Overview

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Coarse Grained Models (ANM & GNM)

With the GNM and ANM we can take a closer look inside the mechanics of the ANS. The result of the GNM computation shows a great peak at the C Terminus. It lead to the assumption that the C terminal region of the ANS is highly flexible. Unfortunately, this region belongs to the active side of the protein.  One can imagine that this region may cover the active site and decrease the probability of substrate binding during the process of catalysis.  

Following figure shows the flexibility of wild-type ANS in a three dimensional model as displayed above. 

LRT

If we simulate the substrate binding in the pocket of the ANS by applying a force vector to the active site and binding region we can observe a strong deformation of the enzyme. This result reveals that the C Terminal region of the ANS is still highly flexible during the process of induced fit. 

Design Prediction

We have to cut of the C-Terminal region to increase the substrate binding and destroy the fluctuating C-Terminal region near the active site. A model corresponding to proteins flexibility is presented below, which ensures our goal.

Molecular Dynamics

RMSD 

As can be seen in Figures RMSD (ANS short ; ANS_long), the wild type has minimal changes in the four calculated distances, which leads to the consumption that the central core stays quite stable during the simulation - equation is shown below.

\[ RMSD(v,w) = \sqrt{\frac{1}{n} \sum_{i=1}^{n} ||v_i - w_i ||^2} \]

\[  = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (v_{ix} - w_{ix} )^2+(v_{iy} - w_{iy} )^2+(v_{iz} - w_{iz} )^2} \]

If we take a closer look at the RMSD distributions (RMSD Histograms) we can observe that the engineered ANS is more stable than the wilt type. Additionally, the wild typt reaches a higher plateau and overall RMSD.

Wild type ANS's results are displayed below.

RMSD of engineered ANS is shown below.

Fazit: Overall structure of the Engineered ANS is more stable over time. 

The RMSF (ref. RMSF Plots) computations reproduced the results derived from the coarse grained simulations (GNM, ANM and LRT).

\[ RMSF= \sqrt{ \frac{1}{T} \sum_{t_j = 1}^T (x_i (t_j) - \tilde{x} )^2  } \] 

This underlines the complexity and importance of coarse grained simulations for rational protein design. With the RMSF we can clearly bring to proof that the C Terminal region is highly flexible and thus a obstacle to the active site of the ANS. 

Plots of RMSF are shown below. On the left side is the native ANS, whereas on the right side engineered ANS's results can be viewed.

Fazit: It was necessary to unleash the active site by cutting of the C- Terminal region. Only with this modification we can increase the turnover of the ANS.