A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations

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/.

We present a simple physical model that demonstrates that the native-state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and energetic constraints placed by the hydrogen bonds and sterics, and hydrophobicity are sufficient to yield a free-energy landscape with broad minima even for a homopolymer. These minima correspond to marginally compact structures comprising the menu of folds that proteins choose from to house their native states in. Our results provide a general framework for understanding the common characteristics of globular proteins. P rotein folding (1-5) is complex because of the sheer size of protein molecules, the twenty types of constituent amino acids with distinct side chains, and the essential role played by the environment. Nevertheless, proteins fold into a limited number (6, 7) of evolutionarily conserved structures (8, 9). It is a familiar, yet remarkable, consequence of symmetry and geometry that ordinary matter crystallizes in a limited number of distinct forms. Indeed, crystalline structures transcend the specifics of the various entities housed in them. Here, we ask the analogous question (10): is the menu of protein folds also determined by geometry and symmetry?We show that a simple model that encapsulates a few general attributes common to all polypeptide chains, such as steric constraints (11-13), hydrogen bonding (14-16), and hydrophobicity (17), gives rise to the emergent free-energy landscape of globular proteins. The relatively few minima in the resulting landscape correspond to putative marginally compact nativestate structures of proteins, which are assemblies of helices, hairpins, and planar sheets. A superior fit (18, 19) of a given protein or sequence of amino acids to one of these predetermined folds dictates the choice of the topology of its native-state structure. Instead of each sequence shaping its own free energy landscape, we find that the overarching principles of geometry and symmetry determine the menu of possible folds that the sequence can choose from.Following Bernal (20), the protein problem can be divided into two distinct steps: first, analogous to the elucidation of crystal structures, one must identify the essential features that account for the common characteristics of all proteins; second, one must understand what makes one protein different from another. Guided by recent work (21,22) that has shown that a faithful description of a chain molecule is a tube and using information from known protein native-state structures, our focus, in this paper, is on the first step: we demonstrate that the native-state folds of proteins emerge from considerations of symmetry and geometry within the context of a simple model.We model a protein as a chain of identical amino acids, represented by their C ␣ atoms, lying along the axis of a selfavoiding flexible tube.

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/.

We report studies of the equilibrium and the dynamics of a general set of lattice models which capture the essence of the force-induced or mechanical DNA unzipping transition. Besides yielding the whole equilibrium phase diagram in the force vs temperature plane, which reveals the presence of an interesting re-entrant unzipping transition for low T , these models enable us to characterize the dynamics of the process starting from a non-equilibrium initial condition. The thermal melting of the DNA strands displays a model dependent time evolution. On the contrary, our results suggest that the dynamical mechanism for the unzipping by force is very robust and the scaling behaviour does not depend on the details of the description we adopt.The replication of DNA is a correlated process involving many proteins and other molecules [1] working at different points in space and time. An understanding of the nature and origin of this correlation is expected to shed light on this complex mechanism. It has recently been shown [2][3][4][5][6] that the force induced unzipping of DNA is a genuine phase transition different from the thermal melting transition of DNA. It was then hypothesized [2] that the initiation of replication at the origins along the DNA, e.g, by dnaA for E.Coli [1,7] or by the "origin recognition complex" (ORC) in eukaryotes [8] is like this unzipping near the critical threshold (with dnaA or ORC acting as the force-inducing agent) and the resulting correlation during unzipping leads the co-operativity required for replication.In contrast to real biological situations, techniques like laser tweezers [9], atomic force microscopes (AFM) [10][11][12] etc have been used to study DNA by pulling at one end. This has led to strand separation by force. In particular, AFM experiments reported hysteresis in the unzipping process, indicating the presence of a first order transition. These mechanical unzipping experiments have opened up new ways of thinking about DNA, just as similar stretching experiments of DNA showed the possibility of several structures other than the most prevalent B-DNA [13]. The activities of polymerases, topoisomerase etc on single stranded DNA have now been analyzed in terms of the force they exert or the force applied against them [14][15][16]. What needs to be investigated, to mimic the biological situation, is the coupling between the opening of the strands and the subsequent events during replication. Such a study involves the dynamics of the unzipping process [3].The purpose of this paper is to define a set of simpler models, in the spirit of Poland and Sheraga [17], for which the unzipping transition can be studied exactly. On the basis of this, the dynamics can be understood. The proposed lattice models (bubble models: b-models) incorporate the mutual-avoidance (hard-core repulsion) of the strands (and also self-avoidance). A further simplification is obtained by suppressing the bubbles along the chains, thereby defining a "fork model" or "Y-model". The phase diagram of the equilibrium...

The conversion from soluble states into cross-β 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 β-strands contributed by distinct protein molecules. Here we assume a universal mechanism is responsible for β-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-β structures. The algorithm predicts that the parallel in-register arrangement of sequence portions that participate in the fibril cross-β 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 β-strands is a key determinant of amyloid fibril formation and of their self-propagating ability.

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments. uncovered anomalous diffusion of the power-law formwith the anomalous diffusion exponent 0<α<1 and the generalised diffusion coefficient D α [11], for the motion of charge carriers in amorphous semiconductors [12]. With the advance of modern microscopy techniques, in particular, superresolution microscopy, as well as massive progress in supercomputing, anomalous diffusion of the type (3) has been reported in numerous complex and biological systems [13,14]. Thus, subdiffusion with 0<α<1 was observed for submicron tracers in the crowded cytoplasm of biological cells [15][16][17][18][19] as well as in artificially crowded environments [20][21][22][23]. Further reports of subdiffusion come from the motion of proteins embedded in the membranes of living cells [24][25][26]. Subdiffusion is also seen in extensive simulations studies, for instance, of lipid bilayer membranes [27][28][29][30] and relative diffusion in proteins [31]. Superdiffusion, due to active motion of molecular motors, was observed in various biological cell types for both introduced and endogenous tracers [16,17,32,33].Most of the anomalous diffusion phenomena mentioned here belong to two main classes of anomalous diffusion: (i) the class of continuous time random walk processes, in which scale-free power-law waiting times in between motion events give rise to the law (3) [12,34], along with a stretched Gaussian displacement probability density G(x, t) [11,12,34] as well as weak ergodicity breaking and ageing [35,36]. We note that similar effects of non-Gaussianity, weak non-ergodicity, and ageing also occur in spatially heterogeneous diffusion processes [37][38][39][40]. (ii) The secon...

Data-collapse is a way of establishing scaling and extracting associated exponents in problems showing self-similar or self-affine characteristics as e.g. in equilibrium or non-equilibrium phase transitions, in critical phases, in dynamics of complex systems and many others. We propose a measure to quantify the nature of data collapse. Via a minimization of this measure, the exponents and their error-bars can be obtained. The procedure is illustrated by considering finite-size-scaling near phase transitions and quite strikingly recovering the exact exponents.