Development of Software Package for Determining Protein Titration Properties

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 pKa 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 pKa 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.

Introduction - 1

1.1Background

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 intrinsicpKa 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.

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.

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.

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)

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 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:

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:

Equation 2:

Equation 3: Remark that this is how we will define the change in free energy

Equation 4: Follow the inner arrows of the thermodynamic cycle

Equation 5: Simplification

Equation 6: Final Form

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:

Equation 8:

Remark:

Equation 9: We redefined the change in free energies

So from equation 6 we redefine the difference of free energy, to account from the neutral to charged state

Equation 9:

Equation 10:

Equation 11: This is away to calulate intrinsic pKa

Equation 12:

To be able to find intrinsic pKa follow much of the above derivation but notice the slighty modified thermodynamic cycle:

Equation 13:

Equation 14: Final form intrinsic pKa for one ionizable residue

Antosiewicz model will then be used to in the spring quarter to calculate apparent pKa value.

2.2.2 Timeline

Winter quarter

Spring Quarter

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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