# MC DNA Help - Analysis PCAZip

## Principal Components

### Method

Following **Essential Dynamics algorithm (ED)**, the orthogonal movements describing the variance of a system trajectory is obtained by diagonalization of the covariance matrix.

The result of the analysis is the generation of a set of **eigenvectors** (the modes or the principal components), which describe the nature of the deformation movements of the protein and a set of **eigenvalues**, which indicate the stiffness associated to every mode.

The **eigenvectors** appear ranked after a **principal component analysis**, the first one is that explaining the largest part of the variance (as indicated by the associated **eigenvalue**). Since the **eigenvectors** represent a full-basis set the original Cartesian trajectory can be always projected into the **eigenvectors space**, without lost of information.

Each of the **eigenvector** obtained from **Principal Component Analysis** of a trajectory is called a **Principal Component**. The associated eigenvalue indicates the amount of variance explained by the component. The Collectivity Index gives a measure of how many atoms of the protein are affected by a Principal Component.

**MC DNA** uses PCAsuite package to compute **Principal Components Flexibility Analysis**. **PCA** is computed using all the atoms of the structure and the compression is reduced to a **90%** of the **explained variance**. Only the first 10 **principal components** are shown in the graphical interface, as the first modes are usually the ones explaining the largest part of the variance.

### Results

The **Principal Component Analysis** graphical interface offers the possibility of studying the real movements of the structure through the **projections** of the trajectory onto the different **essential modes**. An interactive **NGL Viewer** shows these movements, allowing user to **translate**, **rotate** and in general manipulate the visualization. The **first 10 animation modes** are offered for **visualization** and **download**. Associated values as **eigenvalues**, **collectivity indexes** and **eigenvector stiffness constants** are also shown.

For each of the **first 10 eigenvectors**, a plot containing the **displacement** (in Angstroms) of the **projections** of all the trajectory snapshots into the associated **eigenvector** from the first snapshot is also computed and shown. Plots generated contain the corresponding **histogram** attached, and an associated table with calculated **mean** and **standard deviation** values. Raw data and plot are also easily downloadable.