Gene Finding

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Genetic Algorithms and Protein Folding
Based on lecture by Dr. Steffen
Schulze-Kremer http//www.techfak.uni-bielefeld.de
/bcd/Curric/ProtEn/proten.html
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Genetic Algorithm is a heuristic method that
operates on pieces of information like nature
does on genes in the course of evolution.

• Individuals are represented by a linear string of
  letters of an alphabet (in nature nucleotides, in
  genetic algorithms bits)
• Individuals are allowed to mutate, crossover and
  reproduce.
• Fitness function evaluates individuals.
• Depending on the generation replacement mode a
  subset of parents and offspring enters the next
  reproduction cycle.
• After a number of iterations the population
  consists of individuals that are well adapted in
  terms of the fitness function.
• It cannot be proven that the individuals of a
  final generation contain an optimal solution for
  the objective encoded in the fitness function.

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• Initialise a population of individuals.
• This can be done either randomly or with domain
  specific background knowledge to start the search
  with promising seed individuals. (Where available
  the latter is always recommended. )
• Individuals are represented as a string of bits.
• A fitness function must be defined that takes as
  input an individual and returns a number (or a
  vector) that can be used as a measure for the
  quality (fitness) of that individual.
• The application should be formulated in a way
  that the desired solution to the problem
  coincides with the most successful individual
  according to the fitness function.

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II. Evaluate all individuals of the initial
population. III. Generate new individuals. The
reproduction probability for an individual is
proportional to its relative fitness within the
current generation.
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Crossover
two point crossover
0101001111000011010101011110111 10101011010111001
01110001010101
uniform crossover
0101001111000011010101011110111 10101011010111001
01110001010101
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Genetic Operators Mutation. Substitute one or
more bits of an individual randomly by a new
value (0 or 1). Variation. Change the bits in
a way that the number encoded by them is
slightly incremented or decremented.
Crossover. Exchange parts (single bits or
strings of bits) of one individual with the
corresponding parts of another individual.
Originally, only one-point crossover was
performed but theoretically one can process up
to L - 1 different crossover sites (with L as the
length of the individual).                      
                                                  
                                                  
                                                  
                     
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IV. Select individuals for the new parent
generation. Schemes 1) Complete offspring
is selected while all parents are discarded
(original genetic algorithm). This is motivated
by the biological model and is called total
generation replacement. 2) The n best
individuals (from old and new generation)
This method is called elitist generation
replacement. V. Go back to step 2 until either
a desired fitness value was reached or until
a predefined number of iterations was performed
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Init the first generation
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Representation Formalism

• hybrid approach - genetic algorithm is configured
  to operate on numbers, not bit strings as in the
  original genetic algorithm.
• Disadvantages
• the mathematical foundation of genetic algorithms
  holds only for binary representations, although
  some of the mathematical properties are also
  valid for a floating point representation.
• Binary representations run faster in many
  applications.
• An additional encoding/decoding process may be
  required to map numbers onto bit strings.

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Protein Structure Prediction
Individuals - Protein Conformations Fitness
Function Force Field
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Representation
Cartesian 3D coordinates is not a good choice
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• The frequency of each torsion angle in intervals
  of 10 was determined and the ten most frequently
  occurring intervals are made available for
  substitution of individual torsion angles by the
  MUTATE operator.
• At the beginning of the run, individuals were
  initialized with either a completely extended
  conformation where all torsion angles are 180 or
  by a random selection from the ten most
  frequently occurring intervals of each torsion
  angle.
• For the w torsion angle the constant value of
  180 was used because of the rigidity of the
  peptide bond between the atoms Ci and Ni1.

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Search Space

• Generally molecules with n atoms have 3n - 6
  degrees of freedom -gt
• 100 residues approximately 20 atoms per residue
  5994 degrees of freedom
• Systems of equations with this number of
  variables are analytically intractable today.
• Discrete approximation
• (5 torsion angles per residue
• 5 likely values per torsion angle) 25100

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Fitness Function - Potential Energy
Charmm energy func
                         
                       .
bond length potential (set to
const) bond angle potential (set to
const) torsion angle potential improper torsion
angle potential (set to const) van der Waals
pair interactions electrostatic
potential hydrogen bonds (set to
const) interaction with the solvent (set to
const -gt in vacum)
Simplified to
               
(since there are no interactions with the
solvent, there is not enough force to drive the
protein to a compact folded state)
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Simplified Energy Function
Empirical relation between the number of residues
and the diameter
                .
pseudo entropic term
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First Testprotein Crambin, 46 a.a.
Table 3. Steric Energies in the Last Generation
                                                  
                                                 
Table 2. R.m.s. Deviations to Native Crambin
                                                  
                                
The genetic algorithm favoured individuals with
lowest total energy which in this case was most
easily achieved by optimising electrostatic
contributions.
Simple summation of different components has the
disadvantage that components with larger numbers
would dominate the fitness function whether or
not they are important or of any significance at
all for a particular conformation.
In other words -gt bad fitness function
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Improvements

• Instead of using separate phi psi value
  distributions, apply phi-psi (2D) clustering
  procedure.
• Use secondary structure prediction algorithm (70
  accuracy).
• Specialised Genetic Operators
• LOCAL TWIST (local conformation changes by
  performing the ring closure algorithm for
  polymers)

The LOCAL TWIST operator led to significant
improvements in prediction accuracy and also to a
substantial decrease in overall computation time.
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Improvements(2)Fitness Function -gt vector
r.m.s. only for verification
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Vector Fitness Function

• Candidate selection for the next generation
• If there is an individual that has better (i.e.
  lower) values in each fitness component, then we
  take it. Continue until no unambiguously better
  individuals are found.
• Then remove the worst individuals, i.e. those
  with higher values in each fitness component than
  any other individual.
• The remaining set of individuals is heuristically
  reduced until the exact number of individuals for
  the next generation is reached. This is done by
  iteratively removing an individual with the worst
  fitness value in a randomly selected fitness
  component.

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Capability of Genetic Algorithm in General?
Tests on other proteins (Local Twist and rms
fitness) gave also close to native conformations
(less than 3.0 A)
Conclusion applying an appropriate fitness
function genetic algorithm achieves the desired
results.
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Test case Crambin 46 a.a.
polar,     ,     ,    , hydro, Crippen and
solvent
I. Fitness vector
    , hydro, Crippen, solvent decreased with
rms
polar,     ,     mislead the algorithm to
non-native conformation
-gt Rms 6.27
II. Fitness vector
Crippen, clash, hydro and scatter
constraints on the secondary structures
-gt Rms 4.36
trypsin inhibitor -gt 6.65
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Conclusions

• Genetic algorithms proved to be an efficient
  search tool for 3-D representations of proteins.
  For a 3-D protein model with a simple, additive
  force field as fitness function and using a
  rather small population the genetic algorithm
  produced several individuals (i.e. protein
  conformations) of dissimilar topology but each
  with highly optimized fitness values.
• Given an appropriate fitness function the genetic
  algorithm application described here finds the
  desired solution within only small deviations.
• The major problem lies in the fitness function.
  If there were one or a set of indicators that
  return 1for the object is native protein
  conformation and 0 for the object is not a native
  protein conformation one could expect the genetic
  algorithm approach to deliver reasonably accurate
  ab initio predictions. However, neither
  mathematical models, empirical, semi-empirical or
  statistical force fields are yet accurate enough
  to reliably discriminate native from non-native
  conformations without additional constraints.
  Thus, the genetic algorithm produces
  (sub-)optimal conformations in a different sense
  than that of nativeness.

Notice the same problem (fitness-scoring
function) exists in the Protein Docking problem.
The correct transformation (within 3-5A) is found
in realistic time (almost in all cases). However,
to assign a high score to the native complex is a
problematic task. We dont know yet a proper
scoring function.
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Side Chain Placement
rms 1.86