Biomedical subjects

M F Thorpe

Publications and source records attributed to M F Thorpe.

13 recordsLinked to original sources

PubMed2006

The flexibility window in zeolites.

Today synthetic zeolites are the most important catalysts in petrochemical refineries because of their high internal surface areas and molecular-sieving properties. There have been considerable efforts to synthesize new zeolites with specific pore geometries, to add to the 167 available at present. Millions of hypothetical structures have been generated on the basis of energy minimization, and there is an ongoing search for criteria capable of predicting new zeolite structures. Here we show, by geometric simulation, that all realizable zeolite framework structures show a flexibility window over a range of densities. We conjecture that this flexibility window is a necessary structural feature that enables zeolite synthesis, and therefore provides a valuable selection criterion when evaluating hypothetical zeolite framework structures as potential synthetic targets. We show that it is a general feature that experimental densities of silica zeolites lie at the low-density edge of this window--as the pores are driven to their maximum volume by Coulomb inflation. This is in contrast to most solids, which have the highest density consistent with the local chemical and geometrical constraints.

Journal Article↗

PubMed2006

Geometric simulation of perovskite frameworks with Jahn-Teller distortions: applications to the cubic manganites.

A new approach is presented for modeling perovskite frameworks with disordered Jahn-Teller (JT) distortions and has been applied to study the elastic response of the LaMnO3 structure to defects in the JT ordering. Surprisingly, antiphase domain boundary defects in the pattern of ordered JT octahedra, along the [110] and [110] bonding directions, are found to produce 1D stripe patterns rotated 45 degrees along a* directions, similar to stripe structures observed in these systems. Geometric simulation is shown to be an efficient and powerful approach for finding relaxed atomic structures in the presence of disorder in networks of corner-shared JT-distorted octahedra such as the perovskites. Geometric modeling rapidly relaxes large supercells (thousands of octahedra) while preserving the local coordination chemistry, and shows great promise for studying these complex systems.

Journal Article↗

PubMed2006

A natural coarse graining for simulating large biomolecular motion.

Various coarse graining schemes have been proposed to speed up computer simulations of the motion within large biomolecules, which can contain hundreds of thousands of atoms. We point out here that there is a very natural way of doing this, using the rigid regions identified within a biomolecule as the coarse grain elements. Subsequently, computer resources can be concentrated on the flexible connections between the rigid units. Examples of the use of such techniques are given for the protein barnase and the maltodextrin binding protein, using the geometric simulation technique FRODA and the rigidity enhanced elastic network model RCNMA to compute mobilities and atomic displacements.

Bacterial Proteins↗

PubMed2005

Constrained geometric simulation of diffusive motion in proteins.

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.

Algorithms↗

PubMed2005

Protein flexibility using constraints from molecular dynamics simulations.

Proteins are held together in the native state by hydrophobic interactions, hydrogen bonds and interactions with the surrounding water, whose strength as well as spatial and temporal distribution affects protein flexibility and hence function. We study these effects using 10 ns molecular dynamics simulations of pure water and of two proteins, the glutamate receptor ligand binding domain and barnase. We find that most of the noncovalent interactions flicker on and off over typically nanoseconds, and so we can obtain good statistics from the molecular dynamics simulations. Based on this information, a topological network of rigid bonds corresponding to a protein structure with covalent and noncovalent bonds is constructed, with account being taken of the influence of the flickering hydrogen bonds. We define the duty cycle for the noncovalent interactions as the percentage of time a given interaction is present, which we use as an input to investigate flexibility/rigidity patterns, in the algorithm FIRST which constructs and analyses topological networks.

Algorithms↗

PubMed2005

Mean-field conductivity in a certain class of networks.

We consider resistor networks, which are lattices with bonds represented by conductors and some of the bonds removed. It is known that effective medium theories predict that the effective conductivity of such networks is a linear function of the number of bonds present above the percolation threshold, but exact results for completely random networks deviate from linearity. We show that if instead we take a randomly chosen tree spanning the lattice and then start adding bonds to it at random, the conductivity changes linearly with the number of added bonds and coincides with the effective medium result for a given bond concentration. We also make comparisons with some related models.

Journal Article↗

PubMed2004

Modeling correlated main-chain motions in proteins for flexible molecular recognition.

We describe a new method for modeling protein and ligand main-chain flexibility, and show its ability to model flexible molecular recognition. The goal is to sample the full conformational space, including large-scale motions that typically cannot be reached in molecular dynamics simulations due to the computational intensity, as well as conformations that have not been observed yet by crystallography or NMR. A secondary goal is to assess the degree of flexibility consistent with protein-ligand recognition. Flexibility analysis of the target protein is performed using the graph-theoretic algorithm FIRST, which also identifies coupled networks of covalent and noncovalent bonds within the protein. The available conformations of the flexible regions are then explored with ROCK by random-walk sampling of the rotatable bonds. ROCK explores correlated motions by only sampling dihedral angles that preserve the coupled bond networks in the protein and generates conformers with good stereochemistry, without using a computationally expensive potential function. A representative set of the conformational ensemble generated this way can be used as targets for docking with SLIDE, which handles the flexibility of protein and ligand side-chains. The realism of this protein main-chain conformational sampling is assessed by comparison with time-resolved NMR studies of cyclophilin A motions. ROCK is also effective for modeling the flexibility of large cyclic and polycyclic ligands, as demonstrated for cyclosporin and zearalenol. The use of this combined approach to perform docking with main-chain flexibility is illustrated for the cyclophilin A-cyclosporin complex and the estrogen receptor in complex with zearalenol, while addressing the question of how much flexibility is allowed without hindering molecular recognition.

Biochemical Phenomena↗

PubMed2004

Sampling protein conformations and pathways.

Protein flexibility and rigidity can be analyzed using constraint theory, which views proteins as 3D networks of constraints involving covalent bonds and also including hydrophobic interactions and hydrogen bonds. This article describes an algorithm, ROCK (Rigidity Optimized Conformational Kinetics), which generates new conformations for these complex networks with many interlocked rings while maintaining the constraints. These new conformations are tracked for the flexible regions of a protein, while leaving the rigid regions undisturbed. An application to HIV protease demonstrates how large the flap motion can be. The algorithm is also used to generate conformational pathways between two distinct protein conformations. As an example, directed trajectories between the closed and the occluded conformations of the protein dihydrofolate reductase are determined.

Algorithms↗

PubMed2002

Protein unfolding: rigidity lost.

We relate the unfolding of a protein to its loss of structural stability or rigidity. Rigidity and flexibility are well defined concepts in mathematics and physics, with a body of theorems and algorithms that have been applied successfully to materials, allowing the constraints in a network to be related to its deformability. Here we simulate the weakening or dilution of the noncovalent bonds during protein unfolding, and identify the emergence of flexible regions as unfolding proceeds. The transition state is determined from the inflection point in the change in the number of independent bond-rotational degrees of freedom (floppy modes) of the protein as its mean atomic coordination decreases. The first derivative of the fraction of floppy modes as a function of mean coordination is similar to the fraction-folded curve for a protein as a function of denaturant concentration or temperature. The second derivative, a specific heat-like quantity, shows a peak around a mean coordination of = 2.41 for the 26 diverse proteins we have studied. As the protein denatures, it loses rigidity at the transition state, proceeds to a state where just the initial folding core remains stable, then becomes entirely denatured or flexible. This universal behavior for proteins of diverse architecture, including monomers and oligomers, is analogous to the rigid to floppy phase transition in network glasses. This approach provides a unifying view of the phase transitions of proteins and glasses, and identifies the mean coordination as the relevant structural variable, or reaction coordinate, along the unfolding pathway.

Databases, Protein↗

PubMed2002

Identifying protein folding cores from the evolution of flexible regions during unfolding.

The unfolding of a protein can be described as a transition from a predominantly rigid, folded structure to an ensemble of denatured states. During unfolding, the hydrogen bonds and salt bridges break, destabilizing the secondary and tertiary structure. Our previous work shows that the network of covalent bonds, salt bridges, hydrogen bonds, and hydrophobic interactions forms constraints that define which regions of the native protein are flexible or rigid (structurally stable). Here, we test the hypothesis that information about the folding pathway is encoded in the energetic hierarchy of non-covalent interactions in the native-state structure. The incremental thermal denaturation of protein structures is simulated by diluting the network of salt bridges and hydrogen bonds, breaking them one by one, from weakest to strongest. The structurally stable and flexible regions are identified at each step, providing information about the evolution of flexible regions during denaturation. The folding core, or center of structure formation during folding, is predicted as the region formed by two or more secondary structures having the greatest stability against denaturation. For 10 proteins with different architectures, we show that the predicted folding cores from this flexibility/stability analysis are in good agreement with those identified by native-state hydrogen-deuterium exchange experiments.

Bacterial Proteins↗

PubMed2001

Protein flexibility predictions using graph theory.

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.

Adenylate Kinase↗

PubMed2001

Protein flexibility and dynamics using constraint theory.

A new approach is presented for determining the rigid regions in proteins and the flexible joints between them. The short-range forces in proteins are modeled as constraints and we use a recently developed formalism from graph theory to analyze flexibility in the bond network. Forces included in the analysis are the covalent bond-stretching and bond-bending forces, salt bridges, and hydrogen bonds. We use a local function to associate an energy with individual hydrogen bonds, which then can be included or excluded depending on the bond strength. Colored maps of the rigid and flexible regions provide a direct visualization of where the motion of the protein can take place, consistent with these distance constraints. We also define a flexibility index that quantifies the local density of flexible or floppy modes, in terms of the dihedral angles that remain free to rotate in each flexible region. A negative flexibility index provides a measure of the density of redundant bonds in rigid regions. A new application of this approach is to simulate the maximal range of possible motions of the flexible regions by introducing Monte Carlo changes in the free dihedral angles, subject to the distance constraints. This is done using a method that maintains closure of the rings formed by covalent and hydrogen bonds in the flexible parts of the protein, and van der Waals overlaps between atoms are avoided. We use the locus of the possible motions of HIV protease as an example: movies of its motion can be seen at http://www.pa.msu.edu/~lei.

Computer Simulation↗

PubMed2000

Flexibility and critical hydrogen bonds in cytochrome c.

We show that protein flexibility can be characterized using graph theory, from a single protein conformation. Covalent and hydrogen bonds are modeled by distance and angular constraints, and a map is constructed of the regions in this network that are flexible or rigid, based on whether their dihedral bonds remain rotatable or are locked by other interactions in the network. This analysis takes only a second on a typical PC, and interatomic potentials; the most time-consuming aspect of molecular dynamics calculations, are not required. Our preliminary work has shown that this approach identifies the experimentally observed, biologically important flexible regions in HIV protease and lysine-arginine-ornithine binding protein. Here we analyze three evolutionarily distant cytochromes c, and find strong similarity between their flexible regions, despite having only 39% sequence identity. Furthermore, we show how the structural flexibility increases as the weaker hydrogen bonds are removed, as would happen under thermal denaturation of the protein. This approach identifies the critical hydrogen bonds that cross-link the tertiary structure.

Amino Acid Sequence↗