A probabilistic network model for structural transitions in biomolecules

Biological macromolecules often undergo large conformational rearrangements during a functional cycle. To simulate these structural transitions with full atomic detail typically demands extensive computational resources. Moreover, it is unclear how to incorporate, in a principled way, additional experimental information that could guide the structural transition. This article develops a probabilistic model for conformational transitions in biomolecules. The model can be viewed as a network of anharmonic springs that break, if the experimental data support the rupture of bonds. Hamiltonian Monte Carlo in internal coordinates is used to infer structural transitions from experimental data, thereby sampling large conformational transitions without distorting the structure. The model is benchmarked on a large set of conformational transitions. Moreover, we demonstrate the use of the probabilistic network model for integrative modeling of macromolecular complexes based on data from crosslinking followed by mass spectrometry.     

Tryptophan in the Pore of the Mechanosensitive Channel MscS: ASSESSMENT OF PORE CONFORMATIONS BY FLUORESCENCE SPECTROSCOPY*

Structural changes in channel proteins give critical insights required for understanding the gating transitions that underpin function. Tryptophan (Trp) is uniquely sensitive to its environment and can be used as a reporter of conformational changes. Here, we have used site-directed Trp insertion within the pore helices of the small mechanosensitive channel protein, MscS, to monitor conformational transitions. We show that Trp can be inserted in place of Leu at the two pore seal positions, Leu¹⁰⁵ and Leu¹⁰⁹, resulting in functional channels. Using Trp¹⁰⁵ as a probe, we demonstrate that the A106V mutation causes a modified conformation in the purified channel protein consistent with a more open state in solution. Moreover, we show that solubilized MscS changes to a more open conformation in the presence of phospholipids or their lysoforms.     

Fingerprinting polysaccharides with single-molecule atomic force microscopy

We report the use of an atomic force microscopy (AFM)-based force spectroscopy technique to identify, at the single-molecule level, the components of mixtures of polysaccharides. Previously, we showed that the elasticity of certain types of polysaccharides is governed by force-induced conformational transitions of the pyranose ring. These transitions produce atomic fingerprints in the force-extension spectrum that are characteristic of the ground-energy conformation of the pyranose ring and the type of glycosidic linkages. Using this approach we find that commercially available agarose and lambda-carrageenan contain molecules that, when stretched in an atomic force microscope, produce a force spectrum characteristic of alpha-(1-->4) d-glucans. We have identified these molecules as amylopectin or floridean starch, a storage polysaccharide in algae. Our methodology can identify individual polysaccharide molecules in solution, which is not possible by any other spectroscopic technique, and therefore is an important addition to the arsenal of analytical techniques used in carbohydrate research.     

Models for recovering the energy landscape of conformational transitions from single-molecule pulling experiments

Single-molecule force spectroscopy is a powerful experimental technique for probing intermolecular forces and conformational transitions of individual molecules. This technique involves measuring the mechanical response of a molecule subjected to a constant or time-varying force. Statistical mechanics has played a pivotal role in interpreting force measurements in terms of the underlying kinetics and energy landscape of the molecular transition being studied. Here, we provide a didactic review of various statistical–mechanical models used for analysing these measurements, emphasising the theoretical ideas and assumptions used in deriving these models.     

FLIPDock: docking flexible ligands into flexible receptors

Conformational changes of biological macromolecules when binding with ligands have long been observed and remain a challenge for automated docking methods. Here we present a novel protein-ligand docking software called FLIPDock (Flexible LIgand-Protein Docking) allowing the automated docking of flexible ligand molecules into active sites of flexible receptor molecules. In FLIPDock, conformational spaces of molecules are encoded using a data structure that we have developed recently called the Flexibility Tree (FT). While the FT can represent fully flexible ligands, it was initially designed as a hierarchical and multiresolution data structure for the selective encoding of conformational subspaces of large biological macromolecules. These conformational subspaces can be built to span a range of conformations important for the biological activity of a protein. A variety of motions can be combined, ranging from domains moving as rigid bodies or backbone atoms undergoing normal mode-based deformations, to side chains assuming rotameric conformations. In addition, these conformational subspaces are parameterized by a small number of variables which can be searched during the docking process, thus effectively modeling the conformational changes in a flexible receptor. FLIPDock searches the variables using genetic algorithm-based search techniques and evaluates putative docking complexes with a scoring function based on the AutoDock3.05 force-field. In this paper, we describe the concepts behind FLIPDock and the overall architecture of the program. We demonstrate FLIPDock's ability to solve docking problems in which the assumption of a rigid receptor previously prevented the successful docking of known ligands. In particular, we repeat an earlier cross docking experiment and demonstrate an increased success rate of 93.5%, compared to original 72% success rate achieved by AutoDock over the 400 cross-docking calculations. We also demonstrate FLIPDock's ability to handle conformational changes involving backbone motion by docking balanol to an adenosine-binding pocket of protein kinase A.     

Conformational selection or induced fit? A critical appraisal of the kinetic mechanism

For almost five decades, two competing mechanisms of ligand recognition, conformational selection and induced fit, have dominated our interpretation of ligand binding in biological macromolecules. When binding-dissociation events are fast compared to conformational transitions, the rate of approach to equilibrium, k(obs), becomes diagnostic of conformational selection or induced fit based on whether it decreases or increases, respectively, with the ligand concentration, [L]. However, this simple conclusion based on the rapid equilibrium approximation is not valid in general. Here we show that conformational selection is associated with a rich repertoire of kinetic properties, with k(obs) decreasing or increasing with [L] depending on the relative magnitude of the rate of ligand dissociation, k(off), and the rate of conformational isomerization, k(r). We prove that, even for the simplest two-step mechanism of ligand binding, a decrease in k(obs) with [L] is unequivocal evidence of conformational selection, but an increase in k(obs) with [L] is not unequivocal evidence of induced fit. Ligand binding to glucokinase, thrombin, and its precursor prethrombin-2 are used as relevant examples. We conclude that conformational selection as a mechanism for a ligand binding to its target may be far more common than currently believed.     

Fast and robust two-dimensional inverse Laplace transformation of single-molecule fluorescence lifetime data

Fluorescence spectroscopy at the single-molecule scale has been indispensable for studying conformational dynamics and rare states of biological macromolecules. Single-molecule two-dimensional (2D) fluorescence lifetime correlation spectroscopy is an emerging technique that holds promise for the study of protein and nucleic acid dynamics, as the technique is 1) capable of resolving conformational dynamics using a single chromophore, 2) resolves forward and reverse transitions independently, and 3) has a dynamic window ranging from microseconds to seconds. However, the calculation of a 2D fluorescence relaxation spectrum requires an inverse Laplace transform (ILT), which is an ill-conditioned inversion that must be estimated numerically through a regularized minimization. Current methods for performing ILTs of fluorescence relaxation can be computationally inefficient, sensitive to noise corruption, and difficult to implement. Here, we adopt an approach developed for NMR spectroscopy (T1-T2 relaxometry) to perform one-dimensional (1D) and 2D-ILTs on single-molecule fluorescence spectroscopy data using singular-valued decomposition and Tikhonov regularization. This approach provides fast, robust, and easy to implement Laplace inversions of single-molecule fluorescence data. We compare this approach to the widely used maximal entropy method.     

Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.     

Hierarchical and multi-resolution representation of protein flexibility

MOTIVATION: Conformational rearrangements during molecular interactions are observed in a wide range of biological systems. However, computational methods that aim at simulating and predicting molecular interactions are still largely ignoring the flexible nature of biological macromolecules as the number of degrees of freedom is computationally intractable when using brute force representations. RESULTS: In this article, we present a computational data structure called the Flexibility Tree (FT) that enables a multi-resolution and hierarchical encoding of molecular flexibility. This tree-like data structure allows the encoding of relatively small, yet complex sub-spaces of a protein's conformational space. These conformational sub-spaces are parameterized by a small number of variables and can be searched efficiently using standard global search techniques. The FT structure makes it straightforward to combine and nest a wide variety of motion types such as hinge, shear, twist, screw, rotameric side chains, normal modes and essential dynamics. Moreover, the ability to assign shapes to the nodes in a FT allows the interactive manipulation of flexible protein shapes and the interactive visualization of the impact of conformational changes on the protein's overall shape. We describe the design of the FT and illustrate the construction of such trees to hierarchically combine motion information obtained from a variety of sources ranging from experiment to user intuition, and describing conformational changes at different biological scales. We show that the combination of various types of motion helps refine the encoded conformational sub-spaces to include experimentally determined structures, and we demonstrate searching these sub-spaces for specific conformations.     

Differential scanning calorimetry of a conformational transition in heavy meromyosin

We have investigated the potential use of differential scanning calorimetry (DSC) to characterize conformational changes in proteins with emphasis on a conformational change in the myosin head which may be related to the power-stroke providing force production in muscle contraction. Simulations indicate that two-state conformational transitions with enthalpy changes greater than approximately 30 kcal/mol should be observable by DSC. We present here differential scanning calorimetric studies of a predenaturation structural change in heavy meromyosin. The high concentration of protein required for these experiments leads to potential contributions from intermolecular interactions. The technical difficulties associated with studying conformational transitions by DSC are discussed.     

Continuous Interdomain Orientation Distributions Reveal Components of Binding Thermodynamics

The flexibility of biological macromolecules is an important structural determinant of function. Unfortunately, the correlations between different motional modes are poorly captured by discrete ensemble representations. Here, we present new ways to both represent and visualize correlated interdomain motions. Interdomain motions are determined directly from residual dipolar couplings, represented as a continuous conformational distribution, and visualized using the disk-on-sphere representation. Using the disk-on-sphere representation, features of interdomain motions, including correlations, are intuitively visualized. The representation works especially well for multidomain systems with broad conformational distributions.This analysis also can be extended to multiple probability density modes, using a Bingham mixture model. We use this new paradigm to study the interdomain motions of staphylococcal protein A, which is a key virulence factor contributing to the pathogenicity of Staphylococcus aureus. We capture the smooth transitions between important states and demonstrate the utility of continuous distribution functions for computing the reorientational components of binding thermodynamics. Such insights allow for the dissection of the dynamic structural components of functionally important intermolecular interactions.     

An AFM-based stiffness clamp for dynamic control of rigidity

Atomic force microscopy (AFM) has become a powerful tool for measuring material properties in biology and imposing mechanical boundary conditions on samples from single molecules to cells and tissues. Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a ‘force clamp’ or ‘position clamp’. However, stiffness, the third variable in the Hookean relation F = kx that describes AFM cantilever deflection, has not been dynamically controllable in the same way. Here we present and demonstrate a ‘stiffness clamp’ that can vary the apparent stiffness of an AFM cantilever. This method, employable on any AFM system by modifying feedback control of the cantilever, allows rapid and reversible tuning of the stiffness exposed to the sample in a way that can decouple the role of stiffness from force and deformation. We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel. We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1–100 nN/µm. This response was independent of the absolute contractile force and cell height, demonstrating that cells can react directly to changes in stiffness alone. In contrast, the hydrogel used in our experiment maintained a constant expansion velocity (dx/dt) over this range of stiffness, while the traction rate (dF/dt) changed with stiffness, showing that passive materials can also behave differently in different stiffness environments. The AFM stiffness clamp presented here, which is applicable to mechanical measurements on both biological and non-biological samples, may be used to investigate cellular mechanotransduction under a wide range of controlled mechanical boundary conditions.     

Conformational Plasticity of the Essential Membrane-associated Mannosyltransferase PimA from Mycobacteria

Phosphatidyl-myo-inositol mannosyltransferase A (PimA) is an essential glycosyltransferase (GT) that initiates the biosynthetic pathway of phosphatidyl-myo-inositol mannosides, lipomannan, and lipoarabinomannan, which are key glycolipids/lipoglycans of the mycobacterial cell envelope. PimA belongs to a large family of peripheral membrane-associated GTs for which the understanding of the molecular mechanism and conformational changes that govern substrate/membrane recognition and catalysis remains a major challenge. Here we used single molecule force spectroscopy techniques to study the mechanical and conformational properties of PimA. In our studies, we engineered a polyprotein containing PimA flanked by four copies of the well characterized I27 protein, which provides an unambiguous mechanical fingerprint. We found that PimA exhibits weak mechanical stability albeit displaying β-sheet topology expected to unfold at much higher forces. Notably, PimA unfolds following heterogeneous multiple step mechanical unfolding pathways at low force akin to molten globule states. Interestingly, the ab initio low resolution envelopes obtained from small angle x-ray scattering of the unliganded PimA and the PimA·GDP complexed forms clearly demonstrate that not only the “open” and “closed” conformations of the GT-B enzyme are largely present in solution, but in addition, PimA experiences remarkable flexibility that undoubtedly corresponds to the N-terminal “Rossmann fold” domain, which has been proved to participate in protein-membrane interactions. Based on these results and on our previous experimental data, we propose a model wherein the conformational transitions are important for the mannosyltransferase to interact with the donor and acceptor substrates/membrane.     

A proposed time-resolved X-ray scattering approach to track local and global conformational changes in membrane transport proteins

Time-resolved X-ray scattering has emerged as a powerful technique for studying the rapid structural dynamics of small molecules in solution. Membrane-protein-catalyzed transport processes frequently couple large-scale conformational changes of the transporter with local structural changes perturbing the uptake and release of the transported substrate. Using light-driven halide ion transport catalyzed by halorhodopsin as a model system, we combine molecular dynamics simulations with X-ray scattering calculations to demonstrate how small-molecule time-resolved X-ray scattering can be extended to the study of membrane transport processes. In particular, by introducing strongly scattering atoms to label specific positions within the protein and substrate, the technique of time-resolved wide-angle X-ray scattering can reveal both local and global conformational changes. This approach simultaneously enables the direct visualization of global rearrangements and substrate movement, crucial concepts that underpin the alternating access paradigm for membrane transport proteins.     

Single-molecule manipulation of macromolecules on GUV or SUV membranes using optical tweezers

Despite their wide applications in soluble macromolecules, optical tweezers have rarely been used to characterize the dynamics of membrane proteins, mainly due to the lack of model membranes compatible with optical trapping. Here, we examined optical trapping and mechanical properties of two potential model membranes, giant and small unilamellar vesicles (GUVs and SUVs, respectively) for studies of membrane protein dynamics. We found that optical tweezers can stably trap GUVs containing iodixanol with controlled membrane tension. The trapped GUVs with high membrane tension can serve as a force sensor to accurately detect reversible folding of a DNA hairpin or membrane binding of synaptotagmin-1 C2AB domain attached to the GUV. We also observed that SUVs are rigid enough to resist large pulling forces and are suitable for detecting protein conformational changes induced by force. Our methodologies may facilitate single-molecule manipulation studies of membrane proteins using optical tweezers.     

Molecular evolution of protein conformational changes revealed by a network of evolutionarily coupled residues

An improved understanding of protein conformational changes has broad implications for elucidating the mechanisms of various biological processes and for the design of protein engineering experiments. Understanding rearrangements of residue interactions is a key component in the challenge of describing structural transitions. Evolutionary properties of protein sequences and structures are extensively studied; however, evolution of protein motions, especially with respect to interaction rearrangements, has yet to be explored. Here, we investigated the relationship between sequence evolution and protein conformational changes and discovered that structural transitions are encoded in amino acid sequences as coevolving residue pairs. Furthermore, we found that highly coevolving residues are clustered in the flexible regions of proteins and facilitate structural transitions by forming and disrupting their interactions cooperatively. Our results provide insight into the evolution of protein conformational changes and help to identify residues important for structural transitions.     

SIMS: A Hybrid Method for Rapid Conformational Analysis

Proteins are at the root of many biological functions, often performing complex tasks as the result of large changes in their structure. Describing the exact details of these conformational changes, however, remains a central challenge for computational biology due the enormous computational requirements of the problem. This has engendered the development of a rich variety of useful methods designed to answer specific questions at different levels of spatial, temporal, and energetic resolution. These methods fall largely into two classes: physically accurate, but computationally demanding methods and fast, approximate methods. We introduce here a new hybrid modeling tool, the Structured Intuitive Move Selector (sims), designed to bridge the divide between these two classes, while allowing the benefits of both to be seamlessly integrated into a single framework. This is achieved by applying a modern motion planning algorithm, borrowed from the field of robotics, in tandem with a well-established protein modeling library. sims can combine precise energy calculations with approximate or specialized conformational sampling routines to produce rapid, yet accurate, analysis of the large-scale conformational variability of protein systems. Several key advancements are shown, including the abstract use of generically defined moves (conformational sampling methods) and an expansive probabilistic conformational exploration. We present three example problems that sims is applied to and demonstrate a rapid solution for each. These include the automatic determination of “active” residues for the hinge-based system Cyanovirin-N, exploring conformational changes involving long-range coordinated motion between non-sequential residues in Ribose-Binding Protein, and the rapid discovery of a transient conformational state of Maltose-Binding Protein, previously only determined by Molecular Dynamics. For all cases we provide energetic validations using well-established energy fields, demonstrating this framework as a fast and accurate tool for the analysis of a wide range of protein flexibility problems.     

A microplate-based evaluation of complex denaturation pathways: structural stability of Escherichia coli transketolase

We have previously developed a rapid microplate-based approach for measuring the denaturation curves by intrinsic tryptophan fluorescence for simple monomeric and two-state unfolding proteins. Here we demonstrate that it can accurately resolve the multiple conformational transitions that occur during the denaturation of a complex multimeric and cofactor associated protein. We have also analyzed the effect of two active-site mutations, D381A and Y440A upon the denaturation pathway of transketolase using intrinsic fluorescence measurements, and we compare the results from classical and microplate-based instrumentation. This work shows that the rapid assay is able to identify changes in the denaturation pathway, due to mutations or removal of cofactors, which affect the stability of the native and intermediate states. This would be of significant benefit for the directed evolution of protein stability, optimizing enzyme stability under biocatalytic process conditions, and also for engineering specific transitions in protein unfolding pathways.