Protein Design

Problem introduction
Complexity: enormous

• Cryptography: 128-bit cyphers still secure
• Searchspace: 2¹²⁸ ≈ 10³⁸ ≈ 20³⁰

  ⇒ i.e. a protein consisting of 30 residues*
  (20 possible amino acids at each position)

We cannot even enumerate all possible 30-peptid proteins

* not considering different side-chain conformations

Problem introduction
Complexity: enormous

* assuming a small rotamer library with a total of 155 residue conformations

Problem introduction
Complexity: enormous

• Cryptography: 128-bit cyphers still secure
• Searchspace: 2¹²⁸ ≈ 10³⁸ ≈ 20³⁰
• Solutions?
  • Smart algorithms, non-deterministic tricks
    (DEE, Monte Carlo, Genetic Algorithms…)
  • Complexity reduction
    (rotamer libraries, place-dependent amino acids likelyhoods)

Rotamer libraries (since 1987)

• seamingly infinite conformational possibilities for one side-chain
  
  Image: Hanka Venselaar (CMBI, Nijmegen)
• Fix: build libraries with most frequent observed conformations (or some estimate)

Rotamer libraries (2)

Inverse Folding Problem (IFP) (1983)

Image: what-when-how

• Folding problem still unsolved
• Inverse Folding Problem is simpler
  Given a 3D-representation of a protein backbone, find a sequence, that folds to the given structure.

Inverse Folding Problem (IFP) (1983)

• still: same complexity
• but: a lot of sequences fold to the same structure
• Goal: find any! (not: the best)
• ⇒ fixed-backbone algorithms

Energy functions

• quantitative need for measurement of protein stability
• stability ~ melting point
• stable proteins are most likely to actually fit the assumed fold (cf. IFP)
• ⇒ molecular mechanics potential energy functions (MM-PEF, c.f. Boas & Harbury, 2007)

Energy functions: Protein Design Cycle (Bassil et. al., 1996)

• Aim: improve energy functions to increase the accuracy and efficiency in computational protein design
• Protein Design Cycle:
  1. → …RLIEYHTQD…: predict protein sequences likely to achieve a desired fold
  2. peptid synthesis
  3. quantitative analysis (predicted vs. actual stability)
  4. $\displaystyle{ E_{new} = E_{old} + \sum_{i,j} E_{exp}(i, j)} refined energy functions

Energy functions: recent progress (Lippow & Tidor, 2007)

• improve to increase the accuracy and efficiency in computational protein design
• recently:
  • DNA-protein interactions (Morozov et. al., 2005)
  • metall center interactions (Spiegel et. al., 2006)
  • solvent and solvent-mediated effects (Marshall et. al., 2005) (including a pairwise approximation)
  • placement of individual water molecules (Jiang et. al., 2005) (rotamer approach)

Smart Algorithms: Monte Carlo Method (Metropolis, 1949)

• based on repeated random sampling

applied to protein design:

1. initially: pick rotamers for a sequence at random
2. next: rotamer replacement at a randomly picked residue
   ⇒ new energy: E_new
3. accept any move with lower energy
4. accept other moves based on temperature (→ simulated annealing)
5. continue with step 2

Based on Desjarlais & Clarke (1998) and Voigt et. al. (2000), Image: Wikipedia

Smart Algorithms: Monte Carlo: Simulated Annealing (Metropolis, 1953)

• idea stolen from metallurgy: heating and controlled cooling increase size of crystals and reduce defects
• heat: molecules can move freely (escape local minima)

• 
  

  slow cooling: more chances to find lower internal energy configurations

$\displaystyle{ ρ = e^{\frac{E_{new} - E_{old}}{kT}} }
with T being the (virtual) temperature

Images on the right: Wikipedia

Smart Algorithms: Dead End Elimination (Desmet et. al., 1992)

• deterministic algorithm to find the
  Global Minimum Energy Configuration
• requires a pairwise energy description

Idea:$\displaystyle{ E(i_r) + \sum_{j\neq i}^{N} \min_{s} E(i_r, j_s) > E(i_t) + \sum_{j\neq i}^{N} \max_{s} E(i_t, j_s) }$

• eliminate one residue after another ($\displaystyle{ O(n^2) } each)
  (n: total number of rotamers)
• can be extended for pairs ($\displaystyle{ O(n^3) } each)
• still slow, but dramatical improvent to $\displaystyle{ O(p^n) }

An example
Create a new enzyme for a specific reaction

Steps to cover

1. Find a working target fold
2. Remove all residues (backbone-only)
3. Place side-chains and ligand (TS)
4. Fill the rest of the protein (according to IFP)
5. Generate a couple of target designs for experimental classification

An example
1. Find a working target fold

• Manually define the catalysis mechanism:
  typically: stabilize a transition state
  ⇒ model of functional groups at active site
• Find supporting backbone conformations:

  

  • DEZYMER program (Hellinga & Richards, 1990)
  • RosettaMatch approach
  • Inverse rotamer tree approach (Zanghellini et. al., 2006)
• Find/Build an according scaffold

Based on Zanghellini et. al. (2006) and Röthlisberger (2008)

Glimpse to the Future

• 
  Design new protein folds: TOP7 (Kuhlmann et. al., 2003)
• 
  enhanced energy functions (Boas & Harbury, 2007; cf. also Lippow & Tidor, 2007)
• 
  conformational change after ligand binding
  Image: Flynn et. al. (2001)
• 
  multistep reactions
  (Jiang et. al., 2008)