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

We present a statistical model for solving and predicting the transport of large molecules through small flexible channels. The average radius of the channel and the average radius of the molecule are the only two quantities determining the steric part of the potential of mean force for the translocation, in the case of a small rigid particle and a large rigid channel: the barrier is completely entropic and is described by the Fick-Jacobs model. However, the flexibility of the channel's cross section and that of the molecule's size have a significant effect on transport, especially when a large molecule goes through a narrow channel. In this case, the steric barrier changes its statistical nature becoming enthalpic, and we predict a strong temperature enhancement of the diffusion current through the channel. The flexibility is described in terms of the equilibrium fluctuations of the channel and of the molecule. The model is compared with the all-atom MD simulations of the transport of hard spheres of various radii and of drug molecules through a biological nanochannel. For the case of Gaussian fluctuations, we derived a simple analytical expression for the steric barrier, which can be quantified using average size and fluctuations of the channel and of the molecule.

Sensing Single Molecule Penetration into Nanopores: Pushing the Time Resolution to the Diffusion Limit.

To quantify small molecule penetration into and eventually permeation through nanopores, we applied an improved excess-noise analysis of the ion current fluctuation caused by entering molecules. The kinetic parameters of substrate entry and exit are derived from a two-state Markov model, analyzing the substrate concentration dependence of the average ion current and its variance. Including filter corrections allows one to detect the transition rates beyond the cutoff frequency, fc, of the instrumental ion-current filter. As an application of the method, we performed an analysis of the single-channel ion current of Meropenem, an antibiotic of the carbapenem family, interacting with OmpF, the major general outer membrane channel of Escherichia coli bacteria. At 40 °C we detected the residence time of Meropenem inside OmpF of about 500 ns-more than 2 orders of magnitude smaller than fc-1 and close to the diffusion limit of few hundred nanoseconds. We also have established theoretical limit conditions under which the substrate-induced channel blockages can be detected and suggest that submicrosecond-scale gating kinetic parameters are accessible with existing experimental equipment.

A kinetic model for molecular diffusion through pores.

The number of pathogens developing multiple drug resistance is ever increasing. The impact on healthcare systems is huge and the need for novel antibiotics as well a new way to develop them is urgent, especially against Gram-negative bacteria. The first defense of these bacteria is the outer membrane, where unspecific protein channels (porins) modulate nutrients passive diffusion. Also polar antibiotics enter through this path and down-regulation and/or mutation of porins are very common in drug resistant strains. Our inability to come up with novel effective antibiotics mostly relies upon the insufficient comprehension of the key molecular features enabling better penetration through porins. Molecular dynamics simulations offer an extraordinary tool in the study of the dynamics of biological systems; however, one of the major drawbacks of this method is that its use is currently restricted to study time scales of the order of microsecond. Enhanced sampling methods like Metadynamics have been recently used to investigate the diffusion of antibiotics through bacterial porins. The main limitation is that dynamical properties cannot be estimated because of the different potential that the systems under study are experiencing. Recently, the scope of Metadynamics has been extended. By applying an a posteriori analysis one can obtain rates of transitions and rate-limiting steps of the process under study, directly comparable with kinetic data extracted from electrophysiology experiments. In this work, we apply this method to the study of the permeability of Escherichia coli's OmpF with respect to Meropenem, finding good agreement with the residence time obtained analyzing experimental current noise. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.