Elastic network model of allosteric regulation in protein kinase PDK1
© Williams; licensee BioMed Central Ltd. 2010
Received: 22 December 2009
Accepted: 25 May 2010
Published: 25 May 2010
Structural switches upon binding of phosphorylated moieties underpin many signalling networks. The ligand activation is a form of allosteric modulation of the protein, where the binding site is remote from the structural change in the protein. Recently this structural switch has been elegantly demonstrated with the crystallisation of the activated form of 3-phosphoinositide-dependent protein kinase-1 (PDK1). The purpose of the present work is to determine whether the allosteric coupling in PDK1 emerges at the level of a simple coarse grained model of protein dynamics.
It is shown here that the allosteric effects of the agonist binding to the small lobe upon the activation loop in the large lobe of PDK1 are explainable within a simple 'ball and spring' elastic network model (ENM) of protein dynamics. In particular, the model shows that the bound phospho peptide mimetic fluctuations have a high degree of correlation with the activation loop of PDK1.
The ENM approach to small molecule activation of proteins may offer a first pass predictive methodology where affinity is encoded in residues remote from the active site, and aid in the design of specific protein agonists that enhance the allosteric coupling and antagonist that repress it.
Phosphorylation dependent protein interactions are a common feature of biological processes . A relevant kinase attaches a phosphate group to a specific tyrosine, threonine or serine residue on the protein surface resulting in a considerable increase in the binding affinity for a target protein. The binding event triggers a conformational change whereby the target protein switches from inactive to active state or vice versa . It is not possible to generalise the nature of the conformational change and it is only with crystallisation that light has been thrown on the mechanism. PDK1 in common with other AGC kinases have a catalytic domain consisting of an N-terminal small lobe harbouring a PDK1-interacting fragment (PIF) binding pocket, a large C-terminal lobe with an activation loop and an ATP binding site in the cleft between the two lobes . The PDK1 kinase is activated by a phosphorylated peptide binding to the PIF pocket . This binding triggers not only local conformational changes in the pocket and the ATP binding site, but also in the remote activation loop. Structural insight into the mechanism of activation of PDK1 has been gained by the crystallisation in the first instance of the inactive version of the protein  where the activation loop appears unstructured. And the recent development of the first small molecule protein kinase agonist targeting the PIF binding pocket in PDK1 has enabled the crystallisation of the active form of PDK1 and here the activation loop is ordered . Remarkably, the binding of the small ligand induces a significant and critical structural change at a remote site on the protein. The present study addresses the question as to whether these changes could have been predicted (and/or can be explained) by molecular modelling.
The elastic network model (ENM) or Gaussian network model is a simple 'ball and spring' model introduced to describe full atomic fluctuations within the protein  and then to model the deformations of the Cα backbone [8, 9]. The initial successful application of the model showed remarkable agreement between the scalar expectation value of residue fluctuations with crystallographic B-factors or temperature factors [8, 10]. Over the past few years an ENM of protein dynamics has emerged as a viable theoretical framework for the study of allosteric regulation in protein signalling. An ENM model of the chaperonin GroEL has revealed a dominant eigenvector describing the allosteric switch in the protein and first order perturbation theory predicts the critical residues in this transition , Recently, Balabin et al  have looked at the coupling of local fluctuations within GPCR. They show that the distinct features of rhodopsin and β 2-adrenoreceptor activation are encoded in the correlation between these fluctuations and that there are clear allosteric couplings between ligand binding sites outside the membrane and G-protein binding sites within the cell. Protein functional sites that result in structural changes in the protein have also been successfully described using a dynamics perturbation analysis (DPA) [13–16]. Here an interacting ENM comprising the protein and a series of probes covering the protein surface is set up and those probes that couple to the biggest changes in protein conformational distribution are predicted to lie at interaction sites. The present study applies a version ENM to the protein kinase PDK1 and it is demonstrated that the allosteric coupling between the PIF binding site and the activation loop is encoded in the fluctuation correlation coefficient of the vibrational excitations of the protein.
Elastic Network Model
where the 'hat' indicates a unit vector. The eigenvalues of the Hessian matrix correspond to the protein vibrational normal modes. There are six zero modes corresponding to the rotational and translational symmetries, low frequency modes that couple remote parts of the protein and high frequency components that are residue autonomous . The diagonalisation in this study was performed by first reducing the matrix to a tridiagonal form with the Housholder algorithm and then employing the QL algorithm, see .
where λ n are the eigenvalues and the eigenvectors of the Hessian matrix Eq. 2, , see . Only fluctuations that break the rotational/translational symmetry are considered and therefore the zero modes are dropped. Note that in contrast to isotropic ENM Kirchhoff matrix treatment the Hessian matrix is not diagonal in the spatial degrees of freedom and the spring constant isn't an overall factor in the correlation. Hence, the usual factor is missing from Eq. 5.
The average B-factor for each amino acid is obtained by scanning the PDBselect25 database of non-redundant pdb files . The values for the residue specific B-factors are given in Additional file 1. An alternative definition of the residue specific interaction energy can be defined based on residue contact frequencies in a database of protein structures. Here, the energy is given by , where n ab (R c ) is the number of non-chain proximal residue pairs, type a and b, within an interaction radius and N a is the number of residues of a given type in the proteins, this is essentially the MJ matrix [21, 22]. The two energy measures correlate very well, with Rc = 15Å the Pearson correlation is r = 0.89.
Results and Discussion
In the present case the molecule PS48 consists of 20 heavy atoms and has three distinct moieties comprising two phenyl rings and a carboxylate. It is reasonable to replace this molecule with three centroids as illustrated in figure 1 and this is done by K-means clustering . The spring constant, Eq. 1, for these centroids coupling to the protein backbone Cα's and to themselves is taken to be the average of the inter-amino acid spring constant, , where the tick refers to small molecule centroid.
The minimalist 'ball and spring' elastic network model has been applied to the functionally critical allosteric regulation of a protein by ligand binding. The fluctuations induced by the PS48 ligand binding to the PIF pocket in the small lobe of PDK1 are shown to correlate with fluctuations in the remote activation loop in the large lobe of PDK1. The coupling is dominated by the four low energy modes 7, 8, 9 and 11 and is driven by the central phenyl ring and carboxylate moieties of the ligand. The allosteric profile is sensitive to the ligand-protein spring coupling constant and the dominant large lobe peak shifts away from the activation loop to the buried GLY225 when the coupling is weakened. This allosteric coupling is lost when the ligand is removed and substituted by the ligand interacting residues of the protein. However, in a modelled ligand binding structure of the inactive PDK1 protein the PIF-activation loop coupling emerges as the dominant peak in the large lobe allosteric profile. This suggests that the ENM approach can be used to predict the allosteric consequences of modelled agonists.
There are additional sites outside the PIF pocket that undergo structural changes upon ligand binding that are critical for PDK1 activity . These sites, near the ATP binding pocket, are PHE93 in the GLY rich loop GLY89-THR95 and LYS111. The allosteric effects here are in the side chain orientation of PHE93 and LYS111 that leave the local backbone largely unaltered. Within the ENM there does not appear to be any allosteric coupling to the GLY rich loop or to LYS111 and this may be because this model is purely a Cα reduction of PDK1 and consequently side chain movements are invisible. However, the most stricking difference between agonist bound and unbound structures is in the activation loop, with the unbound PDK1 having unstructured residues GLU233-GLN236 within the activation loop and it is here that the ENM allosteric coupling occurs.
In many instances specificity of protein interaction is encoded by the distinct coupling of conserved active sites, e.g. enzyme catalytic, sites to non-local non-conserved parts of the protein. Also, mutations affecting affinity of catalytic sites or protein interaction sites in general can be sensitive to residue mutations far away from the binding interface. It is clear then that the ENM approach may offer a first pass predictive methodology here. Specifically, ENM can inform mutagenesis experiments, but also aid in the design of specific protein agonists that enhance the allosteric coupling and antagonist that repress it.
Thanks to Patrick Doherty for reading the manuscript and offering useful suggestions. This research was supported by the Wolfson CARD.
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