The mean velocity of two-state models of molecular motor

The motion of molecular motor is essential to the biophysical functioning of living cells. In principle, this motion can be regraded as a multiple chemical states process. In which, the molecular motor can jump between different chemical states, and in each chemical state, the motor moves forward or backward in a corresponding potential. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping models or by several coupled Fokker-Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest cases: in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, we find that the mean velocity of molecular motor might be nonzero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is energy input to the molecular motor. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two states, but also on the transition rates between the two chemical states

Noncommutative waves have infinite propagation speed

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.Comment: 15 pages, references adde

The effects of financialisation and financial development on investment: Evidence from firm-level data in Europe

In this paper we estimate the effects of financialization on physical investment in selected western European countries using panel data based on the balance-sheets of publicly listed non-financial companies (NFCs) supplied by Worldscope for the period 1995-2015. We find robust evidence of an adverse effect of both financial payments (interests and dividends) and financial incomes on investment in fixed assets by the NFCs. This finding is robust for both the pool of all Western European firms and single country estimations. The negative impacts of financial incomes are non-linear with respect to the companies’ size: financial incomes crowd-out investment in large companies, and have a positive effect on the investment of only small, relatively more credit-constrained companies. Moreover, we find that a higher degree of financial development is associated with a stronger negative effect of financial incomes on companies’ investment. This finding challenges the common wisdom on ‘finance-growth nexus’. Our findings support the ‘financialization thesis’ that the increasing orientation of the non-financial sector towards financial activities is ultimately leading to lower physical investment, hence to stagnant or fragile growth, as well as long term stagnation in productivity

The age of anxiety? It depends where you look: changes in STAI trait anxiety, 1970–2010

Purpose Population-level surveys suggest that anxiety has been increasing in several nations, including the USA and UK. We sought to verify the apparent anxiety increases by looking for systematic changes in mean anxiety questionnaire scores from research publications. Methods We analyzed all available mean State–Trait Anxiety Inventory scores published between 1970 and 2010. We collected 1703 samples, representing more than 205,000 participants from 57 nations. Results Results showed a significant anxiety increase worldwide, but the pattern was less clear in many individual nations. Our analyses suggest that any increase in anxiety in the USA and Canada may be limited to students, anxiety has decreased in the UK, and has remained stable in Australia. Conclusions Although anxiety may have increased worldwide, it might not be increasing as dramatically as previously thought, except in specific populations, such as North American students. Our results seem to contradict survey results from the USA and UK in particular. We do not claim that our results are more reliable than those of large population surveys. However, we do suggest that mental health surveys and other governmental sources of disorder prevalence data may be partially biased by changing attitudes toward mental health: if respondents are more aware and less ashamed of their anxiety, they are more likely to report it to survey takers. Analyses such as ours provide a useful means of double-checking apparent trends in large population surveys

Kank Is an EB1 Interacting Protein that Localises to Muscle-Tendon Attachment Sites in Drosophila

Little is known about how microtubules are regulated in different cell types during development. EB1 plays a central role in the regulation of microtubule plus ends. It directly binds to microtubule plus ends and recruits proteins which regulate microtubule dynamics and behaviour. We report the identification of Kank, the sole Drosophila orthologue of human Kank proteins, as an EB1 interactor that predominantly localises to embryonic attachment sites between muscle and tendon cells. Human Kank1 was identified as a tumour suppressor and has documented roles in actin regulation and cell polarity in cultured mammalian cells. We found that Drosophila Kank binds EB1 directly and this interaction is essential for Kank localisation to microtubule plus ends in cultured cells. Kank protein is expressed throughout fly development and increases during embryogenesis. In late embryos, it accumulates to sites of attachment between muscle and epidermal cells. A kank deletion mutant was generated. We found that the mutant is viable and fertile without noticeable defects. Further analysis showed that Kank is dispensable for muscle function in larvae. This is in sharp contrast to C. elegans in which the Kank orthologue VAB-19 is required for development by stabilising attachment structures between muscle and epidermal cells

Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions

The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling limit in the noncommutative case, which turns out to be the hierarchy of a `pseudodual chiral model' in 2+1 dimensions (`pseudodual' to a hierarchy extending Ward's (modified) integrable chiral model). Applying the scaling procedure to a method generating exact solutions of a matrix (potential) KP hierarchy from solutions of a matrix linear heat hierarchy, leads to a corresponding method that generates exact solutions of the matrix dispersionless potential KP hierarchy, i.e. the pseudodual chiral model hierarchy. We use this result to construct classes of exact solutions of the su(m) pseudodual chiral model in 2+1 dimensions, including various multiple lump configurations.Comment: 37 pages, 10 figures, 2nd version: some extensions (Fig 3, Appendix A, additional references), 3rd version: some minor changes, additional reference

Ectopic A-lattice seams destabilize microtubules

Natural microtubules typically include one A-lattice seam within an otherwise helically symmetric B-lattice tube. It is currently unclear how A-lattice seams influence microtubule dynamic instability. Here we find that including extra A-lattice seams in GMPCPP microtubules, structural analogues of the GTP caps of dynamic microtubules, destabilizes them, enhancing their median shrinkage rate by >20-fold. Dynamic microtubules nucleated by seeds containing extra A-lattice seams have growth rates similar to microtubules nucleated by B-lattice seeds, yet have increased catastrophe frequencies at both ends. Furthermore, binding B-lattice GDP microtubules to a rigor kinesin surface stabilizes them against shrinkage, whereas microtubules with extra A-lattice seams are stabilized only slightly. Our data suggest that introducing extra A-lattice seams into dynamic microtubules destabilizes them by destabilizing their GTP caps. On this basis, we propose that the single A-lattice seam of natural B-lattice MTs may act as a trigger point, and potentially a regulation point, for catastrophe

Kebab: Kinetochore and EB1 Associated Basic Protein That Dynamically Changes Its Localisation during Drosophila Mitosis

Microtubule plus ends are dynamic ends that interact with other cellular structures. Microtubule plus end tracking proteins are considered to play important roles in the regulation of microtubule plus ends. Recent studies revealed that EB1 is the central regulator for microtubule plus end tracking proteins by recruiting them to microtubule plus ends through direct interaction. Here we report the identification of a novel Drosophila protein, which we call Kebab (kinetochore and EB1 associated basic protein), through in vitro expression screening for EB1-interacting proteins. Kebab fused to GFP shows a novel pattern of dynamic localisation in mitosis. It localises to kinetochores weakly in metaphase and accumulates progressively during anaphase. In telophase, it associates with microtubules in central-spindle and centrosomal regions. The localisation to kinetochores depends on microtubules. The protein has a domain most similar to the atypical CH domain of Ndc80, and a coiled-coil domain. The interaction with EB1 is mediated by two SxIP motifs but is not required for the localisation. Depletion of Kebab in cultured cells by RNA interference did not show obvious defects in mitotic progression or microtubule organisation. Generation of mutants lacking the kebab gene indicated that Kebab is dispensable for viability and fertility

Noncommutative Burgers Equation

We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopf transformation and succeed in the linearization of it. The linearized equation is the (noncommutative) diffusion equation and exactly solved. We also discuss the properties of some exact solutions. The result shows that the noncommutative Burgers equation is completely integrable even though it contains infinite number of time derivatives. Furthermore, we derive the noncommutative Burgers equation from the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, we present a noncommutative version of the Burgers hierarchy by both the Lax-pair generating technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato theory and the integrability added, references added, version to appear in J. Phys.

Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised proton

Measurements of the Collins and Sivers asymmetries for charged pions and charged and neutral kaons produced in semi-inclusive deep-inelastic scattering of high energy muons off transversely polarised protons are presented. The results were obtained using all the available COMPASS proton data, which were taken in the years 2007 and 2010. The Collins asymmetries exhibit in the valence region a non-zero signal for pions and there are hints of non-zero signal also for kaons. The Sivers asymmetries are found to be positive for positive pions and kaons and compatible with zero otherwise.Comment: 15 pages, 13 figures and 1 tabl