Biomod/2011/PSU/BlueGenes/results

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Results GNM with Protein GNM has already been thoroughly and successfully applied to proteins. There is even a database known as iGNM that has calculated protein fluctuations for over 20,000 structures from the protein data bank or PDB. In most cases, carbon atoms are chosen as the nodes to represent the network. A common cutoff value is 7 angstroms. To show you that GNM works, in Figure 1, we calculated the fluctuation for HIV-1 protease and compared it to the temperature factor, which are experimental values. There are 200 nodes in this structure. Figure 1: Fluctuation data for HIV-1 protease predicted by GNM and compared with temperature factor (TF) Qualitatively, it is very easy to see that the GNM results (shown in red) match very well to the TF results (shown in black). Each dot represents a node and lines are simply to help guide your eyes. GNM has been successful in calculating protein fluctuations because of well matching results such as the one in Figure 1. GNM with DNA There haven’t been many applications of GNM on DNA structures. But since GNM filters out the chemistry of the atoms, there is no reason why it shouldn’t work. In Figure 2, we tried it with DNA of PDB ID 307D. We used the phosphate atoms as the nodes and a cutoff distance of 13 angstroms. There are 60 nodes. Results are pretty satisfactory but are slightly less accurate than the comparison with protein. This is because proteins have longer chains than DNA and more nodes, thus it rules out randomness. DNA is more flexible and thus harder to calculate the flexibility. We chose 307D strictly because it had a long chain. Figure 2: Fluctuations of nodes for 307D (PDB ID) predicted by GNM and compared with TF Again, DNA fluctuation results from GNM (in red) are compared to TF results (in black). Points represent nodes and lines are to guide your eyes. GNM with Synthetic DNA Now that we have shown that GNM is applicable in both proteins and DNA, we want to use it to calculate fluctuations of synthetic DNA. Below you can see 2 structures that we've made using NanoEngineer-1, a cube and a prism. High fluctuations are show in warm colors (red, orange, yellow/yellow-green) and low fluctuations are shown in cool colors (green, blue, dark blue). Both structures show similar satisfactory results. It makes sense to think that the vertices of the structure are the least flexible because they are the most confined. The legs of the prism are more flexible because they are not as rigidly confined. Figure 3: Fluctuation data of a cube (top) and prism (bottom) structure created in NanoEngineer-1 and calculated using GNM. To verify that the GNM method gives accurate results to synthetic DNA structures, we compared our data with another method, Finite Element Method (FEM). Figure 4, left, you can see a half-gear structure that we created in NanoEngineer-1 and calculated using GNM. On the left is a similar structure from Dietz et al.[1] with calculation done by CanDo [2]. There is clearly similarities between these two structures. Both show highly fluctuating ends and teeth (in red/yellow/yellow green) and less flexible central body (in blue/dark blue). Note that there are a few differences between the results from GNM and FEM. We hand built the structure in NanoEngineer-1 so thus there is always some error from the FEM version. Additionally, NanoEngineer-1 could not export B-factors in the PDB files. Without these temperature factors, we could not use common biochemistry graphics software to generate better color-based flexibility for our figures. Figure 4: Verification of the results by comparison to Finite Element Method (FEM). Advantages There are multiple advantages of our GNM method. They include: Fast calculation time: results take from seconds to minutes depending on size. Large deformations: there is a solution to every problem. Because GNM only considers the bonds and distances between nodes, it can calculate fluctuations for even large deformations in the structure. Physical relevance: the diagonal of the Kirchhoff matrix corresponds to fluctuation of the structure. Each value corresponds to a node which in turn represents an atom within the structure. Feedback ability: explained below. Feedback Structure feedback is one of the most advantageous parts of our GNM method.