Jianhan Chen

Recent advances in implicit solvent-based methods for biomolecular simulations

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

Can molecular dynamics simulations provide high‐resolution refinement of protein structure?

Recent advances in efficient and accurate treatment of solvent with the generalized Born approximation (GB) have made it possible to substantially refine the protein structures generated by various prediction tools through detailed molecular dynamics simulations. As demonstrated in a recent CASPR experiment, improvement can be quite reliably achieved when the initial models are sufficiently close to the native basin (e.g., 3–4 Å Cα RMSD). A key element to effective refinement is to incorporate reliable structural information into the simulation protocol. Without intimate knowledge of the target and prediction protocol used to generate the initial structural models, it can be assumed that the regular secondary structure elements (helices and strands) and overall fold topology are largely correct to start with, such that the protocol limits itself to the scope of refinement and focuses the sampling in vicinity of the initial structure. The secondary structures can be enforced by dihedral restraints and the topology through structural contacts, implemented as either multiple pair‐wise Cα distance restraints or a single sidechain distance matrix restraint. The restraints are weakly imposed with flat‐bottom potentials to allow sufficient flexibility for structural rearrangement. Refinement is further facilitated by enhanced sampling of advanced techniques such as the replica exchange method (REX). In general, for single domain proteins of small to medium sizes, 3–5 nanoseconds of REX/GB refinement simulations appear to be sufficient for reasonable convergence. Clustering of the resulting structural ensembles can yield refined models over 1.0 Å closer to the native structure in Cα RMSD. Substantial improvement of sidechain contacts and rotamer states can also be achieved in most cases. Additional improvement is possible with longer sampling and knowledge of the robust structural features in the initial models for a given prediction protocol. Nevertheless, limitations still exist in sampling as well as force field accuracy, manifested as difficulty in refinement of long and flexible loops. Proteins 2007.

Intrinsic disorder mediates the diverse regulatory functions of the Cdk inhibitor p21

Traditionally, well-defined three-dimensional structure was thought to be essential for protein function. However, myriad biological functions are performed by highly dynamic, intrinsically disordered proteins (IDPs). IDPs often fold upon binding their biological targets and frequently exhibit “binding diversity” by targeting multiple ligands. We sought to understand the physical basis of IDP binding diversity and herein report that the cyclin-dependent kinase (Cdk) inhibitor, p21Cip1, adaptively binds to and inhibits the various Cdk/cyclin complexes that regulate eukaryotic cell division. Based on results from NMR spectroscopy, and biochemical and cellular assays, we show that structural adaptability of a helical sub-domain within p21 termed LH enables two other sub-domains termed D1 and D2 to specifically bind conserved surface features of the cyclin and Cdk subunits, respectively, within otherwise structurally distinct Cdk/cyclin complexes. Adaptive folding upon binding is likely to mediate the diverse biological functions of the thousands of IDPs present in eukaryotes.

Atomistic Details of the Disordered States of KID and pKID. Implications in Coupled Binding and Folding

Intrinsically disordered proteins (IDPs) are a newly recognized class of functional proteins for which a lack of stable tertiary fold is required for function. Because of the heterogeneous and dynamical nature, molecular modeling is necessary to provide the missing details of disordered states of IDP that are crucial for understanding their functions. In particular, generalized Born (GB) implicit solvent, combined with replica exchange (REX), might offer an optimal balance between accuracy and efficiency for modeling IDPs. We carried out extensive REX simulations in an optimized GB force field to characterize the disordered states of a regulatory IDP, KID domain of transcription factor CREB, and its phosphorylated form, pKID. The results revealed that both KID and pKID, though highly disordered on the tertiary level, are compact and mainly occupy a small number of helical substates. Interestingly, although phosphorylation of KID Ser133 leads only to marginal changes in average helicities on the ensemble level, underlying conformational substates differ significantly. In particular, pSer133 appears to restrict the accessible conformational space of the loop region and thus reduces the entropic cost of KID folding upon binding to the KIX domain of CREB-binding protein. Such an expanded role of phosphorylation in the KID:KIX recognition was not previously recognized because of a lack of substantial conformational changes on the ensemble level and inaccessibility of the structural details from experiments. The results also suggest that an implicit solvent-based modeling framework, despite various existing limitations, might be feasible for accurate atomistic simulation of small IDPs in general.

Exploring atomistic details of pH-dependent peptide folding

Modeling pH-coupled conformational dynamics allows one to probe many important pH-dependent biological processes, ranging from ATP synthesis, enzyme catalysis, and membrane fusion to protein folding/misfolding and amyloid formation. This work illustrates the strengths and capabilities of continuous constant pH molecular dynamics in exploring pH-dependent conformational transitions in proteins by revisiting an experimentally well studied model protein fragment, the C peptide from ribonuclease A. The simulation data reveal a bell-shaped pH profile for the total helix content, in agreement with experiment, and several pairs of electrostatic interactions that control the relative populations of unfolded and partially folded states of various helical lengths. The latter information greatly complements and extends that attainable by current experimental techniques. The present work paves the way for new and exciting applications, such as the study of pH-dependent molecular mechanism in the formation of amyloid comprising peptides from Alzheimers and Parkinsons diseases.

Residual Structures, Conformational Fluctuations, and Electrostatic Interactions in the Synergistic Folding of Two Intrinsically Disordered Proteins

To understand the interplay of residual structures and conformational fluctuations in the interaction of intrinsically disordered proteins (IDPs), we first combined implicit solvent and replica exchange sampling to calculate atomistic disordered ensembles of the nuclear co-activator binding domain (NCBD) of transcription coactivator CBP and the activation domain of the p160 steroid receptor coactivator ACTR. The calculated ensembles are in quantitative agreement with NMR-derived residue helicity and recapitulate the experimental observation that, while free ACTR largely lacks residual secondary structures, free NCBD is a molten globule with a helical content similar to that in the folded complex. Detailed conformational analysis reveals that free NCBD has an inherent ability to substantially sample all the helix configurations that have been previously observed either unbound or in complexes. Intriguingly, further high-temperature unbinding and unfolding simulations in implicit and explicit solvents emphasize the importance of conformational fluctuations in synergistic folding of NCBD with ACTR. A balance between preformed elements and conformational fluctuations appears necessary to allow NCBD to interact with different targets and fold into alternative conformations. Together with previous topology-based modeling and existing experimental data, the current simulations strongly support an “extended conformational selection” synergistic folding mechanism that involves a key intermediate state stabilized by interaction between the C-terminal helices of NCBD and ACTR. In addition, the atomistic simulations reveal the role of long-range as well as short-range electrostatic interactions in cooperating with readily fluctuating residual structures, which might enhance the encounter rate and promote efficient folding upon encounter for facile binding and folding interactions of IDPs. Thus, the current study not only provides a consistent mechanistic understanding of the NCBD/ACTR interaction, but also helps establish a multi-scale molecular modeling framework for understanding the structure, interaction, and regulation of IDPs in general.

Application of torsion angle molecular dynamics for efficient sampling of protein conformations

We investigate the application of torsion angle molecular dynamics (TAMD) to augment conformational sampling of peptides and proteins. Interesting conformational changes in proteins mainly involve torsional degrees of freedom. Carrying out molecular dynamics in torsion space does not only explicitly sample the most relevant degrees of freedom, but also allows larger integration time steps with elimination of the bond and angle degrees of freedom. However, the covalent geometry needs to be fixed during internal coordinate dynamics, which can introduce severe distortions to the underlying potential surface in the extensively parameterized modern Cartesian‐based protein force fields. A “projection” approach (Katritch et al. J Comput Chem 2003, 24, 254–265) is extended to construct an accurate internal coordinate force field (ICFF) from a source Cartesian force field. Torsion crossterm corrections constructed from local molecular fragments, together with softened van der Waals and electrostatic interactions, are used to recover the potential surface and incorporate implicit bond and angle flexibility. MD simulations of dipeptide models demonstrate that full flexibility in both the backbone ϕ/ψ and side chain χ1 angles are virtually restored. The efficacy of TAMD in enhancing conformational sampling is then further examined by folding simulations of small peptides and refinement experiments of protein NMR structures. The results show that an increase of several fold in conformational sampling efficiency can be reliably achieved. The current study also reveals some complicated intrinsic properties of internal coordinate dynamics, beyond energy conservation, that can limit the maximum size of the integration time step and thus the achievable gain in sampling efficiency.

Peptide and protein folding and conformational equilibria: theoretical treatment of electrostatics and hydrogen bonding with implicit solvent models.

Since biomolecules exist in aqueous and membrane environments, the accurate modeling of solvation, and hydrogen bonding interactions in particular, is essential for the exploration of structure and function in theoretical and computational studies. In this chapter, we focus on alternatives to explicit solvent models and discuss recent advances in generalized Born (GB) implicit solvent theories. We present a brief review of the successes and shortcomings of the application of these theories to biomolecular problems that are strongly linked to backbone H-bonding and electrostatics. This discussion naturally leads us to explore existing areas for improvement in current GB theories and our approach towards addressing a number of the key issues that remain in the refinement of these models. Specifically, the critical importance of balancing solvation forces and intramolecular forces in GB models is illustrated by examining the influence of backbone hydrogen bond strength and backbone dihedral energetics on conformational equilibria of small peptids.

Topology-based modeling of intrinsically disordered proteins: Balancing intrinsic folding and intermolecular interactions

Coupled binding and folding is frequently involved in specific recognition of so‐called intrinsically disordered proteins (IDPs), a newly recognized class of proteins that rely on a lack of stable tertiary fold for function. Here, we exploit topology‐based Gō‐like modeling as an effective tool for the mechanism of IDP recognition within the theoretical framework of minimally frustrated energy landscape. Importantly, substantial differences exist between IDPs and globular proteins in both amino acid sequence and binding interface characteristics. We demonstrate that established Gō‐like models designed for folded proteins tend to over‐estimate the level of residual structures in unbound IDPs, whereas under‐estimating the strength of intermolecular interactions. Such systematic biases have important consequences in the predicted mechanism of interaction. A strategy is proposed to recalibrate topology‐derived models to balance intrinsic folding propensities and intermolecular interactions, based on experimental knowledge of the overall residual structure level and binding affinity. Applied to pKID/KIX, the calibrated Gō‐like model predicts a dominant multistep sequential pathway for binding‐induced folding of pKID that is initiated by KIX binding via the C‐terminus in disordered conformations, followed by binding and folding of the rest of C‐terminal helix and finally the N‐terminal helix. This novel mechanism is consistent with key observations derived from a recent NMR titration and relaxation dispersion study and provides a molecular‐level interpretation of kinetic rates derived from dispersion curve analysis. These case studies provide important insight into the applicability and potential pitfalls of topology‐based modeling for studying IDP folding and interaction in general. Proteins 2011;

Structural interpretation of paramagnetic relaxation enhancement-derived distances for disordered protein states.

Paramagnetic relaxation enhancement (PRE) is a powerful technique for studying transient tertiary organizations of unfolded and partially folded proteins. The heterogeneous and dynamic nature of disordered protein states, together with the r(-6) dependence of PRE, presents significant challenges for reliable structural interpretation of PRE-derived distances. Without additional knowledge of accessible conformational substates, ensemble-simulation-based protocols have been used to calculate structure ensembles that appear to be consistent with the PRE distance restraints imposed on the ensemble level with the proper r(-6) weighting. However, rigorous assessment of the reliability of such protocols has been difficult without intimate knowledge of the true nature of disordered protein states. Here we utilize sets of theoretical PRE distances derived from simulated structure ensembles that represent the folded, partially folded and unfolded states of a small protein to investigate the efficacy of ensemble-simulation-based structural interpretation of PRE distances. The results confirm a critical limitation that, due to r(-6) weighting, only one or a few members need to satisfy the distance restraints and the rest of the ensemble are essentially unrestrained. Consequently, calculated structure ensembles will appear artificially heterogeneous no matter whether the PRE distances are derived from the folded, partially unfolded or unfolded state. Furthermore, the nature of the heterogeneous ensembles is largely determined by the protein model employed in structure calculation and reflects little on the true nature of the underlying disordered state. These findings suggest that PRE measurements on disordered protein states alone generally do not contain enough information for a reliable structural interpretation and that the latter will require additional knowledge of accessible conformational substates. Interestingly, when a very large number of PRE measurements is available, faithful structural interpretation might be possible with intermediate ensemble sizes under ideal conditions.