Kinematic Motion Constraints of the Protein Molecule Chains

2011 ◽  
Author(s):  
Zahra Shahbazi ◽  
Horea T. Ilies¸ ◽  
Kazem Kazerounian
Keyword(s):  
Hydrogen Bonds ◽  
Degrees Of Freedom ◽  
Main Chain ◽  
Protein Structures ◽  
Protein Molecule ◽  
Correct Identification ◽  
Closed Loops ◽  
Motion Constraints ◽  
Protein Molecules ◽  
Internal Mobility

The function of protein molecules is defined by their 3-D geometry, as well as their internal mobility, which is heavily influenced by the internal hydrogen bonds. The correct identification of these hydrogen bonds and the prediction of their effect on the mobility of protein molecules can provide an invaluable mechanism to understand protein behavior. Applications of this study ranges from nano-engineering to new drug design. We are extending our recent approach from identifying main-chain main-chain hydrogen bonds to all types of hydrogen bonds that occur in protein structures, such as α-helices and β-sheets. We use the Gru¨bler-Kutzbach kinematic mobility criterion to determine the degrees of freedom of all closed loops (rigid loops as well as closed loops of one or more degrees of freedom) formed by Hydrogen bonds. Furthermore, we systematically develop constraint equations for non-rigid closed loops. Several examples of protein molecules from PDB are used to show that these additions both improve the accuracy of mobility analysis and enable us to study a broader range of the motion of protein molecules. This approach offers theoretical insight as well as extensive numerical efficiencies in protein simulations.

Hydrogen Bonds and Kinematic Mobility of Protein Molecules

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Zahra Shahbazi ◽  
Horea T. Ilieş ◽  
Kazem Kazerounian
Keyword(s):  
Hydrogen Bonds ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Folding Process ◽  
Kinematic Chains ◽  
Protein Molecules ◽  
Internal Mobility ◽  
Lower Mobility ◽  
Folding Simulations ◽  
And Function

Modeling protein molecules as kinematic chains provides the foundation for developing powerful approaches to the design, manipulation, and fabrication of peptide based molecules and devices. Nevertheless, these models possess a high number of degrees of freedom (DOFs) with considerable computational implications. On the other hand, real protein molecules appear to exhibit a much lower mobility during the folding process than what is suggested by existing kinematic models. The key contributor to the lower mobility of real proteins is the formation of hydrogen bonds during the folding process. In this paper, we explore the pivotal role of hydrogen bonds in determining the structure and function of the proteins from the point of view of mechanical mobility. The existing geometric criteria on the formation of hydrogen bonds are reviewed and a new set of geometric criteria is proposed. We show that the new criteria better correlate the number of predicted hydrogen bonds with those established by biological principles than other existing criteria. Furthermore, we employ established tools in kinematics mobility analysis to evaluate the internal mobility of protein molecules and to identify the rigid and flexible segments of the proteins. Our results show that the developed procedure significantly reduces the DOF of the protein models, with an average reduction of 94%. Such a dramatic reduction in the number of DOF can have enormous computational implications in protein folding simulations.

On Hydrogen Bonds and Mobility of Protein Molecules

2009 ◽  
Author(s):  
Zahra Shahbazi ◽  
Horea T. Ilies¸ ◽  
Kazem Kazerounian
Keyword(s):  
Hydrogen Bonds ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Folding Process ◽  
Kinematic Chains ◽  
Protein Molecules ◽  
Internal Mobility ◽  
Lower Mobility ◽  
Folding Simulations ◽  
And Function

Modeling protein molecules as kinematic chains provides the foundation for developing powerful approaches to the design, manipulation and fabrication of peptide based molecules and devices. Nevertheless, these models possess a high number of degrees of freedom (DOF) with considerable computational implications. On the other hand, real protein molecules appear to exhibits a much lower mobility during the folding process than what is suggested by existing kinematic models. The key contributor to the lower mobility of real proteins is the formation of Hydrogen bonds during the folding process. In this paper we explore the pivotal role of Hydrogen bonds in determining the structure and function of the proteins from the point of view of mechanical mobility. The existing geometric criteria on the formation of Hydrogen bonds are reviewed and a new set of geometric criteria are proposed. We show that the new criteria better correlate the number of predicted Hydrogen bonds with those established by biological principles than other existing criteria. Furthermore, we employ established tools in kinematics mobility analysis to evaluate the internal mobility of protein molecules, and to identify the rigid and flexible segments of the proteins. Our results show that the developed procedure significantly reduces the DOF of the protein models, with an average reduction of 94%. Such a dramatic reduction in the number of DOF can have has enormous computational implications in protein folding simulations.

Electron density based analysis of N–H⋯OC hydrogen bonds and electrostatic interaction energies in high-resolution secondary protein structures: insights from quantum crystallographic approaches

CrystEngComm ◽  
2020 ◽  
Vol 22 (26) ◽  
pp. 4363-4373 ◽  
Author(s):  
Suman K. Mandal ◽  
Benoît Guillot ◽  
Parthapratim Munshi
Keyword(s):  
High Resolution ◽  
Hydrogen Bonds ◽  
Electron Density ◽  
Electrostatic Interaction ◽  
Main Chain ◽  
Protein Structures ◽  
Interaction Energies ◽  
Topological Parameters ◽  
Limiting Values ◽  
Qualitative Analyses

Limiting values of the topological parameters and the electrostatic interaction energies to establish the presence of true N–H⋯OC H-bonds in protein main-chain have been identified using quantitative and qualitative analyses of electron densities.

Rigidity Analysis of Protein Molecules

2015 ◽  
Vol 15 (3) ◽  
Author(s):  
Zahra Shahbazi ◽  
Ahmet Demirtas
Keyword(s):  
Protein Structure ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
3D Structure ◽  
Closed Loops ◽  
Matlab Program ◽  
Acid Versus ◽  
Rigidity Analysis ◽  
Protein Molecules ◽  
Pebble Game

Intrinsic flexibility of protein molecules enables them to change their 3D structure and perform their specific task. Therefore, identifying rigid regions and consequently flexible regions of proteins has a significant role in studying protein molecules' function. In this study, we developed a kinematic model of protein molecules considering all covalent and hydrogen bonds in protein structure. Then, we used this model and developed two independent rigidity analysis methods to calculate degrees of freedom (DOF) and identify flexible and rigid regions of the proteins. The first method searches for closed loops inside the protein structure and uses Grübler–Kutzbach (GK) criterion. The second method is based on a modified 3D pebble game. Both methods are implemented in a matlab program and the step by step algorithms for both are discussed. We applied both methods on simple 3D structures to verify the methods. Also, we applied them on several protein molecules. The results show that both methods are calculating the same DOF and rigid and flexible regions. The main difference between two methods is the run time. It's shown that the first method (GK approach) is slower than the second method. The second method takes 0.29 s per amino acid versus 0.83 s for the first method to perform this rigidity analysis.

scholarly journals NMR Protein Structure Calculation and Sphere Intersections

2020 ◽  
Vol 8 (1) ◽  
pp. 89-101
Author(s):  
Carlile Lavor ◽  
Rafael Alves ◽  
Michael Souza ◽  
Luis Aragón José
Keyword(s):  
Protein Structures ◽  
Structure Calculation ◽  
Bp Algorithm ◽  
Main Step ◽  
Combinatorial Method ◽  
Nmr Data ◽  
Sampling Process ◽  
Protein Molecules ◽  
Protein Structure Calculation ◽  
Branch And Prune

AbstractNuclear Magnetic Resonance (NMR) experiments can be used to calculate 3D protein structures and geometric properties of protein molecules allow us to solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i − 3, i − 2, i − 1, with radii given by the atomic distances di−3,i, di−2,i, di−1,i, respectively, to obtain the position for atom i. Because of uncertainty in NMR data, some of the distances di−3,i should be represented as interval distances [{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], where {\underline{d}_{i - 3,i}} \le {d_{i - 3,i}} \le {\bar d_{i - 3,i}}. In the literature, an extension of the BP algorithm was proposed to deal with interval distances, where the idea is to sample values from [{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}]. We present a new method, based on conformal geometric algebra, to reduce the size of [{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], before the sampling process. We also compare it with another approach proposed in the literature.

All-atomistic molecular dynamics study of the glass transition of amorphous polymers

2021 ◽  
Author(s):  
Zhiye Tang ◽  
Susumu Okazaki
Keyword(s):  
Molecular Dynamics ◽  
Glass Transition ◽  
Spatial Scale ◽  
Degrees Of Freedom ◽  
Main Chain ◽  
Polymer Materials ◽  
Coarse Grained ◽  
Mode Analysis ◽  
Radius Of Gyration ◽  
Chemical Structures

Glass transition is an important phenomenon of polymer materials and it has been intensively studied over the past a few decades. However, the influencing factors arising from the chemical structures of the polymers are often ignored due to a continuous or coarse-grained description of the polymer. Here, we approached this phenomenon using all-atomistic molecular dynamics (MD) simulations and two conventionally used polymer materials, polycarbonate (PC) and poly-(methyl methacrylate) (PMMA). We reproduced the glass transition temperatures (Tg) of the two materials reasonably well. Then we characterized and investigated the glass transition process by looking at the changes of potential energy, dihedral transition, and thermal fluctuation of the individual degrees of freedom in the systems, over the entire temperature range of glass transition. As previously reported, the dihedral angles stop their conformational changes gradually at the Tg, especially for the main chain dihedrals, and sidechain rotations immediately rooting from the main chain. The volumetric change during the temperature decrease is confirmed to be because of conformational adjustment, probably due to the tendency of chain stretching for the maintenance of the radius of gyration, and the loss of thermal energy. The strength of motions of single degrees of freedom and polymer chains, and overall slow motions obtained by normal mode analysis (NMA) shows that different motions at different spatial scale may gradually stop at distinct temperature in the MD simulation temporal and spatial scales. Presumably, the small spatial scale do not contribute to the glass transition at the experimental scale since the timescale is much longer than their relaxation time.

scholarly journals Side chain to main chain hydrogen bonds stabilize a polyglutamine helix in the activation domain of a transcription factor

2018 ◽  
Author(s):  
Albert Escobedo ◽  
Busra Topal ◽  
Micha Ben Achim Kunze ◽  
Juan Aranda ◽  
Giulio Chiesa ◽  
...  
Keyword(s):  
Transcription Factor ◽  
Hydrogen Bonds ◽  
Transcriptional Activity ◽  
Main Chain ◽  
Muscular Atrophy ◽  
Helical Structure ◽  
Structural Basis ◽  
Tract Length ◽  
Spinobulbar Muscular Atrophy ◽  
Polyq Tract

Polyglutamine (polyQ) tracts are regions of low sequence complexity of variable length found in more than one hundred human proteins. These tracts are frequent in activation domains of transcription factors and their length often correlates with transcriptional activity. In addition, in nine proteins, tract elongation beyond specific thresholds causes polyQ disorders. To study the structural basis of the association between tract length, transcriptional activity and disease, here we addressed how the conformation of the polyQ tract of the androgen receptor (AR), a transcription factor associated with the polyQ disease spinobulbar muscular atrophy (SBMA), depends on its length. We found that the tract folds into a helical structure stabilized by unconventional hydrogen bonds between glutamine side chains and main chain carbonyl groups. These bonds are bifurcate with the conventional main chain to main chain hydrogen bonds stabilizing α-helices. In addition, since tract elongation provides additional interactions, the helicity of the polyQ tract directly correlates with its length. These findings suggest a plausible rationale for the association between polyQ tract length and AR transcriptional activity and have implications for establishing the mechanistic basis of SBMA.

Protein Molecules as Natural Nano Bio Devices: Mobility Analysis

2010 ◽  
Author(s):  
Zahra Shahbazi ◽  
Horea T. Ilies¸ ◽  
Kazem Kazerounian
Keyword(s):  
Degrees Of Freedom ◽  
Conformational Transitions ◽  
Living Cells ◽  
Mobility Analysis ◽  
Folding Process ◽  
Kinematic Chains ◽  
Protein Molecules ◽  
Kinematic Models ◽  
Lower Mobility ◽  
Molecular Components

Proteins are nature’s nano-robots in the form of functional molecular components of living cells. The function of these natural nano-robots often requires conformational transitions between two or more native conformations that are made possible by the intrinsic mobility of the proteins. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nano-mechanical systems [1]. Modeling protein molecules as kinematic chains provides the foundation for developing powerful approaches to the design, manipulation and fabrication of peptide based molecules and devices. Nevertheless, these models possess a high number of degrees of freedom (DOF) with considerable computational implications. On the other hand, real protein molecules appear to exhibits a much lower mobility during the folding process than what is suggested by existing kinematic models. The key contributor to the lower mobility of real proteins is the formation of Hydrogen bonds during the folding process.

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