PDZ domains are typical examples of binding motifs mediating the formation of protein-protein assemblies in many different cells. A quantitative characterization of the mechanisms intertwining structure, chemistry and dynamics with the PDZ function represent a challenge in molecular biology. Here we investigated the influence of native state topology on the thermodynamics and the dissociation kinetics for a complex PDZ-peptide via Molecular Dynamics simulations based on a coarse-grained description of PDZ domains. Our native-centric approach neglects chemical details but incorporates the basic structural information to reproduce the protein functional dynamics as it couples to the binding. We found that at physiological temperatures the unbinding of a peptide from the PDZ domain becomes increasingly diffusive rather than thermally activated, as a consequence of the significant reduction of the free energy barrier with temperature. In turn, this results in a significant slowing down of the process of two orders of magnitude with respect to the conventional Arrhenius extrapolation from low temperature calculations. Finally, a detailed analysis of a typical unbinding event based on the rupture times of single peptide-PDZ contacts allows to shed further light on the dissociation mechanism and to elaborate a coherent picture of the relation between function and dynamics in PDZ domains.
The role of PDZ domains in the organization of protein complexes at the plasma membrane has been increasingly recognized in the last decade 1 . Proteins containing several PDZ domains (up to 13 in the MUPP1 protein 2 ) act as scaffolds that cluster together different transmembrane, membrane associated and periplasmic proteins involved, among other functions, in signaling pathways 3,4 and ion permeability 5 . The participation of PDZ domains in the organization of supramolecular complexes in skeletal muscle cells has also been documented 6,7 .
PDZ domains associate with other proteins by binding their carboxyl-terminal aminoacids 8,9 , as highlighted by the structure of several PDZ domains, such as the third PDZ domain of PSD95 (Postsynaptic density-95/disks large/zonula occludens-1) 10 and the PDZ domain of ZASP (Z-band alternatively spliced PDZ-motif) 11 , although internal structures, such as β-hairpins that mimic C-terminal geometries can also be recognized, as in the complex between nNOS (neuronal nitric oxide synthase) and syntrophin 12 .
Recently, due to their central role as key mediators of protein-protein interactions in mammalian cells, PDZ domains have been the object of intense study, with the aim of designing small molecules capable of acting as modulators or inhibitors of the PDZ binding activity in a controlled fashion. Efforts have focused in the design of both non-peptide 13,14,15 and peptide 16,17,18 ligands, with the ambition to develop molecular probes to study the biophysical and biochemical properties of PDZ domains and to devise new small molecule-based therapeutic strategies. Hence, the great importance of understanding the principles of peptide-PDZ interactions.
The geometry and chemistry of binding to PDZ domains involve the fit of the last 4 to 5 carboxyl-terminal aminoacids into a groove between a α-helix and a β-strand on the PDZ surface (Fig. 1), with the last Cterminal residue almost invariably hydrophobic. The specificity of each domain is conferred by a few (2 to 3) PDZ surface aminoacids that make contacts with the residues in positions -1 to -4 relative to the C-terminal in the target protein 8 . The surprising simplicity of this binding scheme possibly explains why PDZ domains are one of the most widespread binding modules yet identified, since just a few incremental, concerted mutations involving surface aminoacids (hence unlikely to change the overall protein stability) can tune the affinity of PDZ domains for different targets. On the other hand, a binding architecture that relies on just a few optimized contacts comes at the price of losing strict specificity. Indeed, recent experiments on 26 mouse PDZ domains and domain clusters have confirmed that each PDZ domain can bind to several peptides 19 , and that each peptide, in turn, can bind to several PDZ domains.
In a recent work 20 , we have explored via normal mode analysis (NMA) the mechanical aspects of binding of a peptide to a PDZ domain. In line with the results of NMA analysis of several proteins 21,22,23 , the picture that emerged was that a limited number of low-frequency modes suffice to reconstruct the observed conformational change from the apo to the complexed structure of the PDZ. The long-range spatial correlations that characterize these modes correspond to a concerted breathing motion of the binding cleft, thus suggesting that functional dynamics is deeply rooted in the native architecture itself. However, despite their success in providing a qualitative picture of the coupling between thermal fluctuations of the structure and the binding deformation, the predictive power of normal modes is still limited by the harmonic approximation. Hence, in order to investigate the progressive detachment of the peptide from the PDZ structure, one must resort to more general computational studies.
Molecular dynamics simulations have played a crucial role in understanding the basis of the concomitant selectivity and promiscuity of the PDZ binding dynamics 24,25 . Basdevant et al. 25 , in particular, have used allatom Molecular Dynamics (MD) with a realistic forcefield to correctly reproduce the experimental ranking, but not the precise values, of binding free-energies. The chemical details of the target peptide and of the binding groove have been taken into account, and hydrophobic effects have been shown to be key determinants of the promiscuity, with other interactions conferring stronger or weaker selectivity.
The free energy difference ∆G u b between the unbound and bound states is customarily related to the dissociation constant
where T is the absolute temperature and k B is the Boltzmann constant. However, the constant K D is also related to the dynamics of the system by the equation
where k off and k on are the unbinding and binding rates respectively. At a first approximation, k off and k on depend on the free energy difference between the bound and unbound states and the barrier between them. The di
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