Characterization of Ciprofloxacin Permeation Pathways across the

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Characterization of Ciprofloxacin Permeation Pathways across the Porin OmpC using Metadynamics and a String Method Jigneshkumar Dahyabhai Prajapati, Carlos José Fernández Solano, Mathias Winterhalter, and Ulrich Kleinekathöfer J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.7b00467 • Publication Date (Web): 17 Aug 2017 Downloaded from http://pubs.acs.org on August 23, 2017

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Journal of Chemical Theory and Computation

Characterization of Ciprofloxacin Permeation Pathways across the Porin OmpC using Metadynamics and a String Method Jigneshkumar Dahyabhai Prajapati,†,¶ Carlos José Fernández Solano,†,¶ Mathias Winterhalter,‡ and Ulrich Kleinekathöfer∗,† †Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany ‡Department of Life Sciences and Chemistry, Jacobs University Bremen, 28759 Bremen, Germany ¶Contributed equally to this work E-mail: [email protected]

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Abstract The rapid spreading of antimicrobial resistance in Gram-negative bacteria has become a major threat for humans as well as animals. As one of the main factors involved, the permeability of the outer membrane has attracted quite some attention recently. However, the knowledge regarding the translocation mechanisms for most available antibiotics is so far rather limited. Here, a theoretical study concerning the diffusion route of ciprofloxacin across the outer membrane porin OmpC from E. coli is presented. To this end, we establish a protocol to characterize meaningful permeation pathways by combining metadynamics with the zero-temperature string method. It was found that the lowest-energy pathway requires a reorientation of ciprofloxacin in the extracellular side of the porin before reaching the constriction region with its carboxyl group ahead. Several affinity sites have been identified and their metastability evaluated using unbiased simulations. Such a detailed understanding is potentially very helpful in guiding the development of next generation antibiotics.

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1

Introduction

Antimicrobial resistance to various antibiotics is fueling lethal super bugs, leading to a ’Postantibiotic era’ where common bacterial infections will claim lives once again. 1–3 Fluoroquinolones, especially ciprofloxacin, are recommended as a first line treatment for cystitis, pyelonephritis, and urinary tract infections caused by pathogenic strains of E. coli . 4 In the last decade, E. coli resistance against ciprofloxacin has been raised to 5-36.4% in different countries. 5–9 Among other mechanisms, a reduced bacterial outer membrane (OM) permeability and up-regulated efflux are responsible for the increasing fluoroquinolone resistance in E. coli . 10 As several studies suggest, 11–15 the OmpF and OmpC porins facilitate the transport of antibiotics through the OM of E. coli. However, the knowledge regarding the permeation pathways for most available antibiotics is quite small. 16 Only a few studies have highlighted the importance of the OmpF porin in the translocation mechanism of fluoroquinolones 17–21 while the role of the OmpC porin still remains unclear even when experimental evidence combined with computational simulations indicates its relevance. 17,22,23 In the last decades, all-atom molecular dynamics (MD) simulations have proven to be a powerful tool for studying ion permeation and substrate translocation across OM channels. 24–30 However, the configurational phase space of these systems is generally characterized by the presence of several metastable regions separated by energy barriers higher than thermal energy. Since standard MD simulations are meaningful only if the systems are ergodic in the time scale of the simulation, a large variety of enhanced sampling methods has been proposed to address this issue. 31–38 Here, we focus on metadynamics 37 which enables one to accelerate the sampling and to estimate the free energy surface (FES) by iteratively constructing and applying a bias potential along selected degrees of freedom (DOFs), the socalled collective variables (CVs). Furthermore, an efficient version of the zero-temperature string method 39,40 allows for extracting minimum energy pathways on the reconstructed FESs. 41,42 In this work, we present a theoretical study concerning the main features of ciprofloxacin 3



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Figure 1: (A) System setup for metadynamics simulations of ciprofloxacin translocation across the OmpC channel. An OmpC trimer (cartoon representation) inserted into a POPE lipid bilayer (surface representation) is shown together with ciprofloxacin molecules (van der Waals representation) placed at the EC and PP sides of the porin. Water and ions are shown in surface representation and as balls, respectively. (B) Description of the CVs z and zij used in this work. For CV z, the center of masses difference along the z-axis is calculated by choosing the Cα atoms from the porin barrel and ciprofloxacin atoms from the quinolone moiety (highlighted as green and read beads). The CV zij is defined as the z-component of an interatomic vector connecting two ciprofloxacin selected atoms, shown as red beads. (C) The confinements of the sampling region along the z-axis and in the xy plane are shown. These confinements restrict the motion of the antibiotic inside a virtual rectangular box. translocation across the OmpC porin (see Fig. 1) that successfully combines metadynamics and the string method. Our interest in this system is twofold. On the one hand, it enables us to shed some light on relevant factors involved in the antibiotic translocation process. A detailed analysis of ciprofloxacin affinity sites within the channels of OmpC is given. On the other hand, this system contains an extremely large number of DOFs and hence applying enhanced sampling techniques is far from trivial. In particular, the convergence of the FESs becomes a critical issue that requires a comprehensive analysis since otherwise the

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results might be meaningless. Thus, we adopt a two-stage strategy in which the FES is first computed in an appropriate CV space to achieve convergence and, then, is reweighted as a function of suitable reaction coordinates to describe the permeation process.

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Background

Before introducing our protocol, it seems in order to briefly review the techniques and algorithms involved. For a detailed description of metadynamics, interested readers are referred to reviews in this field. 43–46

2.1

Metadynamics

Metadynamics 37 is a popular and insightful enhanced sampling method for exploring and quantifying free energy landscapes characterized by several metastable states separated by large energy barriers. In metadynamics, the system evolution is biased by a historydependent potential in a limited number of DOFs often referred to as CVs. From a mathematical point of view, CVs can be defined as functions of the atomic coordinates R, i.e., s(R) = {s1 (R), . . . , sd (R)}. After a transient period, the bias potential compensates the underlying FES and provides an estimate of its dependence on the CVs. In reality, one has to taper off the incremental bias additions to zero to achieve true convergence. This fact was the inspiration for well-tempered metadynamics (WTmetaD). 47 In WTmetaD, the dynamical evolution of the system is altered by the addition of a bias potential that is periodically updated 46

Vn−1 (sn ) Vn (s) = Vn−1 (s) + G(s, sn ) exp − kB ∆T

,

(1)

where the initial value of the bias potential is zero, i.e., V0 (s) = 0, kB denotes the Boltzmann constant and ∆T is an input parameter that determines the enhancement of the fluctuations in CV space. By using a finite value of ∆T , one can automatically limit the exploration of 5



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the CVs to an energy range of the order of kB (T + ∆T ), where T denotes the temperature. Furthermore, G(s, s′ ) is a small repulsive biasing kernel which usually takes the form of a Gaussian localized in s space, i.e., d X (sα − s′α )2 G(s, s ) = w exp − 2δs2α α=1 ′

!

,

(2)

where d denotes the dimension of the CV space, w the energy-valued Gaussian height, and δs = (δs1 , . . . , δsd ) the CV-valued Gaussian widths. In Eq. 1, the update consists of adding a Gaussian hill centered at the current value of the CVs sn scaled down by the factor (sn ) . The latter scaling factor decreases as function of the iteration index n exp − Vn−1 kB ∆T

as 1/n. 47,48 Thereby, the change of the bias potential becomes smaller as the simulation

progresses. The update of the bias potential in Eq. 1 is performed every M MD steps, which corresponds to a time interval of λ = M ∆t, where ∆t denotes the MD time step. Thus, the bias potential at MD time t in the interval λk ≤ t < λ(k + 1) is given by k X

Vn−1 (sn ) V (s, t) = G(s, sn ) exp − kB ∆T n=1

.

(3)

The deposition rate β is defined as the ratio between the Gaussian height and the deposition time, i.e., β = w/λ and is one of the critical parameters to be defined in a metadynamics simulation (see Section 4). The temporal evolution of the bias potential can be described asymptotically by an ordinary differential equation 48,49 with the asymptotic solution

V (s, t) = −

∆T F (s) + c(t), T + ∆T

6


(4)

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where F (s) denotes the free energy and ds exp − FkB(s) T c(t) = kB T log R (s,t) ds exp − F (s)+V kB T R

(5)

is an estimator for the reversible work done by the bias. 50 Two interesting consequences arise from these results. On the one hand, a time-independent FES estimator 50 is given by T + ∆T F (s) = − V (s, t) + kB T log ∆T

Z

ds exp

T + ∆T V (s, t) , kB T ∆T

(6)

where the time dependencies of the first and second terms cancel out after an initial transient period. On the other hand, the expectation value of any R-dependent function can be calculated as the simulation proceeds by means of a mathematically rigorous reweighting procedure. 50 This reweighting is valid after a short transient so that the quasistationary approximation is applicable. In WTmetaD, the quasistationary limit is achieved when the bias potential varies very slowly and uniformly in CV space such that the system is at instantaneous equilibrium under the action of the internal potential and the bias potential. Multiple walker metadynamics 51 is a linear scaling algorithm that enables a significant reduction in the elapsed time necessary to reconstruct a FES. A metadynamics simulation can be interpreted as a walker that moves in CV space and periodically deposits a biasing kernel G(s, s′ ) centered at the current CV value s′ . In multiple walker metadynamics several walkers run in parallel, where each walker contributes to the overall history-dependent potential. It has been shown that the resulting error is the same as that one expected of a single walker using the same Gaussian height and deposition time. 51,52 An upper limit to the number of walkers is given by the diffusion properties of the system and the simulation parameters. 51

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2.2

String method

A reasonable assumption is that substrates will roughly follow pathways of minimal free energy while diffusing across membrane channels. Thus, identifying diffusion routes is very similar to finding minimum free energy paths (MFEPs) on the FES. A MFEP is defined as a curve whose tangent is everywhere parallel to the gradient of the free energy calculated in some appropriate metric. The MFEP has been shown to be able to explain the mechanism of reactions in various non-trivial setups. 39–41,53–56 It should be noted, however, that the MFEP depends on the CVs used for describing the reaction, e.g., the substrate translocation and may ignore non-local features of the free energy. 57 Once the FES is calculated by using the metadynamics method, MFEPs can be computed efficiently on this landscape with the zero-temperature string method in CVs (SMCV). 39,40 Given an initial guess for a curve on the FES, the SMCV finds the closest MFEP by moving a discrete set of points on the curve by the steepest descent on the free energy landscape. At the same time, the points are kept at constant distance from each other. The procedure requires the gradient of the underlying FES, which can be easily estimated by a 3rd-order B-spline interpolation previous to storing the FES on a grid in CV space. Note that no more MD simulations are required at this stage. Further details are provided in the Supporting Information, Section S1.

3

Choice of CVs

The CVs are functions of the atomic coordinates that should be able to describe the key features of the physical behavior behind the process under investigation. Briefly, the CVs represent a sort of coarse description of the system which can be used to analyze a given process in a low dimensional space. A basic requirement for the set of CVs is its ability to distinguish among initial, intermediate and final states. Furthermore, it should ideally include all the slow DOFs, i.e., those DOFs that cannot be satisfactorily sampled in the timescale of the simulation. Hereinafter, slow DOFs that may be not adequately described

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by the chosen CVs are referred to as “hidden” variables (HVs). As previously mentioned, the metadynamics scheme works by using a choice of CVs to iteratively build a bias potential that increases the rate of transitions between metastable energy basins. However, the degree to which a bias can actually promote those transitions depends on how well the CVs capture the true reaction coordinates. When the CVs are imperfect, the numerical results may not approach the true FES as fast as would be desirable. Moreover, the cost of building the bias depends on the complexity of the CVs and scales exponentially with the number of CVs. All enhanced sampling methods that rely on CVs share these drawbacks to some extent. Indeed, the lack of convergence of a FES is often due to a suboptimal choice of CVs rather than the specific choice of the enhanced sampling technique. 45 Let N be the number of atoms in the antibiotic molecule. Due to structural restraints, i.e., bond lengths, bond angles, etc., the molecule in general posses a number of DOFs, ν, which is less than 3N . Three of its DOFs are translational, associated with coordinates specifying the position of its center of mass, three are rotational, associated with coordinates specifying its orientation relative to an external frame of reference, and ν − 6 are internal DOFs associated with coordinates specifying the configuration of the N atoms relative to each other. Assuming that the internal DOFs relax faster than the remaining ones, only six DOFs are, in principle, required in order to specify the position and orientation of the antibiotic. However, even this reduced number of CVs is out of scope of multiple walker WTmetaD since it is very difficult to converge metadynamics simulations using more than two or three CVs. 43–45 Furthermore, analyzing a six-dimensional FES is not a simple task. Inside a channel, the motions perpendicular to the pore axis are highly restricted by the channel walls. As a consequence, one can approximate the antibiotic translation as an onedimensional process and hence considers only one DOF for describing the antibiotic position along the channel axis. In addition, the orientation of the antibiotic can be roughly described by an additional DOF, e.g., the angle between a local antibiotic axis and the channel axis.

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In view of these considerations, we propose two CVs labeled as z and zij (see Fig. 1B). On the one hand, z represents the projection along the pore axis of the center of mass for a set of antibiotic atoms with respect to the center of mass for a set of porin atoms, Nprot Nant 1 X 1 X mi z i , mi z i − z= Mant i=1 Mprot i=1

(7)

PNant where Mant = i=1 mi is the sum of masses for selected antibiotic atoms and Mprot = PNprot i=1 mi is the sum of masses for selected porin atoms. Note that the OmpC porin is

aligned along the z axis and only the atoms from the quinolone moiety and the Cα atoms from porin barrel are selected. On the other hand, let φ represents the antibiotic orientation with respect to the pore axis, −1

φ = cos

zij rij

,

(8)

where rij is the norm of the interatomic vector rij between selected antibiotic atoms and zij its z-component. Specifically, rij is the vector connecting the C atom from the carboxyl group and the N atom from the piperazine ring attached to the quinolone scaffold. Because the distance rij remains almost constant around a value of 8 ˚ A during the simulations, the nonlinear CV φ can be replaced by the linear CV zij . The use of linear CVs is advantageous in metadynamics simulations 58 and enables one to apply the string method in a simple manner (see SI, Section S1). Similar CVs were employed in previous metadynamics simulations for substrate translocation across porins. 59,60 A “good” set of CVs enables crossing the free-energy barriers in a reasonable amount of time and leads to convergence of the FES. Clearly these properties can only be verified a posteriori, thus the choice of the CVs proceeds, in general, through a trial and error process. In our particular case, two different sets of CVs are tested, i.e., z and (z, zij ). It should be stressed that the CV z alone is able to discriminate between initial and final antibiotic translocation states. Moreover, in our simulations the CV z clearly showed to be slower than the rotational modes. 10


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4

Modeling Strategy

As shown in Fig. 2A, the OmpC porin of E. coli is a trimer in which each monomer is a 16-stranded hollow β-barrel. In the constriction region, a strong transversal electric field 59 is created as a consequence of the negatively charged residues on L3 loop (D105, E109 and D113) and the positive charges on the opposite side of the pore wall (K16, R37, R74 and R124) that are separated only by a short distance (see Figs. 2B and 2C). Throughout this work we use a trimeric structure of the OmpC system based on the crystal structure by Baslé et al. 61 (PDB code 2J1N). All amino acids were treated in their standard protonation state except residue D299 that stabilizes the fluctuations of the L3 loop in the constriction region. Unbiased MD simulations were performed to elucidate the effect of different protonation states of residues D299 and D315 on the dynamics of the L3 loop (see SI, Section S2). At pH 7, the ciprofloxacin molecule has a zwitterionic configuration with a zero net charge but a permanent dipole moment (see Fig. 2D). The reported pKa values 62 are 6.1 and 8.7 for the carboxyl and the amino group, respectively. The aromatic quinoline scaffold contains polar fluorine and carbonyl groups as well as a non-polar cyclopropyl ring. A

B

D

C

Extracellular side

-

R124

D113 R124 R74 R37

Loop L3 E109

R74

D105 +

R37

D105

D113

K16 K16

E109

Ciprofloxacin

Periplasmic side

Figure 2: Structural features of the OmpC porin and the ciprofloxacin molecule. (A) Top view of the trimeric OmpC crystal structure 61 (PDB ID: 2J1N) in cartoon representation. (B) Cartoon representation of an OmpC monomer in which the relevant negatively charged (red) and positively charged (blue) residues in the constriction region are highlighted. (C) The negatively charged residues located on L3 loop (D105, E109 and D113) and the positively charged residues located on the opposite barrel wall (K16, R124, R74 and R37) are shown as sticks. (D) 2D structure of ciprofloxacin in its zwitterionic configuration.

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4.1

System preparation

The OmpC trimer was aligned to the z axis and inserted into a pre-equilibrated and fully hydrated POPE (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine) bilayer using the VMD package 63 version 1.9. Subsequently, the system was solvated using TIP3P water and neutralized with 42 K+ cations. The K+ cations were placed on both sides of the simulation box near to the edge in equal number (i.e., 21 K+ in each side). Next, two different systems were created by respectively placing ciprofloxacin molecules on the EC and on the PP side for a given monomer at a distance from the constriction region around 25 and 20 ˚ A (see Fig. 1A). Both systems were composed of 135239 atoms. After an energy minimization, the systems were equilibrated during 1 ns using a NVT ensemble with a time step of 1 fs, where velocity rescaling 64 was used to maintain the temperature at 300 K. During this equilibration, ions, antibiotic and protein atoms were fixed as well as harmonic restraints were applied on the atoms belonging to the water molecules and to the head of the lipids with a force constant of k = 1000 kJ mol-1 nm-2 . Then, the systems were equilibrated during 2 ns using a NPT ensemble with a time step of 1 fs, where a Parrinello-Rahman barostat 65 was employed to maintain the pressure at 1 bar. In this step, a Nosé-Hoover thermostat 66 was also used to maintain the temperature at 300 K and position restraints were imposed on ions, antibiotic and protein atoms with k = 1000 kJ mol-1 nm-2 . Following, systems were further equilibrated during 4 ns using a NPT ensemble as in previous step but with a time step of 2 fs. Next, the systems were equilibrated during 16 ns using a NPT ensemble with a time step of 4 fs and harmonic restraints on ions, antibiotic and protein backbone atoms with k = 1000 kJ mol-1 nm-2 . Subsequently, the time step was increased to 5 fs and equilibration was performed during 20 ns using a NPT ensemble where the rest of the parameters remain unaltered. Finally, an equilibration step was performed during 30 ns using a NPT ensemble with a time step of 5 fs and applying position restraints on ions, antibiotic and protein Cα atoms with k = 50 kJ mol-1 nm-2 . To enable these large time steps (i.e., 4 and 5 fs), virtual hydrogen sites were used for the protein, lipids and the 12


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antibiotic molecule. 67–69 Given the structural similarities between POPE and POPC lipids, the optimized virtual site parameters of the POPC lipid 69 have been used also for the POPE lipid. To further substantiate this assumption, the area per lipid was estimated from three 1D multiple walker WTmetaD simulations and compared with experimental values 70–72 (see Section 4.2). All MD simulations were performed using the GROMACS package, 73 version 5.1.2, and the CHARMM36 force field. 74 For the antibiotic molecule, the initial force field parameters were taken from the CGenFF database 75–77 and optimized using the ffTK toolkit 78 (see SI, Section S3). The cutoff for the short-range electrostatics and the van der Waals interactions was set to 12 ˚ A and the long-range electrostatics interactions were treated using the particlemesh Ewald method 79 with a grid size of 1 ˚ A. All bonds were constrained using the LINCS algorithm. 80

4.2

Multiple walker WTmetaD simulations

Since we are interested in extracting the location and orientation of the antibiotic during the translocation process, an intuitive choice for CVs might be the set (z, zij ) as previously defined. However, multiple walker WTmetaD simulations using this CV space, hereafter referred to as 2D multiple walker WTmetaD, do not achieve proper convergence, mainly for high energy regions belonging to the constriction region of the pore, even after quite long simulation times of , e.g., 8 µs (see SI, Section S4). To circumvent this problem, we have adopted a two-stage strategy. 81 A FES is first obtained by only biasing the CV z in multiple walker WTmetaD simulations, hereafter referred to as 1D multiple walker WTmetaD. Subsequently, the FES is recomputed as a function of CVs z and zij , thanks to the mathematically rigorous reweighting technique by Tiwary and Parrinello. 50 Several parameters have to be chosen in a metadynamics simulation although their selection is non-trivial. First, choosing the tuning temperature ∆T requires balancing a trade-off between fast escape from local metastable states and fast convergence of the overall free 13



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energy estimate. Second, the Gaussians should have a size smaller than the relevant features in the FES. For reducing the computational cost, however, it is convenient to use finite Gaussian widths that fill the FES in a reasonable computational time. Last but not least, a critical choice involves the deposition rate since it affects both the error and the speed at which the free energy basins are filled. 45 On the one hand, it should be small enough so that the system is able to relax between consecutive depositions. On the other hand, it should be sufficiently large to allow a reasonable filling rate of the FES and a proper sampling of the CV space. Fortunately, multiple walkers usually ensure a fast filling albeit using a slow deposition rate. Taking into account these considerations, three independent 1D multiple walker WTmetaD simulations were run by using the parameter values listed in Table 1. The hills deposition stride was set to 4 ps and the Gaussian height to 0.24, 0.72 and 1.20 kcal/mol. Moreover, the K+ cations were restrained using harmonic constraints with a force constant of k = 1000 kJ mol-1 nm-2 to prevent them from entering the pore. In addition, the antibiotic position was restricted inside a monomer (see Fig. 1C) by applying half-harmonic walls with k = 800 kJ mol-1 nm-2 on the x, y and z variables (x and y are defined in the same manner as z in Eq. 7). Some FES artifacts near the boundaries were mitigated using a suggested fix. 82 During simulations, the bias was stored on a grid with a size of 0.01 ˚ A which enables an efficient on the fly estimation of the bias forces using an interpolation method. A total of sixteen walkers were activated in the multiple walker WTmetaD simulations, where the initial position of the ciprofloxacin was located at the EC and PP sides for nine and seven of them, respectively. The asymmetrical initial distribution of walkers is due to the unequal spaces in the vestibules at both ends of each monomer. For each simulation, the total simulation time was set to 4 µs (250 ns for each walker) which corresponds to a deposition of 1 million Gaussian hills. The calculations were carried out by distributing sixteen replicas on sixteen nodes (each containing 12 CPUs). The computational time for each simulation was approximately 1 month. The metadynamics simulations were performed using the PLUMED plugin version 2.2.3 83

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Table 1: Parameters used in 1D multiple walker WTmetaD simulations. δz is the Gaussian width, ∆T is the tuning temperature and β is the deposition rate. Simulation 1 2 3

δz [ ˚ A] 0.1 0.1 0.1

∆T [K] 8700 8700 8700

β [kcal mol−1 ps−1 ] 0.06 0.18 0.30

patched to GROMACS package 73 version 5.1.2. The MD time step was set to 5 fs, thanks to the use of virtual hydrogen sites. 67–69 The estimated values of the area per lipid from ˚2 , are 1D multiple walker WTmetaD simulations, i.e., 56.7±0.9, 57.2±0.9 and 56.8±0.8 A in excellent agreement with reported experimental values of 56.6, 58 and 59-60 ˚ A2 . 70–72 We employed the same forces fields, bond distance constraints and treatment for non-bonded interactions as described in previous subsection.

4.3

Translocation pathway and affinity sites

The free energy landscapes were reweighted in the (z, zij ) space by using the TiwaryParrinello technique 50 as implemented in an in-house code. We define a mesh grid covering the region of interest with a grid size of 0.5 ˚ A and 0.4 ˚ A for CVs z and zij , respectively, in 1D multiple walker WTmetaD simulations. Then, we proceeded to determine the ciprofloxacin translocation pathway as a combination of MFEPs that connect neighboring metastable states (see SI, Section S1). The SMCV 39,40 was implemented in an in-house code (see SI, Section S1). As a consequence of the selected CVs, the metric tensor is independent of the instantaneous values for these variables. Special attention is given to the reproducibility of the translocation pathway as extracted from independent 1D multiple walker WTmetaD simulations. Furthermore, unbiased MD simulations starting from different conformations located along the pathway enable us to characterize in detail several minima and evaluate their metastability. For each energy basin, we selected a representative configuration. Then, four independent unbiased MD simulations were performed during 25 ns using a NVT ensemble, where different initial velocities were assigned to the antibiotic according to the

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analysis of the convergence requires to deal with two main issues. First, one needs to check if the quasistationary limit has been reached successfully. Then, one should assess the degree of convergence of the FES through several complementary indicators. In addition, comparing FES estimates obtained from independent 1D multiple walker WTmetaD simulations enables us to evaluate the accuracy of the results. Rt In Fig. 3A, the scaled time τ (t) = 0 exp (c(t′ )/kB T ) dt′ is depicted as a function of the

simulation time t on a log-log scale for the different 1D multiple walker WTmetaD simu-

lations. In the asymptotic limit t → ∞, one obtains the relation 50 log τ ∼ γ log t, where γ = (T + ∆T )/T is the biasing factor. Here, we focus on log t ranges where log τ exhibits a linear behavior. Linear regressions from these ranges provide slopes whose values are in excellent agreement with the biasing factor γ = 30, i.e., 27.7, 30.0 and 29.9 for the simulations labeled as 1, 2 and 3 in Table 1, respectively. This finding clearly suggests that the quasistationary limit has been reached. Nevertheless, this condition is necessary but not sufficient (zn ) for quasistationarity to hold. Fig. 3C displays the scaling factors exp − Vn−1 applied by kB ∆T

each walker in the CV space during the simulations. The scaling factors decay asymptoti-

cally and approach zero without major oscillations. This means that the bias potential varies very slowly after a transient period and hence also supports the fact that the quasistationary (zn ) limit is reached. In Fig. 3B, we show the scaled heights ωn = w exp − Vn−1 for the last kB ∆T

deposited Gaussians in the CV space. To this end, we split the CV space with a grid size of 0.1 ˚ A. As can be seen, the CV space is almost equally sampled and only small differences are observed in the constriction region (i.e., z ∈ [−5, 5] ˚ A), where the main energy barriers are located (see below). Due to that the quality of the free energy reconstruction could be inferior at these barriers since they are visited with a lower frequency. Therefore, we can conclude that the quasistationary limit is reached in all 1D multiple walker WTmetaD simulations. In Fig. 4A, the time evolution of the CV z for each walker is depicted for the different 1D multiple walker WTmetaD simulations. As can be seen, the entire CV space is explored and

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energy minima are visited many times. Thus, the simulations do not display hysteresis since the bias potential grows evenly. A better sampling is accomplished outside the constriction whilst the main energy barriers are located in this region (see Figs. 4B and 4D). In turn, HVs prevent diffusive exploration of walkers even at long simulation times. The time-independent estimator described in Eq. 6 is appropriate for evaluating the overall convergence of a FES given its validity under the quasistationary assumption. Furthermore, using this estimator we can easily ascertain the local quality of convergence at different positions in the CV space. Fig. 4B shows time-independent FES estimates at several simulation times for the different 1D multiple walker WTmetaD simulations. The discrepancies between consecutive estimates decrease progressively in all cases and an acceptable convergence is achieved between last two estimates at 3 and 4 µs for most of the CV space. In Fig. 4C, we represent the time evolution of the time-independent FES estimates at several z values for the different 1D multiple walker WTmetaD simulations. A reasonable local convergence is attained in the basins located away from the eyelet region at the EC and PP sides but, as expected, is relatively poor at those points located on high-energy regions. In Fig. 4D, we show the FES estimates extracted from the Tiwary-Parrinello reweighting procedure using the CV z at several simulation times for the different 1D multiple walker WTmetaD simulations, as well as time-independent FES estimates at 4 µs. It is worth mentioning that an energy shift is not required to align the reweighted and time-independent FES estimates. A remarkable agreement is achieved among reweighted FESs at different simulation times. This is a clear indicator of a proper convergence for WTmetaD simulations. In addition, a good agreement is also achieved between the reweighted and time-independent estimates, which is also proposed as an additional evidence for convergence. 46 Therefore, these observations indicate a proper overall convergence of the free energy landscapes obtained from different 1D multiple walker WTmetaD simulations. Fig. 5 displays the time-independent and reweighted FES estimates obtained from different 1D multiple walker WTmetaD simulations considering the whole simulation time.

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the CV zij is a “poor” biasing coordinate, as demonstrated by the 2D multiple walker WTmetaD simulations (see SI, Section S4), it is still a good descriptor for the permeation process. Thus, the FES is determined as a function of CVs z and zij by using the reweighting algorithm based on different 1D multiple walker WTmetaD simulations (see Fig. 6A). Under the quasistationary assumption, the reweighing is performed in the limit where log τ exhibits a linear behavior with respect to log t, i.e. from 0.5 µs in all three 1D multiple walker WTmetaD simulations. It is worth mentioning that these reweighted 2D FESs have shown extremely high convergence in all cases (see Fig. S14 in SI). To gain more insight into the diffusion routes, the lowest-energy translocation pathways are estimated for each independent simulation as a combination of MFEPs which connect the EC and PP sides through the constriction region (see Fig. 6A). All these pathways share remarkable similarities. Namely, ciprofloxacin is captured in the mouth of the monomer at the EC side (z ∼ −25 ˚ A) with a conformation in which the amino group is ahead pointing towards the eyelet region. Then, a reorientation of the ciprofloxacin is required in the EC side before reaching the constriction region with its carboxyl group ahead. Despite some discrepancies in the free energy along the different translocation pathways (see Fig. 6B), which are generally more pronounced in high-energy regions, the overall shapes are similar and common energy basins can be identified and labeled in Figs. 6A and B. Unbiased MD simulations starting at conformations of the determined FES minima allow to clarify if these metastable states are real or if they are artifacts of the reduced CV space in the FES calculations. 45 Thus, a critical judgment of the consistency of both biased and unbiased simulations are very important to determine the quality of the results. Furthermore, unbiased MD simulations enable us to move back from the reduced CV space to the full configurational space and, thereby, characterize in detail the antibiotic conformations and the key residues involved in each affinity site. In Fig. 7A, the distribution of ciprofloxacin conformations in the previously identified energy basins are mapped into the (z, zij ) space for the unbiased MD simulations. Since one would expect that unstable states relax to

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stable among them, again consistent with the reweighted FESs. In Fig. 7B, representative ciprofloxacin conformations are depicted for the different energy basins, which enable us to extract the main features of the translocation pathway in the Euclidean space. Significantly, two conformations are available when approaching the constriction region from the EC side, e.g., minima 3 and 3b. In basin 3b, the carboxyl group remains at roughly the same position as in basin 2 while the amino group flips facing to L3 loop. In basin 3, the carboxyl group moves facing to L3 loop while the amino group remains at a similar position as in basin 2. The results strongly suggest that ciprofloxacin is crossing the eyelet region mainly starting from basin 3. To further substantiate this claim, we performed additional 1D multiple walker WTmetaD simulations in drastically restricted regions of the CV space, which provides an additional evidence that ciprofloxacin needs to overcome a higher barrier when following a pathway that includes basin 3b (see SI, Section S5). By means of a detailed analysis of the trajectories generated by unbiased MD simulations, we are able to identify the main residues and characterize the interactions involved in the affinity sites associated with each energy basin. Table 2 summarizes this information and Fig. 8 shows representative snapshots for each affinity site. As expected, due to the presence of the polar function groups on the ciprofloxacin molecule, very high number of the salt bridges and hydrogen bonds were observed with pore interior residues in each minima. Moreover, some remarkable issues deserve special attention. First, π-stacking interactions between the benzene ring of ciprofloxacin and some aromatic residues are present at the affinity sites for basins 1 and 3. Interestingly, similar interactions have been found in a different context, i.e., between ciprofloxacin and other quinolones and DNA bases, 86 which play a critical role in the target mechanism of these antibiotics. Furthermore and significantly, the counterpart residues F161, Y211 and W72 are missing in the porin OmpF which implies that these affinity sites are specific for the OmpC porin (see Fig. S15 in SI). Second, the affinity site for the basin 2 requires some residues belonging to the loops L2 and L4 from the neighboring monomers. Therefore, a cooperative effect among different monomers exists

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Table 2: Summary of the some of the prominent interactions observed between the ciprofloxacin functional groups and the OmpC residues in each energy basin. The star symbol * denotes residues in which the backbone atoms take part in the interactions. Energy basin 1

2

Interaction types

Ciprofloxacin interacting groups

Porin residues

Salt bridges Hydrogen bonds

-NH+ 2 −

E68, D171 T208 N155 F161, Y211 P156, A205, A210 E159 (Loop L4, monomer 3) R174, R246 S157 (loop L4, monomer 3) N67 (Loop L2, monomer 2) E109 R174, R246 Y22 S117 R124 N63, N70 Q59 W72 D113 R74, R124 Q123 D113 R37, R74 F110∗ , G111∗ , G112∗ R37, R74 D105 L107∗ Q55 Y94, Y98 K308 D105 D105∗ , L107∗ , P108∗ Q345 Y305 K308 R272 Y305

π-stacking Hydrophobic contact Salt bridges Hydrogen bonds

3b


3


4

π-stacking Salt bridges

5

Hydrogen bonds Salt bridges Hydrogen bonds

6

7

Salt bridges Hydrogen bonds Hydrophobic contact Salt bridges Hydrogen bonds

8

π-stacking Salt bridges Cation-π interactions Hydrophobic contact

-COO -CO Quinoline ring Quinoline, cyclopropyl and piperazinyl rings -NH+ 2 -COO− -NH+ 2 -F -NH+ 2 -COO− -NH+ 2 -F -COO− -NH+ 2 -CO Quinoline ring -NH+ 2 -COO− -COO− -NH+ 2 -COO− -NH+ 2 -CO -NH+ 2 -NH+ 2 -COO− Cyclopropyl ring -COO− -NH+ 2 -NH+ 2 -CO Quinoline ring -COO− Quinoline ring Cyclopropyl ring

that stabilizes the basin 2. Compared to OmpF, L4 loop is substantially longer in OmpC by 14 amino acids, 61 which enables it to bend over to a neighboring monomer and there to form a salt-bridge with the ciprofloxacin molecules. Third, the affinity site at basin 4 exhibits a dipole orientation of ciprofloxacin similar to that known from a crystal structure involving the similar OmpF porin in the bacterium S. typhi bacterium (PDB ID: 4KRA, see Fig. S15 in SI). Finally, we observe cation-π interactions between the quinolone ring and residues R272 and Q266 in the affinity site of basin 8. These interactions are common 26


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between aromatic and polar residues in proteins. 87

6

Conclusions

A computational protocol has been established in this study which enables us to characterize antibiotic permeation pathways through OM channels. By combining metadynamics and the string method, we are able to describe the primary features of ciprofloxacin translocation across the porin OmpC, such as a cooperative effect among different monomers and some specific interactions between ciprofloxacin and the porin that are absent in the counterpart OmpF. We found that the lowest-energy multi-well and multi-barrier pathway requires a reorientation of ciprofloxacin in the EC side before reaching the constriction region with its carboxyl group ahead. Several affinity sites were identified along this ciprofloxacin pathway. Such a detailed understanding is potentially very helpful in guiding the development of next generation antibiotics since the passage of the outer membrane has been identified as a major problem in the activity of antibiotics. 88–90 The results can potentially be tested experimentally in electrophysiology by either mutagenesis of the porin or by chemical modifications of the ciprofloxacin molecule. To this end, most of the residues listed in Table 2 will show an effect, e.g., those residues in the arginine ladder or residues in salt bridges and π-stacking interactions. Concerning chemical modifications of the drug, changes in the carboxyl group should lead to clear effects in the translocation properties though these modifications might also change the binding to the target site leading to a less potent drug. Moreover, we would like to highlight the extensive sampling performed in the present study with different biased and unbiased MD simulations, which is not very commonly done for a system of such complexity. The results reported here represent a total simulation time of ∼ 31.6 µs in production run when adding all unbiased MD and metadynamics trajectories. The consistent nature of the conclusions further increase the confidence in the use of the protocol described in this work for studying the antibiotic permeation routes across

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membrane pores. In this study, the OmpC porin was embedded into a symmetric bilayer composed of POPE lipids. However, the OM of Gram-negative bacteria mainly contains lipopolysaccharides (LPS) molecules in its outer leaflet. Because our main goal was to characterize ciprofloxacin permeation pathways for the most part inside of an OmpC monomer, minor effects are expected from the use of LPS molecules 91 as direct interactions with the membrane are nonexistent. Nevertheless, it has been shown that LPS molecules restrain the dynamics of some extracellular loops 91–93 and play a critical role in the substrate diffusion while approaching the entrance of the pore. 91,94 Further MD simulations will be needed to elaborate the LPS-mediated effects on the antibiotics permeation. Several questions remain open which need to be addressed in future investigations, such as the influence of various physiologically relevant ionic salts, e.g., NaCl, KCl and MgCl2 and of the transmembrane potential. 95–97 For a 0.3 M KCl salt solution it was recently shown that the rate of permeation of β-lactam antibiotics and lactose across the OmpC porin increases to a level comparable to that of the OmpF porin . 97 It was argued that the addition of a salt might disrupt the otherwise strong interactions between water molecules and some charged pore residues. Furthermore, the effect of divalent ions such as Mg2+ might be relevant due to their capability to form stable complexes with fluoroquinolones and acidic residues in the channel lumen. 21,61,86,98–100 In particular, the binding between divalent cations and pore residues have been shown to drastically change the ion selectivity in the OmpF porin 21 and in the CymA channel from K. oxytoca, 101 and thereby also leading to a drastic changes in the permeation rate of molecules. In addition, the effect of the so-called electroosmotic flow induced by ions on the substrate transport needs to be investigated in more detail. 101 Last but not least, comparative studies using different quinolones and porins would be very useful in order to establish general and specific features in the permeation process.

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Acknowledgement We thank Prof. Matteo Ceccarelli for help in setting up the initial metadynamics simulations and for pointing out the cooperative effects between the monomers in OmpC. The research leading to these results was conducted as part of the Translocation consortium (www.translocation.eu) and has received support from the Innovative Medicines Joint Undertaking under Grant Agreement No. 115525, resources which are composed of financial contribution from the European Unions seventh framework programme (FP7/2007- 2013) and EFPIA companies in kind contribution.

Supporting Information Available Supporting figures on computational results are available together with details on the string method and on the force fields for the antibiotics molecules. This information is available free of charge via the Internet at http://pubs.acs.org.

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Characterization of Ciprofloxacin Permeation Pathways across the

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