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Validation of Time Series Technique for Prediction of Conformational States of Amino AcidsDr. Sangeeta Sawant , Bioinformatics Centre, UoP, Pune (Guide)Dr. Mohan Kale, Dept. of Statistics, UoP, Pune (co-guide)
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Concepts Used Ramachandran Plot Time series AR,ARMA,ARIMA models AIC criteria Euclidean distance Potential values for AA residues Feynman Problem Solving Algorithm
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Time Seriesa sequence of data points or set of observations, measuredtypically at successive time instants spaced at uniform timeintervals. Patterns, variations forecasting
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Time Series Models (probability model)Autoregressive (AR) modelsAutoregressive-moving average (ARMA)Autoregressive integrated moving average (ARIMA)models- depend linearly on previous data points
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Materials & Methods R R-Studio, Tinn-R bio3d,itsmr,forecast,tseries,timsac,wordcloud ITSM_2000- Standalone R Nabble BioStars stats.stackexchange
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MethodsA) Calculation of Potential values for AAresiduesB)Forecasting of AA statesC) Clustering
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Calculation of Potential values for AA residues Dataset-I 3829 proteins selected from PDB (Protein Data Bank) –PDBSelect dataset list(25 % seq. similarity) Expt. method-X-ray, R-factor: - 0-0.25 (for best resolved structures) Chain breaks, only CA atomsPhi-Psi values –torsion.pdb() of “bio3d” & verified via PDBGoodies (IISC, Bangalore) & Protein Angle Descriptor utility (IIT, Delhi ) Assignment of Conformational state 1, 2, or 3 - to regions I, II, or III of the Rama. Plot, to each amino-acid residue (Phi_psi values)
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ᵠ ᶲFigure No- 2 Ramachandran plot showing three conformational regions I ,II and III I- closely/tightly packed conformations, Phi-140 to 0,Psi -100 to 0 II-extended conformations, Phi -180 to 0, Psi 80 to 180 III- all remaining confirmations
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Frequencies of single residues in three states calculated& normalized using (Kolaskar, A.S. & Sawant, S.V. -1996 ) nik N Pik = nik nikNik –no. of times the AA of type (i) occurs in state k=1-3;N -total no. of residuesPik -potential values of AA of type (i) in state k Potential values in pdf
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Forecasting of AA states for best models….e.g. for AR(1) process,X t = φ X (t-1) + Z (t), t=0,± 1,….Where {Z t}~ WN (0, s2) & | φ | <1 1st observed potential for AA with index given as data points & t respectively, prediction starts from 2nd position up to last index using forecast() “itsmr”
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Similarly for ARMA (1,1) /ARIMA (1,1)X t = φ X (t-1) + Z (t) + θ Z (t-1), θ+φForecasting Quality by coefficient of determination (R2)using formula R =1 2 (Yi Fi )2 (Yi Y )2 Yi =True value /Observed value Fi = Forecasted/predicted value
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Clustering Dataset-IISCOP Domain specific PDB-style files(ATOM & HETATM records )downloaded fromASTRAL Compendium for Sequence and Structure Analysis -release 1.75 (June 2009)Scan for chain breaks & presence of CA atoms only, breaked fileskept aside
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Length of AA residues(100-110) e.g.10gsa1_a_133_pot.txt File
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Potential values (Time series),each domain divided intostationary (506) & non-stationary process (1692)Non-stationary data kept aside for furthertransformationsAR,ARMA & ARIMA modelsBest model (minimum AIC criteria)Best-AR(22),ARMA(484),ARIMA(No model)AR(p), ARMA(p,q) -distance matrix (Euclidean distance )Dendrogram-Neighbour-joing ( Phylip packages)
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Dendrogram_TS –ARMA models-484• Phylowidget link
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Results & DiscussionFor each AA of all the proteins, 3D-Cartesian co-ordinates were transformedinto 2D info. i.e. conformational states ofAA and potential values were computedand used to build time-distance (index ofAA) dependent statistical model as timeseries for forecasting purposes.
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AR values Autoregressive order (p) 1-18 range Short & long range dependence variations in protein structural arrangements Variations proves diversity exhibits through structural components
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Table No. II – Forecasting results for AR models (44) out of best 90 models (Note- for 46 models, class information not found in SCOP database) All values are in % accuracy All (a)-12 All (b)-5 / (c)-9 + (d)-13 Small Coiled-coil Designed proteins (h)-3 proteins (g)-1 (k)-1 Max Min Max Min Max Min Max Min Max MinAA 26.82 2.41 16.30 8.88 27.77 1.47 28.57 7.04 19.51 22.5 5.88 29.03seq(%)States 55.68 21.77 51.11 44.76 54.76 30.64 51.70 19.04 48.78 26 15 26.88(%)Conformational states accuracy > AA residues accuracy due to lowresolution of potential values(forecasted values)
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Table No. III– Forecasting results for ARMA models (557) out of best 1239 models (Note- for 682 models, class information not found in SCOP database) —All values are in % accuracy All (a)-123 All (b)-146 / (c)-120 + (d)-127 Multi domains Membrane & Small proteins (e)-13 cell surface proteins(g)- (f)-3 17 Max Min Max Min Max Min Max Min Max Min Max Min Max MinAA 32.55 2.63 32.81 3.96 43.47 5 37.96 2.70 24.39 6.034 12.65 7.01 30.64 6.60seq(%)States 65.77 8.06 65.01 17.94 62.89 8.97 68.15 11.11 50 17.80 34.33 11.42 64.51 14.28(%)Due to non-representative dataset & inadequate info. about class, can’t saythat for any particular class i) pred. accuracy ↑ or ↓ & ii) follows mostlyARMA process
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DiscussionTS graphs opens new door in scientific visualization of proteins (no 3D str. info) i.e.specific AA can be visualized on line plot with its value proportional to frequency tooccur into allowed regions of Ramachandran plot.Potential value for each AA adds new feature of selection in machine learningtechniques.Order of AR model tells how current value linearly related to past p valueIntra-dependency of AA shown using models of TS e.g. AR(4),ARMA(1,3)
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CONCLUSIONSFound new way of looking at protein structureprediction.Application of TS technique for predicting conformational states based on theconformational state potentials instead of secondary str. has been attempted.Accuracy of prediction of conformational states for AA, using time series ishigher than that for prediction of AA residues.To increase accuracy for prediction, multivariate time series concept may beuseful instead of uni-variate time seriesIntra-fluctuations inside proteins, due to AA arrangement can be traced outby stationary & non-stationary groups
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FUTURE WORKAR and MA order of TS models -as point of genetic information (distances) topredict evolutionary relationship between different proteins.TS concept can be used to predict conformational states of missing residuesin PDB data filesHierarchical clustering/classification of TS of proteins -birth to new conceptof time dependent clustering (pseudo-clustering) & pseudo-phylogeny.Development of synthetic proteins to combat seasonal diseases & to tacklechemical warfare attacks.TS fluctuations for specific class of proteins can be used as “Pattern” for dataanalysis and pattern-dependent classification of proteins
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ReferencesBlundell TL, Sibanda BL, Sternberg MJ, Thornton JM. Knowledge-based prediction of protein structures and the design of novelmolecules. Nature. 1987 Mar 26-Apr 1;326(6111):347-52. ReviewKolaskar, A.S., Sawant, S.V. (1996). Prediction of conformationalstates of amino acids using a Ramachandran plot. Int.J.PeptideProtein Res.110-116Alessandro G.,Romualdo B.,(2000). Nonlinear Methods in theAnalysis of Protein Sequences:A Case Study in Rubredoxins.Biophysical Journal.136-148
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