LSM3241: Bioinformatics and Biocomputing Lecture 6: Fundamentals of Molecular Modeling Prof. Chen Yu Zong Tel: Room 07-24, level 7, SOC1, National University of Singapore

2 Structural organization of a molecule Three features: Configuration (atom organization). Conformation (atom spatial arrangement). Shape (Surface landscape, steric packing)

3 Structural organization of a molecule I. Configuration: The organization of atoms and chemical bonds. Change of configuration requires breaking of bonds. Switch between H and NH2 requires bond breaking.

4 Structural organization of a molecule An important aspect of configuration is chirality Chirality defines the property of mirror image. The image on the right is an mirror image of the one at left. If mirror image is not the same as the original, the compound is called chiral.

5 Structural organization of a molecule Example of chiral and non-chiral compound:

6 Structural organization of a molecule II. Conformation: Determined by the spatial positions of its constituent atoms. Inter-convertible without breaking and making bonds Rotatable bond

7 Protein structure and conformation change: Movie Show: Drug Binding Induced Conformation Change in Protein

8 Structural organization of a molecule III. Shape Steric packing (what part of space is covered by the compound). Surface features (cavities, grooves where other molecules can bind to).

9 Protein Surface Determines Its Interaction with Other Molecules: Protein-Protein Interaction

10 Protein Surface Determines Its Interaction with Other Molecules: Protein-DNA Interaction

11 Protein Surface Determines Its Interaction with Other Molecules: Protein-RNA Interaction

12 Protein Surface Determines Its Interaction with Other Molecules: 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

13 Atomic motions in a molecule Atoms are not rigidly positioned. External and internal forces can induce atomic motions. Some motions have chemical effect. Movie Show: Protein transient opening for ligand or drug binding and dissociation:

14 Atomic motions in a molecule The effect of motions are described by energy: Energy measures the ability to do work. Motion is associated with energy. Movie Show: Protein transient opening for ligand or drug binding and dissociation:

15 Types of Energy 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.

16 Potential Energy Description of Molecular Motions 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 The total energy of motions is: Energy = Stretching Energy + Angle Bending Energy +Torsion Energy + Non-Bonded Interaction Energy

17 Molecular Modeling: Basic Interactions and Their Models The stretching energy equation is based on Hooke's law. The "kb" parameter controls the stiffness of the bond spring, while "ro" defines its equilibrium length.

18 Molecular Modeling: Basic Interactions and Their Models The stretching energy equation is based on Hooke's law. The "kb" parameter controls the stiffness of the bond spring, while "ro" defines its equilibrium length.

19 Molecular Modeling: Basic Interactions and Their Models The bending energy equation is also based on Hooke's law

20 Molecular Modeling: Basic Interactions and Their Models The bending energy equation is also based on Hooke's law

21 Molecular Modeling: Basic Interactions and Their Models The torsion energy is modeled by a simple periodic function Why?

22 Molecular Modeling: Basic Interactions and Their Models Torsion energy as a function of bond rotation angle.

23 Molecular Modeling: Basic Interactions and Their Models The non-bonded energy accounts for repulsion, van der Waals attraction, and electrostatic interactions.

24 Molecular Modeling: Basic Interactions and Their Models van der Waals attraction occurs at short range, and rapidly dies off as the interacting atoms move apart. Repulsion occurs when the distance between interacting atoms becomes even slightly less than the sum of their contact distance. Electrostatic energy dies out slowly and it can affect atoms quite far apart.

25 Molecular Modeling: Basic Interactions and Their Models Types of Hydrogen Bond: N-H … O N-H … N O-H … N O-H … O Can be modeled by VdW+electrostatic (AMBER) Modified Linard-Jones (CHARM) Morse potential (Prohofsky/Chen)

26 Molecular Modeling: Basic Interactions and Their Models Complete Energy Function:

27 Molecular Modeling: Basic Interactions and Their Models Concept of energy scale is Important for molecular Modeling

28 Molecular Modeling: Basic Interactions and Their Models Concept of energy scale is Important for molecular modeling

29 Molecular Modeling: Basic Interactions and Their Models Sources of force parameters: Bonds, VdW, Electrostatic (for amino acids, nucleotides only): AMBER: J. Am. Chem. Soc. 117, CHARMM: J. Comp. Chem. 4, H-bonds (Morse potential): Nucleic Acids Res. 20, Biophys. J. 66, Electrostatic parameters of organic molecules need to be computed individually by using special software (such as Gaussian)

30 Molecular Modeling: Modeling Method I: Conformation search: Change each torsion angle: Phi -> Phi+dphi Subsequent change of atom positions: xi -> xi+dxi; yi -> yi+dyi; zi -> zi+dzi Energy is changed: E -> E +dE Each set of torsion angles corresponds to a conformation. Find sets with lower energy All possible states can be explored

31 Molecular Modeling: Modeling Method II: Energy minimization: Force guided approach: Initialize: Change atom position: xi -> xi+dxi Compute potential energy change: V -> V +dV Determine next movement: Force: Fxi=-dV/dxi; Fyi=-dV/dyi; Fzi=-dV/dzi Atom displacement: dxi=C*Fxi New position: xi=xi+dxi Energy minimization can only go down hill. Why?

32 Summary of Today’s lecture Structural organization of a molecule. Basic interactions and models Modeling methods (conformation search, energy minimization)