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.

References

References
1.
Lesk
,
A. M.
,
2001
,
Introduction to Protein Architecture
,
Oxford University Press
,
Oxford, UK
.
2.
Lesk
,
A. M.
,
2004
,
Introduction to Protein Science
,
Oxford University Press
,
Oxford, UK
.
3.
Petsko
,
G. A.
, and
Ringe
,
D.
,
2004
,
Protein Structure and Function
,
New Science Press
,
London
.
4.
RCSB PDB, 2016, “Protein Data Bank,” http://www.rcsb.org
5.
Subbiah
,
S.
,
1996
,
Protein Motions
,
R.G. Landes Company
,
Austin, TX
.
6.
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
.
7.
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
.
8.
Cahill
,
S.
,
Cahill
,
M.
, and
Cahill
,
K.
,
2003
, “
On the Kinematics of Protein Folding
,”
J. Comput. Chem.
,
24
(
11
), pp.
1364
1370
.
9.
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
.
10.
Kazerounian
,
K.
,
2004
, “
From Mechanisms and Robotics to Protein Conformation and Drug Design
,”
ASME J. Mech. Des.
,
126
(
1
), pp.
40
45
.
11.
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
.
12.
Subramanian
,
R.
, and
Kazerounian
,
K.
,
2007
, “
Improved Molecular Model of a Peptide Unit for Proteins
,”
ASME J. Mech. Des.
,
129
(
11
), pp.
1130
1136
.
13.
Shahbazi
,
Z.
,
Ilies
,
H. T.
, and
Kazerounian
,
K.
,
2009
, “
On Hydrogen Bonds and Mobility of Protein Molecules
,”
ASME
Paper No. DETC2009-87470.
14.
Kazerounian
,
K.
,
2012
, “
Protein Molecules: Evolution's Design for Kinematic Machines
,”
21st Century Kinematics
,
J. M.
McCarthy
, eds.,
Springer
,
Dordrecht
, pp.
217
244
.
15.
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
.
16.
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
.
17.
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
.
18.
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
.
19.
,
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
.
20.
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
.
21.
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
.
22.
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
.
23.
Tirion
,
M. M.
,
1996
, “
Large Amplitude Elastic Motions in Proteins From a Single-Parameter, Atomic Analysis
,”
Phys. Rev. Lett.
,
77
(
9
), pp.
1905
1908
.
24.
Arikawa
,
K.
,
2010
, “
Investigation of Algorithms for Analyzing Protein Internal Motion From Viewpoint of Robot Kinematics
,”
ASME
Paper No. DETC2010-28551.
25.
Arikawa
,
K.
,
2011
, “
Kinematic Modeling and Internal Motion Analysis of Proteins From a Robot Kinematics Viewpoint
,”
ASME
Paper No. DETC2011-47970.
26.
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
.
27.
Gerstein
,
M.
,
Lesk
,
A. M.
, and
Chothia
,
C.
,
1994
, “
Structural Mechanisms for Domain Movements in Proteins
,”
Biochemistry
,
33
(
22
), pp.
6739
6749
.
28.
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
.
29.
Kabsch
,
W.
,
1976
, “
A Solution for the Best Rotation to Relate Two Sets of Vectors
,”
Acta Crystallogr.
,
32
(
5
), pp.
922
923
.
30.
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
.
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