Predicting the transport of small-molecules through nanopores
Patent Information
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- UNIV DEGLI STUDI DI CAGLIARI
- Filing Date
- 2024-06-26
- Publication Date
- 2026-04-29
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Abstract
Description
[0001]P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI PREDICTING THE TRANSPORT OF SMALL-MOLECULES THROUGH NANOPORES DESCRIPTION FIELD OF INVENTION The present invention relates to a method for determining the permeability score of a molecule used as a biocompatible carrier for transporting an active ingredient, preferably a drug. BACKGROUND OF INVENTION Resistant bacterial infections are a significant global health problem, and without concrete action and strong public innovation, we risk returning to the "pre- antibiotic" era. Gram-negative bacteria, i.e., that category of bacteria that exhibit particular resistance to many classes of antibiotics, owe this meant intrinsic resistance due to the presence of an outer membrane (OM), which imposes a physical barrier that limits the range of molecules that are absorbed by the bacteria by protecting the bacterial cell from substances that are toxic to it. Porins and protein channels in the OM control permeation to small water-soluble molecules, that is, to most currently available antibiotics and inhibitors. The experimental techniques to assess permeation of molecules are neither direct nor robust. This has been recognized as a contributing factor to P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI the difficulty of finding new potent antibacterial agents that act against these organisms. Analyses of compounds with antibacterial activity have shown that antibiotics and their analogs on the market that act against Gram-negative bacteria have narrow ranges of physicochemical properties (e.g., size and lyophilicity), although broader ranges of properties have been observed for compounds that act through nonspecific mechanisms, e.g., membrane disruption. However, emphasis on molecular properties alone is not sufficient to provide clear and determinative rules for the transport of a molecule across the outer membrane of a Gram-negative bacterium. The possibility of sequencing the bacterial genome has shown hundreds of potential new targets and stimulated large pharmaceutical companies to perform high-throughput screening (HTS) that has very high costs but allows the identification of compounds with high efficacy on selected potential targets. However, this classical approach has not been able to produce compounds belonging to truly new classes to combat Gram-negative bacteria and counteract the continuing emergence of resistance by an increasing number of strains that, in some cases, are now resistant to all currently available antibacterials. Acosta-Gutierrez Silvia et al. ‘Getting drugs into Gram- negative bacteria: rotational rules for permeation through general porins” DOI, 10.1021 / acsinfecdis.8b00108 and Acosta-Gutierrez Silvia et al. ‘The influence of permeability though bacterial porins in whole-cell 10.3390 / antibiotics10060635 P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI and Vergalli Julia et al. ‘Porins and small-molecule translocation across the outer membrane of Gram-negative bacteria’ DOI, 10.1038 / S41579-019-0294-2 disclose a permeability model where steric parameters and electrostatic parameters are independent from one another. This causes a relatively low accuracy when predicting experimental permeability of a molecule across the outer membrane of a Gram negative bacterium. Ferreira Ricardo J. et al. ‘Antibiotic uptake across Gram- negative outer membranes: better predictions towards better antibiotics’ DOI, 10.10121 / acsinfecdis.9b00201 discloses a prediction of permeability based on Gibb’s free energy. The latter requires the calculation of enthalpy and entropy of the system; and focuses on the difference between such entropy and enthalpy. Having both enthalpy and entropy a large magnitude, the corresponding difference is heavily affected by small calculation errors. Often, when prediction of permeability is involved, the calculation error is of the same order of magnitude as the difference between enthalpy and entropy, making free energy estimation suffer from large errors. Ropponen Henni-Karoliina et al. ‘Mastering the Gram- negative bacterial barrier – Chemical approaches to increase bacterial bioavailability of antibiotics’ DOI, 10.1016 / J.ADDR.2021.02.014 is a review comprising features in common with the first three papers mentioned above, combined with a machine learning algorithm. Such document explicitly states that the approach is blind to synergistic patterns of physicochemical parameters. P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI SUMMARY OF THE INVENTION The permeation feature is typically overlooked in new drug development campaigns. Instead, the key concept is precisely this feature that for a given molecule, used as a carrier for transporting an active ingredient such as a drug, allows more or less effective passage through the outer membrane of a Gram-negative bacterium. The greater the permeability of the carrier molecule, the greater the overall effectiveness of the transported active ingredient will therefore be. The purpose of the present invention is to provide a predictive method of a permeability score, reliable and rapid, to be implemented as a screening tool on virtual compound databases that carries undoubted advantages and numerous application possibilities. First, it could be a valuable tool to guide the optimization of compounds already identified for their efficacy on the isolated target but suffering from a low permeability score (hit to lead and lead optimization processes). By comparing in-silico, thus with very low cost and extreme speed, hundreds of possible analogs, it would be possible to identify the most promising candidates on which to focus the synthesis and testing efforts of subsequent development phases. Moreover, screening large databases of compounds belonging to different molecular classes would allow from the earliest stages of development to focus attention on molecular scaffolds with good permeation capacity, and only then screen against efficacy on target. P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI From this perspective, another application of particular interest is the possibility of creating a large library of compounds endowed with a high permeability coefficient across the outer membrane of Gram-negative bacteria, so that they can later be developed as carriers of molecules already known to be effective on the isolated target but having a low penetration capacity. Such a prediction tool would ultimately reduce costs and increase the speed of the discovery and development process of new antibiotics specific to Gram-negative bacteria, thereby increasing laboratory productivity. The purpose of the present invention is achieved by a computer implemented method for determining the permeability of a carrier molecule for transporting a drug active agent, comprising the steps of: - defining or receiving a mathematical model based on the average size and fluctuations of a pore of the constriction region of a Gram-negative bacterial cell chosen as a reference, the size and fluctuations of the molecule whose permeability value is to be calculated, the electrostatic interactions of the molecule with the pore of the channel within the bacterial cell outer membrane, through the electrostatic potential and electric field , which interact with the charge and dipole of the molecule, respectively; - applying said mathematical model to a molecule whose permeability is known within the reference Gram-negative bacterial cell chosen as a reference representative of the P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI permeability of the known molecule; - selecting a candidate vector molecule whose permeability within the gram-negative bacterial cell chosen as a reference should be calculated; - calculating the size of the candidate molecule; - calculating the fluctuation associated with said calculated size; - calculating the electrostatic potential and electric field of the pore of the bacterial cell chosen; - calculating the charge and electric dipole of the candidate molecule; - applying said mathematical model to the vector molecule to obtain a second parameter representative of the candidate molecule's permeability; - comparing said first and second parameters to estimate the permeability of the candidate molecule within the reference Gram-negative bacterial cell chosen. The method according to the present invention enables screening of virtual databases of compounds belonging to different molecular classes to identify those molecules having a good permeability coefficient on which to focus the efforts of subsequent development steps. The method according to the present invention enables optimization of compounds that have already been identified for their efficacy on the target bacterial cell but have a low permeability coefficient, with the advantage of reduced cost and research time. of the present invention P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI enables the identification of potential candidate carrier molecules to bring in bacterial cells a compound having a low in-silico permeability coefficient. BRIEF DESCRIPTION OF THE DRAWINGS The present invention is hereafter further explained in some of its preferred forms of practical embodiment, shown for illustrative and non-limiting purposes only, with reference to the attached tables of drawings, in which: − Figure 1 shows a schematic representation of Gram- positive and Gram-Negative cell envelop; − Figure 2 shows a table of OmpF / C orthologues physical properties of different porins from the Enterobacteriaceae family; − Figure 3 shows Molecular structure of the nine clinically relevant antibiotics used in the study; − Figure 4 shows relative permeability of β-lactams through OmpF / C orthologues. Permeation rates determined from LSA experiments; − Figure 5 shows modulation of the total barrier for permeation. Figure 5(a) is an all-atom representation of the permeation of a small molecule through one OmpF (ribbons) monomer. Figure 5(b) is a schematic representation of the relevant descriptors for the scoring function. Figure 5(c) is an energetic decomposition of the total free-energy barrier faced by P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI small molecules during permeation through porins; − Figure 6 shows measured versus predicted permeability of antibiotics through Gram-negative bacterial porins. DETAILED DESCRIPTION OF THE INVENTION Due to widespread misuse, at least one resistant bacterial strain has been identified for almost all antibacterial drugs developed to date, and the number of multi-resistant isolates is steadily increasing. It is therefore increasingly difficult to find new molecular classes that are effective in acting against these organisms, aggravated by a gradual decline in private investment due to the fact that research campaigns for new antibiotics are characterized by high costs and a high risk of nonachievement. There are many fundamental gaps in our knowledge about antibiotics, such as their mode of action in many cases, the actual penetration pathway into the pathogen and the mechanisms adopted by the pathogen to actively pump them out or, in general, to develop resistance. Libraries of compounds used within high-throughput screening protocols to identify novel drug scaffolds are now recognized to be biased. This is due to the selection rules applied to the chemical– physical properties of the compounds included in such libraries, which are often blindly directed towards oral and / or injectable administration. These rules do not necessarily match with other fundamental requirements for a good antibiotic. Conversely, high- throughput screening would definitely be improved by taking P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI into account ‘rules for good antibiotics’, but these general rules still have to be discovered. This is the main innovation-gap that has to be filled to renew the screening platforms, together with leaving the search for a novel broad-spectrum class of antibiotics, but focusing on case- specific goals. In the case of Gram-negative bacteria, the problem of resistance is particularly urgent for different Gram- negative species. Infections from methicillinresistant Staphylococcus aureus (MRSA, Gram + strains resistant to methicillin) strains, for instance, are very difficult to treat but still affordable with glycopeptides like vancomycin and teicoplanin (which are not active against Gram-negative strains, on the other hand). Even against vancomycin-resistant strains, VRSA, daptomycin and linezolid are available. Conversely, multi-drug resistant Gram-negative species, such as Acinetobacter baumannii, Enterobacter spp., Enterococcus faecium, Klebsiella pneumoniae and Pseudomonas aeruginosa are responsible for many serious infections in hospitals, where cases of resistance to all the available drugs have already been reported, including the highly toxic colistin, which is usually considered as the last resort. As shown in Fig. 1, both Gram-positive and -negative bacteria have an inner plasma-membrane protecting their interior, but the latter are characterized by a second protective membrane, the outer membrane OM. The presence of the OM provides Gram-negative bacteria with a very effective intrinsic resistance mechanism, with P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI its permeability properties playing an essential role in their susceptibility to antibiotics. The observation of drug resistance in a large number of species characterized by modifications in the protein or lipid OM composition bolsters the importance of the OM in antibiotic sensitivity. The passive resistance mechanism offered by the presence of the OM is thus additional to the so-called acquired and adaptive resistance, which is basically due to the incorporation of new genetic material or a mutation, ultimately resulting in modified proteins and protein expression levels. While the permeability of the membrane inner core to small hydrophobic molecules is known, Gram-negative bacteria are usually not susceptible to hydrophobic antibiotics like actinomycin D, macrolides or novobiocin. Thus, OM is a very efficient barrier for antibiotics. Generally speaking, by slowing the permeation rate into the periplasmic space, Gram-negative bacteria have to neutralize the threat of a drug whose concentration is several orders of magnitude lower when compared to the extracellular concentration. Porins as main gates for polar compounds Porins are typically arranged in the OM either as homotrimers or monomers, with a basic β-barrel folding, which forms a transmembrane water-filled pore, where the narrower central region (constriction region, CR) provides a steric-type barrier to the passage of any substance. Porins are needed to reduce OM impermeability to hydrophilic compounds, and are recognized as the main route P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI for the entry of antibiotics with a polar character, such as many beta-lactams and some fluoroquinolones. It was shown, in a past combined experimental / computational study, that a polar character drives the antibiotic through the porin pathway, while more hydrophobic antibiotics prefer to diffuse through the membrane itself. Fluoroquinolones, similar to other antibiotics, can adopt different charged (protonation) states depending on the pH, such that under certain conditions they are able to pass through the membrane or exploit the presence of water-filled pores. The majority of hydrophilic antibiotics do make use of the latter to penetrate and eventually reach their intracellular targets. Thus, it is not surprising to find porin mutations as a marker of numerous resistant bacterial strains, especially from Klebsiella pneumoniae. Usually, Escherichia coli is taken as prototypical example for enter Gram-negative bacteria. The two major porins are the trimeric OmpF and OmpC. Although these two porins both share a remarkably similar structure and have a high sequence similarity, their pore size is different, with OmpC being narrower than OmpF. The observation that growth conditions alter the level of expression of these two porins led to the conclusion that pore size was probably the most important feature that determines channel permeability. However, computational and experimental evidence is being gathered that points to the role played by internal electrostatics. It is important to note here that the relative expression of porins is subject to change by varying the P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI environmental composition. This applies not only to nutrients but also to antibiotics. Indeed, one of the strategies adopted by Gram-negative bacteria to resist antibiotic threat is to reduce the expression of the most permeable porins while guaranteeing the uptake of nutrients by the overexpression of other channels. The OM of these bacteria is characterized by the presence of a variety of porins that are specialized for the uptake of the different nutrients needed for growth and survival. The OM can offer a variety of resistance mechanisms for Gram-negative bacteria, all of which are basically oriented to antibiotic reduced permeation. These include the reduced expression of wild-type porins, the expression of restricted and more selective channels, the expression of mutated porins with altered physico– chemical properties, and the synthesis of channel blockers. The very first step in the action of every antibiotic is the permeation through the outer membrane. Our studies focused on characterizing the structure and physicochemical properties of porins, the generic protein channels located in the outer membrane of Gram-negative bacteria, which are responsible for the fine regulation of the uptake of small hydrophilic metabolites and therefore function as nonspecific channels for the passive diffusion of drugs across the OM. Experimental and computational evidence showed the strong role of internal channel electrostatics. In particular, the constriction region CR shows marked segregation of electrical charge. Despite efforts, no P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI obvious correlation between permeation and any of the molecular properties such as size, net charge, hydrophobicity or number of hydrogen bond donors / acceptors had been shown. Our studies focused on the OmpF and OmpC of 4 different Enterobacteriaceae (E. coli, E. cloacae, E. aerogenes and K. pneumoniae), finding remarkable similarity also regarding the energy profile of antibiotic passage of different classes. Porins architecture The crystal structures of OmpF and OmpC orthologues from Enterobacter aerogenes (Omp35 and Omp36), Enterobacter cloacae (OmpE35), and Klebsiella pneumoniae (OmpK35 and OmpK36), E. cloacae OmpE36, E. coli orthologues are known. The porins share on average ∼70% sequence identity as shown in Table of Fig 2. The overall structures are very similar and consist of trimers of 16-stranded β-barrels, each with a constriction region CR halfway down the central axis formed by the extracellular loop L3. The segregation of charged residues on opposite sides of the internal walls creates a strong transverse electric field that plays an important role in stabilizing the desolvated form of polar molecules, thereby aiding their translocation. The acidic residues from the constriction region CR of OmpF (Figure 1b), D113, E117, D121 from L3, are conserved in all structures , while some differences were found for the residues forming the basic ladder on the opposing face, presumably modulating the transverse field in the different orthologues. Structural Determinants for Permeability P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI We modeled each porin in trimeric state embedded in a pre-equilibrated phospholipid bilayer (POPC) with a 200 mM KCl bath solution and performed all-atom MD simulations. We calculated the average geometrical cross-section and the average internal electrostatic field28 and potential from 600 ns-long trajectories. As expected, the pore radii decrease dramatically in the CR. The intensity of the internal electric field is stronger at the constriction region CR and perpendicular to the axis of diffusion (transversal component). In contrast, the longitudinal component is negligible in the constriction region CR for all structures. Despite the structural similarities, we found substantial differences between the calculated electric fields. OmpC and orthologues Omp36, OmpE36, OmpK36 possess a smaller pore radius, lower conductance, and a lower intensity of the transversal electric field compared to OmpF and orthologues Omp35, OmpE35, OmpK35 (crf. Fig.2). Further, the OmpC-like proteins are more cation-selective than OmpF- like (crf. Fig.2). Experimental Determination of Permeability Our working hypothesis is to describe translocation from a microscopic point of view. A complex multi-step process in which reorientation and optimal substrate alignment within the (hourglass-shaped) channel are the main aspects. The corresponding energy terms that can therefore describe the interaction between drug and channel are essentially steric hindrance and electrostatic interaction. We have shown that the central steric barrier can be offset by favorable electrostatic interactions, lowering the overall energy barrier to translocation and actually P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI increasing substrate flux through the protein channel. For a set of selected compounds and channels, the permeability coefficient, and thus the flux of molecules, can be quantified by evaluating the free energy barrier with molecular dynamics simulations at an atomic level of detail. However, this approach is computationally expensive even applying advanced sampling and acceleration techniques, but in fact impractical for rapid screening of large databases. Therefore, the innovation we propose is to replace the costly evaluation of the free energy barrier with an appropriately parameterized predictive function (FP) in which several interaction terms concur to define the overall permeability based on the chemical and physical characteristics of both the channel and substrate. The energy terms we propose are in fact simple functions of basic molecular properties such as size, electric dipole and electric charge, as far as the substrate is concerned, cross- sectional area profile, electrostatic potential and electric field, as far as the channel is concerned. The latter require relatively inexpensive molecular dynamics simulations and post-analysis in computational terms, which are the basic characterization needed. While substrate parameters can be easily obtained through bioinformatics tools widely recognized and used by the scientific community and pharmaceutical companies. Liposome swelling assay (LSA) was selected to measure permeability of molecules through porins. The permeability of nine clinically relevant antibiotics (Figure 3) through eight distinct channels (Figure 4) provides a data set comprising 72 independent measurements. Each set of P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI antibiotics is normalized with respect to glycine permeability for a given porin. In addition, we measured also arginine, glutamic acid and sucrose through the eight channels, for a total of 104 experimental data points. The LSA results for OmpF permeability are consistent with previous LSA data and with influx rate measurements in intact cells. As might be expected from the respective pore sizes (shown in table of Fig 2), molecules have a higher permeability through OmpF orthologues than through OmpC orthologues. The zwitterionic molecules, meropenem (MEM), imipenem (IMI), and cefepime (FEP), exhibited high relative permeabilities (40- 80% of glycine permeability) for all porins. Ampicillin (AMP) had lower relative permeability, resembling more the negatively charged molecules ceftazidime (CAZ), cefotaxime (CTX), piperacillin (PIP), and ticarcillin (TIC), which displayed permeabilities ranging from 0 to 40%. In contrast, ertapenem (ETP), which also has a net negative charge, showed elevated relative permeability, similar to that of zwitterionic molecules, except for OmpE35 and OmpE36 (Figure 3). Overall, MEM showed the highest relative permeability through porins (∼60%) while PIP (larger size and negatively charged) and TIC (dianionic) had the lowest. Scoring Function for Permeability: Connecting Structure to Transport To quantify antibiotic permeability through porins, we need a theoretical model to understand how the molecular- scale properties of porins control the macroscopic flow of molecules. If we treat the antibiotic translocation process P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI as a one-dimensional diffusion-drift problem, the molecular flux through the channel follows the Fick law, J = - Nav•P•S0•Δc, where Δc is the difference of the antibiotic molar concentrations, S0 is the geometrical cross section at the mouth of the channel, and Nav is the Avogadro constant. The permeability coefficient P reflects the ability of a certain molecule to translocate through the channel. Hence, its calculation requires the knowledge of the pore-molecule interaction energy along the whole length of the pore. This interaction energy, U(z), can be determined from all-atom MD simulations, but its determination is computationally expensive even when applying enhanced sampling techniques, prohibiting virtual screening of large compound libraries. Nevertheless, as previously reported, the main contribution to the pore-molecule interaction, U(Z), comes from the free-energy barrier located in the CR. Therefore, the permeability coefficient can be approximated to where Deff is the effective diffusion constant in the constriction region constriction region CR and UCR is the free-energy barrier for the permeating molecule in the CR, ΔL the length of the CR, kB the Boltzmann constant, and T the temperature. Within this approximation, the logarithm of the permeability coefficient can be directly connected to the free-energy barrier in constriction region CR only, P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI Thus, we can define a scoring function for permeability from the knowledge of a few accessible molecular parameters that can be directly calculated from MD: Where the former three terms refer to well defined physical interactions and the latter three terms are defined as cross terms of the former: The prediction function of molecule permeation in Gram-negative bacteria is based on two insights: - the idea of combining both molecular and protein pore parameters through which molecules pass to permeate within the bacterial cell; - the idea of using terms that have energetic meaning and are based on molecular interactions. Furthermore, with formula (1) it is possible to calculate the permeability score of molecules of different sizes such as antibiotics / inhibitors, which are larger, and sugars and amino acids (smaller). The first term accounts for the size exclusion problem inside the constriction region CR (Figure 5), which depends on both the average size and fluctuations of the pore (minimum cross-section) and molecule (minimum projection area). This entropic term determines a barrier for molecules and controls rate of uptake. The second and the third terms of equation (1) account for the electrostatic P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI interactions of the diffusing molecule with the pore, through the electrostatic potential (Vp) and electric field (Ep), interacting respectively with the charge Qm and the dipole Dm of the molecule. These two terms modulate the total barrier for permeation (Fig. 5) and can decrease the effect of the steric barrier. In our model, the selectivity of these porins for cations arises from their interaction with the negative electric potential inside the CR. It should be noticed that although the mechanism is general, an entropic barrier modulated by electrostatic interactions, the same molecule will exhibit different permeability rates in different pores. Pore structural changes are reflected in changes in the minimum cross- section area and electrostatic properties that must be calculated from the MD simulation of the pore in a realistic environment. The last three terms of equation (1) represent the correlation between the pairs of the first three terms, specifically taking into account the inter-dependence of the three terms, since when a molecule changes its size also the dipole moment and the distribution of charge can change: represents the correlation between the steric and electrostatic term represents the correlation between the dipole and the steric part represents the correlation between the dipolar term and the electrostatic term. P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI The presence of the last three cross terms of the formula (1) are aimed at eliminating existing correlations between the first three elements in such a way as to improve the accuracy in calculating the score. To obtain the parameters for the scoring function, from equation (1), we applied standard least- square method using the six coefficients as fitting parameters to reproduce the measured LSA data of Fig. 4 in order to minimize the difference between the calculated permeability score and the experimental data. The results using the additional cross terms show an excellent improvement with respect to the data shown in Fig. 6 referring to permeability scores calculated for antibiotic molecules only using a mathematical model that did not consider cross-terms as shown in equation (1) , with a correlation r = 0.80 versus r=0.72, and an accuracy of 0.62 versus 0.28. The analysis of the results grouped by charge (Figure 6b), size (Figure 6c), or transversal dipole moment of each molecule (Figure 6d) allows several general observations. (i) Anionic molecules are disfavored due to electrostatic repulsion by the porins, which to varying degrees are cation selective (Figure 6b). (ii) The size of the molecule, defined as its minimal projection area, correlates with permeability (Figure 6c). (iii) The magnitude of the transverse dipole moment of a molecule Dxy (with respect to the main inertia axis of the molecule) is directly correlated with permeability (Figure 6d). The alignment of the transversal dipole moment of the molecule to the transversal electric field of the pore is always a favorable interaction, hence it decreases the barrier and P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI increases molecular permeability. Although, from Figure 5d, the correlation of Dxy looks weak when confronted with the charge or the size (Figure 5b,c), in some cases, like ertapenem, it can compensate for the charge penalty imposed by the selectivity of the pore. Ertapenem has a net negative charge and its size (∼57 Å2) is comparable to that of the negatively charged cefotaxime (∼59 Å2) and zwitterionic cefepime (∼58 Å2). However, its permeability is similar to cefepime permeability and higher than that of cefotaxime since its charge distribution shows the biggest transversal dipole moment of the set of antibiotics considered.
Claims
P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI CLAIMS 1. A computer implemented method for determining the permeability of a vector molecule for a drug, in particular an anti-bacterial drug, comprising the steps of: - defining or receiving a mathematical model based on the average size and fluctuations of a pore of the constriction region of a Gram-negative bacterial cell chosen as a reference, the size and fluctuations of the molecule whose permeability value is to be calculated, the electrostatic interactions of the molecule with the pore of the channel within the bacterial cell outer membrane, through the electrostatic potential and electric field , which interact with the charge and dipole of the molecule, respectively; - applying said mathematical model to a molecule whose permeability is known within the reference Gram-negative bacterial cell chosen as a reference to obtain a first parameter representative of the permeability of the known molecule; - selecting a candidate vector molecule whose permeability within the gram-negative bacterial cell chosen as a reference should be calculated; - calculating the size of the candidate molecule; - calculating the fluctuation associated with said calculated size;P7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI - calculating the electrostatic potential and electric field of the pore of the bacterial cell chosen; - calculating the charge and electric dipole of the candidate molecule; - applying said mathematical model to the vector molecule to obtain a second parameter representative of the candidate molecule's permeability; - comparing said first and second parameters to estimate the permeability of the candidate molecule within the reference Gram-negative bacterial cell chosen.
2. The method according to claim 1, in which the mathematical model is defined as:where Usteric takes into account the problem of size exclusion within the constriction region that depends on the average size and fluctuations of a pore of said constriction region and the candidate molecule within the reference Gram-negative bacterial cell; Uelectrostatictakes into account the electrostatic interactions of the candidate molecule with the pore of the constriction region of the Gram-negative bacterial cell, through the product of the electrostatic potential of the pore versus the charge of the candidate molecule; Udipole takes into account the electrostatic interactions of the candidate molecule with the poreP7630PC00 UNIVERSITA' DEGLI STUDI DI CAGLIARI of the constriction region of the Gram-negative bacterial cell, through the dot product of the electric field of the pore and the electric dipole of the candidate molecule; takes into account the possible correlation between the terms Usteric and Uelectrostatic through the;takes into account the possible correlation between the terms Uelectrostatic and Udipole through the.
3. The method according to claim 2, in which the are fitting coefficients in order to minimize the difference between the calculated permeability and the values provided by the experimental data; 4. The method according to the previous claims, in which the vector molecule carries a pharmacological active compound that must penetrate inside the Gram-negative bacterial cell; 5. The method according to the previous claims, in which the candidate molecule can be selected from different molecular classes comprising: antibiotics, inhibitors, amino acids, sugars.