Design of artificial tubular protein structures in 3D hexagonal - PowerPoint PPT Presentation

Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model J´ an Maˇ nuch Arvind Gupta Mehdi Karimi Alireza Hadj Khodabakhshi Arash Rafiey Simon Fraser University, Canada J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 1/17

Proteins Protein is a polymer constructed from a linear sequence (chain) of amino acids. J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 2/17

Proteins Protein is a polymer constructed from a linear sequence (chain) of amino acids. When placed into a solvent it will fold into a unique 3D spatial structure with minimal energy. The structure (shape) determines the function of the protein. J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 2/17

f 0 ; 1 g 1 0 Protein Folding Many forces act on the protein which contribute to changes in free energy including: hydrogen bonding, van der Waals interactions, intrinsic propensities, ion pairing, disulphide bonds, hydrophobic interactions. J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 3/17

f 0 ; 1 g 1 0 Protein Folding Many forces act on the protein which contribute to changes in free energy including: hydrophobic interactions — most significant, cf. Dill (1990) J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 3/17

Protein Folding Many forces act on the protein which contribute to changes in free energy including: f 0 ; 1 g , hydrophobic interactions — most significant, cf. Dill (1990) Amino acids are of two types: hydrophobic or polar depending 1 represents a hydrophobic amino acid, and on their affinity to water. Hence, we can model proteins as sequences over 0 represents a hydrophilic (polar) amino acid. where J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 3/17

Hydrophobic-Polar Model introduced by Dill (1985) the protein sequence is embedded on a lattice (e.g., 2D: square, 3D: cubic) with each amino acid occupying exactly one node and consecutive amino acids occupy neighboring nodes J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 4/17

Hydrophobic-Polar Model introduced by Dill (1985) the protein sequence is embedded on a lattice (e.g., 2D: square, 3D: cubic) with each amino acid occupying exactly one node and consecutive amino acids occupy p = 011001101000011 101 00 11 0 neighboring nodes 0 ” amino acid Example in 2D square lattice: 1 ” amino acid protein: – depicts a polar “ – depicts a hydrophobic “ – depicts a peptide bond between neighboring amino acids in the sequence J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 4/17

Hydrophobic-Polar Model introduced by Dill (1985) the protein sequence is embedded on a lattice (e.g., 2D: square, 3D: cubic) with each amino acid occupying exactly one node and consecutive amino acids occupy neighboring nodes free energy of the fold — in the HP model only hydrophobic interactions (contacts) are considered Example in 2D square lattice: J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 4/17

Hydrophobic-Polar Model the protein sequence is embedded on a lattice (e.g., 2D: square, 3D: cubic) with each amino acid occupying exactly one node and consecutive amino acids occupy neighboring nodes free energy of the fold — in the HP model only hydrophobic interactions (contacts) are considered a fold with minimal free energy corresponds to a fold with the largest number of (hydrophobic) contacts Example in 2D square lattice: 8 contacts (maximum possible) — native fold J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 4/17

3 = 8 6 = 11 3 = 5 Folding in HP model is still hard! To find a native fold is NP-hard for 2D square lattice, cf. Crescenzi, Goldman, Papadimitriou, Piccolboni, Yannakakis (1998) 3D square lattice, cf. Berger, Leighton (1998) J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 5/17

Folding in HP model is still hard! To find a native fold is NP-hard for 2D square lattice, cf. Crescenzi, Goldman, Papadimitriou, Piccolboni, Yannakakis (1998) 3D square lattice, cf. Berger, Leighton (1998) 3 = 8 for 3D square lattice, cf. Hart, Istrail (1995) 6 = 11 and 3 = 5 for 2D and 3D triangular lattices, cg. there are linear time approximations with approximating factor Agarwala, Batzoglou, Danˇ cík, Decatur, Farach, Hannenhalli, Skiena (1997) J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 5/17

Inverse protein folding In many applications such as drug design, nanotechnology , we are interested in the complement problem to protein folding: For a target fold/shape, find a protein sequence whose native fold is the target. target fold J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 6/17

Inverse protein folding In many applications such as drug design, nanotechnology , we are interested in the complement problem to protein folding: For a target fold/shape, find a protein sequence whose native fold is the target. E and K , find a sequence K hydrophobic (“ 1 ”) amino acids and score at A variation of this problem is hard in 3D square lattice: E NP-complete for 3D square lattices, cf. Hart (1997) “The problem”: given constant with at most least this problem is polynomial for 2D square lattice, cf. Berman et al. (2004) J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 6/17

Inverse protein folding In many applications such as drug design, nanotechnology , we are interested in the complement problem to protein folding: For a target fold/shape, find a protein sequence whose native fold is the target. We are interested in a more natural formulation of this problem: For a given shape find a protein with a native fold approximating the shape. J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 6/17

Designs in 2D square lattice Gupta, M., Stacho , JCB (2005): Theorem. (Constructible structures) Connecting many basic building blocks: we can approximate any given shape: J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 7/17

Saturated folds 1 . 1 can have at most two Why it works? The protein string does not start or end with ( 2 ), i.e., they must be native: Thus, in 2D square lattice, every hydrophobic contacts. Since our designs have the maximal number of contacts We call such folds “ saturated ” folds. J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 8/17

p = 011001101000011 10 10 01 10 Stability Example in 2D square lattice: protein: has 82 native folds: J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 9/17

Stable designs in 2D square lattice In article “Prototeins” (1998) in American Scientist , Brian Hayes posed an open problem: Is it possible to design stable sequences of all pos- sible length in HP model for 2D square lattice? J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 10/17

Stable designs in 2D square lattice In article “Prototeins” (1998) in American Scientist , Brian Hayes posed an open problem: Is it possible to design stable sequences of all pos- sible length in HP model for 2D square lattice? Aichholzer et al. (2001/2006): designed stable cyclic sequences for all even length; and stable sequences for all length divisible by 4 in 2D square lattice. Also showed examples of sequences with exponentially many folds. J´ an Maˇ Design of artificial tubular protein structures in 3D hexagonal prism lattice under HP model * * * nuch * * * BIOCOMP 2007, Las Vegas – p. 10/17