An Optimized Kinematic Mobility Analysis of Protein Molecules

2014 ◽  
Author(s):  
Ahmet Demirtas ◽  
Zahra Shahbazi
Keyword(s):  
Degrees Of Freedom ◽  
3D Structure ◽  
Computational Cost ◽  
Random Group ◽  
Kinematic Chains ◽  
Simulation Speed ◽  
Modified Method ◽  
Rigidity Analysis ◽  
Protein Molecules ◽  
Pebble Game

Understanding the 3D structure and consequently the motion of protein molecules contributes to simulate their function. Modeling protein molecules as kinematic chains has been used to predict protein molecules flexible and rigid regions as well as their degrees of freedom to predict their mobility. However, high computational cost for relatively large molecules is one of the major challenges in this field. In this paper we have combined our previously developed rigidity analysis (ProtoFold) with pebble game thus improving computational cost of our simulation. Here, we have determined the required time for all steps of ProtoFold and subsequently the most time consuming step. Results have shown that finding rigid loops inside the protein structure using graph theory and Grübler-Kutzbach criterion is the slowest part of the procedure, taking an average of 75% of the time required for the rigidity analysis. Therefore we have replaced this step with pebble game. The modified method has been applied to a random group of protein molecules and its efficiency in significantly improving the simulation speed has been verified.

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.

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.

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.

Driving Torsion Scans with Wavefront Propagation

2020 ◽  
Author(s):  
Yudong Qiu ◽  
Daniel Smith ◽  
Chaya Stern ◽  
mudong feng ◽  
Lee-Ping Wang
Keyword(s):  
Potential Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Initial Guess ◽  
Field Development ◽  
Force Field Development ◽  
Wavefront Propagation ◽  
Open Source Software Package

<div>The parameterization of torsional / dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields.</div><div>Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms.</div><div>To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values.</div><div>However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses.</div><div>In this paper we propose a systematic and versatile workflow called \textit{TorsionDrive} to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development.</div><div>The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described.</div><div>The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes.</div>

Combined Graph Layout Algorithms for Automated Sketching of Kinematic Chains

2012 ◽  
Author(s):  
Martín A. Pucheta ◽  
Nicolás E. Ulrich ◽  
Alberto Cardona
Keyword(s):  
Computational Cost ◽  
Kinematic Chain ◽  
Initial Position ◽  
Graph Representation ◽  
Combinatorial Algorithms ◽  
Graph Layout ◽  
Kinematic Chains ◽  
Aesthetic Characteristics ◽  
Edge Crossings ◽  
Independent Loops

The graph layout problem arises frequently in the conceptual stage of mechanism design, specially in the enumeration process where a large number of topological solutions must be analyzed. Two main objectives of graph layout are the avoidance or minimization of edge crossings and the aesthetics. Edge crossings cannot be always avoided by force-directed algorithms since they reach a minimum of the energy in dependence with the initial position of the vertices, often randomly generated. Combinatorial algorithms based on the properties of the graph representation of the kinematic chain can be used to find an adequate initial position of the vertices with minimal edge crossings. To select an initial layout, the minimal independent loops of the graph can be drawn as circles followed by arcs, in all forms. The computational cost of this algorithm grows as factorial with the number of independent loops. This paper presents a combination of two algorithms: a combinatorial algorithm followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of vertex-to-edge repulsion to improve aesthetics and minimize crossings. Atlases of graphs of complex kinematic chains are used to validate the results. The layouts obtained have good quality in terms of minimization of edge crossings and maximization of aesthetic characteristics.

An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions

2015 ◽  
Vol 769 ◽  
pp. 369-386 ◽  
Author(s):  
A. Lefebvre-Lepot ◽  
B. Merlet ◽  
T. N. Nguyen
Keyword(s):  
Short Range ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Accurate Method ◽  
Spherical Particles ◽  
Particle Model ◽  
Stokesian Dynamics ◽  
New Feature ◽  
The Many

We address the problem of computing the hydrodynamic forces and torques among $N$ solid spherical particles moving with given rotational and translational velocities in Stokes flow. We consider the original fluid–particle model without introducing new hypotheses or models. Our method includes the singular lubrication interactions which may occur when some particles come close to one another. The main new feature is that short-range interactions are propagated to the whole flow, including accurately the many-body lubrication interactions. The method builds on a pre-existing fluid solver and is flexible with respect to the choice of this solver. The error is the error generated by the fluid solver when computing non-singular flows (i.e. with negligible short-range interactions). Therefore, only a small number of degrees of freedom are required and we obtain very accurate simulations within a reasonable computational cost. Our method is closely related to a method proposed by Sangani & Mo (Phys. Fluids, vol. 6, 1994, pp. 1653–1662) but, in contrast with the latter, it does not require parameter tuning. We compare our method with the Stokesian dynamics of Durlofsky et al. (J. Fluid Mech., vol. 180, 1987, pp. 21–49) and show the higher accuracy of the former (both by analysis and by numerical experiments).

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

A Weighted Rearranged Spectral Equation Method for Structural Model Updating

1995 ◽  
Author(s):  
José Roberto F. Arruda ◽  
Carlson Antonio M. Verçosa
Keyword(s):  
Degrees Of Freedom ◽  
Structural Model ◽  
Model Updating ◽  
Structural Connectivity ◽  
Computational Cost ◽  
Force Balance ◽  
Dynamic Force ◽  
Stiffness Coefficients ◽  
Spring System ◽  
Spectral Equation

Abstract A new structural model updating method based on the dynamic force balance is presented. The method consists of rearranging the spectral equation so that measured modes and natural frequencies can be used to compute directly updated stiffness coefficients. The proposed method preserves both the structural connectivity and reciprocity, which translate into sparsity and symmetry of the stiffness matrix, respectively. Large changes in small-valued stiffness coefficients are avoided using parameter weighting in the rearranged spectral equation solution. It is shown that the proposed method produces results which are similar to the results obtained using Alvar Kabe’s method, with the advantages of simpler formulation and smaller computational cost. A simple example of an 8 degrees-of-freedom mass-spring system, originally used by Kabe to present his method, is used here to evaluate the proposed method.

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