Folding with a protein's native shortcut network

Abstract

A complex network approach to protein folding is proposed, wherein a protein's contact map is reconceptualized as a network of shortcut edges, and folding is steered by a structural characteristic of this network. Shortcut networks are generated by a known message passing algorithm operating on protein residue networks. It is found that the shortcut networks of native structures (SCN0s) are relevant graph objects with which to study protein folding at a formal level. The logarithm form of their contact order (SCN0_lnCO) correlates significantly with folding rate of two-state and nontwo-state proteins. The clustering coefficient of SCN0s (C ) correlates significantly with folding rate, transition-state placement and stability of two-state folders. Reasonable folding pathways for several model proteins are produced when C is used to combine protein segments incrementally to form the native structure. The folding bias captured by C is detectable in non-native structures, as evidenced by Molecular Dynamics simulation generated configurations for the fast folding Villin-headpiece peptide. These results support the use of shortcut networks to investigate the role protein geometry plays in the folding of both small and large globular proteins, and have implications for the design of multibody interaction schemes in folding models. One facet of this geometry is the set of native shortcut triangles, whose attributes are found to be well-suited to identify dehydrated intraprotein areas in tight turns, or at the interface of different secondary structure elements.

The Molten Globule, and Two-State vs. Non-Two-State Folding of Globular Proteins

“…From Figure 5A, both the value of ln(k f /Q d ) and its dependence on Q d in the case of the two-state proteins are very similar to those found in the plots of ln(k I /Q d ) and ln(k f /Q d ) against Q d for the non-two-state proteins. Such similarities between two-state and non-two-state proteins were also found rather generally in the relationships between ln(k f ) and structure-based properties (see Figure 5B), which include ACO [87][88][89], LRO [91], the cliquishness [85], the n-order contact distance [93], the geometric contact number [94], the inter-residue interaction parameter [97], the average topological information [99], the entanglement of the native backbone structure [98], and the other structure-based properties [92,95,96,100]. As to the golden triangle for scaling of protein folding rates, proposed by Garbuzynskiy et al [105], we also find similar distributions of ln(k f ) between the two-state and the non-two-state proteins.…”

“…More sophisticated structure-based properties, well correlating with ln(k f ) for both two-state and non-two-state proteins, have also been proposed [92][93][94][95][96][97][98][99][100]. These structure-based properties include the n-order contact distance [93], the geometric contact number, which is the number of nonlocal contacts well packed by a Voronoi criterion [94], the inter-residue interaction parameter, which considers the distances between all residue pairs in a protein [97], the average topological information, which is derived from probability densities of all residue pairs based on a self-avoiding random walk model [99], the entanglement of the native backbone structure [98], the logarithmic ACO, computed on shortcut networks of the native structure [100], the prediction by an algorithm for the prediction of folding and unfolding rates (PREFUR) using L and the structural class as only protein-specific input [96], and the effective chain length, evaluated from the number of helical residues and the number of helices [92] or from the amino acid composition of a protein [95]. More strict physical models to evaluate ln(k f ) for two-state and non-two-state proteins from the free-energy profiles obtained by simple statistical thermodynamic calculations were also reported [101][102][103][104].…”

The Molten Globule, and Two-State vs. Non-Two-State Folding of Globular Proteins

“…Such similarities between two-state and non-two-state proteins were also found rather generally in the relationships between ln(kf) and structure-based properties (see Fig. 5(B)), which include ACO [77][78][79], LRO [81], the cliquishness [75], the n-order contact distance [83], the geometric contact number [84], the inter-residue interaction parameter [87], the average topological information [89], the entanglement of the native backbone structure [88], and the other structure-based properties [82,85,86,90]. As to the golden triangle for scaling of protein folding rates, proposed by Garbuzynskiy et al [95], we also find similar distributions of ln(kf) between the two-state and the non-two-state proteins.…”

“…More sophisticated structure-based properties, well correlating with ln(kf) for both two-state and non-two-state proteins, have also been proposed [82][83][84][85][86][87][88][89][90]. These structure-based properties include the n-order contact distance [83], the geometric contact number, which is the number of nonlocal contacts well packed by a Voronoi criterion [84], the inter-residue interaction parameter, which considers the distances between all residue pairs in a protein [87], the average topological information, which is derived from probability densities of all residue pairs based on a self-avoiding random walk model [89], the entanglement of the native backbone structure [88], the logarithmic ACO, computed on shortcut networks of the native structure [90], the prediction by an algorithm for the PREdiction of Folding and Unfolding Rates (PREFUR) using L and the structural class as only proteinspecific input [86], and the effective chain length, evaluated from the number of helical residues and the number of helices [82] or from the amino acid composition of a protein [85]. More strict physical models to evaluate ln(kf) for two-state and non-two-state proteins from the free-energy profiles obtained by simple statistical thermodynamic calculations were also reported [91][92][93][94].…”

pyProGA—A PyMOL plugin for protein residue network analysis

“…VanWarth et al [23] examined dynamic models of allostery, see also [24]. Conformational changes in PRNs were elucidated in several works [25][26][27] The field of protein folding also adopted ideas from PRN models [28,29]. There are software options for such dynamic PRN models such as gRINN [30] or RIP-MD [31].…”