Biomedical subjects

M F Thorpe

Publications and source records attributed to M F Thorpe.

7 recordsLinked to original sources

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↗