Overview

In order to optimize the metabolic channeling of ANS, we chose a rational protein engineering approach. 
The first step of our multi scale and rational engineering project was the creation of
a sophisticated 3D model with YASARA structure. This model was then used for a structural refinement with the SCWRL alghorithm and was energy minimized with YASARA nova force field.
Afterwards, we started a true mechanical engineering approach to determine the movements within the protein. Therefore, a Gaussian Network Model (GNM) (Fig. 15) and an Anisotropic Network Model (Fig. 16) were implemented.
Those are simple models which simulate the mechanical behavior of the protein. Moreover, Linear Response Theory (LRT) (Fig. 18) was used to simulate the substrate binding inside the pocket and thus trigger an induced fit mechanism. 
Afterwards we collect our data, defined rational mutations and finally constructed eANS. With this eANS version another MD simulation was started and the sequence of the protein was given to the wetlab for in vitro construction and in vivo characterization.

Coarse Grained Models (ANM & GNM)

With a computed 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, represented by the slow modes, of wild-type ANS in a three dimensional model as displayed above. The results are extracted out of an ANM. The spatial directions of the simulated movement. This directions are represented as arrows with color coated strength (from red ~ strong to blue ~ weak). As one can see only the C- terminus exhibits a large correlated movement

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 process is called induced fit. This result reveals that the C Terminal region of the ANS is still highly flexible during the process of induced fit.  This is a problem because the substrate release as well as the binding is perturbed and thus the reaction rate is limited.

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.

Conclusion: 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.

Conclusion: 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.