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J Mol ModelDOI 10.1007/s00894-010-0698-4 Investigating reaction pathways in rare events simulationsof antibiotics diffusion through protein channels Eric Hajjar & Amit Kumar & Paolo Ruggerone &Matteo Ceccarelli Received: 1 December 2009 / Accepted: 27 February 2010 # Springer-Verlag 2010 Abstract In Gram-negative bacteria, outer-membrane pro- further simulations. This will benefit the screening and design tein channels, such as OmpF of Escherichia coli, constitute for antibiotics with better permeation properties.
the entry point of various classes of antibiotics. Whileantibacterial research and development is declining, bacterial Keywords Accelerated molecular dynamics . Antibacterial resistance to antibiotics is rising and there is an emergency design . Antibiotics uptake . Bacterial porins . Diffusion .
call for a new way to develop potent antibacterial agents and Free energy . Reaction coordinate to bring them to the market faster and at reduced cost. Anemerging strategy is to follow a bottom-up approach based onmicroscopically founded computational based screening, however such strategy needs better-tuned methods. Here wepropose to use molecular dynamics (MD) simulations The permeability to antibiotics, or uptake, is the very first combined with the metadynamics algorithm, to study line of defense of Gram-negative bacteria, that are antibiotic translocation through OmpF at a molecular scale.
protected by an outer-membrane []. In the case of E.coli, This recently designed algorithm overcomes the time scale the uptake of several classes of β-lactam antibiotics, a problem of classical MD by accelerating some reaction prominent group in our current antibacterial arsenal, is coordinates. It is expected that the initial assumption of the largely controlled by general diffusion protein channels reaction coordinates is a key determinant for the efficiency such as outer membrane protein F (OmpF) [Indeed, and accuracy of the simulations. Previous studies using pathogenic strains of Gram-negative bacteria, that were different computational schemes for a similar process only found to be resistant against quinolones and β-lactams used one reaction coordinate, which is the directionality. Here (two of the main classes of antibiotics) frequently have we go further and see how it is possible to include more modulation of the structure or the expression of general informative reaction coordinates, accounting explicitly for: diffusion porin OmpF (i) the antibiotic flexibility and (ii) interactions with the A key feature in the structure of porins, as seen from the channel. As model systems, we select two compounds X-ray structure of OmpF is the presence of the loop L3 covering the main classes of antibiotics, ampicillin and that folds back into the channel to form a gate, also called moxifloxacine. We decipher the molecular mechanism of constriction region (see Fig. In addition to such spatial translocation of each antibiotic and highlight the important constriction, the zone is also characterized by a strong parameters that should be taken into account for improving transversal electric field, generated by negatively chargedresidues D113, E117 (L3 side) that faces a cluster ofpositively charged residues R42, R82, and R132 (anti-L3 E. Hajjar (*) : A. Kumar : P. Ruggerone : M. Ceccarelli side) (see Fig. ).
Department of Physics and UOS-SLACS, While antibacterial research and development is on the Universita di Cagliari and Istituto Officina dei Materiali/CNR, decline, the resistance is on the rise, and we are thus facing SP Monserrato-Sestu Km 0.700, an alarming situation where there is an emergency call for a I-09042 Monserrato, Italye-mail: [email protected] new way to develop potent antibacterial agents and to bring

Fig. 1 a) Structural details of OmpF. The backbone of OmpF is type (positively charged in blue, negatively charged in red). The loop displayed in cyan cartoons to highlight its secondary structure. The L3 is colored in orange. 3D structures of the optimized geometry of charged residues at the constriction region (D113, E117, D121 on the ampicillin (b) and (c) moxifloxacin. The molecules are colored by atom L3 side and R42, R82, R132 on the anti-L3 side) are colored by residue types: blue for nitrogen, red for oxygen, cyan for carbon them to the market faster and at reduced cost. An emerging specifying a single reaction coordinate can lead to a strong strategy is to follow a bottom-up approach, from the approximation of the sampled process.
knowledge of resistant mechanisms to a rational structure- Several studies addressed the challenge of such biased based design and screening of antibiotics. Within this molecular dynamics methods to study the difficult problem scheme, molecular simulations have the potential to provide of molecular diffusion through narrow channels. In their an accurate microscopic explanation of what governs recent paper, Henin et al. highlight the importance of antibiotics diffusion (and thus bacterial resistance) and using another reaction coordinates than the usually taken, Z how to screen for better antibiotics. In principle, standard (distance) coordinate that drives the process under study.
MD simulations would have the required microscopic Indeed it is believed that including an extra reaction accuracy to link the structure and dynamics (of the drug coordinate would allow explicitly to account for reorienta- and porin) to the rate of permeation. However, standard tions and/or relaxation needed for reaching better accuracy simulations are limited to hundred of nanoseconds at most in the sampling of the process studied. In fact, our and and they do not allow the study of the reactive pathway that others previous studies suggested that the flexibility and antibiotics follow during passive diffusion, which is on the orientation of the antibiotic would play a role in its order of hundreds of microseconds diffusion process through OmpF [, However, the To overcome this timescale problem, we propose to use qualitative and quantitative consequences of the choice of accelerated MD simulation algorithms schemes, or metady- RC are still poorly understood and there are very few namics, while keeping an "all atom" description of the studies illustrating this point. The first natural reaction systems The metadynamics algorithm (to accelerate coordinate that could be used in our metadynamics sampling) is based on the following principle: a time- approach is the position of the antibiotic with respect to dependent bias is added on a few chosen reaction coor- the axis of diffusion Z.
dinates (RC). It is important to note that a crucial point of Here we go further and include more informative such metadynamic approach is the choice of appropriate RC.
reaction coordinates, accounting not only for the direction- Unlike other popular techniques (such as steered ality of the transport but also explicitly for: (i) the antibiotic molecular dynamics metadynamics allows more than orientation and (ii) specific interactions with the channel.
one RC to be defined and this is an important advantage as Our approach will allow discussing the two choices of RC in the translocation with the study of two different for system setup and simulation [All simulated systems antibiotics: the beta-lactam ampicillin and the quinolone were validated for convergence and stabilization of energy, moxifloxacine, for which experimental and simulation data temperature and root mean square deviation with respect to are already available [].
the starting structure.
Finally, we conclude by discussing the improved strategies, as highlighted by our study. Indeed, the in- Metadynamics algorithm depth analysis of these two model systems allows us todiscuss for future improvements in the biased methods The metadynamics algorithm employs a bias to accelerate (importance of explicitly including the relative orientation the evolution of some collective variables, defined as the and the specific interactions) to screen and design for relevant reaction coordinates for the process under investi- antibiotics in particular, but also for investigating any other gation. The bias consists of a history dependent potential, complex process of interest.
which is constructed as a sum of repulsive potentialcentered along the trajectory of the collective variables.
These additional energy terms avoid revisiting the same Materials and methods conformations or at least add a penalty term to thepreviously visited conformations. In the present simula- Starting structures for molecular dynamic simulations tions, a Gaussian potential is added every 4 ps with a heightof 1.0 kJ mol−1. The Gaussian width is set to 0.2 Å, 5.0 We followed the same protocol of simulations as described degrees and 0.5, respectively for the distance Z, the angle Θ earlier starting from the crystal structure ‘2OMF' (pdb- and the number of hydrogen bonds. These parameters were code) and residues protonation state as in [We added chosen to allow a better resolution in the sampling of the the required amount of Cl- and K+ counter ions to neutralize free energy and a low error (around 2kBT).
the protein charges. We embedded the system in a The most important point in the metadynamics is to hydrophobic environment of detergent molecules (lauryl select the proper reaction coordinates. These must be dimethyl amine oxide, LDAO) and solvated the system variables that are of interest but difficult to sample with a with ∼8000 water molecules in an hexagonal box.
standard scheme, since the local minima in the space Hexagonal periodic boundary conditions were used and spanned by these variables are separated by barriers that the simulation box edges are 68.4 Å, 68.4 Å, 78.1 Å.
cannot be overcome in the simulation time available. We Electrostatic interactions at long distance were evaluated also wanted to compare the effect of choosing different using the soft particle mesh Ewald scheme while a cutoff of collective variables in this case, and thus we chose the three 10 Å was used for the Lennard-Jones and short electrostatic different collective variables: energy terms. Multiple time step algorithm (MTS Respa) (i) Distance (Z) , defined as: Z ¼ ZGEO an ð tÞ ZGEOðsoluteÞ, was used with the SHAKE algorithm to keep bond lengthsinvolving hydrogens fixed. The simulations were done at where ZGEO is calculated as the average of Z coordinates of 300 K with Nose thermostat to control temperature.
all the heavy atoms of the system, respectively antibiotics We used the Amber potential for protein and TIP3P for and (porin + detergent) water []. The parameters of antibiotics were developed (ii) Angle (Θ), defined as: CosðqÞ ¼ eZ:vant, following the Amber protocol ]: (i) the three dimen-sional chemical structure of the antibiotic was drawn, using with eZ being the eigenvector of inertia tensor (calculated the software package HyperChem; (ii) geometry optimiza- on the porin Cα) that is closest to the axe of diffusion of the tion was performed using the Hartree-Fock (HF) basis set porin, vant being the vector of the long axis of the antibiotic, HF-6-31G* with the Gaussian03 package [(iii) the the closest to the highest component of the dipole moment.
molecular electrostatic potential was generated at HF/6- (iii) Number of hydrogen bonds, defined as a continuous 31G* level; (iv) the atomic charges were fitted to molecular function from the list of all defined donors and electrostatic potential with aid of a module RESP in Amber8 acceptors of the system: program package, adding the restraint for equivalent atoms HB ¼ i¼ 1ðr Þ12 . The structure obtained after full optimization is where nHB is the total number of possible hydrogen bonds considered the starting geometry of the molecule onto calculated at time t; r0 is the reference distance between the which we assign all the force-field parameters. The atom two heavy atoms of the bonds taken as 2.5 Å.
types and parameters were derived using either the program The metadynamics algorithm enables the reconstruction antechamber (Amber-module), when possible, or were of the free energy in the subspace of the collective variables assigned manually on the basis of our optimized geometry.
by integrating the history dependent terms Due to the We used the program ORAC and the Amber force field [ complexity of the process studied, we calculated the free

energy after obtaining the first translocation path, which is Further, we report the molecular properties in terms of considered to be the most probable path because it passes the amount of hydrophilic/hydrophobic surface, as calcu- through the lowest saddle point, as done before for the lated from the PLATINIUM server ].
unthreading of a molecule ]. In fact, once the antibioticcrosses the constriction region, we expected a diffusiveregime, with no significant affinity sites. The error bars Results and discussion associated with the energy calculations were assessed aspreviously done [and are of 1 kcal mol−1 at most.
Metadynamics simulations allow studyingthe translocation process Microscopic analysis methodology Both ampicillin and moxifloxacine have a permanentdipole, being its larger component along their long axis To decipher the molecular details of the translocation (Fig. b–c). As during permeation, antibiotics have to mechanism additional equilibrium MD simulations (1 ns penetrate the constriction region that is rich of charged length) were started from each visited minima along the amino acids, it is important to accurately define the way of diffusion path. In depth analysis using VMD and in-house entry and the interactions with the channel. To do so, we scripts, was performed to characterize the following key included explicitly these degrees of freedom as reaction structural features: coordinate along the metadynamics runs.
(i) The atomic root mean square fluctuations (rmsf) were The Fig. displays the free energy surfaces (FES) of the calculated for each heavy atoms of the backbone of the translocation of the ampicillin beta-lactam antibiotic (Amp) antibiotic with respect to its average position during the through the OmpF channel for two different choices of the reaction coordinates: (A) with the combination of the (ii) Existence of hydrogen bonds (Hb) and hydrophobic distance Z and the number of hydrogen bonds Hb; and contacts (Hc) between atoms of the antibiotics and of (B) with the combination of the distance Z and the angle Θ.
OmpF. Hbs are counted using VMD scripts according Interestingly, the free energy barrier required for ampicillin to the following threshold parameters: a distance of at to translocates is of the same order in the two simulations: most 3 Å and donor-hydrogen-acceptor angle of at 11 kcal mol−1 and 9 kcal mol−1 for the simulation A and B least 130 degrees. Hcs are counted when non-polar respectively (the values correspond to the energy barrier atoms are separated by at most 3 Å.
needed to translocates starting from the deepest minima Fig. 2 Complete free energy surfaces for ampicillin translocating and the number of Hb; (B) the distance Z and the angle Θ. Each isoline through OmpF, associated with the reaction pathway along the subspace correspond to a different color gradient and to 1 kcal mol−1. The blue of the two variables: taken as (A) the distance Z (Z=0 corresponds to points superimposed on the FES correspond to the superimposed values the center of the constriction zone, also indicated by the gray shading) of the RC calculated from the other simulation

above). In both cases, deep energy minima are visited, simulations for the translocation of moxiflocacine. First, which can be related to well defined affinity sites of the free energy barrier required for moxiflocacine to ampicillin inside the channel. In particular, we observe the translocate is much larger in the simulation A, 21 kcal location of a deep energy minimum exactly at the mol−1, compared to the simulation B, 16 kcal mol−1. The constriction region (Mini-CR at Z∼0, see Fig. ). To localization of the energy minima, defining the affinity sites address the similarity (reproducibility) of the process of the antibiotic inside the channel, is also very different. In sampled with different RC, we further calculated the the simulation A we note the absence of a deep energy missing RC of each simulation. Thus, the Hb coordination minimum at the constriction region, instead it is localized number, as calculated in the course of the simulation B, slightly above, at Z∼4 Å (Mini-Above, Fig. In the case were superimposed as blue points in Fig. ; similarly, the of the simulation B we find two energy minima localized Θ angle, as calculated in the course of the simulation A, above but also, in particular, one energy minimum is were superimposed as blue points in Fig. Interestingly, centrally localized at the constriction region, at Z∼0 Å the number of hydrogen bonds needed (about 10 Hbs) to cross the constriction region and translocate is similar in The important differences between these simulations both simulations that were "biased" (A) or "free" (B) for using different RC are seen from the superimposition in the this RC. Similarly, both simulations sample the same FES of the calculated values of the missing RC. As seen in populations of states of the angle Θ (the value of Θ when the blue points superimposed in Fig. , the hydrogen ampicillin crosses the constriction region and translocates is bonds calculated from the simulation B do not follow the around 150 degrees in both simulations A and B), such as same path as the Hb sampled from simulation A. Instead, in the deep minima at the constriction region. The fact that the number of Hb calculated from the simulation B is both both the angle and the hydrogen bond coordinate are more constant and lower than the number of Hb sampled reproducing a very similar path, with a deep energy minimum along simulation A (∼4 Hb from simulation B while there located centrally at the CR, comforts us in the choice of are 8 Hb when the antibiotic crosses the constriction region these RC. For the study of ampicillin's translocation, both in simulation A). Similarly, as seen in Fig. , the RC are appropriate.
superimposed Θ angles calculated from simulation A do Next, we performed metadynamics simulations using the not really follow the path of the Θ angles sampled in same two sets of RC for the quinolone antibiotic: moxi- simulation B. Instead, the Θ angles calculated from floxacine. As seen in the FES displayed in Fig. , there are simulation A reveal a much more stretched and limited some important differences between the two sets of exploration path (the Θ angles only take values from 40 to Fig. 3 Complete free energy surfaces for moxifloxacine translocating through OmpF (see legends in Fig. )

120 degrees in the case of the simulation A, whereas they explained in the Method section). We observe that can cover fully the range from 0 to 180 in the case of ampicillin is able to make a large number of durable polar simulation B), as a consequence some local minima (above Hbs, in particular both the one between its N-terminal the constriction region) are not sampled in the path positive group (N1) and D113 and the one between its C- followed by the simulation A (Fig. ).
terminal carboxylic group (O2) and R132 exceed 70% of To elucidate the microscopic details of the different the equilibrium simulation time. Instead, only one signifi- translocation path and conclude on the importance of the cant Hc (∼20% of the simulation time) is made between the choice of the RC we further performed in-depth analysis CT2 carbon of ampicillin and M114 (Fig. based on equilibrium simulations.
A similar detailed structural analysis was performed when moxifloxacine is bound in Mini-CR, in the simulation Equilibrium MD simulations allow studying the structural B (with the Θ RC), and we find that in this case, the and dynamics properties antibiotic is oriented with its polar carboxyl group pointingup (Fig. ). Instead, it is with its hydrophobic group that In order to characterize the structural and dynamics moxifloxacine is seen to penetrate the constriction region properties that govern the antibiotics diffusion process we (Fig. ). The interaction network analysis indeed reveals a then performed equilibrium MD simulations (of 1 ns predominance of Hcontacts between the antibiotic and the length) starting from the relevant, preferential minima, many hydrophobic residues on the porin side such as F118, identified by the FES. We focus only on the minima where L20, M114, P116 (Fig. The only significant Hb the antibiotics are bound at the constriction region of the identified involves Y124, E117 and to a lesser extend R82.
channel (Mini-CR) as if such interaction was the rate- Differences in the structural, dynamical or physico- limiting step of the process. In the case of ampicillin, we chemical properties of the two antibiotics could explain find that very similar structures are sampled along the two the differences observed in our study - that is, the translocation Mini-CR from both simulations with the Hb and Θ RC, we of ampicillin is described equivalently by both the Hb and the will further only describe the Mini-CR of the simulation B Θ RC while the translocation process of moxifloxacine differs (with the Θ RC). As seen from the snapshot in Fig. , to if choosing the Hb or the Θ RC. Table reports diverse enter the affinity site at the constriction region (Mini-CR) physico-chemical properties of the two antibiotics, such as and further translocates, ampicillin is oriented with its polar the flexibility and solvation pattern, obtained from the carboxyl group pointing down and makes favorable optimized 3D structures or from simulations where they are interactions with the residues of the porin constriction placed in a box of water. We observe that, although both zone. We present in Fig. the lifetime of the hydrogen antibiotics have the same molecular surface size, ampicillin bonds and hydrophobic contact (Hc) interactions between is found to be much more polar while moxifloxacine is much ampicillin and OmpF atoms sampled along Mini-CR (as more hydrophobic (see computed surface properties in Fig. 4 a) Molecular detail of ampicillin at the preferred minimum, at the constriction region (Mini-CR). In the x-axis is represented each the constriction region, Mini-CR, showing the interacting residues of atom of the antibiotic, in y-axis is calculated the lifetime (probability OmpF (colored by residue types, the ones involved in Hbs are of existence along simulation) of each interaction between atoms of displayed as sticks and those involved in Hcontacts are displayed by the antibiotic and atoms of OmpF. In black bars are represented the molecular surface) (see Fig. for coloring code). b) Interaction map hydrogen bonds (Hb) and in gray bars the hydrophobic contacts for the equilibrium MD of ampicillin in the preferential minimum, at (Hcontacts), calculated as explained in

Fig. 5 Molecular details (a) andinteraction map (b) of moxi-floxacine at the preferentialminimum, Mini-CR (see legendsin Fig. ) Table ). This is in agreement with the antibiotics nature of Altogether, from our simulations, we observe that the interactions with OmpF. Interestingly, we also find that the bottleneck for the antibiotics translocation is to overcome ampicillin structure is twice more flexible than the one of the constriction region, where the antibiotic has to moxifloxacine (see calculated rmsf in Table optimally interact with the channel, its dipole has to matchthe strong transversal electrostatic field and its surface hasto adapt to fit to a given size.
In the simulation where the Hb was taken as a RC, we found that ampicillin can make and break Hb easily and it Here we used all-atom metadynamics simulations with a reaches up to 10 Hb but in the case of moxifloxacine this different choice of the RC and followed the translocation number is constant and as low as 4, thus we believe that through OmpF of two commonly used antibiotics. The high overcoming the constriction is more difficult in the case of resolution in time and space that metadynamics simulations a less polar or more hydrophobic antibiotic. The molecular provide has the potential to be used to characterize the details of the simulations allow assessing how the choice of molecular basis of translocation of antibiotics, and further, the RC affects the FES and the molecular mechanism for such strategy might be used to help select/design antibiotics with better permeation properties and thus combat bacterial In the case of ampicillin, although metadynamics is resistance. To improve the accuracy and efficiency of future applied with a different RC, we find a similar antibiotic simulations studies, we must keep on developing the algo- translocation pathway. In both cases, a unique energy rithms at hands. Here we address the consequences of choosing minimum is found for ampicillin at the constriction region, a different RC, which is the crucial point of the accelerated which is well defined with a strong interaction network. In molecular dynamics techniques. Due to the cylindrical shape of this preferential minimum, the (two charged groups) dipole OmpF, a tentative choice of RC is the position of the of the antibiotic matches perfectly with the one of the porin, antibiotic along the main axe of diffusion. Our results on known as the transversal electric field, with negative moxifloxacin and ampicillin support our hypothesis that the residues clustered on the L3 side and positive residues Θ angle defines an optimal RC, as it is an internal variable lining on the anti-L3 side (see Fig. not subject to change as OmpF diffuses during simulation.
Interestingly, a different molecular path is found by moxifloxacine with respect to ampicillin: it translocateswith its hydrophobic group pointing down and we note a Table 1 Structural details of the antibiotic obtained from the predominance of Hcontacts interactions that play an equilibrium MD simulations (see ) important contribution as a driving force. Such a possiblecontribution from hydrophobicity was already raised in the Surface properties [] (in box of waters) pioneer work of Nikaido ]. Indeed, the newer gener- ations of antibiotics that are more hydrophilic have enhanced antibacterial activity, indicating that hydrophilic-ity would enhance their affinity to OmpF. Thus, in such cases, we suggest to include directly the hydrophobic interactions number as a RC in the course of metadynamics simulations. Further analysis allowed extracting important 4. Nestorovich EM, Danelon C, Winterhalter M, Bezrukov SM structural and dynamical properties of the antibiotics, such (2002) Designed to penetrate: time-resolved interaction of singleantibiotic molecules with bacterial pores. Proc Natl Acad Sci USA as solvation and flexibility, and the same could be done with the porin target.
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Translating cell biology intotherapeutic advancesin Alzheimer's diseaseDennis J. Selkoe Studies of the molecular basis of Alzheimer's disease exemplify the increasingly blurred distinction between basic andapplied biomedical research. The four genes so far implicated in familial Alzheimer's disease have each been shown toelevate brain levels of the self-aggregating amyloid-b protein, leading gradually to profound neuronal and glialalteration, synaptic loss and dementia. Progress in understanding this cascade has helped to identify specifictherapeutic targets and provides a model for elucidating other neurodegenerative disorders.