The modified Yule-Walker method for multidimensional infinite-variance periodic autoregressive model of order 1

The time series with periodic behavior, such as the periodic autoregressive (PAR) models belonging to the class of the periodically correlated processes, are present in various real applications. In the literature, such processes were considered in different directions, especially with the Gaussian-distributed noise. However, in most of the applications, the assumption of the finite-variance distribution seems to be too simplified. Thus, one can consider the extensions of the classical PAR model where the non-Gaussian distribution is applied. In particular, the Gaussian distribution can be replaced by the infinite-variance distribution, e.g. by the $\alpha-$stable distribution. In this paper, we focus on the multidimensional $\alpha-$stable PAR time series models. For such models, we propose a new estimation method based on the Yule-Walker equations. However, since for the infinite-variance case the covariance does not exist, thus it is replaced by another measure, namely the covariation. In this paper we propose to apply two estimators of the covariation measure. The first one is based on moment representation (moment-based) while the second one - on the spectral measure representation (spectral-based). The validity of the new approaches are verified using the Monte Carlo simulations in different contexts, including the sample size and the index of stability of the noise. Moreover, we compare the moment-based covariation-based method with spectral-based covariation-based technique. Finally, the real data analysis is presented.Comment: 31 pages, 17 figure

Nuclear magnetic resonance as a quantitative tool to study interactions in biomacromolecules

High-resolution nuclear magnetic resonance (NMR) has emerged as one of the most versatile tools for the quantitative study of structure, kinetics, and thermodynamics of biomolecules and their interactions at atomic resolution. Traditionally, nuclear Overhauser enhancements (NOEs) and chemical shift perturbation methods are used to determine molecular geometries and to identify contact surfaces, but more recently, weak anisotropic orientation, anisotropic diffusion, and scalar couplings across hydrogen bonds provide additional information. Examples of such technologies are shown as applied to the quantitative characterization of function and thermodynamics of several biomacromolecules. In particular, (1) the structural and dynamical changes of the TipA multidrug resistance protein are followed upon antibiotic binding, (2) the trimer-monomer equilibrium and thermal unfolding of foldon, a small and very efficient trimerization domain of the T4 phagehead, is described in atomic detail, and (3) the changes of individual protein hydrogen bonds during thermal unfolding are quantitatively followed by scalar couplings across hydrogen bond

High dimensional and high resolution pulse sequences for backbone resonance assignment of intrinsically disordered proteins

Four novel 5D (HACA(N)CONH, HNCOCACB, (HACA)CON(CA)CONH, (H)NCO(NCA)CONH), and one 6D ((H)NCO(N)CACONH) NMR pulse sequences are proposed. The new experiments employ non-uniform sampling that enables achieving high resolution in indirectly detected dimensions. The experiments facilitate resonance assignment of intrinsically disordered proteins. The novel pulse sequences were successfully tested using δ subunit (20 kDa) of Bacillus subtilis RNA polymerase that has an 81-amino acid disordered part containing various repetitive sequences

Biological activity differences between TGF-β1 and TGF-β3 correlate with differences in the rigidity and arrangement of their component monomers

[Image: see text] TGF-β1, -β2, and -β3 are small, secreted signaling proteins. They share 71–80% sequence identity and signal through the same receptors, yet the isoform-specific null mice have distinctive phenotypes and are inviable. The replacement of the coding sequence of TGF-β1 with TGF-β3 and TGF-β3 with TGF-β1 led to only partial rescue of the mutant phenotypes, suggesting that intrinsic differences between them contribute to the requirement of each in vivo. Here, we investigated whether the previously reported differences in the flexibility of the interfacial helix and arrangement of monomers was responsible for the differences in activity by generating two chimeric proteins in which residues 54–75 in the homodimer interface were swapped. Structural analysis of these using NMR and functional analysis using a dermal fibroblast migration assay showed that swapping the interfacial region swapped both the conformational preferences and activity. Conformational and activity differences were also observed between TGF-β3 and a variant with four helix-stabilizing residues from TGF-β1, suggesting that the observed changes were due to increased helical stability and the altered conformation, as proposed. Surface plasmon resonance analysis showed that TGF-β1, TGF-β3, and variants bound the type II signaling receptor, TβRII, nearly identically, but had small differences in the dissociation rate constant for recruitment of the type I signaling receptor, TβRI. However, the latter did not correlate with conformational preference or activity. Hence, the difference in activity arises from differences in their conformations, not their manner of receptor binding, suggesting that a matrix protein that differentially binds them might determine their distinct activities

The p12 Domain Is Unstructured in a Murine Leukemia Virus p12-CAN Gag Construct

The Gag polyproteins of gammaretroviruses contain a conserved p12 domain between MA and CA that plays critical roles in virus assembly, reverse transcription and nuclear integration. Here we show using nuclear magnetic resonance, that p12 is unstructured in a Moloney murine leukemia virus (MMLV) Gag fragment that includes the N-terminal domain of CA (p12-CAN). Furthermore, no long range interactions were observed between the domains, as has been previously predicted. Flexibility appears to be a common feature of Gag “late” domains required for virus release during budding. Residues near the N-terminus of CAN that form a β-hairpin in the mature CA protein are unfolded in p12-CAN, consistent with proposals that hairpin formation helps trigger capsid assembly

Signal enhancement in protein NMR using the spin-noise tuning optimum

We have assessed the potential of an alternative probe tuning strategy based on the spin-noise response for application in common high-resolution multi-dimensional biomolecular NMR experiments with water signal suppression on aqueous and salty samples. The method requires the adjustment of the optimal tuning condition, which may be offset by several 100 kHz from the conventional tuning settings using the noise response of the water protons as an indicator. Although the radio frequency-pulse durations are typically longer under such conditions, signal-to-noise gains of up to 22% were achieved. At salt concentrations up to 100 mM a substantial sensitivity gain was observed

Molecular Design, Functional Characterization and Structural Basis of a Protein Inhibitor Against the HIV-1 Pathogenicity Factor Nef

Increased spread of HIV-1 and rapid emergence of drug resistance warrants development of novel antiviral strategies. Nef, a critical viral pathogenicity factor that interacts with host cell factors but lacks enzymatic activity, is not targeted by current antiviral measures. Here we inhibit Nef function by simultaneously blocking several highly conserved protein interaction surfaces. This strategy, referred to as “wrapping Nef”, is based on structure-function analyses that led to the identification of four target sites: (i) SH3 domain interaction, (ii) interference with protein transport processes, (iii) CD4 binding and (iv) targeting to lipid membranes. Screening combinations of Nef-interacting domains, we developed a series of small Nef interacting proteins (NIs) composed of an SH3 domain optimized for binding to Nef, fused to a sequence motif of the CD4 cytoplasmic tail and combined with a prenylation signal for membrane association. NIs bind to Nef in the low nM affinity range, associate with Nef in human cells and specifically interfere with key biological activities of Nef. Structure determination of the Nef-inhibitor complex reveals the molecular basis for binding specificity. These results establish Nef-NI interfaces as promising leads for the development of potent Nef inhibitors

Folding Circular Permutants of IL-1β: Route Selection Driven by Functional Frustration

Interleukin-1β (IL-1β) is the cytokine crucial to inflammatory and immune response. Two dominant routes are populated in the folding to native structure. These distinct routes are a result of the competition between early packing of the functional loops versus closure of the β-barrel to achieve efficient folding and have been observed both experimentally and computationally. Kinetic experiments on the WT protein established that the dominant route is characterized by early packing of geometrically frustrated functional loops. However, deletion of one of the functional loops, the β-bulge, switches the dominant route to an alternative, yet, as accessible, route, where the termini necessary for barrel closure form first. Here, we explore the effect of circular permutation of the WT sequence on the observed folding landscape with a combination of kinetic and thermodynamic experiments. Our experiments show that while the rate of formation of permutant protein is always slower than that observed for the WT sequence, the region of initial nucleation for all permutants is similar to that observed for the WT protein and occurs within a similar timescale. That is, even permutants with significant sequence rearrangement in which the functional-nucleus is placed at opposing ends of the polypeptide chain, fold by the dominant WT “functional loop-packing route”, despite the entropic cost of having to fold the N- and C- termini early. Taken together, our results indicate that the early packing of the functional loops dominates the folding landscape in active proteins, and, despite the entropic penalty of coalescing the termini early, these proteins will populate an entropically unfavorable route in order to conserve function. More generally, circular permutation can elucidate the influence of local energetic stabilization of functional regions within a protein, where topological complexity creates a mismatch between energetics and topology in active proteins

Automated NMR relaxation dispersion data analysis using NESSY

<p>Abstract</p> <p>Background</p> <p>Proteins are dynamic molecules with motions ranging from picoseconds to longer than seconds. Many protein functions, however, appear to occur on the micro to millisecond timescale and therefore there has been intense research of the importance of these motions in catalysis and molecular interactions. Nuclear Magnetic Resonance (NMR) relaxation dispersion experiments are used to measure motion of discrete nuclei within the micro to millisecond timescale. Information about conformational/chemical exchange, populations of exchanging states and chemical shift differences are extracted from these experiments. To ensure these parameters are correctly extracted, accurate and careful analysis of these experiments is necessary.</p> <p>Results</p> <p>The software introduced in this article is designed for the automatic analysis of relaxation dispersion data and the extraction of the parameters mentioned above. It is written in Python for multi platform use and highest performance. Experimental data can be fitted to different models using the Levenberg-Marquardt minimization algorithm and different statistical tests can be used to select the best model. To demonstrate the functionality of this program, synthetic data as well as NMR data were analyzed. Analysis of these data including the generation of plots and color coded structures can be performed with minimal user intervention and using standard procedures that are included in the program.</p> <p>Conclusions</p> <p>NESSY is easy to use open source software to analyze NMR relaxation data. The robustness and standard procedures are demonstrated in this article.</p

Backbone and side chain NMR assignments for the intrinsically disordered cytoplasmic domain of human neuroligin-3

Neuroligins act as heterophilic adhesion molecules at neuronal synapses. Their cytoplasmic domains interact with synaptic scaffolding proteins, and have been shown to be intrinsically disordered. Here we report the backbone and side chain 1H, 13C and 15N resonance assignments for the cytoplasmic domain of human neuroligin 3