Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs

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.

Exploring implicit spaces for constrained sampling-based planning

We present a review and reformulation of manifold constrained sampling-based motion planning within a unifying framework, IMACS (implicit manifold configuration space). IMACS enables a broad class of motion planners to plan in the presence of manifold constraints, decoupling the choice of motion planning algorithm and method for constraint adherence into orthogonal choices. We show that implicit configuration spaces defined by constraints can be presented to sampling-based planners by addressing two key fundamental primitives, sampling and local planning, and that IMACS preserves theoretical properties of probabilistic completeness and asymptotic optimality through these primitives. Within IMACS, we implement projection- and continuation-based methods for constraint adherence, and demonstrate the framework on a range of planners with both methods in simulated and realistic scenarios. Our results show that the choice of method for constraint adherence depends on many factors and that novel combinations of planners and methods of constraint adherence can be more effective than previous approaches. Our implementation of IMACS is open source within the Open Motion Planning Library and is easily extended for novel planners and constraint spaces.

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.

Maintaining and Enhancing Diversity of Sampled Protein Conformations in Robotics-Inspired Methods

The ability to efficiently sample structurally diverse protein conformations allows one to gain a high-level view of a protein's energy landscape. Algorithms from robot motion planning have been used for conformational sampling, and several of these algorithms promote diversity by keeping track of "coverage" in conformational space based on the local sampling density. However, large proteins present special challenges. In particular, larger systems require running many concurrent instances of these algorithms, but these algorithms can quickly become memory intensive because they typically keep previously sampled conformations in memory to maintain coverage estimates. In addition, robotics-inspired algorithms depend on defining useful perturbation strategies for exploring the conformational space, which is a difficult task for large proteins because such systems are typically more constrained and exhibit complex motions. In this article, we introduce two methodologies for maintaining and enhancing diversity in robotics-inspired conformational sampling. The first method addresses algorithms based on coverage estimates and leverages the use of a low-dimensional projection to define a global coverage grid that maintains coverage across concurrent runs of sampling. The second method is an automatic definition of a perturbation strategy through readily available flexibility information derived from B-factors, secondary structure, and rigidity analysis. Our results show a significant increase in the diversity of the conformations sampled for proteins consisting of up to 500 residues when applied to a specific robotics-inspired algorithm for conformational sampling. The methodologies presented in this article may be vital components for the scalability of robotics-inspired approaches.

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.

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

Proteins operate and interact with partners by dynamically exchanging between functional substates of a conformational ensemble on a rugged free energy landscape. Understanding how these substates are linked by coordinated, collective motions requires exploring a high-dimensional space, which remains a tremendous challenge. While molecular dynamics simulations can provide atomically detailed insight into the dynamics, computational demands to adequately sample conformational ensembles of large biomolecules and their complexes often require tremendous resources. Kinematic models can provide high-level insights into conformational ensembles and molecular rigidity beyond the reach of molecular dynamics by reducing the dimensionality of the search space. Here, we model a protein as a kinematic linkage and present a new geometric method to characterize molecular rigidity from the constraint manifold Q and its tangent space Q at the current configuration q. In contrast to methods based on combinatorial constraint counting, our method is valid for both generic and non-generic, e.g., singular configurations. Importantly, our geometric approach provides an explicit basis for collective motions along floppy modes, resulting in an efficient procedure to probe conformational space. An atomically detailed structural characterization of coordinated, collective motions would allow us to engineer or allosterically modulate biomolecules by selectively stabilizing conformations that enhance or inhibit function with broad implications for human health.