BLN Off-Lattice Protein Model

The general three-colour bead protein model is specified by keyword BLN. The potential follows the form described in Proc. Natl. Acad. Sci. USA, 100, 10712, 2003, expect that the coefficients A_i, B_i, C_i and D_i include a factor of ε explicitly.

0pt

$${\frac{{1}}{{2}}} \sum_{{i=1}}^{{N-1}} {\frac{{1}}{{2}}} \sum_{i}^{{N-2}}$$ V   =  

$$\sum_{i}^{{N-3}} \Big[ \varphi_{i}^{} \varphi_{i}^{}$$

$$\varphi_{i}^{} \left(\vphantom{1+\cos\left[\varphi_i+\pi/4\right]}\right. \left[\vphantom{\varphi_i+\pi/4}\right. \varphi_{i}^{} \left.\vphantom{\varphi_i+\pi/4}\right] \left.\vphantom{1+\cos\left[\varphi_i+\pi/4\right]}\right) \Big]$$

$$\sum_{{i=1}}^{{N-2}} \sum_{{j=i+2}}^{N} \left[\vphantom{S_{12}\left(\frac{\sigma}{R_{ij}}\right)^{\!12} +S_6\!\left(\frac{\sigma}{R_{ij}}\right)^{\!6}}\right. \left(\vphantom{\frac{\sigma}{R_{ij}}}\right. {\frac{{\sigma}}{{R_{ij}}}} \left.\vphantom{\frac{\sigma}{R_{ij}}}\right)^{{\!12}}_{} \left(\vphantom{\frac{\sigma}{R_{ij}}}\right. {\frac{{\sigma}}{{R_{ij}}}} \left.\vphantom{\frac{\sigma}{R_{ij}}}\right)^{{\!6}}_{} \left.\vphantom{S_{12}\left(\frac{\sigma}{R_{ij}}\right)^{\!12} +S_6\!\left(\frac{\sigma}{R_{ij}}\right)^{\!6}}\right]$$ (9)

where R_ij is the separation between beads i and j and the units of distance and energy are σ and ε, respectively. The first term represents the bonds linking successive beads in the linear chain, and a value of K_r = 231.2 εσ^-2 was used in most of the work on the Honeycutt and Thirumalai frustrated 46-bead model. The second term is a sum over the bond angles, θ_i, defined by the triplets of atomic positions $\bf R_{i}^{}$ to $\bf R_{{i+2}}^{}$, and values K_θ = 20 ε rad^-2 and θ_e = 105^o were used for the 46-bead model. The third term is a sum over the dihedral angles, $\varphi_{i}^{}$, defined by the quartets $\bf R_{i}^{}$ to $\bf R_{{i+3}}^{}$. In the 46-bead model A_i = C_i = 1.2 if the quartet involved no more than one N monomer, generating a preference for the trans conformation ( $\varphi_{i}^{}$ = 180^o), whereas if two or three N monomers are involved then A_i = 0 and C_i = 0.2. This choice makes the three neutral segments of the chain flexible and enables them to accommodate turns. A general specification of these parameters is possible in the new BLN framework via the auxiliary file BLNsequence. The last term in (9) represents the nonbonded interactions. In the current BLN implementation R_e is set equal to σ, i.e. to unity in reduced units.

An appropriate BLNsequence file for the usual 46-bead model contains the following lines:

comment: S₁₂ > 0 and S₆ < 0 for B-B, L-L and L-B, N-L and N-B and N-N 1.0D0 -1.0D0 0.33333333333333D0 0.33333333333333D0 1.0D0 0.0D0 comment: coefficients A, B, C, D comment: for Helical, Extended and Turn residues in order, four per line 0.0D0 1.2D0 1.2D0 1.2D0 0.9D0 0.0D0 1.2D0 0.0D0 0.0D0 0.0D0 0.2D0 0.0D0 LBLBLBLBBNNNBBBLBLBBBNNNLLBLLBBLLBNBLBLBLBLNNNLBBLBLBBBL EEEEEETEHTHEEEEEEEEHHEHHHHHHHHHHEHTEEEEEEETTTEEEEEEEE

The penultimate line defines the sequence, and the final line defines which set of A_i, B_i, C_i and D_i parameters apply to which parts of the structure.[33]