MODEL
Molecular Dynamics
Introduction
We aim to develop a molecular dynamics model that acts as a bridge between the theoretical design and its experimental realization of our design, gaining preliminary insights into the physical properties and functionality of our designed peptides. Each peptide was simulated for 80 ns.
Aims of the molecular dynamics model:
- Determine the structural stability of the peptide
- Determine the distance between tryptophan and the Pd(II) ions
- Interpret data from trajectory file
Methods
Software Package and Force Field
The molecular Dynamics simulation was carried out in GROMACS1 (GROningen MAchine for Chemical Simulations). We have also parameterized CHARMM272 (Chemistry at HARvard Macromolecular Mechanics) force field to suit our simulation.
Parameterization of Force Field and Creating Topology for the PdCl42- Ion
Since the default force field included inside GROMACS does not include information of palladium-chlorine bond information, a topology of the PdCl42- ion cannot be generated. In order to start the simulation, parameterization of the force field is inevitable. We have created a .itp (include topology file), .rtp( residue topology file) and, .atp(atom type library) inside the root directory of the force field and added the atom name inside the residuetypes.dat at the root directory of GROMACS. Hence, topology of the PdCl42- ion can be generated. Below is a snapshot of the .rtp file we have created.
 |
[ bondtypes ] |
| Definte the numbers of bonds of the PdCl42- ion. | |
| [ atoms ] | |
| Defines the atom name and elctron charge3 | |
| [ bonds ] | |
| Defines the bond length [b0](in nm) and bond stretching harmonic force constants [kb] (in kcal Å-2)for PdCl42- | |
| [ angles ] | |
| Defines the bond angle(in °) |
Preparation of Initial Peptide Structure
The 25 peptides, including 21 designed by our team, and 4 library peptides, were predicted by PEPFOLD 3.5 de novo peptide structure prediction server4,5,6. 200 structures were generated and only the model with the highest sOPEP score was used for the simulation.
Solvation
We created our simulation box to be 1.0 nm of distance from the solute to the box borders. spc2167 was used for solvation.
Energy Minimization
Energy minimization was carried out to ensure that the system has no steric clashes or inappropriate geometry. The steepest gradient algorithm was used.
NVT ensemble
After Energy minimization, we obtained a reasonable starting structure. To begin molecular dynamics, we must equilibrate the solvent, Pd(II) complex and ions around the protein. NVT ensemble was carried out to bring the system to the right temperature and establish the proper orientation about the solute (the peptide and Pd(II) complex). After arriving at the correct temperature (based on kinetic energies), we applied pressure to the system until it reached the proper density. One modification we have made to the parameter file is that we have increased the equilibration time to 1 ns according to literature7.
NPT ensemble
Then, NPT ensemble was carried out to equilibrate the system. One modification we made to the parameter file was increasing the equilibration time to 1ns according to literature.
Produce MD
Finally, we can run the MD simualtion.
Determine the Structural stability of the peptide
The stability of the peptide is determined by the RMSD and the radius of the gyration (Rg)
RMSD measures the average distance each atom deviated from the start of the simulation. A small deviation in RMSD indicates a stable structure.
The radius of gyration is the measure of peptide’s compactness. If the peptide unfolds during the simulation, it will have an unstable value of Rg, but if the peptide is stably folded, it will maintain a stable value of Rg.
Determine the distance between tryptophan and the Pd(II)
Although the detailed mechanism of electron donation of tryptophan to palladium (II) is still unknown, especially the required distance between tryptophan and the palladium (II) required to initiate electron donation, which has never been reported in previous literature. However, prior to electron transfer, distance is still an important factor for the initiation of electron transfer. Therefore, peptides with tryptophan indole ring’s nitrogen closest to Pd during the simulation are considered as better candidates for palladium nanoparticles production.
Interpreting data from trajectory file
We have also evaluated the total energy of the system during the simulation. If the total energy of the system varies a lot, it indicates that the law of energy conservation has not been fulfilled and the peptide will not be seen as a candidate of the palladium reducing peptide.
Results
Results of the molecular dynamics will be discussed in our results pagebecause we did not have the chance to access the lab this year.
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ODE Model
To find out the impact of byproducts of tryptophan reduction on producing palladium nanoparticles, an Ordinary Differential Equation (ODE) model was used. Scheme 1 illustrates a tryptophan reduction pathway in Pd2+ compounds suggested by Si and Mandal. In an alkaline medium, an indole NH group in tryptophan is deprotonated. Tryptophan subsequently donates electrons to the Pd2+ compounds and forms tryptophyl radical1. The formed radical subsequently transfers to its oxidized form as shown in Scheme 1 and subsequently reverses back to its naive structure, converting to the kynurenine form of the peptide or dimerizes to a ditryptophan form of peptide1. In which, tryptophan will be the main product. As the deprotonation of tryptophan counter balances the hydroxide ions present in the medium, the pH of the reaction medium will decrease. In below, we will explain the rate equation of each product formed in the reduction.
An overall equation of the tryptophan reduction is shown in scheme 2. The definitions of different symbols mentioned in scheme 2 is shown in table 1. The formation of tryptophan radical is an irreversible reaction while other reactions are all reversible reactions.
| Et | Tryptophan |
| Ed | Ditryptophan |
| Ek | Kynurenine |
| EtPd(II) | Pd2+ ions binded with palladium |
| EtPD(0) | Palladium nanoparticles binded with tryptophan |
| EdPD(0) | Palladium nanoparticles binded with ditryptophan |
| EkPD(0) | Palladium nanoparticles binded with kynurenine |
| k | The rate constants of the reaction |
Table 1, definitions of symbols in the overall equation
It is important to note that experimental data is required to find out the rates constant in the equations. The reaction conditions can then be optimized and the production of palladium nanoparticles can be maximized.
The rate equations of the three main products of tryptophan reduction which is tryptophan, ditryptophan and kynurenine are given in Eq.1, Eq.2 and Eq.3 respectively.
The rate equations of Pd2+ ions and Pd2+ ions binded with tryptophan are given in Eq.4 and Eq.5 respectively.
The rate equations of palladium nanoparticles binded with tryptophan, ditryptophan and kynurenine are given in Eq.6, Eq,7 and Eq,8 respectively.
Finally, the rate equation of palladium nanoparticles is shown in Eq.9.
As tryptophan will be the main product for a single tryptophan PdRp, we can deduce k21 will be much greater than k22 and k23. It was also suggested that the reduction of Pd(II) takes four hours8. k22 and k23 are approximately zero as the main product of Pd reduction is tryptophan8. Then, we have Eq.10, which can be rewritten to Eq.11.
Therefore, we expect the order of k21 (in mol sec-1) to be 10-4.
To further find out the effectiveness of tryptophan reduction, experimental data is needed for curve fitting to estimate the amount of palladium nanoparticles formed through the reduction process (Fig. 4). We hope to find out the efficiency of the tryptophan reduction pathway and further improve it to increase the productivity of producing palladium nanoparticles.
As there is no experimental data, our rate constants will be based on the experiment results done in literature1 (Fig. 3), where curve a is the emission spectra of tryptophan, curve b is the emission spectra of ditryptophan, curve c is the emission spectra of cross-linked products formed and curve d is the emission spectra of kynurenine. The intensity of the product reflects the amount of product formed. It can be observed that the intensity of tryptophan is the highest among the four kinds of products. It implies that most tryptophan remained its naive structure after the reduction process. We will use a spectrophotometer to find out the intensity of the product formed.
Fig. 3 Emission spectra of peptide-1, desorbed from the GNPs surface by ligand exchange with MUA. a) Eem=370, Eex=280nm; b) Eem=395, Eex=320 nm; c) Eem=460, Eex=365 nm; d) Eem=481 and Eex=410 nm. The emission spectra of adsorbed peptide-1 on the GNPs surface. a’) Eex=280 nm; b’) Eex=320 nm; c’) Eex =365 nm; d’) Eex =410 nm1.
In our MATLAB graph, the rates of forming tryptophan radicals are based on Fig.3 and assuming other rates are the same. We started the simulation with 50M of Pd(II) compounds and tryptophan initially. K and D are the products formed by kynurenine and ditryptophan binds with Pd(II) ions respectively. The final products of tryptophan reduction are shown in Fig. 3b and the theoretical yield of palladium nanoparticles is about 11M.
Fig. 4a
Fig. 4b
Fig. 4c
References
[1] Lindahl, Abraham, Hess, & van der Spoel. (2020, July 9). GROMACS 2020.3 Manual (Version 2020.3). Zenodo. http://doi.org/10.5281/zenodo.3923644
[2] Vanommeslaeghe K., et. al. CHARMM general force field: A force field for drug‐like molecules compatible with the CHARMM all‐atom additive biological force fields. J. Comput. Chem., 2010. 31: 671-90.
[3] Lienke, A.; Klatt, G.; Robinson, D. J.; Koch, K. R.; Naidoo, K. J. Modeling Platinum Group Metal Complexes in Aqueous Solution. Inorganic Chemistry 2001, 40 (10), 2352-2357.
[4] Lamiable A, Thévenet P, Rey J, Vavrusa M, Derreumaux P, Tufféry P. PEP-FOLD3: faster de novo structure prediction for linear peptides in solution and in complex. Nucleic Acids Res. 2016 Jul 8;44(W1):W449-54.
[5] Shen Y, Maupetit J, Derreumaux P, Tufféry P. Improved PEP-FOLD approach for peptide and miniprotein structure prediction J. Chem. Theor. Comput. 2014; 10:4745-4758
[6] Thévenet P, Shen Y, Maupetit J, Guyon F, Derreumaux P, Tufféry P. PEP-FOLD: an updated de novo structure prediction server for both linear and disulfide bonded cyclic peptides.Nucleic Acids Res. 2012. 40, W288-293.
[7]Berendsen H.J.C., Postma J.P.M., van Gunsteren W.F., Hermans J. (1981) Interaction Models for Water in Relation to Protein Hydration. In: Pullman B. (eds) Intermolecular Forces. The Jerusalem Symposia on Quantum Chemistry and Biochemistry, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7658-1_21
[8] Mahnam, K et al. “Design of a novel metal binding peptide by molecular dynamics simulation to sequester Cu and Zn ions.” Research in pharmaceutical sciences vol. 9,1 (2014): 69-82.
[9] Tryptophan-based peptides to synthesize gold and silver nanoparticles: a mechanistic and kinetic study | Satyabrata Si, Tarun K Mandal
[10] Size-controlled synthesis of Pd nanocrystals using a specific multifunctional peptide | CY Chiu, Y Li, Y Huang