CZ5225 Modeling and Simulation in Biology

1. CZ5225 Modeling and Simulation in Biology  Proteins Chen Yu Zong   csccyz@nus.edu.sg 6874-6877

2. Mechanism of Protein function

3. Protein sequence-structure-function relationship Protein structure determines its function Function of Proteins is determined by their four level structures Primary- Sequence of amino acids Secondary - Shape of specific region along chain mostly through H-bonding Tertiary - 3 Dimensional structure of globular protein through molecular folding Quaternary- Combination of separate polypeptide and prosthetic group. Aggregation and prosthetic.

4. 1. Primary structure Proteins are polymers of a set of 20 amino acids. 20 amino acids = building units. Chiral Center asymmetric carbon The general formula for α-amino acid. 20 different R groups in the commonly occurring amino acids.

5. All naturally occurring amino acids that make up proteins are in the L conformation The CORN method for L isomers: put the hydrogen towards you and read off CO R N clockwise around the Ca This works for all amino acids.

6. Classification of 20 R groups Aliphatic residues

7. Aromatic residues

8. Acidic Charged residues Basic Negatively charged Positively charged

9. Polar residues

10. The unique couple Cg Cb Side chain = H Imino H Cd Ca Ca

11. Structure of peptide bonds Through hydrolysis reactions, amino acids are connected through peptide bond to form a peptide/protein. + H2O

12. Key features: • 1. Planar • 2. Rigid due to partial double bond character. • 3. Almost always in trans configuration. • 4. Polar. Can form at least two hydrogen bonds.

13. 2. Secondary structure Local organization mainly involving the protein backbone: -a-helix, -b-strand (further assemble into b-sheets) -turn and interconnecting loop

14. The (right-handed) a-helix • First structure to be predicted (Pauling, Corey, Branson: 1951) and experimentally solved (Kendrew et al. 1958) – myoglobin • Turn: 3.6 residues • Pitch: 5.4 Å/turn • Rise: 1.5 Å/residue -d i+8 i+4 Hydrogen bond i +d

15. The b-sheet • Side chains project alternately up or down b strand

16. Turn Structures

17. Loop structures

18. 3.1. b-hairpins

19. 3.2. b-corners

20. 3.3. Helix hairpins

21. 3.4. The a-a corner

22. 3.5. Helix-turn-helix

23. 4. Tertiary structure • secondary structure elements pack into a compact spatial unit • “Two methods now available to determine 3D structures of proteins: X-ray crystallography and Nuclear Magnetic Resonance(NMR)

24. Mad cows disease and the Prion protein Prion protein---- ---Memory? Protein mis-folding can cause diseases

25. Protein-Protein Interaction Protein-Protein interaction: Surface contact, shape complementarity Intermolecular forces: Van der Waals, hydrogen bonding, electrostatic force

26. Hydrogen Bond • Types of Hydrogen Bond: • N-H … O • N-H … N • O-H … N • O-H … O V r

27. Protein-DNA Interaction Protein-DNA interaction: • DNA recognition by proteins is primarily mediated by certain classes of DNA binding domains and motifs

28. Protein-RNA Interaction Protein-RNA interaction: • RNA recognition by proteins is primarily mediated by certain classes of RNA binding domains and motifs

29. Protein-Ligand Interaction Ligand Binding: A small molecule ligand normally binds to a cavity of a protein. Why? Effect of Binding: Activate, inhibit, being metabolized or transported by, the protein

30. Protein-Ligand Interaction Ligand Binding: A small molecule ligand normally binds to a cavity of a protein. Why? Effect of Binding: Activate, inhibit, being metabolized or transported by, the protein

31. Protein-Ligand Interaction Ligand Binding: A small molecule ligand normally binds to a cavity of a protein. Why? Effect of Binding: Activate, inhibit, being metabolized or transported by, the protein

32. Protein-Drug Interaction Mechanism of Drug Action: A drug interferes with the function of a disease protein by binding to it. This interference stops the disease process Drug Design: Structure of disease protein is very useful

33. Protein-Drug Interaction Mechanism of Drug Action: A drug interferes with the function of a disease protein by binding to it. This interference stops the disease process Drug Design: Structure of disease protein is very useful

34. Example of Binding Induced Shape Change

35. Example 2: Induced Fit of Hexokinase (blue) Upon Binding of Glucose (red). Note that the active site is a pocket within the enzyme.

36. Energy Description • Energy is needed to make things or objects change: • Movement, Chemical reaction, Binding, Dissociation, Structural Change, • Conformational change etc. • Why Energy Description for molecular structure? • Structure determination (“evolution” of a structural-template into the correct structure) • Binding induced shape change (binding sometimes induces shape change, one of the mechanisms for the interference of the function of a molecule by another) • Protein motions (proteins undergo internal motions that have implications such as the switch between active and in-active state)

37. Energy Description Kinetic energy -- motional energy Kinetic energy is related to the speed and mass of a moving object. The higher the speed and the heavier the object is, the bigger work it can do. Potential Energy -- "positional" energy. Water falls from higher ground to lower ground. In physics such a phenomenon is modeled by potential energy description: Objects move from higher potential energy place to lower potential energy place.

38. Potential Energy Description ofProtein Structure “Evolution” • A molecule changes from higher potential energy form to lower potential energy form. • Potential energy is determined by inter-molecular, intra-molecular, and environmental forces • Protein structural “evolution” can be performed by systematic variation of the atom positions towards the lower energy directions. This procedure is called “structure optimization” or “energy minimization”

39. Energy Minimization for Structural Optimization • Protein structure “evolution” can be performed by systematical variation of the atom positions towards the lower energy directions. This procedure is called “structure optimization” or “energy minimization”

40. energy coordinates Potential Energy Surface (PES) • A force field defines for each molecule a unique PES. • Each point on the PES represents a molecular conformation characterized by its structure and energy. • Energy is a function of the coordinates. • (Next) Coordinates are function of the energy.

41. A PES is characterized by stationary points: • Minima (stable conformations) • Maxima • Saddle points (transition states) • Goal of Energy Minimization • Finding the stable conformations energy coordinates Goal of Energy Minimization • A system of N atoms is defined by 3N Cartesian coordinates or 3N-6 internal coordinates. These define a multi-dimensional potential energy surface (PES).

42. Type Minimum Maximum Saddle point 1st Derivative 0 0 0 2nd Derivative* positive negative negative 20.0 16.0 12.0 8.0 transition state 4.0 0.0 energy 0 90 180 270 360 local minimum global minimum coordinate Classification of Stationary Points • Refers to the eigenvalues of the second derivatives (Hessian) matrix

43. Minimization Definitions • Given a function: • Find values for the variables for which f is a minimum: • Functions • Quantum mechanics energy • Molecular mechanics energy • Variables • Cartesian (molecular mechanics) • Internal (quantum mechanics) • Minimization algorithms • Derivatives-based • Non derivatives-based

44. A Schematic Representation Starting geometry • Easy to implement; useful for well defined structures • Depends strongly on starting geometry

45. Population of Minima Active Structure Most populated minimum Global minimum • Most minimization method can only go downhill and so locate the closest (downhill sense) minimum. • No minimization method can guarantee the location of the global energy minimum. • No method has proven the best for all problems.

46. A General Minimization Scheme Starting Point x0 yes Minimum? Stop No Calculate New Point xk+1 = f(xk)

47. f(x,y) Two Questions • Where to go (direction)? • How far to go (magnitude)? This is where we want to go

48. Line search in one dimension • Find 3 points that bracket the minimum • (e.g., by moving along the lines and recording function values). • Fit a quadratic function to the points. • Find the function’s minimum through • differentiation. • Improved iteratively. • Arbitrary Step • xk+1 = xk + lksk, lk = step size. • Increase l as long as energy reduces. • Decrease l when energy increases. 3 1 2 Real function Cycle 1: 1, 2, 3 Cycle 2: 1, 2, 4 4 5 How Far To Go? Until the Minimum

49. Steepest Descent • Where to go? • Parallel to the force (straight downhill): Sk = -gk • How far to go? • Line search • Arbitrary Step

50. 15 Starting point: (9, 9) Cycle 1: Step direction: (-18, -36) Line search equation: Minimum: (4, -1) Cycle 2: Step direction: (-8, 4) Line search equation: Minimum: (2/3, 2/3) 441 361 10 289 225 169 121 5 81 49 25 0 9 1 -5 -10 -15 -15 -10 -5 0 5 10 15 Steepest Descent: Example