Unraveling of a Strongly Correlated Dynamical Network of Residues Controlling the Permeation of Potassium in KcsA Ion Channel.

The complicated patterns of the single-channel currents in potassium ion channel KcsA are governed by the structural variability of the selectivity filter. A comparative analysis of the dynamics of the wild type KcsA channel and several of its mutants showing different conducting patterns was performed. A strongly correlated dynamical network of interacting residues is found to play a key role in regulating the state of the wild type channel. The network is centered on the aspartate D80 which plays the role of a hub by strong interacting via hydrogen bonds with residues E71, R64, R89, and W67. Residue D80 also affects the selectivity filter via its backbones. This network further compromises ions and water molecules located inside the channel that results in the mutual influence: the permeation depends on the configuration of residues in the network, and the dynamics of network's residues depends on locations of ions and water molecules inside the selectivity filter. Some features of the network provide a further understanding of experimental results describing the KcsA activity. In particular, the necessity of anionic lipids to be present for functioning the channel is explained by the interaction between the lipids and the arginine residues R64 and R89 that prevents destabilizing the structure of the selectivity filter.

Changes in Ion Selectivity Following the Asymmetrical Addition of Charge to the Selectivity Filter of Bacterial Sodium Channels.

Voltage-gated sodium channels (NaVs) play fundamental roles in eukaryotes, but their exceptional size hinders their structural resolution. Bacterial NaVs are simplified homologues of their eukaryotic counterparts, but their use as models of eukaryotic Na+ channels is limited by their homotetrameric structure at odds with the asymmetric Selectivity Filter (SF) of eukaryotic NaVs. This work aims at mimicking the SF of eukaryotic NaVs by engineering radial asymmetry into the SF of bacterial channels. This goal was pursued with two approaches: the co-expression of different monomers of the NaChBac bacterial channel to induce the random assembly of heterotetramers, and the concatenation of four bacterial monomers to form a concatemer that can be targeted by site-specific mutagenesis. Patch-clamp measurements and Molecular Dynamics simulations showed that an additional gating charge in the SF leads to a significant increase in Na+ and a modest increase in the Ca2+ conductance in the NavMs concatemer in agreement with the behavior of the population of random heterotetramers with the highest proportion of channels with charge -5e. We thus showed that charge, despite being important, is not the only determinant of conduction and selectivity, and we created new tools extending the use of bacterial channels as models of eukaryotic counterparts.

Control of heart rate through guided high-rate breathing.

Understanding the complex dynamics of cardio-respiratory coupling sheds light on the underlying mechanisms governing the communication between these two physiological systems. Previous research has predominantly considered the coupling at respiratory rates slower than the heart rate and shown that respiratory oscillations lead to modulation and/or synchronization of the heart rate. Whereas the mechanisms of cardio-respiratory communication are still under discussion, peripheral nervous regulation is considered to be the predominant factor. This work offers a novel experimental design and applies the concept of instantaneous phase to detect cardio-respiratory entrainment at elevated respiration rates, close to the resting heart rate. If such 1:1 entrainment exists, it would suggest direct neuronal communication between the respiration and heart centres in the brain. We have observed 1:1 entrainment in all volunteers, with consistently longer synchronization episodes seen in physically fitter people, and demonstrated that cardio-respiratory synchronization at both low and high respiration rates is associated with a common underlying communication mechanism.

Different roles for aspartates and glutamates for cation permeation in bacterial sodium channels.

A key driving force for ion channel selectivity is represented by the negative charge of the Selectivity Filter carried by aspartate (D) and glutamate (E) residues. However, the structural effects and specific properties of D and E residues have not been extensively studied. In order to investigate this issue we studied the mutants of NaChBac channel with all possible combinations of D and E in the charged rings in position 191 and 192. Electrophysiological measurements showed significant Ca2+ currents only when position 191 was occupied by E. Equilibrium Molecular Dynamics simulations revealed the existence of two binding sites, corresponding to the charged rings and another one, more internal, at the level of L190. The simulations showed that the ion in the innermost site can interact with the residue in position 191 only when this is glutamate. Based on the MD simulations, we suggest that a D in position 191 leads to a high affinity Ca2+ block site resulting from a significant drop in the free energy of binding for an ion moving between the binding sites; in contrast, the free energy change is more gradual when an E residue occupies position 191, resulting in Ca2+ permeability. This scenario is consistent with the model of ion channel selectivity through stepwise changes in binding affinity proposed by Dang and McCleskey. Our study also highlights the importance of the structure of the selectivity filter which should contribute to the development of more detailed physical models for ion channel selectivity.

On the selectivity of the NaChBac channel: an integrated computational and experimental analysis of sodium and calcium permeation.

Ion channel selectivity is essential for their function, yet the molecular basis of a channel's ability to select between ions is still rather controversial. In this work, using a combination of molecular dynamics simulations and electrophysiological current measurements we analyze the ability of the NaChBac channel to discriminate between calcium and sodium. Our simulations show that a single calcium ion can access the Selectivity Filter (SF) interacting so strongly with the glutamate ring so as to remain blocked inside. This is consistent with the tiny calcium currents recorded in our patch-clamp experiments. Two reasons explain this scenario. The first is the higher free energy of ion/SF binding of Ca2+ with respect to Na+. The second is the strong electrostatic repulsion exerted by the resident ion that turns back a second potentially incoming Ca2+, preventing the knock-on permeation mechanism. Finally, we analyzed the possibility of the Anomalous Mole Fraction Effect (AMFE), i.e. the ability of micromolar Ca2+ concentrations to block Na+ currents. Current measurements in Na+/Ca2+ mixed solutions excluded the AMFE, in agreement with metadynamics simulations showing the ability of a sodium ion to by-pass and partially displace the resident calcium. Our work supports a new scenario for Na+/Ca2+ selectivity in the bacterial sodium channel, challenging the traditional notion of an exclusion mechanism strictly confining Ca2+ ions outside the channel.

Sodium Binding Sites and Permeation Mechanism in the NaChBac Channel: A Molecular Dynamics Study.

NaChBac was the first discovered bacterial sodium voltage-dependent channel, yet computational studies are still limited due to the lack of a crystal structure. In this work, a pore-only construct built using the NavMs template was investigated using unbiased molecular dynamics and metadynamics. The potential of mean force (PMF) from the unbiased run features four minima, three of which correspond to sites IN, CEN, and HFS discovered in NavAb. During the run, the selectivity filter (SF) is spontaneously occupied by two ions, and frequent access of a third one is often observed. In the innermost sites IN and CEN, Na+ is fully hydrated by six water molecules and occupies an on-axis position. In site HFS sodium interacts with a glutamate and a serine from the same subunit and is forced to adopt an off-axis placement. Metadynamics simulations biasing one and two ions show an energy barrier in the SF that prevents single-ion permeation. An analysis of the permeation mechanism was performed both computing minimum energy paths in the axial-axial PMF and through a combination of Markov state modeling and transition path theory. Both approaches reveal a knock-on mechanism involving at least two but possibly three ions. The currents predicted from the unbiased simulation using linear response theory are in excellent agreement with single-channel patch-clamp recordings.

Time-phase bispectral analysis.

Bispectral analysis, a technique based on high-order statistics, is extended to encompass time dependence for the case of coupled nonlinear oscillators. It is applicable to univariate as well as to multivariate data obtained, respectively, from one or more of the oscillators. It is demonstrated for a generic model of interacting systems whose basic units are the Poincaré oscillators. Their frequency and phase relationships are explored for different coupling strengths, both with and without Gaussian noise. The distinctions between additive linear or quadratic, and parametric (frequency modulated), interactions in the presence of noise are illustrated.

Comment on "Signal-to-noise ratio gain in neuronal systems".

We discuss the gain in signal-to-noise ratio (SNR) recently reported by Liu et al. [Phys. Rev. E 63, 051912 (2001)] in the Hodgkin-Huxley neuronal model. We show first that the possibility of signal-to-noise ratio enhancements can be checked by consideration of the statistical characteristics of switching between the system states, and we examine how the SNR depends on the shape of a periodic signal. Second, we attempt to verify the SNR gain reported by Liu et al.: based on spectral calculations and analyses of switching statistics, we are unable to find any SNR gain in the Hodgkin-Huxley model.