Protein disulfide isomerase: the structure of oxidative folding

Cellular functions hinge on the ability of proteins to adopt their correct folds, and misfolded proteins can lead to disease. Here, we focus on the proteins that catalyze disulfide bond formation, a step in the oxidative folding pathway that takes place in specialized cellular compartments. In the endoplasmic reticulum of eukaryotes, disulfide formation is catalyzed by protein disulfide isomerase (PDI); by contrast, prokaryotes produce a family of disulfide bond (Dsb) proteins, which together achieve an equivalent outcome in the bacterial periplasm. The recent crystal structure of yeast PDI has increased our understanding of the function and mechanism of PDI. Comparison of the structure of yeast PDI with those of bacterial DsbC and DsbG reveals some similarities but also striking differences that suggest directions for future research aimed at unraveling the catalytic mechanism of disulfide bond formation in the cell.

Using directional curvatures to visualize folding patterns of the GTM projection manifolds

In data visualization, characterizing local geometric properties of non-linear projection manifolds provides the user with valuable additional information that can influence further steps in the data analysis. We take advantage of the smooth character of GTM projection manifold and analytically calculate its local directional curvatures. Curvature plots are useful for detecting regions where geometry is distorted, for changing the amount of regularization in non-linear projection manifolds, and for choosing regions of interest when constructing detailed lower-level visualization plots.

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

Why are MD simulated protein folding times wrong?

The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that in the framework of Markov State Model (MSM) describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples, we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care.

Self-contained encrypted image folding

The recently introduced approach for Encrypted Image Folding is generalized to make it self-contained. The goal is achieved by enlarging the folded image so as to embed all the necessary information for the image recovery. The need for extra size is somewhat compensated by considering a transformation with higher folding capacity. Numerical examples show that the size of the resulting cipher image may be significantly smaller than the plain text one. The implementation of the approach is further extended to deal also with color images.

Sparsity and "something else": an approach to encrypted image folding

A property of sparse representations in relation to their capacity for information storage is discussed. It is shown that this feature can be used for an application that we term Encrypted Image Folding. The proposed procedure is realizable through any suitable transformation. In particular, in this paper we illustrate the approach by recourse to the Discrete Cosine Transform and a combination of redundant Cosine and Dirac dictionaries. The main advantage of the proposed technique is that both storage and encryption can be achieved simultaneously using simple processing steps.

Dynamic complexity of chaotic transitions in high-dimensional classical dynamics:Leu-Enkephalin folding

Leu-Enkephalin in explicit water is simulated using classical molecular dynamics. A ß-turn transition is investigated by calculating the topological complexity (in the "computational mechanics" framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the ß-turn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to high-dimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a "quasi-regular" dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated. © Springer-Verlag Berlin Heidelberg 2006.

Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.

The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Quantifying protein folding pathways

A deep understanding of the proteins folding dynamics can be get quantifying folding landscape by calculating how the number of microscopic configurations (entropy) varies with the energy of the chain, Ω=Ω(E). Because of the incredibly large number of microstates available to a protein, direct enumeration of Ω(E) is not possible on realistic computer simulations. An estimate of Ω(E) can be obtained by use of a combination of statistical mechanics and thermodynamics. By combining different definitions of entropy that are valid for a system whose probability for occupying a state is given by the canonical Boltzmann probability, computers allow the determination of Ω(E). ^ The energy landscapes of two similar, but not identical model proteins were studied. One protein contains no kinetic tracks. Results show a smooth funnel for the folding landscape. That allows the contour determination of the folding funnel. Also it was presented results for the folding landscape for a modified protein with kinetic traps. Final results show that the computational approach is able to distinguish and explore regions of the folding landscape that are due to kinetic traps from the native state folding funnel.^

Synthesis of aromatic monothiols and aromatic dithiols to increase the folding rate and yield of disulfide containing proteins

Most pharmaceutically relevant proteins and many extracellular proteins contain disulfide bonds. Formation of the correct disulfide bonds is essential for stability in almost all cases. Disulfide containing proteins can be rapidly and inexpensively overexpressed in bacteria. However, the overexpressed proteins usually form aggregates inside the bacteria, called inclusion bodies, which contains inactive and non-native protein. To obtain native protein, inclusion bodies need to be isolated and resolubilized, and then the resulting protein refolded in vitro. In vitro protein folding is aided by the addition of a redox buffer, which is composed of a small molecule disulfide and/or a small molecule thiol. The most commonly used redox buffer contains reduced and oxidized glutathione. Recently, aliphatic dithiols and aromatic monothiols have been employed as redox buffers. Aliphatic dithiols improved the yield of native protein as compared to the aliphatic thiol, glutathione. Dithiols mimic the in vivo protein folding catalyst, protein disulfide isomerase, which has two thiols per active site. Furthermore, aromatic monothiols increased the folding rate and yield of lysozyme and RNase A relative to glutathione. By combining the beneficial properties of aliphatic dithiols and aromatic monothiols, aromatic dithiols were designed and were expected to increase in vitro protein folding rates and yields. Aromatic monothiols (1-4) and their corresponding disulfides (5-8), two series of ortho- and para-substituted ethylene glycol dithiols (9-15), and a series of aromatic quaternary ammonium salt dithiols (16-17) were synthesized on a multigram scale. Monothiols and disulfides (1-8) were utilized to fold lysozyme and bovine pancreatic trypsin inhibitor. Dithiols (11-17) were tested for their ability to fold lysozyme. At pH 7.0 and pH 8.0, and high protein concentration (1 mg/mL), aromatic dithiols (16, 17) and a monothiol (3) significantly enhanced the in vitro folding rate and yield of lysozyme relative to the aliphatic thiol, glutathione. Additionally, aromatic dithiols (16, 17) significantly enhance the folding yield as compared to the corresponding aromatic monothiol (3). Thus, the folding rate and yield enhancements achieved in in vitro protein folding at high protein concentration will decrease the volume of renaturation solution required for large scale processes and consequently reduce processing time and cost.