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Gene & Protein in Disease                                             In silico application of the CoM method



            distance. The conclusion was derived by measuring the   the convergent state. In such cases, prior-convergent
            average of the CoM distance between the ligands and   oscillations may easily suppress the impact of relative flat
            SARS-CoV-2 main protease, during the course of 100-  and convergent CoM distance amplitudes. Having them
            ns MD simulation. The average of the CoM distance for   averaged during the course of the whole MD simulation,
            erylosides B was less than the average CoM distance for   a wrong conclusion about the real direction of the affinity
            lopinavir, which was taken as a clue that erylosides B binds   change may be derived.
            the SARS-CoV-2 main protease more effectively than   To explain this situation better, let’s take two random
            lopinavir, demonstrating higher inhibitory potential.  systems  A  and  B, with  a total of  eight  CoM distance
              Kumar et al.  analyzed pi-stacking interaction between   snapshots [nm], such as the first five are prior-convergent
                        3
            Omicron receptor binding domain (RBD) Tyr501 and   samples and the last three convergent: A={4; 4.5; 3.9; 3.8; 3.5;
            human angiotensin-converting enzyme 2 (hACE2)      2.8; 2.75; 2.75} and B={3; 4; 4.5; 3; 3.2; 2.83; 2.82; 2.81}. By
            Tyr41, as N501Y is one of the key mutations responsible   considering the integral systems’ dynamics, upon the eight
            for increased infectivity. 1,7,8  The CoM distance between   CoM distance snapshots, the average CoM distance in the
            the aromatic rings has been measured, which in the   system A is higher than the one in the system B (3.5 nm vs.
            case of pi-stacking interaction should not exceed 5 Å.    3.27 nm), which is interpreted in terms of reduced binding
                                                          9
            Such interaction is going to increase hACE2–surface   affinity between the units in system A in comparison to the
            glycoprotein (S-protein) binding affinity that will ultimately   binding affinity between the units in system B. However,
            increase infectivity. The average CoM distance between   the opposite of the previous conclusion is actually true, as
            aromatic rings of <5 Å in most of the conformations   the average CoM distance throughout the convergent state
            confirmed pi-stacking interaction between hACE2 Tyr41   upon the last three snapshots in the system A is less than
            and Omicron RBD Tyr501, which has been regarded as   the one in system B (2.77 nm versus 2.82 nm).
            one of the reasons that explains the higher viral load and   An intuitive solution to this problem is to compute the
            infectivity of the N501Y-bearing SARS-CoV-2 variant.
                                                               average  of  the  intermolecular  CoM  distance  during  the
              Apart from the CoM distance method, which is     convergent phase only and neglect the non-convergent
            the main point of discussion in this study, researchers   system’s behavior. It is of crucial importance in the cases
            have also exploited additional in silico methods, such as   where the individual impact of a particular mutation or
            residue fluctuation, radius of gyration, solvent accessible   a combination of a few mutations need to estimated, a
            surface area and free energy landscapes, in order to   situation in which the wild-type and mutant complex share
            analyze the fundamental properties of SARS-CoV-2   very similar CoM distance plots.
            proteins’ interactions 10,11  or evaluate the structural impact
            of selected mutations. 12-14  Docking studies proved to be   2. Method overview
            especially useful in selecting highly effective SARS-CoV-2   Let W be the wild-type heterodimer and M the mutant of
            inhibitors. Stability of the formed complexes has been used   W. W can be retrieved from the Protein Data Bank in.pdb
            as a prime criterion to evaluate the inhibitory potential of   format. Molecular visualization software, such as PyMol,
            each candidate. Ahamad et al.  found that anidulafungin   can be used to mutate the wild-type heterodimer W to M.
                                    10
            has the same neutralizing capacity as the well-studied   Initially, both systems, W and M, need to be well-prepared
            lopinavir. In another study, Ahamad  et al.  evaluated   and energetically optimized within self and toward the
                                                11
            the efficiency of several N-protein targeted antagonists   solvent that will guarantee that the systems are stable enough
            and suggested 4E1RCat and TMCB as candidate drugs.   to undergo the process of MD simulation. The details of
            MD simulations have also been used to study the impact   systems’ preparation steps are described in the section 3. The
            of selected mutations.  In silico findings that RBD and   method is formally described in the next section (Figure 1).
            Heptad Repeat 1 mutations can impose major structural
            destabilization, affecting pre-binding protein structure,   2.1. Formal description of the method
            which may negatively impact current therapeutic efforts,
            have been presented in several papers. 12-14       The CoM of a monomer of  n atoms at positions  r  and
                                                                                                         j
                                                               masses: m ,m ,…,m  can be computed as:
              In some instances, using the average of the              1  2   n
            intermolecular CoM distance during the whole MD           n i1 mr
                                                                          ii
            simulation,  may give rise wrong conclusions related to   com    n  m                        (I)
                     2,3
            the binding affinity change. The reason for this is the fact   i1  i
            that molecules usually exhibit sudden and sharp local and   where  com is an oscillating point in the time (t):
            global movements, one relative to another, before entering   com(t)=(x(t),y(t),z(t),z(t)).


            Volume 3 Issue 1 (2024)                         2                        https://doi.org/10.36922/gpd.2657
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