Research Papers

Structural Compliance Analysis and Internal Motion Properties of Proteins From a Robot Kinematics Perspective: Formulation of Basic Equations

[+] Author and Article Information
Keisuke Arikawa

Department of Mechanical Engineering,
Kanagawa Institute of Technology,
Atsugi, Kanagawa 243-0292, Japan
e-mail: arikawa@me.kanagawa-it.ac.jp

Manuscript received March 18, 2015; final manuscript received January 7, 2016; published online February 24, 2016. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 8(2), 021028 (Feb 24, 2016) (8 pages) Paper No: JMR-15-1064; doi: 10.1115/1.4032588 History: Received March 18, 2015; Revised January 07, 2016

From a perspective of robot kinematics, we develop a method for predicting internal motion properties and understanding the functions of proteins from their three-dimensional (3D) structural data (protein data bank (PDB) data). The key ideas are based on the structural compliance analysis of proteins. In this paper, we mainly discuss the basic equations for the analysis. First, a kinematic model of a protein is introduced. Proteins are simply modeled as serial manipulators constrained by linear springs, where the dihedral angles on the main chains correspond to the joint angles of manipulators. Then, the kinematic equations of the protein model are derived. In particular, the forced response or the deformation caused by the forces in static equilibrium forms the basis for the structural compliance analysis. In the formulations, the protein models are regarded as manipulators that control the positions in the model or the distances between them, by the dihedral angles on the main chains. Next, the structural compliance of the protein model is defined, and a method for extracting the information about the internal motion properties from the structural compliance is shown. In general, the structural compliance refers to the relationship between the applied forces and the deformation of the parts surrounded by the application points. We define it in a more general form by separating the parts whose deformations are evaluated from those where forces are applied. When decomposing motion according to the magnitude of the structural compliance, we can infer that the lower compliance motion will easily occur. Finally, we show two application examples using PDB data of lactoferrin and hemoglobin. Despite using an approximate protein model, the predicted internal motion properties agree with the measured ones.

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Lesk, A. M. , 2001, Introduction to Protein Architecture, Oxford University Press, Oxford, UK.
Lesk, A. M. , 2004, Introduction to Protein Science, Oxford University Press, Oxford, UK.
Petsko, G. A. , and Ringe, D. , 2004, Protein Structure and Function, New Science Press, London.
RCSB PDB, 2016, “Protein Data Bank,” http://www.rcsb.org
Subbiah, S. , 1996, Protein Motions, R.G. Landes Company, Austin, TX.
Parsons, D. , and Canny, J. , 1994, “ Geometric Problems in Molecular Biology and Robotics,” 2nd International Conference on Intelligent Systems for Molecular Biology, (ISBM '94), Stanford, CA, Aug. 14–17, pp. 322–330.
Canutescu, A. A. , and Dunbrack, R. L., Jr. , 2003, “ Cyclic Coordinate Descent: A Robotics Algorithm for Protein Loop Closure,” Protein Sci., 12(5), pp. 963–972. [CrossRef] [PubMed]
Cahill, S. , Cahill, M. , and Cahill, K. , 2003, “ On the Kinematics of Protein Folding,” J. Comput. Chem., 24(11), pp. 1364–1370. [CrossRef] [PubMed]
Kazerounian, K. , 2002, “ Is Design of New Drugs a Challenge for Kinematics?,” Advances in Robot Kinematics, J. Lenarčič and F. Thomas , eds., Springer, Dordrecht, pp. 134–144.
Kazerounian, K. , 2004, “ From Mechanisms and Robotics to Protein Conformation and Drug Design,” ASME J. Mech. Des., 126(1), pp. 40–45. [CrossRef]
Kazerounian, K. , Latif, K. , and Alvarado, C. , 2005, “ Protofold: A Successive Kinetostatic Compliance Method for Protein Conformation Prediction,” ASME J. Mech. Des., 127(4), pp. 712–717. [CrossRef]
Subramanian, R. , and Kazerounian, K. , 2007, “ Improved Molecular Model of a Peptide Unit for Proteins,” ASME J. Mech. Des., 129(11), pp. 1130–1136. [CrossRef]
Shahbazi, Z. , Ilies, H. T. , and Kazerounian, K. , 2009, “ On Hydrogen Bonds and Mobility of Protein Molecules,” ASME Paper No. DETC2009-87470.
Kazerounian, K. , 2012, “ Protein Molecules: Evolution's Design for Kinematic Machines,” 21st Century Kinematics, J. M. McCarthy , eds., Springer, Dordrecht, pp. 217–244.
Sharma, G. , Badescu, M. , Dubey, A. , Mavroidis, C. , Tomassone, S. M. , and Yarmush, M. L. , 2005, “ Kinematics and Workspace Analysis of Protein Based Nano-Actuators,” ASME J. Mech. Des., 127(4), pp. 718–727. [CrossRef]
Chirikjian, G. S. , Kazerounian, K. , and Mavroidis, C. , 2005, “ Analysis and Design of Protein Based Nanodevices: Challenges and Opportunities in Mechanical Design,” ASME J. Mech. Des., 127(4), pp. 695–698. [CrossRef]
Diez, M. , Petuya, V. , Martínez-Cruz, L. A. , and Hernández, A. , 2011, “ A Biokinematic Approach for the Computational Simulation of Proteins Molecular Mechanism,” Mech. Mach. Theory, 46(12), pp. 1854–1868. [CrossRef]
Gipson, B. , Hsu, D. , Kavraki, L. E. , and Latombe, J.-C. , 2012, “ Computational Models of Protein Kinematics and Dynamics: Beyond Simulation,” Annu. Rev. Anal. Chem., 5(1), pp. 273–291. [CrossRef]
Gō, N. , 1990, “ A Theorem on Amplitudes of Thermal Fluctuations in Large Molecules Assuming Specific Conformations Calculated by Normal Mode Analysis,” Biophys. Chem., 35(1), pp. 105–112. [CrossRef] [PubMed]
Atilgan, A. R. , Durell, S. R. , Jeringan, R. L. , Demirel, M. C. , Keskin O. , and Bahar I. , 2001, “ Anisotropy of Fluctuation Dynamics of Proteins With an Elastic Network Model,” Biophys. J., 80(1), pp. 505–515. [CrossRef] [PubMed]
Schuyler, A. D. , and Chirikjian, G. S. , 2003, “ Normal Mode Analysis of Proteins: A Comparison of Rigid Cluster Modes With Cα Coarse Graining,” J. Mol. Graphics Model., 22(3), pp. 183–193. [CrossRef]
Petrone, P. , and Pande, V. S. , 2006, “ Can Conformational Change be Described by Only a Few Normal Modes?,” Biophys. J., 90(5), pp. 1583–1593. [CrossRef] [PubMed]
Tirion, M. M. , 1996, “ Large Amplitude Elastic Motions in Proteins From a Single-Parameter, Atomic Analysis,” Phys. Rev. Lett., 77(9), pp. 1905–1908. [CrossRef] [PubMed]
Arikawa, K. , 2010, “ Investigation of Algorithms for Analyzing Protein Internal Motion From Viewpoint of Robot Kinematics,” ASME Paper No. DETC2010-28551.
Arikawa, K. , 2011, “ Kinematic Modeling and Internal Motion Analysis of Proteins From a Robot Kinematics Viewpoint,” ASME Paper No. DETC2011-47970.
Gerstein, M. , Anderson, B. F. , Norris, G. E. , Baker, E. N. , Lesk, A. M. , and Chothia, C. , 1993, “ Domain Closure in Lactoferrin: Two Hinges Produce a See-Saw Motion Between Alternative Close-Packed Interfaces,” J. Mol. Biol., 234(2), pp. 357–372. [CrossRef] [PubMed]
Gerstein, M. , Lesk, A. M. , and Chothia, C. , 1994, “ Structural Mechanisms for Domain Movements in Proteins,” Biochemistry, 33(22), pp. 6739–6749. [CrossRef] [PubMed]
Anderson, B. F. , Baker, H. M. , Norris, G. E. , Rumball, S. V. , and Baker E. N. , 1990, “ Apolactoferrin Structure Demonstrates Ligand-Induced Conformational Change in Transferrins,” Nature, 344(6268), pp. 784–787. [CrossRef] [PubMed]
Kabsch, W. , 1976, “ A Solution for the Best Rotation to Relate Two Sets of Vectors,” Acta Crystallogr., 32(5), pp. 922–923. [CrossRef]
Kabsch, W. , 1978, “ A Discussion of the Solution for the Best Rotation to Relate Two Sets of Vectors,” Acta Crystallogr., 34(5), pp. 827–828. [CrossRef]


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Fig. 1

Basic structure of proteins

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Fig. 2

Conformation variables

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Fig. 4

Protein model as robotic mechanism

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Fig. 5

Calculation of Jacobian matrix Jlen through Jpos

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Fig. 7

Balanced external forces

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Fig. 8

Example of constraint to protein model

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Fig. 9

Relationship between displacements ΔX and ΔXb

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Fig. 10

Definition of structural compliance

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Fig. 11

Prediction of motion properties

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Fig. 13

Kinematic model of lactoferrin

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Fig. 14

Calculated motion of lactoferrin

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Fig. 16

Kinematic model of hemoglobin

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Fig. 17

Calculated motion of hemoglobin




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