High-resolution experimental and computational electrophysiology reveals weak β-lactam binding events in the porin PorB

The permeation of most antibiotics through the outer membrane of Gram-negative bacteria occurs through porin channels. To design drugs with increased activity against Gram-negative bacteria in the face of the antibiotic resistance crisis, the strict constraints on the physicochemical properties of the permeants imposed by these channels must be better understood. Here we show that a combination of high-resolution electrophysiology, new noise-filtering analysis protocols and atomistic biomolecular simulations reveals weak binding events between the β-lactam antibiotic ampicillin and the porin PorB from the pathogenic bacterium Neisseria meningitidis. In particular, an asymmetry often seen in the electrophysiological characteristics of ligand-bound channels is utilised to characterise the binding site and molecular interactions in detail, based on the principles of electro-osmotic flow through the channel. Our results provide a rationale for the determinants that govern the binding and permeation of zwitterionic antibiotics in porin channels.

For electrophysiological measurements in the presence of ampicillin including the corresponding control experiments, BLMs were used. BLMs were prepared by adding 1-2 µL of lipids (DPhPC/cholesterol, 9:1) dissolved in n-decane (30 mg/mL) to an aperture (d = 50 µm) in a PTFE foil (DF100 cast film, Saint-Gobain Performance Plastics, Rochdale, Great Britain) fixed between two cylindrical PTFE-chambers filled with 3.0 mL buffer (1 M KCl, 10 mM HEPES, pH 7.5 or pH 6). Protein was added to the cis chamber and inserted by stirring at an applied DC potential of +40 mV. After protein insertion, ampicillin was added from a stock solution (25 mM in 1 M KCl, 10 mM HEPES, pH 7.5 or pH 6.0) to both sides of the BLM. For control experiments, ampicillin was added only to the trans side. Current traces were recorded at a sampling rate of 50 kHz and filtered at 5 kHz.
Analysis of current traces in the presence of ampicillin. Model-free idealizations are obtained by JULES. 2 Its combination of multiresolution techniques and local deconvolution allows a precise idealization of events below the filter length, in particular amplitudes and residence times that are smoothed by the filter are reconstructed with high precision (Fig. S3). In this manner, JULES extends the model-free idealization method JSMURF 3 to scales below the filter length. The idealized blockage supports a two state Markov model. The conductance losses by blocking a single channel are determined by Gaussian fits of the amplitudes. Residence times and frequencies are determined by fitting the Markov model taking missed events into account. An analysis with a new Hidden Markov model approach, which is able to take the lowpass Bessel filter explicitly into account, confirms these results.

Technical details of the statistical analysis
Idealizations. Model-free idealizations are obtained by JULES (JUmp Local dEcovolution Segmentation filter) 2 by calling the R-function jules in the package clampSeg (https://CRAN.R-project.org/package=clampSeg) with default parameters. Its combination of multiresolution techniques and local deconvolution allows a precise idealization of events below the filter length, in particular amplitudes and residence times that are smoothed by the filter are reconstructed with high precision (Fig. S3B).
For comparison, idealizations using a discrete time Hidden Markov model (HMM) taking into account the filter are obtained. The Markov assumption is confirmed (see below). In a pre-processing step, artifacts caused by the electronics, fluctuations on large time scales and outliers are removed. For the HMM the following parameters are used: A digital filter of length six approximating the used Bessel filter, the amplitude found by JULES, 2 a fluctuating base line given by local medians and a global variance computed by sdrobnorm (stepR package, https://CRAN.R-project.org/package=stepR). A new forward algorithm 4 is used to learn the transition matrix based on a likelihood approach. The final idealizations are obtained by a Viterbi algorithm. In order to cope with the discrete filter, both procedures use a meta state space, resulting in 2 6 states. Code is available on request.
Missed events. Simulations show that JULES detects events with residence times of at least 80 µs with probability almost one at the worst signal to noise ratio. Hence, the analysis is based on detected events between 80 -200 µs, since some shorter events are missed and some larger events might be rare gating events of the channel itself and not ampicillin blockage.
The event histograms of the idealized amplitudes, i.e., the difference of the conductance levels of the open and blocked channel, show one well-separated peak not found in the absence of ampicillin ( Fig. 1). All other events are neglected as they cannot be associated with the ampicillin blockage. For visualization, additional kernel density fits with Gauss kernel and bandwidth 0.05 by the Rfunction bkde in the package KernSmooth (https://CRAN.Rproject.org/package=KernSmooth) are shown. The conductance losses by ampicillin blockage are determined by Gauss fits.
The HMM approach is able to detect events with residence time of at least 20 µs corresponding to one sample point, but detects in addition artifacts of a length of one and two sample points. Therefore, only events of at least three sampling points in length are included in the analysis. To compensate for this, for both approaches the later analysis has to take into account missed events.
Confirmation of the Markov model. The events detected by JULES with a length between 80 -200 µs are used to explore the dwell times, i.e., the residence times and the times between two blockage events. Their occurrence decreases exponentially in their duration, see exemplary the histogram of the residence S5 times in Fig. S3C. Note that for visualization purposes the exponential fit is rescaled such that the surface under the curve in the shown range is one as it is for the histogram. Moreover, Fig. S4 shows uncorrelated dwell times. Together with the exponential decay this supports a Markov assumption. FIGURE S4. Empirical autocorrelation between the idealized dwell times, i.e., residence times and time between two events. The correlations close to zero support a Markov model.

Residence times and frequencies.
The average residence time is calculated for both approaches via maximization of their corresponding likelihood assuming an exponential decay and a missing of events as described above. Maximization is performed by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, 5 using the R-function optim. The Markov model assumption allows determination of the ampicillin blockage frequency for a single channel. To this end, the observed distances between two events are multiplied with the probability that an event is not missed and with the number of channels. The frequencies are obtained by the inverse of the mean of these rescaled times. The number of channels is calculated by dividing the conductance without blockage by the amplitude of a blockage, both determined by Gaussian fits.
Additionally, 95%-confidence intervals are computed for the residence times (Fig.  S5A) by a normal approximation and for the frequencies (Fig. S5B) by an exact confidence interval. For illustration, we report standard deviations for the averaged residence times and frequencies (Fig. S5A), but note that no significance statements can be drawn from these intervals. We stress that the averaged residence times and frequencies based on JULES and the HMM approach were always close to each other and lead in all cases to the same conclusions, as illustrated in Fig. S5. System set up. PorB was modelled using the X-ray structure obtained by Kattner et al. (PDB entry 3VY8). 9 PorB trimers were embedded into a preequilibrated 160×160 Å 2 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer accounting for 942 POPC molecules. A 25 Å layer of SPC/E water molecules was set up at both sides of the bilayer, and Na + and Clwere added to achieve an ionic strength of 1 M. GROMACS utility membed 12,13 was used to embed PorB trimers into a POPC bilayer. The aqueous solution consisted of about 57000 water molecules and 1866 Na + and 1896 Clions in both the apo and ampicillin bound system. The Parm99SB force field, 14,15 and virtual sites for hydrogen atoms 16 were used for the protein. The POPC molecules were parameterized according to the lipid parameters derived by Berger et al., 15,17 the SPC/E water model was used to model water molecules 18 and Joung and Cheatham parameters 19 were used to model the counter ions. The zwitterionic ampicillin molecule was parameterized using the gaff force field 20 in conjunction with RESP (HF/6-31G(d)) charges 21 as implemented in the Antechamber module of the AMBER12 software package. 22 Molecular dynamics simulations. Molecular simulations were carried out with the GROMACS molecular dynamics package, version 5.1.5. 23 For each system, the geometry was minimized in four cycles that combined 3500 steps of steepest descent algorithm followed by 4500 of conjugate gradient. Thermalization of the system was performed in 6 steps of 5 ns; each step gradually increased the temperature form 50 K to 320 K, while the protein was restrained with a force constant of 10 kJ mol -1 Å -2 . The systems were equilibrated for 100 ns keeping the protein restrained. Production runs accounted of 200 ns-long trajectories. The temperature was kept constant by weakly coupling (t = 0.1 ps) the membrane, protein, and solvent separately to a temperature bath of 320 K with the velocityrescale thermostat of Bussi et al. 24 The slightly higher temperature was chosen to ensure that the membrane remains in a fluid phase. The pressure was kept constant at 1 bar using semi-isotropic Berendsen coupling. 25 Long-range electrostatic interactions were calculated using the smooth particle mesh Ewald method 26 beyond a short-range Coulomb cut-off of 10 Å. A 10 Å cut-off was also set for Lennard-Jones interactions. The LINCS algorithm 27 was used to restrain the system and the SETTLE algorithm 28 was used to constrain bond lengths and angles of water molecules. Periodic boundary conditions were applied. Taking advantage of the Berger lipid model and the virtual sites, the integration time-step was set to 4 fs.
Computational Electrophysiology simulations (CompEL). Each system was duplicated along the z-axis to construct a double bilayer system, and ionic imbalances from 4, 8 and 12 Na + were used between the aqueous compartments to generate a range of transmembrane potentials as from ± 130, ± 350 and ± 500 mV, as previously described by Kutzner et al. 29 Production runs accounted of 200 ns-long trajectories for the apo systems and 400ns-long trajectories for the ampicillin-bound systems. The applied membrane potential was calculated using the GROMACS utility gmx potential overlapping 20-ns time windows. Following the protocol outlined in Kutzner et al. 29 , conductance (G) calculations (G = I/ΔU) were based on the observed ion current I, as a function of the potential difference ΔU between the compartments. Since potential and flux are time-dependent, ΔU(t) and I(t) were determined within 20-ns time windows (with a 10-ns overlap among consecutive windows) in the case of apo PorB and within 50-ns windows (with 25-ns overlap among consecutive windows) for ampicillin bound PorB simulations. The longer windows in the latter case were used in order to improve sampling in these lower-conductance situations.
Analysis of the molecular dynamics trajectories. MDAnalysis 30 and MDtraj 31 were used to analyze RMSD, distances, flux of water molecules and computational conductance values.