A dynamic network-centric approach to study two-state folding from native structure called network dynamics (ND) is introduced. ND applies two fundamental principles of protein folding : hydrophobicity and loop-entropy, on a protein's native residue network (PRN0) to generate its native shortcut network (SCN0). ND generates barrier heights that correlate significantly (-0.7) with folding rate, and positions the transition-state (TS) for 52 proteins within 0.1 <= Q < 0.5 of its reaction coordinate, which monitors SCN0 completion. ND trajectories through SCN0 space are reasonable; they support our previous work on identifying initial fold steps. Both relative contact order (RCO) and network clustering coefficient C, computed on ND generated SCN0s, correlate significantly with all three folding kinetic variables: folding rate, TS placement and native-state (NS) stability. Some of these correlations are stronger or become significant when computed on partial than on complete SCN0s. In particular, contrary to previous findings, RCO can correlate significantly with NS stability. This revelation is made possible by ND, which provides a computationally light way to explore partially folded proteins via incomplete SCN0s. ND analysis affirms the presence of NS topology in its TS SCN0s, and finds C to be a better measure of protein topology than RCO, to shed light on the hypothesized relationship between NS structure and folding rate. Within the ND-TS region, C_SCN0 correlates significantly with folding rate, while SCN0_RCO does not. However, strong TS NS structural correlations, in terms of both SCN0_RCO and C_SCN0, is also producible by a randomized version of ND .
The Network Dynamics (ND) model is proposed. ND views protein folding as a partial ordering of contacts in a native-state Protein Residue Network (PRN0) . The ND process recreates a PRN0, which gives rise to edges called shortcuts, named for their backtracking avoidance role in small-world communication between nodes in a PRN0. Clustering of native shortcut edges were previously shown able to identify folding pathways. ND applies two fundamental folding principles: loop-entropy and hydrophobic (and other key folding) interactions, via two model parameters which control the probability of edge creation and the probability of node selection. Correlation between experimental folding rates and ND simulated folding rates is strongest when the probability of edge creation is higher for contacts with smaller sequence separation, and when the probability of node selection is higher for nodes with larger remaining degree within a local neighborhood. These two conditions also induce a wider range of simulated folding rates, which is a sign of cooperative folding for two-state folders; and better correspondence between experimental phi-values and calculated phi-values. The calculated phi-values based on centrality of nodes in ND networks are competitive with phi-values calculated from transition-state ensemble PRNs, but are less so than phi-values calculated as local centrality (a measure introduced in this paper) of nodes in PRN0s. Taken together, the two influences on the ordering of PRN0 contacts, result in more route-like formation of native shortcut networks, and hence more two-state like folding. Of the five ND variants tested, the best results at the macroscopic, mesoscopic and microscopic levels, were produced by a single variant. These ND results extend the utility of protein structure networks to the investigation of partially folded structures, and to the folding process itself .
R
A dynamic network-centric approach to study two-state folding from native structure called network dynamics
The Network Dynamics
R
is introduced. ND applies two fundamental principles of protein folding : hydrophobicity and loop-entropy, on a protein's native residue network
model is proposed. ND views protein folding as a partial ordering of contacts in a native-state Protein Residue Network
R
to generate its native shortcut network (SCN0). ND generates barrier heights that correlate significantly (-0.7) with folding rate, and positions the transition-state (TS) for 52 proteins within 0.1 <= Q < 0.5 of its reaction coordinate, which monitors SCN0 completion. ND trajectories through SCN0 space are reasonable; they support our previous work on identifying initial fold steps. Both relative contact order (RCO) and network clustering coefficient C, computed on ND generated SCN0s, correlate significantly with all three folding kinetic variables: folding rate, TS placement and native-state (NS) stability. Some of these correlations are stronger or become significant when computed on partial than on complete SCN0s. In particular, contrary to previous findings, RCO can correlate significantly with NS stability. This revelation is made possible by ND, which provides a computationally light way to explore partially folded proteins via incomplete SCN0s. ND analysis affirms the presence of NS topology in its TS SCN0s, and finds C to be a better measure of protein topology than RCO, to shed light on the hypothesized relationship between NS structure and folding rate. Within the ND-TS region, C_SCN0 correlates significantly with folding rate, while SCN0_RCO does not. However, strong TS NS structural correlations, in terms of both SCN0_RCO and C_SCN0, is also producible by a randomized version of ND
. The ND process recreates a PRN0, which gives rise to edges called shortcuts, named for their backtracking avoidance role in small-world communication between nodes in a PRN0. Clustering of native shortcut edges were previously shown able to identify folding pathways. ND applies two fundamental folding principles: loop-entropy and hydrophobic (and other key folding) interactions, via two model parameters which control the probability of edge creation and the probability of node selection. Correlation between experimental folding rates and ND simulated folding rates is strongest when the probability of edge creation is higher for contacts with smaller sequence separation, and when the probability of node selection is higher for nodes with larger remaining degree within a local neighborhood. These two conditions also induce a wider range of simulated folding rates, which is a sign of cooperative folding for two-state folders; and better correspondence between experimental phi-values and calculated phi-values. The calculated phi-values based on centrality of nodes in ND networks are competitive with phi-values calculated from transition-state ensemble PRNs, but are less so than phi-values calculated as local centrality (a measure introduced in this paper) of nodes in PRN0s. Taken together, the two influences on the ordering of PRN0 contacts, result in more route-like formation of native shortcut networks, and hence more two-state like folding. Of the five ND variants tested, the best results at the macroscopic, mesoscopic and microscopic levels, were produced by a single variant. These ND results extend the utility of protein structure networks to the investigation of partially folded structures, and to the folding process itself