Download Preliminary Proposal

Development of Software Package for
Determining Protein Titration Properties
By
Kaila Bennett, Amitoj Chopra, Jesse Johnson, Enrico Sagullo
Bioengineering 175-Senior Design
University of California Riverside
1/19/2010
Executive Summary
This proposal outline how our group will work to establish a stand-alone
software package that will be capable of elucidating protein titration
characteristics. This software package will be integrative, and will be coded in the
programming language of R. The proposal will briefly outline the algorithms that
will be used to calculate certain titration properties such as pK a values both
intrinsic and apparent. pKa values will be calculated using model established by Jan
Antosiewicz. We will also briefly mention pervious software’s created that use a
web based interface, and how we will work to show how we correlate our pK a values
to these established software’s to test the accuracy of our software package. The
proposal will also work to outline our aims for both the winter and spring quarter.
And how these goals or objectives will be fused together to make create our software
package.
Figure 1- Antosiewicz et al
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Introduction - 1
1.1 Background
Understanding protein functions and properties is paramount in designing new
technologies and advancing fields such as pharmaceuticals and engineering.
Elucidating protein titration characteristics will aid in understanding the
mechanisms behind pH-dependent processes, and furthermore will aid in the
understanding of the protein structure-function paradigm. All protein structure are
highly dependent on pH. Ionizable amino acids have the capability to release and
extract protons, this is characterized as a proton transfer phenomena. This
capability is highly dependent on the pH of the environment, whether neutral,
acidic, or basic and leads to establishing the electrostatic contributions of a protein.
The charged to uncharged residues ratio is unique to each protein, and helps to
establish their function inside and outside the body and more importantly their
stability. Fluctuations in a proteins environment can disrupt its overall charge
characteristics and abolish this idea of the structure-function paradigm. Ionizable
or charged amino acids, which include Arginine, Lysine, Glutamic Acid, Aspartic
acid, and Histadine all, have a common characteristic. This common characteristic
can be defined as the intrinsic pKa value.
pKa it is a property of a compound that goes through acid-base chemistry based on
the compound’s propensity for giving up hydrogen or accepting hydrogen.
It is based on the acidic or basic environment, which is
the pH. pH is the negative logarithm of the hydrogen ion
concentration in a solution. pKa is the negative logarithm
of the equilibrium constant (Ka) of the acid-based
reaction of the compound of interest. pKa more
specifically is how the compound will ionize depending on
the environmental pH.
This is extremely important for functional groups of many important organic and
biological molecules because function of that particular molecule is dependent on its
charge. The intrinsic pKa describes the ionization process of a specific ionizable
group when all other ionizable groups are held constant (Morikis et al). The
intrinsic pKa can be used to discern the apparent pKa value of an ionizable group.
The intrinsic pKa can be extracted using the thermodynamic cycle. Other factors
that affect pKa values of ionizable amino acids include ionic strength, temperature,
and dielectric constants of the medium.
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The thermodynamic cycle presented by
Morikis et al allows for the calculation of
pKa values for amino acids residues free
in solution and within the protein.
Furthermore this cycle allows for the
calculation of pKa’s values in both acidic
and alkaline environments to help in
discerning weather or not the protein is
in a favorable environment.
Figure 2-Morikis et al
As a result of using the thermodynamic cycle, one must also consider the free
energies of the ionizable groups. Free energies can be described as the energy in a
physical system that can be converted into work. This work is change in the
protonated to deprotonated which is a reversible process.
R is a computer programming language used for statistical computing, and
will be our main tool for calculating pKa values. Furthermore it will be used to
integrate free energy calculations from APBS software to calculate both intrinsic
and apparent pKa values. R is important for this particular project because it has
an effective data handling and storage facility, a larger collection of intermediate
tools for data analysis and well developed simple programming language, which
allows loops and other conditions for larger amounts of data. APBS or Adaptive
Poisson-Boltzmann Solver is used as a way to calculate free energies and
electrostatic interaction between molecular solutes this software was developed by
Nathan Baker.
1.2 Purpose of the Project
Using R programming, we want to write a function that converts PDB files to
PQR files. Once the program is complete, we will use APBS software to calculate
free energies and electric static potentials. These calculations will then aid us in
writing a program that will calculate intrinsic pKa values and other thermodynamic
properties.
1.3 Pervious Work Done by Others
There are two other web software developed to calculate and perform protein
titration curves. Once our software is coded and able to output titration curves of
various proteins, we will then apply a method to compare our results to these
established software. Our suite or convenience package however will be able to
integrate other established software like APBS to run and calculate pKa values of a
desired protein.
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1.3.1 Products
The other software available to do these types of calculations are:
1) Dr. Jens Nielsen pKD Residing Protein pKa Values software package
developed at the Technical University of Denmark
2) Karlsberg+ software, there method is based on the numerical solutions of the
linearized Poisson Boltzmann equation. This software is also capable of doing
Monte-Carlo sampling of protein protonation patterns.
3) http://biophysics.cs.vt.edu/H++
1) H++: a server for estimating pKa‘s and adding missing hydrogens to
macromolecules. By Gordon JC, Myers JB, Folta T, Shoja V, Heath LS,
Onufriev
A;
Nucleic
Acids
Res.
33,
W368-71
(2005)
2) Analysis of Basic Clustering Algorithms for Numerical Estimation of
Statistical Averages in Biomolecules. By Anandakrishnan, R and
Onufriev, A; Journal of Computational Biology, 15, 165-184 (2008)
1.3.2 Possible references
1) Trylska, Joanna. "View Continuum Molecular Electrostatics, Salt Effects,
and Continuum Molecular Electrostatics, Salt Effects, and Counterion
Binding—A Review of the Poisson–Boltzmann Counterion Binding—A
Review." Wiley InterScience 28.2 (2007). Print
2) Antosiewicz, Jan M. "Protonation Free Energy Levels in Complex Molecular
Systems." Wiley InterScience 89.4 (2007). Print
3) Gilson, Micheal K. "INTRODUCTION TO CONTINUUM
ELECTROSTATICS, WITH MOLECULAR APPLICATIONS." Editorial. 13
Jan. 2006. Print
4) Morikis, Dimitrios. "Molecular thermodynamics for charged
biomacromolecules." Fluid Phase Equilibria (2006). Print
5) Nielsen, Jens. "Analyzing Enzymatic pH Activity Profiles and Protein
Titration Curves Using Structure-Based pKa Calculations and Titration
Curve Fitting." Methods in Enzymology. Print.
Product Description - 2
2.1 Objectives
The purpose of our project will be to write a script using the programming
language R, which will take any pdb file and calculate the desired thermodynamic
properties along with electrostatic potentials, and the incorporation of other
programs to create a local and portable convenience package for any to use. This
convenience package will be divided into two phases corresponding to winter and
Page 5 of 14
spring quarters. The winter phase will consist of first learning the programming
language R with the help of graduate student Chris Kieslich and Dr. Thomas Girke,
who will be holding an introduction workshop the end of January. We will be
working on the incorporation of APBS, which will allow us to calculate the intrinsic
pKa values. These pKa values will be calculated much like they were in BIEN 135,
by the use and understanding of the thermodynamic cycle. Upon the completion of
the winter phase, we will continue with algorithms that will calculate different
thermodynamic properties. At this time, we will be able to take the “divide and
conquer” approach and each group member will be responsible for a particular
algorithm. The Spring Phase will cover the statistical approximation for the
calculation of apparent pKa values using the intrinsic values. We will approach the
algorithm by either the method of clustering or the Monte Carlo method. To further
continue in the convenience of the total package, we will add scripts to print out
titration curves for each and all ionizable amino acids; to calculate protein
stabilities and, in the case of complexes, binding free energies. The scripts will then
be optimized to reduce their size, also to increase speed and efficiency, and to create
a pleasant and effective computer-user interface
2.2 Methodology
Winter:
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Spring:
2.2.1 Relevant Equations
While leaving leave one amino acid charged and the others neutral, we will use this
Antosiewicz model to calculate intrinsic pKa. At the cartoon depicts the procedure
for calculations with four amino acids, which will then extrapolated into the
calculation of n amount of amino acids in a protein.
Below is thermodynamic cycle chosen please follow inner arrows to understand
derivation:
Equation 1:
Page 7 of 14
m
G(x1, x 2 ,..., x m , pH)  2.303RT  (pH  pK M
a, i ) ,  x = 1,0
i1
Equation 2:

MP
P
2.303RT(pH  pK pa, i )  2.303RT(pH  pK M
 G M
a, i )  (G i, p
i,dp )
Equation 3: Remark that this is how we will define the change in free energy

M P
P
M
M P
Gdp,
 G Pp, i  G M
i  G dp, i  G dp, i , and G p, i
p, i
where :

M = Model
P = Polymer
dp = deprotonated state
p = protonated
Equation 4: Follow the inner arrows of the thermodynamic cycle

MP
2.303RT(pH)  2.303RT(pK Pa, i )  2.303RT(pH)  2.303RT(pK M
 G MP
a, i )  (G i, p
i,dp )
Equation 5: Simplification

M P
M P
2.303RT(pK Pa, i )  2.303RT(pK M
a, i )  (G i, protonated  G i,dp )

Equation 6: Final Form
pK

P
a,i
 pK 
M
a,i
(G MP
 G MP
i,p
i,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
G(x1", x "2 ,..., x "m , pH)  2.303RT  x1   i (pH  pK Pa, i )
i1
Equation 8:

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M
M
i1
i1
dpp
dp p
"
G(x1", x "2 ,..., x "M , pH)  2.303RT  x1"   i (pH  pK M
a, i )   x1 i (G i, P  G i, 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

n c
n c
Gdpp
 defines free energy for acidic residues
i,P  G i,P   iG i,P
Gdpp
 G ni, Pc   iG ni, pc
i, 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
i1
i1
 x1c   i    i  (G ni,Pc  G ni,Mc )
Equation 10:

m
x
'
1
n c
2
 2i (G ni, c
p  G i,M ) note, that  i will be ignored because it is inherently postive
i1

Equation 11: This is away to calulate intrinsic pKa
n c
n c
G(1, 0,...,0, pH)  2.303RT  i (pH  pK M
a, i )  (DG 1,p,2n,..., Mn  DG1,m )
Equation 12:


n c
G11  G1,n c
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:
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Equation 13:
2.303RT(pH  pKintrinsic
)  2.303RT(pH  pKM
a
a )  1  G11
Equation 14: Final form intrinsic pKa for one ionizable residue


pK intrinsic
 pK M
a
a 
G11
1  G11
 pK M
a 
12.303RT
2.303RT
Antosiewicz model will then be used to in the spring quarter to calculate apparent
pKa value.
2.2.2 Timeline
Winter quarter
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Spring Quarter
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Budgets - 3
N/A
Conclusion - 4
The goal of this project is to create a local downloadable software package
that will be able to calculate the titration properties for any protein. The software
will first calculate the intrinsic pKa values of each residue which will then be
correlated into the apparent pKa values. The software will work to generate
titration curves for easy to view analysis. The software will integrate already
defined software such as APBS to in essence create a user-friendly convenience
package. It will be a stand-alone software free and available for anyone to use.
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