenotypic heterogeneity and plasticity and in turn their fitness. To quantify fluctuations in the partitioning of cellular elements, imaging-based approaches are used, whose accuracy is limited by the difficulty of detecting cell divisions. Our work addresses this gap proposing a general method based on high-throughput flow cytometry measurements coupled with a theoretical frameworks. We applied our method to a panel of both normal and cancerous human colon cells, showing that different kinds of colon adenocarcinoma cells display very distinct extents of fluctuations in their cytoplasm partition, explained by an asymmetric division of their size. To test the accuracy of our population-level protocol, we directly measure the inherited fractions of cellular elements from extensive time-lapses of live-cell laser scanning microscopy, finding excellent agreement across the cell types. Ultimately, our flow cytometry-based method promise to be accurate and easily applicable to a wide range of biological systems where the quantification of partition fluctuations would help accounting for the observed phenotypic heterogeneity and plasticity, Comment: 17 pages, 4 figures

In Super-resolution, a varying-illumination image stack is required. This enriched the dataset typically necessitates precise mechanical control and micron scale optical alignment and repeatability. Here, we introduce a novel methodology for super-resolution microscopy called Stochastically Structured Illumination Microscopy (S2IM), which bypasses the need for illumination control instead exploiting the random, uncontrolled movement of the target object. We tested our methodology within the clinically relevant ophthalmoscopic setting, harnessing the inherent saccadic motion of the eye to induce stochastic displacement of the illumination pattern on the retina. We opted to avoid human subjects by utilizing a phantom eye model, featuring a retina composed of human induced pluripotent stem cells (iPSC) retinal neurons, and replicating the ocular saccadic movements by custom actuators. Our findings demonstrate that S$^2$IM unlocks scan-less super-resolution with a resolution enhancement of 1.91, with promising prospects also beyond ophthalmoscopy applications such as active matter or atmospheric/astronomical observation.

The ability of a cancer cell population to achieve heterogeneity in their phenotype distributions offers advantages in tumor invasiveness and drug resistance. Studying the mechanisms behind such observed heterogeneity in mammalian cells presents challenges due for instance to the prolonged proliferation times compared to widely studied unicellular organisms like bacteria and yeast. Here, we studied the response of leukemia cell populations to serum starvation via a protocol, we recently developed, that makes use of live cell fluorescence and flow cytometry in combination with a quantitative analytical model to follow the population proliferation while monitoring the dynamics of its phenotype distributions. We found that upon switching between a serum-rich to a serum-poor media, leukemia cells (i) maintain a memory of the previous environment up to one generation even in the presence of severe medium-depletion, before (ii) adapting their growth and division rates to the novel environment while preserving a sizer-like division strategy. Finally, looking at the mitochondria content of the proliferating vs non-proliferating cells, we found that the latter is characterized by a higher number of older mitochondria, suggesting a possible functional role of the observed asymmetric partitioning of (aged) mitochondria in leukemia cells., Comment: 10 pages, 4 figures, 1 table. arXiv admin note: text overlap with arXiv:2306.10905

Predicting interactions between biomolecules, such as protein-protein complexes, remains a challenging problem. Despite the many advancements done so far, the performances of docking protocols are deeply dependent on their capability of identify binding regions. In this context, we present a novel approach that builds upon our previous works modeling protein surface patches via sets of orthogonal polynomials to identify regions of high shape/electrostatic complementarity. By incorporating another key binding property, such as the balance between hydrophilic and hydrophobic contributions, we define new binding matrices that serve an effective inputs for training a neural network. Our approach also allows for the quantitative definition of a typical binding site area - approximately 10\AA~in radius - where hydrophobic contribution and shape complementarity, which reflects the Lennard-Jones interaction, are maximized. Using this new architecture, CIRNet (Core Interacting Residues Network), we achieve an accuracy of approximately 0.82 in identifying pairs of core interacting residues on a balanced dataset. In a blind search for core interacting residues, CIRNet distinguishes these from decoys with a ROC AUC of 0.72. This protocol can enahnce docking algorithms by rescaling the proposed poses. When applied to the top ten models from three popular docking server, CIRNet improves docking outcomes, reducing the the average RMSD between the refined poses and the native state by up to 58%., Comment: 15 pages, 5 figures, 1 table

Shape complementarity of molecular surfaces at the interfaces is a well-known characteristic of protein-protein binding regions, and it is critical in influencing the stability of the complex. Measuring such complementarity is at the basis of methods for both the prediction of possible interactions and for the design/optimization of speficic ones. However, only a limited number of tools are currently available to efficiently and rapidly assess it. Here, we introduce Zepyros, a webserver for fast measuring of the shape complementarity between two molecular interfaces of a given protein-protein complex using structural information. Zepyros is implemented as a publicly available tool with a user-friendly interface. Our server can be found at the following link (all major browser supported): https://zepyros.bio-groups.com, Comment: 4 pages, 1 figure

It is shown that a Hopfield recurrent neural network, informed by experimentally derived brain topology, recovers the scaling picture recently introduced by Deco et al., according to which the process of information transfer within the human brain shows spatially correlated patterns qualitatively similar to those displayed by turbulent flows, although with a more singular exponent, 1/2 instead of 2/3. Both models employ a coupling strength which decays exponentially with the euclidean distance between the nodes, but their mathematical nature is very different, Hopf oscillators versus a Hopfield neural network, respectively. Hence, their convergence for the same data parameters, suggests an intriguing robustness of the scaling picture. The present analysis shows that the Hopfield model brain remains functional by removing links above about five decay lengths, corresponding to about one sixth of the size of the global brain. This suggests that, in terms of connectivity decay length, the Hopfield brain functions in a sort of intermediate ``turbulent liquid''-like state, whose essential connections are the intermediate ones between the connectivity decay length and the global brain size. Finally, the scaling exponents are shown to be highly sensitive to the value of the decay length, as well as to number of brain parcels employed. As a result, any quantitative assessment regarding the specific nature of the scaling regime must be taken with great caution.

We propose a novel approach to detect the binding between proteins making use of the anomalous diffraction of natively present heavy elements inside the molecule 3D structure. In particular, we suggest considering sulfur atoms contained in protein structures at lower percentages than the other atomic species. Here, we run an extensive preliminary investigation to probe both the feasibility and the range of usage of the proposed protocol. In particular, we (i) analytically and numerically show that the diffraction patterns produced by the anomalous scattering of the sulfur atoms in a given direction depend additively on the relative distances between all couples of sulfur atoms. Thus the differences in the patterns produced by bound proteins with respect to their non-bonded states can be exploited to rapidly assess protein complex formation. Next, we (ii) carried out analyses on the abundances of sulfurs in the different proteomes and molecular dynamics simulations on a representative set of protein structures to probe the typical motion of sulfur atoms. Finally, we (iii) suggest a possible experimental procedure to detect protein-protein binding. Overall, the completely label-free and rapid method we propose may be readily extended to probe interactions on a large scale even between other biological molecules, thus paving the way to the development of a novel field of research based on a synchrotron light source., Comment: 9 pages, 4 figures

Using heterogeneous-elasticity theory (HET) and a generalisation of HET theory (GHET), obtained by applying a newly developed procedure for obtaining the continuum limit of the glass's Hessian, we investigate the nature of vibrational excitations, which are present in small systems, which do not allow for low-frequency phonons. We identify two types of such non-phononic excitations. In marginally stable systems, which can be prepared by quenching from a rather high parental temperature, the low-frequency regime is dominated by random-matrix vibrational wavefunctions (type-I) which in macroscopic samples gives rise to the boson peak. They show a density of states (DOS), which scales as $g(\omega)\sim \omega^2$. In more stable systems (reached by a somewhat lower parental temperature) a gap appears in the type-I spectrum. This gap is filled with other type-II non-phononic excitations, which are not described by the previous version of HET, and have a DOS, which scales as $g(\omega)\sim\omega^s$ with $3

The aging dynamics of a colloidal glass has been studied by multiangle Dynamic Light Scattering, Neutron Spin Echo, X-ray Photon Correlation Spectroscopy and Molecular Dynamics simulations. The two relaxation processes, microscopic (fast) and structural (slow), have been investigated in an unprecedentedly wide range of time and length scales covering both ergodic and nonergodic regimes. The microscopic relaxation time remains diffusive at all length scales across the glass transition scaling with wavevector Q as Q^{-2}. The length-scale dependence of structural relaxation time changes from diffusive, characterized by a Q^{-2}-dependence in the early stages of aging, to Q^{-1}- dependence in the full aging regime which marks a discontinuous hopping dynamics. Both regimes are associated with a stretched behaviour of the correlation functions. We expect these findings to provide a general description of both relaxations across the glass transition., Comment: 6 pages, 4 figures

An unexpected dichotomic long time aging behaviour is observed in a glassy colloidal clay suspension investigated by X-Ray Photon Correlation Spectroscopy and Dynamic Light Scattering. In the long time aging regime the intensity autocorrelations are non-exponential, following the Kohlrausch-Williams-Watts functional form with exponent bQ. We show that for spontaneously aged samples a stretched behaviour (\beta_Q < 1) is always found. Surprisingly a compressed exponent (\beta_Q > 1) appears only when the system is rejuvenated by application of a shear field. In both cases the relaxation times scale as Q^{-1}. These observations shed light on the origin of compressed exponential behaviour and helps in classifying previous results in the literature on anomalous dynamics., Comment: 5 pages, 5 figures

Heterogeneity in the size distribution of cancer cell populations has been recently linked to drug resistance and invasiveness. However, despite many progresses have been made in understanding how such heterogeneous size distributions arise in fast-proliferating cell types -like bacteria and yeast-, comprehensive investigations on cancer cell populations are still lacking mainly due to the difficulties of monitoring the proliferation of the time scales typical of mammalian cells. From a reductionist cell dynamics point of view, the strategies allowing size homeostasis are roughly grouped into three classes, \emph{i.e.} timer, sizer, or adder. These strategies are empirically distinguishable given the phenomenological measurable relationship between the cell size at birth and at division, which requires following the proliferation at the single-cell level. Here, we show how it is possible to infer the growth regime and division strategy of leukemia cell populations using live cell fluorescence labeling and flow cytometry in combination with a quantitative analytical model where both cell growth and division rates depend on powers of the cell size. Using our novel approach, we found that the dynamics of the size distribution of leukemia Jurkat T-cells is quantitatively reproduced by (i) a sizer-like division strategy, with (ii) division times following an Erlang distribution given by the sum of at least three independent exponentially-distributed times and (iii) fluctuations up to 15\% of the inherited fraction of size at division with respect to the mother cell size. Finally, we note that our experimental and theoretical apparatus can be easily extended to other cell types and environmental conditions, allowing for a comprehensive characterization of the growth and division model different cells can adopt., Comment: 16 pages, 5 figures

Disorder is a pervasive characteristic of natural systems, offering a wealth of non-repeating patterns. In this study, we present a novel storage method that harnesses naturally-occurring random structures to store an arbitrary pattern in a memory device. This method, the stochastic emergent storage (SES), builds upon the concept of emergent archetypes, where a training set of imperfect examples (prototypes) is employed to instantiate an archetype in an Hopfield-like network through emergent processes. We demostrate this non-Hebbian paradigm in the photonic domain by utilizing random transmission matrices, which govern light scattering in a white-paint turbid medium, as prototypes. Through the implementation of programmable hardware, we successfully realize and experimentally validate the capability to store an arbitrary archetype and perform classification at the speed of light. Leveraging the vast number of modes excited by mesoscopic diffusion, our approach enables the simultaneous storage of thousands of memories without requiring any additional fabrication efforts. Similar to a content addressable memory, all stored memories can be collectively assessed against a given pattern to identify the matching element. Furthermore, by organizing memories spatially into distinct classes, they become features within a higher-level categorical (deeper) optical classification layer.

Enhanced stabilisation of protein structures via the presence of inert excipients is a key mechanism adopted both by physiological systems and in biotechnological applications. While the intrinsic stability of proteins is ultimately fixed by their amino acid composition and organisation, the interactions between excipients and proteins together with their concentrations introduce an additional layer of complexity and in turn, method of modulating protein stability. Here, we combined experimental measurements with molecular dynamics simulations and graph-theory based analyses to assess the stabilising/destabilising effects of different kinds of osmolytes on proteins during heat-mediated denaturation. We found that (i) proteins in solution with stability-enhancing osmolytes tend to have more compact interaction networks than those assumed in presence of destabilising excipients; (ii) a strong negative correlation (R = -0.85) characterises the relationship between the melting temperature Tm and the preferential interaction coefficient defined by the radial distribution functions of osmolytes and water around the protein and (iii) a positive correlation exists between osmolyte-osmolyte clustering and the extent of preferential exclusion from the local domain of the protein, suggesting that exclusion may be driven by enhanced steric hindrance of aggregated osmolytes., Comment: 24 pages, 13 figures, 3 tables

We show that the Kubelka-Munk equations for the description of the intensity transfer of light in turbid media are equivalent to a one-dimensional diffusion equation, which is obtained by averaging the three-dimensional diffusion equation over the lateral directions. This enables us to identify uniquely the Kubelka-Munk parameters and derive expressions for diffuse reflection and transmission coefficients including the effect of internal reflections. Without internal reflections we recover the Kubelka-Munk formulas for these coefficients. We show that the Kubelka-Munk equations are the proper radiative-transfer equations for the one-dimensional diffusion problem and comment on previous attempts to derive the Kubelka-Munk equations.

We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic problem, we transform Maxwell's equations and the electric and magnetic fields in such a way that the linear operator in the resulting secular equations is manifestly Hermitian, in order to deal with a proper eigenvalue problem. As an application of our general formalism, we use an appropriate version of the Coherent-Potential approximation (CPA) to calculate the photon density of states and scattering-mean-free path. Applying standard localization theory, we find that in the presence of both electric and magnetic disorder the spectral range of Anderson localization appears to be much larger than in the case of electric (or magnetic) disorder only. Our result could explain the absence of experimental evidence of 3D Anderson localization of light (all the existing experiments has been performed with electric disorder only) and pave the way towards a successful search of this, up to now, elusive phenomenon.

The concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. While in glasses instantaneous configurations correspond to minima of the potential-energy hypersurface and all eigenvalues of the associated Hessian matrix are therefore positive, in liquids this is no longer true, and modes corresponding to both positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum has been numerically investigated in the past, and it has been demonstrated to bring important information on the liquid dynamics. A systematic deeper theoretical understanding is now needed. Heterogeneous-elasticity theory has proven to be successful in explaining many details of the low-frequency excitations in glasses, ranging from the thoroughly studied boson peak, down to the more elusive non-phononic excitations observed in numerical simulations at the lowest frequencies. Here we present an extension of heterogeneous-elasticity theory to the liquid state, and show that the outcome of the theory agrees well to the results of extensive molecular-dynamics simulations of a model liquid at different temperatures. We show that the spectral shape strongly depends on temperature, being symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we demonstrate that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, known from a few previous numerical studies, has been generally overlooked in the past due to a misleading representation of the data. We provide a thorough analysis of this issue, based on both very accurate predictions of our theory, and computational studies of model liquid systems with extended size.

Phantom eye devices are designed to mimic the optical properties of the human eye; however, the retinal structures are typically emulated with synthetic tissues. Thus, it is currently impossible to exploit phantom eye devices for fluorescence microscopy experiments on cultures, or ex-vivo tissues, although these ophthalmic measurements would be of importance for many applications such as the testing of retinal biomarkers. Here we report and describe the development of a phantom eye designed to host biological samples, such as retinal cultures differentiated from human induced pluripotent stem cells. We characterized the imaging performance of the humanized phantom eye on standard biomarkers such as Alexa Fluor 532 and Alexa fluor 594.

The measurement of the optical Transmission Matrix (TM) enables to access "open channels": input patterns, specific to each scattering structure, capable to deliver very high transmission. Various approaches, based either on multiple interferometric measurements or on systematic random testing of incident wavefronts, enable to estimate the inputs required to excite these open channels. Here, we provide for the first time an approach enabling the complete and reference-less retrieval of the open channels. It is based on the full mapping all the pairwise interference terms resulting from all the input modes couples. We show that these interference terms are organized into a bi-dyadic coupling matrix whose eigenvalues enables to access the open channel. A disordered optical system, is thus behaving exactly like an Hopfield neural network, where a specific input vector (an eigenvalue of the neurons' coupling matrix) enables to retrieve a specific memory pattern. The proposed Hopfield like open-channel-retrieval approach, enables to reach almost 100$\%$ of the theoretically expected value of the Intensity. Moreover employing a digital micromirror device to modulate light, we demonstrate high speed laser scanning at the back of a disordered medium., Comment: 6 pages, 5 figures

In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi order parameter, we focus on the systems where the measurement has been possible for the first time: random lasers. Starting from first principles of light-matter interaction we sketch the main steps leading to the construction of the statistical mechanical model for the dynamics of light modes in a random laser, a spherical multi-p-spin model with complex spins. A new overlap is introduced, the intensity fluctuation overlap, whose probability distribution, under specific assumptions, is equivalent to the Parisi overlap distribution. The experimental protocol for measuring this overlap is based on the possibility of experimentally realizing real replicas. After a description of the first experiment on the random laser made of T5CO$_x$ grains we review and discuss various experiments measuring the overlap distribution, as well as the possible connection with Levy-like distribution of the intensity of the light modes around the laser threshold, the connection with turbulence in fiber lasers and the role of spatial etherogeneities of light modes in random media., Comment: Contribution to the edited volume "Spin Glass Theory and Far Beyond - Replica Symmetry Breaking after 40 years", World Scientific. 30 pages, 16 figures

Understanding the molecular mechanisms driving the binding between bio-molecules is a crucial challenge in molecular biology. In this respect, characteristics like the preferentially hydrophobic composition of the binding interfaces, the role of van der Waals interactions (short range forces), and the consequent shape complementarity between the interacting molecular surfaces are well established. However, no consensus has yet been reached on how and how much electrostatic participates in the various stages of protein-protein interactions. Here, we perform extensive analyses on a large dataset of protein complexes for which both experimental binding affinity and pH data were available. We found that (i) although different classes of dimers do not present marked differences in the amino acid composition and charges disposition in the binding region, (ii) homodimers with identical binding region show higher electrostatic compatibility with respect to both homodimers with non-identical binding region and heterodimers. The level of electrostatic compatibility also varies with the pH of the complex, reaching the lowest values for low pH. Interestingly, (iii) shape and electrostatic complementarity behave oppositely when one stratifies the complexes by their binding affinity. Conversely, complexes with low values of binding affinity exploit Coulombic complementarity to acquire specificity, suggesting that electrostatic complementarity may play a greater role in transient (or less stable) complexes. In light of these results, (iv) we provide a fast and efficient method to measure electrostatic complementarity without the need of knowing the complex structure. Expanding the electrostatic potential on a basis of 2D orthogonal polynomials, we can discriminate between transient and permanent protein complexes with an AUC of the ROC of 0.8., Comment: 16 pages, 5 figures, 3 tables

Microgel particles composed of Interpenetrated Polymer Networks (IPN) of poly(N-isopropylacrylamide) (PNIPAM) and poly(acrylic acid) (PAAc) dispersed in water have been investigated through dynamic light scattering. The study of the temperature, concentration and pH dependence of the relaxation time has highlighted the existence of a thermoreversible transition corresponding to the swollen-shrunken volume phase transition. The presence of PAAc introduces an additional pH-sensitivity with respect to the temperature-sensitivity due to PNIPAM and leads to interesting differences in the transition process at acid and neutral pH.

Bone pain typically occurs immediately following skeletal damage with mechanical distortion or rupture of nociceptive fibres. The pain mechanism is also associated with chronic pain conditions where the healing process is impaired. Any load impacting on the area of the fractured bone will increase the intraosseous pressure, consequently stimulating the nociceptive response, necessitating rapid clinical intervention to relieve pain associated with the bone damage and appropriate mitigation of any processes involved with the loss of bone mass, muscle, mobility and, to prevent death. The following review has examined the mechanisms of pain associated with trauma or cancer-related skeletal damage focusing on new approaches for the development of innovative therapeutic interventions. In particular, the current review highlights tissue engineering approaches that offer considerable promise in the application of functional biomimetic fabrication of bone and nerve tissues, resembling the pathological micro-environment. The strategic combination of bone and nerve tissue engineered models provides significant potential to develop a new class of in vitro platforms, capable of replacing in vivo models and testing the safety and efficacy of novel drug treatments aimed at the resolution of bone-associated pain. To date, the field of bone pain research has centred on animal models, with accompanying disparity within models often noted and a paucity of data correlating to the human physiological response. This review explores the evident gap in pain drug development research and suggests a step change in approach to harness tissue engineering technologies to recapitulate the complex pathophysiological environment of the damaged bone tissue enabling evaluation of the associated pain-mimicking mechanism with, ultimately, significant therapeutic potential therein for improved patient quality of life., Comment: Submitted to In Vitro Models journal

In a recent paper (Phys. Rev. E {\bf 104}, 014103 (2021) ) M. Baggioli and A. Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of states (DOS) which they claim to represent the instantaneous-normal-mode (INM) spectrum of a liquid. However, the quantum-mechanical procedure of Debye cannot be used for a classical liquid and the authors' formula for the INM spectrum does not represent the known INM spectra of simple liquids. Furthermore, the derivation of this formula from their model equation of motion is mathematically in error. Finally experimental test of the teory for the specific heat of {\it liquids} is performed by fitting the data of {\it supercritical fluids}. \new{To our opinion,} these and a lot of other inconsistencies render this work not suitable for studying the specific heat of liquids., Comment: 3 pages, 1 figure

We discuss a field-theoretical approach to liquids, solids and glasses, published recently [Phys.Rev.E {\bf105}, 034108 (2022)], which aims to describe these materials in a common quantum formalism. We argue that such quantum formalism is not applicable to classical liquids, and the results presented, which rely heavily on the concept of phase relaxation borrowed from quantum fluids, contradict the known hydrodynamic theory of classical liquids. In particular, the authors miss the important particle-number conservation law and the density fluctuations as hydrodynamic slow variable. Instead, the authors invoke Goldstone bosons as elementary hydrodynamic excitations. We point out that in a classical liquid there are no broken continuous symmetries and consequently no Goldstone bosons. The authors claim that the Goldstone bosons would be responsible for the existence of sound in liquids, instead of resulting from combined particle-number and momentum conservation, a fact well documented in fluid-mechanics textbooks., Comment: 3 pages, 0 figures

A disciplinary profile of a country is defined as the versor whose components are the numbers of articles produced in a given discipline divided the overall production of the country. Starting from the Essential Science Indicators (ESI) schema of classification of subject area, we obtained the yearly disciplinary profiles of a worldwide graph, where on each node sits a country, in the two time intervals [1980-1988] and [1992-2017], the fall of the Berlin Wall being the watershed. We analyse the empirical pairwise cross-correlation matrices of the time series of disciplinary profiles. The contrast with random matrix theory proves that, beyond measurement noise, the empirical cross-correlation matrices bring genuine information. Arising from the Shannon theorem as the least-structured model consistent with the measured pairwise correlations, the stationary probability distribution of disciplinary profiles can be described by a Boltzmann distribution related to a generalized $n_d$-dimensional Heisenberg model. The set of network interactions of the Heisenberg model have been inferred and to it they have been applied two clusterization methods, hierarchical clustering and principal component analysis. On a geopolitical plane this allow to obtain a characterization of the worldwide bilateral interactions based on physical modeling. A simple geopolitical analysis reveals the consistency of the results obtained and gives a boost to deeper historical analysis. In order to obtain the optimal set of pairwise interactions we used a Pseudo-Likelihood approach. We analytically computed the Pseudo-Likelihood and its gradient. The analytical computations deserve interest in whatever inference Bayesian problem involving a $n_d$-dimensional Heisenberg model.

The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We analyze the stability of the stored memories: basins of attraction obtained by the Hebbian unlearning technique are found to be comparable in size to those obtained in the symmetric perceptron, while the two algorithms are found to converge in the same region of Gardner's space of interactions, having followed similar learning paths. A geometric interpretation of Hebbian unlearning is proposed to explain its optimal performances. Because the Hopfield model is also a prototypical model of disordered magnetic system, it might be possible to translate our results to other models of interest for memory storage in materials., Comment: 11 pages, 13 figures, 43 references

Many of the molecular mechanisms underlying the pathological aggregation of proteins observed in neurodegenerative diseases are still not fully understood. Among the diseases associated with protein aggregates, for example, Amyotrophic Lateral Sclerosis (ALS) is of relevant importance. Although understanding the processes that cause the disease is still an open challenge, its relationship with protein aggregation is widely known. In particular, human TDP-43, an RNA/DNA binding protein, is a major component of pathological cytoplasmic inclusions described in ALS patients. The deposition of the phosphorylated full-length TDP-43 in spinal cord cells has been widely studied, and it has been shown that the brain cortex presents an accumulation of phosphorylated C-terminal fragments (CTFs). Even if it is debated whether CTFs represent a primary cause of ALS, they are a hallmark of TDP-43 related neurodegeneration in the brain. Here, we investigate the CTFs aggregation process, providing a possible computational model of interaction based on the evaluation of shape complementarity at the interfaces. To this end, extensive Molecular Dynamics (MD) simulations were conducted for different types of fragments with the aim of exploring the equilibrium configurations. Adopting a newly developed approach based on Zernike polynomials, for finding complementary regions of the molecular surface, we sampled a large set of exposed portions of the molecular surface of CTFs structures as obtained from MD simulations. The analysis proposes a set of possible associations between the CTFs, which could drive the aggregation process of the CTFs., Comment: 9 pages, 4 figures, 1 table

What are the molecular mechanisms that dictate protein-protein binding stability and whether those are related to the ones behind protein fold stability are still largely open questions. Indeed, despite many past efforts, we still lack definitive models to account for experimental quantities like protein melting temperature or complex binding affinity. Here, we investigate and compare chemical and physical features on a dataset of protein with known melting temperature as well as a large dataset of protein-protein complexes with reliable experimental binding affinity. In particular, we probed the aminoacid composition and the organization of the network of intramolecular and intermolecular interaction energies among residues. We found that hydrophobic residues present on the protein surfaces are preferentially located in the binding regions, while charged residues behave oppositely. In addition, the abundance of polar amino acid like Serine and Proline correlates with the binding affinity of the complexes. Analysing the interaction energies we found that distant Coulombic interactions are responsible for thermal stability while the total inter-molecular van der Waals energy correlates with protein-protein binding affinity., Comment: 8 pages, 3 figures

Most proteins perform their biological function by interacting with one or more molecular partners. In this respect, characterizing the features of the molecular surface, especially in the portions where the interaction takes place, turned out to be a crucial step in the investigation of the mechanisms of recognition and binding between molecules. Predictive methods often rely on extensive samplings of molecular patches with the aim to identify hot spots on the surface. In this framework, analysis of large proteins and/or many molecular dynamics frames is often unfeasible due to the high computational cost. Thus, finding optimal ways to reduce the number of points to be sampled maintaining the biological information carried by the molecular surface is pivotal. Here, we present a new theoretical and computational algorithm with the aim of determining a subset of surface points, appropriately selected in space, in order to maximize the information of the overall shape of the molecule by minimizing the number of total points. We test our procedure by looking at the local shape of the surface through a recently developed method based on the formalism of Zernike polynomials in two dimensions, which is able to characterize the local shape properties of portions of molecular surfaces. The results of this method show that a remarkably higher ability of this algorithm to reproduce the information of the complete molecular surface compared to uniform random sampling., Comment: 8 pages, 5 figures

Many factors influence biomolecules binding, and its assessment constitutes an elusive challenge in computational structural biology. In this respect, the evaluation of shape complementarity at molecular interfaces is one of the main factors to be considered. We focus on the particular case of antibody-antigen complexes to quantify the complementarities occurring at molecular interfaces. We relied on a method we recently developed, which employs the 2D Zernike descriptors, to characterize investigated regions with an ordered set of numbers summarizing the local shape properties. Collected a structural dataset of antibody-antigen complexes, we applied this method and we statistically distinguished, in terms of shape complementarity, pairs of interacting regions from non-interacting ones. Thus, we set up a novel computational strategy based on \textit{in-silico} mutagenesis of antibody binding site residues. We developed a Monte Carlo procedure to increase the shape complementarity between the antibody paratope and a given epitope on a target protein surface. We applied our protocol against several molecular targets in SARS-CoV-2 spike protein, known to be indispensable for viral cell invasion. We, therefore, optimized the shape of template antibodies for the interaction with such regions. As the last step of our procedure, we performed an independent molecular docking validation of the results of our Monte Carlo simulations., Comment: 13 pages, 4 figures

Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a non-equilibrium phase transition into a quasi-hexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.

Speckle is maybe the most fundamental interference effect of light in disordered media, giving rise to fascinating physical phenomena and enabling applications in imaging, spectroscopy or cryptography, to name a few. While speckle formed outside a sample is easily measured and analysed, true bulk speckle, as formed inside random media, is difficult to investigate directly due to the obvious issue of physical access. Furthermore, its proper theoretical description poses enormous challenges. Here we report on the first direct measurements of intensity correlations of light inside a disordered medium, using embedded DNA strings decorated with emitters separated by a controlled nanometric distance. Our method provides in situ access to fundamental properties of bulk speckles as their size and polarization degrees of freedom, both of which are found to deviate significantly from theoretical predictions. The deviations are explained, by comparison with rigorous numerical calculations, in terms of correlations among polarization components and non-universal near-field contributions at the nanoscale.

The vibrational anomalies of glasses, in particular the boson peak, are addressed from the standpoint of heterogeneous elasticity, namely the spatial fluctuations of elastic constants caused by the structural disorder of the amorphous materials. In the first part of this review article a mathematical analogy between diffusive motion in a disordered environment and a scalar simplification of vibrational motion under the same condition is emploited. We demonstrate that the disorder-induced long-time tails of diffusion correspond to the Rayleigh scattering law in the vibrational system and that the cross-over from normal to anomalous diffusion corresponds to the boson peak. The anomalous motion arises as soon as the disorder-induced self-energy exceeds the frequency-independent diffusivity/elasticity. For this model a variational scheme is emploited for deriving two mean-field theories of disorder, the self-consistent Born approximation (SCBA) and coherent-potential approximation (CPA). The former applies if the fluctuations are weak and Gaussian, the latter applies for stronger and non-Gaussian fluctuations. In the second part the vectorial theory of heterogenous elasticity is presented and solved in SCBA and CPA, introduced for the scalar model. Both approaches predict and explain the boson-peak and the associated anomalies, namely a dip in the acoustic phase velocity and a characteristic strong increase of the acoustic attenuation below the boson peak. Explicit expressions for the density of states and the inelastic Raman, neutron and X-ray scattering laws are given. Recent conflicting ways of explaining the boson-peak anomalies are discussed., Comment: 17 pages, 8 figures, Contributed chapter to "Low-Temperature Thermal and Vibrational Properties of Disoredered Solids" (A Half-Century of universal "anomalies" of glasses), Ed. M. A. Ramos, to appear

Despite the huge effort to contain the infection, the novel SARS-CoV-2 coronavirus has rapidly become pandemics, mainly due to its extremely high human-to-human transmission capability, and a surprisingly high viral charge of symptom-less people. While the seek of a vaccine is still ongoing, promising results have been obtained with antiviral compounds. In particular, lactoferrin is found to have beneficial effects both in preventing and soothing the infection. Here, we explore the possible molecular mechanisms with which lactoferrin interferes with SARS-CoV-2 cell invasion, preventing attachment and/or entry of the virus. To this aim, we search for possible interactions lactoferrin may have with virus structural proteins and host receptors. Representing the molecular iso-electron surface of proteins in terms of 2D-Zernike descriptors, we (i) identified putative regions on the lactoferrin surface able to bind sialic acid receptors on the host cell membrane, sheltering the cell from the virus attachment; (ii) showed that no significant shape complementarity is present between lactoferrin and the ACE2 receptor, while (iii) two high complementarity regions are found on the N- and C-terminal domains of the SARS-CoV-2 spike protein, hinting at a possible competition between lactoferrin and ACE2 for the binding to the spike protein., Comment: 9 pages, 4 figures

Among the many aspects that characterize the COVID-19 pandemic, two seem particularly challenging to understand: (i) the great geographical differences in the degree of virus contagiousness and lethality which were found in the different phases of the epidemic progression, and (ii) the potential role of the infected people's blood type in both the virus infectivity and the progression of the disease. A recent hypothesis could shed some light on both aspects. Specifically, it has been proposed that in the subject-to-subject transfer SARS-CoV-2 conserves on its capsid the erythrocytes' antigens of the source subject. Thus these conserved antigens can potentially cause an immune reaction in a receiving subject that has previously acquired specific antibodies for the source subject antigens. This hypothesis implies a blood type-dependent infection rate. The strong geographical dependence of the blood type distribution could be, therefore, one of the factors at the origin of the observed heterogeneity in the epidemics spread. Here, we present an epidemiological deterministic model where the infection rules based on blood types are taken into account and compare our model outcomes with the exiting worldwide infection progression data. We found an overall good agreement, which strengthens the hypothesis that blood types do play a role in the COVID-19 infection., Comment: 6 figures, 4 tables

We propose a novel numerical method able to determine efficiently and effectively the relationship of complementarity between portions of proteins surfaces. This innovative and general procedure, based on the representation of the molecular iso-electron density surface in terms of 2D Zernike polynomials, allows the rapid and quantitative assessment of the geometrical shape complementarity between interacting proteins, that was unfeasible with previous methods. We first tested the method with a large dataset of known protein complexes obtaining an overall area under the ROC curve of 0.76 in the blind recognition of binding sites and then applied it to investigate the features of the interaction between the Spike protein of SARS-Cov-2 and human cellular receptors. Our results indicate that SARS-CoV-2 uses a dual strategy: its spike protein could also interact with sialic acid receptors of the cells in the upper airways, in addition to the known interaction with Angiotensin-converting enzyme 2., Comment: 10 pages, 4 figures

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems have more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered as proxy for the stored memories. We enumerate them using numerical simulation and extend the analysis to large systems sizes using belief propagation. We find that the logarithm of the number of such cycles is a non monotonic function of the mean connectivity and we discuss the similarities with biological neural networks describing the memory capacity of the hippocampus., Comment: 10 pages, 11 figures