Calculations of binding affinity between C8-substituted GTP analogs and the bacterial cell-division protein FtsZ

Ligand Strain and Entropic Effects on the Binding of Macrocyclic and Linear Inhibitors: Molecular Modeling of Penicillopepsin Complexes

Using extensive molecular dynamics simulations, we investigate the structure and dynamics of the complexes formed between penicillopepsin and two peptidomimetic inhibitors: a linear compound, isovaleryl(P₄)-valine(P₃)-asparagine(P₂)-leucine(P₁)-phosphonate-phenylalanine(P₁'), and its macrocylic analog that includes a methylene bridge between the Asn(P₂) and Phe(P₁') side chains. The macrocyclic inhibitor, which has a 420-fold stronger affinity than that of the acyclic one, has been considered to lower the entropic penalty for binding. To better understand this binding preference, the solution structure of the inhibitors is studied by molecular dynamics simulations. Subsequently, we assess the influence of the enzyme/inhibitor contacts, the enzyme-induced inhibitor strain, the variation of the ligand configurational entropy and the enzyme reorganization by combining molecular-mechanics Poisson-Boltzmann surface area and normal mode calculations with conformational entropy calculations. We find that there is no relevant entropic stabilization on the binding of the cyclic inhibitor with respect to the acyclic analog because the methylene bridge does not reduce appreciably the conformational flexibility of the free inhibitor. The most important factors explaining the stronger affinity of the macrocyclic inhibitor are the conformational filtering and the lower ligand strain induced by the methylene bridge.

Kinetic barriers in the isomerization of substituted ureas: implications for computer-aided drug design

Urea derivatives are ubiquitously found in many chemical disciplines. N,N'-substituted ureas may show different conformational preferences depending on their substitution pattern. The high energetic barrier for isomerization of the cis and trans state poses additional challenges on computational simulation techniques aiming at a reproduction of the biological properties of urea derivatives. Herein, we investigate energetics of urea conformations and their interconversion using a broad spectrum of methodologies ranging from data mining, via quantum chemistry to molecular dynamics simulation and free energy calculations. We find that the inversion of urea conformations is inherently slow and beyond the time scale of typical simulation protocols. Therefore, extra care needs to be taken by computational chemists to work with appropriate model systems. We find that both knowledge-driven approaches as well as physics-based methods may guide molecular modelers towards accurate starting structures for expensive calculations to ensure that conformations of urea derivatives are modeled as adequately as possible.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Interactions of bacterial cell division protein FtsZ with C8-substituted guanine nucleotide inhibitors. A combined NMR, biochemical and molecular modeling perspective

FtsZ is the key protein of bacterial cell-division and target for new antibiotics. Selective inhibition of FtsZ polymerization without impairing the assembly of the eukaryotic homologue tubulin was demonstrated with C8-substituted guanine nucleotides. By combining NMR techniques with biochemical and molecular modeling procedures, we have investigated the molecular recognition of C8-substituted-nucleotides by FtsZ from Methanococcus jannaschii (Mj-FtsZ) and Bacillus subtilis (Bs-FtsZ). STD epitope mapping and trNOESY bioactive conformation analysis of each nucleotide were employed to deduce differences in their recognition mode by each FtsZ species. GMP binds in the same anti conformation as GTP, whereas 8-pyrrolidino-GMP binds in the syn conformation. However, the anti conformation of 8-morpholino-GMP is selected by Bs-FtsZ, while Mj-FtsZ binds both anti- and syn-geometries. The inhibitory potencies of the C8-modified-nucleotides on the assembly of Bs-FtsZ, but not of Mj-FtsZ, correlate with their binding affinities. Thus, MorphGTP behaves as a nonhydrolyzable analog whose binding induces formation of Mj-FtsZ curved filaments, resembling polymers formed by the inactive forms of this protein. NMR data, combined with molecular modeling protocols, permit explanation of the mechanism of FtsZ assembly impairment by C8-substituted GTP analogs. The presence of the C8-substituent induces electrostatic remodeling and small structural displacements at the association interface between FtsZ monomers to form filaments, leading to complete assembly inhibition or to formation of abnormal FtsZ polymers. The inhibition of bacterial Bs-FtsZ assembly may be simply explained by steric clashes of the C8-GTP-analogs with the incoming FtsZ monomer. This information may facilitate the design of antibacterial FtsZ inhibitors replacing GTP.

Free-energy differences between states with different conformational ensembles

Multiple conformations separated by high-energy barriers represent a challenging problem in free-energy calculations due to the difficulties in achieving adequate sampling. We present an application of thermodynamic integration (TI) in conjunction with the local elevation umbrella sampling (LE/US) method to improve convergence in alchemical free-energy calculations. TI-LE/US was applied to the guanosine triphosphate (GTP) to 8-Br-GTP perturbation, molecules that present high-energy barriers between the anti and syn states and that have inverted preferences for those states. The convergence and reliability of TI-LE/US was assessed by comparing with previous results using the enhanced-sampling one-step perturbation (OSP) method. A linear interpolation of the end-state biasing potentials was sufficient to dramatically improve sampling along the chosen reaction coordinate. Conformational free-energy differences were also computed for the syn and anti states and compared to experimental and theoretical results. Additionally, a coupled OSP with LE/US was carried out, allowing the calculation of conformational and alchemical free energies of GTP and 8-substituted GTP analogs.

GTP regulates the interaction between MciZ and FtsZ: a possible role of MciZ in bacterial cell division

MciZ, a peptide with 40 amino acid residues, has been shown to be expressed during bacterial sporulation, to inhibit Z-ring formation in bacteria, and to inhibit the assembly of FtsZ in vitro. Here, MciZ was found to bind to FtsZ in vitro with a dissociation constant of 0.3 ± 0.1 μM. Guanosine nucleotides inhibited the binding of MciZ to FtsZ; however, GTP inhibited the binding of MciZ to FtsZ more strongly than GDP. In addition, MciZ inhibited the binding of 2',3'-O-(2,4,6-trinitrocyclohexadienylidene)-GTP, a fluorescent analogue of GTP, to FtsZ. The results indicated that MciZ shares its binding site on FtsZ with GTP. Furthermore, M19I, an N-terminal 19-residue peptide (MKVHRMPKGVVLVGKAWEI) of MciZ, inhibited the assembly and GTPase activity of FtsZ in vitro. The results suggested that GTP plays an important role in the regulation of the interaction between FtsZ and MciZ and that M19I may be used as a lead peptide to design peptide inhibitors of FtsZ assembly.

Simulating GTP:Mg and GDP:Mg with a simple force field: a structural and thermodynamic analysis

Di- and tri-phosphate nucleotides are essential cofactors for many proteins, usually in an Mg(2+) -bound form. Proteins like GTPases often detect the difference between NDP and NTP and respond by changing conformations. To study such complexes, simple, fixed charge force fields have been used, which allow long simulations and precise free energy calculations. The preference for NTP or NDP binding depends on many factors, including ligand structure and Mg(2+) coordination and the changes they undergo upon binding. Here, we use a simple force field to examine two Mg(2+) coordination modes for the unbound GDP and GTP: direct, or "Inner Sphere" (IS) coordination by one or more phosphate oxygens and indirect, "Outer Sphere" (OS) coordination involving one or more bridging waters. We compare GTP: and GDP:Mg binding with OS and IS coordination; combining the results with experimental data then indicates that GTP prefers the latter. We also examine different kinds of IS coordination and their sensitivity to a key force field parameter: the optimal Mg:oxygen van der Waals distance Rmin . Increasing Rmin improves the Mg:oxygen distances, the GTP: and GDP:Mg binding affinities, and the fraction of GTP:Mg with β + γ phosphate coordination, but does not improve or change the GTP/GDP affinity difference, which remains much larger than experiment. It has no effect on the free energy of GDP binding to a GTPase.

Targeting the assembly of bacterial cell division protein FtsZ with small molecules

FtsZ is the key protein of bacterial cell division and an emergent target for new antibiotics. It is a filament-forming GTPase and a structural homologue of eukaryotic tubulin. A number of FtsZ-interacting compounds have been reported, some of which have powerful antibacterial activity. Here we review recent advances and new approaches in modulating FtsZ assembly with small molecules. This includes analyzing their chemical features, binding sites, mechanisms of action, the methods employed, and computational insights, aimed at a better understanding of their molecular recognition by FtsZ and at rational antibiotic design.

Conformational selection through electrostatics: Free energy simulations of GTP and GDP binding to archaeal initiation factor 2

Archaeal Initiation Factor 2 is a GTPase involved in protein biosynthesis. In its GTP-bound, "ON" conformation, it binds an initiator tRNA and carries it to the ribosome. In its GDP-bound, "OFF" conformation, it dissociates from tRNA. To understand the specific binding of GTP and GDP and their dependence on the conformational state, molecular dynamics free energy simulations were performed. The ON state specificity was predicted to be weak, with a GTP/GDP binding free energy difference of -1 kcal/mol, favoring GTP. The OFF state specificity is larger, 4 kcal/mol, favoring GDP. The overall effects result from a competition among many interactions in several complexes. To interpret them, we use a simpler, dielectric continuum model. Several effects are robust with respect to the model details. Both nucleotides have a net negative charge, so that removing them from solvent into the binding pocket carries a desolvation penalty, which is large for the ON state, and strongly disfavors GTP binding compared to GDP. Short-range interactions between the additional GTP phosphate group and ionized sidechains in the binding pocket offset most, but not all of the desolvation penalty; more distant groups also contribute significantly, and the switch 1 loop only slightly. The desolvation penalty is lower for the more open, wetter OFF state, and the GTP/GDP difference much smaller. Short-range interactions in the binding pocket and with more distant groups again make a significant contribution. Overall, the simulations help explain how conformational selection is achieved with a single phosphate group.

Free energy calculations from one-step perturbations

The one-step perturbation approach offers an efficient means to estimate free energy differences. It may be applied to estimate solvation free energies, conformational preferences or relative free energies of binding of series of compounds to a common receptor. Applicability of the method depends on the possibility to define a proper reference state which may in itself be an unphysical molecule. Here, we describe practical considerations and explicit guidelines to define a proper reference state, and to efficiently calculate relative free energies. The strengths and limitations of the method are highlighted and special considerations are noted. The method may be applied using many different simulation programs. Here, analyses are exemplified at the hand of the GROMOS simulation package.

Free energy calculations of protein-ligand interactions

In the calculation of free energies of binding for protein-ligand complexes, we distinguish endpoint methods, methods involving alchemical modifications and methods that physically displace the ligand from the protein. Most methodological advances seem to come from a clever combination of multiple existing methods to enhance the sampling or to utilize specific advantages of various approaches. The coupling parameters common in thermodynamic integration and in Hamiltonian replica exchange are for instance combined to yield replica exchange thermodynamic integration. As new methods mostly aim to improve efficiency or to attain more complete sampling, there are good prospects to understand and tackle the sampling problem better and to shift the focus towards the scoring problem in the context of more robust and accurate force fields.

Free energy simulations of a GTPase: GTP and GDP binding to archaeal initiation factor 2

Archaeal initiation factor 2 (aIF2) is a protein involved in the initiation of protein biosynthesis. In its GTP-bound, "ON" conformation, aIF2 binds an initiator tRNA and carries it to the ribosome. In its GDP-bound, "OFF" conformation, it dissociates from tRNA. To understand the specific binding of GTP and GDP and its dependence on the ON or OFF conformational state of aIF2, molecular dynamics free energy simulations (MDFE) are a tool of choice. However, the validity of the computed free energies depends on the simulation model, including the force field and the boundary conditions, and on the extent of conformational sampling in the simulations. aIF2 and other GTPases present specific difficulties; in particular, the nucleotide ligand coordinates a divalent Mg(2+) ion, which can polarize the electronic distribution of its environment. Thus, a force field with an explicit treatment of electronic polarizability could be necessary, rather than a simpler, fixed charge force field. Here, we begin by comparing a fixed charge force field to quantum chemical calculations and experiment for Mg(2+):phosphate binding in solution, with the force field giving large errors. Next, we consider GTP and GDP bound to aIF2 and we compare two fixed charge force fields to the recent, polarizable, AMOEBA force field, extended here in a simple, approximate manner to include GTP. We focus on a quantity that approximates the free energy to change GTP into GDP. Despite the errors seen for Mg(2+):phosphate binding in solution, we observe a substantial cancellation of errors when we compare the free energy change in the protein to that in solution, or when we compare the protein ON and OFF states. Finally, we have used the fixed charge force field to perform MDFE simulations and alchemically transform GTP into GDP in the protein and in solution. With a total of about 200 ns of molecular dynamics, we obtain good convergence and a reasonable statistical uncertainty, comparable to the force field uncertainty, and somewhat lower than the predicted GTP/GDP binding free energy differences. The sign and magnitudes of the differences can thus be interpreted at a semiquantitative level, and are found to be consistent with the experimental binding preferences of ON- and OFF-aIF2.

Insights into nucleotide recognition by cell division protein FtsZ from a mant-GTP competition assay and molecular dynamics

Essential cell division protein FtsZ forms the bacterial cytokinetic ring and is a target for new antibiotics. FtsZ monomers bind GTP and assemble into filaments. Hydrolysis to GDP at the association interface between monomers leads to filament disassembly. We have developed a homogeneous competition assay, employing the fluorescence anisotropy change of mant-GTP upon binding to nucleotide-free FtsZ, which detects compounds binding to the nucleotide site in FtsZ monomers and measures their affinities within the millimolar to 10 nM range. We have employed this method to determine the apparent contributions of the guanine, ribose, and the α-, β-, and γ-phosphates to the free energy change of nucleotide binding. Similar relative contributions have also been estimated through molecular dynamics and binding free energy calculations, employing the crystal structures of FtsZ-nucleotide complexes. We find an energetically dominant contribution of the β-phosphate, comparable to the whole guanosine moiety. GTP and GDP bind with similar observed affinity to FtsZ monomers. Loss of the regulatory γ-phosphate results in a predicted accommodation of GDP which has not been observed in the crystal structures. The binding affinities of a series of C8-substituted GTP analogues, known to inhibit FtsZ but not eukaryotic tubulin assembly, correlate with their inhibitory capacity on FtsZ polymerization. Our methods permit testing of FtsZ inhibitors targeting its nucleotide site, as well as compounds from virtual screening of large synthetic libraries. Our results give insight into the FtsZ-nucleotide interactions, which could be useful in the rational design of new inhibitors, especially GTP phosphate mimetics.