Fig 1.
Pictorial representations of three major components of the model developed in this work.
(A) The illustration of the ligand free and ligand bound states on the basis of the Cα harmonic approximation. The presence of a ligand at the allosteric binding site is modeled by local restraining of the residue pairs that belong to the binding site. Example of the ligated site is shown in red color. (B) Schematic representation of the concept of allosteric potential: neighbors of a residue i (residues j, k, l), assume different displacements as a consequence of the difference in the structure dynamics of the free and ligated proteins. (C) Cartoon representation of the configurational work gain/loss per residue caused by restraining of the allosteric binding sites. The radius ρi per residuei in the tube-like protein representation is determined by the value of the configurational work per corresponding residue, scaled according to the function ρi = (Δgi − mini Δgi)/(maxi Δgi − mini Δgi). Thus, protein portions (residues, sites, domains) represented with a thick tube show increased dynamics upon restraining of the allosteric binding site and vice versa.
Fig 2.
Two examples of the hetero-oligomeric allosteric proteins, the 12-mer Aspartate carbamoyltransferase ATCase (A) and 4-mer Anthranilate Synthase AnthS (B).
In (A) the averaged free energy Δgi(0 → 6xATP/CPT) profiles per monomer (red curves) are shown for the catalytic (PAL site) and regulatory (ATP-CTP site) chains with gray error bands. The positions of residues that belong to the allosteric and catalytic sites are marked with corresponding symbols. In the upper right panel the complex surface is colored according to the values of the conformational work per residue. The regulatory chains are strongly stabilized (red part of the Δg scale), whereas the chains that carry catalytic sites yield a significant increase of configurational work (blue part of the Δg scale) as a result of allosteric communication between sites. Catalytic (PAL) and regulatory (ATP-CTP) sites are shown in green and red, respectively. In (B) the averaged free energy Δgi(0 → 2xTRP) profiles are shown for chains 1–2 (BEZ and TRP site) and chains 3–4 (GLU site) of Anthranilate Synthase AnthS. Similarly to the ATCase allosteric sites, the restraining in chains 1–2 induces high configurational work in the chains 3–4 that contain catalytic sites. Here and in the following figures containing data on proteins the red curve in the chart shows allosteric free energy profiles, the grey error band reflects the range in the amount of work exerted per residue in each monomer, because of the structural differences between homologous monomers in the oligomeric structure. Surface representations are colored according to the conformational work exerted per residues in corresponding part of the protein (red—negative values of the conformational work, showing local stabilization; blue—positive values of the work, pointing to increase of the local dynamics). We also show representative structures with color-marked locations of the corresponding ligands.
Table 1.
Results on allosteric causality and energetics obtained for proteins analyzed in this work.
Data for only one representative structure is given in this table (for the complete list of proteins see S1 Table). First column provides protein names, degree of oligomerization and total number of residues. Second column: PDB ID of the protein and names of ligands (if not the apo form). Third column: number, name, and type ((†)(A) allosteric activator, (I) allosteric inhibitor, and (S) substrate) of ligated binding sites in our model. Fourth column: the mean allosteric free energy difference of the ligated binding site A averaged over all the residues belonging to A in all protein monomers, and the mean allosteric free energy difference averaged over all the residues of the protein monomers (in parentheses). Fifth column: names of the binding site under allosteric regulation, typically catalytic sites. Sixth column: the mean allosteric free energy difference (or work exerted at) of the regulated binding site F
averaged over all the residues belonging to F in all protein monomers, and the mean allosteric free energy difference averaged over all the residues of the protein monomers (in parentheses
). ATCase: (*) and (**) the values corresponding to the regulatory ΔgR − mer and catalytic ΔgC − mer monomers, respectively. AnthS: (⋆) and (⋆⋆) the values corresponding to the monomers containing TRP ΔgTRP − mer and GLU ΔgGLU − mer. CAP: (*) and (**) the values corresponding to the bound monomer ΔgB − mer and free monomer ΔgF − mer.
Fig 3.
Free energy profiles and structural representatives.
(A) bovine glutamate dehydrogenase BGDH free energy profile Δgi(0 → 6xADP) with marked residue positions of the GTP, NDP, GLU, and ADP binding sites. (B) Catabolite activator protein (CAP) free energy profile Δgi(0 → 2xcAMP) with marked locations of the cAMP and DNA binding sites. (C) The 3-Deoxy-D-arabinoheptulosonate 7-phosphate synthase DAHPS free energy profile Δgi(0 → 4xPHE) with marked positions of the PHE and PGA binding sites. (D) The dihydroxyacetone kinase DAK free energy profile Δgi(0 → 2xANP), ANP and ARG are ligands.
Fig 4.
Schematic representation of the details of allosteric communication.
(A) bovine glutamate dehydrogenase, BGDH; (B) catabolite activator protein, CAP; (C) phosphofructokinase, PFK. Structures show locations of the binding sites, which have node shapes in the diagrams on the right. Grey ovals show ligated allosteric sites in corresponding modes of regulation. Arrows illustrate the causal relations between the allosteric and functional sites. Numbers on the arrows provide the allosteric free energy (or work exerted, in kcal/mol) at the catalytic site F as a result of binding at the allosteric site, . (A) BGDH. Simultaneous binding of ADP and GTP is compared to independent ones. In both PFK and BGDH schemes the dashed line ovals represent the whole protein complex. (B) CAP. There are two possible scenarios of regulation, depending on whether one (1xcAMP) or two (2xcAMP) allosteric ligands are bound. The dashed line ovals represents the protein monomers. (C) PFK. The mode of regulation in which bothPEP/ADPa and ADPf ligands are independently bound is compared to the case in which both effector and substrate are simultaneously bound, revealing the modulating role of ADPf in the configurational work exerted at the F6P site.
Fig 5.
Free energy profiles and structural representatives of (A) G6PD, (B) NADME, (C) SSUPTR, and (D) ThrS.
(A) 6-mer glucose-6-phosphate dehydrogenase G6PD free energy profile Δgi(0 → 6x16G) with marked locations of the 16G and AGP binding sites. (B) Malate dehydrogenase (decarboxylating) enzyme NADME free energy profile Δgi(0 → 4xFUM) with indicated positions of ATP, NAD and FUM binding sites. (C) Sulfolobus solfataricus uracil phosphoribosyltransferase SSUPTR free energy profile Δgi(0 → 4xCTP) with marked CTP and U5P binding sites. (D) Threonine synthase ThrS free energy profile Δgi(0 → 2xSAM) with shown locations of the TRS, SAM and LPP binding sites.
Fig 6.
Free energy profiles and structural representations of the D-3-phosphoglycerate dehydrogenase PGDH.
The profiles Δgi(0 → 8×SER) are based on calculations performed on two protein forms, 1psd and 1yba, respectively. Protein structures are shown using a colored tube-like representation with both colors, and radius of the tube scaled according to the configurational work exerted per corresponding residue (the radius ρi per residue i is scaled according to the functionρi = (Δgi − mini Δgi)/(maxi Δgi − mini Δgi)). Structures in the middle represent two forms of the protein analyzed in this work: inactive (1psd, top) and active (1yba, bottom). The structure in the right panel illustrates locations of the protein’s ligands: SER (red), NAD (green), and AKG (blue).
Fig 7.
Free energy profiles and representative structures of Phosphofructokinase PFK upon restraining its various sites.
All the results shown here are obtained from the analysis of the protein apo form (PDB ID: 3pfk). Three situations are shown: the inhibitor/activator PEP/ADPa is bound Δgi(0 → 4xPEP/ADPa); the substrate (ADPf) is bound Δgi(0 → 4xADPf); and both (PEP/ADPa and ADPf) ligands are bound Δgi(0 → 4x(PEP/ADPa + ADPf)). The free energy profiles are shown with the colored protein surfaces according to the configurational work exerted per residue (middle column), and with representative structures where the locations of the bound ligands are marked by different colors (right column).