Calculate pKas of Lysozyme

Background

Lysozyme is a small enzyme that dissolves bacterial cell walls, thus killing bacteria. It was discovered as the first antibiotic to inhibit bacterial growth in food—before penicillin.

Structure: Crystal structure of hen egg white lysozyme (PDB ID: 4LZT)

The experimental pKₐ values of all lysozyme residues are provided at the bottom of this tutorial.
Here, we will focus on two residues in the active site with perturbed pKₐ values:

  • GLU 35 — acts as a proton donor.
  • ASP 52 — stabilizes the charged intermediate.

For lysozyme to attack the glucose molecule of the substrate:

  • GLU 35 needs a high pKₐ to remain protonated and donate a proton to the glycosidic oxygen.
  • ASP 52 needs a low pKₐ to remain deprotonated and stabilize the reaction intermediate.

Reference: Jens Erik Nielsen and J. Andrew McCammon, Protein Sci. 2003 Sep; 12(9): 1894–1901

Prepare the Calculation

After MCCE is installed and the PATH environment variable is configured (see installation guide), prepare a working directory for the calculation:

mkdir 4lzt
cd 4lzt

Download the PDB file for 4LZT:

getpdb 4lzt

Output should look like:

Saving as 4LZT.pdb ...
Download completed.

Explicit Waters

We suggest removing explicit waters from the input pdb file. The protonation states and pKas with or without are similar, but calculations are much faster without explicit waters.

grep -v HOH 4LZT.pdb > 4LZT_noHOH.pdb

Run the 4 Steps of MCCE

MCCE expects to run in a single directory containing only one calculation. There are 4 sequential steps. Each step’s output feeds into the next. You can re-run later steps without starting over.

For each step command, you may use the help information to see parameter options:

step#.py -h

Step 1 — Convert PDB to MCCE PDB

Checks for inconsistencies between the PDB file and MCCE topology files:

  • Adds missing sidechain atoms.
  • Flags unknown residues.
  • Removes waters with >5% surface exposure.
  • Separates chain termini as NTR and CTR (treated as protonatable).
step1.py 4LZT.pdb

This command generates step1_out.pdb which is required for step 2.

Step 2. Make side chain conformers

This step makes alternative side chain locations and ionization states.

step2.py

This command generates step2_out.pdb which is required of step 3.

Step 3. Make energy table

This step calculates conformer self energy and pairwise interaction table.

step3.py

This command generates opp files under energies/ folder and file head3.lst which are required of step 4.

Step 4. Simulate a titration with Monte Carlo sampling

This step simulates a titration and writes out the conformation and ionization states of each side chain at various conditions.

step4.py --xts
  • fort.38. is the primary output file. It gives the average occupancy of each conformer.
  • sum_crg.out give the net charge on all residues. Residues where all conformers have a zero charge are not reported in this file.
  • pK.out calculates the best single pKa for each residue given the change in charge with pH in sum_crg.out.

Results

The pKa report is in file pK.out.

cat pK.out

From the result, GLU 35 (pKa = 5.13) has a higher pKa than ASP 52 (pKa = 3.33).

To analyze the ionization energy of an ionizable residue at the mid point pH=5.13 with pairwise cutoff 0.1:

mfe.py ASP-A0052_ -c 0.1

To analyze the ionization energy of this residue pH 7 with pairwise cutoff 0.1:

mfe.py ASP-A0052_  -p 7 -c 0.1

A more detailed explanation of mfe.py program can be found here [To be linked]

Benchmark pKas for Lysozyme

There are 20 experimentally measured pKas in hen white lysozyme.

These pKa values have been used to benchmark MCCE and other programs that calculate pKas. For example:

pKas of residues in Lysozyme

Residue pKₐ
LYS 1 10.8
GLU 7 2.85
LYS 13 10.5
HIS 15 5.36
ASP 18 2.66
TYR 20 10.3
TYR 23 9.8
LYS 33 10.4
GLU 35 6.2
ASP 48 1.6
ASP 52 3.68
ASP 66 0.9
ASP 87 2.07
LYS 96 10.8
LYS 97 10.3
ASP 101 4.08
LYS 116 10.2
ASP 119 3.2
CTR 2.75