Notes 20101006 CHEM 731 Meiering Protein Design

From SnOwy - Ed's Wiki Notebook

Arrived late -- was proctoring BIOL 208 midterm 1 of 2

ROSETTA / ROBETTA

• homology modelling
• start with a predicted initial conformation, then "relax" to fit into low energy conformation
• has facilities to predict ligand binding conformation
• example -- designed a protein switch -- trimeric coil-coiled protein when zinc was absent; is a zinc-finger when available
  • -- how? optimized sequence for both targets
• a "rosetta potential" is the resulting energy term for each amino acid

CASP / CAPRI (sp?)

• CASP -- sequence to structure prediction contest
• CAPRI -- ligand-protein, protein-protein docking contest

Quantum Mechanics

• expensive or intractable to perform comprehensive quantum mechanical calculation for all rotamers in a system
• able to use a rotamer library of precalculated values to do prediction
• depending on the purpose and the library, the rotamer library may take into account the backbone
• suggested that predictions can be improved upon if backbone potentials are used

CHARMM, AMBER

• Φ, Ψ angles for amino acids

Gaussian

• Precise quantum mechanical tool to evaluate protein conformation energetics

Rotamer Libraries

• many libraries have been made, depends on application
• example: secondary structure predictions
• which rotamers are present in a known structures?
• most side chains may only exist in a few conformations in a stable structure
• example: hydrophobic positions have less liberty than exposed surface sidechains
• provides a distribution of Φ, Ψ angles -- generally provides only a few due to computational expense
• Monte Carlo construction
• rotamers -- staggered and eclipsed --
• libraries can:
  • be used to evaluate energy functions
  • be used to search for new (non-favoured?) conformations given an energy conformation
  • take solubility into account
  • take backbone into account
• good libraries are available -- will likely improve in content as more structures are solved

Title: Rotamer libraries in the 21^st century

• Ramachandron plot was the very first rotamer library
• proteins used have changed -- increasing resolution, increasing number of exemplars is good
• secondary structure dependent or backbone dependent
• able to switch between rotamer libraries during optimization between iterations of
  1. annealing (energy minimization)
  2. human searching
• backbone dependence is not really useful for distant-from-optimal predictions
• backbone dependence and secondary structure libraries are really only useful for high identity homologous sequences
• not much work in the following
  1. covariance -- such as
     • correlations between rotamers of different columns
     • correlations between a backbone rotamer and a sidechain rotamer of the same column
  2. entropy -- we have more information and can likely comment on the math
• current libraries are not good on the atomic level -- solved crystal structures are used to evaluate how good a prediction made with such libraries are

Search Algorithms

• E(r) = Σ_iE(r_i) + Σ_i,jE(r_i,r_j)
• E(r_i) = in reaction of rotamer i with fixed template (self energy)
• E(r_i,r_j) = a rotamer i with a different rotamer j ( ? )
• Stochastic algorithms
  • Monte Carlo, Genetic Algorithms, FASTER
  • samples subset of search space and discovers a good local minimum
• Deterministic algorithms
  • Dead-End Elimination, Self-Consistent Mean Field, Belief Propagation, Linear Programming
  • attempts to find actual minimum -- computationally expensive -- likelihood of finding solution decreases as problem space increases

Monte Carlo

• assign rotamers randomly to starting sequence
• evaluate energy (E)
• make random changes to the sequence or to the rotamers
• evaluate energy
• accept new state according to Metropolis criterion
  • if energy decreased -- accept
  • if energy increased, accept subject to ...
    • probability (p) -- given Boltzmann ...
      • p = e^{(E_new - E_previous)} / k_BT
      • k_B is the Boltzmann constant, T is the absolute temperature
• anneal from high to low temperature -- simulated annealing (SA)
  • high temperature allows for many many bad high energy conformations
  • the conformation "settles" down as the simulation goes on

Genetic Algorithm

• generate a population of sequences
• mutate randomly at a rate of 1 to 2 mutations per sequence
• evaluate, rank energies of the different sequences
• recombine sequences with lowest energies
• evaluate energies -- randomly select sequences with best energies
• repeat
  • advantage: recombination overcomes barriers in sequence space
  • disadvantage: performs poorly on highly coupled systems (hydrophobic cores)

Dead-end Elimination

• eliminate all rotamers or combinations of rotamers that are incompatible with global minimal energy criterion (GMEC)
• criterion ...
  • E(r_i) + Σ_jmin_tjE(r_i,t_j) > E(s_i) + Σ_ijmax_tjE(s_i,t_j)
  • r is the original rotamer
  • t is a neighboring position -- t_j is a neighbouring rotamer
  • s is a new rotamer to consider
• if the minimum energy is reduced by the substituted rotamer, then keep the new rotamer
• the assumption must hold that this whole energy function is a sum of all pairwise interactions

Improving energy functions

• loads of research occurring here -- will discuss some of the most prominent ones

Missing Terminology

• gauche plus / gauche minus (conformation)
• Χ value
• rotamer -- I need to really understand this topic -- will make some notes later
• actually ... this page does a good job: http://en.wikipedia.org/wiki/Rotamer

Title: Automated design of specificity in molecular recognition

• genetic algorithm example
• multi-state design -- one desired outcome, multiple undersirable states
• algorithm that correctly selects homodimers but not heterodimers
  • desired state: homodimer
  • undersired state: heterodimers

Title: De Novo Protein Design: Fully Automated Sequence Selection

• dead-end elimination
• for a given target structure
• beta-beta-alpha protein motif

The FASTER algorithm

• assume all rotamers at all positions are correct except for one
• find the best rotamer for that position
• do this for each position in the sequence
• update all positions simultaneously
• repeat until convergence

Title: Full-sequence Computational Design and Solution Structure of a Thermalstable Protein Variant

• redesign the engrailed homeodomain -- 51 amino acids
• proteins are synthesized after design and characterization done

Title: NMR-detected conformational exchange observed in a computationally designed variant of protein Gβ1

• dead-end elimination