Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate q kappa for binding (with a binding strength kappa); except for the case of no binding kappa=0 the presence of the chaperones give rise to an effective force that drives the translocation process. Based on a (2+1) variate master equation, we study in detail the coupled dynamics of diffusive translocation and (partial) rectification by the binding proteins. In particular, we calculate the mean translocation time as a function of the various physical parameters.Comment: 22 pages, 5 figures, IOP styl

Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolarComment: 4 pages, 1 figure, REVTeX4, accepted to Phys Rev Lett, some typos correcte

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.Comment: 12 pages, 8 figure

Bulk-mediated surface diffusion on a cylinder: propagators and crossovers

We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, in particular, a saturation regime characteristic for the cylindrical geometry. This saturation, however, in a finite system is not terminal but eventually turns over to normal surface diffusion. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.Comment: 4 pages REVTeX4, 2 figure

Continuous time random walk with correlated waiting times

Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly decaying persistent power-law correlations between the waiting times as two generic examples and obtain the corresponding mean squared displacements as functions of time. In the case of exponential-type correlations the (sub)diffusion at short times is slower than in the absence of correlations. At long times the behavior of the mean squared displacement is the same as in uncorrelated CTRW. For power-law correlations we find subdiffusion characterized by the same exponent at all times, which appears to be smaller than the one in uncorrelated CTRW. Interestingly, in the limiting case of an extremely long power-law correlations, the (sub)diffusion exponent does not tend to zero, but is bounded from below by the subdiffusion exponent corresponding to a short time behavior in the case of exponential correlations

First passage and first hitting times of Lévy flights and Lévy walks

Abstract For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it (‘leapovers’), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed

Widespread white matter degeneration preceding the onset of dementia

Background—Brain atrophy in subjects with mild cognitive impairment (MCI) introduces partial volume effects, limiting the sensitivity of diffusion tensor imaging to white matter microstructural degeneration. Appropriate correction isolates microstructural effects in MCI that might be precursors of Alzheimer’s disease (AD). Methods—Forty-eight participants (18 MCI, 15 AD and 15 healthy controls) had MRI scans and clinical evaluations at baseline and follow-up after 36 month. 10 MCI subjects were diagnosed with AD at follow-up and 8 remained MCI. Free-water corrected measures on the white matter skeleton were compared between groups. Results—Free-water-corrected radial diffusivity, but not un-corrected radial diffusivity, was increased across the brain of the converted group compared to the non-converted group (P<0.05). The extent of increases was similar to that found comparing AD with controls. Conclusion—Partial volume elimination reveals microstructural alterations preceding dementia. These alterations may prove to be an effective and feasible early biomarker of AD

Bosutinib in Resistant and Intolerant Pediatric Patients With Chronic Phase Chronic Myeloid Leukemia:Results From the Phase I Part of Study ITCC054/COG AAML1921

PURPOSE Bosutinib is approved for adults with chronic myeloid leukemia (CML): 400 mg once daily in newly diagnosed (ND); 500 mg once daily in resistant/intolerant (R/I) patients. Bosutinib has a different tolerability profile than other tyrosine kinase inhibitors (TKIs) and potentially less impact on growth (preclinical data). The primary objective of this first-in-child trial was to determine the recommended phase II dose (RP2D) for pediatric R/I and ND patients. PATIENTS AND METHODS In the phase I part of this international, open-label trial (ClinicalTrials.gov identifier: NCT04258943), children age 1-18 years with R/I (per European LeukemiaNet 2013) Ph+ CML were enrolled using a 6 + 4 design, testing 300, 350, and 400 mg/m2 once daily with food. The RP2D was the dose resulting in 0/6 or 1/10 dose-limiting toxicities (DLTs) during the first cycle and achieving adult target AUC levels for the respective indication. As ND participants were only enrolled in phase II, the ND RP2D was selected based on data from R/I patients. Results Thirty patients were enrolled; 27 were evaluable for DLT: six at 300 mg/m2, 11 at 350 mg/m2 (one DLT), and 10 at 400 mg/m2 (one DLT). The mean AUCs at 300 mg/m2, 350 mg/m2, and 400 mg/m2 were 2.20 g h/mL, 2.52 g h/mL, and 2.66 g h/mL, respectively. The most common adverse event was diarrhea (93%; ≥grade 3: 11%). Seven patients stopped because of intolerance and eight because of insufficient response. Complete cytogenetic and major molecular response to bosutinib appeared comparable with other published phase I/II trials with second-generation TKIs in children. CONCLUSION Bosutinib was safe and effective. The pediatric RP2D was 400 mg/m2 once daily (max 600 mg/d) with food in R/I patients and 300 mg/m2 once daily (max 500 mg/d) with food in ND patients, which achieved targeted exposures as per adult experience.</p