Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments ( for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.

Dinâmica de modelos minimalistas de solvente em reações de transferência de elétrons: aplicação à experimentos de única molécula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Neurogranin controls the spatiotemporal pattern of postsynaptic Ca2+/CaM signaling.

Neurogranin (Ng) is a postsynaptic IQ-motif containing protein that accelerates Ca(2+) dissociation from calmodulin (CaM), a key regulator of long-term potentiation and long-term depression in CA1 pyramidal neurons. The exact physiological role of Ng, however, remains controversial. Two genetic knockout studies of Ng showed opposite outcomes in terms of the induction of synaptic plasticity. To understand its function, we test the hypothesis that Ng could regulate the spatial range of action of Ca(2+)/CaM based on its ability to accelerate the dissociation of Ca(2+) from CaM. Using a mathematical model constructed on the known biochemistry of Ng, we calculate the cycle time that CaM molecules alternate between the fully Ca(2+) saturated state and the Ca(2+) unbound state. We then use these results and include diffusion of CaM to illustrate the impact that Ng has on modulating the spatial profile of Ca(2+)-saturated CaM within a model spine compartment. Finally, the first-passage time of CaM to transition from the Ca(2+)-free state to the Ca(2+)-saturated state was calculated with or without Ng present. These analyses suggest that Ng regulates the encounter rate between Ca(2+) saturated CaM and its downstream targets during postsynaptic Ca(2+) transients.

(Tables 1,2) Tracking records and space use statistics of polar bears (Ursus maritimus) in Storfjorden, Svalbard

Arctic sea ice is declining rapidly, making it vital to understand the importance of different types of sea ice for ice-dependent species such as polar bears Ursus maritimus. In this study we used GPS telemetry (25 polar bear tracks obtained in Svalbard, Norway, during spring) and high-resolution synthetic aperture radar (SAR) sea-ice data to investigate fine-scale space use by female polar bears. Space use patterns differed according to reproductive state; females with cubs of the year (COYs) had smaller home ranges and used fast-ice areas more frequently than lone females. First-passage time (FPT) analysis revealed that females with COYs displayed significantly longer FPTs near (<10 km) glacier fronts than in other fast-ice areas; lone females also increased their FPTs in such areas, but they also frequently used drifting pack ice. These results clearly demonstrate the importance of fast-ice areas, in particular close to glacier fronts, especially for females with COYs. Access to abundant and predictable prey (ringed seal pups), energy conservation and reluctance to cross large open water areas are possible reasons for the observed patterns. However, glacier fronts are retracting in Svalbard, and declines in land-fast ice have been notable over the past decade. The eventual disappearance of these important habitats might become critical for the survival of polar bear cubs in Svalbard and other regions with similar habitat characteristics. Given the relatively small size of many fast-ice areas in Svalbard, the results observed in this study would not have been revealed using less accurate location data or lower-resolution sea-ice data.

Non-Arrhenius kinetics for the loop closure of a DNA hairpin

Intramolecular chain diffusion is an elementary process in the conformational fluctuations of the DNA hairpin-loop. We have studied the temperature and viscosity dependence of a model DNA hairpin-loop by FRET (fluorescence resonance energy transfer) fluctuation spectroscopy (FRETfs). Apparent thermodynamic parameters were obtained by analyzing the correlation amplitude through a two-state model and are consistent with steady-state fluorescence measurements. The kinetics of closing the loop show non-Arrhenius behavior, in agreement with theoretical prediction and other experimental measurements on peptide folding. The fluctuation rates show a fractional power dependence (β = 0.83) on the solution viscosity. A much slower intrachain diffusion coefficient in comparison to that of polypeptides was derived based on the first passage time theory of SSS [Szabo, A., Schulten, K. & Schulten, Z. (1980) J. Chem. Phys. 72, 4350–4357], suggesting that intrachain interactions, especially stacking interaction in the loop, might increase the roughness of the free energy surface of the DNA hairpin-loop.

Navigating uncertain waters: a critical review of inferring foraging behaviour from location and dive data in pinnipeds

In the last thirty years, the emergence and progression of biologging technology has led to great advances in marine predator ecology. Large databases of location and dive observations from biologging devices have been compiled for an increasing number of diving predator species (such as pinnipeds, sea turtles, seabirds and cetaceans), enabling complex questions about animal activity budgets and habitat use to be addressed. Central to answering these questions is our ability to correctly identify and quantify the frequency of essential behaviours, such as foraging. Despite technological advances that have increased the quality and resolution of location and dive data, accurately interpreting behaviour from such data remains a challenge, and analytical methods are only beginning to unlock the full potential of existing datasets. This review evaluates both traditional and emerging methods and presents a starting platform of options for future studies of marine predator foraging ecology, particularly from location and two-dimensional (time-depth) dive data. We outline the different devices and data types available, discuss the limitations and advantages of commonly-used analytical techniques, and highlight key areas for future research. We focus our review on pinnipeds - one of the most studied taxa of marine predators - but offer insights that will be applicable to other air-breathing marine predator tracking studies. We highlight that traditionally-used methods for inferring foraging from location and dive data, such as first-passage time and dive shape analysis, have important caveats and limitations depending on the nature of the data and the research question. We suggest that more holistic statistical techniques, such as state-space models, which can synthesise multiple track, dive and environmental metrics whilst simultaneously accounting for measurement error, offer more robust alternatives. Finally, we identify a need for more research to elucidate the role of physical oceanography, device effects, study animal selection, and developmental stages in predator behaviour and data interpretation.

Global and local contributions to the optical specification of time to contact: Observer sensitivity to composite tau

First-order time remaining until a moving observer will pass an environmental element is optically specified in two different ways. The specification provided by global tau (based on the pattern of change of angular bearing) requires that the element is stationary and that the direction of motion is accurately detected, whereas the specification provided by composite tau (based on the patterns of change of optical size and optical distance) does not require either of these. We obtained converging evidence,for our hypothesis. that observers are sensitive to composite tau in four experiments involving, relative judgments of, time to, passage with forced-choice methodology. Discrimination performance was enhanced in the presence of a local expansion component, while being unaffected when the detection of the direction of heading was impaired. Observers relied on the information carried in composite tau rather than on the information carried in its constituent components. Finally, performance was similar under conditions of observer motion and conditions of object motion. Because composite tau specifies first-order time remaining for a large number of situations, the different ways in which it may be detected are discussed.

A macroscopic kinetic model for DNA polymerase elongation and high-fidelity nucleotide election

The enzymatically catalyzed template-directed extension of ssDNA/primer complex is an impor-tant reaction of extraordinary complexity. The DNA polymerase does not merely facilitate the insertion of dNMP, but it also performs rapid screening of substrates to ensure a high degree of fidelity. Several kinetic studies have determined rate constants and equilibrium constants for the elementary steps that make up the overall pathway. The information is used to develop a macro-scopic kinetic model, using an approach described by Ninio [Ninio J., 1987. Alternative to the steady-state method: derivation of reaction rates from first-passage times and pathway probabili-ties. Proc. Natl. Acad. Sci. U.S.A. 84, 663–667]. The principle idea of the Ninio approach is to track a single template/primer complex over time and to identify the expected behavior. The average time to insert a single nucleotide is a weighted sum of several terms, in-cluding the actual time to insert a nucleotide plus delays due to polymerase detachment from ei-ther the ternary (template-primer-polymerase) or quaternary (+nucleotide) complexes and time delays associated with the identification and ultimate rejection of an incorrect nucleotide from the binding site. The passage times of all events and their probability of occurrence are ex-pressed in terms of the rate constants of the elementary steps of the reaction pathway. The model accounts for variations in the average insertion time with different nucleotides as well as the in-fluence of G+C content of the sequence in the vicinity of the insertion site. Furthermore the model provides estimates of error frequencies. If nucleotide extension is recognized as a compe-tition between successful insertions and time delaying events, it can be described as a binomial process with a probability distribution. The distribution gives the probability to extend a primer/template complex with a certain number of base pairs and in general it maps annealed complexes into extension products.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Development of an ultra-thin fibroin membrane for RPE cell transplantation

Purpose: One of the challenges associated with cell-based therapies for repairing the retina is the development of suitable materials on which to grow and transplant retinal cells. Using the ARPE-19 cell line, we have previously demonstrated the feasibility of growing RPE-derived cells on membranes prepared from the silk protein fibroin. The present study was aimed at developing a porous, ultra-thin fibroin membrane that might better support development of apical-basal polarity in culture, and to extend this work to primary cultures of human RPE cells. Methods: Ultra-thin fibroin membranes were prepared using a highly polished casting table coated with Topas® (a cyclic olefin copolymer) and a 1:0.03 aqueous solution of fibroin and PEO (Mv 900 000 g/mol). Following drying, the membranes were water annealed to make them water-stable, washed in water to remove PEO, sterilised by treatment with 95% ethanol, and washed extensively in saline. Primary cultures containing human RPE cells were established from donor posterior eye cups and maintained in DMEM/F12 medium supplemented with 10% fetal bovine serum and antibiotics. First passage cultures were seeded onto fibroin membranes pre-coated with vitronectin and grown for 6 weeks in medium supplemented with 1% serum. Comparative cultures were established on porous 1.0 µm pore PET membrane (Millipore) and using ARPE-19 cells. Results: The fibroin membranes displayed an average thickness of 3 µm and contained numerous dimples/pore-like structures of up to 3-5 µm in diameter. The primary cultures predominantly contained pigmented epithelial cells, but mesenchymal cells (presumed fibroblasts) were also often present. Passaged cultures appeared to attach equally well to either fibroin or PET membranes. Over time cells on either material adopted a more cobblestoned morphology. Conclusions: Progress has been made towards developing a porous ultra-thin fibroin membrane that supports cultivation of RPE cells. Further studies are required to determine the degree of membrane permeability and RPE polarity.