Apo adenylate kinase encodes its holo form: a principal component and varimax analysis

Adenylate kinase undergoes large-scale motions of its LID and AMP-binding (AMPbd) domains when its apo, open form closes over its substrates, AMP and Mg2+-ATP. It may be an example of an enzyme that provides an ensemble of conformations in its apo state from which its substrates can select and bind to produce catalytically competent conformations. In this work, the fluctuations of the enzyme apo Escherichia coli adenylate kinase (AKE) are obtained with molecular dynamics. The resulting trajectory is analyzed with principal component analysis (PCA) that decomposes the atom motions into orthogonal modes ordered by their decreasing contributions to the total protein fluctuation. In apo AKE, a small set of the PCA modes describes the bulk of the fluctuations. Identification of the atom motions that are important contributors to these modes is improved with the use of a varimax rotation method that rotates the PCA modes to a new mode set that concentrates the atom contributions to a smaller set of atoms in these new modes. In this way, the nature of the important motions of the LID and AMPbd domains are clarified. The dominant PCA modes are used to investigate if apo AKE can fluctuate to conformations that are holo-like, even though the apo trajectory is mainly confined to a region around the initial apo structure. This is accomplished by expressing the difference between the protein coordinates, obtained from the holo and apo crystal structures, using as a basis the PCA modes from the apo AKE trajectory. The coherent motion described by a small set of the apo PCA modes is shown to be able to produce protein conformations that are quite similar to the holo conformation of the protein. In this sense, apo AKE does encode in its fluctuations information about holo-like conformations.