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 ...

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.

Mutations in polycystin-1 and transient receptor potential polycystin 2 (TRPP2) account for almost all clinically identified cases of autosomal dominant polycystic kidney disease (ADPKD), one of the most common human genetic diseases. TRPP2 functions as a cation channel in its homomeric complex and in the TRPP2/ polycystin-1 receptor/ion channel complex. The activation mechanism of TRPP2 is unknown, which significantly limits the study of its function and regulation. Here, we generated a constitutively active gain-of-function (GOF) mutant of TRPP2 by applying a mutagenesis scan on the S4-S5 linker and the S5 transmembrane domain, and studied functional properties of the GOF TRPP2 channel. We found that extracellular divalent ions, including Ca 2+, inhibit the permeation of monovalent ions by directly blocking the TRPP2 channel pore. We also found that D643, a negatively charged amino acid in the pore, is crucial for channel permeability. By introducing singlepoint ADPKD pathogenic mutations into the GOF TRPP2, we showed that different mutations could have completely different effects on channel activity. The in vivo function of the GOF TRPP2 was investigated in zebrafish embryos. The results indicate that, compared with wild type (WT), GOF TRPP2 more efficiently rescued morphological abnormalities, including curly tail and cyst formation in the pronephric kidney, caused by down-regulation of endogenous TRPP2 expression. Thus, we established a GOF TRPP2 channel that can serve as a powerful tool for studying the function and regulation of TRPP2. The GOF channel may also have potential application for developing new therapeutic strategies for ADPKD.autosomal dominant polycystic kidney disease | TRP channels | TRPP2 | polycystin | gain of function

Because of its appealing simplicity, the anisotropic network model (ANM) has been widely accepted and applied to study many molecular motion problems: such as ribosome motions, the molecular mechanisms of GroEL-GroES function, allosteric changes in hemoglobin, motorprotein motions, and conformational changes in general. However, the validity of the ANM has not been closely examined. In this work, we use ANM to predict the anisotropic temperature factors of proteins obtained from X-ray and NMR data. The rich, directional anisotropic temperature factor data available for hundreds of proteins in the Protein Data Bank (PDB) are used as validation data to closely test the ANM model. The significance of this work is that it presents a timely, important evaluation of the model, shows the extent of its accuracy in reproducing experimental anisotropic temperature factors, and suggests ways to improve the model. An improved model will help us better understand the internal dynamics of proteins, which in turn can greatly expand the usefulness of the models, which has already been demonstrated in many applications. Keywords anisotropic displacement parameters (ADPs); anisotropic network model (ANM); anisotropic temperature factors; Gaussian network model (GNM); protein dynamics