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Week 7 Progress Report
Development of Software Package for Determining Protein Titration
Properties
By
Kaila Bennett, Amitoj Chopra, Jesse Johnson, Enrico Sagullo
Work completed:
As right now we have successfully completed four scripts. One to clean
a PDB files, we also have written a script to convert our cleaned PDB file to a
PQR file. The rational behind this script is to obtain a file that is compatible
to the Adaptive Poisson-Boltzmann Solver. PQR format incorporates
van der Waals radii and partial charge. We then have successfully written a
script that can successfully call to APBS to calculate free energies. It should
be noted that to calculate free energies, we need to use the thermodynamic
cycle, the thermodynamic cycle has four proposed states, so our scripts for the
conversion to PQR has to able to generate four PQR files. Our group is
working to make all scripts platform independent, but right now are script
for PDB2PQR can only run on LINUX and UNIX based systems. It should
also be noted that right now all calculations have been performed on PDB
1LY2. We have also successfully completed a script that can extrapolate free
energies from output calculation of APBS. Our group also presented our
accomplishments thus far, creating PPT the outlined our accomplishment, we
worked on this from Saturday to Monday.
Future work:
As a group we are coming up with a detailed plan for a way of
completing the rest of our goals for the winter quarter. First and for most we
need to make all our codes platform independent. Next we need to make sure
our free energies values are accurate for our PDB file 1LY2. We then to
optimize all our scripts, so that we can move onto our next step. Using the
thermodynamic cycles proposed by Morikis et al and Antosiewicz et al to write
a input script for calculations of intrinsic pKa. We will first write the script
that it will only calculate intrinsic pKa for four ionizable residues. These pKa
values will then be correlated to other software. Once we are sure of our
outputs values, we will then make this code capable of calculating pK a values
for m ionizable residues. We will then need to create codes that are able to
output calculated pKa for m residues on a titration curve. Then eventually
down the road these values will then be used to calculate our ultimate goal of
apparent pKa for our protein. Apparent pKa values will also be outputted on a
titration curve.
Project review:
As of right now our group is slightly behind. Although we do have some
codes done, we should have already completed codes that calculate intrinsic
pKa’s, and should have already optimized those codes, and correlated our
values to check their accuracy. To that end we know the theoretical
knowledge for calculations of intrinsic pKa’s starting first with one ionizable
Amino acid residue and then moving to m ionizable amino acids. We have
included in the appendix our derivations of pKa for the thermodynamic cycle.
These derivations will help us in our efforts to write scripts for calculations of
the pKa intrinsic.
Appendix:
Equation 1:
m
M
G(x1, x 2 ,..., x m , pH)  2.303RT ( pH  pK a,i
) ,  x =1,0
Equation 2:

i1
p
M
M P
M P
2.303RT( pH  pK a,i
)  2.303RT( pH  pK a,i
)  (Gi,p
 Gi,dp
)
Equation 3: Remark that this is how we will define the change in free energy


M P
P
M
M P
P
M
Gdp,i
 Gdp,i
 Gdp,i
, and Gp,i
 Gp,i
 Gp,i
where :
M=
P =
dp =
p =
Model
Polymer
deprotonated state
protonated
Equation 4: Follow the inner arrows of the thermodynamic cycle

P
M
M P
M P
2.303RT( pH)  2.303RT( pK a,i
)  2.303RT(pH)  2.303RT( pK a,i
)  (Gi,p
 Gi,dp
)
Equation 5: Simplification


P
M
M P
M P
2.303RT( pK a,i
)  2.303RT( pK a,i
)  (Gi,protonated
 Gi,dp
)
Equation 6: Final Form
P
M
pK a,i
 pK a,i


M P
(Gi,Mp P  Gi,dp
)
2.303RT
Corollary: the next derivation will now look at on ionized amino acid while
the other are neutralized. Eventually this prove will be extrapolated to
account for M ionizable amino acids.
Equation 7:
M
P
G(x1', x '2,..., x 'm , pH)  2.303RT  x1   i ( pH  pK a,i
)
i1
Equation 8:

M
M
i1
i1
M
dp p
dp p
G(x1', x '2 ,..., x 'M , pH)  2.303RT  x1'   i ( pH  pK a,i
)   x1' i (Gi,P
 Gi,M
)
Remark:

x1'  0,1 where 0,1 correlates to the state of thermodynamic state either being neurtral ,
charged
 i  1,1 where -1, 1 accounts for the amino acid state either being a basic or charged residues
Equation 9: We redefined the change in free energies

dp p
n c
n c
Gi,P
 Gi,P
  iGi,P
 defines free energy for acidic residues
dp p
n c
n c
Gi,P
 Gi,P
  iGi,p


 defines free energy for basic residues
So from equation 6 we redefine the difference of free energy, to account from
the neutral to charged state
Equation 9:
m
m
 x      (G
'
1
i1
i
i
n c
i,P
n c
 Gi,M
)
i1
Equation 10:

m
x 
' 2
1 i
i1

n c
nc
(Gi,p
 Gi,M
) note, that  i2 will be ignored because it is inherently postive
Equation 11: This is away to calulate intrinsic pKa
M
n c
n c
G(1,0,...,0, pH)  2.303RT   i ( pH  pK a,i
)  (G1,p,2n,...,
Mn  G1,m )
Equation 12:


nc
nc
G11  G1,p,2n,...,
Mn  G1,m
To be able to find intrinsic pKa follow much of the above derivation but notice
the slighty modified thermodynamic cycle:
Equation 13:
2.303RT ( pH  pK aintrinsic)  2.303RT ( pH  pK aM )  1  G11
Equation 14: Final form intrinsic pKa for one ionizable residue


pK aintrinsic  pK aM 
G11
  G11
 pK aM  1
12.303RT
2.303RT
Antosiewicz model will then be used to in the spring quarter to calculate
apparent pKa value.