The S$_2$ site of the KcsA K$^+$ channel has eight carbonyl ligands in the ion-binding site. A recent study suggests that the K$^+$-over-Na$^+$ selectivity of the S$_2$ site can be understood by noting the larger free energy change involved in enforcing an eight water coordination state around Na$^+$ relative to K$^+$. The free energies were obtained from the probabilities of observing eight water molecules within a coordination sphere whose radius ($λ_{\rm Na^+} \approx 3.1$ Å and $λ_{\rm K^+} \approx 3.5$ Å) extends to the first minimum of the ion-water oxygen pair correlation function. Curiously, using the same coordination radius led to results that question the very idea of using coordination states in water to understand selectivity in the channel. We show that density fluctuations in neat water at the length scale of the coordination volume enter the description of the hydration thermodynamics of the ion expressed in terms of its coordination states. Density fluctuations explain the sensitivity to the choice of radius. After accounting for this effect, the results lead to the conclusion that free energy changes involved in the transition between coordination states in water are inadequate to explain selectivity in the ion-channel.
We introduce a self-consistent multi-species kinetic theory based on the structure of the narrow voltage-gated potassium channel. Transition rates depend on a complete energy spectrum with contributions including the dehydration amongst species, interaction with the dipolar charge of the filter and, bulk solution properties. It displays high selectivity between species coexisting with fast conductivity, and Coulomb blockade phenomena, and it fits well to data.
The KcsA potassium channel belongs to a class of K+ channels that is selective for K+ over Na+ at rates of K+ transport approaching the diffusion limit. This selectivity is explained thermodynamically in terms of favorable partitioning of K+ relative to Na+ in a narrow selectivity filter in the channel. One mechanism for selectivity based on the atomic structure of the KcsA channel invokes the size difference between K+ and Na+, and the molecular complementarity of the selectivity filter with the larger K+ ion. An alternative view holds that size-based selectivity is precluded because atomic s…
Potassium (K$^+$) channels regulate the flux of K$^+$ ions through cell membranes and plays significant roles in many physiological functions. This work studies the KcsA potassium channel, including the selectivity and current-voltage (IV) relations. A modified Poisson-Nernst-Planck system is employed, which include the size effect by Bikerman model and solvation energy by Born model. The selectivity of KcsA for various ions (K$^+$, Na$^+$, Cl$^-$, Ca$^{2+}$ and Ba$^{2+}$) is studied analytically, and the profiles of concentrations and electric potential are provided. The selectivity is mainly…
It has been suggested that quantum coherence in the selectivity filter of ion channel may play a key role in fast conduction and selectivity of ions. However, it has not been clearly elucidated yet why classical coherence is not sufficient for this purpose. In this paper, we investigate the classical vibrational coherence between carbonyl groups oscillations in the selectivity filter of KcsA ion channels based on the data obtained from molecular dynamics simulations. Our results show that classical coherence plays no effective role in fast ionic conduction.
The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion's dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a frac…
Assuming that the selectivity filter of KcsA potassium ion channel may exhibit quantum coherence, we extend a previous model by Vaziri and Plenio (2010) to take into account Coulomb repulsion between potassium ions. We show that typical ion transit timescales are determined by this interaction, which imposes optimal input/output parameter ranges. Also, as observed in other examples of quantum tunneling in biological systems, addition of moderate noise helps coherent ion transport.
We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutations. We derive an effective grand-canonical ensemble and generalised Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K$^+$ channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding …
Potassium channels play critical roles in many physiological processes, providing a selective permeation route for K+ ions in and out of a cell, by employing a carefully designed selectivity filter, evolutionarily conserved from viruses to mammals. The structure of the selectivity filter was determined at atomic resolution by x-ray crystallography, showing a tight coordination of desolvated K+ ions by the channel. However, the molecular mechanism of K+ ions permeation through potassium channels remains unclear, with structural, functional and computational studies often providing conflicting d…
We study the effect of intracellular ion diffusion on ionic currents permeating through the cell membrane. Ion flux across the cell membrane is mediated by special proteins forming specific channels. The structure of potassium channels have been widely studied in recent years with remarkable results: very precise measurements of the true current across a single channel are now available. Nevertheless, a complete understanding of the behavior of the channel is still lacking, though molecular dynamics and kinetic models have provided partial insights. In this paper we demonstrate, by analyzing t…
Despite a large body of work, the exact molecular details underlying ion-selectivity and transport in the potassium channel have not been fully laid to rest. One major reason has been the lack of experimental methods that can probe these mechanisms dynamically on their biologically relevant time scales. Recently it was suggested that quantum coherence and its interplay with thermal vibration might be involved in mediating ion-selectivity and transport. In this work we present an experimental strategy for using time resolved infrared spectroscopy to investigate these effects. We show the feasib…
Ion channels form pores across the lipid bilayer, selectively allowing inorganic ions to cross the membrane down their electrochemical gradient. While the study of ion desolvation free-energies have attracted much attention, the role of water inside the pore is less clear. Here, molecular dynamics simulations of a reduced model of the KcsA selectivity filter indicate that the equilibrium position of Na+, but not of K+, is strongly influenced by confined water. The latter forms a stable complex with Na+, moving the equilibrium position of the ion to the plane of the backbone carbonyls. Almost a…
We present an equilibrium statistical-mechanical theory of selectivity in biological ion channels. In doing so, we introduce a grand canonical ensemble for ions in a channel's selectivity filter coupled to internal and external bath solutions for a mixture of ions at arbitrary concentrations, we use linear response theory to find the current through the filter for small gradients of electrochemical potential, and we show that the conductivity of the filter is given by the generalized Einstein relation. We apply the theory to the permeation of ions through the potassium selectivity filter, and …
Ion channels are specific proteins present in the membranes of living cells. They control the flow of specific ions through a cell, initiated by an ion channel's electrochemical gradient. In doing so, they control important physiological processes such as muscle contraction and neuronal connectivity, which cannot be properly activated if these channels go haywire, leading to life-threatening diseases and psychological disorders. Here, we will develop a generalized microscopic theory of ion selectivity applicable to KcsA, Na$_{\rm v}$Rh and Ca$_{\rm v}$ (L-type) ion channels. We unambiguously e…
In this work, we present a quantum transport model for the selectivity filter in the KcsA potassium ion channel. This model is fully consistent with the fact that two conduction pathways are involved in the translocation of ions thorough the filter, and we show that the presence of a second path may actually bring advantages for the filter as a result of quantum interference. To highlight interferences and resonances in the model, we consider the selectivity filter to be driven by a controlled time-dependent external field which changes the free energy scenario and consequently the conduction …
We investigate the possible influence of poly unsaturated fatty acids (PUFAs) in the lipid bilayer of cell membranes on the conduction properties of the selectivity filter of voltage gated ion channels. Any change of this conductivity can have major consequences on electrical signalling in brain and other cells. At the microscopic level a change in the concentration of PUFAs can cause a change in the pressure distribution within the lipid bilayer, and this in turn can lead to a change in the length of the selectivity filter. In order to estimate the consequences this might entail for the ion c…
Potassium (K-) channels catalyze K+ ion permeation across cellular membranes while simultaneously discriminating their permeation over Na+ ions by more than a factor of a thousand. Structural studies show bare K+ ions occupying the narrowest channel regions in a state of high coordination by all 8 surrounding oxygen ligands from the channel walls. As in most channels, the driving force for selectivity occurs when one ion is preferentially stabilized or destabilized by the channel compared to water. In the common view of mechanism, made vivid by textbook graphics, the driving force for selectiv…
There are many controversial and challenging discussions about quantum effects in microscopic structures in neurons of the human brain. The challenge is mainly because of quick decoherence of quantum states due to hot, wet and noisy environment of the brain which forbids long life coherence for brain processing. Despite these critical discussions, there are only a few number of published papers about numerical aspects of decoherence in neurons. Perhaps the most important issue is offered by Max Tegmark who has calculated decoherence times for the systems of "ions" and "microtubules" in neurons…
Voltage gated channel proteins cooperate in the transmission of membrane potentials between nerve cells. With the recent progress in atomic-scaled biological chemistry it has now become established that these channel proteins provide highly correlated atomic environments that may maintain electronic coherences even at warm temperatures. Here we demonstrate solutions of the Schrödinger equation that represent the interaction of a single potassium ion within the surrounding carbonyl dipoles in the Berneche-Roux model of the bacterial \textit{KcsA} model channel. We show that, depending on the su…
The finely tuned structures of membrane channels allow selective passage of ions through the available aqueous pores. In order to understand channel function, it is crucial to locate the pore and study its physical and chemical properties. Recently obtained X-ray crystal structures of bacterial chloride channel homologues reveal a complicated topology with curvilinear pores. The commonly used HOLE program encounters difficulties in studying such pores. Here we propose a new pore-searching algorithm (TransPath) which uses the Configurational Bias Monte Carlo (CBMC) method to generate transmembr…
A hydrophobic constriction site can act as an efficient barrier to ion and water permeation if its diameter is less than the diameter of an ion's first hydration shell. This hydrophobic gating mechanism is thought to operate in a number of ion channels, e.g. the nicotinic receptor, bacterial mechanosensitive channels (MscL and MscS) and perhaps in some potassium channels (e.g. KcsA, MthK, and KvAP). Simplified pore models allow one to investigate the primary characteristics of a conduction pathway, namely its geometry (shape, pore length, and radius), the chemical character of the pore wall su…
