Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure

The Sandia Fracture Challenge: blind round robin predictions of ductile tearing

Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments

The fractal globule as a model of chromatin architecture in the cell

The fractal globule is a compact polymer state that emerges during polymer condensation as a result of topological constraints which prevent one region of the chain from passing across another one. This long-lived intermediate state was introduced in 1988 (Grosberg et al. 1988) and has not been observed in experiments or simulations until recently (Lieberman-Aiden et al. 2009). Recent characterization of human chromatin using a novel chromosome conformational capture technique brought the fractal globule into the spotlight as a structural model of human chromosome on the scale of up to 10 Mb (Lieberman-Aiden et al. 2009). Here, we present the concept of the fractal globule, comparing it to other states of a polymer and focusing on its properties relevant for the biophysics of chromatin. We then discuss properties of the fractal globule that make it an attractive model for chromatin organization inside a cell. Next, we connect the fractal globule to recent studies that emphasize topological constraints as a primary factor driving formation of chromosomal territories. We discuss how theoretical predictions, made on the basis of the fractal globule model, can be tested experimentally. Finally, we discuss whether fractal globule architecture can be relevant for chromatin packing in other organisms such as yeast and bacteria

Dynamically-Driven Inactivation of the Catalytic Machinery of the SARS 3C-Like Protease by the N214A Mutation on the Extra Domain

Despite utilizing the same chymotrypsin fold to host the catalytic machinery, coronavirus 3C-like proteases (3CLpro) noticeably differ from picornavirus 3C proteases in acquiring an extra helical domain in evolution. Previously, the extra domain was demonstrated to regulate the catalysis of the SARS-CoV 3CLpro by controlling its dimerization. Here, we studied N214A, another mutant with only a doubled dissociation constant but significantly abolished activity. Unexpectedly, N214A still adopts the dimeric structure almost identical to that of the wild-type (WT) enzyme. Thus, we conducted 30-ns molecular dynamics (MD) simulations for N214A, WT, and R298A which we previously characterized to be a monomer with the collapsed catalytic machinery. Remarkably, three proteases display distinctive dynamical behaviors. While in WT, the catalytic machinery stably retains in the activated state; in R298A it remains largely collapsed in the inactivated state, thus implying that two states are not only structurally very distinguishable but also dynamically well separated. Surprisingly, in N214A the catalytic dyad becomes dynamically unstable and many residues constituting the catalytic machinery jump to sample the conformations highly resembling those of R298A. Therefore, the N214A mutation appears to trigger the dramatic change of the enzyme dynamics in the context of the dimeric form which ultimately inactivates the catalytic machinery. The present MD simulations represent the longest reported so far for the SARS-CoV 3CLpro, unveiling that its catalysis is critically dependent on the dynamics, which can be amazingly modulated by the extra domain. Consequently, mediating the dynamics may offer a potential avenue to inhibit the SARS-CoV 3CLpro

Cross-Species Analyses Identify the BNIP-2 and Cdc42GAP Homology (BCH) Domain as a Distinct Functional Subclass of the CRAL_TRIO/Sec14 Superfamily

The CRAL_TRIO protein domain, which is unique to the Sec14 protein superfamily, binds to a diverse set of small lipophilic ligands. Similar domains are found in a range of different proteins including neurofibromatosis type-1, a Ras GTPase-activating Protein (RasGAP) and Rho guanine nucleotide exchange factors (RhoGEFs). Proteins containing this structural protein domain exhibit a low sequence similarity and ligand specificity while maintaining an overall characteristic three-dimensional structure. We have previously demonstrated that the BNIP-2 and Cdc42GAP Homology (BCH) protein domain, which shares a low sequence homology with the CRAL_TRIO domain, can serve as a regulatory scaffold that binds to Rho, RhoGEFs and RhoGAPs to control various cell signalling processes. In this work, we investigate 175 BCH domain-containing proteins from a wide range of different organisms. A phylogenetic analysis with ∼100 CRAL_TRIO and similar domains from eight representative species indicates a clear distinction of BCH-containing proteins as a novel subclass within the CRAL_TRIO/Sec14 superfamily. BCH-containing proteins contain a hallmark sequence motif R(R/K)h(R/K)(R/K)NL(R/K)xhhhhHPs (‘h’ is large and hydrophobic residue and ‘s’ is small and weekly polar residue) and can be further subdivided into three unique subtypes associated with BNIP-2-N, macro- and RhoGAP-type protein domains. A previously unknown group of genes encoding ‘BCH-only’ domains is also identified in plants and arthropod species. Based on an analysis of their gene-structure and their protein domain context we hypothesize that BCH domain-containing genes evolved through gene duplication, intron insertions and domain swapping events. Furthermore, we explore the point of divergence between BCH and CRAL-TRIO proteins in relation to their ability to bind small GTPases, GAPs and GEFs and lipid ligands. Our study suggests a need for a more extensive analysis of previously uncharacterized BCH, ‘BCH-like’ and CRAL_TRIO-containing proteins and their significance in regulating signaling events involving small GTPases

Structural, Stability, Dynamic and Binding Properties of the ALS-Causing T46I Mutant of the hVAPB MSP Domain as Revealed by NMR and MD Simulations

T46I is the second mutation on the hVAPB MSP domain which was recently identified from non-Brazilian kindred to cause a familial amyotrophic lateral sclerosis (ALS). Here using CD, NMR and molecular dynamics (MD) simulations, we characterized the structure, stability, dynamics and binding capacity of the T46I-MSP domain. The results reveal: 1) unlike P56S which we previously showed to completely eliminate the native MSP structure, T46I leads to no significant disruption of the native secondary and tertiary structures, as evidenced from its far-UV CD spectrum, as well as Cα and Cβ NMR chemical shifts. 2) Nevertheless, T46I does result in a reduced thermodynamic stability and loss of the cooperative urea-unfolding transition. As such, the T46I-MSP domain is more prone to aggregation than WT at high protein concentrations and temperatures in vitro, which may become more severe in the crowded cellular environments. 3) T46I only causes a 3-fold affinity reduction to the Nir2 peptide, but a significant elimination of its binding to EphA4. 4) EphA4 and Nir2 peptide appear to have overlapped binding interfaces on the MSP domain, which strongly implies that two signaling networks may have a functional interplay in vivo. 5) As explored by both H/D exchange and MD simulations, the MSP domain is very dynamic, with most loop residues and many residues on secondary structures highly fluctuated or/and exposed to bulk solvent. Although T46I does not alter overall dynamics, it does trigger increased dynamics of several local regions of the MSP domain which are implicated in binding to EphA4 and Nir2 peptide. Our study provides the structural and dynamic understanding of the T46I-causing ALS; and strongly highlights the possibility that the interplay of two signaling networks mediated by the FFAT-containing proteins and Eph receptors may play a key role in ALS pathogenesis

Diffusion-Driven Looping Provides a Consistent Framework for Chromatin Organization

Chromatin folding inside the interphase nucleus of eukaryotic cells is done on multiple scales of length and time. Despite recent progress in understanding the folding motifs of chromatin, the higher-order structure still remains elusive. Various experimental studies reveal a tight connection between genome folding and function. Chromosomes fold into a confined subspace of the nucleus and form distinct territories. Chromatin looping seems to play a dominant role both in transcriptional regulation as well as in chromatin organization and has been assumed to be mediated by long-range interactions in many polymer models. However, it remains a crucial question which mechanisms are necessary to make two chromatin regions become co-located, i.e. have them in spatial proximity. We demonstrate that the formation of loops can be accomplished solely on the basis of diffusional motion. The probabilistic nature of temporary contacts mimics the effects of proteins, e.g. transcription factors, in the solvent. We establish testable quantitative predictions by deriving scale-independent measures for comparison to experimental data. In this Dynamic Loop (DL) model, the co-localization probability of distant elements is strongly increased compared to linear non-looping chains. The model correctly describes folding into a confined space as well as the experimentally observed cell-to-cell variation. Most importantly, at biological densities, model chromosomes occupy distinct territories showing less inter-chromosomal contacts than linear chains. Thus, dynamic diffusion-based looping, i.e. gene co-localization, provides a consistent framework for chromatin organization in eukaryotic interphase nuclei

Unique Structure and Dynamics of the EphA5 Ligand Binding Domain Mediate Its Binding Specificity as Revealed by X-ray Crystallography, NMR and MD Simulations

10.1371/journal.pone.0074040PLoS ONE89-POLN

Study of e+e−→ppˉe^+e^- \rightarrow p\bar{p} in the vicinity of ψ(3770)\psi(3770)

Using 2917 $\rm{pb}^{-1}$ of data accumulated at 3.773~$\rm{GeV}$, 44.5~$\rm{pb}^{-1}$ of data accumulated at 3.65~$\rm{GeV}$ and data accumulated during a $\psi(3770)$ line-shape scan with the BESIII detector, the reaction $e^+e^-\rightarrow p\bar{p}$ is studied considering a possible interference between resonant and continuum amplitudes. The cross section of $e^+e^-\rightarrow\psi(3770)\rightarrow p\bar{p}$, $\sigma(e^+e^-\rightarrow\psi(3770)\rightarrow p\bar{p})$, is found to have two solutions, determined to be ($0.059\pm0.032\pm0.012$) pb with the phase angle $\phi = (255.8\pm37.9\pm4.8)^\circ$ ($<$0.11 pb at the 90% confidence level), or $\sigma(e^+e^-\rightarrow\psi(3770)\rightarrow p\bar{p}) = (2.57\pm0.12\pm0.12$) pb with $\phi = (266.9\pm6.1\pm0.9)^\circ$ both of which agree with a destructive interference. Using the obtained cross section of $\psi(3770)\rightarrow p\bar{p}$, the cross section of $p\bar{p}\rightarrow \psi(3770)$, which is useful information for the future PANDA experiment, is estimated to be either ($9.8\pm5.7$) nb ($<17.2$ nb at 90% C.L.) or $(425.6\pm42.9)$ nb

Knotted vs. Unknotted Proteins: Evidence of Knot-Promoting Loops

Knotted proteins, because of their ability to fold reversibly in the same topologically entangled conformation, are the object of an increasing number of experimental and theoretical studies. The aim of the present investigation is to assess, on the basis of presently available structural data, the extent to which knotted proteins are isolated instances in sequence or structure space, and to use comparative schemes to understand whether specific protein segments can be associated to the occurrence of a knot in the native state. A significant sequence homology is found among a sizeable group of knotted and unknotted proteins. In this family, knotted members occupy a primary sub-branch of the phylogenetic tree and differ from unknotted ones only by additional loop segments. These "knot-promoting" loops, whose virtual bridging eliminates the knot, are found in various types of knotted proteins. Valuable insight into how knots form, or are encoded, in proteins could be obtained by targeting these regions in future computational studies or excision experiments