Fully-Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection

We propose a new model-free segmentation method, JULES, which combines recent statistical multiresolution techniques with local deconvolution for idealization of ion channel recordings. The multiresolution criterion takes into account scales down to the sampling rate enabling the detection of flickering events, i.e., events on small temporal scales, even below the filter frequency. For such small scales the deconvolution step allows for a precise determination of dwell times and, in particular, of amplitude levels, a task which is not possible with common thresholding methods. This is confirmed theoretically and in a comprehensive simulation study. In addition, JULES can be applied as a preprocessing method for a refined hidden Markov analysis. Our new methodolodgy allows us to show that gramicidin A flickering events have the same amplitude as the slow gating events. JULES is available as an R function jules in the package clampSeg

Efficient Maximum Likelihood Estimation of Kinetic Rate Constants from Macroscopic Currents

A new method is described that accurately estimates kinetic constants, conductance and number of ion channels from macroscopic currents. The method uses both the time course and the strength of correlations between different time points of macroscopic currents and utilizes the property of semiseparability of covariance matrix for computationally efficient estimation of current likelihood and its gradient. The number of calculation steps scales linearly with the number of channel states as opposed to the cubic dependence in a previously described method. Together with the likelihood gradient evaluation, which is almost independent of the number of model parameters, the new approach allows evaluation of kinetic models with very complex topologies. We demonstrate applicability of the method to analysis of synaptic currents by estimating accurately rate constants of a 7-state model used to simulate GABAergic macroscopic currents

Heterogeneous Idealization of Ion Channel Recordings -- Open Channel Noise

We propose a new model-free segmentation method for idealizing ion channel recordings. This method is designed to deal with heterogeneity of measurement errors. This in particular applies to open channel noise which, in general, is particularly difficult to cope with for model-free approaches. Our methodology is able to deal with lowpass filtered data which provides a further computational challenge. To this end we propose a multiresolution testing approach, combined with local deconvolution to resolve the lowpass filter. Simulations and statistical theory confirm that the proposed idealization recovers the underlying signal very accurately at presence of heterogeneous noise, even when events are shorter than the filter length. The method is compared to existing approaches in computer experiments and on real data. We find that it is the only one which allows to identify openings of the PorB porine at two different temporal scales. An implementation is available as an R package

Single-channel kinetics of BK (Slo1) channels

Single-channel kinetics has proven a powerful tool to reveal information about the gating mechanisms that control the opening and closing of ion channels. This introductory review focuses on the gating of large conductance Ca2+- and voltage-activated K+ (BK or Slo1) channels at the single-channel level. It starts with single-channel current records and progresses to presentation and analysis of single-channel data and the development of gating mechanisms in terms of discrete state Markov (DSM) models). The DSM models are formulated in terms of the tetrameric modular structure of BK channels, consisting of a central transmembrane pore-gate domain (PGD) attached to four surrounding transmembrane voltage sensing domains (VSD) and a large intracellular cytosolic domain (CTD), also referred to as the gating ring. The modular structure and data analysis shows that the Ca2+ and voltage dependent gating considered separately can each be approximated by 10-state two-tiered models with 5 closed states on the upper tier and 5 open states on the lower tier. The modular structure and joint Ca2+ and voltage dependent gating are consistent with a 50 state two-tiered model with 25 closed states on the upper tier and 25 open states on the lower tier. Adding an additional tier of brief closed (flicker states) to the 10-state or 50-state models improved the description of the gating. For fixed experimental conditions a channel would gate in only a subset of the potential number of states. The detected number of states and the correlations between adjacent interval durations are consistent with the tiered models. The examined models can account for the single-channel kinetics and the bursting behavior of gating. Ca2+ and voltage activate BK channels by predominantly increasing the effective opening rate of the channel with a smaller decrease in the effective closing rate. Ca2+ and depolarization thus activate by mainly destabilizing the closed states

Asymmetric Interplay Between K+ and Blocker and Atomistic Parameters From Physiological Experiments Quantify K+ Channel Blocker Release

Modulating the activity of ion channels by blockers yields information on both the mode of drug action and on the biophysics of ion transport. Here we investigate the interplay between ions in the selectivity filter (SF) of K+ channels and the release kinetics of the blocker tetrapropylammonium in the model channel KcvNTS. A quantitative expression calculates blocker release rate constants directly from voltage-dependent ion occupation probabilities in the SF. The latter are obtained by a kinetic model of single-channel currents recorded in the absence of the blocker. The resulting model contains only two adjustable parameters of ion-blocker interaction and holds for both symmetric and asymmetric ionic conditions. This data-derived model is corroborated by 3D reference interaction site model (3D RISM) calculations on several model systems, which show that the K+ occupation probability is unaffected by the blocker, a direct consequence of the strength of the ion-carbonyl attraction in the SF, independent of the specific protein background. Hence, KcvNTS channel blocker release kinetics can be reduced to a small number of system-specific parameters. The pore-independent asymmetric interplay between K+ and blocker ions potentially allows for generalizing these results to similar potassium channels

Bayesian approaches for modeling protein biophysics

textProteins are the fundamental unit of computation and signal processing in biological systems. A quantitative understanding of protein biophysics is of paramount importance, since even slight malfunction of proteins can lead to diverse and severe disease states. However, developing accurate and useful mechanistic models of protein function can be strikingly elusive. I demonstrate that the adoption of Bayesian statistical methods can greatly aid in modeling protein systems. I first discuss the pitfall of parameter non-identifiability and how a Bayesian approach to modeling can yield reliable and meaningful models of molecular systems. I then delve into a particular case of non-identifiability within the context of an emerging experimental technique called single molecule photobleaching. I show that the interpretation of this data is non-trivial and provide a rigorous inference model for the analysis of this pervasive experimental tool. Finally, I introduce the use of nonparametric Bayesian inference for the analysis of single molecule time series. These methods aim to circumvent problems of model selection and parameter identifiability and are demonstrated with diverse applications in single molecule biophysics. The adoption of sophisticated inference methods will lead to a more detailed understanding of biophysical systems.Neuroscienc

Biophysical Sources of 1/f Noises in Neurological Tissue

High levels of random noise are a defining characteristic of neurological signals at all levels, from individual neurons up to electroencephalograms (EEG). These random signals degrade the performance of many methods of neuroengineering and medical neuroscience. Understanding this noise also is essential for applications such as real-time brain-computer interfaces (BCIs), which must make accurate control decisions from very short data epochs. The major type of neurological noise is of the so-called 1/f-type, whose origins and statistical nature has remained unexplained for decades. This research provides the first simple explanation of 1/f-type neurological noise based on biophysical fundamentals. In addition, noise models derived from this theory provide validated algorithm performance improvements over alternatives. Specifically, this research defines a new class of formal latent-variable stochastic processes called hidden quantum models (HQMs) which clarify the theoretical foundations of ion channel signal processing. HQMs are based on quantum state processes which formalize time-dependent observation. They allow the quantum-based calculation of channel conductance autocovariance functions, essential for frequency-domain signal processing. HQMs based on a particular type of observation protocol called independent activated measurements are shown to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. These unique biophysical concepts developed to understand the mechanisms of ion channel kinetics have the potential of revolutionizing our understanding of neurological computation. To apply this theory, the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments is used to derive the activation eigenenergies for the Hodgkin-Huxley K+ and Na+ ion channels. It is shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating S(f) = 1/f, thus offering a biophysical explanation for this ubiquitous noise component. These new channel-based noise processes are called generalized van der Ziel-McWhorter (GVZM) power spectral densities (PSDs). This is the only known EEG noise model that has a small, fixed number of parameters, matches recorded EEG PSD\u27s with high accuracy from 0 Hz to over 30 Hz without infinities, and has approximately 1/f behavior in the mid-frequencies. In addition to the theoretical derivation of the noise statistics from ion channel stochastic processes, the GVZM model is validated in two ways. First, a class of mixed autoregressive models is presented which simulate brain background noise and whose periodograms are proven to be asymptotic to the GVZM PSD. Second, it is shown that pairwise comparisons of GVZM-based algorithms, using real EEG data from a publicly-available data set, exhibit statistically significant accuracy improvement over two well-known and widely-used steady-state visual evoked potential (SSVEP) estimators

Voltage- and cold-dependent gating of single TRPM8 ion channels

Transient receptor potential (TRP) channels play critical roles in cell signaling by coupling various environmental factors to changes in membrane potential that modulate calcium influx. TRP channels are typically activated in a polymodal manner, thus integrating multiple stimuli. Although much progress has been made, the underlying mechanisms of TRP channel activation are largely unknown. The TRPM8 cation channel has been extensively investigated as a major neuronal cold sensor but is also activated by voltage, calcium store depletion, and some lipids as well as by compounds that produce cooling sensations, such as menthol or icilin. Several models of TRPM8 activation have been proposed to explain the interaction between these diverse stimuli. However, a kinetic scheme is not yet available that can describe the detailed single-channel kinetics to gain further insight into the underlying gating mechanism. To work toward this goal, we investigated voltage-dependent single-channel gating in cell-attached patches at two different temperatures (20 and 30°C) using HEK293 cells stably expressing TRPM8. Both membrane depolarization and cooling increased channel open probability (Po) mainly by decreasing the duration of closed intervals, with a smaller increase in the duration of open intervals. Maximum likelihood analysis of dwell times at both temperatures indicated gating in a minimum of five closed and two open states, and global fitting over a wide range of voltages identified a seven-state model that described the voltage dependence of Po, the single-channel kinetics, and the response of whole-cell currents to voltage ramps and steps. The major action of depolarization and cooling was to accelerate forward transitions between the same two sets of adjacent closed states. The seven-state model provides a general mechanism to account for TRPM8 activation by membrane depolarization at two temperatures and can serve as a starting point for further investigations of multimodal TRP activation

Verbesserte sub-µs Schaltanalyse weist auf Konformationsänderungen hin, verursacht durch Ion-Pore-Wechselwirkungen im MaxiK-Kanal

This thesis aims at the analysis of fast gating events in ion channels. Experiments were done on single MaxiK channels expressed in HEK cells using the patch clamp technique in voltage clamp mode. Crucial for high temporal resolution was the signal-to-noise ratio which was improved by optimizing the set-up and pipette treatment. Furthermore, temporal resolution was increased by sharpening the mathematical tools employed in the analysis of the kinetic behavior of single-channel currents. This was done along four lines. 1. Splitting amplitude histograms into distributions-per-level and investigating their properties with respect to model discrimination, determination of the rate constants of fast gating and the detection of failures of jump detection. 2. Creating the SQ fit, a two-step fit algorithm consisting of a direct fit of patch clamp time series, by means of a 1-step prediction algorithm and a fit of the distribution-per-open-level by means of beta distributions. 3. Finding and testing the ability of the beta fit to determine the true single-channel current in time series where the apparent current was attenuated by averaging over undetected fast gating. 4. Comparing the SQ fit with the 2-dimensional dwell-time fit as improved by T. Huth. After having developed the new tools, they were applied to the analysis of fast gating events. Two phenomena could gain the outmost benefit from the new analytical tools: 1. The negative slope in the current-voltage curve occurring at positive potentials in symmetrical solutions with K+ as the only monovalent cation. 2. The negative slope occurring at negative potentials in luminal K+/Tl+ solution when the current dragged Tl+ into the channel. Both kinds of measurement resulted in insights about ion/protein interaction. The key for the creation of molecular models of ion/channel interactions was found in the experiments with K+ as the sole monovalent cation. In the range of the negative slope, saturation of the true single-channel current and onset of fast gating occurred in the same voltage range. This finding suggested a mechanistic model: On the cytosolic side, diffusion limitation produced saturation of outward-current. This caused ion depletion in the selectivity filter. The idea that gating occurred when permeant ions did no longer compensate the repulsive forces of the carbonyl groups was supported by MD simulations reported in the literature. The model correctly predicted the effect of different K+ concentrations. For explaining the negative slope induced by negative membrane potentials when luminal Tl+ was dragged into the channel, the basic model had to be extended. Here, the effect of luminal diffusion limitation on voltage-induced gating was not sufficient for explaining the experimental findings. This effect had to be modulated by additional Tl+ binding sites in the cavity or at the inner side of the selectivity filter. Describing the full set of gating phenomena induced by Tl+ would require the analysis of the “Great Markov Model” of the MaxiK channel. It is shown by preliminary approaches with classical tools what kind of insights would be obtained from this kind of analysis and what kind of problems keep the ratio “scientific output/time” at a very low level. Nevertheless, examples are given that the analysis of beta distributions can be helpful for the extension of the Markov model. Especially the picture of a rattly channel has arisen, implying that open states are not really open and closed states are not really closed. Finally, it is discussed that using the viral channel Kcv instead of MaxiK offers better chances to continue the building of a bridge between electrophysiology and structural biology as has been initiated in this thesis.Die vorliegende Arbeit befasst sich mit der Analyse schneller Schaltprozesse in einzelnen Ionenkanälen. Die Patch-Clamp Experimente wurden an mit humanen MaxiK-Kanälen stabil transfizierten HEK-Zellen vorgenommen. Wichtig zur Erzielung einer guten Zeitauflösung ist das Signal-Rausch-Verhältnis. Dazu diente die Verbesserung des Messaufbaus und der Patchpipetten. Entscheidender für die Verbesserung der Zeitauflösung war hier jedoch die Weiterentwicklung der Programme zur kinetischen Analyse von Einzelkanalaufzeichnungen. Die vier Kernpunkte hierbei waren folgende: 1. Aufspaltung der Amplitudenhistogramme in Einzelhistogramme. Diese so genannten „distributions-per-level“ erwiesen sich als nützlich in den Bereichen der Modellunterscheidung, der Bestimmung schneller Ratenkonstanten und der Erkennung von Fehlern in der Sprungdetektion. 2. Die Entwicklung eines Programms, das zwei Fitverfahren miteinander kombiniert (SQ-Fit): Den direkten Fit der Zeitreihe mit Einschrittprädiktion und den Fit der Amplitudenhistogramme mit Betaverteilungen. 3. Entwicklung und Erprobung einer neuen Anwendung für Betaverteilungen zur Rekonstruktion des wahren Einzelkanalstroms in Aufzeichnungen, in denen der scheinbare Strom durch nicht aufgelöstes schnelles Schalten stark reduziert ist. 4. Vergleich der Leistungsfähigkeit des SQ-Fits mit dem von Tobias Huth weiterentwickelten Fit der zweidimensionalen Dwell-Time-Histogramme. Die neuen Werkzeuge wurden zur Analyse schneller Schaltereignisse eingesetzt. Zwei Phänomene waren dabei besonders interessant, weil sie wichtige Hinweise zur Ionen-Protein-Interaktion gaben: 1. Die negative Kennlinie bei positiven Membranpotentialen in der Stromspannungskurve in symmetrischen Messlösungen mit K+ als einzigem einwertigen Kation. 2. Die negative Kennlinie bei negativen Membranpotentialen wenn eine K+/Tl+- Mischung von der luminalen Seite in die Pore gezogen wird. Der Schlüssel zur Modellbildung für die Ionen-Protein-Interaktion fand sich in den Kalium-Experimenten: Im Bereich der negativen Kennlinie setzten das schnelle Schalten und die Sättigung des wahren Einzelkanalstroms ungefähr gleichzeitig ein. Dies führte zu folgendem Modell: Eine Diffusionslimitierung am cytosolischen Porenmund bewirkt eine Sättigung des Auswärtsstromes und eine Verarmung an Kaliumionen im Selektivitätsfilter. Letzteres destabilisiert das Filter und führt zu Schließungen, weil die abstoßenden Kräfte der sich gegenüberliegenden Karbonylgruppen nicht mehr kompensiert werden. MD-Simulationen in der Literatur unterstützen diese Annahme. Das Modell war in der Lage, die Spannungs- und Konzentrationsabhängigkeit der beobachteten Effekte vorherzusagen. Zur Erklärung der Tl+-induzierten negativen Kennlinie bei negativen Spannungen musste das Modell erweitert werden, da die Annahme ähnlicher Diffusionslimitierungen am luminalen Porenmund nicht ausreichend war, um die Messergebnisse zu erklären. Es wurde vermutet, dass es in der Cavity oder am inneren Ende des Selektivitätsfilters Tl+-Bindungsstellen gibt, die das Schalten zusätzlich modulieren. Das gesamte Schaltverhalten der Kanäle mit und ohne Tl+ zu beschreiben, erfordert ein wesentlich größeres Markov-Modell als jenes mit nur zwei Zuständen, das zur Analyse des schnellen Schalten in den Bursts benutzt wurde. Ein rein mathematisches Vorgehen, um dieses Modell zu finden, würde unverhältnismäßig viel Zeit erfordern. Darum wurde die Analyse nur kurz angerissen, um aufzuzeigen, in welche Richtung es gehen kann. Dabei zeigte sich, dass die Analyse von Betaverteilungen wichtige Beiträge zur Modellentwicklung liefern kann: So entstand das Bild des „klapprigen“ Kanals, bei dem die Offenzustände nicht richtig offen und die Geschlossenzustände nicht richtig geschlossen sind. Zum Schluss wird noch diskutiert, dass ein Wechsel des Untersuchungsobjektes vom MaxiK zum wesentlich einfacheren viralen Kcv in zukünftigen Arbeiten vermutlich die hier begonnene Brückenbildung zwischen Elektrophysiologie und Strukturbiologie besser fördern wird

Markov, fractal, diffusion, and related models of ion channel gating. A comparison with experimental data from two ion channels

The gating kinetics of single-ion channels are generally modeled in terms of Markov processes with relatively small numbers of channel states. More recently, fractal (Liebovitch et al. 1987. Math. Biosci. 84:37–68) and diffusion (Millhauser et al. 1988. Proc. Natl. Acad. Sci. USA. 85:1502–1507) models of channel gating have been proposed. These models propose the existence of many similar conformational substrates of the channel protein, all of which contribute to the observed gating kinetics. It is important to determine whether or not Markov models provide the most accurate description of channel kinetics if progress is to be made in understanding the molecular events of channel gating. In this study six alternative classes of gating model are tested against experimental single-channel data. The single-channel data employed are from (a) delayed rectifier K+ channels of NG 108–15 cells and (b) locust muscle glutamate receptor channels. The models tested are (a) Markov, (b) fractal, (c) one-dimensional diffusion, (d) three-dimensional diffusion, (e) stretched exponential, and (f) expo-exponential. The models are compared by fitting the predicted distributions of channel open and closed times to those observed experimentally. The models are ranked in order of goodness-of-fit using a boot-strap resampling procedure. The results suggest that Markov models provide a markedly better description of the observed open and closed time distributions for both types of channel. This provides justification for the continued use of Markov models to explore channel gating mechanisms