Rigidity analysis of HIV-1 protease

We present a rigidity analysis on a large number of X-ray crystal structures of the enzyme HIV-1 protease using the 'pebble game' algorithm of the software FIRST. We find that although the rigidity profile remains similar across a comprehensive set of high resolution structures, the profile changes significantly in the presence of an inhibitor. Our study shows that the action of the inhibitors is to restrict the flexibility of the beta-hairpin flaps which allow access to the active site. The results are discussed in the context of full molecular dynamics simulations as well as data from NMR experiments.Comment: 4 pages, 3 figures. Conference proceedings for CMMP conference 2010 which was held at the University of Warwic

A Central Partition of Molecular Conformational Space. IV. Extracting information from the graph of cells

In previous works [physics/0204035, physics/0404052, physics/0509126] a procedure was described for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data sampled in molecular dynamics trajectories: the graph of cells, that encodes the set of cells in conformational space that are visited by the system in its thermal wandering. Here we outline a set of procedures for extracting useful information from this structure: 1st) interesting regions in the volume occupied by the system in conformational space can be bounded by a polyhedral cone whose faces are determined empirically from a set of relations between the coordinates of the molecule, 2nd) it is also shown that this cone can be decomposed into a hierarchical set of smaller cones, 3rd) the set of cells in a cone can be encoded by a simple combinatorial sequence.Comment: added an intrduction and reference

Atomic-Level Characterization of the Activation Mechanism of SERCA by Calcium

We have performed molecular dynamics (MD) simulations to elucidate, in atomic detail, the mechanism by which the sarcoplasmic reticulum Ca2+-ATPase (SERCA) is activated by Ca2+. Crystal structures suggest that activation of SERCA occurs when the cytoplasmic head-piece, in an open (E1) conformation stabilized by Ca2+, undergoes a large-scale open-to-closed (E1 to E2) transition that is induced by ATP binding. However, spectroscopic measurements in solution suggest that these structural states (E1 and E2) are not tightly coupled to biochemical states (defined by bound ligands); the closed E2 state predominates even in the absence of ATP, in both the presence and absence of Ca2+. How is this loose coupling consistent with the high efficiency of energy transduction in the Ca2+-ATPase? To provide insight into this question, we performed long (500 ns) all-atom MD simulations starting from the open crystal structure, including a lipid bilayer and water. In both the presence and absence of Ca2+, we observed a large-scale open-to-closed conformational transition within 400 ns, supporting the weak coupling between structural and biochemical states. However, upon closer inspection, it is clear that Ca2+ is necessary and sufficient for SERCA to reach the precise geometrical arrangement necessary for activation of ATP hydrolysis. Contrary to suggestions from crystal structures, but in agreement with solution spectroscopy, the presence of ATP is not required for this activating transition. Principal component analysis showed that Ca2+ reshapes the free energy landscape of SERCA to create a path between the open conformation and the activated closed conformation. Thus the malleability of the free energy landscape is essential for SERCA efficiency, ensuring that ATP hydrolysis is tightly coupled to Ca2+ transport. These results demonstrate the importance of real-time dynamics in the formation of catalytically competent conformations of SERCA, with broad implications for understanding enzymatic catalysis in atomic detail

Protein Structure along the Order–Disorder Continuum

Thermal fluctuations cause proteins to adopt an ensemble of conformations wherein the relative stability of the different ensemble members is determined by the topography of the underlying energy landscape. “Folded” proteins have relatively homogeneous ensembles, while “unfolded” proteins have heterogeneous ensembles. Hence, the labels “folded” and “unfolded” represent attempts to provide a qualitative characterization of the extent of structural heterogeneity within the underlying ensemble. In this work, we introduce an information-theoretic order parameter to quantify this conformational heterogeneity. We demonstrate that this order parameter can be estimated in a straightforward manner from an ensemble and is applicable to both unfolded and folded proteins. In addition, a simple formula for approximating the order parameter directly from crystallographic B factors is presented. By applying these metrics to a large sample of proteins, we show that proteins span the full range of the order–disorder axis.National Institutes of Health (U.S.) (NIH Grant 5R21NS063185-02

Manipulating Protein Conformations By Single-molecule Afm-fret Nanoscopy

Combining atomic force microscopy and fluorescence resonance energy transfer spectroscopy (AFM-FRET), we have developed a single-molecule AFM-FRET nanoscopy approach capable of effectively pinpointing and mechanically manipulating a targeted dye-labeled single protein in a large sampling area and simultaneously monitoring the conformational changes of the targeted protein by recording single-molecule FRET time trajectories. We have further demonstrated an application of using this nanoscopy on manipulation of single-molecule protein conformation and simultaneous single-molecule FRET measurement of a Cy3-Cy5-labeled kinase enzyme, HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase). By analyzing time-resolved FRET trajectories and correlated AFM force pulling curves of the targeted single-molecule enzyme, we are able to observe the protein conformational changes of a specific coordination by AFM mechanic force pulling

On the conservation of the slow conformational dynamics within the amino acid kinase family: NAGK the paradigm

N-Acetyl-L-Glutamate Kinase (NAGK) is the structural paradigm for examining the catalytic mechanisms and dynamics of amino acid kinase family members. Given that the slow conformational dynamics of the NAGK (at the microseconds time scale or slower) may be rate-limiting, it is of importance to assess the mechanisms of the most cooperative modes of motion intrinsically accessible to this enzyme. Here, we present the results from normal mode analysis using an elastic network model representation, which shows that the conformational mechanisms for substrate binding by NAGK strongly correlate with the intrinsic dynamics of the enzyme in the unbound form. We further analyzed the potential mechanisms of allosteric signalling within NAGK using a Markov model for network communication. Comparative analysis of the dynamics of family members strongly suggests that the low-frequency modes of motion and the associated intramolecular couplings that establish signal transduction are highly conserved among family members, in support of the paradigm sequence→structure→dynamics→function © 2010 Marcos et al

Order without design

Experimental reality in molecular and cell biology, as revealed by advanced research technologies and methods, is manifestly inconsistent with the design perspective on the cell, thus creating an apparent paradox: where do order and reproducibility in living systems come from if not from design

Mathematical treatment of adiabatic fast passage pulses for the computation of nuclear spin relaxation rates in proteins with conformational exchange

Although originally designed for broadband inversion and decoupling in NMR spectroscopy, recent methodological developments have introduced adiabatic fast passage (AFP) pulses into the field of protein dynamics. AFP pulses employ a frequency sweep, and have not only superior inversion properties with respect to offset effects, but they are also easily implemented into a pulse sequence. As magnetization is dragged from the +z to the −z direction, Larmor precession is impeded since magnetization becomes spin-locked, which is a potentially useful feature for the investigation of microsecond to millisecond dynamics. A major drawback of these pulses as theoretical prediction is concerned, however, results from their time-dependent offset: simulations of spin density matrices under the influence of a time-dependent Hamiltonian with non-commuting elements are costly in terms of computational time, rendering data analysis impracticable. In this paper we suggest several ways to reduce the computational time without compromising accuracy with respect to effects such as cross-correlated relaxation and modulation of the chemical shift