An Algorithm for Optimal Bipartite PLA Folding

This paper presents some results of PLA area optimizing by means of its column and row folding. A more restricted type of PLA simple folding is considered. It is introduced by Egan and Liu and called as bipartite folding. An efficient approach is presented which allows finding an optimal bipartite folding without exhaustive computational efforts.

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.

Synthesis of aromatic monothiols to increase the folding rate and yields of disulfide-containing proteins

Almost all pharmaceutically relevant proteins and many extracellular proteins contain disulfide bonds, which are essential for protein functions. In many cases, disulfidecontaining proteins are produced via in vitro protein folding that involves the oxidation of reduced protein to native protein, a complex process. The in vitro folding of reduced lysozyme has been extensively studied as a model system because native lysozyme is small, inexpensive, and has only four disulfide bonds. The folding of reduced lysozyme is conducted with the aid of a redox buffer consisting of a small molecule disulfide and a small molecule thiol, such as oxidized and reduced glutathione. Herein, in vitro folding rates and yields of lysozyme obtained in the presence of a series of aromatic thiols and oxidized glutathione are compared to those obtained with reduced and oxidized glutathione. Results showed that aromatic thiols significantly increase the folding rate of lysozyme compared to glutathione.

Global relativistic folding optical potential and the relativistic Green's function model

Optical potentials provide critical input for calculations on a wide variety of nuclear reactions, in particular, for neutrino-nucleus reactions, which are of great interest in the light of the new neutrino oscillation experiments. We present the global relativistic folding optical potential (GRFOP) fits to elastic proton scattering data from C-12 nucleus at energies between 20 and 1040 MeV. We estimate observables, such as the differential cross section, the analyzing power, and the spin rotation parameter, in elastic proton scattering within the relativistic impulse approximation. The new GRFOP potential is employed within the relativistic Green's function model for inclusive quasielastic electron scattering and for (anti) neutrino-nucleus scattering at MiniBooNE kinematics.

Fracture patterns and petrophysical properties of carbonates undergoing regional folding : A case study from Kurdistan, N Iraq

Acknowledgements The authors thank the Ministry of Natural Resources in Iraqi Kurdistan Region for permission to publish this paper. Gulf Keystone Petroleum Ltd. and HKN Energy Ltd. are acknowledged for providing the subsurface datasets. Great thanks to Colin Taylor at the University of Aberdeen for his assistance in the laboratory work. Thoughtful reviews by two anonymous referees improved the clarity of the paper. Graham Banks is thanked for his helpful and constructive review on a late version of the manuscript, which has significantly improved this paper.

Development and Application of Covalent-Labeling Strategies for the Large-Scale Thermodynamic Analysis of Protein Folding and Ligand Binding

Thermodynamic stability measurements on proteins and protein-ligand complexes can offer insights not only into the fundamental properties of protein folding reactions and protein functions, but also into the development of protein-directed therapeutic agents to combat disease. Conventional calorimetric or spectroscopic approaches for measuring protein stability typically require large amounts of purified protein. This requirement has precluded their use in proteomic applications. Stability of Proteins from Rates of Oxidation (SPROX) is a recently developed mass spectrometry-based approach for proteome-wide thermodynamic stability analysis. Since the proteomic coverage of SPROX is fundamentally limited by the detection of methionine-containing peptides, the use of tryptophan-containing peptides was investigated in this dissertation. A new SPROX-like protocol was developed that measured protein folding free energies using the denaturant dependence of the rate at which globally protected tryptophan and methionine residues are modified with dimethyl (2-hydroxyl-5-nitrobenzyl) sulfonium bromide and hydrogen peroxide, respectively. This so-called Hybrid protocol was applied to proteins in yeast and MCF-7 cell lysates and achieved a ~50% increase in proteomic coverage compared to probing only methionine-containing peptides. Subsequently, the Hybrid protocol was successfully utilized to identify and quantify both known and novel protein-ligand interactions in cell lysates. The ligands under study included the well-known Hsp90 inhibitor geldanamycin and the less well-understood omeprazole sulfide that inhibits liver-stage malaria. In addition to protein-small molecule interactions, protein-protein interactions involving Puf6 were investigated using the SPROX technique in comparative thermodynamic analyses performed on wild-type and Puf6-deletion yeast strains. A total of 39 proteins were detected as Puf6 targets and 36 of these targets were previously unknown to interact with Puf6. Finally, to facilitate the SPROX/Hybrid data analysis process and minimize human errors, a Bayesian algorithm was developed for transition midpoint assignment. In summary, the work in this dissertation expanded the scope of SPROX and evaluated the use of SPROX/Hybrid protocols for characterizing protein-ligand interactions in complex biological mixtures.

Electrostatic Contributions to the Thermodynamics of Ribonuclease P Protein Folding

Electrostatic interactions are of fundamental importance in determining the structure and stability of macromolecules. For example, charge-charge interactions modulate the folding and binding of proteins and influence protein solubility. Electrostatic interactions are highly variable and can be both favorable and unfavorable. The ability to quantify these interactions is challenging but vital to understanding the detailed balance and major roles that they have in different proteins and biological processes. Measuring pKa values of ionizable groups provides a sensitive method for experimentally probing the electrostatic properties of a protein.

pKa values report the free energy of site-specific proton binding and provide a direct means of studying protein folding and pH-dependent stability. Using a combination of NMR, circular dichroism, and fluorescence spectroscopy along with singular value decomposition, we investigated the contributions of electrostatic interactions to the thermodynamic stability and folding of the protein subunit of Bacillus subtilis ribonuclease P, P protein. Taken together, the results suggest that unfavorable electrostatics alone do not account for the fact that P protein is intrinsically unfolded in the absence of ligand because the pKa differences observed between the folded and unfolded state are small. Presumably, multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

The (Un)Folding of Multidomain Proteins Through the Lens of Single-molecule Force-spectroscopy and Computer Simulation

Proteins are specialized molecules that catalyze most of the reactions that can sustain life, and they become functional by folding into a specific 3D structure. Despite their importance, the question, "how do proteins fold?" - first pondered in in the 1930's - is still listed as one of the top unanswered scientific questions as of 2005, according to the journal Science. Answering this question would provide a foundation for understanding protein function and would enable improved drug targeting, efficient biofuel production, and stronger biomaterials. Much of what we currently know about protein folding comes from studies on small, single-domain proteins, which may be quite different from the folding of large, multidomain proteins that predominate the proteomes of all organisms.

In this thesis I will discuss my work to fill this gap in understanding by studying the unfolding and refolding of large, multidomain proteins using the powerful combination of single-molecule force-spectroscopy experiments and molecular dynamic simulations.

The three model proteins studied - Luciferase, Protein S, and Streptavidin - lend insight into the inter-domain dependence for unfolding and the subdomain stabilization of binding ligands, and ultimately provide new insight into atomistic details of the intermediate states along the folding pathway.

Enhancing the Manufacturing Knowledge of Undergraduate Engineering Students: A Case Study of a Design-Build-Test Challenge Involving Folding Bicycles

Many engineers currently in professional practice will have gained a degree level qualification which involved studying a curriculum heavy with mathematics and engineering science. While this knowledge is vital to the engineering design process so also is manufacturing knowledge, if the resulting designs are to be both technically and commercially viable.
The methodology advanced by the CDIO Initiative aims to improve engineering education by teaching in the context of Conceiving, Designing, Implementing and Operating products, processes or systems. A key element of this approach is the use of Design-Built-Test (DBT) projects as the core of an integrated curriculum. This approach facilitates the development of professional skills as well as the application of technical knowledge and skills developed in other parts of the degree programme. This approach also changes the role of lecturer to that of facilitator / coach in an active learning environment in which students gain concrete experiences that support their development.
The case study herein describes Mechanical Engineering undergraduate student involvement in the manufacture and assembly of concept and functional prototypes of a folding bicycle.

Analysis of Molecular Dynamics Simulations of Protein Folding

Microsecond long Molecular Dynamics (MD) trajectories of biomolecular processes are now possible due to advances in computer technology. Soon, trajectories long enough to probe dynamics over many milliseconds will become available. Since these timescales match the physiological timescales over which many small proteins fold, all atom MD simulations of protein folding are now becoming popular. To distill features of such large folding trajectories, we must develop methods that can both compress trajectory data to enable visualization, and that can yield themselves to further analysis, such as the finding of collective coordinates and reduction of the dynamics. Conventionally, clustering has been the most popular MD trajectory analysis technique, followed by principal component analysis (PCA). Simple clustering used in MD trajectory analysis suffers from various serious drawbacks, namely, (i) it is not data driven, (ii) it is unstable to noise and change in cutoff parameters, and (iii) since it does not take into account interrelationships amongst data points, the separation of data into clusters can often be artificial. Usually, partitions generated by clustering techniques are validated visually, but such validation is not possible for MD trajectories of protein folding, as the underlying structural transitions are not well understood. Rigorous cluster validation techniques may be adapted, but it is more crucial to reduce the dimensions in which MD trajectories reside, while still preserving their salient features. PCA has often been used for dimension reduction and while it is computationally inexpensive, being a linear method, it does not achieve good data compression. In this thesis, I propose a different method, a nonmetric multidimensional scaling (nMDS) technique, which achieves superior data compression by virtue of being nonlinear, and also provides a clear insight into the structural processes underlying MD trajectories. I illustrate the capabilities of nMDS by analyzing three complete villin headpiece folding and six norleucine mutant (NLE) folding trajectories simulated by Freddolino and Schulten [1]. Using these trajectories, I make comparisons between nMDS, PCA and clustering to demonstrate the superiority of nMDS. The three villin headpiece trajectories showed great structural heterogeneity. Apart from a few trivial features like early formation of secondary structure, no commonalities between trajectories were found. There were no units of residues or atoms found moving in concert across the trajectories. A flipping transition, corresponding to the flipping of helix 1 relative to the plane formed by helices 2 and 3 was observed towards the end of the folding process in all trajectories, when nearly all native contacts had been formed. However, the transition occurred through a different series of steps in all trajectories, indicating that it may not be a common transition in villin folding. The trajectories showed competition between local structure formation/hydrophobic collapse and global structure formation in all trajectories. Our analysis on the NLE trajectories confirms the notion that a tight hydrophobic core inhibits correct 3-D rearrangement. Only one of the six NLE trajectories folded, and it showed no flipping transition. All the other trajectories get trapped in hydrophobically collapsed states. The NLE residues were found to be buried deeply into the core, compared to the corresponding lysines in the villin headpiece, thereby making the core tighter and harder to undo for 3-D rearrangement. Our results suggest that the NLE may not be a fast folder as experiments suggest. The tightness of the hydrophobic core may be a very important factor in the folding of larger proteins. It is likely that chaperones like GroEL act to undo the tight hydrophobic core of proteins, after most secondary structure elements have been formed, so that global rearrangement is easier. I conclude by presenting facts about chaperone-protein complexes and propose further directions for the study of protein folding.

A biochemical analysis into the co-translational folding of a G protein-coupled receptor; GPR35

The folding and targeting of membrane proteins poses a major challenge to the cell, as they must remain insertion competent while their highly hydrophobic transmembrane (TM) domains are transferred from the ribosome, through the aqueous cytosol and into the lipid bilayer. The biogenesis of a mature membrane protein takes place through the insertion and integration into the lipid bilayer. A number of TM proteins have been shown to gain some degree of secondary structure within the ribosome tunnel and to retain this conformation throughout maturation. Although studies into the folding and targeting of a number of membrane proteins have been carried out to date, there is little information on one of the largest class of eukaryotic membrane proteins; the G-protein-coupled receptors (GPCRs). This project studies the early folding events of the human ortholog of GPR35. To analyse the structure of the 1st TM domain, intermediates were generated and assessed by the biochemical method of pegylation (PEG-MAL). A structurally-similar microbial opsin (Bacterioopsin) was also used to investigate the differences in the early protein folding within eukaryotic and prokaryotic translation systems. Results showed that neither the 1st TM domain of GPR35 nor Bacterioopsin were capable of compacting in the ribosome tunnel before their N-terminus reached the ribosome exit point. The results for this assay remained consistent whether the proteins were translated in a eukaryotic or prokaryotic translation system. To examine the communication mechanism between the ribosome, the nascent chain and the protein targeting pathway, crosslinking experiments were carried out using the homobifunctional lysine cross-linker BS3. Specifically, the data generated here show that the nascent chain of GPR35 reaches the ribosomal protein uL23 in an extended conformation and interacts with the SRP protein as it exits the ribosome tunnel. This confirms the role of SRP in the co-translational targeting of GPR35. Using these methods insights into the early folding of GPCRs has been obtained. Further experiments using site-directed mutagenesis to reduce hydrophobicity in the 1st TM domain of GPR35, highlighted the mechanisms by which GPCRs are targeted to the endoplasmic reticulum. Confirming that hydrophobicity within the signal anchor sequence is essential of SRP-dependent targeting. Following the successful interaction of the nascent GPR35 and SRP, GPR35 is successfully targeted to ER membranes, shown here as dog pancreas microsomes (DPMs). Glycosylation of the GPR35 N-terminus was used to determine nascent chain structure as it is inserted into the ER membrane. These glycosylation experiments confirm that TM1 has obtained its compacted state whilst residing in the translocon. Finally, a site-specific cross-linking approach using the homobifunctional cysteine cross-linker, BMH, was used to study the lateral integration of GPR35 into the ER. Cross-linking of GPR35 TM1 and TM2 could be detected adjacent to a protein of ~45kDa, believed to be Sec61α. The loss of this adduct, as the nascent chain extends, showed the lateral movement of GPR35 TM1 from the translocon was dependent on the subsequent synthesis of TM2.

An investigation into the folding and assembly of engineered antibodies and novel antibody formats

Monoclonal antibodies and novel antibody formats are currently one of the principal therapeutic in the biopharmaceutical industry worldwide and are widely used in the treatment of autoimmune diseases and cancer. It is for this reason that the productivity and quality of antibody production requires improvement; specifically investigations into the engineering of antibodies and any issues that may arise from the production of these therapeutics. The work presented in this thesis describes an investigation into the folding and assembly of seven antibodies plus the novel antibody format FabFv. IgG is comprised of two identical HCs and two identical LCs. The folding process of immunoglobulin is controlled by the CH1 domain within the HC. The CH1 domain remains in a disordered state and is sequestered by BiP in the endoplasmic reticulum. Upon the addition of a folded CL domain, BiP is displaced, the CH1 domain is able to fold and the complete IgG protein can then be secreted from the cell. The results presented in this thesis however, have outlined an additional mechanism for the folding of the CH1 domain. We have shown that the CH1 domain is able to fold in the absence of LC resulting in the secretion of HC dimers in a VH dependent manner. The proposed mechanism for the secretion of HC dimers suggests that some VH domains can interact with each other in order to bring the CH1 domains in close proximity to enable folding to occur. As HC dimer secretion is a hindrance in antibody production, this result has highlighted an engineering target to improve antibody yield. Examination of the folding of IgG4 with the variable region A33 has revealed the inability to secrete LC dimers, cleavage of the HC during expression and secretion of HC dimers in the Fab, FabFv and full length forms. The attributes described have also been shown to be variable region dependent. This has introduced a new concept that the variable domain is important in determining the expression and secretion of antibodies and their individual chains. Pulse chase and 2D gel electrophoresis analysis of the novel antibody format FabFv has revealed that the folding and expression of the LC and HC causes multimeric species of FabFv to be secreted, as opposed to the monomeric form which is the desired therapeutic. Our hypothesis is that this process occurs via a LC dependent mechanism. The proposed hypothesis suggests that further engineering to the LC could diminish the formation and secretion of FabFv multimers. The results from these investigations can be applied to increase the productivity of therapeutics and increase the biological understanding of the domain interactions of IgG during folding, assembly and secretion.