Wenfei Li

Frustration, specific sequence dependence, and nonlinearity in large-amplitude fluctuations of allosteric proteins

Proteins have often evolved sequences so as to acquire the ability for regulation via allosteric conformational change. Here we investigate how allosteric dynamics is designed through sequences with nonlinear interaction features. First, for 71 allosteric proteins of which two, open and closed, structures are available, a statistical survey of interactions using an all-atom model with effective solvation shows that those residue contact interactions specific to one of the two states are significantly weaker than are the contact interactions shared by the two states. This interaction feature indicates there is underlying sequence design to facilitate conformational change. Second, based on the energy landscape theory, we implement these interaction features into a new atomic-interaction-based coarse-grained model via a multiscale simulation protocol (AICG). The AICG model outperforms standard coarse-grained models for predictions of the native-state mean fluctuations and of the conformational change direction. Third, using the new model for adenylate kinase, we show that intrinsic fluctuations in one state contain rare and large-amplitude motions nearly reaching the other state. Such large-amplitude motions are realized partly by sequence specificity and partly by the nonlinear nature of contact interactions, leading to cracking. Both features enhance conformational transition rates.

Metal-coupled folding of Cys2His2 zinc-finger.

Zinc-fingers, which widely exist in eukaryotic cell and play crucial roles in life processes, depend on the binding of zinc ion for their proper folding. To computationally study the zinc-coupled folding of the zinc-fingers, charge transfer and metal induced protonation/deprotonation effects have to be considered. Here, by attempting to implicitly account for such effects in classical molecular dynamics and performing intensive simulations with explicit solvent for the peptides with and without zinc binding, we investigate the folding of the Cys2His2-type zinc-finger motif and the coupling between the peptide folding and zinc binding. We find that zinc ion not only stabilizes the native structure but also participates in the whole folding process. It binds to the peptide at an early stage of folding and directs or modulates the folding and stabilizations of the component beta-hairpin and alpha-helix. Such a crucial role of zinc binding is mediated by the packing of the conserved hydrophobic residues. We also find that the packing of the hydrophobic residues and the coordination of the native ligands are coupled. Meanwhile, the processes of zinc binding, mis-ligation, ligand exchange, and zinc induced secondary structure conversion as well as the water behavior due to the involvement of zinc ion are characterized. Our results are in good agreement with related experimental observations and provide significant insight into the general mechanisms of the metal cofactor dependent protein folding and other metal-induced conformational changes of biological importance.

Energy landscape and multiroute folding of topologically complex proteins adenylate kinase and 2ouf-knot

While fast folding of small proteins has been relatively well characterized by experiments and theories, much less is known for slow folding of larger proteins, for which recent experiments suggested quite complex and rich folding behaviors. Here, we address how the energy landscape theory can be applied to these slow folding reactions. Combining the perfect-funnel approximation with a multiscale method, we first extended our previous atomic-interaction based coarse grained (AICG) model to take into account local flexibility of protein molecules. Using this model, we then investigated the energy landscapes and folding routes of two proteins with complex topologies: a multidomain protein adenylate kinase (AKE) and a knotted protein 2ouf-knot. In the AKE folding, consistent with experimental results, the kinetic free energy surface showed several substates between the fully unfolded and native states. We characterized the structural features of these substates and transitions among them, finding temperature-dependent multiroute folding. For protein 2ouf-knot, we found that the improved atomic-interaction based coarse-grained model can spontaneously tie a knot and fold the protein with a probability up to 96%. The computed folding rate of the knotted protein was much slower than that of its unknotted counterpart, in agreement with experimental findings. Similar to the AKE case, the 2ouf-knot folding exhibited several substates and transitions among them. Interestingly, we found a dead-end substate that lacks the knot, thus suggesting backtracking mechanisms.

Protein folding simulations: From coarse‐grained model to all‐atom model

Protein folding is an important and challenging problem in molecular biology. During the last two decades, molecular dynamics (MD) simulation has proved to be a paramount tool and was widely used to study protein structures, folding kinetics and thermodynamics, and structure–stability–function relationship. It was also used to help engineering and designing new proteins, and to answer even more general questions such as the minimal number of amino acid or the evolution principle of protein families. Nowadays, the MD simulation is still undergoing rapid developments. The first trend is to toward developing new coarse‐grained models and studying larger and more complex molecular systems such as protein–protein complex and their assembling process, amyloid related aggregations, and structure and motion of chaperons, motors, channels and virus capsides; the second trend is toward building high resolution models and explore more detailed and accurate pictures of protein folding and the associated processes, such as the coordination bond or disulfide bond involved folding, the polarization, charge transfer and protonate/deprotonate process involved in metal coupled folding, and the ion permeation and its coupling with the kinetics of channels. On these new territories, MD simulations have given many promising results and will continue to offer exciting views. Here, we review several new subjects investigated by using MD simulations as well as the corresponding developments of appropriate protein models. These include but are not limited to the attempt to go beyond the topology based Gō‐like model and characterize the energetic factors in protein structures and dynamics, the study of the thermodynamics and kinetics of disulfide bond involved protein folding, the modeling of the interactions between chaperonin and the encapsulated protein and the protein folding under this circumstance, the effort to clarify the important yet still elusive folding mechanism of protein BBL, the development of discrete MD and its application in studying the α–β conformational conversion and oligomer assembling process, and the modeling of metal ion involved protein folding.

Energy landscape views for interplays among folding, binding, and allostery of calmodulin domains

Significance Protein dynamics can conceptually be classified into three factors: folding, conformational transitions, and chemical events. Although couplings between every two of these factors have been well studied, explicit coupling among the three factors has not been examined due to its difficulty in direct experimental measurements. Toward this direction, calmodulin is a suitable model system. Here, constructing a computational model that integrates folding, ligand binding, and allosteric motions based on the energy landscape theory, we studied interplay among the three factors, in detail, for calmodulin domains. The analysis includes three conformational states and three binding states, resulting into nine states in total. We found multiple routes and their intriguing modulation by ligand concentration. Ligand binding modulates the energy landscape of proteins, thus altering their folding and allosteric conformational dynamics. To investigate such interplay, calmodulin has been a model protein. Despite much attention, fully resolved mechanisms of calmodulin folding/binding have not been elucidated. Here, by constructing a computational model that can integrate folding, binding, and allosteric motions, we studied in-depth folding of isolated calmodulin domains coupled with binding of two calcium ions and associated allosteric conformational changes. First, mechanically pulled simulations revealed coexistence of three distinct conformational states: the unfolded, the closed, and the open states, which is in accord with and augments structural understanding of recent single-molecule experiments. Second, near the denaturation temperature, we found the same three conformational states as well as three distinct binding states: zero, one, and two calcium ion bound states, leading to as many as nine states. Third, in terms of the nine-state representation, we found multiroute folding/binding pathways and shifts in their probabilities with the calcium concentration. At a lower calcium concentration, “combined spontaneous folding and induced fit” occurs, whereas at a higher concentration, “binding-induced folding” dominates. Even without calcium binding, we observed that the folding pathway of calmodulin domains can be modulated by the presence of metastable states. Finally, full-length calmodulin also exhibited an intriguing coupling between two domains when applying tension.

All-atom replica exchange molecular simulation of protein BBL.

Downhill folding is one of the most important predictions of energy landscape theory. Recently, the Escherichia coli 2‐oxoglutarate dehydrogenase PSBD was described as a first example of global downhill folding (Garcia‐Mira et al., Science 2002;298:2191), classification that has been later subject of significant controversy. To help resolve this problem, by using intensive all‐atom simulation with explicit water model and the replica exchange method, we sample the phase space of protein BBL and depict the free energy landscape. We give an estimate of the free energy barrier height of 1–2 kBT, dependent on the way the energy landscape is projected. We also study the conformational distribution of the transition region and find that the three helices generally take the similar positions as that in the native states whereas their spatial orientations show large variability. We further detect the inconsistency between different signals by individually fitting the thermal denaturation curves of five structural features using two‐state model, which gives a wide spread melting temperature of 19 K. All of these features are consistent with a picture of folding with very low cooperativities. Compared with the experimental data (Sadqi et al., Nature 2006; 442:317), our results indicate that the Naf‐BBL (pH5.3) may have an even lower barrier height and cooperativity. Proteins 2008.

Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations

Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablos group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to emulate one ATP cycle of a molecular motor, kinesin. Second, nonspecific protein-DNA binding was studied by a combination of elaborate protein and DNA models. Third, a transcription factor, p53, that contains highly fluctuating regions was simulated on two perpendicularly arranged DNA segments, addressing intersegmental transfer of p53. Fourth, we simulated structural dynamics of dinucleosomes connected by a linker DNA finding distinct types of internucleosome docking and salt-concentration-dependent compaction. Finally, we discuss many of limitations in the current approaches and future directions. Especially, more accurate electrostatic treatment and a phospholipid model that matches our CG resolutions are of immediate importance.

Multiscale methods for protein folding simulations.

Inherently hierarchic nature of proteins makes multiscale computational methods especially useful in the studies of folding and other functional dynamics. With the multiscale strategies, one can achieve improved accuracy and efficiency by coupling the atomistic and the coarse grained simulations. Depending on the problems studied, very different implementation protocols can be used to realize the multiscale idea. Here, we give detailed introductions to the currently used multiscale protocols, together with some recent applications to the protein folding simulations in our group. The advantages and weakness, as well as the application scopes of these multiscale protocols are discussed. The directions for the future developments are also proposed.

Single-molecule force spectroscopy reveals force-enhanced binding of calcium ions by gelsolin

Force is increasingly recognized as an important element in controlling biological processes. Forces can deform native protein conformations leading to protein-specific effects. Protein–protein binding affinities may be decreased, or novel protein–protein interaction sites may be revealed, on mechanically stressing one or more components. Here we demonstrate that the calcium-binding affinity of the sixth domain of the actin-binding protein gelsolin (G6) can be enhanced by mechanical force. Our kinetic model suggests that the calcium-binding affinity of G6 increases exponentially with force, up to the point of G6 unfolding. This implies that gelsolin may be activated at lower calcium ion levels when subjected to tensile forces. The demonstration that cation–protein binding affinities can be force-dependent provides a new understanding of the complex behaviour of cation-regulated proteins in stressful cellular environments, such as those found in the cytoskeleton-rich leading edge and at cell adhesions.

Folding of a Small RNA Hairpin Based on Simulation with Replica Exchange Molecular Dynamics

The folding of a small RNA tetraloop hairpin is studied based on intensive molecular dynamics simulation, aiming to understand the folding mechanism of this small and fast RNA folder. Our results showed that this RNA hairpin has very complicated folding behavior in spite of its small size. It is found that the folding transition has low cooperativity. Instead of a two-state folding, four major states are observed, including the native state, the intermediate, the unfolded state, and the misfolded state. The misfolded state is mainly stabilized by the non-native hydrogen bonds, and is more compact. Two potential folding pathways, in which two basepairs formed with different order, are observed, and the pathway with the inboard basepair formed before the terminal one is much more favorable, and dominates the folding of the RNA hairpin.