Bias-Exchange Metadynamics Simulations: An Efficient Strategy for the Analysis of Conduction and Selectivity in Ion Channels

Phage display assisted discovery of a pH-dependent anti-α-cobratoxin antibody from a natural variable domain library

Recycling IgG antibodies bind to their target antigen at physiological pH in the blood stream and release them upon endocytosis when pH levels drop, allowing the IgG antibodies to be recycled into circulation via FcRn-mediated cellular pathways, while the antigens undergo lysosomal degradation. This enables recycling antibodies to achieve comparable therapeutic effect at lower doses than their non-recycling counterparts. The development of such antibodies is typically achieved by histidine doping of their variable regions or by performing in vitro antibody selection campaigns utilizing histidine doped libraries. Both are strategies that may introduce sequence liabilities. Here, we present a methodology that employs a naïve antibody phage display library, consisting of natural variable domains, to discover antibodies that bind α-cobratoxin from the venom of Naja kaouthia in a pH-dependent manner. As a result, an antibody was discovered that exhibits a 7-fold higher off-rate at pH 5.5 than pH 7.4 in bio-layer interferometry experiments. Interestingly, no histidine residues were found in its variable domains, and in addition, the antibody showed pH-dependent binding to a histidine-devoid antigen mutant. As such, the results demonstrate that pH-dependent antigen-antibody binding may not always be driven by histidine residues. By employing molecular dynamics simulations, different protonation states of titratable residues were found, which potentially could be responsible for the observed pH-dependent antigen binding properties of the antibody. Finally, given the typically high diversity of naïve antibody libraries, the methodology presented here can likely be applied to discover recycling antibodies against different targets ab initio without the need for histidine doping.

Computational study of ion permeation through claudin-4 paracellular channels

Claudins (Cldns) form a large family of protein homologs that are essential for the assembly of paracellular tight junctions (TJs), where they form channels or barriers with tissue-specific selectivity for permeants. In contrast to several family members whose physiological role has been identified, the function of claudin 4 (Cldn4) remains elusive, despite experimental evidence suggesting that it can form anion-selective TJ channels in the renal epithelium. Computational approaches have recently been employed to elucidate the molecular basis of Cldns' function, and hence could help in clarifying the role of Cldn4. In this work, we use structural modeling and all-atom molecular dynamics simulations to transfer two previously introduced structural models of Cldn-based paracellular complexes to Cldn4 to reproduce a paracellular anion channel. Free energy calculations for ionic transport through the pores allow us to establish the thermodynamic properties driving the ion-selectivity of the structures. While one model shows a cavity permeable to chloride and repulsive to cations, the other forms barrier to the passage of all the major physiological ions. Furthermore, our results confirm the charge selectivity role of the residue Lys65 in the first extracellular loop of the protein, rationalizing Cldn4 control of paracellular permeability.

Conjugates of Desmycosin with Fragments of Antimicrobial Peptide Oncocin: Synthesis, Antibacterial Activity, Interaction with Ribosome

Design and synthesis of conjugates consisting of the macrolide antibiotic desmycosin and fragments of the antibacterial peptide oncocin were performed in attempt to develop new antimicrobial compounds. New compounds were shown to bind to the E. coli 70S ribosomes, to inhibit bacterial protein synthesis in vitro, as well as to suppress bacterial growth. The conjugates of N-terminal hexa- and tripeptide fragments of oncocin and 3,2',4''-triacetyldesmycosin were found to be active against some strains of macrolide-resistant bacteria. By simulating molecular dynamics of the complexes of these compounds with the wild-type bacterial ribosomes and with ribosomes, containing A2059G 23S RNA mutation, the specific structural features of their interactions were revealed.

Nanobody Paratope Ensembles in Solution Characterized by MD Simulations and NMR

Variable domains of camelid antibodies (so-called nanobodies or V_HH) are the smallest antibody fragments that retain complete functionality and therapeutic potential. Understanding of the nanobody-binding interface has become a pre-requisite for rational antibody design and engineering. The nanobody-binding interface consists of up to three hypervariable loops, known as the CDR loops. Here, we structurally and dynamically characterize the conformational diversity of an anti-GFP-binding nanobody by using molecular dynamics simulations in combination with experimentally derived data from nuclear magnetic resonance (NMR) spectroscopy. The NMR data contain both structural and dynamic information resolved at various timescales, which allows an assessment of the quality of protein MD simulations. Thus, in this study, we compared the ensembles for the anti-GFP-binding nanobody obtained from MD simulations with results from NMR. We find excellent agreement of the NOE-derived distance maps obtained from NMR and MD simulations and observe similar conformational spaces for the simulations with and without NOE time-averaged restraints. We also compare the measured and calculated order parameters and find generally good agreement for the motions observed in the ps–ns timescale, in particular for the CDR3 loop. Understanding of the CDR3 loop dynamics is especially critical for nanobodies, as this loop is typically critical for antigen recognition.

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.

Pseudocyclic Form of 4-Hydroxypyrrolidine-2-carboxanilide Podands with Trioxyethylene Chain: Modeling, Conformational Search, and NMR Analysis

The 4-hydroxypyrrolidine-2-carboxanilide podand salt demonstrates catalytic activity in asymmetric Biginelli reaction. The systematic search for prevalent conformational state of the cation was carried out by computer simulations in combination with one- and two-dimensional NMR experiments. For that purpose, we proposed a novel algorithm for the generation and selection of conformers based on molecular dynamics and clustering in the space of principal components. The search had found an important trend of the podand to form a pseudocyclic structure with a horseshoe-shaped conformation of the oligooxyethylene fragment. This conformation is stabilized by different types of intramolecular hydrogen bonds between the acidic and basic centers of the two 4-hydroxypyrrolidine-2-carboxanilide residuals (branches). The proposed approach had made it possible to identify the major structural factors, providing a correlation between the calculated and experimental chemical shifts of hydrogen atoms in the ¹H NMR spectra of the protonated podand.

Determinants of conductance of a bacterial voltage-gated sodium channel

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel Na_vMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Na_v channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na⁺ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.

Defining a novel domain that provides an essential contribution to site-specific interaction of Rep protein with DNA

An essential feature of replication initiation proteins is their ability to bind to DNA. In this work, we describe a new domain that contributes to a replication initiator sequence-specific interaction with DNA. Applying biochemical assays and structure prediction methods coupled with DNA–protein crosslinking, mass spectrometry, and construction and analysis of mutant proteins, we identified that the replication initiator of the broad host range plasmid RK2, in addition to two winged helix domains, contains a third DNA-binding domain. The phylogenetic analysis revealed that the composition of this unique domain is typical within the described TrfA-like protein family. Both in vitro and in vivo experiments involving the constructed TrfA mutant proteins showed that the newly identified domain is essential for the formation of the protein complex with DNA, contributes to the avidity for interaction with DNA, and the replication activity of the initiator. The analysis of mutant proteins, each containing a single substitution, showed that each of the three domains composing TrfA is essential for the formation of the protein complex with DNA. Furthermore, the new domain, along with the winged helix domains, contributes to the sequence specificity of replication initiator interaction within the plasmid replication origin.

Exploration of Free Energy Surfaces Across a Membrane Channel Using Metadynamics and Umbrella Sampling

To reach their site of action, it is essential for antibiotic molecules to cross the bacterial outer membrane. The progress of enhanced sampling techniques in molecular dynamics simulations enables us to understand these translocations at an atomic level. To this end, calculations of free energy surfaces for these permeation processes are of key importance. Herein, we investigate the translocation of a variety of anionic solutes through the outer membrane pore OprO of the Gram-negative bacterium Pseudomonas aeruginosa using the metadynamics and umbrella sampling techniques at the all-atom level. Free energy calculations have been performed employing these two distinct methods in order to illustrate the difference in computed free energies, if any. The investigated solutes range from a single atomic chloride ion over a multiatomic monophosphate ion to a more bulky fosmidomycin antibiotic. The role of complexity of the permeating solutes in estimating accurate free energy profiles is demonstrated by performing extensive convergence analysis. For simple monatomic ions, good agreement between the well-tempered metadynamics and the umbrella sampling approaches is achieved, while for the permeation of the monophosphate ion differences start to appear. In the case of larger molecules such as fosmidomycin it is a tough challenge to achieve converged free energy profiles. This issue is mainly due to neglecting orthogonal degrees of freedom during the free energy calculations. Nevertheless, the freely driven metadynamics approach leads to clearly advantageous results. Additionally, atomistic insights of the translocation mechanisms of all three solutes are discussed.

IR Spectroscopy Can Reveal the Mechanism of K+ Transport in Ion Channels

Ion channels like KcsA enable ions to move across cell membranes at near diffusion-limited rates and with very high selectivity. Various mechanisms have been proposed to explain this phenomenon. Broadly, there is disagreement among the proposed mechanisms about whether ions occupy adjacent sites in the channel during the transport process. Here, using a mixed quantum-classical approach to calculate theoretical infrared spectra, we propose a set of infrared spectroscopy experiments that can discriminate between mechanisms with and without adjacent ions. These experiments differ from previous ones in that they independently probe specific ion binding sites within the selectivity filter. When ions occupy adjacent sites in the selectivity filter, the predicted spectra are significantly redshifted relative to when ions do not occupy adjacent sites. Comparisons between theoretical and experimental peak frequencies will therefore discriminate the mechanisms.

Computational insights into lipid assisted peptide misfolding and aggregation in neurodegeneration

An overview of recent advances in computational investigation of peptide–lipid interactions in neurodegeneration – Alzheimer's, Parkinson's and Huntington's disease.

Molecular Dynamics of Ion Conduction through the Selectivity Filter of the NaVAb Sodium Channel

The determination of the atomic structures of voltage-gated bacterial sodium channels using X-ray crystallography has provided a first view of this family of membrane proteins. Molecular dynamics simulations offer one approach to clarify the underlying mechanism of permeation and selectivity in these channels. However, it appears that the intracellular gate of the pore domain is either closed or only open partially in the available X-ray structures. The lack of structure with a fully open intracellular gate poses a special challenge to computational studies aimed at simulating ion conduction. To circumvent this problem, we simulated a model of the Na_VAb channel in which the transmembrane S5 and S6 helices of the pore domain have been truncated to provide direct open access to the intracellular entryway to the pore. Molecular dynamics simulations were carried out over a range of membrane potential and ion concentration of sodium and potassium. The simulations show that the Na_VAb selectivity filter is essentially a cationic pore supporting the conduction of ions at a rate comparable to aqueous diffusion with no significant selectivity for sodium. Conductance and selectivity vary as a function of ion concentration for both cations. Permeation occurs primarily via a knock-on mechanism for both sodium and potassium, although the ion ordering in single file along the pore is not strictly maintained. The character of the outward current appears quite different from the inward current, with a buildup on ions in the selectivity filter prior to escape toward the extracellular side, indicating the presence of a rectification effect that is overcome by nonphysiological applied voltages.

Why are reactions of 2- and 8-thioquinoline derivatives with iodine different?

The crystal structures of 1,2-dihydro-1,1′-bi[thiazolo[3,2-a]quinoline]-10a,10a′-diium diiodide hemihydrate, C22H16N2S2 2+·2I−·0.5H2O, and 1,2-dihydro-1,1′-bi[thiazolo[3,2-a]quinoline]-10a,10a′-diium iodide triiodide, C22H16N2S2 2+·I−·I3 −, obtained during the reaction of 1,4-bis(quinolin-2-ylsulfanyl)but-2-yne (2TQB) with iodine, have been determined at 120 K. The crystalline products contain the dication as a result of the reaction proceeding along the iodocyclization pathway. This is fundamentally different from the previously observed reaction of 1,4-bis(quinolin-8-ylsulfanyl)but-2-yne (8TQB) with iodine under similar conditions. A comparative analysis of the possible conformational states indicates differences in the relative stabilities and free rotation for the 2- and 8-thioquinoline derivatives which lead to a disparity in the convergence of the potential reaction centres for 2TQB and 8TQB.

Ion-triggered selectivity in bacterial sodium channels

Since the availability of the first crystal structure of a bacterial Na⁺ channel in 2011, understanding selectivity across this family of membrane proteins has been the subject of intense research efforts. Initially, free energy calculations based on molecular dynamics simulations revealed that although sodium ions can easily permeate the channel with their first hydration shell almost intact, the selectivity filter is too narrow for efficient conduction of hydrated potassium ions. This steric view of selectivity was subsequently questioned by microsecond atomic trajectories, which proved that the selectivity filter appears to the permeating ions as a highly degenerate, liquid-like environment. Although this liquid-like environment looks optimal for rapid conduction of Na⁺, it seems incompatible with efficient discrimination between similar ion species, such as Na⁺ and K⁺, through steric effects. Here extensive molecular dynamics simulations, combined with Markov state model analyses, reveal that at positive membrane potentials, potassium ions trigger a conformational change of the selectivity toward a nonconductive metastable state. It is this transition of the selectivity filter, and not steric effects, that prevents the outward flux of K⁺ at positive membrane potentials. This description of selectivity, triggered by the nature of the permeating ions, might have implications on the current understanding of how ion channels, and in particular bacterial Na⁺ channels, operate at the atomic scale.

Ion Permeation Mechanism in Epithelial Calcium Channel TRVP6

Calcium is the most abundant metal in the human body that plays vital roles as a cellular electrolyte as well as the smallest and most frequently used signaling molecule. Calcium uptake in epithelial tissues is mediated by tetrameric calcium-selective transient receptor potential (TRP) channels TRPV6 that are implicated in a variety of human diseases, including numerous forms of cancer. We used TRPV6 crystal structures as templates for molecular dynamics simulations to identify ion binding sites and to study the permeation mechanism of calcium and other ions through TRPV6 channels. We found that at low Ca²⁺ concentrations, a single calcium ion binds at the selectivity filter narrow constriction formed by aspartates D541 and allows Na⁺ permeation. In the presence of ions, no water binds to or crosses the pore constriction. At high Ca²⁺ concentrations, calcium permeates the pore according to the knock-off mechanism that includes formation of a short-lived transition state with three calcium ions bound near D541. For Ba²⁺, the transition state lives longer and the knock-off permeation occurs slower. Gd³⁺ binds at D541 tightly, blocks the channel and prevents Na⁺ from permeating the pore. Our results provide structural foundations for understanding permeation and block in tetrameric calcium-selective ion channels.

Energetics of Ion Permeation in an Open-Activated TRPV1 Channel

Ion channels enable diffusion of ions down physiological electrochemical gradients. Modulation of ion permeation is crucial for the physiological functioning of cells, and misregulation of ion channels is linked to a myriad of channelopathies. The ion permeation mechanism in the transient receptor potential (TRP) ion channel family is currently not understood at an atomistic level. In this work, we employed a simulation strategy for ion permeation (molecular-dynamics simulations with bias-exchange metadynamics) to study and compare monovalent (Na(+), K(+)) ion permeation in the open-activated TRP vanniloid-1 (TRPV1) ion channel. Using ∼3.6 μs of simulation trajectories, we obtained atomistic evidence for the nonselective nature of TRPV1. Our analysis shows that solvated monovalent ions permeate through the selectivity filter with comparable energetic barriers via a two-site mechanism. Finally, we confirmed that an intracellular binding site is located between the intracellular gate residues I679 and E684.

Assessing Generic Collective Variables for Determining Reaction Rates in Metadynamics Simulations

A persistent challenge in using the metadynamics method is deciding which degrees of freedom, or collective variables, should be biased because these selections are not obvious and require intuition about the system being studied. There are, however, collective variables, which can be constructed with only basic knowledge about the system studied, that provide an opportunity to alleviate this issue. We simulated two different reacting systems where two types of such collective variables (SPRINT coordinates and the collective variable-driven hyperdynamics method) were biased following the infrequent metadynamics method in order to recover the rates of reactions. We demonstrate that both generic collective variables are capable of reproducing the reaction rates of both systems and can enhance the efficiency of the simulation when compared to typical collective variables.

Binding Mechanisms of Intrinsically Disordered Proteins: Theory, Simulation, and Experiment

In recent years, protein science has been revolutionized by the discovery of intrinsically disordered proteins (IDPs). In contrast to the classical paradigm that a given protein sequence corresponds to a defined structure and an associated function, we now know that proteins can be functional in the absence of a stable three-dimensional structure. In many cases, disordered proteins or protein regions become structured, at least locally, upon interacting with their physiological partners. Many, sometimes conflicting, hypotheses have been put forward regarding the interaction mechanisms of IDPs and the potential advantages of disorder for protein-protein interactions. Whether disorder may increase, as proposed, e.g., in the “fly-casting” hypothesis, or decrease binding rates, increase or decrease binding specificity, or what role pre-formed structure might play in interactions involving IDPs (conformational selection vs. induced fit), are subjects of intense debate. Experimentally, these questions remain difficult to address. Here, we review experimental studies of binding mechanisms of IDPs using NMR spectroscopy and transient kinetic techniques, as well as the underlying theoretical concepts and numerical methods that can be applied to describe these interactions at the atomic level. The available literature suggests that the kinetic and thermodynamic parameters characterizing interactions involving IDPs can vary widely and that there may be no single common mechanism that can explain the different binding modes observed experimentally. Rather, disordered proteins appear to make combined use of features such as pre-formed structure and flexibility, depending on the individual system and the functional context.

Voltage-Gated Sodium Channels: Mechanistic Insights From Atomistic Molecular Dynamics Simulations

The permeation of ions and other molecules across biological membranes is an inherent requirement of all cellular organisms. Ion channels, in particular, are responsible for the conduction of charged species, hence modulating the propagation of electrical signals. Despite the universal physiological implications of this property, the molecular functioning of ion channels remains ambiguous. The combination of atomistic structural data with computational methodologies, such as molecular dynamics (MD) simulations, is now considered routine to investigate structure-function relationships in biological systems. A fuller understanding of conduction, selectivity, and gating, therefore, is steadily emerging due to the applicability of these techniques to ion channels. However, because their structure is known at atomic resolution, studies have consistently been biased toward K(+) channels, thus the molecular determinants of ionic selectivity, activation, and drug blockage in Na(+) channels are often overlooked. The recent increase of available crystallographic data has eminently encouraged the investigation of voltage-gated sodium (NaV) channels via computational methods. Here, we present an overview of simulation studies that have contributed to our understanding of key principles that underlie ionic conduction and selectivity in Na(+) channels, in comparison to the K(+) channel analogs.

Computational studies of transport in ion channels using metadynamics

Molecular dynamics simulations have played a fundamental role in numerous fields of science by providing insights into the structure and dynamics of complex systems at the atomistic level. However, exhaustive sampling by standard molecular dynamics is in most cases computationally prohibitive, and the time scales accessible remain significantly shorter than many biological processes of interest. In particular, in the study of ion channels, realistic models to describe permeation and gating require accounting for large numbers of particles and accurate interaction potentials, which severely limits the length of the simulations. To overcome such limitations, several advanced methods have been proposed among which is metadynamics. In this algorithm, an external bias potential to accelerate sampling along selected collective variables is introduced. This bias potential discourages visiting regions of the configurational space already explored. In addition, the bias potential provides an estimate of the free energy as a function of the collective variables chosen once the simulation has converged. In this review, recent contributions of metadynamics to the field of ion channels are discussed, including how metadynamics has been used to search for transition states, predict permeation pathways, treat conformational flexibility that underlies the coupling between gating and permeation, or compute free energy of permeation profiles. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.