Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This Gō-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht φ values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate φ, whereas highly frustrated systems display a bimodal distribution peaked at low and high φ values. The distribution of φ values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at φ = 0.3 with tails extending to low and high φ values, indicating the presence of a small amount of topological frustration. The contacts with high φ values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of φ values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration.

The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Conformational influences of glycosylation of a peptide: A possible model for the effect of glycosylation on the rate of protein folding

Improved strategies for synthesis make it possible to expand the range of glycopeptides available for detailed conformational studies. The glycopeptide 1 was synthesized using a new solid phase synthesis of carbohydrates and a convergent coupling to peptide followed by deprotection. Its conformational properties were subjected to NMR analysis and compared with a control peptide 2 prepared by conventional solid phase methods. Whereas peptide 2 fails to manifest any appreciable secondary structure, the glycopeptide 1 does show considerable conformational bias suggestive of an equilibrium between an ordered and a random state. The implications of this ordering effect for the larger issue of protein folding are considered.

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

Red blood cell adhesion on a solid/liquid interface

Red blood cells (RBCs), previously fixed with glutaraldehyde, adhere to glass slides coated with fibrinogen. The RBC deposition process on the horizontal glass surface is investigated by analyzing the relative surface covered by the RBCs, as well as the variance of this surface coverage, as a function of the concentration of particles. This study is performed by optical microscopy and image analysis. A model, derived from the classical random sequential adsorption model, has been developed to account for the experimental results. This model highlights the strong influence of the hydrodynamic interactions during the deposition process.

Diversity Arrays: a solid state technology for sequence information independent genotyping

Here we present the successful application of the microarray technology platform to the analysis of DNA polymorphisms. Using the rice genome as a model, we demonstrate the potential of a high-throughput genome analysis method called Diversity Array Technology, DArT‘. In the format presented here the technology is assaying for the presence (or amount) of a specific DNA fragment in a representation derived from the total genomic DNA of an organism or a population of organisms. Two different approaches are presented: the first involves contrasting two representations on a single array while the second involves contrasting a representation with a reference DNA fragment common to all elements of the array. The Diversity Panels created using this method allow genetic fingerprinting of any organism or group of organisms belonging to the gene pool from which the panel was developed. Diversity Arrays enable rapid and economical application of a highly parallel, solid-state genotyping technology to any genome or complex genomic mixtures.

Cooperative enhancement of specificity in a lattice of T cell receptors

Two of the most important models to account for the specificity and sensitivity of the T cell receptor (TCR) are the kinetic proofreading and serial ligation models. However, although kinetic proofreading provides a means for individual TCRs to measure accurately the length of time they are engaged and signal appropriately, the stochastic nature of ligand dissociation means the kinetic proofreading model implies that at high concentrations the response of the cell will be relatively nonspecific. Recent ligand experiments have revealed the phenomenon of both negative and positive crosstalk among neighboring TCRs. By using a Monte Carlo simulation of a lattice of TCRs, we integrate receptor crosstalk with the kinetic proofreading and serial ligation models and discover that receptor cooperativity can enhance T cell specificity significantly at a very modest cost to the sensitivity of the response.

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.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

The folding mechanism of larger model proteins: role of native structure.

The folding mechanism of a 125-bead heteropolymer model for proteins is investigated with Monte Carlo simulations on a cubic lattice. Sequences that do and do not fold in a reasonable time are compared. The overall folding behavior is found to be more complex than that of models for smaller proteins. Folding begins with a rapid collapse followed by a slow search through the semi-compact globule for a sequence-dependent stable core with about 30 out of 176 native contacts which serves as the transition state for folding to a near-native structure. Efficient search for the core is dependent on structural features of the native state. Sequences that fold have large amounts of stable, cooperative structure that is accessible through short-range initiation sites, such as those in anti-parallel sheets connected by turns. Before folding is completed, the system can encounter a second bottleneck, involving the condensation and rearrangement of surface residues. Overly stable local structure of the surface residues slows this stage of the folding process. The relation of the results from the 125-mer model studies to the folding of real proteins is discussed.

Three-dimensional tracking of motile bacteria near a solid planar surface.

Knowing how motile bacteria move near and along a solid surface is crucial to understanding such diverse phenomena as the migration of infectious bacteria along a catheter, biofilm growth, and the movement of bacteria through the pore spaces of saturated soil, a critical step in the in situ bioremediation of contaminated aquifers. In this study, a tracking microscope is used to record the three-dimensional motion of Escherichia coli near a planar glass surface. Data from the tracking microscope are analyzed to quantify the effects of bacteria-surface interactions on the swimming behavior of bacteria. The speed of cells approaching the surface is found to decrease in agreement with the mathematical model of Ramia et al. [Ramia, M., Tullock, D. L. & Phan-Tien, N. (1993) Biophys J. 65,755-778], which represents the bacteria as spheres with a single polar flagellum rotating at a constant rate. The tendency of cells to swim adjacent to the surface is shown in computer-generated reproductions of cell traces. The attractive interaction potential between the cells and the solid surface is offered as one of several possible explanations for this tendency.

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

Applications of EPR with an Emphasis on Tau Fibril Structure

Substances containing unpaired electrons have been studied by electron paramagnetic resonance (EPR) for nearly 70 years. With continual development and enhancement of EPR techniques, questions have arisen regarding optimum method selection for a given sample based on its properties. In this work, radiation defects, natural lattice defects, solid organic radicals, radicals in solution, and spin-labeled proteins were analyzed using CW, pulse, and rapid scan EPR to compare methods. Studies of solid BDPA, EOe in quartz, Ns0 in diamond, and a-Si:H, showed that rapid scan could overcome many obstacles presented by other techniques, cementing rapid scan as an effective alternative to CW and pulse methods. Relaxation times of six nitroxide radicals were characterized from 0.25-34 GHz, guiding synthesis of improved nitroxides for in vivo imaging experiments. Processes contributing to T1 of DPPH in polystyrene were found through variable temperature measurements at X- and Q-band, resolving previously-reported discrepancies in relaxation properties and providing new insight into this commonly-used standard. In the history of EPR, the study of proteins is relatively new. Double electron-electron resonance (DEER) has emerged as a powerful technique for the study of amyloid fibrils, a class of protein aggregates implicated in a number of neurodegenerative disorders. Microtubule-associated protein tau forms fibrils linked to Alzheimerfs disease through seeded conversion of monomer. Self-assembly is mediated by the microtubule binding repeats in tau, and there are either three or four repeats present depending on the isoform. DEER was used to show that filaments of 3R and 4R tau are conformationally distinct and that 4R fibrils adopt a heterogeneous mixture of conformations. Populations of 4R fibril conformations, which were independently validated using a model system, can be modulated by introduction of mutations to the primary sequence or by varying fibril growth conditions. These findings provided unprecedented insights into the seed selection of tau monomers and established conformational compatibility as an important driving force in tau fibril propagation. Lastly, DEER acquisition was improved through addition of paramagnetic metal to spin-labeled protein, decreasing collection time, and through use of a novel spin label with increased T2, thereby lengthening the available acquisition window.

The Identification of Best Management Practices in a Materials Recovery Facility to Increase Solid Waste Diversion in the Department of Defense (DoD) Installations along the Front Range of Colorado to Satisfy the DoD Solid Waste Diversion Goal of 40 Percent

The five installations operated by the Department of Defense (DoD) in the Front Range region of Colorado do not meet the DoD non-hazardous solid waste diversion goal of 40 percent, further impacting landfills and generating greenhouse gases. This applied capstone project identifies and evaluates best management practices of a Materials Recovery Facility (MRF), qualitatively and quantitatively, to increase solid waste diversion at a DoD MRF. An environmental benefits model quantified the externalities of increasing solid waste diversion at the installations. By implementing best management practices at a MRF, the DoD would divert an additional 1,400 tons of solid waste per year, resulting in the equivalent of 1,502,567 gallons of gasoline being saved, among many benefits presented in this capstone.

Comparison of Lattice-Fluid Binary Parameters For Mixtures and Block Copolymers

The aim of this report is to discuss the method of determination of lattice-fluid binary interaction parameters by comparing well characterized immiscible blends and block copolymers of poly(methyl methacrylate) (PMMA) and poly(ϵ−caprolactone) (PCL). Experimental pressure-volume-temperature (PVT) data in the liquid state were correlated with the Sanchez—Lacombe (SL) equation of state with the scaling parameters for mixtures and copolymers obtained through combination rules of the characteristic parameters for the pure homopolymers. The lattice-fluid binary parameters for energy and volume were higher than those of block copolymers implying that the copolymers were more compatible due to the chemical links between the blocks. Therefore, a common parameter cannot account for both homopolymer blend and block copolymer phase behaviors based on current theory. As we were able to adjust all data of the mixtures with a single set of lattice-binary parameters and all data of the block copolymers with another single set we can conclude that both parameters did not depend on the composition for this system. This characteristic, plus the fact that the additivity law of specific volumes can be suitably applied for this system, allowed us to model the behavior of the immiscible blend with the SL equation of state. In addition, a discussion on the relationship between lattice-fluid binary parameters and the Flory–Huggins interaction parameter obtained from Leibler's theory is presented.