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

Elastic network models (ENM) 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 non-covalent interactions, analogous to the eigenspectrum of normal modes, and decomposes proteins into rigid clusters identical to those from topological rigidity. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, and enables a detailed analysis of motion modes obtained from both approaches. Our analysis reveals that collectivity of protein motions, reported by the Shannon entropy, is significantly lower for rigidity theory versus 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 protein stiffness changes observed from experiment and molecular dynamics simulations. 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 analysis suggests that hydrogen bond networks have evolved to modulate protein structure and dynamics

Rigidity and flexibility of biological networks

The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is given. We also briefly discuss the network aspects of cytoskeletal tensegrity. Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks. Our summary raises the possibility that the concepts of flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl

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 ﾑﾑactiveﾒﾒ 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

High Performance Computing Techniques to Better Understand Protein Conformational Space

This thesis presents an amalgamation of high performance computing techniques to get better insight into protein molecular dynamics. Key aspects of protein function and dynamics can be learned from their conformational space. Datasets that represent the complex nuances of a protein molecule are high dimensional. Efficient dimensionality reduction becomes indispensable for the analysis of such exorbitant datasets. Dimensionality reduction forms a formidable portion of this work and its application has been explored for other datasets as well. It begins with the parallelization of a known non-liner feature reduction algorithm called Isomap. The code for the algorithm was re-written in C with portions of it parallelized using OpenMP. Next, a novel data instance reduction method was devised which evaluates the information content offered by each data point, which ultimately helps in truncation of the dataset with much fewer data points to evaluate. Once a framework has been established to reduce the number of variables representing a dataset, the work is extended to explore algebraic topology techniques to extract meaningful information from these datasets. This step is the one that helps in sampling the conformations of interest of a protein molecule. The method employs the notion of hierarchical clustering to identify classes within a molecule, thereafter, algebraic topology is used to analyze these classes. Finally, the work is concluded by presenting an approach to solve the open problem of protein folding. A Monte-Carlo based tree search algorithm is put forth to simulate the pathway that a certain protein conformation undertakes to reach another conformation. The dissertation, in its entirety, offers solutions to a few problems that hinder the progress of solution for the vast problem of understanding protein dynamics. The motion of a protein molecule is guided by changes in its energy profile. In this course the molecule gradually slips from one energy class to another. Structurally, this switch is transient spanning over milliseconds or less and hence is difficult to be captured solely by the work in wet laboratories

Dynamics and electrostatics define an allosteric druggable site within the receptor-binding domain of SARS-CoV-2 spike protein

The pathogenesis of the SARS-CoV-2 virus initiates through recognition of the angiotensin-converting enzyme 2 (ACE2) receptor of the host cells by the receptor-binding domain (RBD) located at the spikes of the virus. Here, using molecular dynamics simulations, we have demonstrated the allosteric crosstalk within the RBD in the apo- and the ACE2 receptor-bound states, revealing the contribution of the dynamics-based correlated motions and the electrostatic energy perturbations to this crosstalk. While allostery, based on correlated motions, dominates inherent distal communication in the apoRBD, the electrostatic energy perturbations determine favorable pairwise crosstalk within the RBD residues upon binding to ACE2. Interestingly, the allosteric path is composed of residues which are evolutionarily conserved within closely related coronaviruses, pointing toward the biological relevance of the communication and its potential as a target for drug development

Essential dynamics of proteins using geometrical simulations and subspace analysis

Essential dynamics is the application of principal component analysis to a dynamic trajectory derived from a simulation protocol in order to extract biologically relevant information contained in the high dimensional data. In this work, we apply the methodology of essential dynamics to protein trajectories derived from geometrical simulations, which are based on the perturbation of geometrical constraints inherent in a protein. Specifically, we show that the geometrical simulation model is highly efficient for the determination of native state dynamics. Furthermore, by the application of subspace analysis to the essential subspaces of multiple sets of proteins that were simulated under multiple modeling paradigms, we show that the geometrical modeling paradigm is internally consistent and provides results that are qualitatively and quantitatively similar to results obtained from the more commonly employed methods of elastic network models and molecular dynamics. The geometrical paradigm is therefore established as a viable alternative or co-model for the investigation of native state protein dynamics with application to both small, single domain proteins as well as large, multi domain systems

Development of Integrated Machine Learning and Data Science Approaches for the Prediction of Cancer Mutation and Autonomous Drug Discovery of Anti-Cancer Therapeutic Agents

Few technological ideas have captivated the minds of biochemical researchers to the degree that machine learning (ML) and artificial intelligence (AI) have. Over the last few years, advances in the ML field have driven the design of new computational systems that improve with experience and are able to model increasingly complex chemical and biological phenomena. In this dissertation, we capitalize on these achievements and use machine learning to study drug receptor sites and design drugs to target these sites. First, we analyze the significance of various single nucleotide variations and assess their rate of contribution to cancer. Following that, we used a portfolio of machine learning and data science approaches to design new drugs to target protein kinase inhibitors. We show that these techniques exhibit strong promise in aiding cancer research and drug discovery

Structure and Function in Homodimeric Enzymes:Simulations of Cooperative and Independent Functional Motions

Large-scale conformational change is a common feature in the catalytic cycles of enzymes. Many enzymes function as homodimers with active sites that contain elements from both chains. Symmetric and anti-symmetric cooperative motions in homodimers can potentially lead to correlated active site opening and/or closure, likely to be important for ligand binding and release. Here, we examine such motions in two different domain-swapped homodimeric enzymes: the DcpS scavenger decapping enzyme and citrate synthase. We use and compare two types of all-atom simulations: conventional molecular dynamics simulations to identify physically meaningful conformational ensembles, and rapid geometric simulations of flexible motion, biased along normal mode directions, to identify relevant motions encoded in the protein structure. The results indicate that the opening/closure motions are intrinsic features of both unliganded enzymes. In DcpS, conformational change is dominated by an anti-symmetric cooperative motion, causing one active site to close as the other opens; however a symmetric motion is also significant. In CS, we identify that both symmetric (suggested by crystallography) and asymmetric motions are features of the protein structure, and as a result the behaviour in solution is largely non-cooperative. The agreement between two modelling approaches using very different levels of theory indicates that the behaviours are indeed intrinsic to the protein structures. Geometric simulations correctly identify and explore large amplitudes of motion, while molecular dynamics simulations indicate the ranges of motion that are energetically feasible. Together, the simulation approaches are able to reveal unexpected functionally relevant motions, and highlight differences between enzymes