Consequences of Non-Uniformity in the Stoichiometry of Component Fractions within One and Two Loops Models of α-Helical Peptides
Affiliation(s)
1 United State Department of Agriculture, Agricultural Research Service, Beltsville, Maryland, USA. 2 Department of Biology, School of Computer, Mathematical, and Natural Sciences, Morgan State University, Baltimore, Maryland, USA. 3 Clarence M. Mitchell Jr. School of Engineering, Morgan State University, Baltimore, Maryland, USA.
1 United State Department of Agriculture, Agricultural Research Service, Beltsville, Maryland, USA. 2 Department of Biology, School of Computer, Mathematical, and Natural Sciences, Morgan State University, Baltimore, Maryland, USA. 3 Clarence M. Mitchell Jr. School of Engineering, Morgan State University, Baltimore, Maryland, USA.
ABSTRACT
A 3-D electrostatic density map generated using the Wavefront Topology System and Finite Element Method clearly demonstrates the non-uniformity and periodicity present in even a single loop of an α-helix. The four dihedral angles (N-C*-C-N, C*-C-N-C*, and C-N-C*-C) fully define a helical shape independent of its length: the three dihedral angles, φ = -33.5°, ω = 177.3°, and Ψ = -69.4°, generate the precise (and identical) redundancy in a one loop (or longer) α-helical shape (pitch = 1.59
/residue; r = 2.25 
). Nevertheless the pattern of dihedral angles within an 11 and a 22-peptide backbone atom sequence cannot be distributed evenly because the stoichiometry in fraction of four atoms never divides evenly into 11 or 22 backbone atoms. Thus, three sequential sets of 11 backbone atoms in an α-helix will have a discretely different chemical formula and correspondingly different combinations of molecular forces depending upon the assigned starting atom in an 11-step sequence. We propose that the unit cell of one loop of an α-helix occurs in the peptide backbone sequence C-(N-C*-C)3-N which contains an odd number of C* plus even number of amide groups. A two-loop pattern (C*-C-N)7-C* contains an even number of C* atoms plus an odd number of amide groups. Dividing the two-loop pattern into two equal lengths, one fraction will have an extra half amide (N-H) and the other fraction will have an extra half amide C=O, i.e., the stoichiometry of each half will be different. Also, since the length of N-C*-C-N, C*-C-N-C*, and C-N-C*-C are unequal, the summation of the number of each in any fraction of n loops of an α-helix in sequence will always have unequal length, depending upon the starting atom (N, C*, or C).
A 3-D electrostatic density map generated using the Wavefront Topology System and Finite Element Method clearly demonstrates the non-uniformity and periodicity present in even a single loop of an α-helix. The four dihedral angles (N-C*-C-N, C*-C-N-C*, and C-N-C*-C) fully define a helical shape independent of its length: the three dihedral angles, φ = -33.5°, ω = 177.3°, and Ψ = -69.4°, generate the precise (and identical) redundancy in a one loop (or longer) α-helical shape (pitch = 1.59
/residue; r = 2.25 ). Nevertheless the pattern of dihedral angles within an 11 and a 22-peptide backbone atom sequence cannot be distributed evenly because the stoichiometry in fraction of four atoms never divides evenly into 11 or 22 backbone atoms. Thus, three sequential sets of 11 backbone atoms in an α-helix will have a discretely different chemical formula and correspondingly different combinations of molecular forces depending upon the assigned starting atom in an 11-step sequence. We propose that the unit cell of one loop of an α-helix occurs in the peptide backbone sequence C-(N-C*-C)3-N which contains an odd number of C* plus even number of amide groups. A two-loop pattern (C*-C-N)7-C* contains an even number of C* atoms plus an odd number of amide groups. Dividing the two-loop pattern into two equal lengths, one fraction will have an extra half amide (N-H) and the other fraction will have an extra half amide C=O, i.e., the stoichiometry of each half will be different. Also, since the length of N-C*-C-N, C*-C-N-C*, and C-N-C*-C are unequal, the summation of the number of each in any fraction of n loops of an α-helix in sequence will always have unequal length, depending upon the starting atom (N, C*, or C).
KEYWORDS
Pattern Recognition, α-Helix, Dihedral Angle Patterns, Peptide Backbone Sequence, Molecular Orbital Theory, Electrostatic Density Gradient, Wavefront Topology System, Finite Element Method
Pattern Recognition, α-Helix, Dihedral Angle Patterns, Peptide Backbone Sequence, Molecular Orbital Theory, Electrostatic Density Gradient, Wavefront Topology System, Finite Element Method
Cite this paper
Schmidt, W. , Hapeman, C. , Wachira, J. and Thomas, C. (2014) Consequences of Non-Uniformity in the Stoichiometry of Component Fractions within One and Two Loops Models of α-Helical Peptides. Journal of Biophysical Chemistry, 5, 125-133. doi: 10.4236/jbpc.2014.54014.
Schmidt, W. , Hapeman, C. , Wachira, J. and Thomas, C. (2014) Consequences of Non-Uniformity in the Stoichiometry of Component Fractions within One and Two Loops Models of α-Helical Peptides. Journal of Biophysical Chemistry, 5, 125-133. doi: 10.4236/jbpc.2014.54014.
References
[1] Schmidt, W.F. and Thomas, C.G. (2012) More Precise Model of α-Helix and Transmembrane α-Helical Peptide Backbone Structure. Journal of Biophysical Chemistry, 3, 295-303.
http://dx.doi.org/10.4236/jbpc.2012.34036 [2] Thomas, C.G. (2013) The Wavefront Topology System and Finite Element Method Applied to Engineering Visualization. Morgan State University, Baltimore, 160 p. [3] Meskers, A.J.H., Voigt, D. and Spronck, J.W. (2013) Relative Optical Wavefront Measurement in Displacement Measuring Interferometer Systems with Sub-nm Precision. Optics Express, 21, 1-12.
http://dx.doi.org/10.1364/OE.21.017920 [4] Barlow, D.J. and Thornton, J.M. (1988) Helix Geometry in Proteins. Journal Molecular Biology, 201, 601-619. [5] Harper, E.T. and Rose, G.D. (1993) Helix Stop Signals in Proteins and Peptides: The Capping Box. Biochemistry, 32, 7605-7609.
http://dx.doi.org/10.1012/bi00081aoo1 [6] Kumar, S. and Bansal, M. (1998) Dissecting α-Helices: Position-Specific Analysis of Alpha-Helices in Globular Proteins. Proteins, 31, 460-476. [7] Olivella, M. Deupi, X., Govaerts, C. and Pardo, L. (2002) Influence of the Environment in the Conformation of α-Helices Studied by Protein Database Search and Molecular Dynamics Simulations. Biophysical Journal, 82, 3207-3213.
http://dx.doi.org/10.1016/S0006-3495(02)75663-4 [8] Maiti, N.C., Apetri, M.M., Zagorski, M.G., Carey, P.R. and Anderson, V.E. (2004) Raman Spectroscopic Characterization of Secondary Structure in Natively Unfolded Proteins: α-Synuclein. Journal of American Chemical Society, 126, 2399-2408.
http://dx.doi.org/10.1012/ja0356176 [9] Guo, Z., Kraka, E. and Cremer, D. (2013) Description of Local and Global Shape Properties of Protein Helices. Journal of Molecular Modeling, 19, 2901-2911.
http://dx.doi.org/10.1007/s00894-013-1819-7. [10] Eisenberg, D. (2003) The Discovery of the α-Helix and β-Sheet, the Principal Structural Features of Proteins. Proceedings of the National Academy of Sciences USA, 100, 11207-11210. [11] Bishop, D.M. (1973) Group Theory and Chemistry. Dover Publications, New York, 300 p. [12] Hypercube, Inc. (2007) HyperChem 8.0 for Windows Molecular Modeling Systems. Gainsville. [13] Hayward, S., Leader, D.P., Al-Shubailly, F. and Milner-White, E.J. (2014) Rings and Ribbons in Protein Structures: Characterization Using Helical Parameters and Ramachandran Plots for Repeating Dipeptides. Proteins: Structure, Function, and Bioinformatics, 82, 230-239.
http://dx.doi.org/10.1002/prot.24357 [14] Uesake, A., Ueda, M., Makino, A., Imai, T., Sugiyama, J. and Kimura, S. (2014) Morphology Control between Twisted Ribbon, Helical Ribbon, and Nanotube Self-Assembies with His-Containing Helical Peptides in Response to pH Change. Langmuir, 30, 1022-1028.
http://dx.doi.org/10.1021/la404784e [15] Hayward, S. and Collins, J.F. (1992) Limits on α-Helical Prediction with Neural Network Models. Proteins, 14, 372-381.
http://dx.doi.org/10.1002/prot.340140306 [16] Albrecht, B., Grant, G.H., Sisu, C. and Richards, W.G. (2008) Classification of Proteins Based on Similarity of Two-Dimensional Maps. Biophysical Chemistry, 138, 11-22.
http://dx.doi.org/10.1016/j.bpc.2008.08.004 [17] Cantoni, V., Ferone, A., Ozbudak, O. and Petrosino, A. (2013) Protein Motifs Retrieval by SS Terns Occurrences. Pattern Recognition Letters, 34, 559-563.
http://dx.doi.org/10.1016/j.patrec.2012.12.003 [18] Ho, B.K. and Brasseur, R. (2005) The Ramachandran Plot of Glycine and Pre-Proline. BMC Structural Biology, 5, 14-29.
http://dx.doi.org/10.1186/1472-6807-5-14 [19] Kachlishvili, K. and Brenna, J.T. (2013) Steric Effects in the Interaction between Transmembrane Proteins and Polyunsaturated Phospholipids. Journal of Biological Physics and Chemistry, 13, 36-44.
http://dx.doi.org/10.4024/33KA12A.jbpc.13.01
[1] Schmidt, W.F. and Thomas, C.G. (2012) More Precise Model of α-Helix and Transmembrane α-Helical Peptide Backbone Structure. Journal of Biophysical Chemistry, 3, 295-303.
http://dx.doi.org/10.4236/jbpc.2012.34036 [2] Thomas, C.G. (2013) The Wavefront Topology System and Finite Element Method Applied to Engineering Visualization. Morgan State University, Baltimore, 160 p. [3] Meskers, A.J.H., Voigt, D. and Spronck, J.W. (2013) Relative Optical Wavefront Measurement in Displacement Measuring Interferometer Systems with Sub-nm Precision. Optics Express, 21, 1-12.
http://dx.doi.org/10.1364/OE.21.017920 [4] Barlow, D.J. and Thornton, J.M. (1988) Helix Geometry in Proteins. Journal Molecular Biology, 201, 601-619. [5] Harper, E.T. and Rose, G.D. (1993) Helix Stop Signals in Proteins and Peptides: The Capping Box. Biochemistry, 32, 7605-7609.
http://dx.doi.org/10.1012/bi00081aoo1 [6] Kumar, S. and Bansal, M. (1998) Dissecting α-Helices: Position-Specific Analysis of Alpha-Helices in Globular Proteins. Proteins, 31, 460-476. [7] Olivella, M. Deupi, X., Govaerts, C. and Pardo, L. (2002) Influence of the Environment in the Conformation of α-Helices Studied by Protein Database Search and Molecular Dynamics Simulations. Biophysical Journal, 82, 3207-3213.
http://dx.doi.org/10.1016/S0006-3495(02)75663-4 [8] Maiti, N.C., Apetri, M.M., Zagorski, M.G., Carey, P.R. and Anderson, V.E. (2004) Raman Spectroscopic Characterization of Secondary Structure in Natively Unfolded Proteins: α-Synuclein. Journal of American Chemical Society, 126, 2399-2408.
http://dx.doi.org/10.1012/ja0356176 [9] Guo, Z., Kraka, E. and Cremer, D. (2013) Description of Local and Global Shape Properties of Protein Helices. Journal of Molecular Modeling, 19, 2901-2911.
http://dx.doi.org/10.1007/s00894-013-1819-7. [10] Eisenberg, D. (2003) The Discovery of the α-Helix and β-Sheet, the Principal Structural Features of Proteins. Proceedings of the National Academy of Sciences USA, 100, 11207-11210. [11] Bishop, D.M. (1973) Group Theory and Chemistry. Dover Publications, New York, 300 p. [12] Hypercube, Inc. (2007) HyperChem 8.0 for Windows Molecular Modeling Systems. Gainsville. [13] Hayward, S., Leader, D.P., Al-Shubailly, F. and Milner-White, E.J. (2014) Rings and Ribbons in Protein Structures: Characterization Using Helical Parameters and Ramachandran Plots for Repeating Dipeptides. Proteins: Structure, Function, and Bioinformatics, 82, 230-239.
http://dx.doi.org/10.1002/prot.24357 [14] Uesake, A., Ueda, M., Makino, A., Imai, T., Sugiyama, J. and Kimura, S. (2014) Morphology Control between Twisted Ribbon, Helical Ribbon, and Nanotube Self-Assembies with His-Containing Helical Peptides in Response to pH Change. Langmuir, 30, 1022-1028.
http://dx.doi.org/10.1021/la404784e [15] Hayward, S. and Collins, J.F. (1992) Limits on α-Helical Prediction with Neural Network Models. Proteins, 14, 372-381.
http://dx.doi.org/10.1002/prot.340140306 [16] Albrecht, B., Grant, G.H., Sisu, C. and Richards, W.G. (2008) Classification of Proteins Based on Similarity of Two-Dimensional Maps. Biophysical Chemistry, 138, 11-22.
http://dx.doi.org/10.1016/j.bpc.2008.08.004 [17] Cantoni, V., Ferone, A., Ozbudak, O. and Petrosino, A. (2013) Protein Motifs Retrieval by SS Terns Occurrences. Pattern Recognition Letters, 34, 559-563.
http://dx.doi.org/10.1016/j.patrec.2012.12.003 [18] Ho, B.K. and Brasseur, R. (2005) The Ramachandran Plot of Glycine and Pre-Proline. BMC Structural Biology, 5, 14-29.
http://dx.doi.org/10.1186/1472-6807-5-14 [19] Kachlishvili, K. and Brenna, J.T. (2013) Steric Effects in the Interaction between Transmembrane Proteins and Polyunsaturated Phospholipids. Journal of Biological Physics and Chemistry, 13, 36-44.
http://dx.doi.org/10.4024/33KA12A.jbpc.13.01