Dihedral angle
The dihedral angle of torsion or describes the geometry of the angle between two surfaces; This applies in particular in a chemical compound for the angle between two imaginary surfaces. Here, the dihedral angle α is defined by four atoms and their positions to each other; it corresponds in the example of the organic compound ethane angle, the ' take each spanned planes, as shown in the following figure (C and C are the two carbon atoms, R and R' both by RCC and CCR any two hydrogen atoms):
Are both carbon atoms linked by a single bond ( σ - bond) and not locked in a cyclic molecule, the dihedral angle can continuously take all values from 0 ° to 180 °. Because of repulsive interactions between the substituents R and R ' is preferred, as a rule, an angle of α = 180 ° (trans see, below).
The fact that many sugar unexpectedly assume a conformation that a dihedral angle of α = the number of substituents prefer 120 ° is attributed to the anomeric effect.
The for binding varying with the rotation enthalpy of the molecule can be calculated approximately by a special function:
The resultant from this function potential curve ( approximated with values for A, B and C as n- butane) is shown for illustration below.
In the case of ethane A and B are zero, so that the equation above is in the Pitzer potential. The rotational barriers are generally in a few kJ / mol. This means that there is always a small fraction ( <20%) of the molecules have a dihedral angle of α = 0 °. It must be taken into account that the gauche forms have an entropy advantage of 1.7 kJ / mol, as it in two rotational isomers ( / - synclinal ) occur. Costs incurred on certain values of the dihedral angle conformers have their own names:
The forms with α = 60 °, respectively, 300 ° are enantiomers. If the rotational barrier too high, the two resulting shapes are not able to move by rotation each other. They can be isolated separately under certain circumstances. This is used in the case of special Binaphthylderivaten to obtain extremely selective reagents.
If there is a double bond between the carbon atoms, the rotation is severely restricted because a specialist bond breaking would take place. There are only two possible angles: α = 180 ° ( trans) and α = 0 ° ( cis). Are the very bulky substituents, there may be deviations from the 0 ° angle in the latter case, however.
To determine the dihedral angles of real compounds, various methods are available. These include the measurement of the dipole moment, the absorption of the electron diffraction spectra, the measurement of coupling constants, by NMR or the calculation of the optimum geometry of the molecule by means of specific computer programs.
Torsion angles in proteins
The torsion angles of the backbone of proteins
- φ ( between C ' - N - Cα - C')
- ψ ( between N - Cα - C ' - N) and
- ω ( between Cα - C ' - N - Cα )
Mentioned. Characterized the angle φ controls the distance between two carbonyl carbon atoms, the distance between two ψ amide nitrogens and ω the distance between two α - carbons.
The planarity of the peptide bond forces the ω - angle normally to 180 ° (the frequent trans conformation ) or 0 ° ( the rare cis conformation ). The distance between the α - carbon atoms is in the trans and cis conformation about 3.8 and 2.8 Å. The cis conformation is mainly observed in the X-Pro peptide bond (X is an arbitrary amino acid ) and therefore is valid in addition to the proline achiral glycine as structure breakers. The dihedral angles φ and ψ of a protein in the Ramachandran plot shown and should be less than 80% in the core areas and at most isolated in the forbidden areas of the map. In the particularly advantageous α -helices, for example, the angle φ is approximately 60 °, the angle ψ about -30 °, both angles allow a tolerance of about ± 30 °.
The torsion angle of the side chains are referred to with χ1 χ5, depending on the distance from the backbone. χ1 is the torsion angle between the atoms N - Cα - Cβ - C?, χ2 between Cα - Cβ - C? - Cδ etc.
The Seitenkettentorsionswinkel appear around the 180 ° to accumulate 60 ° and -60 °. These conformations are used as anti- ( or trans), ( ) -gauche and designated (-) -gauche () synclinal or ( ) - - or (). Which torsion angle is in a side chain, is determined by the dihedral adjacent side chains and the backbone; the ( ) -gauche conformation, as follows rarely more ( )- gauche conformation ( at the same (-) -gauche ) because this increases the probability of a collision atom.