Molecular Dynamic Simulations

Determining the behaviour of a protein or peptide in response to environmental stresses is crucial in establishing the efficacy of the peptide in a system. Thus, molecular dynamics simulation can help us subject the peptide to different conditions that mimic the natural environment that it may exist in, in silico.

Multiple tools can be used to perform MDS, such as GROMACS [1][2][3], CHARMM [4], AMBER [5] and Desmond [6]. However, MDS requires high computational power. Given our limited resources, we partnered with IISER Pune II, to run molecular dynamics simulations on their supercomputer PARAM. The results were then analysed by us to check for the stability of the peptide in the given environment.

We discovered that a pH of 7.5 and a temperature of 298K are the typical characteristics of an aquaculture system for consumable fish through our human practices and research. These parameters were applied to a cubic system and an OPLS-AA/M force field was applied across the system to analyse the dynamic changes in the conformation of the peptide.

RMSD

RMSD or root mean squared distance is the numerical representation of the difference between the peptide's initial structure and the structure at a given moment in time. Generally, an RMSD variation of less than 2 Angstorms is supposed to be very close and stable. \[ \text{RMSD} = \sqrt{\frac{\sum [m_i(x_i-y_i)^2]}{M}} \]

The RMSD value was seen to increase for the first 50ns, which is a given due to the peptide stabilizing to the given conditions in the system. It was observed that the RMSD values decreased briefly and then stabilized with a fluctuation of approximately 1 Angstorms, which falls comfortably below the accepted threshold of 2 Angstorms, indicating that our peptide is very stable in the given environment. It also shows that no conformational changes occur within the first 100 ns of the simulation, which could otherwise hamper its target interaction.

RMSF

RMSF or root mean squared fluctuations is a calculation of individual residue flexibility, or how much a particular residue moves (fluctuates) during a simulation. \[ \text{RMSF} = {\sqrt{\frac{\sum [m_i(x_i(t_j)-x_{ref})^2]}{T}}} \]

The residues at the very beginning and end of our peptide show the highest fluctuations and this indicates that they are less stable than the residues with fewer fluctuations. For example, the amino acid residues between 14 to 24 are much more stable than the residues from 36 to 40, which correspond to loops in the structure of the peptide.

Radius of Gyration

The radius of gyration for a given molecule is a measure of the compactness of the molecule or how far apart the mass of the object is distributed around its centre of mass. \[ R_g = \sqrt{\frac{\sum [m_i(x_i-x_c)^2]}{M}} \]

From the resulting plot of the radius of gyration versus time, we can see that the net radius of gyration remains fairly constant and is within the range of 1 Angstorm. This indicates that the peptide does not fold or unfold over time, thereby contributing to no change in the compactness of the peptide. We can also conclude that the peptide does not undergo any major conformational changes which can result in changes in the folded volume of the protein, and thereby talks about the stability of the peptide.

MD Simulations on the MAM7-peptide dock would give a lot more information about the interactions present, the stability of the complex, interaction energies, compactness and the effect of conformational changes on the interaction. Parameters such as RMSF would give crucial information regarding the interacting residues present in the complex. Induced conformational changes upon docking could be analyzed using graphs for RMSD as well as observing the trajectory file. We planned on performing these simulations to analyze the MAM7-peptide interaction but were limited by time and resources.

IC₅₀

The optimum dosage values of the peptide is essential for effective prevention of the disease Since both the peptide and fibronectin are in a position to interact with MAM7, we concluded that our peptide would act as a competitive inhibitor against fibronectin. Therefore, our mathematical model describes the relationship between the concentration of peptide required for a given concentration of fibronectin present in the system.

• IC₅₀ is the concentration of the drug or displacing ligand in a competitive inhibition mechanism that reduces or inhibits the receptor-ligand interaction by 50%. It is a measure of the potency of a drug.
• IC₅₀ values are typically calculated via an IC₅₀ assay using a serial dilution of the drug. Based on the definition of IC₅₀, we arrived at an equation for the IC₅₀ concentration for our antimicrobial peptide
• Our peptide competitively binds to MAM7 and inhibits its interaction with Fibronectin, therefore fitting the reaction mechanism. We derived an equation for the IC₅₀ value of our peptide with the following steps:

  1. The reaction mechanism can be considered to be a parallel reaction scheme where MAM7 gets partitioned between Fibronectin and our peptide.

     Equations for the Association and Dissociation constant can be written as follows:

     

  2. Given the total concentration of MAM7 in a system, the MAM7 would be partitioned between the MAM7-Fibronectin complex, MAM7-peptide complex and free MAM7.

  3. We defined \(\rho\) as the ratio of the concentration of the MAM7-Fibronectin complex to the total MAM7 concentration.

  4. We defined \(\rho_{in}\) as the interaction ratio in the absence of our peptide.

  5. The below relation was arrived at from the definition of IC₅₀.

  6. On simplification, the final equation for IC₅₀ value of our peptide was found.

• The dissociation constant values substituted here were predicted using PRODIGY, thereby, giving us a prediction of the IC₅₀ concentration. The actual values of the dissociation constants would be found using Isothermal Calorimetric analysis.

  The PRODIGY predicted values are:

  
  

As an example,

• MW of peptide = 4 kDa = 4 kg/mol
• Say [F] = 1 nM
• IC₅₀ = 10.67 microM = 42 mg/L

References

1. S. Pronk et al., “GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit,” Bioinformatics, vol. 29, no. 7, pp. 845–854, Apr. 2013, doi: 10.1093/BIOINFORMATICS/BTT055.
2. M. J. Abraham et al., “GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers,” SoftwareX, vol. 1–2, pp. 19–25, Sep. 2015, doi: 10.1016/J.SOFTX.2015.06.001.
3. S. Páll, M. J. Abraham, C. Kutzner, B. Hess, and E. Lindahl, “Tackling exascale software challenges in molecular dynamics simulations with GROMACS,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 8759, pp. 3–27, 2015, doi: 10.1007/978-3-319-15976-8_1/FIGURES/7.
4. B. R. Brooks et al., “CHARMM: The Biomolecular Simulation Program,” J. Comput. Chem., vol. 30, no. 10, p. 1545, Jul. 2009, doi: 10.1002/JCC.21287.
5. D.A. Case, H.M. Aktulga, K. Belfon, I.Y. Ben-Shalom, J.T. Berryman, S.R. Brozell, D.S. Cerutti, T.E. Cheatham, III, G.A. Cisneros, V.W.D. Cruzeiro, T.A. Darden, R.E. Duke, G. Giambasu, M.K. Gilson, H. Gohlke, A.W. Goetz, R. Harris, S. Izadi, S.A. Izmailov, K. Kasavajhala, M.C. Kaymak, E. King, A. Kovalenko, T. Kurtzman, T.S. Lee, S. LeGrand, P. Li, C. Lin, J. Liu, T. Luchko, R. Luo, M. Machado, V. Man, M. Manathunga, K.M. Merz, Y. Miao, O. Mikhailovskii, G. Monard, H. Nguyen, K.A. O'Hearn, A. Onufriev, F. Pan, S. Pantano, R. Qi, A. Rahnamoun, D.R. Roe, A. Roitberg, C. Sagui, S. Schott-Verdugo, A. Shajan, J. Shen, C.L. Simmerling, N.R. Skrynnikov, J. Smith, J. Swails, R.C. Walker, J. Wang, J. Wang, H. Wei, R.M. Wolf, X. Wu, Y. Xiong, Y. Xue, D.M. York, S. Zhao, and P.A. Kollman (2022), Amber 2022, University of California, San Francisco.
6. Kevin J. Bowers, Edmond Chow, Huafeng Xu, Ron O. Dror, Michael P. Eastwood, Brent A. Gregersen, John L. Klepeis, Istvan Kolossvary, Mark A. Moraes, Federico D. Sacerdoti, John K. Salmon, Yibing Shan, and David E. Shaw, "Scalable Algorithms for Molecular Dynamics Simulations on Commodity Clusters," Proceedings of the ACM/IEEE Conference on Supercomputing (SC06), Tampa, Florida, 2006, November 11-17

   Schrödinger Release 2022-3: Desmond Molecular Dynamics System, D. E. Shaw Research, New York, NY, 2021. Maestro-Desmond Interoperability Tools, Schrödinger, New York, NY, 2021.