Maximum likelihood estimation and identification directly from single-channel recordings.

We present a method for analysis of noisy sampled data from a single-channel patch clamp which bypasses restoration of an idealized quantal signal. We show that, even in the absence of a specific model, the conductance levels and mean dwell times within those levels can be estimated. Estimation of the rate constants of a hypothesized kinetic scheme is more difficult. We present examples in which the rate constants can be effectively estimated and examples in which they cannot.     

Patch recordings from the electrocytes of electrophorus. Na channel gating currents

Gating currents were recorded at 11 degrees C in cell-attached and inside-out patches from the innervated membrane of Electrophorus main organ electrocytes. With pipette tip diameters of 3-8 microns, maximal charge measured in patches ranged from 0.74 to 7.19 fC. The general features of the gating currents are similar to those from the squid giant axon. The steady-state voltage dependence of the ON gating charge was characterized by an effective valence of 1.3 +/- 0.4 and a midpoint voltage of -56 +/- 7 mV. The charge vs. voltage relation lies approximately 30 mV negative to the channel open probability curve. The ratio of the time constants of the OFF gating current and the Na current was 2.3 at -120 mV and equal at -80 mV. Charge immobilization and Na current inactivation develop with comparable time courses and have very similar voltage dependences. Between 60 and 80% of the charge is temporarily immobilized by inactivation.     

Maximum likelihood vs. minimum chi-square

In minimum chi-square logit or probit analysis of quantal bioassay data, a requirement for proper asymptotic behavior of the estimates made is that test-group sizes get indefinitely large. Inconsistent estimates result if group sizes are small, however numerous the groups. Maximum likelihood estimates do not show this inconsistent behavior, even if all the many group sizes are only unity. The inconsistent behavior for minimum chi-square results from a bias toward 0.5 for response probabilities. At 0.5 the binomial variance is at a maximum of 0.25, so tending to minimize the calculated value of chi square. The principle of minimum chi-square should not be confused with the principle of least squares.     

Glutamate activation of a single NMDA receptor-channel produces a cluster of channel openings.

Activations of the N-methyl-D-aspartate (NMDA) receptor by glutamate were studied in outside-out patches from CA1 cells in rat hippocampal slices. Very low glutamate concentrations (20-100 nM) were used so that individual receptor activations would be well separated. The shut-time distribution contained at least five components, only the longest component being obviously concentration dependent. The three briefest shut-time components had time constants of 56 microseconds, 0.68 ms and 10.1 ms; all of these were independent of glutamate concentration. An individual activation of the receptor therefore produces a long cluster of channel openings that contains longer gaps than have been reported for receptor activations by other fast neurotransmitters. In addition, (i) some activations may contain still longer (mean 78 ms) shut periods generating 'super clusters', and (ii) a significant amount of NMDA current may be carried by prolonged ('high P(open)') periods during which the channel is open for most of the time. Such periods occur intermittently even at these very low glutamate concentrations. It is suggested that the slow time course of the NMDA receptor-mediated synaptic currents may be determined mainly by the channel activation kinetics.     

Maximum likelihood estimation of recombination rates from population data

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Theta are accurate and apparently unbiased for a wide range of parameter values. However, when both Theta and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.     

Maximum likelihood of phylogenetic networks

Bioinformatics (2006) 22(21), 2604–2611 The authors would like to apologize for errors of graph misplacementin Figures 4–6, and an     

Maximum likelihood of phylogenetic networks

MOTIVATION: Horizontal gene transfer (HGT) is believed to be ubiquitous among bacteria, and plays a major role in their genome diversification as well as their ability to develop resistance to antibiotics. In light of its evolutionary significance and implications for human health, developing accurate and efficient methods for detecting and reconstructing HGT is imperative. RESULTS: In this article we provide a new HGT-oriented likelihood framework for many problems that involve phylogeny-based HGT detection and reconstruction. Beside the formulation of various likelihood criteria, we show that most of these problems are NP-hard, and offer heuristics for efficient and accurate reconstruction of HGT under these criteria. We implemented our heuristics and used them to analyze biological as well as synthetic data. In both cases, our criteria and heuristics exhibited very good performance with respect to identifying the correct number of HGT events as well as inferring their correct location on the species tree. AVAILABILITY: Implementation of the criteria as well as heuristics and hardness proofs are available from the authors upon request. Hardness proofs can also be downloaded at http://www.cs.tau.ac.il/~tamirtul/MLNET/Supp-ML.pdf     

Maximum likelihood estimation of ion channel kinetics from macroscopic currents

We describe a maximum likelihood method for direct estimation of rate constants from macroscopic ion channel data for kinetic models of arbitrary size and topology. The number of channels in the preparation, and the mean and standard deviation of the unitary current can be estimated, and a priori constraints can be imposed on rate constants. The method allows for arbitrary stimulation protocols, including stimuli with finite rise time, trains of ligand or voltage steps, and global fitting across different experimental conditions. The initial state occupancies can be optimized from the fit kinetics. Utilizing arbitrary stimulation protocols and using the mean and the variance of the current reduce or eliminate problems of model identifiability (Kienker, 1989). The algorithm is faster than a recent method that uses the full autocovariance matrix (Celentano and Hawkes, 2004), in part due to the analytical calculation of the likelihood gradients. We tested the method with simulated data and with real macroscopic currents from acetylcholine receptors, elicited in response to brief pulses of carbachol. Given appropriate stimulation protocols, our method chose a reasonable model size and topology.     

Maximum likelihood estimation of linkage and interference from tetrad data

Maximum likelihood equations have been derived for estimation of map distance and interference from two-point and ranked tetrad data. The estimators have been applied to data from Saccharomyces cerevisiae and Schizosaccharomyces pombe. S. cerevisiae consistently shows quite strong interference over the mapped genome. In striking contrast, S. pombe consistently shows much weaker interference and many crosses exhibit negative interference. In neither species was there a conspicuous tendency for intervals spanning a centromere to show less interference than those that did not. Since the amount of recombination per microgram of DNA in the two species is similar, the difference in interference characteristics seems to be a reflection of some fundamental difference in the recombination process of the two species.     

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves

The usefulness of fluorescence techniques for the study of macromolecular structure and dynamics depends on the accuracy and sensitivity of the methods used for data analysis. Many methods for data analysis have been proposed and used, but little attention has been paid to the maximum likelihood method, generally known as the most powerful statistical method for parameter estimation. In this paper we study the properties and behavior of maximum likelihood estimates by using simulated fluorescence intensity decay data. We show that the maximum likelihood method provides generally more accurate estimates of lifetimes and fractions than does the standard least-squares approach especially when the lifetime ratios between individual components are small. Three novelties to the field of fluorescence decay analysis are also introduced and studied in this paper: a) discretization of the convolution integral based on the generalized integral mean value theorem: b) the likelihood ratio test as a tool to determine the number of exponential decay components in a given decay profile; and c) separability and detectability indices which provide measures on how accurately, a particular decay component can be detected. Based on the experience gained from this and from our previous study of the Padé-Laplace method, we make some recommendations on how the complex problem of deconvolution and parameter estimation of multiexponential functions might be approached in an experimental setting. Offprint requests to: F. G. Prendergast     

Maximum likelihood molecular clock comb: analytic solutions.

Maximum likelihood (ML) is increasingly used as an optimality criterion for selecting evolutionary trees, but finding the global optimum is a hard computational task. Because no general analytic solution is known, numeric techniques such as hill climbing or expectation maximization (EM), are used in order to find optimal parameters for a given tree. So far, analytic solutions were derived only for the simplest model--three taxa, two state characters, under a molecular clock. Four taxa rooted trees have two topologies--the fork (two subtrees with two leaves each) and the comb (one subtree with three leaves, the other with a single leaf). In a previous work, we devised a closed form analytic solution for the ML molecular clock fork. In this work, we extend the state of the art in the area of analytic solutions ML trees to the family of all four taxa trees under the molecular clock assumption. The change from the fork topology to the comb incurs a major increase in the complexity of the underlying algebraic system and requires novel techniques and approaches. We combine the ultrametric properties of molecular clock trees with the Hadamard conjugation to derive a number of topology dependent identities. Employing these identities, we substantially simplify the system of polynomial equations. We finally use tools from algebraic geometry (e.g., Gr?bner bases, ideal saturation, resultants) and employ symbolic algebra software to obtain analytic solutions for the comb. We show that in contrast to the fork, the comb has no closed form solutions (expressed by radicals in the input data). In general, four taxa trees can have multiple ML points. In contrast, we can now prove that under the molecular clock assumption, the comb has a unique (local and global) ML point. (Such uniqueness was previously shown for the fork.).     

Maximum likelihood estimation of growth yields

This work is concerned with statistical methods to estimate yield and maintenance parameters associated with microbial growth. For a given dilution rate, an experimenter typically measures substrate concentration, oxygen utilization rate, the rate of carbon dioxide evolution, and biomass concentration. These correlated response variables each contain information about the maintenance and yield parameters of interest. A maximum likelihood estimator which combines this correlated information for the yield and maintenance parameters is proposed, evaluated, and tested on literature data. Both point and interval estimators are considered.     

Maximum likelihood estimation of subsequence conservation

A statistical method is presented for comparing protein sequences by partitioning the polymers and estimating each subsegment's degree of conservation. Conservation is measured as a function of the number of transitions occurring in the underlying time homogeneous Markov process assumed to govern amino acid mutations. The Markovian assumption also permits estimation of the ancestral sequence. Partitioning and estimation are carried out via maximum likelihood. The method is contrasted with the commonly utilized percent homology measure. A moving likelihood ratio plot to aid in identifying regions of high conservation is suggested as an analogue to moving hydrophobicity plots. An application is presented which identifies highly conserved regions in thymidylate synthase from L. casei and E. coli.     

Maximum likelihood alignment of DNA sequences

The optimal alignment problem for pairs of molecular sequences under a probabilistic model of evolutionary change is equivalent to the problem of estimating the maximum likelihood time required to transform one sequence to the other. When this time has been estimated, various alignments of high posterior probability may be written down. A simple model with two parameters is presented and a method is described by which the likelihood may be computed. Maximum likelihood estimates for some pairs of tRNA genes illustrate the method and allow us to obtain the best alignments under the model.     

Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings

Patch-clamp data may be analysed in terms of Markov process models of channel gating mechanisms. We present a maximum likelihood algorithm for estimation of gating parameters from records where only a single channel is present. Computer simulated data for three different models of agonist receptor gated channels are used to demonstrate the performance of the procedure. Full details of the implementation of the algorithm are given for an example gating mechanism. The effects of omission of brief openings and closings from the single-channel data on parameter estimation are explored. A strategy for discriminating between alternative possible gating models, based upon use of the Schwarz criterion, is described. Omission of brief events is shown not to lead to incorrect model identification, except in extreme circumstances. Finally, the algorithm is extended to include channel gating models exhibiting multiple conductance levels.