TY - JOUR
T1 - Quantitative symmetry and chirality-A fast computational algorithm for large structures
T2 - Proteins, macromolecules, nanotubes, and unit cells
AU - Dryzun, Chaim
AU - Zait, Amir
AU - Avnir, David
PY - 2011/9
Y1 - 2011/9
N2 - Symmetry is one of the most fundamental properties of nature and is used to understand and investigate physical properties. Classically, symmetry is treated as a binary qualitative property, although other physical properties are quantitative. Using the continuous symmetry measure (CSM) methodology one can quantify symmetry and correlate it quantitatively to physical, chemical, and biological properties. The exact analytical procedures for calculating the CSM are computationally expensive and the calculation time grows rapidly as the structure contains more atoms. In this article, we present a new method for calculating the CSM and the related continuous chirality measure (CCM) for large systems. The new method is much faster than the full analytical procedures and it reduces the calculation time dependency from N! to N 2, where N is the number of atoms in the structure. We evaluate the cost of the applied approximations, estimate the error of the method, and show that deviations from the analytical solutions are within an error of 2%, and in many cases even less. The method is applicable at the moment for the cyclic symmetry point groups- C i, C s, C n, and S n, and therefore it can be used also for chirality measures, which are the minimal of the S n measures. We demonstrate the application of the method for large structures across chemistry: proteins, macromolecules, nanotubes, and large unit cells of crystals.
AB - Symmetry is one of the most fundamental properties of nature and is used to understand and investigate physical properties. Classically, symmetry is treated as a binary qualitative property, although other physical properties are quantitative. Using the continuous symmetry measure (CSM) methodology one can quantify symmetry and correlate it quantitatively to physical, chemical, and biological properties. The exact analytical procedures for calculating the CSM are computationally expensive and the calculation time grows rapidly as the structure contains more atoms. In this article, we present a new method for calculating the CSM and the related continuous chirality measure (CCM) for large systems. The new method is much faster than the full analytical procedures and it reduces the calculation time dependency from N! to N 2, where N is the number of atoms in the structure. We evaluate the cost of the applied approximations, estimate the error of the method, and show that deviations from the analytical solutions are within an error of 2%, and in many cases even less. The method is applicable at the moment for the cyclic symmetry point groups- C i, C s, C n, and S n, and therefore it can be used also for chirality measures, which are the minimal of the S n measures. We demonstrate the application of the method for large structures across chemistry: proteins, macromolecules, nanotubes, and large unit cells of crystals.
KW - chirality
KW - chirality measure
KW - nanotube chirality
KW - proteins symmetry
KW - supramolecular structures
KW - symmetry
KW - symmetry measure
KW - unit cells chirality
UR - http://www.scopus.com/inward/record.url?scp=79959743872&partnerID=8YFLogxK
U2 - 10.1002/jcc.21828
DO - 10.1002/jcc.21828
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
C2 - 21618558
AN - SCOPUS:79959743872
SN - 0192-8651
VL - 32
SP - 2526
EP - 2538
JO - Journal of Computational Chemistry
JF - Journal of Computational Chemistry
IS - 12
ER -