Homology modeling LECTURE 7 From step 2): the alignment of sequences is available E.g. homology modeling of trypsin IV (target) with 4CHA PDB file (template) Contents ▪ Homology modeling ▪ Molecular dynamics (Basic concepts) Homology modeling Homology modeling 3) Backbone generation - Making a copy of the backbone coordinates of template protein. - Problems: PDB files are erroneous due to missing residues in many cases. Check of the template structure is necessary before and after the alignment. - Multiple template modeling can be used if no error-free templates are available (merging) 4) Loop modeling - Gaps: in model sequence. Insertions: in template sequence - Gaps: a hole is created in template for gaps by deleting extra residues and closed later - Insertion: the template is cut and extra residues are inserted Homology modeling Homology modeling 4) Loop modeling (cont.) - This works for high - Both procedures require conformational change of backbone sequence identitites. - These modifications should be made in the loop regions as At identity < 35 % the in regular α-helix or β-sheet the conformational change of rotamers of conserved backbone is not permitted. residues may differ in - N.B. loops are highly flexible regions, often having high up to 45 %. B-factors. Conformation of a loop can easily vary in free state - The core region of a protein and in crystal structure (artifacts). often includes such conserved sequences and side-chain conformations can be predicted 5) Side-chain modeling with high accuracy there. - Modeling of surface side-chains is more problematic (solvent). - Coordinates corresponding to side-chain conformations at - The side-chain conformations are dependent on the backbone 100 % conserved sequences can be copied very often from the conformation, and, therefore knowledge-based construction template into the modeled protein structure due to the of side-chains often starts with alignment of backbones of conservation of χ angles. peptide fragments from known PDB structures. Homology modeling Homology modeling 5) Side-chain modeling (cont.) Classification of homology models - Other problems: - disulphide bridges (Cys-Cys): pre-defined parameters 1) Models based on incorrect alignments between target or constraints at model optimization. and template sequences. Low accuracy. - metal ion – side-chain contacts (Fe-S, Zn-S, etc.) 2) Models based on correct alignments are better, but their - modeling of hetero groups and co-factors accuracy can still be medium to low. Such models are very useful tools for the rational 6) Model optimization mutagenesis experiment design. They are of very limited use for ligand binding studies Molecular dynamics, preferably with explicit solvent model. and rational drug design. 3) Models of a high degree of sequence identity (> 70%) 7) Model validation with the target. Such models have proven useful during drug design - Energy-based, using V of the MM force-field projects and allowed the taking of key decisions in - Trial and error: reproduction of e.g. binding free energies of compound optimization and chemical synthesis. different ligands to the active site of the protein (docking) Molecular dynamics Molecular dynamics Molecular dynamics (MD) Why dynamics? - is a deterministic global search method Newton’s 2nd law formulates a basic principle of the - generates statistical amount of ensembles of dynamics of a body configurations, i.e. coordinates and velocities of all atoms The rate of change of momentum of a body is proportional of the system to the resultant force acting on the body and is in the same - is a simulation method for calculation of microscopic direction. and macroscopic properties of the systems r d r r Some history Fi ( t ) = [mi v i ( t )] = miai ( t ) 1957 Alder és Wainwright, simple mechanical systems dt 1964 Rahman, Ar liquid 1971 Rahman, water i: the body (atom); m: mass of the body; F: the force 1977 McCammon és Karplus, protein in vacuum acting on i; a: acceleration; t: time 1983 Gunsteren és Berendsen, protein in water Molecular dynamics Molecular dynamics How can we calculate the force? Examples of calculation of forces For a system with N atoms we know the potential energy Non-bonding interactions function (V) from molecular mechanics r r r V( r1, r2 ,..., rN ) = Vbonding + Vnon −bonding For conservative forces (electrostatic, spring force, etc.) the force can be calculated as a gradient of the potential r r ∂ ∂ ∂ Fi = ∇V( ri ) wher e ∇ , , ∂x ∂y ∂z Bonding interaction ∇: the nabla vector differential operator Integration Molecular dynamics Molecular dynamics An example: the Verlet algorithm r r Fi ( t ) r d r d2 r r dr r r r r ai ( t ) = ; ai ( t ) = v i (t) = 2 ri (t) ; v i (t) = ri (t) r (t + ∆t) = r (t) + v(t)∆t + 2 a( t )∆t 2 + ... 1 mi dt dt dt r r r r r (t − ∆t) = r (t) − v(t)∆t + 2 a( t )∆t 2 + ... 1 The motions of all particles By adding the two equations are coupled. The many body r r r r r (t + ∆t) = 2r (t) − r ( t − ∆t ) + a( t )∆t 2 problem cannot be solved analytically. Velocities can be calculated from positions r r r Finite difference methods v( t ) = [r ( t + ∆t ) − r ( t − ∆t )]/ 2∆t are used to generate MD trajectories. The Verlet algorithm requires 2 sets of atomic positions and 2 r r dr 1 d r one set of accelerations. Modest storage requirements. r (t + ∆t) = r (t) + r (t)∆t + 2 2 r (t)∆t 2 + ... dt dt Disadvantages: velocities are separately calculated and r r r r Taylor series expansion r (t + ∆t) = r (t) + v(t)∆t + 2 a( t )∆t 2 + ... 1 (index i is omitted) it is not self-starting. Molecular dynamics Molecular dynamics Recipe of an MD simulation (1 protein) INGREDIENTS - 1good-looking protein structure (preferably a PDB coordinate file) - Water - Some ions (for seasoning) DIRECTIONS Take a pretty simulation box which fits to the size of the protein. Fill up the box with water and add some ions until the charge becomes 0 (PME). Soak the protein in water until most H-bonds are formed. After equilibration put the system into an MD pot and start cooking. You can apply pressure and heat if necessary. The cooking time varies from ps’s to µs’s. Molecular dynamics Molecular dynamics Periodic boundary conditions Minimum image convention - At the faces of the box Only the closest image of a molecule is considered water molecules have no during the calculation of short-range interactions. interaction partners, which is not the case in real solutions - The box is surrounded by d > 2R c + Rprotein its images. Atoms at the faces interact with atoms d: edge of the box of the other image. Rc: cut-off value of - Molecules can leave at one interactions side and enter at the opposite Rprotein: length of protein along side to keep particle number the edge constant.
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