Emergent excitations in a geometrically frustrated magnet

Frustrated systems are ubiquitous and interesting because their behavior is difficult to predict. Magnetism offers extreme examples in the form of spin lattices where all interactions between spins cannot be simultaneously satisfied. Such geometrical frustration leads to macroscopic degeneracies, and offers the possibility of qualitatively new states of matter whose nature has yet to be fully understood. Here we have discovered how novel composite spin degrees of freedom can emerge from frustrated interactions in the cubic spinel ZnCr2O4. Upon cooling, groups of six spins self-organize into weakly interacting antiferromagnetic loops whose directors, defined as the unique direction along which the spins are aligned parallel or antiparallel, govern all low temperature dynamics. The experimental evidence comes from a measurement of the magnetic form factor by inelastic neutron scattering. While the data bears no resemblance to the atomic form factor for chromium, they are perfectly consistent with the form factor for hexagonal spin loop directors. The hexagon directors are to a first approximation decoupled from each other and hence their reorientations embody the long-sought local zero energy modes for the pyrochlore lattice.Comment: 10 pages, 4 figures upon reques

Direct entropy determination and application to artificial spin ice

From thermodynamic origins, the concept of entropy has expanded to a range of statistical measures of uncertainty, which may still be thermodynamically significant. However, laboratory measurements of entropy continue to rely on direct measurements of heat. New technologies that can map out myriads of microscopic degrees of freedom suggest direct determination of configurational entropy by counting in systems where it is thermodynamically inaccessible, such as granular and colloidal materials, proteins and lithographically fabricated nanometre-scale arrays. Here, we demonstrate a conditional-probability technique to calculate entropy densities of translation-invariant states on lattices using limited configuration data on small clusters, and apply it to arrays of interacting nanometre-scale magnetic islands (artificial spin ice). Models for statistically disordered systems can be assessed by applying the method to relative entropy densities. For artificial spin ice, this analysis shows that nearest-neighbour correlations drive longer-range ones.Comment: 10 page

A spatio-temporal mining approach towards summarizing and analyzing protein folding trajectories

Understanding the protein folding mechanism remains a grand challenge in structural biology. In the past several years, computational theories in molecular dynamics have been employed to shed light on the folding process. Coupled with high computing power and large scale storage, researchers now can computationally simulate the protein folding process in atomistic details at femtosecond temporal resolution. Such simulation often produces a large number of folding trajectories, each consisting of a series of 3D conformations of the protein under study. As a result, effectively managing and analyzing such trajectories is becoming increasingly important. In this article, we present a spatio-temporal mining approach to analyze protein folding trajectories. It exploits the simplicity of contact maps, while also integrating 3D structural information in the analysis. It characterizes the dynamic folding process by first identifying spatio-temporal association patterns in contact maps, then studying how such patterns evolve along a folding trajectory. We demonstrate that such patterns can be leveraged to summarize folding trajectories, and to facilitate the detection and ordering of important folding events along a folding path. We also show that such patterns can be used to identify a consensus partial folding pathway across multiple folding trajectories. Furthermore, we argue that such patterns can capture both local and global structural topology in a 3D protein conformation, thereby facilitating effective structural comparison amongst conformations. We apply this approach to analyze the folding trajectories of two small synthetic proteins-BBA5 and GSGS (or Beta3S). We show that this approach is promising towards addressing the above issues, namely, folding trajectory summarization, folding events detection and ordering, and consensus partial folding pathway identification across trajectories

Time-dependent ARMA modeling of genomic sequences

<p>Abstract</p> <p>Background</p> <p>Over the past decade, many investigators have used sophisticated time series tools for the analysis of genomic sequences. Specifically, the correlation of the nucleotide chain has been studied by examining the properties of the power spectrum. The main limitation of the power spectrum is that it is restricted to stationary time series. However, it has been observed over the past decade that genomic sequences exhibit non-stationary statistical behavior. Standard statistical tests have been used to verify that the genomic sequences are indeed not stationary. More recent analysis of genomic data has relied on time-varying power spectral methods to capture the statistical characteristics of genomic sequences. Techniques such as the evolutionary spectrum and evolutionary periodogram have been successful in extracting the time-varying correlation structure. The main difficulty in using time-varying spectral methods is that they are extremely unstable. Large deviations in the correlation structure results from very minor perturbations in the genomic data and experimental procedure. A fundamental new approach is needed in order to provide a stable platform for the non-stationary statistical analysis of genomic sequences.</p> <p>Results</p> <p>In this paper, we propose to model non-stationary genomic sequences by a time-dependent autoregressive moving average (TD-ARMA) process. The model is based on a classical ARMA process whose coefficients are allowed to vary with time. A series expansion of the time-varying coefficients is used to form a generalized Yule-Walker-type system of equations. A recursive least-squares algorithm is subsequently used to estimate the time-dependent coefficients of the model. The non-stationary parameters estimated are used as a basis for statistical inference and biophysical interpretation of genomic data. In particular, we rely on the TD-ARMA model of genomic sequences to investigate the statistical properties and differentiate between coding and non-coding regions in the nucleotide chain. Specifically, we define a quantitative measure of randomness to assess how far a process deviates from white noise. Our simulation results on various gene sequences show that both the coding and non-coding regions are non-random. However, coding sequences are "whiter" than non-coding sequences as attested by a higher index of randomness.</p> <p>Conclusion</p> <p>We demonstrate that the proposed TD-ARMA model can be used to provide a stable time series tool for the analysis of non-stationary genomic sequences. The estimated time-varying coefficients are used to define an index of randomness, in order to assess the statistical correlations in coding and non-coding DNA sequences. It turns out that the statistical differences between coding and non-coding sequences are more subtle than previously thought using stationary analysis tools: Both coding and non-coding sequences exhibit statistical correlations, with the coding regions being "whiter" than the non-coding regions. These results corroborate the evolutionary periodogram analysis of genomic sequences and revoke the stationary analysis' conclusion that coding DNA behaves like random sequences.</p

Do Natural Proteins Differ from Random Sequences Polypeptides? Natural vs. Random Proteins Classification Using an Evolutionary Neural Network

Are extant proteins the exquisite result of natural selection or are they random sequences slightly edited by evolution? This question has puzzled biochemists for long time and several groups have addressed this issue comparing natural protein sequences to completely random ones coming to contradicting conclusions. Previous works in literature focused on the analysis of primary structure in an attempt to identify possible signature of evolutionary editing. Conversely, in this work we compare a set of 762 natural proteins with an average length of 70 amino acids and an equal number of completely random ones of comparable length on the basis of their structural features. We use an ad hoc Evolutionary Neural Network Algorithm (ENNA) in order to assess whether and to what extent natural proteins are edited from random polypeptides employing 11 different structure-related variables (i.e. net charge, volume, surface area, coil, alpha helix, beta sheet, percentage of coil, percentage of alpha helix, percentage of beta sheet, percentage of secondary structure and surface hydrophobicity). The ENNA algorithm is capable to correctly distinguish natural proteins from random ones with an accuracy of 94.36%. Furthermore, we study the structural features of 32 random polypeptides misclassified as natural ones to unveil any structural similarity to natural proteins. Results show that random proteins misclassified by the ENNA algorithm exhibit a significant fold similarity to portions or subdomains of extant proteins at atomic resolution. Altogether, our results suggest that natural proteins are significantly edited from random polypeptides and evolutionary editing can be readily detected analyzing structural features. Furthermore, we also show that the ENNA, employing simple structural descriptors, can predict whether a protein chain is natural or random

Inversion of the balance between hydrophobic and hydrogen bonding interactions in protein folding and aggregation.

Identifying the forces that drive proteins to misfold and aggregate, rather than to fold into their functional states, is fundamental to our understanding of living systems and to our ability to combat protein deposition disorders such as Alzheimer's disease and the spongiform encephalopathies. We report here the finding that the balance between hydrophobic and hydrogen bonding interactions is different for proteins in the processes of folding to their native states and misfolding to the alternative amyloid structures. We find that the minima of the protein free energy landscape for folding and misfolding tend to be respectively dominated by hydrophobic and by hydrogen bonding interactions. These results characterise the nature of the interactions that determine the competition between folding and misfolding of proteins by revealing that the stability of native proteins is primarily determined by hydrophobic interactions between side-chains, while the stability of amyloid fibrils depends more on backbone intermolecular hydrogen bonding interactions

Atomic-Resolution Simulations Predict a Transition State for Vesicle Fusion Defined by Contact of a Few Lipid Tails

Membrane fusion is essential to both cellular vesicle trafficking and infection by enveloped viruses. While the fusion protein assemblies that catalyze fusion are readily identifiable, the specific activities of the proteins involved and nature of the membrane changes they induce remain unknown. Here, we use many atomic-resolution simulations of vesicle fusion to examine the molecular mechanisms for fusion in detail. We employ committor analysis for these million-atom vesicle fusion simulations to identify a transition state for fusion stalk formation. In our simulations, this transition state occurs when the bulk properties of each lipid bilayer remain in a lamellar state but a few hydrophobic tails bulge into the hydrophilic interface layer and make contact to nucleate a stalk. Additional simulations of influenza fusion peptides in lipid bilayers show that the peptides promote similar local protrusion of lipid tails. Comparing these two sets of simulations, we obtain a common set of structural changes between the transition state for stalk formation and the local environment of peptides known to catalyze fusion. Our results thus suggest that the specific molecular properties of individual lipids are highly important to vesicle fusion and yield an explicit structural model that could help explain the mechanism of catalysis by fusion proteins

An analysis of single amino acid repeats as use case for application specific background models

Background Sequence analysis aims to identify biologically relevant signals against a backdrop of functionally meaningless variation. Increasingly, it is recognized that the quality of the background model directly affects the performance of analyses. State-of-the-art approaches rely on classical sequence models that are adapted to the studied dataset. Although performing well in the analysis of globular protein domains, these models break down in regions of stronger compositional bias or low complexity. While these regions are typically filtered, there is increasing anecdotal evidence of functional roles. This motivates an exploration of more complex sequence models and application-specific approaches for the investigation of biased regions. Results Traditional Markov-chains and application-specific regression models are compared using the example of predicting runs of single amino acids, a particularly simple class of biased regions. Cross-fold validation experiments reveal that the alternative regression models capture the multi-variate trends well, despite their low dimensionality and in contrast even to higher-order Markov-predictors. We show how the significance of unusual observations can be computed for such empirical models. The power of a dedicated model in the detection of biologically interesting signals is then demonstrated in an analysis identifying the unexpected enrichment of contiguous leucine-repeats in signal-peptides. Considering different reference sets, we show how the question examined actually defines what constitutes the 'background'. Results can thus be highly sensitive to the choice of appropriate model training sets. Conversely, the choice of reference data determines the questions that can be investigated in an analysis. Conclusions Using a specific case of studying biased regions as an example, we have demonstrated that the construction of application-specific background models is both necessary and feasible in a challenging sequence analysis situation

Lethal Mutants and Truncated Selection Together Solve a Paradox of the Origin of Life

BACKGROUND: Many attempts have been made to describe the origin of life, one of which is Eigen's cycle of autocatalytic reactions [Eigen M (1971) Naturwissenschaften 58, 465-523], in which primordial life molecules are replicated with limited accuracy through autocatalytic reactions. For successful evolution, the information carrier (either RNA or DNA or their precursor) must be transmitted to the next generation with a minimal number of misprints. In Eigen's theory, the maximum chain length that could be maintained is restricted to 100-1000 nucleotides, while for the most primitive genome the length is around 7000-20,000. This is the famous error catastrophe paradox. How to solve this puzzle is an interesting and important problem in the theory of the origin of life. METHODOLOGY/PRINCIPAL FINDINGS: We use methods of statistical physics to solve this paradox by carefully analyzing the implications of neutral and lethal mutants, and truncated selection (i.e., when fitness is zero after a certain Hamming distance from the master sequence) for the critical chain length. While neutral mutants play an important role in evolution, they do not provide a solution to the paradox. We have found that lethal mutants and truncated selection together can solve the error catastrophe paradox. There is a principal difference between prebiotic molecule self-replication and proto-cell self-replication stages in the origin of life. CONCLUSIONS/SIGNIFICANCE: We have applied methods of statistical physics to make an important breakthrough in the molecular theory of the origin of life. Our results will inspire further studies on the molecular theory of the origin of life and biological evolution

Molecular Dynamics Simulation of Phosphorylated KID Post-Translational Modification

BACKGROUND:Kinase-inducible domain (KID) as transcriptional activator can stimulate target gene expression in signal transduction by associating with KID interacting domain (KIX). NMR spectra suggest that apo-KID is an unstructured protein. After post-translational modification by phosphorylation, KID undergoes a transition from disordered to well folded protein upon binding to KIX. However, the mechanism of folding coupled to binding is poorly understood. METHODOLOGY:To get an insight into the mechanism, we have performed ten trajectories of explicit-solvent molecular dynamics (MD) for both bound and apo phosphorylated KID (pKID). Ten MD simulations are sufficient to capture the average properties in the protein folding and unfolding. CONCLUSIONS:Room-temperature MD simulations suggest that pKID becomes more rigid and stable upon the KIX-binding. Kinetic analysis of high-temperature MD simulations shows that bound pKID and apo-pKID unfold via a three-state and a two-state process, respectively. Both kinetics and free energy landscape analyses indicate that bound pKID folds in the order of KIX access, initiation of pKID tertiary folding, folding of helix alpha(B), folding of helix alpha(A), completion of pKID tertiary folding, and finalization of pKID-KIX binding. Our data show that the folding pathways of apo-pKID are different from the bound state: the foldings of helices alpha(A) and alpha(B) are swapped. Here we also show that Asn139, Asp140 and Leu141 with large Phi-values are key residues in the folding of bound pKID. Our results are in good agreement with NMR experimental observations and provide significant insight into the general mechanisms of binding induced protein folding and other conformational adjustment in post-translational modification