Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments and find their corresponding long-time, asymptotic behaviors. The generally anomalous diffusive regimes of the particles are classified, and their dependence on the friction coefficient and the characteristics of the noises is analyzed in detail. The asymptotic predictions are confirmed by exact solutions for two examples.Comment: 15 page

Substantiation of the choice diversification strategy for ensuring the safety of the enterprise activity

The development of diversification enables the enterprise to provide economic security, achieve competitive advantages and minimise the risks of its activities. The research in the article is divided into three main blocks: In the first, the theoretical foundations for substantiating the choice of strategy for diversification of the production enterprise were summarized. The second proposes a methodologyof technology of choice of production strategies for ensuring the safety of the enterprise activity. The third block contains the development of recommendations to justify the choice of diversification strategy:the mechanism of formation and realization of diversification policy of the enterprise is offered;the use of the peer review method to justify the choice of diversification strategy is clearly presented (possible directions of strategy of diversification of activity are identified and the most promising directions of strategy of diversification of activity of investigated enterprise are selected by the method of a priori ranking);developed the methodological foundations for managing the diversification strategies of an industrial enterprise, which is a necessary element of the systematic support of the strategy of diversification of the enterprise activity (proposed an integrated algorithm for managing the diversification strategies of industrial enterprises; a fragment of the matrix of the choice of the type of diversification was developed, based on the goals and motivational reasons;the hierarchical structure of the decision-making system for the choice of rational diversification strategy is proposed and the scale of values of confidence coefficients is developed

Distinct Type of Transmission Barrier Revealed by Study of Multiple Prion Determinants of Rnq1

Prions are self-propagating protein conformations. Transmission of the prion state between non-identical proteins, e.g. between homologous proteins from different species, is frequently inefficient. Transmission barriers are attributed to sequence differences in prion proteins, but their underlying mechanisms are not clear. Here we use a yeast Rnq1/[PIN+]-based experimental system to explore the nature of transmission barriers. [PIN+], the prion form of Rnq1, is common in wild and laboratory yeast strains, where it facilitates the appearance of other prions. Rnq1's prion domain carries four discrete QN-rich regions. We start by showing that Rnq1 encompasses multiple prion determinants that can independently drive amyloid formation in vitro and transmit the [PIN+] prion state in vivo. Subsequent analysis of [PIN+] transmission between Rnq1 fragments with different sets of prion determinants established that (i) one common QN-rich region is required and usually sufficient for the transmission; (ii) despite identical sequences of the common QNs, such transmissions are impeded by barriers of different strength. Existence of transmission barriers in the absence of amino acid mismatches in transmitting regions indicates that in complex prion domains multiple prion determinants act cooperatively to attain the final prion conformation, and reveals transmission barriers determined by this cooperative fold

Prion Formation and Polyglutamine Aggregation Are Controlled by Two Classes of Genes

Prions are self-perpetuating aggregated proteins that are not limited to mammalian systems but also exist in lower eukaryotes including yeast. While much work has focused around chaperones involved in prion maintenance, including Hsp104, little is known about factors involved in the appearance of prions. De novo appearance of the [PSI+] prion, which is the aggregated form of the Sup35 protein, is dramatically enhanced by transient overexpression of SUP35 in the presence of the prion form of the Rnq1 protein, [PIN+]. When fused to GFP and overexpressed in [ps−] [PIN+] cells, Sup35 forms fluorescent rings, and cells with these rings bud off [PSI+] daughters. We investigated the effects of over 400 gene deletions on this de novo induction of [PSI+]. Two classes of gene deletions were identified. Class I deletions (bug1Δ, bem1Δ, arf1Δ, and hog1Δ) reduced the efficiency of [PSI+] induction, but formed rings normally. Class II deletions (las17Δ, vps5Δ, and sac6Δ) inhibited both [PSI+] induction and ring formation. Furthermore, class II deletions reduced, while class I deletions enhanced, toxicity associated with the expanded glutamine repeats of the huntingtin protein exon 1 that causes Huntington's disease. This suggests that prion formation and polyglutamine aggregation involve a multi-phase process that can be inhibited at different steps.National Institutes of Health (U.S.) (grant GM56350)National Institutes of Health (U.S.) (NSRA F32 postdoctoral fellowship GM072340)National Institutes of Health (U.S.) (grant GM25874)Howard Hughes Medical Institut

[PSI+] Maintenance Is Dependent on the Composition, Not Primary Sequence, of the Oligopeptide Repeat Domain

[PSI+], the prion form of the yeast Sup35 protein, results from the structural conversion of Sup35 from a soluble form into an infectious amyloid form. The infectivity of prions is thought to result from chaperone-dependent fiber cleavage that breaks large prion fibers into smaller, inheritable propagons. Like the mammalian prion protein PrP, Sup35 contains an oligopeptide repeat domain. Deletion analysis indicates that the oligopeptide repeat domain is critical for [PSI+] propagation, while a distinct region of the prion domain is responsible for prion nucleation. The PrP oligopeptide repeat domain can substitute for the Sup35 oligopeptide repeat domain in supporting [PSI+] propagation, suggesting a common role for repeats in supporting prion maintenance. However, randomizing the order of the amino acids in the Sup35 prion domain does not block prion formation or propagation, suggesting that amino acid composition is the primary determinant of Sup35's prion propensity. Thus, it is unclear what role the oligopeptide repeats play in [PSI+] propagation: the repeats could simply act as a non-specific spacer separating the prion nucleation domain from the rest of the protein; the repeats could contain specific compositional elements that promote prion propagation; or the repeats, while not essential for prion propagation, might explain some unique features of [PSI+]. Here, we test these three hypotheses and show that the ability of the Sup35 and PrP repeats to support [PSI+] propagation stems from their amino acid composition, not their primary sequences. Furthermore, we demonstrate that compositional requirements for the repeat domain are distinct from those of the nucleation domain, indicating that prion nucleation and propagation are driven by distinct compositional features

Localization of HET-S to the Cell Periphery, Not to [Het-s] Aggregates, Is Associated with [Het-s]–HET-S Toxicity

Prion diseases are associated with accumulation of the amyloid form of the prion protein, but the mechanisms of toxicity are unknown. Amyloid toxicity is also associated with fungal prions. In Podospora anserina, the simultaneous presence of [Het-s] prion and its allelic protein HET-S causes cell death in a self-/nonself-discrimination process. Here, using the prion form of a fragment of HET-s ([PrD(157)(+)]), we show that [Het-s]–HET-S toxicity can be faithfully recapitulated in yeast. Overexpression of Hsp40 chaperone, Sis1, rescues this toxicity by curing cells of [PrD(157)(+)]. We find no evidence for toxic [PrD(157)(+)] conformers in the presence of HET-S. Instead, [PrD(157)(+)] appears to seed HET-S to accumulate at the cell periphery and to form aggregates distinct from visible [PrD(157)(+)] aggregates. Furthermore, HET-S mutants that cause HET-S to be sequestered into [PrD(157)(+)] prion aggregates are not toxic. The localization of HET-S at the cell periphery and its association with cell death was also observed in the native host Podospora anserina. Thus, upon interaction with [Het-s], HET-S localizes to the cell periphery, and this relocalization, rather than the formation of mixed HET-s/HET-S aggregates, is associated with toxicity