Research Papers

Rigidity Analysis of Protein Molecules

[+] Author and Article Information
Zahra Shahbazi

Assistant Professor
Department of Mechanical Engineering,
Manhattan College,
Riverdale, NY 10471
e-mail: Zahra.shahbazi@manhattan.edu

Ahmet Demirtas

Department of Mechanical Engineering,
Manhattan College,
Riverdale, NY 10471
e-mail: ademirtas.student@manhattan.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received November 11, 2014; final manuscript received February 15, 2015; published online April 24, 2015. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 15(3), 031009 (Sep 01, 2015) (6 pages) Paper No: JCISE-14-1384; doi: 10.1115/1.4029977 History: Received November 11, 2014; Revised February 15, 2015; Online April 24, 2015

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.

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Grahic Jump Location
Fig. 2

Geometric parameters of hydrogen bonds

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Fig. 3

Closed loop created by a hydrogen bond

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Fig. 4

Three nonrigid loops connected to each other—transparent circles show shared joints

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Fig. 5

DOF of different structures calculated using method 1

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Fig. 6

Pebble movement in specific direction

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Fig. 7

Path to move a free pebble

Grahic Jump Location
Fig. 8

First pebble motion (a), creating a path to neighbor vertex through p16 (b), and moving the free pebbles (c)

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Fig. 9

(a) Converted structure for pebble game. (b) Pebbles were placed onto each vertex. (c) Pebble game result for the given structure.

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Fig. 10

DOF of various structures using method 2

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Fig. 11

Flexible and rigid regions of sample proteins



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