Diffusion of large particles through small pores: From entropic to enthalpic transport

Machine Learning Prediction of Small Molecule Accumulation in Escherichia Coli Enhanced with Descriptor Statistics

Antibiotic resistance, particularly among Gram-negative bacteria, poses a significant healthcare challenge due to their ability to evade antibiotic action through various mechanisms. In this study, we explore the prediction of small molecule accumulation in Gram-negative bacteria by using machine learning techniques enhanced with statistical descriptors derived from molecular dynamics simulations. We begin by identifying a minimal set of molecular descriptors that maximize the model's predictive power while preserving human interpretability. We optimize model accuracy, precision, and the area under the receiver operating characteristic curve through an iterative process. We demonstrate that the inclusion of statistical descriptors significantly improves model performance across various prediction metrics. Particularly, the addition of statistical descriptors related to dipole moment and minimum projection radius enhances the model's predictive capabilities, shedding light on the physicochemical properties crucial for small molecule accumulation. Our findings highlight the importance of considering statistical moments beyond mean values in predictive modeling and suggest avenues for future research. Overall, our study provides insights into the complex dynamics of antibiotic accumulation in Escherichia coli bacterial cells, generalizable to other Gram-negative species, offering a promising approach for the discovery of effective antibacterial agents, identifying new hits, and improving them to define effective lead agents.

Sensing PEGylated Peptide Conformations Using a Protein Nanopore

Membrane pores are exploited for the stochastic sensing of various analytes, and here, we use electrical recordings to explore the interaction of PEGylated peptides of different sizes with a protein pore, CymA. This wide-diameter natural pore comprises densely filled charged residues, facilitating electrophoretic binding of polyethylene glycol (PEG) tagged with a nonaarginine peptide. The small PEG 200 peptide conjugates produced monodisperse blockages and exhibited voltage-dependent translocation across the pores. Notably, the larger PEG 1000 and 2000 peptide conjugates yielded heterogeneous blockages, indicating a multitude of PEG conformations hindering their translocation through the pore. Furthermore, a much larger PEG 5000 peptide occludes the pore entrance, resulting in complete closure. The competitive binding of different PEGylated peptides with the same pore produced specific blockage signals reflecting their identity, size, and conformation. Our proposed model of sensing distinct polypeptide conformations corresponds to disordered protein unfolding, suggesting that this pore can find applications in proteomics.

The mechanism of an electrostatic nanofilter: overcoming entropy with electrostatics

General porins are nature's sieving machinery in the outer membrane of Gram-negative bacteria. Their unique hourglass-shaped architecture is highly conserved among different bacterial membrane proteins and other biological channels. These biological nanopores have been designed to protect the interior of the bacterial cell from leakage of toxic compounds while selectively allowing the entry of the molecules needed for cell growth and function. The mechanism of transport through porins is of utmost and direct interest for drug discovery, extending toward nanotechnology applications for blue energy, separations, and sequencing. Here we present a theoretical framework for analysing the filter of general porins in relation to translocating molecules with the aid of enhanced molecular simulations quantitatively. Using different electrostatic probes in the form of a series of related molecules, we describe the nature of this filter and how to finely tune permeability by exploiting electrostatic interactions between the pore and the translocating molecule. Eventually, we show how enhanced simulations constitute today a valid tool for characterising the mechanism and quantifying energetically the transport of molecules through nanopores.

Converging PMF Calculations of Antibiotic Permeation across an Outer Membrane Porin with Subkilocalorie per Mole Accuracy

The emergence of multidrug-resistant pathogens led to a critical need for new antibiotics. A key property of effective antibiotics against Gram-negative bacteria is their ability to permeate through the bacterial outer membrane via transmembrane porin proteins. Molecular dynamics (MD) simulations are, in principle, capable of modeling antibiotic permeation across outer membrane porins (OMPs). However, owing to sampling problems, it has remained challenging to obtain converged potentials of mean force (PMFs) for antibiotic permeation across OMPs. Here, we investigated the convergence of PMFs along a single collective variable aimed at quantifying the permeation of the antibiotic fosmidomycin across the OprO porin. We compared standard umbrella sampling (US) with three advanced flavors of the US technique: (i) Hamiltonian replica exchange with solute tempering in combination with US, (ii) simulated tempering-enhanced US, and (iii) replica-exchange US. To quantify the PMF convergence and to reveal hysteresis problems, we computed several independent sets of US simulations starting from pulling simulations in the outward and inward permeation directions. We find that replica-exchange US in combination with well-chosen restraints is highly successful for obtaining converged PMFs of fosmidomycin permeation through OprO, reaching PMFs converged to subkilocalorie per mole accuracy.

Boundary design regulates the diffusion of active matter in heterogeneous environments

Physical boundaries play a key role in governing the overall transport properties of nearby self-propelled particles. In this work, we develop dispersion theories and conduct Brownian dynamics simulations to predict the coupling between surface accumulation and effective diffusivity of active particles in boundary-rich media. We focus on three models that are well-understood for passive systems: particle transport in (i) an array of fixed volume-excluding obstacles; (ii) a pore with spatially heterogeneous width; and (iii) a tortuous path with kinks and corners. While the impact of these entropic barriers on passive particle transport is well established, we find that these classical models of porous media flows break down due to the unique interplay between activity and the microstructure of the internal geometry. We study the activity-induced slowdown of effective diffusivity by formulating a Smoluchowski description of long-time self diffusivity which contains contributions from the density and fluctuation fields of the active particles. Particle-based and finite element simulations corroborate this perspective and reveal important nonequilibrium considerations of active transport.

Closed Formula for Transport across Constrictions

In the last decade, the Fick-Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response regime. For this case, we derive a very simple formula that captures the correct trends and can be exploited as a simple tool to design experiments or simulations. Lastly, we show that higher-order corrections in the flux may appear for nonsymmetric channels.

Percolation transition prescribes protein size-specific barrier to passive transport through the nuclear pore complex

Nuclear pore complexes (NPCs) control biomolecular transport in and out of the nucleus. Disordered nucleoporins in the complex's pore form a permeation barrier, preventing unassisted transport of large biomolecules. Here, we combine coarse-grained simulations of experimentally derived NPC structures with a theoretical model to determine the microscopic mechanism of passive transport. Brute-force simulations of protein transport reveal telegraph-like behavior, where prolonged diffusion on one side of the NPC is interrupted by rapid crossings to the other. We rationalize this behavior using a theoretical model that reproduces the energetics and kinetics of permeation solely from statistics of transient voids within the disordered mesh. As the protein size increases, the mesh transforms from a soft to a hard barrier, enabling orders-of-magnitude reduction in permeation rate for proteins beyond the percolation size threshold. Our model enables exploration of alternative NPC architectures and sets the stage for uncovering molecular mechanisms of facilitated nuclear transport.

The Optimal Permeation of Cyclic Boronates to Cross the Outer Membrane via the Porin Pathway

We investigated the diffusion of three cyclic boronates formulated as beta-lactamase inhibitors through the porin OmpF to evaluate their potential to cross OM via the porin pathway. The three nonbeta-lactam molecules diffuse through the porin eyelet region with the same mechanism observed for beta-lactam molecules and diazobicyclooctan derivatives, with the electric dipole moment aligned with the transversal electric field. In particular, the BOH group can interact with both the basic ladder and the acidic loop L3, which is characteristic of the size-constricted region of this class of porins. On one hand, we confirm that the transport of small molecules through enterobacter porins has a common general mechanism; on the other, the class of cyclic boronate molecules does not seem to have particular difficulties in diffusing through enterobacter porins, thus representing a good scaffold for new anti-infectives targeting Gram-negative bacteria research.

Machine learning reveals key ion selectivity mechanisms in polymeric membranes with subnanometer pores

Designing single-species selective membranes for high-precision separations requires a fundamental understanding of the molecular interactions governing solute transport. Here, we comprehensively assess molecular-level features that influence the separation of 18 different anions by nanoporous cellulose acetate membranes. Our analysis identifies the limitations of bulk solvation characteristics to explain ion transport, highlighted by the poor correlation between hydration energy and the measured permselectivity (R² = 0.37). Entropy-enthalpy compensation, spanning 40 kilojoules per mole, leads to a free-energy barrier (∆G^‡) variation of only ~8 kilojoules per mole across all anions. We apply machine learning to elucidate descriptors for energetic barriers from a set of 126 collected features. Notably, electrostatic features account for 75% of the overall features used to describe ∆G^‡, despite the relatively uncharged state of cellulose acetate. Our work presents an approach for studying ion transport across nanoporous membranes that could enable the design of ion-selective membranes.

Computational methods and theory for ion channel research

Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.

The Influence of Permeability through Bacterial Porins in Whole-Cell Compound Accumulation

The lack of new drugs for Gram-negative pathogens is a global threat to modern medicine. The complexity of their cell envelope, with an additional outer membrane, hinders internal accumulation and thus, the access of molecules to their targets. Our limited understanding of the molecular basis for compound influx and efflux from these pathogens is a major bottleneck for the discovery of effective antibacterial compounds. Here we analyse the correlation between the whole-cell compound accumulation of ~200 molecules and their predicted porin permeability coefficient (influx), using a recently developed scoring function. We found a strong linear relationship (74%) between the two, confirming porins key in compound uptake in Gram-negative bacteria. The analysis of this unique dataset aids to better understand the molecular descriptors behind whole-cell accumulation and molecular uptake in Gram-negative bacteria.

Transport of neutral and charged nanorods across varying-section channels

We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods with diverse lengths, aspect ratios and charge. Our analysis shows that the dynamics of charged rods is sensitive to the geometry of the channel and that their transport can be controlled by tuning both the shape of the confining walls and the charge of the rod. Interestingly, we find that the channel permeability does not depend monotonically on the charge of the rod. This opens the possibility of a novel mechanism to separate charged rods.

Permeation of β-Lactamase Inhibitors through the General Porins of Gram-Negative Bacteria

Modern medicine relies upon antibiotics, but we have arrived to the point where our inability to come up with new effective molecules against resistant pathogens, together with the declining private investment, is resulting in the number of untreatable infections increasing worldwide at worrying pace. Among other pathogens, widely recognized institutions have indicated Gram-negative bacteria as particularly challenging, due to the presence of the outer membrane. The very first step in the action of every antibiotic or adjuvant is the permeation through this membrane, with small hydrophilic drugs usually crossing through protein channels. Thus, a detailed understanding of their properties at a molecular level is crucial. By making use of Molecular Dynamics simulations, we compared the two main porins of four members of the Enterobacteriaceae family, and, in this paper, we show their shared geometrical and electrostatic characteristics. Then, we used metadynamics simulations to reconstruct the free energy for permeation of selected diazobicyclooctans through OmpF. We demonstrate how porins features are coupled to those of the translocating species, modulating their passive permeation. In particular, we show that the minimal projection area of a molecule is a better descriptor than its molecular mass or the volume. Together with the magnitude and orientation of the electric dipole moment, these are the crucial parameters to gain an efficient compensation between the entropic and enthalpic contributions to the free energy barrier required for permeation. Our results confirm the possibility to predict the permeability of molecules through porins by using a few molecular parameters and bolster the general model according to which the free energy increase is mostly due to the decrease of conformational entropy, and this can be compensated by a favorable alignment of the electric dipole with respect to the channel intrinsic electric field.

The mechanism and energetics of a ligand-controlled hydrophobic gate in a mammalian two pore channel

In the last decade two-pore intracellular channels (TPCs) attracted the interest of researchers, still some key questions remain open. Their importance for vacuolar (plants) and endo-lysosomal (animals) function highlights them as a very attractive system to study, both theoretically and experimentally. Indicated as key players in the trafficking of the cell, today they are considered a new potential target for avoiding virus infections, including those from coronaviruses. A particular boost for theoretical examinations has been made with recent high-resolution X-ray and cryo-EM structures. These findings have opened the way for efficient and precise computational studies at the atomistic level. Here we report a set of multiscale-calculations performed on the mTPC1, a ligand- and voltage-gated sodium selective channel. The molecular dynamics and enhanced molecular dynamics simulations were used for a thorough analysis of the mammalian TPC1 behaviour in the presence and absence of the ligand molecule, with a special accent on the supposed bottleneck, the hydrophobic gate. Moreover, from the reconstructed free energy obtained from enhanced simulations, we have calculated the macroscopic conductance of sodium ions through the mTPC1, which we compared with measured single-channel conductance values. The hydrophobic gate works as a steric barrier and the key parameters are its flexibility and the dimension of the sodium first hydration shell.