Abstract
The Langevin dynamics method and statistical correlation analysis were used to study the α-helical structure folding dynamics of the (Ala)50, (AlaGly)25, and (AlaGly)75 polypeptides depending on the viscosity of the medium. Friction forces that arise when the effective viscosity of the medium is similar to the viscosity of water were found to result in strong correlations between the backbone torsion angles. The polypeptides under study folded mainly to produce α-helical structures. A structure of two contacting α-helices that were approximately equal in length and had a loop between them was observed for a longer chain of 150 residues. A method to visualize the correlation matrix of the dihedral angles of a polypeptide chain was developed for analyzing the effects of the dynamic correlation of conformational degrees of freedom. The analysis of the dynamics of the correlation matrix showed that rotations involving angles of the same type (φ–φ and ψ–ψ) occur predominantly in one direction. Rotations invoving different angles (φ–ψ) occur predominantly in opposite directions, so that the total macromolecule does not rotate. A significant reduction in the effective viscosity of the medium disrupts the correlation and makes the rotations stochastic, thus distorting the formation of the regular (helical) structure. The effects of correlated conformational motions are consequences of viscous friction forces. This conclusion agrees with our previous results that outlined the principle of the minimum rate of energy dissipation and the equipartition of energy dissipation rate between conformational degrees of freedom.
Similar content being viewed by others
References
K. V. Shaitan, Biophysics (Moscow) 60 (5), 692 (2015).
K. V. Shaitan, Biophysics (Moscow) 62 (1), 1 (2017).
C. Levinthal, J. Chem. Phys. 65, 44 (1968).
P. G. Wolynes, Phil. Trans. R. Soc. 363, 453 (2005).
J. N. Onuchic and P. G. Wolynes, Curr. Opin. Struct. Biol. 14, 70 (2004).
E. R. Henry, R. B. Best, and W. A. Eaton, Proc. Natl. Acad. Sci. U. S. A. 110, 17880 (2013).
J. Kubelka, T. K. Chiu, D. R. Davies, et al., J. Mol. Biol. 359, 546 (2006).
E. I. Shakhnovich and A. M. Gutin, Nature (Lond.) 346, 773 (1990).
E. Shakhnovich, Chem. Rev. 106, 1559 (2006).
A. V. Finkelstein and O. B. Ptitsyn, Protein Physics (KDU, Moscow, 2002; Academic Press, New York, 2002).
A. V. Finkelstein and O.V. Galzitskaya, Phys. Life Rev. 1, 23 (2004).
K. A. Dill and J. L. MacCallum, Science 338, 1042 (2012).
R. Lindorff-Larsen, S. Piana, R. O. Dror, and D. E. Shaw, Science 334, 517 (2011).
D. A. Dolgikh, M. P. Kirpichnikov, O. V. Ptitsyn, and V. V. Chemeris, Mol. Biol. (Moscow) 30, 261 (1996).
K. V. Shaitan, G. A. Armeev and A. K. Shaytan, Biophysics (Moscow) 61 (2), 177 (2016).
K. V. Shaitan, M. P. Kirpichnikov, V. S. Lamzin, et al., Vestn. RFBR No. 4 (80), 38 (2013).
S. Pronk, S. Pall, R. Schulz, et al., Bioinformatics 29, 845 (2013).
E. J. Sorin and V. S. Pande, Biophys. J. 88, 2472 (2005).
D. Frenkel and B. Smit, Understanding Molecular Simulation. From Algorithms to Applications (Academic Press, New York, 2002).
C. V. Heer, Statistical Mechanics: Kinetic, Theory and Stochastic Processes (Academic Press, New York, 1972; Mir, Moscow, 1976).
K. V. Shaitan and A. B. Rubin, Mol. Biol. (Moscow) 14, 1323 1980.
K. V. Shaitan and S. S. Saraikin, Biophysics (Moscow) 45 (3), 397 (2000).
K. V. Shaitan, M. A. Lozhnikov and G. M. Kobelkov, Biophysics (Moscow) 61 (4), 531 (2016).
K. V. Shaitan, M. A. Lozhnikov and G. M. Kobelkov, Biophysics (Moscow) 62 (2), 182 (2017).
M. Lutz, Programming Python, 4th ed. (O’Reilly Media, 2010; Simvol-Plyus, St. Petersburg, 2011), Vol.1.
G. Kramer, Matematicheskie metody statistiki (Mir, M.: 1975).
D. J. Hudson, Statistics: Lectures on Elementary Statistics and Probability (CERN, Geneva, 1964; Mir, Moscow, 1970).
K. V. Shaitan and I. A. Orshanskiy, Biophysics (Moscow) 60, 538 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.V. Shaitan, F.Yu. Popelenskii, G.A. Armeev, 2017, published in Biofizika, 2017, Vol. 62, No. 3, pp. 443–451.
Rights and permissions
About this article
Cite this article
Shaitan, K.V., Popelenskii, F.Y. & Armeev, G.A. Conformational motion correlations in the formation of polypeptide secondary structure in a viscous medium. BIOPHYSICS 62, 348–355 (2017). https://doi.org/10.1134/S0006350917030186
Received:
Published:
Issue date:
DOI: https://doi.org/10.1134/S0006350917030186