This is the final presentation that my team gave at the culmination of our undergraduate research project. It involved building a protein folding simulation program using VBA in Microsoft Excel. It uses a genetic algorithm, essentially "evolving" the best fit, as determined by the fitness function, from a randomly generated seed population.

2. ►Introduction
‫ ٭‬Background
‫ ٭‬Problem
‫ ٭‬Energy Forms
►Methods
‫ ٭‬Genetic Algorithm
►Results and Discussion
►Conclusion
►VBA (Visual Basic Add-in) Program Demonstration

3. ►A protein is a string of amino acids connected
by peptide bonds.
►Amino acid
‫٭‬ Acidic N-Terminus C-Terminus
‫٭‬ Basic
‫٭‬ Aliphatic
‫٭‬ Polar uncharged
‫٭‬ Aromatic

10. ►Proteins catalyze over 1,000 biochemical reactions in
the human body.

11. ►Protein misfoldings are responsible for over 20
diseases.
‫ ٭‬Mad Cow disease caused by an “evil” protein - The “evil”
protein and normal protein have identical primary
structures, but their tertiary structures are different.
Normal PrP Diseased PrP

12. ►Some proteins fold as fast as a millionth of a second
►Theoretically, a protein of only 100 amino acids
following the trial and error method would take 100
billion years to try out all possible conformations!
►Protein structures are highly dependent upon various
environmental parameters.
‫ ٭‬Such as temperature, pH, solvent, etc.

13. ► Comparative - Use evolutionary related protein
‫ ٭‬Advantages: fast and simple
‫ ٭‬Disadvantages: conformation depends upon environmental parameters
► Folding Recognition - Utilize a database of known 3-D protein
structure
‫ ٭‬Advantages: more accurate than comparative
‫ ٭‬Disadvantages: not enough NMR confirmed protein structures
► Ab Initio - Uses both scientific and engineering approach
‫ ٭‬Advantages: has potential to predict exact shape and immediate
structures
‫ ٭‬Disadvantages: computing limitations, difficulty in selecting correct
potential energy function

14. ►Not enough NMR confirmed protein structure in Protein
Data Bank (PDB)
►Evolutionary relatedness does not necessarily translate to
similar structure
►Ab initio difficulties
‫ ٭‬Hydrophilic and hydrophobic modeling gives only general
arrangement of the protein
‫-2 ٭‬D modeling does not predict 3-D shape of the protein
‫ ٭‬Monte-carlo computing method is time consuming and does not
necessarily reach global minimum

15. ►Develop a genetic algorithm based program to predict
protein conformation
►Reduce the generations needed for prediction, thus
enhance the efficiency of the search
►Explore different additional operators to modify genetic
algorithm
►Predict the protein conformation of a short 5-AA
peptide, Enkephalin

17. ►Electrostatic Energy
►Nonbonding Energy
►Hydrogen Bonding Energy
►Cystein-Cystein Loop Energy

18. ►Energy term calculated in atom pairs
‫ ٭‬Modeled after coulomb force
►Forces between two charges at certain distance
(rij )

19. + +
E, Joule
r
Electrostatic term
r, Angstrom

20. ►Two types of Lennard-Jones potential
o 1-4 atom - connected by three bonds
o 1-5 atom, higher interaction - connected by more than three
bonds

21. ►Modeled after Lennard-Jones Potential Repulsion/Attractive forces
F
-F

 2
1
1-4 Interactions
1-5 Interactions

22. ►Energy associated with the hydrogen bonding in the
protein.

23. ►Included if there are one or more intramolecular
disulfide bonds

25. ►The rotational angle
between the bond between
one pair of adjacent atoms
and the next pair’s bond is
called a dihedral angle
►Phi is between N and C, psi
is between C and C’, omega
is between C’ and N

26. ► First 3 atoms on the peptide x
chain are fixed
► The coordinate system is q
arbitrarily determined around Ca (-1.52,1.37,0)
the first H atom of the N-
terminus N (-1.04 ,0,0)
w
► Assumptions:
‫ ٭‬Minimal bond length stretch
H- (0,0,0)
‫ ٭‬Bond angle stays constant
Y
‫ ٭‬Torsion angle (dihedral angle)
applies to the 4th atom
Z

27.   cos q ij  sin q ij  ri  1 j cos q ij
 x n1  0  
0
    
sin q ij cos w ij  cos q ij cos w ij  sin w ij ri  1 j sin q ij cos w ij
xn2 0
   B B ... B    
Bn 
 x n3  0   sin q ij sin w ij ri  1 j sin q ij sin w ij 
1 2 n
 cos q ij sin w ij cos w ij
    
1   
1  0 0 0 1
The first 3 Bn parameters are fixed due to the previous assumption, B1, B2, and B3 corresponds
to the H-, -N-, Ca
  cos q 13  sin q 13  r23 cos q 13 
 1  r12 
1 0 0
0 0 0 0
 
    sin q 13  cos q 13 r23 sin q 13
0
0 1 0 0 0 1 0 0
B3   
B1    B2   
 
0 0 0 0
1 0 0 1 0
0 1 0
 
   
 
0 0 0 1
0 1 0 1
0 0 0 0

28. ►Fisher projections to w1= dihedral angle
determine the
dihedral angle of
side-group atoms w2= 120 + w1
w2= 180 + w1
►Assumption:
w1
‫ ٭‬Tetrahedral structure:
120o apart
‫ ٭‬Bent structure: 180o
apart

30. ► Search and optimization method
that mimics the natural selection
► Terms to define
‫ ٭‬Chromosome – a set of torsion angles
‫ ٭‬Gene – an individual torsion angle
‫ ٭‬Generation – a single loop within GA
loop search
► Loops through the reproduction,
mutation, and adaptation process
to obtain best fit model

31. ►Use a computer
simulation to perform
an intelligent
search/optimization to
find the native protein
conformation that
requires the least
amount of energy
Native Conformation

32. ►GAPSS is developed under Visual Basic Add-in
environment
►Modified genetic operators
‫٭‬ Fitness function based selection
‫٭‬ Multiple entries crossover
‫٭‬ Non-uniform mutation
‫٭‬ Adaptation
►Advantages
‫ ٭‬Faster convergence
‫ ٭‬User-friendly

33. ► Basic three primary energy:
Eletrostatic, Nonbonded (6-
12), and Hydrogen Bonded
► Exclude Torsion Energy
‫ ٭‬Not real interaction energy
‫ ٭‬Introduce penalty for positive
torsion
► Cystine Loop-Closing
introduced only when more
than one cysteins are present
in the protein

34. ►Selection Operator
Higher rank
‫ ٭‬Ranked Selection – higher or better
the rank higher the fitness
probability of being chosen
‫ ٭‬Fitness Selection – better
the fitness higher the
probability of being chosen
►Benefits of Selection Lower rank
or worse
‫ ٭‬Aid the Elitism Search fitness

35. ► Mutation Operator
‫ ٭‬Uniform Mutation – randomly
replace with a value from
-180 to 180
‫ ٭‬Non-uniform mutation – add
or subtract a random value
between 0 and 180
► Effects of Mutation
‫ ٭‬Introduce variance to search
‫ ٭‬Aid the search for global
minimum by directing
gradient search out of the
local minima

36. ►Crossover Operator
‫ ٭‬Random 2-point Crossover
– randomly exchange
between parents 2 angles at
a time
‫ ٭‬Multiple Entries Crossover
– multiple random
exchange
►Benefits of Crossover
‫ ٭‬Aid the search for elites
‫ ٭‬Optimize the search by
keeping the optimal folding
segments

37. ►Adaptation Operator
‫ ٭‬Gradient search applied to
each chromosome
‫ ٭‬Predict energy profile
►Benefits of Adaptation
‫ ٭‬Provide the local minima
search
‫ ٭‬Determine the energy
profile of the native folding
process

38. ► Free GA search – no restriction on dihedral angles with
exception of omega and ring structure
‫ ٭‬Advantages: use in any protein search, empirical way of obtaining
protein conformation, and useful for energy profile search
► α-helices and b-sheets specific GA search – randomly select
segment of protein as α-helices and b-sheets
‫ ٭‬Advantages: enhance the speed of free GA and accurate search for α-
helices and b-sheets
► Binary GA search – use binary to represent dihedral angles
instead decimal
‫ ٭‬Advantages: No barrier when doing crossover

39. ►Creates α-helices and b-sheets
of random lengths at random
start positions
►Each α-helix or b-sheet created
in this way is described by two
parameters
►Crossover will involve trading
the two parameters between
two individuals

40. ►When α-helices are crossed
over, each individual’s new
energy is compared to its old
energy. If there is a net Green
region
improvement, the crossover
is kept.
►The “former helix” regions Blue
region
will be filled with random
torsion angles like normal

41. ►Transfer torsion angles to binary code
‫ ٭‬Integer and decimal coded separately to shorten the total
number of digits - 17 digits altogether
►Idea is to make the torsion angles on a single
chromosome represented by one long continuous
chain
‫ ٭‬Cross over and Mutation operators all similar to GA
10100101010010000101001110101100001
01011010100100001010010101001000010
10010101001010010100101010011100

43. ►All single AA was predicted with GAPSS
►GA parameters
‫ ٭‬Initial population: 20
‫ ٭‬Generation limitation: 15
‫ ٭‬Percentage of mutations: 90%
►Compared to native single AA folding

44. Asparagine
Alanine Asparatic Acid
N
A D
Asn
Ala Asp
Cysteine
C
Cys
Glutamine Glutamic Acid
Q E Glycine Isoleucine
Gln Glu G I
Gly Ile

45. Leucine Serine
Methionine
L S
M
Leu Ser
Met
Valine
Threonine
V
T
Val
Thr

46. ►Enkephalin is pentapeptide that is involved in
regulating pain
►Two forms of enkephalin
‫ ٭‬Methylated-enkephalin – Tyr-Gly-Gly-Phe-Met
‫ ٭‬Leucine-enkephalin – Tyr-Gly-Gly-Phe-Leu
►Short enough to confirm the accuracy of the
GAPSS, however still contains complex ring side
groups

47. ►Gradient zero conformations suggests the GAPSS
are capable of obtaining local minima
►Backbone conformations showed incredible
similarities
►Side group conformations still show discrepancy
between predicted and theoretical

48. ►GAPSS was able to locate a few local minimum
protein conformations

49. ►Backbone structure was predicted by the GAPSS
GA NMR
predicted Confirmed
Backbone Backbone
Structure Structure

50. ► Discrepancies between side groups due to the lack of
entropy, solvation energy, and center partial charge
assumption
GA
predicted
Backbone
Structure NMR
Confirmed
Backbone
Structure

51. ► (a) The minimum energy of each
generation with different initial
population at 3 generation limit
and 20% mutation
► (b) The minimum energy of each
generation with different the
percentage of mutation at 10
generation limit and 20 initial
population.
► The optimal condition was found
to be 30 initial population,15
generation limits, and 90%
mutation percentage

52. ► Progression of protein folding of the best prediction, potential energy
continue to reduce suggest that more stringent GA parameters could lead to
global minimum

53. ►Due to computing capability limitation, less stringent GA
parameters were used
►Energy level of predicted enkephalin structure is less than
the theoretical, however, the code is still showing energy
decrease
►More sophisticated partial charge calculation and non-
bonded energy could improve the prediction
►There are zero gradient structures predicted by the GAPSS

54. ► GA based search and optimization is a simple and efficient method
for the isolated native protein structure prediction
► Continuous decimal representation of dihedral angles is more
efficient than binary representation of dihedral angles, despite the
crossover barriers
► a-helices and b-sheets search converges faster than free torsion
angle search
► Similar backbone dihedrals predicted from VBA GA compared to
Protein Databank

55. Chemical, Biological, and Materials Engineering
Department, University of Oklahoma
Advanced Design II

56. ►Distance calculation from the origin
   
 x   R cos    q 1      R cos( q 1 )
 
2  2 
   
 y  R sin    q 1    cos( b 1 )  R sin( q 1 ) cos( b 1 )
 
x 2  2 
   
 z  R sin    q 1    sin( b 1 )  R sin( q 1 ) sin( b 1 )
 
q 2  2 
Ca (-
1.52,1.37,0)
N (-1.04 ,0,0)
(x)  (y )  (z )
2 2 2
w
  R cos( q 1 )  2   R sin( q 1 ) cos( b 1 )    R sin( q 1 ) sin( b 1 ) 
2 2
H- (0,0,0)
Y
 
   R cos( q 1 )   sin( q 1 ) R  cos( b 1 )  sin( b 1 )
2 2 2 2
Z    R cos( q 1 )   sin( q 1 ) R  (1)
2 2
cos( q 
)  sin( q 1 )
R
2 2 2
1
 R (1)
2

57. ►Rotate one axis at a time to compensate for bond
and dihedral angle, there is no rotation around y
x’ z’
x z
qz qx
y y
qz qx
y’ y’
z =z’ x =x’

59. Qy is 0, cancelation of most of trigonometry functions
1 1
1
1

60.   cos q ij  sin q ij  ri  1 j cos q ij
 
0
 

sin q ij cos w ij  cos q ij cos w ij  sin w ij ri  1 j sin q ij cos w ij 

Det  Bn    1

 sin q ij sin w ij ri  1 j sin q ij sin w ij 
 cos q ij sin w ij cos w ij
 

 
 
0 0 0 1

  cos q ij  sin q ij  ri  1 j cos q ij 
0
 R cos( q ij )
 x i 1   
 x i 1   
sin q ij cos w ij  cos q ij cos w ij  sin w ij ri  1 j sin q ij cos w ij  
   
y i  1  Det   y i  1   R sin( q ij ) cos( w ij ) 
   
 sin q ij sin w ij ri  1 j sin q ij sin w ij 
 cos q ij sin w ij cos w ij
 z i  1   R sin( q ij ) sin( w ij ) 
 z i 1   
    
 
2
2
 
 R cos( q ij )
  x i 1   x i 1  
 
 
 
  y i  1    y i  1      R sin( q ij ) cos( w ij )  

 R sin( q ) sin( w )  
  
  z i 1   z i 1  
   ij  
ij