Narrow Results

The free-energy landscape of two peptides is evaluated at various temperatures and an estimate for its fractal dimension at these temperatures calculated. We show that monitoring this quantity as a function of temperature allows to determine the glass transition temperature.

We consider two types of Go models of a protein (crambin) and study their kinetics through molecular dynamics simulations. In the first model, the residue–residue contact interactions are selected based on a cutoff distance, R_c. The folding times strongly depend on the value of R_c and nonmonotonically. This indicates a need for a physically determined set of native contacts. One may accomplish it by considering the van der Waals radii of the residual atoms and checking if the atoms overlap. In the second model, non-native attractive contacts are added to the system. This leads to bad foldability. However, for a small number of such extra contacts there is a slight acceleration in the kinetics of folding.

Lattice simulation is one important method to investigate the universal principle of protein folding. The move set is a basic element in lattice simulation. We used two move sets, dynamic move set and rigid rotation move, to run simulation and compare the thermodynamic and kinetic properties. The results indicate that the dynamic move set has advantage to simulate protein folding.

We compare the efficiency of two prominent techniques for simulation of complex systems: parallel tempering and Wang–Landau sampling. We show that both methods are of comparable efficiency but are optimized for different platforms. Parallel tempering should be chosen on multi-processor system while Wang–Landau sampling is easier to implement on a single-processor computer.

For many years the emphasis in protein-folding simulations has been laid as to how to predict the three-dimensional structure of proteins. Only recently has there be a shift in interest towards the thermodynamics of folding. We show that generalized-ensemble techniques are well suited to study both questions for realistic protein models.

We present two recent integer programming models in molecular biology and study practical reformulations to compute solutions to some of these problems. In extension of previously tested linearization techniques, we formulate corresponding semidefinite relaxations and discuss practical rounding strategies to find good feasible approximate solutions. Our computational results highlight the possible advantages and remaining challenges of this approach especially on large-scale problems.

xProtein folding in a two-dimensional lattice with an unrestricted boundary is simulated by means of the simplified HP model. The proteins are regarded as peptide chains and fold into compact structures. These structures are classified by the number of core sites. It is found that the number of structures with the given designability and given number of core sites versus designability appears as the normal distribution. The simulation shows that the structures with a large number of core sites have a high designability.

Based on two-dimensional square lattice models of proteins, the relation between folding time and temperature is studied by Monte Carlo simulation. The results can be represented by a kinetic model with three states — random coil, molten globule, and native state. The folding process is composed of nonspecific collapse and final searching for the native state. At high temperature, it is easy to escape from local traps in the folding process. With decreasing temperature, because of the trapping in local traps, the final searching speed decreases. Then the folding shows chevron rollover. Through the analysis of the fitted parameters of the kinetic model, it is found that the main difference between the energy landscapes of the HP model and the Go model is that the number of local minima of the Go model is less than that of the HP model.

Based on two-dimensional Gō model of proteins and Monte Carlo simulation method, it is found that different compact conformations have different accessibility, i.e., some are easy to reach in the Monte Carlo simulation from a random conformation, while others are not. The logarithm of folding time is approximately a linear function of the contact order of the native conformation, which is consistent with published experimental results. Transition barrier is the main factor to determine the folding time at low temperature when proteins are stable. To fold to native structure with bigger contact order, higher barrier needs to be overcome. To study the folding properties of some prion-like proteins which have two possible conformations, the normal Gō model is extended to double-Gō model with two native states. In folding simulations, the native state with high accessibility is reached with much higher probability than the other. The accessibility of compact structures determines which structure is easy to reach in folding process.

We propose three stages in protein folding, based on physical arguements involving the interplay between the hydrophobic effect and hydrogen bonding, and computer simulations using the CSAW (conditioned self-avoiding walk) model. These stages are characterized by universal exponents ν = 3/5, 3/7, 2/5 in the power law R ~ N^ν, where R is the radius of gyration and N is the number of residues. They correspond to the experimentally observed stages: unfolded, preglobule, molten globule.

We introduce the concept of multi-directional width-bounded geometric separators and obtain an improved separator for grid graphs. This yields an improved exact algorithm for the protein folding problem in the HP-model. For a grid graph G with n grid points P, there exists a separator A ⊆ P such that A has at most points, and G − A has two disconnected subgraphs each with at most nodes. This improves the previous upper bound of . We also derive a lower bound for such a separator in grid graphs.

Hard discrete optimization problems using randomized methods such as genetic algorithms require large numbers of samples from the solution space. Each candidate sample/solution must be evaluated using the target fitness/energy function being optimized. Such fitness computations are a bottleneck in sampling methods such as genetic algorithms. We observe that the caching of partial results from these fitness computations can reduce this bottleneck. We provide a rigorous analysis of the run-times of GAs with and without caching. By representing fitness functions as classic Divide and Conquer algorithms, we provide a formal model to predict the efficiency of caching GAs vs. non-caching GAs. Finally, we explore the domain of protein folding with GAs and demonstrate that caching can significantly reduce expected run-times through both theoretical and extensive empirical analyses.

Predicting native conformations using computational protein models requires a large number of energy evaluations even with simplified models such as hydrophobic-hydrophilic (HP) models. Clearly, energy evaluations constitute a significant portion of computational time. We hypothesize that given the structured nature of algorithms that search for candidate conformations such as stochastic methods, energy evaluation computations can be cached and reused, thus saving computational time and effort. In this paper, we present a caching approach and apply it to 2D triangular HP lattice model. We provide theoretical analysis and prediction of the expected savings from caching as applied this model. We conduct experiments using a sophisticated evolutionary algorithm that contains elements of local search, memetic algorithms, diversity replacement, etc. in order to verify our hypothesis and demonstrate a significant level of savings in computational effort and time that caching can provide.

High-Throughput Sequencing on a Next Generation Sequencer to Identify Specific Binders from a Phage Library

Antibody Solution Viscosity and Intermolecular Interactions: Considerations for Development of Highly Concentrated Formulations

Display of Membrane Proteins on a Viral Envelope for Antibody Generation

Sequence and Structural Determinants of Antigen Binding in Antibody CDR Loops

Enhancement of the Stability of Single Chain Fv Molecules with the Amino Acid Substitutions Predicted by High-Performance Computer

Thermal Stability of Camelid Single Domain VHH Antibody

The sequence and structure of a large body of proteins are becoming increasingly available. It is desirable to explore mathematical tools for efficient extraction of information from such sources. The principles of graph theory, which was earlier applied in fields such as electrical engineering and computer networks are now being adopted to investigate protein structure, folding, stability, function and dynamics. This review deals with a brief account of relevant graphs and graph theoretic concepts. The concepts of protein graph construction are discussed. The manner in which graphs are analyzed and parameters relevant to protein structure are extracted, are explained. The structural and biological information derived from protein structures using these methods is presented.

We optimized five existing sets of force-field parameters for protein systems by our recently proposed method. The five force fields are AMBER parm94, AMBER parm96, AMBER parm99, CHARMM version 22, and OPLS-AA. The method consists of minimizing the sum of the square of the force acting on each atom in the proteins with the structures from the Protein Data Bank (PDB). We selected the partial-charge and backbone torsion-energy parameters for this optimization, and 100 molecules from the PDB were used. We gave detailed comparisons of the optimized force fields and found that there is a tendency of convergence towards the same function for the torsion-energy term.

In Paper I of this series, the formulations of the optimization method of existing force-field parameters for protein systems have been presented. We then applied it to five sets of force-field parameters, namely, AMBER parm94, AMBER parm96, AMBER parm99, CHARMM version 22, and OPLS-AA. In order to test the validity of these force fields, the folding simulations of α-helical and β-hairpin peptides have been performed with each of the original and optimized force-field parameters. We found that all five modified force-field parameters gave both α-helical and β-hairpin structures more consistent with the experimental implications than the original force fields.

A method for analyzing the topological relation of any two peptide fragments in a protein structure is given by making analogy of the two fragments with a braid. Knotted relations are analyzed by calculating polynomials for the two fragments separately and for the two as a whole, respectively. Twisting is calculated from the writhe number, which is a measure to the internal relative rotation during formation of the protein structure. Statistical analysis on the internal rotations of all known structures found that the relative rotation like a one-dimensional random walk with decreasing step lengths.

We studied two three-dimensional off-lattice protein models with two species of monomers, hydrophobic and hydrophilic. Low energy configurations in both models were optimized using the energy landscape paving (ELP) method and subsequent gradient descent. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. For all sequences with lengths 13 ≤ n ≤ 55, the algorithm finds states with lower energy than previously proposed putative ground states.

We have investigated the folding of two helix-bundle proteins, 36-residue Villin headpiece and 56-residue E-domain of Staphylococcal protein A, by combining molecular dynamics (MD) simulations with Coarse-Grained United-Residue (UNRES) Force Field and all-atom force field. Starting from extended structures, each of the proteins was folded to a stable structure within a short time frame using the UNRES model. However, the secondary structures of helices were not well formed. Further refinement using MD simulations with the all-atom force field was able to fold the protein structure into the native-like state with the smallest main-chain root-mean-square deviation of around 3 Å. Detailed analysis of the folding trajectories was presented and the performance of GPU-based MD simulations was also discussed.