Folding and form: Insights from lattice simulations

Monte Carlo simulations of a Miyazawa-Jernigan lattice-polymer model indicate that, depending on the native structure’s geometry, the model exhibits two broad classes of folding mechanisms for two-state folders. Folding to native structures of low contact order is driven by backbone distance and is characterized by a progressive accumulation of structure towards the native fold. By contrast, folding to high contact order targets is dominated by intermediate stage contacts not present in the native fold, yielding a more cooperative folding process.

Figure 1

Frequency with which a native contact (numbered from 1 to 57) occurs in the folding simulations of six randomly chosen sequences trained for targets $T1$ (a) and $T5$ (b). The contact frequency is the ratio of the number of times a native contact occurs in a MC simulation to the folding time. Note how frequency of occurrence of particular contacts has strong correlation between different trained sequences, which is a clear dependence on conformation alone.

Figure 2

(Color online). Frequency maps of targets $T1$ (a) and $T5$ (b) and energy maps of targets $T1$ (c) and $T5$ (d). A colored square represents a native contact with an averaged mean frequency $⟨\omega ⟩$ or an averaged mean energy $E$. Averages are taken over 100 MC runs.

Figure 3

The backbone frequency $⟨{\omega }_{\mid i-j\mid }⟩$ as a function of the backbone distance for the low-CO (a), high-CO (b), and intermediate-CO targets (c). The backbone frequency is the mean value of $⟨\omega ⟩$, averaged over the number of contacts in each interval of backbone distance as shown in Table . The backbone distance is measured in units of lattice spacing.

Figure 4

The averaged contact time ${\ln }_e⟨t_0⟩$ as a function of the backbone distance. $t_0$, the number of MC steps up to the first time the contact is formed, was averaged over the number of contacts in each interval of backbone distance as shown in Table . The backbone distance is measured in units of lattice spacing.

Figure 5

Number of contacts $C$ with a given probability of being formed $P$ as a function of $Q$, the fraction of native contacts for targets $T1$ (a) and $T5$ (b). These are results averaged over 100 MC folding runs. See text for details.

Figure 6

Mean number of non-native contacts $⟨N_{nnat}⟩$, averaged over 100 MC runs, as a function of the fraction of native contacts $Q$ for targets $T1$ and $T5$.

Figure 7

Dependence of the folding probability $P_{\mathit{fold}}$ on ${\log }_{10}\left(t\right)$ for targets $T1$ and $T5$. $P_{\mathit{fold}}$ was calculated as the number of folding simulations which ended up to time $t$ normalized to the total number of runs.