## 3 Results and Discussion
### Molecular Dynamics and Thermodynamics Analysis
A different trend can be gleaned from the TNFR-1-A system, as shown in Figure 9. The RMSD ranges from 0.8 to 1.4 nm in the majority of the run. Although the magnitude of the RMSD is not as great as that for the DR4-Q system, the rises and dips throughout this system imply some conformational flexibility, as was observed for DR5-Q. This is supported by the RMSF where there are sharp rises, indicating that some atoms experience a great degree of change from their initial positions, and of the Rg, where the profile sees  
Figure 7: 100 ns molecular dynamics results for the death receptor 4 and Q system. more ups and downs than the previous two systems, implying its greater susceptibility to conformational changes. Still, the magnitude of the conformational changes is not enough to destroy the complex. The SASA's profile is interesting, as it plateaus to a value of around 350 cm\({}^{2}\). This shows that the system is much less susceptible to intrusion by solvents. Hydrogen bond, hydrogen bond distribution, and minimum distance are still the same as in the previous systems, suggesting good overall stability for the associated complex. Another unique scenario can be seen for the Fas-I system, as given in Figure 10. The RMSD profile relatively stays flat, disregarding the transient blips at around 80 and 90 ns. Magnitude-wise, it is similar to DR-5-Q, given that towards the end of the run, the RMSD settles at above 2.5 nm. This behavior shows that the system is more consistent with the degree of deviations from the initial state, unlike the other previous systems where the presence of rises and falls throughout the system implies flexibility fluctuations. The flexibility of the system is supported by the rises and falls in the RMSF plot, where there are some groups that are more susceptible to changes in conformation than others. The Rg and SASA plots are predominantly plateau-like, suggesting some form of complex stability in that it cannot be easily disrupted by intramolecular (folding on itself) and intermolecular (solvent) agents which call for the dissociation of the complex. Figure 8: 100 ns molecular dynamics results for the death receptor 5 and Q system. The other three parameters are still the same as for the previous systems, which still solidify the notion of stability of the complex. The four different profiles show that the DR-4 and DR-5 systems behave differently upon association with peptide Q, even though these receptors are from the same family and are structurally similar. Flexibility is the greatest in the DR-4 system and the least in DR-5. No other peptides besides Q are shared with the other receptors, and thus a definitive comparison cannot be drawn. From the plots, it can be gleaned that the complexes show varying degrees of flexibility upon association, with some being more rigid than others. These can then mirror the behavior of the systems in the body. Although these are the case, two parameters are consistent with the four systems--the hydrogen bond distribution and the minimum distance between receptor and peptide. The lack of significant deviations in these plots allows us to conclude that the systems will not spontaneously dissociate appreciably, meaning that the docked conformations are favored. The ultimate measure of the receptor-peptide complexes' stability is in the end-state binding energy, given in \(\Delta G\). MMPBSA calculations were initiated, as this model accounts for electrostatics. This model gave lower \(\Delta G\) values than MMGBSA during the initial end-state thermodynamics calculations. For the four final systems, a chart of the \(\Delta H\), \(T\Delta S\), and \(\Delta G\) is given in Figure 11. Here, the most negative \(\Delta G\) value is associated with the DR-5 system, while the highest is that of the Fas. This means that the association of DR-5 and Q is the most energetically favorable out of the four systems, while Fas, being the only system with a positive \(\Delta G\) value, is the least stable.