Efficient Generation of Feasible Pathways for Protein Conformational Transitions

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284

Elastic network models (ENMs) are entropic models that have demonstrated in many previous studies their abilities to capture overall the important internal motions, with comparisons having been made against crystallographic B-factors and NMR conformational variabilities. ENMs have become an increasingly important tool and have been widely used to comprehend protein dynamics, function, and even conformational changes. However, reliance upon an arbitrary cutoff distance to delimit the range of interactions has presented a drawback for these models, because the optimal cutoff values can differ somewhat from protein to protein and can lead to quirks such as some shuffling in the order of the normal modes when applied to structures that differ only slightly. Here, we have replaced the requirement for a cutoff distance and introduced the more physical concept of inverse power dependence for the interactions, with a set of elastic network models that are parameter-free, with the distance cutoff removed. For small fluctuations about the native forms, the power dependence is the inverse square, but for larger deformations, the power dependence may become inverse 6th or 7th power. These models maintain and enhance the simplicity and generality of the original ENMs, and at the same time yield better predictions of crystallographic B-factors (both isotropic and anisotropic) and of the directions of conformational transitions. Thus, these parameter-free ENMs can be models of choice whenever elastic network models are used.B factors ͉ conformational entropy P rotein dynamics can provide important insights into protein function. Most proteins carry out their functions through conformational changes of the structures. In X-ray structures, the information about thermal motions is provided by the Debye-Waller temperature factors or B-factors, which are proportional to the mean square fluctuations of atom positions in a crystal. Thus, accurate predictions of crystalline B-factors offer a good starting point for understanding the functional dynamics of proteins.A number of computational and statistical approaches has been proposed to predict protein B-factors from protein sequence (1-7), atomic coordinates (8-13), and electron density maps (14). The atomic coordinate-based methods such as molecular dynamics (MD) (15-18) and normal mode analysis (NMA) (19)(20)(21)(22) are computationally expensive, and thus, in the past decade, the elastic network model (ENM), with NMA, using a single parameter harmonic potential, usually coarse-grained, has been widely used for studying protein dynamics including B-factor predictions. The ENM for isotropic fluctuations is called the Gaussian network model (GNM) (23,24), where only the magnitudes of the fluctuations are considered. Its anisotropic counterpart, where the directions of the collective motions are also examined, is called the anisotropic network model (ANM) (25), and these can be compared with the experimental anisotropic temperature factors (26-29), but generally these comparisons are ...

Section: Discussionmentioning

confidence: 99%

Protein elastic network models and the ranges of cooperativity

Yang

Song²,

Jernigan³

2009

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284

“…The minimum value of f ␦E for mode 1 is statistically significant (Z ϭ Ϫ2. 16). There are several other modes (modes 2 and 3) with fairly low f ␦E .…”

Section: Fig 3 Enm and Sequence Analysis For Dictyostelium Myosinmentioning

confidence: 99%

“…A number of studies on vastly different enzymes have shown that the domain movements are dominated by one or a few normal modes (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17). To understand how the allosteric transitions are executed with high fidelity, it is important to explore the relationship between the global dynamics at the macromolecular level and the amino acid variations at the microscopic level.…”

mentioning

confidence: 99%

Low-frequency normal modes that describe allosteric transitions in biological nanomachines are robust to sequence variations

Zheng

Brooks

Thirumalai

2006

259

298

By representing the high-resolution crystal structures of a number of enzymes using the elastic network model, it has been shown that only a few low-frequency normal modes are needed to describe the large-scale domain movements that are triggered by ligand binding. Here we explore a link between the nearly invariant nature of the modes that describe functional dynamics at the mesoscopic level and the large evolutionary sequence variations at the residue level. By using a structural perturbation method (SPM), which probes the residue-specific response to perturbations (or mutations), we identify a sparse network of strongly conserved residues that transmit allosteric signals in three structurally unrelated biological nanomachines, namely, DNA polymerase, myosin motor, and the Escherichia coli chaperonin. Based on the response of every mode to perturbations, which are generated by interchanging specific sequence pairs in a multiple sequence alignment, we show that the functionally relevant low-frequency modes are most robust to sequence variations. Our work shows that robustness of dynamical modes at the mesoscopic level is encoded in the structure through a sparse network of residues that transmit allosteric signals.DNA polymerase ͉ myosin ͉ GroEL ͉ elastic network model ͉ robustness A common theme in the function of many biological nanomachines is that they undergo large-scale domain movements in response to binding of ligands or other biomolecules. DNA polymerases are well studied examples in which such large conformational changes have been described using crystal structures and biophysical studies (1, 2). The global structure of polymerases is described by using the hand metaphor (3). The first step in the function involves the binding of the duplex DNA to the unliganded polymerases, which triggers the closing of the thumb domain around the DNA. Subsequent binding of dNTP to the binary complex results in the rotation of the fingers from the open conformation to the closed state. Similarly, large-scale conformational changes, induced by ATP binding and hydrolysis, are involved in the directed movements of myosins on actin filaments (4). In another class of nanomachines, binding of ATP to the equatorial domain of the Escherichia coli chaperonin GroEL results in a downward movement of the intermediate domain, which results in the locking of the ATP-binding sites (5). Upon binding of GroES, the apical domain swings upward and simultaneously twists, thus doubling the volume of the cavity as compared with the unliganded state. Such large-scale conformational changes are linked to the function of GroEL (6).To obtain insights into these universally prevalent motions, normal modes analysis (NMA) of the elastic network model (ENM) representations of large protein complexes have been used to describe ligand-induced conformational changes. A number of studies on vastly different enzymes have shown that the domain movements are dominated by one or a few normal modes (7-17). To understand how the allosteric transitions are...

“…Analysis of the free-energy surface parameterized by {C,␣} follows the program developed to describe folding (42): the mechanism controlling the kinetics of the transitions is determined by the ensemble of structures characterized by the monomer density at the saddlepoints of the free energy. At this point, we simplify our model and restrict the interpolation parameter ␣i to be the same for all residues, ␣i ϭ ␣0 (45). With this simplification, the numerical problem of finding saddlepoints with respect to {C,␣} simplifies to minimizing the free-energy F({C},␣ 0) with respect to {C} for a fixed ␣0.…”

Section: Variational Model Of Conformational Transitionsmentioning

confidence: 99%

Inherent flexibility determines the transition mechanisms of the EF-hands of calmodulin

Tripathi

Portman

2009

We explore how inherent flexibility of a protein molecule influences the mechanism controlling allosteric transitions by using a variational model inspired from work in protein folding. The striking differences in the predicted transition mechanism for the opening of the two domains of calmodulin (CaM) emphasize that inherent flexibility is key to understanding the complex conformational changes that occur in proteins. In particular, the Cterminal domain of CaM (cCaM), which is inherently less flexible than its N-terminal domain (nCaM), reveals ''cracking'' or local partial unfolding during the open/closed transition. This result is in harmony with the picture that cracking relieves local stresses caused by conformational deformations of a sufficiently rigid protein. We also compare the conformational transition in a recently studied even-odd paired fragment of CaM. Our results rationalize the different relative binding affinities of the EF-hands in the engineered fragment compared with the intact odd-even paired EF-hands (nCaM and cCaM) in terms of changes in flexibility along the transition route. Aside from elucidating general theoretical ideas about the cracking mechanism, these studies also emphasize how the remarkable intrinsic plasticity of CaM underlies conformational dynamics essential for its diverse functions.T o understand protein function, it is often essential to characterize large conformational changes that occur upon ligand binding. Within the population shift mechanism of allosteric conformational change (1), the bound complex is formed when a ligand selects and stabilizes a weakly populated conformational ensemble from the kinetically accessible states of the unbound folded protein. Such conformational dynamics imply an inherent flexibility or ''intrinsic plasticity'' of the folded state. In this article, we focus on how this inherent flexibility of a protein molecule influences the mechanism controlling the kinetics of allosteric transitions. There are a couple of possible scenarios for the transition mechanism in terms of changes in conformational flexibility. One possibility is that the flexibility adjusts smoothly to conformational deformations connecting two specific metastable states in the free-energy surface. In this case, the inherent flexibility of the protein remains relatively constant if the metastable states have similar flexibilities or else changes smoothly between the flexibilities of the metastable states if the flexibilities are different. An alternative mechanism, called ''cracking'' (2), has recently been proposed. In terms of conformational f lexibility, cracking involves nonmonotonic changes in flexibility along the transitions route. In particular, the flexibility of specific regions of the protein may transiently increase through local unfolding. As explained in ref. 2, local unfolding can relieve specific areas of high stress during conformational deformations that would result in high free-energy barriers if the protein remained uniformly folded throughout the transi...