Protein Folding with Shortcut Networks

2ci2 cartoon 2ci2 PRN0 with SCN0 contact map
Cartoon of 2CI2, and the contact map of its native-state protein residue network with shortcuts denoted in red.
  1. Khor S (2016). Protein residue networks from a local search perspective. Journal of Complex Networks 4(2):245-278.
  2. Khor S (2017). Comparing local search paths with global search paths on protein residue networks: allosteric communication. Journal of Complex Networks 5:409-432.
  3. Khor S (2018). Folding with a protein's native shortcut network. Proteins: Structure, Function and Bioinformatics 86(9):924-934.
  4. Khor S (2020). The ND folding model. arXiv:1902.06333 version3+ Submitted.
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Mixed ND models and combining ND models by chain fold type

Mixed ND models adopt the simplest global node policy (uniform at random), with context-sensitive edge formation policies. E.g. different levels of unscaling may be applied to select edges by SStype or to edges incident on nodes within a certain SSneighborhood.

ND results by SStype: edv=a probes previous macroscopic results (peak E corr. with exp. fold rate) by secondary structure type (A, AB, B).

Preliminary results:

UZcorrs by SStype UZ NDmixed models
Left: Fold rate correlations by SStype and ND variant for Uzunoglo dataset. Right: Combines peak Es from ND variants: m4-a-m4
Kcorrs by SStype K NDmixed models
Left: Fold rate correlations by SStype and ND variant for Kamagata dataset. Right: Combines peak Es from ND variants: t1-a-t3

Pure ND models

Pure ND models (craxy, and unscaled versions of acx: ua, uc and ux) implement global node selection and edge formation policies.

Mesoscopic investigations

2ci2 SCN0 folding pathway
Folding pathway (green arcs) for 2CI2 from native shortcut network.

EDS variants: abslv and their folding pathways from native shortcut networks.

Folding pathways from ND generated protein residue networks: $P_{fold}$

Dashboard to explore contact probability maps as a function of Q

Obtain SSEs for a protein sequence from DSSP

Macroscopic investigations

2ci2 ND energy profile UZ fold corr

Linear correlation with experimental folding rate: edv=a, ndv=craxy

  1. Simulated folding rate (peak ND energy): strongest corr. is with 'a' (-0.73).
  2. Contact-Order of native shortcut networks (SCN0).
  3. Network clustering (C) of SCN0.

Explore edge probability and energy interactions on fold rate correlation

Model ND energy distributions: edv=a, ndv=craxy

Locating TSE networks within the ND reaction coordinate denoted by Q which is fraction of native shortcuts.

  1. with ND energy (E) Gaussians
  2. with SCN0 Contact-Order and with SCN0 network clustering
The above three features highlight different aspects of a contact: (i) E is particular about amino acid pairing by native and non-native shortcuts, (ii) Contact-Order is sensitive to sequence distance of native shortcuts, and (iii) C considers the arrangement of native shortcuts relative to each other.

Adjusting ND energies

Microscopic investigations

phi from NS local centrality phi from ND centrality
Top: Calculating phi-values with local node centrality from native-state PRNs.
Bottom: Calculating phi-values with node centrality from ND generated PRNs.

Calculating phi-values from native-state and transition-state PRNs

Calculating phi-values from ND PRNs: edv=a, ndv=craxy

Calculating phi-values from ND PRNs with NS normalization

Edge q-labelling reports how ordering PRN0 edges by their avg-q values (otained from ND snaps) can identify TSE PRN0 edges with average AUC = 0.80 over the three biased ND variants a, c, and x.