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Template Free Protein Structure Modeling

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Jianlin Cheng, PhD Professor Department of EECS Informatics Institute University of Missouri, Columbia 2019 Template Free Protein Structure Modeling
Outline • Traditional template-free (ab initio) modeling • Distance-based ab initio modeling empowered by deep learning
Protein Energy Landscape & Free Sampling http://pubs.acs.org/subscribe/archive/mdd/v03/i09/html/willis.html
Two Approaches for 3D Structure Prediction •Ab Initio Structure Prediction •Template-Based Structure Prediction Physical force field – protein folding Contact map - reconstruction MWLKKFGINLLIGQSV… …… Select structure with minimum free energy MWLKKFGINKH… Protein Data Bank Fold Recognition Alignmen t Template Simulation Query protein
-logP(d) Funnel-shaped landscape Demo of Our Protein Structure Prediction Software (FUSION)
Part I. Traditional Ab Initio Modeling Methods
Energy Functions • T. Lazaridis, M. Karplus. Effective energy functions for protein structure prediction. Current Opinion in Structural Biology. 2000 • A. Liwo, C. Czaplewski, S. Oldiej, H.A. Scheraga. Computational techniques for efficient conformational sampling of proteins. 2008 • K. Simons et al. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. JMB. 1997. (Rosetta – a case study) -- reading assignment due Feb. 26
Protein Energy Function • The native state of a protein is the state of lowest free energy under physiological conditions • This state corresponds to the lowest basin of the effective energy surface. • The term ‘effective energy’ refers to the free energy of the system (protein plus solvent)
Two Kinds of Energy Functions • Physical effective energy function (PEEF): fundamental analysis of forces between particles • Statistical effective energy function: data derived from known protein structures (e.g., statistics concerning pair contacts and surface area burial)
Statistical Effective Energy Function (SEEF) • Less sensitive to small displacements • Because of their statistical nature, they can, in principle, include all known and unrecognized, physical effects. • Works better for protein structure prediction
SEEF • Employ a reduced representation of the protein: a single interaction center at Ca or Cb for each residue. • Basic idea: log (Pab / Pa * Pb). Pab: is the observed probability that residues a and b are in contact. Pa is frequency of a and Pb is the frequency of b • Energy = -log (Pab / Pa * Pb) • More info: use secondary structure, solvent accessibility, distance as conditions.
Energy Terms • Pairwise contact potentials • Hydrogen bonds • Torsion angle • Burial energy (solvation energy) • Sidechain orientation coupling, rotamer energy
Rotamer Energy http://dunbrack.fccc.edu/scwrl4/
Physical / Statistical Effective Energy Function (PEEF) • CHARMM implementation (http://www.charmm.org ) • AMBER implementation (http://ambermd.org ) • Dfire energy: http://sparks-lab.org/tools-dfire.html (program) • RW energy: http://zhanglab.ccmb.med.umich.edu/RW/ (program available)
Benchmark • Can a function select a native structure from a large pool of decoys? • Can a function be used effectively in conformation sampling to generate a high proportion of near-native conformations?
Representation for Conformation Sampling How to change position of one residue? ITASSER: http://zhanglab.ccmb.med.umich.edu/I-TASSER/
Torsion Angles How to change position of one residue?
Vector Space
Simulated Annealing • Accept a move based on a probability related to temperature, e.g., P ~ e^ (-ΔE / T) • Temperature (T) controls the degree of exploration. Higher temperature, more exploration? Why? • Temperature decreases as the sampling process progresses (from iteration to iteration): cooling schedule
An Example
Pseudo Code
A TFM Example: Rosetta • K. Simons, C. Kooperberg, E. Huang, D. Baker. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. JMB, 1997. Rosetta: https://www.rosettacommons.org
Basic Idea • Short sequence segments are restricted to the local structures adopted by the most closely related sequences in the PDB • Use the observed local conformations of similar local sequences to reduce sampling space
Fragment Assembly (e.g. Rosetta) SDDEVYQYIVSQVKQYGIEPAELLSRKYGDK AKYHLSQ (X, Y, Z) Angles Coordinates Fragment Angles SDDEQYQRK (130,-120, …) …. …. 9-Residue Fragment DB Randomly pick 9 residues Find a similar fragment Replace angles Reduce search space!
Two ways of obtaining fragments • Database-based approach: https://www.rosettacommons.org • Model-based approach: http://sysbio.rnet.missouri.edu/FRAGSION/
Shortcomings of Fragment Assembly Approach Based on Database Search • Computationally expensive • Incomplete coverage ~80,000 proteins • Restricted to small proteins Fragment Structure Database
IOHMM (Input-Output Hidden Markov Model) to model protein conformational space Bhattacharya & Cheng, Bioinformatics, 2016 Bhattacharya & Cheng, Scientific Reports, 2015
20
hidden node 30 x 30 x 20 transition matrix 30 x 30 x 20 transition matrix residue class 1 … 10 … 20 discrete bivariate von Mises von Mises secondary structure (ϕ, ψ) angles ω angle 1 … 15 … 30 hidden node 1 … 15 … 30 hidden node 1 … 15 … 30 20 x 20 transition matrix 20 x 20 transition matrix residue class 1 … 10 … 20 residue class 1 … 10 … 20 H E C 1 17 20 25 30 24 1 … 15 30 … 1 … 15 30 … 21 11 19 7 15 23 Bhattacharya et al. 2015
Parameter Learning using EM algorithm • 1,740 experimentally solved proteins • 270,350 observations • Training using stochastic EM algorithm Bhattacharya et al. 2015; Van et al. 2005; Paluszewski et al. 2010
Selecting optimal model using information theory Bhattacharya et al. 2015; Burnham et al. 2002 L(d|m) : likelihood d : data n : parameters 30 hidden nodes 7,812 parameters
Function of IOHMM Model of Protein Conformation • Sample the conformation of a (sub) sequence of any size • Software: Fragsion: http://sysbio.rnet.missouri.edu/FRAGSION/
Protein Folding Video • https://www.youtube.com/watch? v=HBONCqN9U4k
Scoring Functions of Selecting Local Conformations • Knowledge-based potential functions • Bayesian scoring function One native assumption is P(structure) = 1 / # of structures.
P(a structure) • 0 for configurations with overlaps between atoms • Proportional to exp(-radius of gyration^2) for all other configurations. • Independent of secondary structure elements
Considering Beta-Sheet Pairing
Scoring – P(Sequence | Structure) Ei can represent a variety of features of the local structural environment around residue i. (8)
Implementation • Second term: for pairs separated for more than 10 residues along the chain • Buried environment: >16 other Cb atoms within 10 Angstrom of the Cb atom of the residue; otherwise, exposed
Negative Log of Interaction Probability Function
Structure Generation • Initialization: Splicing together fragments of proteins of known structure with similar local sequences and evaluating them initially using equation.
Simulated Annealing • Low scoring conformations with distributions of residues similar to those of known proteins are resampled by simulated annealing in conjunction with a simple move set that involves replacing the torsion angles of a segment of the chain with the torsion angles of a different protein fragment with a related amino acid sequence. • The simulated conformation is evaluated by (8)
Methods • Structures are represented using a simplified model consisting of heavy atoms of the main- chain and the Cb atom of the side chain. • All bond lengths and angles are held constant according to the ideal geometry of alanine (Engh & Huber 91); the only remaining variables are the backbone torsional angles.
Fragment Databases • Nimers / trimers (sequences) and their conformations extracted from known structures in the database • Identify sequence neighbors: simple amino acid frequency matching score.
Simulation • The starting configuration in all simulations was the fully extended chain. • A move consists of substituting the torsional angles of a randomly chosen neighbor at a randomly chosen position for those of the current configuration. • Moves which bring two atoms within 2.5 Angstrom are immediately rejected; other moves are evaluated according to the Metropolis criterion using the scoring equation. • Simulated annealing was carried out by reducing the temperature from 2500 to 10 linearly over the course of 10,000 cycles (attempted moves).
Simulated Structure Examples
Rosetta Software
Part II. Distance-Based Ab Initio Modeling Empowered by Deep Learning
• Work better on small, simple topology • Low accuracy (0.2 – 0.3 GDT-TS score) • Huge bottleneck (30% proteins) Walk in darkness without much clue!
Protein Contact Map http://gremlin.bakerlab.org/gremlin_faq.php
Eickholt et al., 2011
N C 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
N C Anti-parallel beta strands 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
N C Alpha helix 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
N C Anti-parallel beta strands 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
N C Parallel beta strands 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
Objective: Predict if two residues (i, j) are in contact, i.e. distance(i, j) < 8 Å, for |i-j| >= 6 SDDEVYQYIVSQVKQYGIEPAELLSRKYGDKAKYHLSQRW i j N C Anti-parallel beta strands Alpha helix Parallel beta strands Anti-parallel beta strands 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
Objective: Predict if two residues (i, j) are in contact (spatially close), i.e. Distance(i, j) < 8 Angstrom SDDEVYQYIVSQVKQYGIEPAELLSRKYGDKAKYHLSQRW 1D Sequence 3D Structure Cheng, Baldi, 2007; Eickholt, Cheng, 2012
ConEVA Demo • ConEVA: http://iris.rnet.missouri.edu/cgi-bin/coneva/main_v2.0. cgi • A protein structure: CASP13 target - T0958
Protein Contact Distance Prediction – A Major Breakthrough in Ab Initio Protein Structure Prediction in the Last 20 Years • Contact prediction (1994) • Contact prediction until 2010 (little attention) • Co-evolution and deep learning (2011 and 2012 in CASP10) – two major advances • Contact prediction improved ab initio structure prediction (CASP11, 2014 and CASP12, 2016) • CASP13 (Google’s AlphaFold, MULTICOM, etc)
Breakthrough I – Residue- Residue Co-evolutionary Analysis
MetaPSICOV Dr. David Jones at University College London (UCL) CMAppro Dr. Pierre Baldi UC Irvine GREMLIN Dr. David Baker at University of Washington CCMpred Dr. Johannes Söding at University of Munich FreeContact Dr. Burkhard Rost at Technische Universität München (TUM) DNcon / SVMcon / NNcon Dr. Jianlin Cheng at University of Missouri Columbia EVFOLD Dr. Chris Sander at Memorial Sloan Kettering Cancer Center EVFOLD Dr. Debora Marks Harvard Medical School Contact Prediction Distill Dr. Gianluca Pollastri U. College. Dublin
Direct Co-Evolutionary Coupling Analysis Calculate direct correlation caused by co-evolution (Marks et al., 2011) Co-evolution plus neural networks (Jones et al., 2014; CASP11)
How to Get Multiple Sequence Alignment • Hhblits – search a sequence against UniRef protein sequence database: https://github.com/soedinglab/hh-suite • Jackhmmer – search a sequence aginast UniRef protein sequence database: http://hmmer.org
CCMpred https://github.com/soedinglab/CCMpred
CCMPred https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4201158/ How to generate co-evolutionary scores
Breakthrough II • Deep Learning for Contact Prediction (DNCON1) (Eickholt, Cheng, 2012) • No. 1 in CASP10, 2012 • One of the first deep learning methods for bioinformatics
Deep Learning Revolution
Jesse Eickholt Zheng Wang Algorithm
SDDEVYQYIVSQVKQYGIEPCSAELLSRKYGDKAKYHLSQRW Residue identity, secondary structure, solvent accessibility, … A Vector of ~400 Features (numbers between 0 and 1) Probability that V and Y are in contact? Cheng & Baldi, 2007; Tegge et al., 2009; Eickholt, Cheng, 2012 i j
SDDEVYQYIVSQVKQYGIEPCSAELLSRKYGDKAKYHLSQRW i j A 10000000000000000000 C 01000000000000000000 D 00100000000000000000 . . . . . . . Y 00000000000000000001 Strand Helix Coil Helix 100 Strand 010 Coil 001 Exposed Buried Exposed 10 Buried 01 20 binary numbers 3 numbers 2 numbers 25 * 18 = 400 features for a pair (i, j)
A Vector of ~400 Features (numbers between 0 and 1) ~400 input nodes ~500 nodes ~500 nodes ~350 nodes wi,j
… … … … … … … [0,1] 1239 Proteins for Training Residue Pairs (|i-j| >= 6)
Speed up training by CUDAMat and GPUs Train DNs with over 1M parameters in about an hour … … … … … … [0,1] … LSDEKIINVDF KPSEERVREII
… … … … … … [0,1] … … … … … … … [0,1] … … … … … … … [0,1] … …… [0,1] Final output of ensemble is a performance weighted sum of individual DN outputs. Eickholt and Cheng, Bioinformatics (2012)
… … … … … … [0,1] … … … … … … … [0,1] … … … … … … … [0,1] … …… [0,1] Final output of ensemble is a performance weighted sum of individual DN outputs. Eickholt and Cheng, Bioinformatics (2012)
Accuracy of top L, L/5, or L/10 predictions for various ranges of sequence separation (medium- and long-range): [ TP/(TP+FP) ]
Metric Acc. L/5 Acc. L/5 (one shift) Short Range (6 <= |i-j| <12) 0.51 0.79 Medium Range (12 <= |i-j| <24) 0.38 0.65 Long Range (|i-j| >= 24) 0.34 0.55 An Example:
Method Acc. L/5 DNcon 0.30 SVMcon 0.19 Method δ Acc. L/5 DNcon 1 0.53 SVMcon 1 0.37 DNcon 2 0.62 SVMcon 2 0.45 Exact match (96 proteins, long-range contacts) Inexact match with minor shifts 9-fold better than random
Target : T0716 (CASP10) Length : 71 RMSD : 4.3A GDT-TS : 0.58 Contacts : DNcon (filtered and selected 0.4L) Selection: Best Structure Contact selection and filtering
Deep Learning • Deep Learning (CASP10; Eickholt and Cheng, 2012) • 2D Convolutional Neural Networks (CASP12; Wang et al., 2017; Adhikari et al., 2017) Contact 1 Contact 2
Deep Convolutional Neural Network • Automatic feature extraction without hand crafting • Feature composition from local (low level) to global (high level) Google Image
A Convolution Example Deep Learning lecture, Google
2D Convolutional Neural Network for Contact Prediction (DNCON2) i j • Co-evolution • Secondary structure • Solvent accessibility • Mutual information • Contact potentials • … D Input Matrices Adhikari et al., 2017 L x L L x L L x L L x L L x L L: sequence length
Two-Level Deep Convolutional Neural Networks • Training dataset: 1426 proteins with known contact maps • Validation dataset: 196 proteins • Test datasets: CASP10, CASP11 and CASP12 datasets • Implementation: Keras and TensorFlow • Hardware: Tesla K20 Nvidia GPUs Adhikari et al., 2017 Level 1 Level 2
• Use global information • Capture correlation between contacts (high-level contact patterns / clusters) Local Window Contact 1 Contact 2 Key advantages:
Test on CASP Datasets Method Accuracy of top L/5 contacts on 115 CASP13 domains DNCON2 (deep learning) 75% CCMpred (co-evolution) 45%
What are deep learning methods doing that other methods do not? • Use more long-range information (CNN, RNN, LSTM, ResNet, …) • One deep model for proteins of variable length • Capture correlations between contacts (clusters), signal reinforcement, chain propagation • Recall missing contacts and remove noise • More powerful in recognizing weak patterns (deep learning versus shallow learning) Top 5 Top L/5 Top L CCMpred 60 59 33 DNCON2 100 75 61 Co-Evolution VS Deep Learning: T0953S2 (blue: true; red: predicted) Jianlin Cheng - University of Missouri - Columbia DNCON2 CCMpred
When did the deep learning methods perform well or poorly? • Key factor: num. of effective sequences (high versus low) • Other features: secondary structure, solvent accessibility, etc (accurate versus inaccurate) • Topology of protein structure (alpha, beta, alpha/beta, alpha+beta, and non-globular) Jianlin Cheng - University of Missouri - Columbia Accuracy of top L/5 predictions VS num. of effective sequences (Neff) in CASP13
Fig 1. Illustration of our deep learning model for contact prediction where L is the sequence length of one protein under prediction. Wang S, Sun S, Li Z, Zhang R, Xu J (2017) Accurate De Novo Prediction of Protein Contact Map by Ultra-Deep Learning Model. PLOS Computational Biology 13(1): e1005324. https://doi.org/10.1371/journal.pcbi.1005324 https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005324 RaptorX
Bioinformatics, Volume 34, Issue 19, 26 April 2018, Pages 3308–3315, https://doi.org/10.1093/bioinformatics/bty341 The content of this slide may be subject to copyright: please see the slide notes for details. The architecture of the neural network models used for DeepCov.
DeepCov at GitHub: https://github.com/psipred/DeepCov
DMPFold
ResTriplet http://predictioncenter.org/casp13/doc/presentations/ Pred_CASP13_contacts_ResTriplet_TripletRes_Redacted.pdf
AlphaFold of Google DeepMind
http://predictioncenter.org/casp13/doc/presentations/Pred_CASP13- DeepLearning-AlphaFold-Senior.pdf
Reconstruct 3D protein structures from contacts / distances • Fragment Assembly + Contact Distances (Rosetta, FUSION, UniCon3D) • CONFOLD • DMPfold • AlphaFold
Fragment Assembly + Contact Distances Advantage: using fragment information Disadvantage: contact distance plays an indirect role; sampling fails for large/complicated protein structures
CONFOLD Advantage: directly translating distances into structures; contact distances play dominant role Disadvantage: fail if there is no sufficient amount of accurate distances
CONFOLD: Residue residue contact guided ab initio protein folding ‐ ‐ Proteins: Structure, Function, and Bioinformatics, Volume: 83, Issue: 8, Pages: 1436-1449, First published: 13 May 2015, DOI: (10.1002/prot.24829) Best models reconstructed for the protein 5p21 using Modeler (A), reconstruct (B), customized CNS DGSA protocol (C), and CONFOLD (D). All models are superimposed with native structure (green). The TM‐ scores of Models A, B, C, and D are 0.53, 0.86, 0.88, and 0.94, respectively. Model D reconstructed by CONFOLD has higher TM‐score and also much better secondary structure quality than the other models.
Distribution of TM‐scores of the best models reconstructed by the four methods for 150 FRAGFOLD proteins.
CONFOLD VS EVFOLD Best predicted models for the proteins RNH_ECOLI (A) and SPTB2_HUMAN (B) using EVFOLD (purple) and CONFOLD (orange) superimposed with native structures (green). The TM‐scores of these models are reported in Table IV. CONFOLD models have higher TM‐score and better secondary structure quality than EVAFOLD.
Distribution of model quality of the EVFOLD models and the models built by CONFOLD. Distribution of models built in first stage of CONFOLD (Stage 1), second stage with contact filtering only (rr filter), and second stage with β‐sheet detection only (sheet detect) are also presented. Each curve represents the distribution of 400 times 15 models.
Contact Filtering Contact filtering from Stages 1 to 2 for the protein 1NRV. (A) Superimposition of the best model in stage 1 reconstructed with top‐0.6 L contacts by CONFOLD (orange) with the native structure (green). The model has TM‐score of 0.50. Among the top‐0.6 L (60) contacts, 5 out of 8 erroneous contacts that were removed in Stage 2 are visualized in the native structure along with the distance between their Cβ‐Cβ atoms. The filtered, predicted contacts (20–59, 53–73, 30–36, 49–56, and 88–93) have Cβ‐Cβ distances of 23, 23, 20, 12, and 9 Å, respectively, in the native structure. Each pair of residues predicted to be in contact is denoted by the same color. (B) Superimposition of the best model in Stage 2 reconstructed
Comparison on T1000 – FM Domain (residues: 282-523) TM-score: 0.80 GDT-TS-score: 0.64 TM-score: 0.33 GDT-TS-score: 0.23 DNCON2 (red) VS Native (blue) (L/5: 100%, L: 79%, 2L: 50%) CONFOLD (red) VS Native (L/5: 67%, L: 65%, 2L: 55%) Rosetta-Con (red) VS Native (L/5: 20%, L: 18%, 2L: 17%) L/5 contacts on native structure Purple: model Green: native Red: model Green: native
(1) Success of Building Models for T1021s3-D1 (FM) by CONFOLD DNCON2 (red) VS Native (blue) CONFOLD (red) VS Native (blue) Top L/5 long-range contacts on native structure Blue: predicted; Green: native TM-score: 0.50 GDT-TS-score: 0.41 Top 5 Top L/10 Top L/5 Top L/2 Top L Acc. 100% 94% 97% 88% 61% Top 5 Top L/10 Top L/5 Top L/2 Top L Acc. 80% 47% 52% 51% 46%
(2) Success of Building Models from Contacts with Rosetta When Failing to Identify Templates for T1019s2 (TBM) TM-score: 0.68 GDT-TS-score: 0.67 Top L/5 long-range contacts on native structure NCON2 (red) VS Native (blue) Rosetta-Con (red) VS Native (blue) Top L/10 Top L/5 Top L/2 Top L Acc. 78% 61% 39% 26% Top L/10 Top L/5 Top L/2 Top L Acc. 56% 56% 39% 36% Purple: predicted Green: native
(2) Failure of predicting / using contacts (T0998 FM) Top L/10 Top L/5 Top L/2 Top L Acc. 6% 6% 5% 5% Top L/5 medium-range contacts on native structure DNCON2 (red) VS Native (blue) Model (red) VS Native (blue) # of effective sequences = 2 TM-score: 0.21 GDT-TS-score: 0.15 Top L/10 Top L/5 Top L/2 Top L Acc. 6% 6% 6% 4% Red: model Green: native
DMPfold
https://arxiv.org/pdf/1811.12355.pdf
AlphaFold http://predictioncenter.org/casp13/doc/presentations/ Pred_CASP13-Structure-AlphaFold-Jumper.pdf
Project 2 • Develop a simple prototype of contact distance-based ab initio protein structure prediction system • You may use existing contact prediction tools and distance-based model reconstruction tools or develop you own tools (e.g. gradient descent based model construction tools). • Test it on three CASP12 or CASP13 targets
Timeline • March 18: discussion of the plan • March 20: presentation of the plan • April 3rd , presentation of the results • April 8th , report due
Discussion of Project Plan • Select targets (two easy, one hard?) • Contact prediction (co-evolution-based methods, deep learning methods (DNCON2, DeepCov)) • Contact-based modeling (CONFOLD2, Rosetta, UniCon3D, Modeller, your own gradient descent) • Model Refinement • Evaluation and Analysis • Visualization (contact map, 3D structures, modeling movies) • Project management / task assignment
Technical Resources • DNCON2: https://github.com/multicom-toolbox/DNCON2 • DeepCov: https://github.com/psipred/DeepCov • CCMpred: https://github.com/soedinglab/CCMpred Contact Visualization • ConEVA: http://iris.rnet.missouri.edu/coneva/index.php Contact prediction
Technical Resources Model reconstruction Model Refinement (both software and web servers) CONFOLD2: https://github.com/multicom-toolbox/CONFOLD2 Rosetta: https://www.rosettacommons.org/manuals/archive/rosetta3.4_ user_guide/index.html UniCon3D: https://github.com/multicom-toolbox/UniCon3D i3DRefine: http://protein.rnet.missouri.edu/i3drefine/ 3DRefine: http://sysbio.rnet.missouri.edu/3Drefine/index.html

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Template Free Protein Structure Modeling

  • 1.
    Jianlin Cheng, PhD Professor Departmentof EECS Informatics Institute University of Missouri, Columbia 2019 Template Free Protein Structure Modeling
  • 2.
    Outline • Traditional template-free(ab initio) modeling • Distance-based ab initio modeling empowered by deep learning
  • 3.
    Protein Energy Landscape& Free Sampling http://pubs.acs.org/subscribe/archive/mdd/v03/i09/html/willis.html
  • 4.
    Two Approaches for3D Structure Prediction •Ab Initio Structure Prediction •Template-Based Structure Prediction Physical force field – protein folding Contact map - reconstruction MWLKKFGINLLIGQSV… …… Select structure with minimum free energy MWLKKFGINKH… Protein Data Bank Fold Recognition Alignmen t Template Simulation Query protein
  • 5.
    -logP(d) Funnel-shaped landscape Demo ofOur Protein Structure Prediction Software (FUSION)
  • 6.
    Part I. TraditionalAb Initio Modeling Methods
  • 7.
    Energy Functions • T.Lazaridis, M. Karplus. Effective energy functions for protein structure prediction. Current Opinion in Structural Biology. 2000 • A. Liwo, C. Czaplewski, S. Oldiej, H.A. Scheraga. Computational techniques for efficient conformational sampling of proteins. 2008 • K. Simons et al. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. JMB. 1997. (Rosetta – a case study) -- reading assignment due Feb. 26
  • 8.
    Protein Energy Function •The native state of a protein is the state of lowest free energy under physiological conditions • This state corresponds to the lowest basin of the effective energy surface. • The term ‘effective energy’ refers to the free energy of the system (protein plus solvent)
  • 9.
    Two Kinds ofEnergy Functions • Physical effective energy function (PEEF): fundamental analysis of forces between particles • Statistical effective energy function: data derived from known protein structures (e.g., statistics concerning pair contacts and surface area burial)
  • 10.
    Statistical Effective Energy Function(SEEF) • Less sensitive to small displacements • Because of their statistical nature, they can, in principle, include all known and unrecognized, physical effects. • Works better for protein structure prediction
  • 11.
    SEEF • Employ areduced representation of the protein: a single interaction center at Ca or Cb for each residue. • Basic idea: log (Pab / Pa * Pb). Pab: is the observed probability that residues a and b are in contact. Pa is frequency of a and Pb is the frequency of b • Energy = -log (Pab / Pa * Pb) • More info: use secondary structure, solvent accessibility, distance as conditions.
  • 12.
    Energy Terms • Pairwisecontact potentials • Hydrogen bonds • Torsion angle • Burial energy (solvation energy) • Sidechain orientation coupling, rotamer energy
  • 13.
  • 14.
    Physical / StatisticalEffective Energy Function (PEEF) • CHARMM implementation (http://www.charmm.org ) • AMBER implementation (http://ambermd.org ) • Dfire energy: http://sparks-lab.org/tools-dfire.html (program) • RW energy: http://zhanglab.ccmb.med.umich.edu/RW/ (program available)
  • 15.
    Benchmark • Can afunction select a native structure from a large pool of decoys? • Can a function be used effectively in conformation sampling to generate a high proportion of near-native conformations?
  • 16.
    Representation for Conformation Sampling Howto change position of one residue? ITASSER: http://zhanglab.ccmb.med.umich.edu/I-TASSER/
  • 17.
    Torsion Angles How tochange position of one residue?
  • 18.
  • 19.
    Simulated Annealing • Accepta move based on a probability related to temperature, e.g., P ~ e^ (-ΔE / T) • Temperature (T) controls the degree of exploration. Higher temperature, more exploration? Why? • Temperature decreases as the sampling process progresses (from iteration to iteration): cooling schedule
  • 20.
  • 21.
  • 22.
    A TFM Example:Rosetta • K. Simons, C. Kooperberg, E. Huang, D. Baker. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions. JMB, 1997. Rosetta: https://www.rosettacommons.org
  • 23.
    Basic Idea • Shortsequence segments are restricted to the local structures adopted by the most closely related sequences in the PDB • Use the observed local conformations of similar local sequences to reduce sampling space
  • 24.
    Fragment Assembly (e.g.Rosetta) SDDEVYQYIVSQVKQYGIEPAELLSRKYGDK AKYHLSQ (X, Y, Z) Angles Coordinates Fragment Angles SDDEQYQRK (130,-120, …) …. …. 9-Residue Fragment DB Randomly pick 9 residues Find a similar fragment Replace angles Reduce search space!
  • 25.
    Two ways ofobtaining fragments • Database-based approach: https://www.rosettacommons.org • Model-based approach: http://sysbio.rnet.missouri.edu/FRAGSION/
  • 26.
    Shortcomings of FragmentAssembly Approach Based on Database Search • Computationally expensive • Incomplete coverage ~80,000 proteins • Restricted to small proteins Fragment Structure Database
  • 27.
    IOHMM (Input-Output Hidden MarkovModel) to model protein conformational space Bhattacharya & Cheng, Bioinformatics, 2016 Bhattacharya & Cheng, Scientific Reports, 2015
  • 28.
  • 29.
    hidden node 30 x30 x 20 transition matrix 30 x 30 x 20 transition matrix residue class 1 … 10 … 20 discrete bivariate von Mises von Mises secondary structure (ϕ, ψ) angles ω angle 1 … 15 … 30 hidden node 1 … 15 … 30 hidden node 1 … 15 … 30 20 x 20 transition matrix 20 x 20 transition matrix residue class 1 … 10 … 20 residue class 1 … 10 … 20 H E C 1 17 20 25 30 24 1 … 15 30 … 1 … 15 30 … 21 11 19 7 15 23 Bhattacharya et al. 2015
  • 30.
    Parameter Learning using EMalgorithm • 1,740 experimentally solved proteins • 270,350 observations • Training using stochastic EM algorithm Bhattacharya et al. 2015; Van et al. 2005; Paluszewski et al. 2010
  • 31.
    Selecting optimal model usinginformation theory Bhattacharya et al. 2015; Burnham et al. 2002 L(d|m) : likelihood d : data n : parameters 30 hidden nodes 7,812 parameters
  • 33.
    Function of IOHMMModel of Protein Conformation • Sample the conformation of a (sub) sequence of any size • Software: Fragsion: http://sysbio.rnet.missouri.edu/FRAGSION/
  • 34.
    Protein Folding Video •https://www.youtube.com/watch? v=HBONCqN9U4k
  • 35.
    Scoring Functions ofSelecting Local Conformations • Knowledge-based potential functions • Bayesian scoring function One native assumption is P(structure) = 1 / # of structures.
  • 36.
    P(a structure) • 0for configurations with overlaps between atoms • Proportional to exp(-radius of gyration^2) for all other configurations. • Independent of secondary structure elements
  • 38.
  • 39.
    Scoring – P(Sequence| Structure) Ei can represent a variety of features of the local structural environment around residue i. (8)
  • 40.
    Implementation • Second term:for pairs separated for more than 10 residues along the chain • Buried environment: >16 other Cb atoms within 10 Angstrom of the Cb atom of the residue; otherwise, exposed
  • 41.
  • 42.
    Structure Generation • Initialization: Splicingtogether fragments of proteins of known structure with similar local sequences and evaluating them initially using equation.
  • 43.
    Simulated Annealing • Lowscoring conformations with distributions of residues similar to those of known proteins are resampled by simulated annealing in conjunction with a simple move set that involves replacing the torsion angles of a segment of the chain with the torsion angles of a different protein fragment with a related amino acid sequence. • The simulated conformation is evaluated by (8)
  • 44.
    Methods • Structures arerepresented using a simplified model consisting of heavy atoms of the main- chain and the Cb atom of the side chain. • All bond lengths and angles are held constant according to the ideal geometry of alanine (Engh & Huber 91); the only remaining variables are the backbone torsional angles.
  • 45.
    Fragment Databases • Nimers/ trimers (sequences) and their conformations extracted from known structures in the database • Identify sequence neighbors: simple amino acid frequency matching score.
  • 46.
    Simulation • The startingconfiguration in all simulations was the fully extended chain. • A move consists of substituting the torsional angles of a randomly chosen neighbor at a randomly chosen position for those of the current configuration. • Moves which bring two atoms within 2.5 Angstrom are immediately rejected; other moves are evaluated according to the Metropolis criterion using the scoring equation. • Simulated annealing was carried out by reducing the temperature from 2500 to 10 linearly over the course of 10,000 cycles (attempted moves).
  • 47.
  • 53.
  • 54.
    Part II. Distance-BasedAb Initio Modeling Empowered by Deep Learning
  • 55.
    • Work betteron small, simple topology • Low accuracy (0.2 – 0.3 GDT-TS score) • Huge bottleneck (30% proteins) Walk in darkness without much clue!
  • 56.
  • 57.
  • 58.
    N C 1 2 3… 100 1 2 3 . . . . 100 2 1 4 3 Contact map
  • 59.
    N C Anti-parallel beta strands 12 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
  • 60.
    N C Alpha helix 1 23 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
  • 61.
    N C Anti-parallel beta strands 12 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
  • 62.
    N C Parallel beta strands 12 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
  • 63.
    Objective: Predict if tworesidues (i, j) are in contact, i.e. distance(i, j) < 8 Å, for |i-j| >= 6 SDDEVYQYIVSQVKQYGIEPAELLSRKYGDKAKYHLSQRW i j N C Anti-parallel beta strands Alpha helix Parallel beta strands Anti-parallel beta strands 1 2 3 … 100 1 2 3 . . . . 100 2 1 4 3 Contact map
  • 64.
    Objective: Predict if tworesidues (i, j) are in contact (spatially close), i.e. Distance(i, j) < 8 Angstrom SDDEVYQYIVSQVKQYGIEPAELLSRKYGDKAKYHLSQRW 1D Sequence 3D Structure Cheng, Baldi, 2007; Eickholt, Cheng, 2012
  • 65.
  • 66.
    Protein Contact DistancePrediction – A Major Breakthrough in Ab Initio Protein Structure Prediction in the Last 20 Years • Contact prediction (1994) • Contact prediction until 2010 (little attention) • Co-evolution and deep learning (2011 and 2012 in CASP10) – two major advances • Contact prediction improved ab initio structure prediction (CASP11, 2014 and CASP12, 2016) • CASP13 (Google’s AlphaFold, MULTICOM, etc)
  • 67.
    Breakthrough I –Residue- Residue Co-evolutionary Analysis
  • 68.
    MetaPSICOV Dr. David Jonesat University College London (UCL) CMAppro Dr. Pierre Baldi UC Irvine GREMLIN Dr. David Baker at University of Washington CCMpred Dr. Johannes Söding at University of Munich FreeContact Dr. Burkhard Rost at Technische Universität München (TUM) DNcon / SVMcon / NNcon Dr. Jianlin Cheng at University of Missouri Columbia EVFOLD Dr. Chris Sander at Memorial Sloan Kettering Cancer Center EVFOLD Dr. Debora Marks Harvard Medical School Contact Prediction Distill Dr. Gianluca Pollastri U. College. Dublin
  • 69.
    Direct Co-Evolutionary Coupling Analysis Calculatedirect correlation caused by co-evolution (Marks et al., 2011) Co-evolution plus neural networks (Jones et al., 2014; CASP11)
  • 70.
    How to GetMultiple Sequence Alignment • Hhblits – search a sequence against UniRef protein sequence database: https://github.com/soedinglab/hh-suite • Jackhmmer – search a sequence aginast UniRef protein sequence database: http://hmmer.org
  • 71.
  • 72.
  • 73.
    Breakthrough II • DeepLearning for Contact Prediction (DNCON1) (Eickholt, Cheng, 2012) • No. 1 in CASP10, 2012 • One of the first deep learning methods for bioinformatics
  • 74.
  • 75.
  • 76.
    SDDEVYQYIVSQVKQYGIEPCSAELLSRKYGDKAKYHLSQRW Residue identity, secondarystructure, solvent accessibility, … A Vector of ~400 Features (numbers between 0 and 1) Probability that V and Y are in contact? Cheng & Baldi, 2007; Tegge et al., 2009; Eickholt, Cheng, 2012 i j
  • 77.
    SDDEVYQYIVSQVKQYGIEPCSAELLSRKYGDKAKYHLSQRW i j A 10000000000000000000 C01000000000000000000 D 00100000000000000000 . . . . . . . Y 00000000000000000001 Strand Helix Coil Helix 100 Strand 010 Coil 001 Exposed Buried Exposed 10 Buried 01 20 binary numbers 3 numbers 2 numbers 25 * 18 = 400 features for a pair (i, j)
  • 78.
    A Vector of~400 Features (numbers between 0 and 1) ~400 input nodes ~500 nodes ~500 nodes ~350 nodes wi,j
  • 79.
    … … … … … … … [0,1] 1239 Proteins forTraining Residue Pairs (|i-j| >= 6)
  • 80.
    Speed up trainingby CUDAMat and GPUs Train DNs with over 1M parameters in about an hour … … … … … … [0,1] … LSDEKIINVDF KPSEERVREII
  • 81.
    … … … … … … [0,1] … … … … … … … [0,1] … … … … … … … [0,1] … …… [0,1] Final output ofensemble is a performance weighted sum of individual DN outputs. Eickholt and Cheng, Bioinformatics (2012)
  • 82.
    … … … … … … [0,1] … … … … … … … [0,1] … … … … … … … [0,1] … …… [0,1] Final output ofensemble is a performance weighted sum of individual DN outputs. Eickholt and Cheng, Bioinformatics (2012)
  • 83.
    Accuracy of topL, L/5, or L/10 predictions for various ranges of sequence separation (medium- and long-range): [ TP/(TP+FP) ]
  • 84.
    Metric Acc. L/5Acc. L/5 (one shift) Short Range (6 <= |i-j| <12) 0.51 0.79 Medium Range (12 <= |i-j| <24) 0.38 0.65 Long Range (|i-j| >= 24) 0.34 0.55 An Example:
  • 85.
    Method Acc. L/5 DNcon0.30 SVMcon 0.19 Method δ Acc. L/5 DNcon 1 0.53 SVMcon 1 0.37 DNcon 2 0.62 SVMcon 2 0.45 Exact match (96 proteins, long-range contacts) Inexact match with minor shifts 9-fold better than random
  • 86.
    Target : T0716(CASP10) Length : 71 RMSD : 4.3A GDT-TS : 0.58 Contacts : DNcon (filtered and selected 0.4L) Selection: Best Structure Contact selection and filtering
  • 87.
    Deep Learning • DeepLearning (CASP10; Eickholt and Cheng, 2012) • 2D Convolutional Neural Networks (CASP12; Wang et al., 2017; Adhikari et al., 2017) Contact 1 Contact 2
  • 88.
    Deep Convolutional Neural Network •Automatic feature extraction without hand crafting • Feature composition from local (low level) to global (high level) Google Image
  • 89.
    A Convolution Example DeepLearning lecture, Google
  • 90.
    2D Convolutional NeuralNetwork for Contact Prediction (DNCON2) i j • Co-evolution • Secondary structure • Solvent accessibility • Mutual information • Contact potentials • … D Input Matrices Adhikari et al., 2017 L x L L x L L x L L x L L x L L: sequence length
  • 91.
    Two-Level Deep ConvolutionalNeural Networks • Training dataset: 1426 proteins with known contact maps • Validation dataset: 196 proteins • Test datasets: CASP10, CASP11 and CASP12 datasets • Implementation: Keras and TensorFlow • Hardware: Tesla K20 Nvidia GPUs Adhikari et al., 2017 Level 1 Level 2
  • 92.
    • Use globalinformation • Capture correlation between contacts (high-level contact patterns / clusters) Local Window Contact 1 Contact 2 Key advantages:
  • 93.
    Test on CASPDatasets Method Accuracy of top L/5 contacts on 115 CASP13 domains DNCON2 (deep learning) 75% CCMpred (co-evolution) 45%
  • 94.
    What are deeplearning methods doing that other methods do not? • Use more long-range information (CNN, RNN, LSTM, ResNet, …) • One deep model for proteins of variable length • Capture correlations between contacts (clusters), signal reinforcement, chain propagation • Recall missing contacts and remove noise • More powerful in recognizing weak patterns (deep learning versus shallow learning) Top 5 Top L/5 Top L CCMpred 60 59 33 DNCON2 100 75 61 Co-Evolution VS Deep Learning: T0953S2 (blue: true; red: predicted) Jianlin Cheng - University of Missouri - Columbia DNCON2 CCMpred
  • 95.
    When did thedeep learning methods perform well or poorly? • Key factor: num. of effective sequences (high versus low) • Other features: secondary structure, solvent accessibility, etc (accurate versus inaccurate) • Topology of protein structure (alpha, beta, alpha/beta, alpha+beta, and non-globular) Jianlin Cheng - University of Missouri - Columbia Accuracy of top L/5 predictions VS num. of effective sequences (Neff) in CASP13
  • 96.
    Fig 1. Illustrationof our deep learning model for contact prediction where L is the sequence length of one protein under prediction. Wang S, Sun S, Li Z, Zhang R, Xu J (2017) Accurate De Novo Prediction of Protein Contact Map by Ultra-Deep Learning Model. PLOS Computational Biology 13(1): e1005324. https://doi.org/10.1371/journal.pcbi.1005324 https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005324 RaptorX
  • 97.
    Bioinformatics, Volume 34,Issue 19, 26 April 2018, Pages 3308–3315, https://doi.org/10.1093/bioinformatics/bty341 The content of this slide may be subject to copyright: please see the slide notes for details. The architecture of the neural network models used for DeepCov.
  • 98.
    DeepCov at GitHub:https://github.com/psipred/DeepCov
  • 99.
  • 100.
  • 101.
  • 102.
  • 111.
    Reconstruct 3D proteinstructures from contacts / distances • Fragment Assembly + Contact Distances (Rosetta, FUSION, UniCon3D) • CONFOLD • DMPfold • AlphaFold
  • 113.
    Fragment Assembly +Contact Distances Advantage: using fragment information Disadvantage: contact distance plays an indirect role; sampling fails for large/complicated protein structures
  • 114.
    CONFOLD Advantage: directly translatingdistances into structures; contact distances play dominant role Disadvantage: fail if there is no sufficient amount of accurate distances
  • 115.
    CONFOLD: Residue residuecontact guided ab initio protein folding ‐ ‐ Proteins: Structure, Function, and Bioinformatics, Volume: 83, Issue: 8, Pages: 1436-1449, First published: 13 May 2015, DOI: (10.1002/prot.24829) Best models reconstructed for the protein 5p21 using Modeler (A), reconstruct (B), customized CNS DGSA protocol (C), and CONFOLD (D). All models are superimposed with native structure (green). The TM‐ scores of Models A, B, C, and D are 0.53, 0.86, 0.88, and 0.94, respectively. Model D reconstructed by CONFOLD has higher TM‐score and also much better secondary structure quality than the other models.
  • 116.
    Distribution of TM‐scoresof the best models reconstructed by the four methods for 150 FRAGFOLD proteins.
  • 117.
    CONFOLD VS EVFOLD Bestpredicted models for the proteins RNH_ECOLI (A) and SPTB2_HUMAN (B) using EVFOLD (purple) and CONFOLD (orange) superimposed with native structures (green). The TM‐scores of these models are reported in Table IV. CONFOLD models have higher TM‐score and better secondary structure quality than EVAFOLD.
  • 118.
    Distribution of modelquality of the EVFOLD models and the models built by CONFOLD. Distribution of models built in first stage of CONFOLD (Stage 1), second stage with contact filtering only (rr filter), and second stage with β‐sheet detection only (sheet detect) are also presented. Each curve represents the distribution of 400 times 15 models.
  • 119.
    Contact Filtering Contact filteringfrom Stages 1 to 2 for the protein 1NRV. (A) Superimposition of the best model in stage 1 reconstructed with top‐0.6 L contacts by CONFOLD (orange) with the native structure (green). The model has TM‐score of 0.50. Among the top‐0.6 L (60) contacts, 5 out of 8 erroneous contacts that were removed in Stage 2 are visualized in the native structure along with the distance between their Cβ‐Cβ atoms. The filtered, predicted contacts (20–59, 53–73, 30–36, 49–56, and 88–93) have Cβ‐Cβ distances of 23, 23, 20, 12, and 9 Å, respectively, in the native structure. Each pair of residues predicted to be in contact is denoted by the same color. (B) Superimposition of the best model in Stage 2 reconstructed
  • 120.
    Comparison on T1000– FM Domain (residues: 282-523) TM-score: 0.80 GDT-TS-score: 0.64 TM-score: 0.33 GDT-TS-score: 0.23 DNCON2 (red) VS Native (blue) (L/5: 100%, L: 79%, 2L: 50%) CONFOLD (red) VS Native (L/5: 67%, L: 65%, 2L: 55%) Rosetta-Con (red) VS Native (L/5: 20%, L: 18%, 2L: 17%) L/5 contacts on native structure Purple: model Green: native Red: model Green: native
  • 121.
    (1) Success ofBuilding Models for T1021s3-D1 (FM) by CONFOLD DNCON2 (red) VS Native (blue) CONFOLD (red) VS Native (blue) Top L/5 long-range contacts on native structure Blue: predicted; Green: native TM-score: 0.50 GDT-TS-score: 0.41 Top 5 Top L/10 Top L/5 Top L/2 Top L Acc. 100% 94% 97% 88% 61% Top 5 Top L/10 Top L/5 Top L/2 Top L Acc. 80% 47% 52% 51% 46%
  • 122.
    (2) Success ofBuilding Models from Contacts with Rosetta When Failing to Identify Templates for T1019s2 (TBM) TM-score: 0.68 GDT-TS-score: 0.67 Top L/5 long-range contacts on native structure NCON2 (red) VS Native (blue) Rosetta-Con (red) VS Native (blue) Top L/10 Top L/5 Top L/2 Top L Acc. 78% 61% 39% 26% Top L/10 Top L/5 Top L/2 Top L Acc. 56% 56% 39% 36% Purple: predicted Green: native
  • 123.
    (2) Failure ofpredicting / using contacts (T0998 FM) Top L/10 Top L/5 Top L/2 Top L Acc. 6% 6% 5% 5% Top L/5 medium-range contacts on native structure DNCON2 (red) VS Native (blue) Model (red) VS Native (blue) # of effective sequences = 2 TM-score: 0.21 GDT-TS-score: 0.15 Top L/10 Top L/5 Top L/2 Top L Acc. 6% 6% 6% 4% Red: model Green: native
  • 124.
  • 125.
  • 127.
  • 137.
    Project 2 • Developa simple prototype of contact distance-based ab initio protein structure prediction system • You may use existing contact prediction tools and distance-based model reconstruction tools or develop you own tools (e.g. gradient descent based model construction tools). • Test it on three CASP12 or CASP13 targets
  • 138.
    Timeline • March 18:discussion of the plan • March 20: presentation of the plan • April 3rd , presentation of the results • April 8th , report due
  • 139.
    Discussion of ProjectPlan • Select targets (two easy, one hard?) • Contact prediction (co-evolution-based methods, deep learning methods (DNCON2, DeepCov)) • Contact-based modeling (CONFOLD2, Rosetta, UniCon3D, Modeller, your own gradient descent) • Model Refinement • Evaluation and Analysis • Visualization (contact map, 3D structures, modeling movies) • Project management / task assignment
  • 140.
    Technical Resources • DNCON2:https://github.com/multicom-toolbox/DNCON2 • DeepCov: https://github.com/psipred/DeepCov • CCMpred: https://github.com/soedinglab/CCMpred Contact Visualization • ConEVA: http://iris.rnet.missouri.edu/coneva/index.php Contact prediction
  • 141.
    Technical Resources Model reconstruction ModelRefinement (both software and web servers) CONFOLD2: https://github.com/multicom-toolbox/CONFOLD2 Rosetta: https://www.rosettacommons.org/manuals/archive/rosetta3.4_ user_guide/index.html UniCon3D: https://github.com/multicom-toolbox/UniCon3D i3DRefine: http://protein.rnet.missouri.edu/i3drefine/ 3DRefine: http://sysbio.rnet.missouri.edu/3Drefine/index.html

Editor's Notes

  • #28 glycines, prolines, β-branched residues isoleucine and valine, most frequently encountered ‘generic’ class, and each of these groups preceding prolines.
  • #68 amount of effort currently being spent to improve contact prediction accuracy
  • #86 Contact Filtering: Contact filtering was applied to predicted DNcon contacts. Contacts were divided into Long Range (LR), Short Range (SR), and Medium Range (MR). From each of these groups top contacts were selected to make the top 0.4L contacts. The grey structure with red lines shows the predicted structure and the contacts used to fold the structure.
  • #97 Fig. 1. The architecture of the neural network models used for DeepCov. The number of intermediate convolutional layers and the size of the convolutional filters in these layers is variable. The three values in brackets in the right-hand cells describe the dimensionality of the data output from each layer. The values are given in the order: (number of feature channels, width, height). The width and height describe the spatial dimensions of the data and are both equal to the number of columns in the input alignment, m Unless provided in the caption above, the following copyright applies to the content of this slide: © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.comThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
  • #112 We consider each region of genome as a bead and the entire genome is a string of beads. Then we place those beads in 3D such that the distances between beads are consistent with the 2D contact map.
  • #115 Best models reconstructed for the protein 5p21 using Modeler (A), reconstruct (B), customized CNS DGSA protocol (C), and CONFOLD (D). All models are superimposed with native structure (green). The TM‐scores of Models A, B, C, and D are 0.53, 0.86, 0.88, and 0.94, respectively. Model D reconstructed by CONFOLD has higher TM‐score and also much better secondary structure quality than the other models. IF THIS IMAGE HAS BEEN PROVIDED BY OR IS OWNED BY A THIRD PARTY, AS INDICATED IN THE CAPTION LINE, THEN FURTHER PERMISSION MAY BE NEEDED BEFORE ANY FURTHER USE. PLEASE CONTACT WILEY'S PERMISSIONS DEPARTMENT ON PERMISSIONS@WILEY.COM OR USE THE RIGHTSLINK SERVICE BY CLICKING ON THE 'REQUEST PERMISSIONS' LINK ACCOMPANYING THIS ARTICLE. WILEY OR AUTHOR OWNED IMAGES MAY BE USED FOR NON-COMMERCIAL PURPOSES, SUBJECT TO PROPER CITATION OF THE ARTICLE, AUTHOR, AND PUBLISHER.