First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a Cα structure-based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well-separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non-native contact interactions in different folding scenarios. These findings strongly correlate with the protein free-energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins. © 2013 Wiley Periodicals, Inc.

Regimes de frustração ótima em enovelamento de proteínas com modelos baseado em estrutura

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Visualization of Protein Folding Funnels in Lattice Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estudo da interação não-nativa no enovelamento de proteínas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.

Studies of Protein-Protein and Protein-Water Interactions by Small Angle X-Ray Scattering, Terahertz Spectroscopy, ASMOS, And Computer Simulation

The protein folding problem has been one of the most challenging subjects in biological physics due to its complexity. Energy landscape theory based on statistical mechanics provides a thermodynamic interpretation of the protein folding process. We have been working to answer fundamental questions about protein-protein and protein-water interactions, which are very important for describing the energy landscape surface of proteins correctly. At first, we present a new method for computing protein-protein interaction potentials of solvated proteins directly from SAXS data. An ensemble of proteins was modeled by Metropolis Monte Carlo and Molecular Dynamics simulations, and the global X-ray scattering of the whole model ensemble was computed at each snapshot of the simulation. The interaction potential model was optimized and iterated by a Levenberg-Marquardt algorithm. Secondly, we report that terahertz spectroscopy directly probes hydration dynamics around proteins and determines the size of the dynamical hydration shell. We also present the sequence and pH-dependence of the hydration shell and the effect of the hydrophobicity. On the other hand, kinetic terahertz absorption (KITA) spectroscopy is introduced to study the refolding kinetics of ubiquitin and its mutants. KITA results are compared to small angle X-ray scattering, tryptophan fluorescence, and circular dichroism results. We propose that KITA monitors the rearrangement of hydrogen bonding during secondary structure formation. Finally, we present development of the automated single molecule operating system (ASMOS) for a high throughput single molecule detector, which levitates a single protein molecule in a 10 µm diameter droplet by the laser guidance. I also have performed supporting calculations and simulations with my own program codes.

Theory of unitarity bounds and low-energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarily. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K-l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.

A model for energy and morphology of crystalline grain boundaries with arbitrary geometric character

It has been well-established that interfaces in crystalline materials are key players in the mechanics of a variety of mesoscopic processes such as solidification, recrystallization, grain boundary migration, and severe plastic deformation. In particular, interfaces with complex morphologies have been observed to play a crucial role in many micromechanical phenomena such as grain boundary migration, stability, and twinning. Interfaces are a unique type of material defect in that they demonstrate a breadth of behavior and characteristics eluding simplified descriptions. Indeed, modeling the complex and diverse behavior of interfaces is still an active area of research, and to the author's knowledge there are as yet no predictive models for the energy and morphology of interfaces with arbitrary character. The aim of this thesis is to develop a novel model for interface energy and morphology that i) provides accurate results (especially regarding "energy cusp" locations) for interfaces with arbitrary character, ii) depends on a small set of material parameters, and iii) is fast enough to incorporate into large scale simulations.

In the first half of the work, a model for planar, immiscible grain boundary is formulated. By building on the assumption that anisotropic grain boundary energetics are dominated by geometry and crystallography, a construction on lattice density functions (referred to as "covariance") is introduced that provides a geometric measure of the order of an interface. Covariance forms the basis for a fully general model of the energy of a planar interface, and it is demonstrated by comparison with a wide selection of molecular dynamics energy data for FCC and BCC tilt and twist boundaries that the model accurately reproduces the energy landscape using only three material parameters. It is observed that the planar constraint on the model is, in some cases, over-restrictive; this motivates an extension of the model.

In the second half of the work, the theory of faceting in interfaces is developed and applied to the planar interface model for grain boundaries. Building on previous work in mathematics and materials science, an algorithm is formulated that returns the minimal possible energy attainable by relaxation and the corresponding relaxed morphology for a given planar energy model. It is shown that the relaxation significantly improves the energy results of the planar covariance model for FCC and BCC tilt and twist boundaries. The ability of the model to accurately predict faceting patterns is demonstrated by comparison to molecular dynamics energy data and experimental morphological observation for asymmetric tilt grain boundaries. It is also demonstrated that by varying the temperature in the planar covariance model, it is possible to reproduce a priori the experimentally observed effects of temperature on facet formation.

Finally, the range and scope of the covariance and relaxation models, having been demonstrated by means of extensive MD and experimental comparison, future applications and implementations of the model are explored.

Reaction Mechanisms of Crotonaldehyde Hydrogenation on Pt(111): Density Functional Theory and Microkinetic Modeling

The microkinetics based on density function theory (DFT) calculations is utilized to investigate the reaction mechanism of crotonaldehyde hydrogenation on Pt(111) in the free energy landscape. The dominant reaction channel of each hydrogenation product is identified. Each of them begins with the first surface hydrogenation of the carbonyl oxygen of crotonaldehyde on the surface. A new mechanism, 1,4-addition mechanism generating enols (butenol), which readily tautomerize to saturated aldehydes (butanal), is identified as a primary mechanism to yield saturated aldehydes instead of the 3,4-addition via direct hydrogenation of the ethylenic bond. The calculation results also show that the full hydrogenation product, butylalcohol, mainly stems from the deep hydrogenation of surface open-shell dihydrogenation intermediates. It is found that the apparent barriers of the dominant pathways to yield three final products are similar on P(111), which makes it difficult to achieve a high selectivity to the desired crotyl alcohol (COL).

Activity and coke formation of nickel and nickel carbide in dry reforming: A deactivation scheme from density functional theory

Dry reforming is a promising reaction to utilise the greenhouse gases CO2 and CH4. Nickel-based catalysts are the most popular catalysts for the reaction, and the coke formation on the catalysts is the main obstacle to the commercialisation of dry reforming. In this study, the whole reaction network of dry reformation on both flat and stepped nickel catalysts (Ni(111) and Ni(211)) as well as nickel carbide (flat: Ni3C(001); stepped: Ni3C(111)) is investigated using density functional theory calculations. The overall reaction energy profiles in the free energy landscape are obtained, and kinetic analyses are utilised to evaluate the activity of the four surfaces. By careful examination of our results, we find the following regarding the activity: (i) flat surfaces are more active than stepped surfaces for the dry reforming and (ii) metallic nickel catalysts are more active than those of nickel carbide, and therefore, the phase transformation from nickel to nickel carbide will reduce the activity. With respect to the coke formation, the following is found: (i) the coke formation probability can be measured by the rate ratio of CH oxidation pathway to C oxidation pathway (r(CH)/r(C)) and the barrier of CO dissociation, (ii) on Ni(111), the coke is unlikely to form, and (iii) the coke formations on the stepped surfaces of both nickel and nickel carbide can readily occur. A deactivation scheme, using which experimental results can be rationalised, is proposed. 

Game theory in sugarcane crop residue and available energy optimization

This work proposes a mathematical model to aid variety selection and planting quantity of sugarcane in order to reduce crop residues, maximize energy generated by this residue, and satisfy all the supply of the mill. We propose Linear Programming with two objective. The conflict between these objectives allows the use of the Nonzero-sum Game Theory. (C) 2003 Elsevier B.V. Ltd. All rights reserved.

Theory and calculation of the nonlinear energy transfer between sea waves in deep water /

"May 1982."

Reconnecting the interrupted landscape : a cultural landscape approach to Australian open-cut coal mining landscapes

In the late 20th century, a value-shift began to influence political thinking, recognising the need for environmentally, socially and culturally sustainable resource development. This shift entailed moves away from thinking of nature and culture as separate entities - The former existing merely to serve the latter. Cultural landscape theory recognises 'nature' as at once both 'natural', and as a 'cultural' construct. As such it may offer a framework through which to progress in the quest for 'sustainable development'. This 2005 Masters thesis makes a contribution to that quest by asking whether contemporary developments in cultural landscape theory can contribute to rehabilitation strategies for Australian open-cut coal mining landscapes, an examplar resource development landscape. A thematic historial overview of landscape values and resource development in Australis post-1788, and a review of cultural landscape theory literature contribute to the formation of the theoretical framework: "reconnecting the interrupted landscape". The author then explores a possible application of this framework within the Australian open-cut coal mining landscape.