Time scales of slow motions in ubiquitin explored by heteronuclear double resonance

Understanding how proteins function at the atomic level relies in part on a detailed characterization of their dynamics. Ubiquitin, a small single-domain protein, displays rich dynamic properties over a wide range of time scales. In particular, several regions of ubiquitin show the signature of chemical exchange, including the hydrophobic patch and the β4-α2 loop, which are both involved in many interactions. Here, we use multiple-quantum relaxation techniques to identify the extent of chemical exchange in ubiquitin. We employ our recently developed heteronuclear double resonance method to determine the time scales of motions that give rise to chemical exchange. Dispersion profiles are obtained for the backbone NH(N) pairs of several residues in the hydrophobic patch and the β4-α2 loop, as well as the C-terminus of helix α1. We show that a single time scale (ca. 50 μs) can be used to fit the data for most residues. Potential mechanisms for the propagation of motions and the possible extent of correlation of these motions are discussed.     

Role of rigidity on the activity of proteinase inhibitors and their peptide mimics

The Bowman-Birk inhibitors (BBIs) are a family of proteins that share a canonical loop structure whose presence in a conserved conformation is linked to their inhibitory activity. We study the conformational properties of the canonical loop using a graph theoretical approach as implemented in the floppy inclusions and rigid substructure topography (FIRST). We find that the canonical loop is an independent rigid cluster in the natural inhibitors. We have further used this technique to identify residues that play an important role in the structural rigidity of the protein by quantifying their contribution to the overall rigidity of the inhibitor. We find that the conserved elements among the natural and synthetic peptides are the ones that contribute the most to rigidity, even if they are located far from the active site, as rigidity effects are nonlinear and hence nonlocal. The results help to elucidate why certain mutations in the loop of the BBI produce peptides that fail to have the designed inhibitory activity.     

A kinematic view of loop closure

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.     

Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.     

Simple model of membrane proteins including solvent

We report a numerical simulation for the phase diagram of a simple two-dimensional model, similar to the one proposed by Noro and Frenkel [J. Chem. Phys. 114, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Carlo simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three-dimensional model.     

Assessing protein loop flexibility by hierarchical Monte Carlo sampling

Loop flexibility is often crucial to protein biological function in solution. We report a new Monte Carlo method for generating conformational ensembles for protein loops and cyclic peptides. The approach incorporates the triaxial loop closure method which addresses the inverse kinematic problem for generating backbone move sets that do not break the loop. Sidechains are sampled together with the backbone in a hierarchical way, making it possible to make large moves that cross energy barriers. As an initial application, we apply the method to the flexible loop in triosephosphate isomerase that caps the active site, and demonstrate that the resulting loop ensembles agree well with key observations from previous structural studies. We also demonstrate, with 3 other test cases, the ability to distinguish relatively flexible and rigid loops within the same protein.     

Models to Approximate the Motions of Protein Loops

We approximate the loop motions of various proteins by using a coarse-grained model and the theory of rubberlike elasticity of polymer chains. The loops are considered as chains where only the first and the last residues thereof are tethered by their connections to the main structure; while within the loop, the loop residues are connected only to their sequence neighbors. We applied these approximate models to five proteins. Our approximation shows that the loop motions can usually be computed locally which shows these motions are robust and not random. But most interestingly, the new method presented here can be used to compute the likely motions of loops that are missing in the structures.     

A Three-dimensional Model of the Human Immunodeficiency Virus Type 1 Integration Complex

Summary While the general features of HIV-1 integrase function are understood, there is still uncertainty about the composition of the integration complex and how integrase interacts with viral and host DNA. We propose an improved model of the integration complex based on current experimental evidence including a comparison with the homologous Tn5 transposase containing bound DNA and an analysis of DNA binding sites using Goodford’s GRID. Our model comprises a pair of integrase dimers, two strands of DNA to represent the viral DNA ends and a strand of bent DNA representing the host chromosome. In our model, the terminal four base pairs of each of the viral DNA strands interact with the integrase dimer providing the active site, while bases one turn away interact with a flexible loop (residues 186–194) on the second integrase dimer. We propose that residues E152, Q148 and K156 are involved in the specific recognition of the conserved CA dinucleotide and that the active site mobile loop (residues 140–149) stabilises the integration complex by acting as a barrier to separate the two viral DNA ends. In addition, the residues responsible for DNA binding in our model show a high level of amino acid conservation.     

Energy landscapes of dynamic ensembles of rolling triplet repeat bulge loops: implications for DNA expansion associated with disease states

DNA repeat domains can form ensembles of canonical and noncanonical states, including stable and metastable DNA secondary structures. Such sequence-induced structural diversity creates complex conformational landscapes for DNA processing pathways, including those triplet expansion events that accompany replication, recombination, and/or repair. Here we demonstrate further levels of conformational complexity within repeat domains. Specifically, we show that bulge loop structures within an extended repeat domain can form dynamic ensembles containing a distribution of loop positions, thereby yielding families of positional loop isomers, which we designate as "rollamers". Our fluorescence, absorbance, and calorimetric data are consistent with loop migration/translocation between sites within the repeat domain ("rollamerization"). We demonstrate that such "rollameric" migration of bulge loops within repeat sequences can invade and disrupt previously formed base-paired domains via an isoenthalpic, entropy-driven process. We further demonstrate that destabilizing abasic lesions alter the loop distributions so as to favor "rollamers" with the lesion positioned at the duplex/loop junction, sites where the flexibility of the abasic "universal hinge" relaxes unfavorable interactions and/or facilitates topological accommodation. Another strategic siting of an abasic site induces directed loop migration toward denaturing domains, a phenomenon that merges destabilizing domains. In the aggregate, our data reveal that dynamic ensembles within repeat domains profoundly impact the overall energetics of such DNA constructs as well as the distribution of states by which they denature/renature. These static and dynamic influences within triplet repeat domains expand the conformational space available for selection and targeting by the DNA processing machinery. We propose that such dynamic ensembles and their associated impact on DNA properties influence pathways that lead to DNA expansion.     

Design of an adenosine analogue that selectively improves the affinity of a mutant U1A protein for RNA

The RNA recognition motif (RRM), one of the most common RNA binding domains, contains three highly conserved aromatic amino acids that participate in stacking interactions with RNA bases. We have investigated the contribution of these highly conserved aromatic amino acids to the affinity of the complex formed between the N-terminal RRM of the U1A protein and stem loop 2 of U1 snRNA. Previously, we found that substitution of one of these conserved aromatic amino acids, Phe56, with Ala resulted in a large destabilization of the complex. Here, we have modified A6, the base in stem loop 2 RNA that stacks with Phe56, to compensate for a portion of the destabilization caused by the Phe56Ala mutation. We have designed two modified adenosines, A-3CPh and A-4CPh, in which a phenyl group is linked to the adenosine such that it may replace the phenyl group that is eliminated by the Phe56Ala mutation in the complex. We have found that incorporation of A-3CPh into stem loop 2 RNA stabilizes the complex formed with Phe56Ala by 0.6 kcal/mol, while incorporation of A-4CPh into stem loop 2 RNA stabilizes this complex by 1.8 kcal/mol. Either base modification destabilizes the wild-type complex by 0.8-0.9 kcal/mol. Experiments with other U1A mutant proteins suggest that the stabilization of the complex between the Phe56Ala U1A protein and stem loop 2 RNA is due to a specific interaction between the Phe56Ala U1A protein and A6-4CPh stem loop 2 RNA.     

First cytoplasmic loop of glucagon-like peptide-1 receptor can function at the third cytoplasmic loop position of rhodopsin

G protein-coupled receptors (GPCRs) are classified into several families based on their amino acid sequences. In family 1, GPCRs such as rhodopsin and adrenergic receptor, the structure-function relationship has been extensively investigated to demonstrate that exposure of the third cytoplasmic loop is essential for selective G protein activation. In contrast, much less is known about other families. Here we prepared chimeric mutants between Gt-coupled rhodopsin and Gi/Go- and Gs-coupled glucagon-like peptide-1 (GLP-1) receptor of family 2 and tried to identify the loop region that functions at the third cytoplasmic loop position of rhodopsin. We succeeded in expressing a mutant having the first cytoplasmic loop of GLP-1 receptor and found that this mutant activated Gi and Go efficiently but did not activate Gt. Moreover, the rhodopsin mutant having the first loop of Gs-coupled secretin receptor of family 2 decreased the Gi and Go activation efficiencies. Therefore, the first loop of GLP-1 receptor would share a similar role to the third loop of rhodopsin in G protein activation. This result strongly suggested that different families of GPCRs have maintained molecular architectures of their ancestral types to generate a common mechanism, namely exposure of the cytoplasmic loop, to activate peripheral G protein.     

Anchor Residues Guide Form and Function in Grafted Peptides

Loops at protein–protein interfaces are a rich source of peptide leads that have high specificity and low toxicity. Although such peptides typically need to be constrained to overcome thermodynamic and metabolic limitations, design guidelines to obtain a successfully constrained peptides, and thus facilitate the transition from loop to drug, are relatively poorly formulated. In this work, we surveyed the structures of interface loops and found the position of the terminal residues to be a key determinant of conformation. We used this knowledge to improve the process of molecular grafting, a valuable approach for constraining and stabilising peptides by fusing them to a suitable scaffold. We show that an informed choice of where a loop is “anchored” to a scaffold improves its form and function. This knowledge can help guide the choice of loop and its matching scaffold, and thus increase the success rate for designing stable and potent peptide drug leads.     

New insights from molecular dynamic simulation studies of the multiple binding modes of a ligand with G-quadruplex DNA

G-quadruplexes are higher-order DNA and RNA structures formed from guanine-rich sequences. These structures have recently emerged as a new class of potential molecular targets for anticancer drugs. An understanding of the three-dimensional interactions between small molecular ligands and their G-quadruplex targets in solution is crucial for rational drug design and the effective optimization of G-quadruplex ligands. Thus far, rational ligand design has been focused mainly on the G-quartet platform. It should be noted that small molecules can also bind to loop nucleotides, as observed in crystallography studies. Hence, it would be interesting to elucidate the mechanism underlying how ligands in distinct binding modes influence the flexibility of G-quadruplex. In the present study, based on a crystal structure analysis, the models of a tetra-substituted naphthalene diimide ligand bound to a telomeric G-quadruplex with different modes were built and simulated with a molecular dynamics simulation method. Based on a series of computational analyses, the structures, dynamics, and interactions of ligand-quadruplex complexes were studied. Our results suggest that the binding of the ligand to the loop is viable in aqueous solutions but dependent on the particular arrangement of the loop. The binding of the ligand to the loop enhances the flexibility of the G-quadruplex, while the binding of the ligand simultaneously to both the quartet and the loop diminishes its flexibility. These results add to our understanding of the effect of a ligand with different binding modes on G-quadruplex flexibility. Such an understanding will aid in the rational design of more selective and effective G-quadruplex binding ligands.     

Effects of ground loop currents on signal intensities in electrospray mass spectrometry

The occurrence of electrochemical processes during the operation of an electrospray ionization (ESI) source is well established. In the positive ion mode, electrons are drawn from the ESI metal capillary to a high voltage power supply. These electrons are the product of charge-balancing oxidation reactions taking place at the liquid/metal interface of the ion source. In a recent study, (Anal. Chem.2001, 73, 4836-4844), our group has shown that the introduction of a ground loop can dramatically enhance the rate of these oxidation processes. Such a ground loop can be introduced by connecting the sample infusion syringe (or the liquid chromatography column, in the case of LC-MS studies) to ground. The magnitude of the ground loop current can be controlled by the electrolyte concentration in the analyte solution, and by the dimensions of the capillary connecting the syringe needle and the ESI source. Using ferrocene as a model system, it is demonstrated that the introduction of such a ground loop can significantly enhance the signal intensity of analytes that form electrochemically ionized species during ESI. However, analytes that form protonated molecular ions, such as reserpine, also show higher signal intensities when a ground loop is introduced into the system. This latter observation is attributed to the occurrence of electrolytic solvent (acetonitrile and/or water) oxidation processes. These reactions generate protons within the ion source, and thus facilitate the formation of [M + nH](n+) ions. Overall, this work provides an example of how the careful control of electrochemical parameters can be exploited to optimize signal intensities in ESI-MS.     

GCMC simulation of argon adsorption in wedge shaped mesopores of finite length

We have used Grand Canonical Monte Carlo simulation to study argon adsorption at 87 K in wedge shaped mesopores. The structural parameters, including mean pore size, wall length and wedge angle, were varied to investigate their effects on the size, shape and the position of the hysteresis loop. Although the effects of pore size have been studied previously, the wall length and wedge angle have received little attention. We find that the wedge angle can have a significant effect on the existence, position, size and shape of the hysteresis loop, while the wall length affects the adsorptive capacity associated with the loop and the behaviour of the isotherm beyond the loop. The results of this work have far-reaching consequences for the characterization of pore size distribution where it is commonly assumed, when constructing a kernel of local isotherms, that pore size is uniform, since even a small deviation from a constant pore width can shift the condensation and evaporation pressures significantly and thus lead to an incorrect estimation of pore size.     

Disorder-to-order transition of an intrinsically disordered region of sortase revealed by multiscale enhanced sampling

Molecular functions of intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs), such as molecular recognition and cellular signaling, are ascribed to dynamic changes in the conformational space in response to binding of target molecules. Sortase, a transpeptitase in Gram-positive bacteria, has an IDR in a loop which undergoes a disordered-to-ordered transition (called "disordered loop"), accompanying a tilt of another loop ("dynamic loop"), upon binding of a signal peptide and a calcium ion. In this study, all-atom conformational ensembles of sortase were calculated for the four different binding states (with/without the peptide and with/without a calcium ion) by the multiscale enhanced sampling (MSES) simulation to examine how the binding of the peptide and/or calcium influences the conformational ensemble. The MSES is a multiscale and multicopy simulation method that allows an enhanced sampling of the all-atom model of large proteins including explicit solvent. A 100 ns MSES simulation of the ligand-free sortase using 20 replicas (in total 2 μs) demonstrated large flexibility in both the disordered and dynamic loops; however, their distributions were not random but had a clear preference which populates the N-terminal part of the disordered loop near the bound form. The MSES simulations of the three binding states clarified the allosteric mechanism of sortase: the N- and C-terminal parts of the disordered loop undergo a disorder-to-order transition independently of each other upon binding of the peptide and a calcium ion, respectively; however, upon binding of both ligands, the two parts work cooperatively to stabilize the bound peptide.     

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

基因网络前馈环路中的涨落共振

应用化学主方程和线性涨落近似方法,重点研究了前馈环路（FFL）对外界输入弱信号的响应,特别考察了它的涨落共振现象．研究发现Z基因的FR行为很大程度上依赖于FFL的协同性：协同FFL中Z的FR曲线呈明显的单峰,而非协同FFL中该曲线出现明显双峰．由于振荡信号常常在实际应用中用来探测网络的调控结构,因此可以利用涨落共振曲线的定性差别来区分FFL网络的性能．