Origin of Scaling Behavior of Protein Packing Density: A Sequential Monte Carlo Study of Compact Long Chain Polymers

Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find that the radius of gyration provides poor description of protein packing but the alpha contact number we introduce here characterize proteins well. We further demonstrate that protein-like scaling relationship between packing density and chain length is observed in off-lattice self-avoiding walks. A key problem in studying compact chain polymer is the attrition problem: It is difficult to generate independent samples of compact long self-avoiding walks. We develop an algorithm based on the framework of sequential Monte Carlo and succeed in generating populations of compact long chain off-lattice polymers up to length $N=2,000$. Results based on analysis of these chain polymers suggest that maintaining high packing density is only characteristic of short chain proteins. We found that the scaling behavior of packing density with chain length of proteins is a generic feature of random polymers satisfying loose constraint in compactness. We conclude that proteins are not optimized by evolution to eliminate packing voids.Comment: 9 pages, 10 figures. Accepted by J. Chem. Phy

Designability of alpha-helical Proteins

A typical protein structure is a compact packing of connected alpha-helices and/or beta-strands. We have developed a method for generating the ensemble of compact structures a given set of helices and strands can form. The method is tested on structures composed of four alpha-helices connected by short turns. All such natural four-helix bundles that are connected by short turns seen in nature are reproduced to closer than 3.6 Angstroms per residue within the ensemble. Since structures with no natural counterpart may be targets for ab initio structure design, the designability of each structure in the ensemble -- defined as the number of sequences with that structure as their lowest energy state -- is evaluated using a hydrophobic energy. For the case of four alpha-helices, a small set of highly designable structures emerges, most of which have an analog among the known four-helix fold families, however several novel packings and topologies are identified.Comment: 21 pages, 6 figures, to appear in PNA

A de novo designed protein-protein interface

As an approach to both explore the physical/chemical parameters that drive molecular self-assembly and to generate novel protein oligomers, we have developed a procedure to generate protein dimers from monomeric proteins using computational protein docking and amino acid sequence design. A fast Fourier transform-based docking algorithm was used to generate a model for a dimeric version of the 56-amino-acid β1 domain of streptococcal protein G. Computational amino acid sequence design of 24 residues at the dimer interface resulted in a heterodimer comprised of 12-fold and eightfold variants of the wild-type protein. The designed proteins were expressed, purified, and characterized using analytical ultracentrifugation and heteronuclear NMR techniques. Although the measured dissociation constant was modest (~300 µM), 2D-[^1H,^(15)N]-HSQC NMR spectra of one of the designed proteins in the absence and presence of its binding partner showed clear evidence of specific dimer formation

Experimental library screening demonstrates the successful application of computational protein design to large structural ensembles

The stability, activity, and solubility of a protein sequence are determined by a delicate balance of molecular interactions in a variety of conformational states. Even so, most computational protein design methods model sequences in the context of a single native conformation. Simulations that model the native state as an ensemble have been mostly neglected due to the lack of sufficiently powerful optimization algorithms for multistate design. Here, we have applied our multistate design algorithm to study the potential utility of various forms of input structural data for design. To facilitate a more thorough analysis, we developed new methods for the design and high-throughput stability determination of combinatorial mutation libraries based on protein design calculations. The application of these methods to the core design of a small model system produced many variants with improved thermodynamic stability and showed that multistate design methods can be readily applied to large structural ensembles. We found that exhaustive screening of our designed libraries helped to clarify several sources of simulation error that would have otherwise been difficult to ascertain. Interestingly, the lack of correlation between our simulated and experimentally measured stability values shows clearly that a design procedure need not reproduce experimental data exactly to achieve success. This surprising result suggests potentially fruitful directions for the improvement of computational protein design technology

Determinants of Profitability: Evidence from Brokerage Companies Listed at Amman Stock Exchange

This paper examines the factors determining the profitability of the brokerage companies (Brokers) listed at Amman Stock Exchange during the period from 2013 to 2017. The profitability of brokerage companies is measured by Return on Assets (ROA) as a function of broker specific and macroeconomic determinants. Simple regression was also used to analyze the data, examine the relations, and measure the effect of determinants on brokerage companies’ profitability. The findings revealed that assets quality and Capital adequacy have a positive and significant impact on broker profitability. Furthermore, the results of the study show that broker size has a negative (inverse) impact on broker profitability, while the analysis of macroeconomic variables records that economic activity measured by inflation and Gross Domestic Product (GDP) has no effect on brokers’ profitability

An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

Computationally designed libraries of fluorescent proteins evaluated by preservation and diversity of function

To determine which of seven library design algorithms best introduces new protein function without destroying it altogether, seven combinatorial libraries of green fluorescent protein variants were designed and synthesized. Each was evaluated by distributions of emission intensity and color compiled from measurements made in vivo. Additional comparisons were made with a library constructed by error-prone PCR. Among the designed libraries, fluorescent function was preserved for the greatest fraction of samples in a library designed by using a structure-based computational method developed and described here. A trend was observed toward greater diversity of color in designed libraries that better preserved fluorescence. Contrary to trends observed among libraries constructed by error-prone PCR, preservation of function was observed to increase with a library's average mutation level among the four libraries designed with structure-based computational methods

One- and two-body decomposable Poisson-Boltzmann methods for protein design calculations

Successfully modeling electrostatic interactions is one of the key factors required for the computational design of proteins with desired physical, chemical, and biological properties. In this paper, we present formulations of the finite difference Poisson-Boltzmann (FDPB) model that are pairwise decomposable by side chain. These methods use reduced representations of the protein structure based on the backbone and one or two side chains in order to approximate the dielectric environment in and around the protein. For the desolvation of polar side chains, the two-body model has a 0.64 kcal/mol RMSD compared to FDPB calculations performed using the full representation of the protein structure. Screened Coulombic interaction energies between side chains are approximated with an RMSD of 0.13 kcal/mol. The methods presented here are compatible with the computational demands of protein design calculations and produce energies that are very similar to the results of traditional FDPB calculations

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe