Clustering the Temporal Sequences of 3D Protein StructureMayumi Kamada+*, Sachi Kimura, Mikito Toda, Masami Takata+, Kazuki Joe++Graduate School of Humanities and Science, Information and Computer Sciences, Nara Womens UniversityDepartments of physics, Nara Womens University

OutlineMotivationFlexibility DockingFeature Extraction using MotionAnalysis Conclusions and Future Work

MotivationProtein in biological molecules DockingTransform oneself and Combine with other materials

Prediction of Docking Prediction of resultant functions

Existing Docking SimulationPredicted structuresfrom dockingstructureAstructureBDocking simulationPDB*Rigid structures* Protein Data BankFluctuating in living cells Low prediction accuracyDocking simulationConsidering fluctuations

Flexibility DockingPredicted structuresfrom dockingstructureAstructureBDocking simulationPDBFlexibility handling Considering fluctuation of proteins in living cellsExtraction of fluctuated structuresConsideration ofstructural fluctuation of proteins

Flexibility HandlingFlexibility handlingMDFilteroutputfileRepresentativestructureFiltering Selection of representative structures from similar structuresMolecular dynamic simulation(MD) Simulation of motion of molecules in a polyatomic systemoutputfileoutputfileoutputfileoutputfileRepresentativestructure

Filters using RMSDRMSD(Root Mean Square Deviation)Comparison of the similarity of two structures

Propose two filtering algorithms Maximum RMSD selection filter Below RMSD 1 deletion filterResult Useful for the heat fluctuation conditionRMSD Unification of topology information Lapse of informationFeature extraction focusing on Protein Motion not Structure

Capture Protein Motion MDWavelet transformClusteringContinuous wavelet transform: Morlet wavelet Clustering algorithm:Affinity PropagationSelection of representative motionsFeature extractionThe frequency may change momentarily!

Target Protein1TIBResidue length: 269MD simulationSoftware: AMBERSimulation run time: 2 nsec Result data files: 200Space coordinates of C atoms

Singular Value DecompositionSVD(Singular value decomposition)

Definition:

Unitary matrix U: Left-singular vectorsSpatial motionUnitary matrix V: Right-singular vectorsFrequency fluctuationmatrix-size of A: 807199

Singular Value DecompositionSVD(Singular value decomposition)

Definition:

Unitary matrix U: Left-singular vectorsSpatial motionUnitary matrix V: Right-singular vectorsFrequency fluctuationmatrix-size of A: 807199

Verification of ReproducibilitySingular values and principal components

Left Singular Vectors(Spatial motion)Right Singular Vectors(Frequency fluctuation)

ReproducibilityUsing the eight principal components, the motion expressed by 199 componentscan be reproduced !Almost adjusted !

Examination (1) Each of singular values

(2)The first singular valueAccounted for about 30% overExpression of the original motion Possible by the six singular valuesThe first singular value is useful

Clustering AnalysisFocus on the first principal componentDefinitionSimilarities and Preference

Clustering by using the above values

Similarities (1)For left singular vectorsDifference of spatial directs Inner products

Similarity : C

Similarities (2)For right singular vectorsDifference between distributions of spectrum Hellinger Distance

Similarity:

Clustering MethodAffinity propagation(AP)Brendan J. Frey and Delbert Dueck Clustering by Passing Messages Between Data Points. Science 315, 972976.2007Obtain Exemplars: cluster centers

PreferenceLeft singular vectorsAverage of similaritiesRight singular vectorsminimum of similaritiesmaximum of similaritiesminimum

Similarities between Left Singular Vectors

Clusteringof Left Singular Vectors

Similarities between Right Singular Vectors

Clustering of Right Singular Vectors

DiscussionsEach of motionsSpatial motionRepetition of several similar spatial motions in time variationFrequency fluctuationRepetition of similar frequency patterns in time variation Relationship Characteristic Frequency fluctuation Group transition on spatial motion

Conclusions and Future WorkFlexibility dockingFlexibility handling: MD and FilterFeature extraction based motionWavelet analysisAnalysis of motions ClusteringFuture workCollective motionRelationship Perform the docking simulation

Conclusions and Future WorkFlexibility dockingFlexibility handling: MD and FilterFeature extraction based motionWavelet analysisAnalysis of motions ClusteringFuture workCollective motionRelationship Perform the docking simulation