Avishek Kumar

Amorphous graphene: a realization of Zachariasen’s glass

Amorphous graphene is a realization of a two-dimensional Zachariasen glass as first proposed 80 years ago. Planar continuous random networks of this archetypal two-dimensional network are generated by two complementary simulation methods. In the first, a Monte Carlo bond switching algorithm is employed to systematically amorphize a crystalline graphene sheet. In the second, molecular dynamics simulations are utilized to quench from the high temperature liquid state. The two approaches lead to similar results as detailed here, through the pair distribution function and the associated diffraction pattern. Details of the structure, including ring statistics and angular distortions, are shown to be sensitive to preparation conditions, and await experimental confirmation.

Rigidity loss in disordered systems : three scenarios

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings.

The Role of Conformational Dynamics and Allostery in the Disease Development of Human Ferritin

Determining the three-dimensional structure of myoglobin, the first solved structure of a protein, fundamentally changed the way protein function was understood. Even more revolutionary was the information that came afterward: protein dynamics play a critical role in biological functions. Therefore, understanding conformational dynamics is crucial to obtaining a more complete picture of protein evolution. We recently analyzed the evolution of different protein families including green fluorescent proteins (GFPs), β-lactamase inhibitors, and nuclear receptors, and we observed that the alteration of conformational dynamics through allosteric regulation leads to functional changes. Moreover, proteome-wide conformational dynamics analysis of more than 100 human proteins showed that mutations occurring at rigid residue positions are more susceptible to disease than flexible residue positions. These studies suggest that disease-associated mutations may impair dynamic allosteric regulations, leading to loss of function. Thus, in this study, we analyzed the conformational dynamics of the wild-type light chain subunit of human ferritin protein along with the neutral and disease forms. We first performed replica exchange molecular dynamics simulations of wild-type and mutants to obtain equilibrated dynamics and then used perturbation response scanning (PRS), where we introduced a random Brownian kick to a position and computed the fluctuation response of the chain using linear response theory. Using this approach, we computed the dynamic flexibility index (DFI) for each position in the chain for the wild-type and the mutants. DFI quantifies the resilience of a position to a perturbation and provides a flexibility/rigidity measurement for a given position in the chain. The DFI analysis reveals that neutral variants and the wild-type exhibit similar flexibility profiles in which experimentally determined functionally critical sites act as hinges in controlling the overall motion. However, disease mutations alter the conformational dynamic profile, making hinges more loose (i.e., softening the hinges), thus impairing the allosterically regulated dynamics.

Insulating behavior of an amorphous graphene membrane

threefold coordinated networks consisting of hexagonal rings but also includingmany pentagons and heptagons distributed in a random fashion. Using the Kubo transport methodology andthe Lanczos method, the density of states, mean free paths, and semiclassical conductivities of such amorphousgraphene membranes are computed. Despite a large increase in the density of states close to the charge neutralitypoint, all electronic properties are dramatically degraded, evidencing an Anderson insulating state caused bytopological disorder alone. These results are supported by Landauer-Buttiker conductance calculations, which¨show a localization length as short as 5 nm.DOI: 10.1103/PhysRevB.86.121408 PACS number(s): 72

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Integration of structural dynamics and molecular evolution via protein interaction networks: A new era in genomic medicine

Sequencing technologies are revealing many new non-synonymous single nucleotide variants (nsSNVs) in each personal exome. To assess their functional impacts, comparative genomics is frequently employed to predict if they are benign or not. However, evolutionary analysis alone is insufficient, because it misdiagnoses many disease-associated nsSNVs, such as those at positions involved in protein interfaces, and because evolutionary predictions do not provide mechanistic insights into functional change or loss. Structural analyses can aid in overcoming both of these problems by incorporating conformational dynamics and allostery in nSNV diagnosis. Finally, protein-protein interaction networks using systems-level methodologies shed light onto disease etiology and pathogenesis. Bridging these network approaches with structurally resolved protein interactions and dynamics will advance genomic medicine.

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template‐based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug‐design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr‐REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native‐like structures from a template and to provide a set of persistent contacts to be employed during re‐folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled. Proteins 2015; 83:2279–2292.

Loss in Allosteric Regulations through Structural Dynamics Lead to Disease

Determining the three-dimensional structure of myoglobin, the first solved structure of a protein, fundamentally changed the way protein function was understood. Even more revolutionary was the information that came afterward: structure encoded protein dynamics underlies biological functions. In protein evolution, the classical view of the one sequence-one structure-one function paradigm is now being extended to a new view: an ensemble of conformations in equilibrium that can evolve new functions. Therefore, understanding structural dynamics is crucial to obtaining a more complete picture of protein evolution. We recently analyzed the evolution of different protein families including GFP proteins, beta-lactamase inhibitors, and nuclear receptors. Using Molecular Dynamics to compute the equilibrium dynamics and quantifying the contribution of each residue to the dynamics through the Dynamic Flexibility Index (DFI), we have observed that the alteration of conformational dynamics through allosteric regulation leads to functional changes. Moreover, our proteome-wide conformational dynamics analysis of over 100 human proteins shows that mutations occurring at rigid residue positions are more susceptible to disease. Analysis of the wild type light chain subunit of human ferritin protein along with the neutral and disease forms reveal that disease-associated mutations may impair dynamic allosteric regulations leading to a loss of function. Indeed, neutral variants and the wild type exhibit similar DFI profiles in which experimentally determined functionally critical sites act as hinges in controlling the overall motion. On the other hand, disease mutations make hinges more loose (i.e., softens the hinges),impairing the allosterically regulated dynamics

174 Mechanism of protein evolution: conformational dynamics and allostery

of observed structural patterns as modules or “building blocks” in large proteins (higher secondary structure content). From structural descriptor analysis, observed patterns are found to be within similar deviation, however frequent patterns are found to be distinctly occurring in diverse functions e.g. in enzymatic classes and reactions (Khan & Ghosh, in press). We have further analyzed and compared the kinetic accessibility of structural patterns using structure based models (SBM) and Go-like potential (Lammert, Schug, & Onuchic, 2009). Monitoring the folding/unfolding transitions, our result shows that homogeneity in tertiary contacts contributes to the distinct transition phases (unfolding/folding basins). The balance between tertiary and local contacts contributes to the cooperative nature of folding, which are found to be prominent characteristic in prevalent structural patterns.