Learning continuous potentials from smFRET

Potential energy landscapes are useful models in describing events such as protein folding and binding. While single-molecule fluorescence resonance energy transfer (smFRET) experiments encode information on continuous potentials for the system probed, including rarely visited barriers between putative potential minima, this information is rarely decoded from the data. This is because existing analysis methods often model smFRET output assuming, from the onset, that the system probed evolves in a discretized state space to be analyzed within a hidden Markov model (HMM) paradigm. By contrast, here, we infer continuous potentials from smFRET data without discretely approximating the state space. We do so by operating within a Bayesian nonparametric paradigm by placing priors on the family of all possible potential curves. As our inference accounts for a number of required experimental features raising computational cost (such as incorporating discrete photon shot noise), the framework leverages a structured-kernel-interpolation Gaussian process prior to help curtail computational cost. We show that our structured-kernel-interpolation priors for potential energy reconstruction from smFRET analysis accurately infers the potential energy landscape from a smFRET binding experiment. We then illustrate advantages of structured-kernel-interpolation priors for potential energy reconstruction from smFRET over standard HMM approaches by providing information, such as barrier heights and friction coefficients, that is otherwise inaccessible to HMMs.     

Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes

The hidden Markov model (HMM) is a framework for time series analysis widely applied to single-molecule experiments. Although initially developed for applications outside the natural sciences, the HMM has traditionally been used to interpret signals generated by physical systems, such as single molecules, evolving in a discrete state space observed at discrete time levels dictated by the data acquisition rate. Within the HMM framework, transitions between states are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, whereas measurements are often performed at discrete time levels in the natural sciences, physical systems evolve in continuous time according to transition rates. It then follows that the modeling assumptions underlying the HMM are justified if the transition rates of a physical process from state to state are small as compared to the data acquisition rate. In other words, HMMs apply to slow kinetics. The problem is, because the transition rates are unknown in principle, it is unclear, a priori, whether the HMM applies to a particular system. For this reason, we must generalize HMMs for physical systems, such as single molecules, because these switch between discrete states in “continuous time”. We do so by exploiting recent mathematical tools developed in the context of inferring Markov jump processes and propose the hidden Markov jump process. We explicitly show in what limit the hidden Markov jump process reduces to the HMM. Resolving the discrete time discrepancy of the HMM has clear implications: we no longer need to assume that processes, such as molecular events, must occur on timescales slower than data acquisition and can learn transition rates even if these are on the same timescale or otherwise exceed data acquisition rates.     

Denoising Single-Molecule FRET Trajectories with Wavelets and Bayesian Inference

A method to denoise single-molecule fluorescence resonance energy (smFRET) trajectories using wavelet detail thresholding and Bayesian inference is presented. Bayesian methods are developed to identify fluorophore photoblinks in the time trajectories. Simulated data are used to quantify the improvement in static and dynamic data analysis. Application of the method to experimental smFRET data shows that it distinguishes photoblinks from large shifts in smFRET efficiency while maintaining the important advantage of an unbiased approach. Known sources of experimental noise are examined and quantified as a means to remove their contributions via soft thresholding of wavelet coefficients. A wavelet decomposition algorithm is described, and thresholds are produced through the knowledge of noise parameters in the discrete-time photon signals. Reconstruction of the signals from thresholded coefficients produces signals that contain noise arising only from unquantifiable parameters. The method is applied to simulated and observed smFRET data, and it is found that the denoised data retain their underlying dynamic properties, but with increased resolution.     

小波变换及滚球算法在单分子荧光能量共振转移图像分析中的应用

单分子荧光共振能量转移技术是通过检测单个分子内的荧光供体及受体间荧光能量转移的效率来研究分子构象的变化．要得到这些生物大分子的信息就需要对大量的单分子信号进行统计分析,人工分析这些信息,既费时费力又不具备客观性和可重复性,因此本文将小波变换及滚球算法应用到单分子荧光能量共振转移图像中对单分子信号进行统计分析．在保证准确检测到单分子信号的前提下,文章对滚球算法和小波变换算法处理图像后的线性进行了分析,结果表明,滚球算法和小波变换算法不但能够很好地去除单分子FRET图像的背景噪声,同时还能很好地保持单分子荧光信号的线性．最后本文还利用滚球算法处理单分子FRET图像及统计15 bp DNA的FRET效率的直方图,通过计算得到了15 bp DNA的FRET效率值．     

Learning Rates and States from Biophysical Time Series: A Bayesian Approach to Model Selection and Single-Molecule FRET Data

Time series data provided by single-molecule Förster resonance energy transfer (smFRET) experiments offer the opportunity to infer not only model parameters describing molecular complexes, e.g., rate constants, but also information about the model itself, e.g., the number of conformational states. Resolving whether such states exist or how many of them exist requires a careful approach to the problem of model selection, here meaning discrimination among models with differing numbers of states. The most straightforward approach to model selection generalizes the common idea of maximum likelihood—selecting the most likely parameter values—to maximum evidence: selecting the most likely model. In either case, such an inference presents a tremendous computational challenge, which we here address by exploiting an approximation technique termed variational Bayesian expectation maximization. We demonstrate how this technique can be applied to temporal data such as smFRET time series; show superior statistical consistency relative to the maximum likelihood approach; compare its performance on smFRET data generated from experiments on the ribosome; and illustrate how model selection in such probabilistic or generative modeling can facilitate analysis of closely related temporal data currently prevalent in biophysics. Source code used in this analysis, including a graphical user interface, is available open source via http://vbFRET.sourceforge.net.     

Robust Data Driven Model Order Estimation for Independent Component Analysis of fMRI Data with Low Contrast to Noise

Independent component analysis (ICA) has been successfully utilized for analysis of functional MRI (fMRI) data for task related as well as resting state studies. Although it holds the promise of becoming an unbiased data-driven analysis technique, a few choices have to be made prior to performing ICA, selection of a method for determining the number of independent components (nIC) being one of them. Choice of nIC has been shown to influence the ICA maps, and various approaches (mostly relying on information theoretic criteria) have been proposed and implemented in commonly used ICA analysis packages, such as MELODIC and GIFT. However, there has been no consensus on the optimal method for nIC selection, and many studies utilize arbitrarily chosen values for nIC. Accurate and reliable determination of true nIC is especially important in the setting where the signals of interest contribute only a small fraction of the total variance, i.e. very low contrast-to-noise ratio (CNR), and/or very focal response. In this study, we evaluate the performance of different model order selection criteria and demonstrate that the model order selected based upon bootstrap stability of principal components yields more reliable and accurate estimates of model order. We then demonstrate the utility of this fully data-driven approach to detect weak and focal stimulus-driven responses in real data. Finally, we compare the performance of different multi-run ICA approaches using pseudo-real data.     

On identification of Na+ channel gating schemes using moving-average filtered hidden Markov models

 Transitions between distinct kinetic states of an ion channel are described by a Markov process. Hidden Markov models (HMM) have been successfully applied in the analysis of single ion channel recordings with a small signal-to-noise ratio. However, we have recently shown that the anti-aliasing low-pass filter misleads parameter estimation. Here, we show for the case of a Na⁺ channel recording that the standard HMM do neither allow parameter estimation nor a correct identification of the gating scheme. In particular, the number of closed and open states is determined incorrectly, whereas a modified HMM considering the anti-aliasing filter (moving-average filtered HMM) is able to reproduce the characteristic properties of the time series and to perform gating scheme identification. Received: 11 February 1999 / Revised version: 18 June 1999 / Accepted: 21 June 1999     

In-cell single-molecule FRET measurements reveal three conformational state changes in RAF protein

BackgroundThe structures of proteins are intimately related to their functions. Significant efforts have been dedicated to the structural investigation of proteins, mainly those of purified proteins in in vitro environments. Proteins function in living cells and thus protein structures must be regulated by interactions with various molecules, some of which participate in reaction networks, depending on the states, conditions, or actions of the cell. Therefore, it is very important to understand the structural behavior of proteins in living cells.MethodsSingle-molecule Förster resonance energy transfer (smFRET) measurements were conducted using the alternative laser excitation (ALEX) technique. smFRET distributions of cytosolic Rapidly Accelerated Fibrosarcoma (RAF) proteins in living HeLa cells were obtained with exclusion of the negative effects of photobleached fluorophores and incompletely labeled proteins on smFRET.ResultssmFRET histograms of wildtype (wt) RAF in live cells exhibited two major peaks, whereas that of the S621A mutant, which has been thought to have an expanded structure, was almost single-peaked. A population shift involving the peaks for wt RAF was detected upon epidermal growth factor stimulation. Spontaneous transitions between the conformational states corresponding to the two peaks were also detected using the FRET-two-channel kernel-based density distribution estimator method in comparison to static double-stranded DNA samples.ConclusionsCytosolic CRAF has at least three conformational states; in addition to the closed and open forms, the fully-open form was distinctly specified. Based on the results, we propose a speculative structural model for CRAF.General significanceStructural distribution and changes to proteins in live cells as a result of intracellular interactions were successfully identified. smFRET using ALEX is applicable to any other cytosolic proteins.     

隐马尔科夫过程在生物信息学中的应用

隐马尔科夫过程（hidden markov model,简称HMM）是20世纪70年代提出来的一种统计方法,以前主要用于语音识别。1989年Churchill将其引入计算生物学。目前,HMM是生物信息学中应用比较广泛的一种统计方法,主要用于：线性序列分析、模型分析、基因发现等方面。对HMM进行了简明扼要的描述,并对其在上述几个方面的应用作一概略介绍。     

Human secretory signal peptide description by hidden Markov model and generation of a strong artificial signal peptide for secreted protein expression

A hidden Markov model (HMM) has been used to describe, predict, identify, and generate secretory signal peptide sequences. The relative strengths of artificial secretory signals emitted from the human signal peptide HMM (SP-HMM) correlate with their HMM bit scores as determined by their effectiveness to direct alkaline phosphatase secretion. The nature of the signal strength is in effect the closeness to the consensus. The HMM bit score of 8 is experimentally determined to be the threshold for discriminating signal sequences from non-secretory ones. An artificial SP-HMM generated signal sequence of the maximum model bit score (HMM + 38) was selected as an ideal human signal sequence. This signal peptide (secrecon) directs strong protein secretion and expression. We further ranked the signal strengths of the signal peptides of the known human secretory proteins by SP-HMM bit scores. The applications of high-bit scoring HMM signals in recombinant protein production and protein engineering are discussed.     

Optimally-connected hidden markov models for predicting MHC-binding peptides

Hidden Markov models (HMMs) are one of various methods that have been applied to prediction of major histo-compatibility complex (MHC) binding peptide. In terms of model topology, a fully-connected HMM (fcHMM) has the greatest potential to predict binders, at the cost of intensive computation. While a profile HMM (pHMM) performs dramatically fewer computations, it potentially merges overlapping patterns into one which results in some patterns being missed. In a profile HMM a state corresponds to a position on a peptide while in an fcHMM a state has no specific biological meaning. This work proposes optimally-connected HMMs (ocHMMs), which do not merge overlapping patterns and yet, by performing topological reductions, a model's connectivity is greatly reduced from an fcHMM. The parameters of ocHMMs are initialized using a novel amino acid grouping approach called "multiple property grouping." Each group represents a state in an ocHMM. The proposed ocHMMs are compared to a pHMM implementation using HMMER, based on performance tests on two MHC alleles HLA (Human Leukocyte Antigen)-A*0201 and HLA-B*3501. The results show that the heuristic approaches can be adjusted to make an ocHMM achieve higher predictive accuracy than HMMER. Hence, such obtained ocHMMs are worthy of trial for predicting MHC-binding peptides.     

The application of independent component analysis to the multi-channel surface electromyographic signals for separation of motor unit action potential trains: part II-modelling interpretation.

The purpose of this article was to investigate whether or not FastICA can separate identical motor unit action potential trains (MUAPTs) of the 8-channel surface electromyographic (sEMG) signals constructed by an sEMG model into the independent components. Firstly, we have examined how much the increase of motor units (MUs) in the simulated sEMG signals influenced the performance on the separation of MUAPTs by kurtosis. The decreased trend of mean kurtosis on both sEMG signals and their independent components were observed as MUs were increased. These data suggested that the separation performance decayed when MUs were increased. Secondary, the differences between the independent components and the principal components have been also applied to the simulated sEMG signals with or without time delay between the sEMG channels. FastICA could successfully separate identical MUAPTs with no time delay but principal component analysis (PCA) could not do so. Against it, both FastICA and PCA could not separate MUAPTs with some time delay. In conclusion, our results suggested that FastICA could separate identical MUAPTs with no time delay into the independent components by FastICA, which might offer a new technique for the separation of interfered MUAP waveforms based on statistical properties of sEMG signal distributions.     

A probabilistic framework for a physiological representation of dynamically evolving sleep state

This work presents a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. We show that the mapping produced from human data robustly separates rapid eye movement sleep (REM) from slow wave sleep (SWS). A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.     

Training HMM structure with genetic algorithm for biological sequence analysis

SUMMARY: Hidden Markov models (HMMs) are widely used for biological sequence analysis because of their ability to incorporate biological information in their structure. An automatic means of optimizing the structure of HMMs would be highly desirable. However, this raises two important issues; first, the new HMMs should be biologically interpretable, and second, we need to control the complexity of the HMM so that it has good generalization performance on unseen sequences. In this paper, we explore the possibility of using a genetic algorithm (GA) for optimizing the HMM structure. GAs are sufficiently flexible to allow incorporation of other techniques such as Baum-Welch training within their evolutionary cycle. Furthermore, operators that alter the structure of HMMs can be designed to favour interpretable and simple structures. In this paper, a training strategy using GAs is proposed, and it is tested on finding HMM structures for the promoter and coding region of the bacterium Campylobacter jejuni. The proposed GA for hidden Markov models (GA-HMM) allows, HMMs with different numbers of states to evolve. To prevent over-fitting, a separate dataset is used for comparing the performance of the HMMs to that used for the Baum-Welch training. The GA-HMM was capable of finding an HMM comparable to a hand-coded HMM designed for the same task, which has been published previously.     

Improved hidden Markov models for molecular motors, part 2: extensions and application to experimental data

Unbiased interpretation of noisy single molecular motor recordings remains a challenging task. To address this issue, we have developed robust algorithms based on hidden Markov models (HMMs) of motor proteins. The basic algorithm, called variable-stepsize HMM (VS-HMM), was introduced in the previous article. It improves on currently available Markov-model based techniques by allowing for arbitrary distributions of step sizes, and shows excellent convergence properties for the characterization of staircase motor timecourses in the presence of large measurement noise. In this article, we extend the VS-HMM framework for better performance with experimental data. The extended algorithm, variable-stepsize integrating-detector HMM (VSI-HMM) better models the data-acquisition process, and accounts for random baseline drifts. Further, as an extension, maximum a posteriori estimation is provided. When used as a blind step detector, the VSI-HMM outperforms conventional step detectors. The fidelity of the VSI-HMM is tested with simulations and is applied to in vitro myosin V data where a small 10 nm population of steps is identified. It is also applied to an in vivo recording of melanosome motion, where strong evidence is found for repeated, bidirectional steps smaller than 8 nm in size, implying that multiple motors simultaneously carry the cargo.     

Estimating animal behavior and residency from movement data

We present a process‐based approach to estimate residency and behavior from uncertain and temporally correlated movement data collected with electronic tags. The estimation problem is formulated as a hidden Markov model (HMM) on a spatial grid in continuous time, which allows straightforward implementation of barriers to movement. Using the grid to explicitly resolve space, location estimation can be supplemented by or based entirely on environmental data (e.g. temperature, daylight). The HMM method can therefore analyze any type of electronic tag data. The HMM computes the joint posterior probability distribution of location and behavior at each point in time. With this, the behavioral state of the animal can be associated to regions in space, thus revealing migration corridors and residence areas. We demonstrate the inferential potential of the method by analyzing satellite‐linked archival tag data from a southern bluefin tuna Thunnus maccoyii where longitudinal coordinates inferred from daylight are supplemented by latitudinal information in recorded sea surface temperatures.