Analysis of single-molecule FRET trajectories using hidden Markov modeling

The analysis of single-molecule fluorescence resonance energy transfer (FRET) trajectories has become one of significant biophysical interest. In deducing the transition rates between various states of a system for time-binned data, researchers have relied on simple, but often arbitrary methods of extracting rates from FRET trajectories. Although these methods have proven satisfactory in cases of well-separated, low-noise, two- or three-state systems, they become less reliable when applied to a system of greater complexity. We have developed an analysis scheme that casts single-molecule time-binned FRET trajectories as hidden Markov processes, allowing one to determine, based on probability alone, the most likely FRET-value distributions of states and their interconversion rates while simultaneously determining the most likely time sequence of underlying states for each trajectory. Together with a transition density plot and Bayesian information criterion we can also determine the number of different states present in a system in addition to the state-to-state transition probabilities. Here we present the algorithm and test its limitations with various simulated data and previously reported Holliday junction data. The algorithm is then applied to the analysis of the binding and dissociation of three RecA monomers on a DNA construct.     

Classification method for disease risk mapping based on discrete hidden Markov random fields

Risk mapping in epidemiology enables areas with a low or high risk of disease contamination to be localized and provides a measure of risk differences between these regions. Risk mapping models for pooled data currently used by epidemiologists focus on the estimated risk for each geographical unit. They are based on a Poisson log-linear mixed model with a latent intrinsic continuous hidden Markov random field (HMRF) generally corresponding to a Gaussian autoregressive spatial smoothing. Risk classification, which is necessary to draw clearly delimited risk zones (in which protection measures may be applied), generally must be performed separately. We propose a method for direct classified risk mapping based on a Poisson log-linear mixed model with a latent discrete HMRF. The discrete hidden field (HF) corresponds to the assignment of each spatial unit to a risk class. The risk values attached to the classes are parameters and are estimated. When mapping risk using HMRFs, the conditional distribution of the observed field is modeled with a Poisson rather than a Gaussian distribution as in image segmentation. Moreover, abrupt changes in risk levels are rare in disease maps. The spatial hidden model should favor smoothed out risks, but conventional discrete Markov random fields (e.g. the Potts model) do not impose this. We therefore propose new potential functions for the HF that take into account class ordering. We use a Monte Carlo version of the expectation-maximization algorithm to estimate parameters and determine risk classes. We illustrate the method's behavior on simulated and real data sets. Our method appears particularly well adapted to localize high-risk regions and estimate the corresponding risk levels.     

Mining gene expression data using a novel approach based on hidden Markov models

In this work we have developed a new framework for microarray gene expression data analysis. This framework is based on hidden Markov models. We have benchmarked the performance of this probability model-based clustering algorithm on several gene expression datasets for which external evaluation criteria were available. The results showed that this approach could produce clusters of quality comparable to two prevalent clustering algorithms, but with the major advantage of determining the number of clusters. We have also applied this algorithm to analyze published data of yeast cell cycle gene expression and found it able to successfully dig out biologically meaningful gene groups. In addition, this algorithm can also find correlation between different functional groups and distinguish between function genes and regulation genes, which is helpful to construct a network describing particular biological associations. Currently, this method is limited to time series data. Supplementary materials are available at http://www.bioinfo.tsinghua.edu.cn/~rich/hmmgep_supp/.     

Comparison of glycosyltransferase families using the profile hidden Markov model

In order to investigate the relationship between glycosyltransferase families and the motif for them, we classified 47 glycosyltransferase families in the CAZy database into four superfamilies, GTS-A, -B, -C, and -D, using a profile Hidden Markov Model method. On the basis of the classification and the similarity between GTS-A and nucleotidylyltransferase family catalyzing the synthesis of nucleotide-sugar, we proposed that ancient oligosaccharide might have been synthesized by the origin of GTS-B whereas the origin of GTS-A might be the gene encoding for synthesis of nucleotide-sugar as the donor and have evolved to glycosyltransferases to catalyze the synthesis of divergent carbohydrates. We also suggested that the divergent evolution of each superfamily in the corresponding subcellular component has increased the complexities of eukaryotic carbohydrate structure.     

Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences.

Techniques for characterizing very small single-channel currents buried in background noise are described and tested on simulated data to give confidence when applied to real data. Single channel currents are represented as a discrete-time, finite-state, homogeneous, Markov process, and the noise that obscures the signal is assumed to be white and Gaussian. The various signal model parameters, such as the Markov state levels and transition probabilities, are unknown. In addition to white Gaussian noise, the signal can be corrupted by deterministic interferences of known form but unknown parameters, such as the sinusoidal disturbance stemming from AC interference and a drift of the base line owing to a slow development of liquid-junction potentials. To characterize the signal buried in such stochastic and deterministic interferences, the problem is first formulated in the framework of a Hidden Markov Model and then the Expectation Maximization algorithm is applied to obtain the maximum likelihood estimates of the model parameters (state levels, transition probabilities), signals, and the parameters of the deterministic disturbances. Using fictitious channel currents embedded in the idealized noise, we first show that the signal processing technique is capable of characterizing the signal characteristics quite accurately even when the amplitude of currents is as small as 5-10 fA. The statistics of the signal estimated from the processing technique include the amplitude, mean open and closed duration, open-time and closed-time histograms, probability of dwell-time and the transition probability matrix. With a periodic interference composed, for example, of 50 Hz and 100 Hz components, or a linear drift of the baseline added to the segment containing channel currents and white noise, the parameters of the deterministic interference, such as the amplitude and phase of the sinusoidal wave, or the rate of linear drift, as well as all the relevant statistics of the signal, are accurately estimated with the algorithm we propose. Also, if the frequencies of the periodic interference are unknown, they can be accurately estimated. Finally, we provide a technique by which channel currents originating from the sum of two or more independent single channels are decomposed so that each process can be separately characterized. This process is also formulated as a Hidden Markov Model problem and solved by applying the Expectation Maximization algorithm. The scheme relies on the fact that the transition matrix of the summed Markov process can be construed as a tensor product of the transition matrices of individual processes.     

Characterization of single channel currents using digital signal processing techniques based on Hidden Markov Models.

Techniques for extracting small, single channel ion currents from background noise are described and tested. It is assumed that single channel currents are generated by a first-order, finite-state, discrete-time, Markov process to which is added 'white' background noise from the recording apparatus (electrode, amplifiers, etc). Given the observations and the statistics of the background noise, the techniques described here yield a posteriori estimates of the most likely signal statistics, including the Markov model state transition probabilities, duration (open- and closed-time) probabilities, histograms, signal levels, and the most likely state sequence. Using variations of several algorithms previously developed for solving digital estimation problems, we have demonstrated that: (1) artificial, small, first-order, finite-state, Markov model signals embedded in simulated noise can be extracted with a high degree of accuracy, (2) processing can detect signals that do not conform to a first-order Markov model but the method is less accurate when the background noise is not white, and (3) the techniques can be used to extract from the baseline noise single channel currents in neuronal membranes. Some studies have been included to test the validity of assuming a first-order Markov model for biological signals. This method can be used to obtain directly from digitized data, channel characteristics such as amplitude distributions, transition matrices and open- and closed-time durations.     

Bayesian restoration of ion channel records using hidden Markov models

Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.     

The analysis of hospital infection data using hidden Markov models

Surveillance data for communicable nosocomial pathogens usually consist of short time series of low-numbered counts of infected patients. These often show overdispersion and autocorrelation. To date, almost all analyses of such data have ignored the communicable nature of the organisms and have used methods appropriate only for independent outcomes. Inferences that depend on such analyses cannot be considered reliable when patient-to-patient transmission is important. We propose a new method for analysing these data based on a mechanistic model of the epidemic process. Since important nosocomial pathogens are often carried asymptomatically with overt infection developing in only a proportion of patients, the epidemic process is usually only partially observed by routine surveillance data. We therefore develop a 'structured' hidden Markov model where the underlying Markov chain is generated by a simple transmission model. We apply both structured and standard (unstructured) hidden Markov models to time series for three important pathogens. We find that both methods can offer marked improvements over currently used approaches when nosocomial spread is important. Compared to the standard hidden Markov model, the new approach is more parsimonious, is more biologically plausible, and allows key epidemiological parameters to be estimated.     

COACH: profile-profile alignment of protein families using hidden Markov models

MOTIVATION: Alignments of two multiple-sequence alignments, or statistical models of such alignments (profiles), have important applications in computational biology. The increased amount of information in a profile versus a single sequence can lead to more accurate alignments and more sensitive homolog detection in database searches. Several profile-profile alignment methods have been proposed and have been shown to improve sensitivity and alignment quality compared with sequence-sequence methods (such as BLAST) and profile-sequence methods (e.g. PSI-BLAST). Here we present a new approach to profile-profile alignment we call Comparison of Alignments by Constructing Hidden Markov Models (HMMs) (COACH). COACH aligns two multiple sequence alignments by constructing a profile HMM from one alignment and aligning the other to that HMM. RESULTS: We compare the alignment accuracy of COACH with two recently published methods: Yona and Levitt's prof_sim and Sadreyev and Grishin's COMPASS. On two sets of reference alignments selected from the FSSP database, we find that COACH is able, on average, to produce alignments giving the best coverage or the fewest errors, depending on the chosen parameter settings. AVAILABILITY: COACH is freely available from www.drive5.com/lobster     

A quantitative approach for polymerase chain reactions based on a hidden Markov model

Polymerase chain reaction (PCR) is a major DNA amplification technology from molecular biology. The quantitative analysis of PCR aims at determining the initial amount of the DNA molecules from the observation of typically several PCR amplifications curves. The mainstream observation scheme of the DNA amplification during PCR involves fluorescence intensity measurements. Under the classical assumption that the measured fluorescence intensity is proportional to the amount of present DNA molecules, and under the assumption that these measurements are corrupted by an additive Gaussian noise, we analyze a single amplification curve using a hidden Markov model(HMM). The unknown parameters of the HMM may be separated into two parts. On the one hand, the parameters from the amplification process are the initial number of the DNA molecules and the replication efficiency, which is the probability of one molecule to be duplicated. On the other hand, the parameters from the observational scheme are the scale parameter allowing to convert the fluorescence intensity into the number of DNA molecules and the mean and variance characterizing the Gaussian noise. We use the maximum likelihood estimation procedure to infer the unknown parameters of the model from the exponential phase of a single amplification curve, the main parameter of interest for quantitative PCR being the initial amount of the DNA molecules. An illustrative example is provided. This research was financed by the Swedish foundation for Strategic Research through the Gothenburg Mathematical Modelling Centre.     

Prediction of mitochondrial proteins using support vector machine and hidden Markov model

Mitochondria are considered as one of the core organelles of eukaryotic cells hence prediction of mitochondrial proteins is one of the major challenges in the field of genome annotation. This study describes a method, MitPred, developed for predicting mitochondrial proteins with high accuracy. The data set used in this study was obtained from Guda, C., Fahy, E. & Subramaniam, S. (2004) Bioinformatics 20, 1785-1794. First support vector machine-based modules/methods were developed using amino acid and dipeptide composition of proteins and achieved accuracy of 78.37 and 79.38%, respectively. The accuracy of prediction further improved to 83.74% when split amino acid composition (25 N-terminal, 25 C-terminal, and remaining residues) of proteins was used. Then BLAST search and support vector machine-based method were combined to get 88.22% accuracy. Finally we developed a hybrid approach that combined hidden Markov model profiles of domains (exclusively found in mitochondrial proteins) and the support vector machine-based method. We were able to predict mitochondrial protein with 100% specificity at a 56.36% sensitivity rate and with 80.50% specificity at 98.95% sensitivity. The method estimated 9.01, 6.35, 4.84, 3.95, and 4.25% of proteins as mitochondrial in Saccharomyces cerevisiae, Drosophila melanogaster, Caenorhabditis elegans, mouse, and human proteomes, respectively. MitPred was developed on the above hybrid approach.     

Evaluation of agonist selectivity for the NMDA receptor ion channel in bilayer lipid membranes based on integrated single-channel currents

A new method for evaluating chemical selectivity of agonists to activate the N-methyl-D-aspartate (NMDA) receptor was presented by using typical agonists NMDA, L-glutamate and (2S, 3R, 4S)-2-(carboxycyclopropyl)glycine (L-CCG-IV) and the mouse epsilon1/zeta1 NMDA receptor incorporated in bilayer lipid membranes (BLMs) as an illustrative example. The method was based on the magnitude of an agonist-induced integrated single-channel current corresponding to the number of total ions passed through the open channel. The very magnitudes of the integrated single-channel currents were compared with the different BLMs as a new measure of agonist selectivity. The epsilon1/zeta1 NMDA receptor was partially purified from Chinese hamster ovary (CHO) cells expressing the epsilon1/zeta1 NMDA receptor and incorporated in BLMs formed by the tip-dip method. The agonist-induced integrated single-channel currents were obtained at 50 microM agonist concentration, where the integrated current for NMDA was shown to reach its saturated value. The obtained integrated currents were found to be (4.5 +/- 0.55) x 10(-13) C/s for NMDA, (5.8 +/- 0.72) x 10(-13) C/s for L-glutamate and (6.6 +/- 0.61) x 10(-13) C/s for L-CCG-IV, respectively. These results suggest that the agonist selectivity in terms of the total ion flux through the single epsilon1/zeta1 NMDA receptor is in the order of L-CCG-IV approximately = L-glutamate > NMDA.     

Whole-cell and single-channel currents across the plasmalemma of corn shoot suspension cells

Summary Whole-cell sealed-on pipettes have been used to measure electrical properties of the plasmalemma surrounding protoplasts isolated from Black Mexican sweet corn shoot cells from suspension culture. In these protoplasts the membrane resting potential (V _m ) was found to be –59±23 mV (n=23) in 1mm K _o ^– . The meanV _m became more negative as [K^–] _o decreased, but was more positive than the K⁺ equilibrium potential. There was no evidence of electrogenic pump activity. We describe four features of the current-voltage characteristic of the plasmalemma of these protoplasts which show voltagegated channel activity. Depolarization of the whole-cell membrane from the resting potential activates time- and voltage-dependent outward current through K⁺-selective channels. A local minimum in the outward current-voltage curve nearV _m =150 mV suggests that these currents are mediated by two populations of K⁺-selective channels. The absence of this minimum in the presence of verapamil suggests that the activation of one channel population depends on the influx of Ca²⁺ into the cytoplasm. We identify unitary currents from two K⁺-selective channel populations (40 and 125 pS) which open when the membrane is depolarized; it is possible that these mediate the outward whole-cell current. Hyperpolarization of the membrane from the resting potential produces time- and voltage-dependent inward whole-cell current. Current activation is fast and follows an exponential time course. The current saturates and in some cases decreases at membrane potentials more negative than –175 mV. This current is conducted by poorly selective K⁺ channels, whereP _Cl/P _K=0.43±0.15. We describe a low conductance (20 pS) channel population of unknown selectivity which opens when the membrane is hyperpolarized. It is possible that these channels mediate inward whole-cell current. When the membrane is hyperpolarized to potentials more negative than –250 mV large, irregular inward current is activated. A third type of inward whole-cell current is briefly described. This activates slowly and with a U-shaped current-voltage curve over the range of membrane potentials –90<V _m <0 mV.     

Ca-independent effects of BAPTA and EGTA on single-channel Cl currents in brown adipocytes

The Cl⁻ channels of brown adipocytes electrophysiologically resemble outwardly rectifying Cl⁻ channels (ORCC). To study tentative Ca²⁺ regulation of these channels, we attempted to control Ca²⁺ levels at the cytoplasmic side of the inside-out membrane patches with Ca²⁺-chelating agents. However, we found that the commonly used Ca²⁺-chelators EGTA and BAPTA by themselves influenced the Cl⁻ channel currents, unrelated to their calcium chelating effects. Consequently, in this report we delineate effects of Ca²⁺-chelators (acting from the cytoplasmic side) on the single Cl⁻ channel currents in patch-clamp experiments. Using fixed (1-2 mM) concentrations of chelators, two types of Cl⁻ channels were identified, as discriminated by their reaction to the Ca²⁺-chelators and by their conductance: true-blockage channels (31 pS) and quasi-blockage channels (52 pS). In true-blockage channels, EGTA and BAPTA inhibited channel activity in a classical flickery type manner. In quasi-blockage channels, chelators significantly shortened the duration of individual openings, as in a flickering block, but the overall channel activity tended to increase. This dual effect of mean open time decrease accompanied by a tendency of open probability to increase we termed a quasi-blockage. Despite the complications due to the chelators as such, we could detect a moderate inhibitory effect of Ca²⁺. The anionic classical Cl⁻ channel blockers DIDS and SITS could mimic the true/quasi blockage of EGTA and BAPTA. It was concluded that at least in this experimental system, standard techniques for Ca²⁺ level control in themselves could fundamentally affect the behaviour of Cl⁻ channels.     

Prediction of protein binding sites in protein structures using hidden Markov support vector machine

Background  

Predicting the binding sites between two interacting proteins provides important clues to the function of a protein. Recent research on protein binding site prediction has been mainly based on widely known machine learning techniques, such as artificial neural networks, support vector machines, conditional random field, etc. However, the prediction performance is still too low to be used in practice. It is necessary to explore new algorithms, theories and features to further improve the performance.     

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     

Prediction of protein secondary structure by the hidden Markov model

The purpose of this paper is to introduce a new method for analyzingthe amino acid sequences of proteins using the hidden Markovmodel (HMM), which is a type of stochastic model. Secondarystructures such as helix, sheet and turn are learned by HMMs,and these HMMs are applied to new sequences whose structuresare unknown. The output probabilities from the HMMs are usedto predict the secondary structures of the sequences. The authorstested this prediction system on 100 sequences from a publicdatabase (Brookhaven PDB). Although the implementation is ‘withoutgrammar’ (no rule for the appearance patterns of secondarystructure) the result was reasonable.