Effect of chain connectivity on the structure of Lennard-Jones liquid and its implication on statistical potentials for protein folding

Statistical contact potentials and bead-spring models have been widely used for computational studies of protein folding. However, there has been speculation that systematic error may arise in the contact energy calculations when the statistical potentials are deduced under the assumption that the chain connectivity in proteins can be ignored. To address this issue, we have performed molecular-dynamics simulations to study the structure and dynamics of a simple liquid system in which the beads are either connected or unconnected with springs. Results from the present study provide useful information for assessing the accuracy of the statistical potentials for protein structure simulations.

Figure 1

Cartoon view of the single-bead model.

Figure 2

Cartoon view of the double-bead model. The white balls are the $A$-type beads and the gray balls are the side-chain $B$-type beads.

Figure 3

Density profile of side-chain residues in proteins obtained from our estimations as described in the text.

Figure 4

Illustration of the scheme for renormalizing the pair correlation function $g\left(r\right)$ due to the exclusion of nearest (or next nearest) neighbors along the chain.

Figure 5

The corrected $g\left(r\right)$ (solid lines) for the single-bead model and double-bead model with $k=0.001$ are compared with that of the unconnected LJ system (dotted lines). The reduced $g_0\left(r\right)$ (dashed lines) are also plotted. Note that $g_0\left(r\right)$ is clearly below the corrected $g\left(r\right)$.

Figure 6

Pair correlation functions as a function of spring constant $k$. (a) The raw data (without exclusion and correction) from the single-bead model; (b) corrected $g\left(r\right)$ of the single-bead model; (c) the raw data from the double-bead model; (d) corrected $g\left(r\right)$ of the double-bead model.

Figure 7

Simulation results of the pair correlation function, with two-neighbor corrections, of the single-bead model $\left(k=1.0\right)$ at the various temperatures and densities (dotted line indicates the unconnected system).

Figure 8

Mean-square displacement of the residue particles as a function of time steps in the unconnected, single-bead, and double-bead systems.

Figure 9

Simulation results of the pair correlation function, with one-neighbor corrections, of the double-bead model $\left(k=1.0\right)$ at the various temperatures and densities (dotted line indicates the unconnected system).