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 $ \epsilon$ explicitly.

0pt

$\displaystyle V$ $\displaystyle \,=\,$ $\displaystyle \frac{1}{2} K_r\sum_{i=1}^{N-1}(R_{i,i+1}-R_{\rm e})^2
+\frac{1}{2} K_\theta\sum_i^{N-2}(\theta_i-\theta_{\rm e})^2$  
    $\displaystyle +\,\epsilon\sum_i^{N-3}\Big[A_i(1+\cos\varphi_i)+B_i(1-\cos\varphi_i)$  
    $\displaystyle \qquad +C_i(1+\cos3\varphi_i)+D_i\left(1+\cos\left[\varphi_i+\pi/4\right]\right)\Big]$  
    $\displaystyle +\,4\epsilon\sum_{i=1}^{N-2}\sum_{j=i+2}^N \left[S_{12}\left(\fra...
...a}{R_{ij}}\right)^{\!12}
+S_6\!\left(\frac{\sigma}{R_{ij}}\right)^{\!6}\right],$ (3)

where $ R_{ij}$ is the separation between beads $ i$ and $ j$ and the units of distance and energy are $ \sigma$ and $ \epsilon$, respectively. The first term represents the bonds linking successive beads in the linear chain, and a value of $ K_r=231.2\,\epsilon\sigma^{-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, $ \theta_i$, defined by the triplets of atomic positions $ {\bf R}_i$ to $ {\bf R}_{i+2}$, and values $ K_\theta=20\,\epsilon\,{\rm rad}^{-2}$ and $ \theta_{\rm e}=105^\circ$ 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^\circ$), 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 ([*]) represents the nonbonded interactions. In the current BLN implementation $ R_{\rm e}$ is set equal to $ \sigma$, i.e. to unity in reduced units.

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

comment: $ S_{12}>0$ and $ S_6<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.[#!BrownFH03!#]

David Wales 2017-09-21