Geometric analysis characterizes molecular rigidity in generic and non-generic protein configurations

Kinematic analysis of kinases and their oncogenic mutations - Kinases and their mutation kinematic analysis

Protein kinases are crucial cellular enzymes that facilitate the transfer of phosphates from adenosine triphosphate (ATP) to their substrates, thereby regulating numerous cellular activities. Dysfunctional kinase activity often leads to oncogenic conditions. Chosen by using structural similarity to 5UG9, we selected 79 crystal structures from the PDB and based on the position of the phenylalanine side chain in the DFG motif, we classified these 79 crystal structures into 5 group clusters. Our approach applies our kinematic flexibility analysis (KFA) to explore the flexibility of kinases in various activity states and examine the impact of the activation loop on kinase structure. KFA enables the rapid decomposition of macromolecules into different flexibility regions, allowing comprehensive analysis of conformational structures. The results reveal that the activation loop of kinases acts as a "lock" that stabilizes the active conformation of kinases by rigidifying the adjacent α-helices. Furthermore, we investigate specific kinase mutations, such as the L858R mutation commonly associated with non-small cell lung cancer, which induces increased flexibility in active-state kinases. In addition, through analyzing the hydrogen bond pattern, we examine the substructure of kinases in different states. Notably, active-state kinases exhibit a higher occurrence of α-helices compared to inactive-state kinases. This study contributes to the understanding of biomolecular conformation at a level relevant to drug development.

SARS-CoV-2 main protease mutation analysis via a kinematic method

The Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2) is the virus responsible for the COVID-19 pandemic. COVID-19 continues to cause millions of deaths globally in part due to immune-evading mutations. SARS-CoV-2 main protease (Mpro) is an important enzyme for viral replication and potentially an effective drug target. Mutations affect the dynamics of enzymes and thereby their activity and ability to bind ligands. Here, we use kinematic flexibility analysis (KFA) to identify how mutations and ligand binding changes the conformational flexibility of Mpro. KFA decomposes macromolecules into regions of different flexibility near-instantly from a static structure, allowing conformational dynamics analysis at scale. Altogether, we analyzed 47 mutation sites across 69 Mpro-ligand complexes resulting in more than 3300 different structures which includes 69 mutated structures with all 47 sites mutated simultaneously and 3243 single residue mutated structures. We found that mutations generally increased the conformational flexibility of the protein. Understanding the impact of mutations on the flexibility of Mpro is essential for identifying potential drug targets in the treatment of SARS-CoV-2. Further studies in this area can offer valuable insights into the mechanisms of molecular recognition.

Kinematic Vibrational Entropy Assessment and Analysis of SARS CoV-2 Main Protease

The three-dimensional conformations of a protein influence its function and select for the ligands it can interact with. The total free energy change during protein-ligand complex formation includes enthalphic and entropic components, which together report on the binding affinity and conformational states of the complex. However, determining the entropic contribution is computationally burdensome. Here, we apply kinematic flexibility analysis (KFA) to efficiently estimate vibrational frequencies from static protein and protein-ligand structures. The vibrational frequencies, in turn, determine the vibrational entropies of the structures and their complexes. Our estimates of the vibrational entropy change caused by ligand binding compare favorably to values obtained from a dynamic Normal Mode Analysis (NMA). Higher correlation factors can be achieved by increasing the distance cutoff in the potential energy model. Furthermore, we apply our new method to analyze the entropy changes of the SARS CoV-2 main protease when binding with different ligand inhibitors, which is relevant for the design of potential drugs.

Shining light on cysteine modification: connecting protein conformational dynamics to catalysis and regulation

Cysteine is a rare but functionally important amino acid that is often subject to covalent modification. Cysteine oxidation plays an important role in many human disease processes, and basal levels of cysteine oxidation are required for proper cellular function. Because reactive cysteine residues are typically ionized to the thiolate anion (Cys-S-), their formation of a covalent bond alters the electrostatic and steric environment of the active site. X-ray-induced photo-oxidation to sulfenic acids (Cys-SOH) can recapitulate some aspects of the changes that occur under physiological conditions. Here we propose how site-specific cysteine photo-oxidation can be used to interrogate ensuing changes in protein structure and dynamics at atomic resolution. Although this powerful approach can connect cysteine covalent modification to global protein conformational changes and function, careful biochemical validation must accompany all such studies to exclude misleading artifacts. New types of X-ray crystallography experiments and powerful computational methods are creating new opportunities to connect conformational dynamics to catalysis for the large class of systems that use covalently modified cysteine residues for catalysis or regulation.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Elastic network models (ENMs) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by noncovalent interactions, analogous to the eigenspectrum of normal modes. The zero modes decompose proteins into rigid clusters identical to those from topological rigidity, while nonzero modes rank protein motions by their hydrogen bond collective energy penalty. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, enabling a detailed analysis of motion modes obtained from both approaches. Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize experimental and simulated protein stiffness variations. Kinematic motion modes highly correlate with reported crystallographic B factors and molecular dynamics simulations of adenylate kinase. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our results suggest that hydrogen bond networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra-high dimensional configuration spaces, and the requirement to avoid (self-) collisions, which results in low acceptance rates. Here, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near-colliding links. The resulting constraint varieties instantaneously redirect the search for collision-free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson-disk motion planner, which prevents local oversampling and widens the search, to ultra-high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Correlated protein motions identified with our algorithm agree with those from MD simulations. © 2018 Wiley Periodicals, Inc.

Fast, clash-free RNA conformational morphing using molecular junctions

Motivation

Non-coding ribonucleic acids (ncRNA) are functional RNA molecules that are not translated into protein. They are extremely dynamic, adopting diverse conformational substates, which enables them to modulate their interaction with a large number of other molecules. The flexibility of ncRNA provides a challenge for probing their complex 3D conformational landscape, both experimentally and computationally.

Results

Despite their conformational diversity, ncRNAs mostly preserve their secondary structure throughout the dynamic ensemble. Here we present a kinematics-based procedure to morph an RNA molecule between conformational substates, while avoiding inter-atomic clashes. We represent an RNA as a kinematic linkage, with fixed groups of atoms as rigid bodies and rotatable bonds as degrees of freedom. Our procedure maintains RNA secondary structure by treating hydrogen bonds between base pairs as constraints. The constraints define a lower-dimensional, secondary-structure constraint manifold in conformation space, where motions are largely governed by molecular junctions of unpaired nucleotides. On a large benchmark set, we show that our morphing procedure compares favorably to peer algorithms, and can approach goal conformations to within a low all-atom RMSD by directing fewer than 1% of its atoms. Our results suggest that molecular junctions can modulate 3D structural rearrangements, while secondary structure elements guide large parts of the molecule along the transition to the correct final conformation.

Availability and Implementation

The source code, binaries and data are available at https://simtk.org/home/kgs .

Contact

amelie.heliou@polytechnique.edu or vdbedem@stanford.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Probing RNA Native Conformational Ensembles with Structural Constraints

Noncoding ribonucleic acids (RNA) play a critical role in a wide variety of cellular processes, ranging from regulating gene expression to post-translational modification and protein synthesis. Their activity is modulated by highly dynamic exchanges between three-dimensional conformational substates, which are difficult to characterize experimentally and computationally. Here, we present an innovative, entirely kinematic computational procedure to efficiently explore the native ensemble of RNA molecules. Our procedure projects degrees of freedom onto a subspace of conformation space defined by distance constraints in the tertiary structure. The dimensionality reduction enables efficient exploration of conformational space. We show that the conformational distributions obtained with our method broadly sample the conformational landscape observed in NMR experiments. Compared to normal mode analysis-based exploration, our procedure diffuses faster through the experimental ensemble while also accessing conformational substates to greater precision. Our results suggest that conformational sampling with a highly reduced but fully atomistic representation of noncoding RNA expresses key features of their dynamic nature.

Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs

Proteins perform their function or interact with partners by exchanging between conformational substates on a wide range of spatiotemporal scales. Structurally characterizing these exchanges is challenging, both experimentally and computationally. Large, diffusional motions are often on timescales that are difficult to access with molecular dynamics simulations, especially for large proteins and their complexes. The low frequency modes of normal mode analysis (NMA) report on molecular fluctuations associated with biological activity. However, NMA is limited to a second order expansion about a minimum of the potential energy function, which limits opportunities to observe diffusional motions. By contrast, kino-geometric conformational sampling (KGS) permits large perturbations while maintaining the exact geometry of explicit conformational constraints, such as hydrogen bonds. Here, we extend KGS and show that a conformational ensemble of the α subunit Gαs of heterotrimeric stimulatory protein Gs exhibits structural features implicated in its activation pathway. Activation of protein Gs by G protein-coupled receptors (GPCRs) is associated with GDP release and large conformational changes of its α-helical domain. Our method reveals a coupled α-helical domain opening motion while, simultaneously, Gαs helix α5 samples an activated conformation. These motions are moderated in the activated state. The motion centers on a dynamic hub near the nucleotide-binding site of Gαs, and radiates to helix α4. We find that comparative NMA-based ensembles underestimate the amplitudes of the motion. Additionally, the ensembles fall short in predicting the accepted direction of the full activation pathway. Taken together, our findings suggest that nullspace sampling with explicit, holonomic constraints yields ensembles that illuminate molecular mechanisms involved in GDP release and protein Gs activation, and further establish conformational coupling between key structural elements of Gαs.