Protein structure descriptors

alpha: $\alpha$ -helix content of a protein segment.

The block alpha {...} defines the parameters to calculate the helical content of a segment of protein residues. The $\alpha$ -helical content across the $N+1$ residues $N_{0}$ to $N_{0}+N$ is calculated by the formula:

$${ \alpha\left( \mathrm{C}_{\alpha}^{(N_{0})}, \mathrm{O}^{(N_{0})... ...thrm{N}^{(N_{0}+N)}, \mathrm{C}_{\alpha}^{(N_{0}+N)} \right) } \; = \; \; \; \;$$ (13.10)

$$\; \; \; \; { \frac{1}{2(N-2)} \sum_{n=N_{0}}^{N_{0}+N-2} \mathrm... ...-4} \mathrm{hbf}\left( \mathrm{O}^{(n)}, \mathrm{N}^{(n+4)}\right) \mathrm{,} }$$

where the score function for the $\mathrm{C}_{\alpha} - \mathrm{C}_{\alpha} - \mathrm{C}_{\alpha}$ angle is defined as:

$${ \mathrm{angf}\left( \mathrm{C}_{\alpha}^{(n)}, \mathrm{C}_{\alp... ...eta_{0}\right)^{4} / \left(\Delta\theta_{\mathrm{tol}}\right)^{4}} \mathrm{,} }$$ (13.11)

and the score function for the $\mathrm{O}^{(n)} \leftrightarrow \mathrm{N}^{(n+4)}$ hydrogen bond is defined through a hBond colvar component on the same atoms.

List of keywords (see also for additional options):

• residueRange $\langle\,$ Potential $\alpha$ -helical residues$\,\rangle$
  Context: alpha
  Acceptable values: ``$<$ Initial residue number$>$ -$<$ Final residue number$>$ ''
  Description: This option specifies the range of residues on which this component should be defined. The Colvars module looks for the atoms within these residues named ``CA'', ``N'' and ``O'', and raises an error if any of those atoms is not found.

• psfSegID $\langle\,$ PSF segment identifier$\,\rangle$
  Context: alpha
  Acceptable values: string (max 4 characters)
  Description: This option sets the PSF segment identifier for the residues specified in residueRange. This option is only required when PSF topologies are used.

• hBondCoeff $\langle\,$ Coefficient for the hydrogen bond term$\,\rangle$
  Context: alpha
  Acceptable values: positive between 0 and 1
  Default value: 0.5
  Description: This number specifies the contribution to the total value from the hydrogen bond terms. 0 disables the hydrogen bond terms, 1 disables the angle terms.

• angleRef $\langle\,$ Reference $\mathrm{C}_{\alpha} - \mathrm{C}_{\alpha} - \mathrm{C}_{\alpha}$ angle$\,\rangle$
  Context: alpha
  Acceptable values: positive decimal
  Default value: 88$^{\circ}$
  Description: This option sets the reference angle used in the score function (13.12).

• angleTol $\langle\,$ Tolerance in the $\mathrm{C}_{\alpha} - \mathrm{C}_{\alpha} - \mathrm{C}_{\alpha}$ angle$\,\rangle$
  Context: alpha
  Acceptable values: positive decimal
  Default value: 15$^{\circ}$
  Description: This option sets the angle tolerance used in the score function (13.12).

• hBondCutoff $\langle\,$ Hydrogen bond cutoff$\,\rangle$
  Context: alpha
  Acceptable values: positive decimal
  Default value: 3.3 Å
  Description: Equivalent to the cutoff option in the hBond component.

• hBondExpNumer $\langle\,$ Hydrogen bond numerator exponent$\,\rangle$
  Context: alpha
  Acceptable values: positive integer
  Default value: 6
  Description: Equivalent to the expNumer option in the hBond component.

• hBondExpDenom $\langle\,$ Hydrogen bond denominator exponent$\,\rangle$
  Context: alpha
  Acceptable values: positive integer
  Default value: 8
  Description: Equivalent to the expDenom option in the hBond component.

This component returns positive values, always comprised between 0 (lowest $\alpha$ -helical score) and 1 (highest $\alpha$ -helical score).

dihedralPC: protein dihedral principal component

The block dihedralPC {...} defines the parameters to calculate the projection of backbone dihedral angles within a protein segment onto a dihedral principal component, following the formalism of dihedral principal component analysis (dPCA) proposed by Mu et al.[51] and documented in detail by Altis et al.[52]. Given a peptide or protein segment of $N$ residues, each with Ramachandran angles $\phi_i$ and $\psi_i$ , dPCA rests on a variance/covariance analysis of the $4(N-1)$ variables $\cos(\psi_1), \sin(\psi_1), \cos(\phi_2), \sin(\phi_2) \cdots \cos(\phi_N), \sin(\phi_N)$ . Note that angles $\phi_1$ and $\psi_N$ have little impact on chain conformation, and are therefore discarded, following the implementation of dPCA in the analysis software Carma.[53]

For a given principal component (eigenvector) of coefficients $(k_i)_{1 \leq i \leq 4(N-1)}$ , the projection of the current backbone conformation is:

$$\xi = \sum_{n=1}^{N-1} k_{4n-3} \cos(\psi_n) + k_{4n-2} \sin (\psi_n) + k_{4n-1} \cos (\phi_{n+1}) + k_{4n} \sin(\phi_{n+1})$$ (13.12)

dihedralPC expects the same parameters as the alpha component for defining the relevant residues (residueRange and psfSegID) in addition to the following:

List of keywords (see also for additional options):

• residueRange: see definition of residueRange (alpha component)

• psfSegID: see definition of psfSegID (alpha component)

• vectorFile $\langle\,$ File containing dihedral PCA eigenvector(s)$\,\rangle$
  Context: dihedralPC
  Acceptable values: file name
  Description: A text file containing the coefficients of dihedral PCA eigenvectors on the cosine and sine coordinates. The vectors should be arranged in columns, as in the files output by Carma.[53]

• vectorNumber $\langle\,$ File containing dihedralPCA eigenvector(s)$\,\rangle$
  Context: dihedralPC
  Acceptable values: positive integer
  Description: Number of the eigenvector to be used for this component.