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Doug Raiford Lesson 17. Protein Conformation Prediction (Part I). Two folding models. Framework model Secondary structure first Assemble secondary structure segments Hydrophobic collapse Molten : compact but denatured Formation of secondary structure after: settles in

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Doug RaifordLesson 17Protein Conformation Prediction (Part I)Two folding modelsFramework model Secondary structure first Assemble secondary structure segments Hydrophobic collapse Molten: compact but denatured Formation of secondary structure after: settles in van der Waals forces and hydrogen bonds require close proximity Protein Conformation Prediction (Part I)Experimentally determining Isolate protein and crystalize Time consuming process Slowly evaporate Many experiments in parallel Different conditions X-ray crystallography Get XYZ spatial coordinates Protein Conformation Prediction (Part I)PDBsStore these XYZ coordinates in text files PDB website X Y Z Occu Temp ElementATOM 1 N THR A 5 23.200 72.500 13.648 1.00 51.07 N ATOM 2 CA THR A 5 23.930 72.550 12.350 1.00 51.27 C ATOM 3 C THR A 5 23.034 72.048 11.220 1.00 50.34 C ATOM 4 O THR A 5 22.819 72.747 10.228 1.00 51.19 O ATOM 5 CB THR A 5 25.221 71.703 12.416 1.00 51.94 C ATOM 6 OG1 THR A 5 26.159 72.326 13.305 1.00 53.51 O ATOM 7 CG2 THR A 5 25.849 71.583 11.046 1.00 53.33 CProtein Conformation Prediction (Part I)Modeling To fully model the folding action of a polypeptide chain Must know all the forces acting on each aa Must be able to predict the motion of the aa’s given the forces Protein Conformation Prediction (Part I)How to aa’s move?Recall that proteins are able to fold because of the torsional rotation of the aa bonds R almost always 180RProtein Conformation Prediction (Part I)In order to model folding…Must be able to take phi and psi angles and transform into xyz coordinates of various atoms Don’t forget about R groups What places in space are occupied? Bump checking Protein Conformation Prediction (Part I)Anatomy of a carbon atomTetrahedron Protein Conformation Prediction (Part I)RememberKnow distances Each angle is 109.5 R almost always 180RProtein Conformation Prediction (Part I)The angles4 atoms on same plane , , and ω all relative to R group (O in case of ω) Protein Conformation Prediction (Part I)Torsion angles to xyzOne approach Given xyz of last three, and next torsion angle… Transform so that C is at origin, BC on new X, AB on plane of new Y Then apply torsion Start D on X Swing out 70.5 (180-109.5; in the plane of Y) Rotate by torsion angle Protein Conformation Prediction (Part I)New vector spaceTo transform a vector space… XCZYBAProtein Conformation Prediction (Part I)New vector spaceTo transform a vector space… XCZYBNew X axisNew Z axisNew Y axisAProtein Conformation Prediction (Part I)New vector spaceIt’s all about projections If target vector is a unit vector then simple dot product ABProtein Conformation Prediction (Part I)New vector spaceDot product of a row with vector yields the projection of the vector onto the vector represented by the row All three dot products yields all three components XCZBYANew XNew ZNew YProtein Conformation Prediction (Part I)What is the new X?The new X is BC (as a unit vector) X’CZ’Y’BAProtein Conformation Prediction (Part I)But what is BC?Remember, all we have is the last xyz coordinates All vectors are assumed to originate at the origin So BC is actually [XC,YC,ZC]-[XB,YB,ZB] CBOriginProtein Conformation Prediction (Part I)And what is ||BC||?Magnitude of BC X’CZ’Y’BAProtein Conformation Prediction (Part I)New vector spaceFirst row of transformation matrix XCZBYANew XProtein Conformation Prediction (Part I)Second RowAB in plane of new Y so Z component is zero XCZBYImportant piece: Y componentAProtein Conformation Prediction (Part I)New vector spaceSecond row of transformation matrix XCZBYANew YProtein Conformation Prediction (Part I)New vector spaceThird row of transformation matrix easy once have first two: Cross Product XCZBYANew YProtein Conformation Prediction (Part I)The next point: it’s all trigKnow distance to next atom Know angle is 70.5° (180-109.5) X component = ||CD|| cos(70.5°) Y component starts out at ||CD|| sin(70.5°) This is the distance from X to the new D XDCZYBAProtein Conformation Prediction (Part I)Final torsional rotationYZ component is that distance times sinθ(torsion angle) Y = ||CD|| sin(70.5°)*cos θ Z = ||CD|| sin(70.5°)*sin θ Dnewin plane of xy70.5°ZCXDfinalΘ (torsional angle)CDnewin plane of xyYProtein Conformation Prediction (Part I)Going from xyz to anglesTransform next xyz into new vector space coordinates (same as before Determine ||CD|| XDCZYBAProtein Conformation Prediction (Part I)An exampleXYZ coordinates for an amino acid Build the linear transform matrix used to transform the original vector space into the space defined by the three atoms above. Protein Conformation Prediction (Part I)ExampleBC? XCalculator makes life easier:[2.863,-15.219,-0.703] sto A[3.920,-14.209,-0.705] sto B[5.265,-14.836,-1.065] sto CunitV (C-B)unitV under “VECTR / MATH”[XC,YC,ZC]-[XB,YB,ZB][5.265 -14.836 -1.065]-[3.920 -14.209 -0.705][1.345 -0.627 -0.36]Magnitude of BC?CZdistance B to C: 1.527BNew X axis:[0.880 -0.410 -0.236]YAProtein Conformation Prediction (Part I)ExampleCalculatorA-C sto AB-C sto BC-C sto CB-Asto ABC-Bsto BCunitV BC (same answer)unitV under “VECTR / MATH”Actually forgot a step Need to translate all three points Move in direction of negative C Will place C and origin and keep A and B relative to C XCZBYANo change to XProtein Conformation Prediction (Part I)ExampleNew Y? XCalculatorunitV(AB-(dot(AB,BC)/(norm BC)2 * BC))Norm under “VECTR / MATH”CZBYANew Y axis:[0.440 0.894 0.088]Protein Conformation Prediction (Part I)ExampleCalculatorunitV BC entersto XunitV(AB-(dot(AB,BC)/(norm BC)2 * BC))entersto Ycross(X,Y)Cross under “VECTR / MATH”New Z? XCZBYANew Z axis:[0.174 -0.181 0.968]Protein Conformation Prediction (Part I)Two approachesDe novo From first principles Comparative/Homology Based Sequence similarity Protein Conformation Prediction (Part I)Protein Conformation Prediction (Part I)

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