Maximum likelihood estimation of oncogenetic tree models

We present a new approach for modelling the dependences between genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumour development and progression is assumed to follow a probabilistic tree model. We show how maximum likelihood estimation can be used to reconstruct a tree model for the dependences between genetic alterations in a given tumour type. We illustrate the use of the proposed method by applying it to cytogenetic data from 173 cases of clear cell renal cell carcinoma, arriving at a model for the karyotypic evolution of this tumour.     

Thermal stability of a flavoprotein assessed from associative analysis of polarized time-resolved fluorescence spectroscopy

Upon gradually heating a particular mutant of the flavoprotein NADH peroxidase, it was found from the peculiar time-resolved fluorescence anisotropy pattern of the flavin prosthetic group (FAD) that, at elevated temperature, FAD is released from the tetrameric enzyme. Since in this case a mixture of free and enzyme-bound FAD contributes to the time-dependent fluorescence anisotropy, its analysis can only be accomplished by an associative fitting model, in which specific fluorescence lifetimes of both species are linked to specific correlation times. In this letter the general approach to the associative polarized fluorescence decay analysis is described. The procedure can be used for other flavoproteins to determine the temperature at which the onset of thermal denaturation will start, leading to release of the flavin prosthetic group. Received: 20 November 1998 / Revised version: 6 April 1999 / Accepted: 8 April 1999     

Maximum likelihood with multiparameter models of substitution

Maximum-likelihood approaches to phylogenetic estimation have the potential of great flexibility, even though current implementations are highly constrained. One such constraint has been the limitation to one-parameter models of substitution. A general implementation of Newton's maximization procedure was developed that allows the maximum likelihood method to be used with multiparameter models. The Estimate and Maximize (EM) algorithm was also used to obtain a good approximation to the maximum likelihood for a certain class of multiparameter models. The condition for which a multiparameter model will only have a single maximum on the likelihood surface was identified. Two-and three-parameter models of substitution in base-paired regions of RNA sequences were used as examples for computer simulations to show that these implementations of the maximum likelihood method are not substantially slower than one-parameter models. Newton's method is much faster than the EM method but may be subject to divergence in some circumstances. In these cases the EM method can be used to restore convergence.     

On the maximum likelihood method for estimating molecular trees: Uniqueness of the likelihood point

Summary Studies are carried out on the uniqueness of the stationary point on the likelihood function for estimating molecular phylogenetic trees, yielding proof that there exists at most one stationary point, i.e., the maximum point, in the parameter range for the one parameter model of nucleotide substitution. The proof is simple yet applicable to any type of tree topology with an arbitrary number of operational taxonomic units (OTUs). The proof ensures that any valid approximation algorithm be able to reach the unique maximum point under the conditions mentioned above. An algorithm developed incorporating Newton's approximation method is then compared with the conventional one by means of computers simulation. The results show that the newly developed algorithm always requires less CPU time than the conventional one, whereas both algorithms lead to identical molecular phylogenetic trees in accordance with the proof. Contribution No. 1780 from the National Institute of Genetics, Mishima 411, Japan     

Property and efficiency of the maximum likelihood method for molecular phylogeny

Summary The maximum likelihood (ML) method for constructing phylogenetic trees (both rooted and unrooted trees) from DNA sequence data was studied. Although there is some theoretical problem in the comparison of ML values conditional for each topology, it is possible to make a heuristic argument to justify the method. Based on this argument, a new algorithm for estimating the ML tree is presented. It is shown that under the assumption of a constant rate of evolution, the ML method and UPGMA always give the same rooted tree for the case of three operational taxonomic units (OTUs). This also seems to hold approximately for the case with four OTUs. When we consider unrooted trees with the assumption of a varying rate of nucleotide substitution, the efficiency of the ML method in obtaining the correct tree is similar to those of the maximum parsimony method and distance methods. The ML method was applied to Brown et al.'s data, and the tree topology obtained was the same as that found by the maximum parsimony method, but it was different from those obtained by distance methods.     

Maximum likelihood estimation for cytogenetic dose-response curves

In vitro dose-response curves are used to describe the relation between chromosome aberrations and radiation dose for human lymphocytes. The lymphocytes are exposed to low-LET radiation, and the resulting dicentric chromosome aberrations follow the Poisson distribution. The expected yield depends on both the magnitude and the temporal distribution of the dose. A general dose-response model that describes this relation has been presented by Kellerer and Rossi (1972, Current Topics on Radiation Research Quarterly 8, 85-158; 1978, Radiation Research 75, 471-488) using the theory of dual radiation action. Two special cases of practical interest are split-dose and continuous exposure experiments, and the resulting dose-time-response models are intrinsically nonlinear in the parameters. A general-purpose maximum likelihood estimation procedure is described, and estimation for the nonlinear models is illustrated with numerical examples from both experimental designs. Poisson regression analysis is used for estimation, hypothesis testing, and regression diagnostics. Results are discussed in the context of exposure assessment procedures for both acute and chronic human radiation exposure.     

Phylogenetic analysis using parsimony and likelihood methods

The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.     

Lateral heterogeneity in human platelet plasma membrane and lipids from the time-resolved fluorescence of trans-parinaric acid

We have investigated the complex behaviour of the time resolved fluorescence intensity and anisotropy of trans-parinaric acid, incorporated into fragments of the plasma membrane of human platelets and in multibilayers of lipids extracted from that membrane. It is shown that the observation of anisotropies that increase at long times can be satisfactorily interpreted by assuming two populations of the fluorescence probe with distinct lifetimes, rotational relaxation times and order parameters. The heterogeneous probe distribution was correlated with a similar heterogeneity in the lipid composition of the bilayer, modulated by temperature. Below 35°C an important fraction of the lipids of the plasma membrane are apparently in the form of solid-like domains (20% at 20°C). However, in the physiological temperature range that solid/fluid heterogeneity is almost negligible. Since these effects were also observed in multibilayers of lipids from the platelet membrane, the formation of solid-like clusters appears to arise from lipid-lipid interactions only, and most probably involving cholesterol. These results support the previous finding of a lateral phase separation for temperatures less than 37°C described by Gordon et al. (1983) in a spin-probe study of the platelet plasma membrane.Abbreviations DPH 1,6-diphenyl-1,3,5-hexatriene - DPPC dipalmitoyl-phosphatidylcholine - tPnA trans-parinaric acid Offprint requests to: A. U. Acuña     

On the maximum likelihood method in molecular phylogenetics

Summary The efficiency of obtaining the correct tree by the maximum likelihood method (Felsenstein 1981) for inferring trees from DNA sequence data was compared with trees obtained by distance methods. It was shown that the maximum likelihood method is superior to distance methods in the efficiency particularly when the evolutionary rate differs among lineages.     

Time-dependent decay and anisotropy of fluorescence from diphenylhexatriene embedded in the chloroplast thylakoid membrane

The hydrophobic fluorescent probe 1,6-diphenyl-1,3,5-hexatriene has been incorporated into the membranes of isolated thylakoids, separated granal and stromal lamellae and aqueous dispersions of extracted thylakoid galactolipids. Time-resolved fluorescence decays have been recorded on a nanosecond scale using single-photon counting in order to assess the motional properties of the probe. All the experimental systems used showed biphasic decay kinetics and the anisotropies of the decays have been interpreted in terms of a model for wobbling diffusion confined to a cone. The analysis has given information about dynamic and structural restraints of the lipid acyl chains. In the intact thylakoid membrane the degree of order of the fatty acid acyl chains is higher and their rate of motion slower than for isolated lipids. Even so, the dynamic and structural parameters indicate that the thylakoids can be considered as a relatively fluid membrane system when compared with many other biological membranes, a property which is probably required to facilitate efficient long-range diffusion of lipophilic mobile electron-transport components. It is suggested that the optimization of thylakoid fluidity is linked to regulation of the membrane protein/lipid ratio which is also likely to be responsible for the higher fluidity of stromal membranes relative to those of the grana.     

Maximum likelihood estimation of neutral model parameters for multiple samples with different degrees of dispersal limitation

In a recent paper, I presented a sampling formula for species abundances from multiple samples according to the prevailing neutral model of biodiversity, but practical implementation for parameter estimation was only possible when these samples were from local communities that were assumed to be equally dispersal limited. Here I show how the same sampling formula can also be used to estimate model parameters using maximum likelihood when the samples have different degrees of dispersal limitation. Moreover, it performs better than other, approximate, parameter estimation approaches. I also show how to calculate errors in the parameter estimates, which has so far been largely ignored in the development of and debate on neutral theory.     

Anisotropy decay of fluorescence as an experimental approach to protein dynamics

This minireview makes an initial assessment of the progress made using anisotropy decay measurements for investigating the conformational changes and molecular dynamics in soluble systems. A critical analysis of available data is presented. The anisotropy decays of the tryptophan fluorescence of staphylococcal nuclease, adrenocorticotropin, melittin and of labeled transfer RNA were studied for investigating the functional conformational changes of these systems. The emissions of variously labeled immunoglobulins have been used to elucidate the conformations of these proteins before and after the binding of specific antibodies. Labeled myosin and its fragments have given information on the functional motions of the protein domains. The anisotropy decays of labeled and natural hemoglobin systems have been utilized for exploring the allosteric behavior of these molecules. The data suggest a wide applicability of this technique to the study of protein dynamics and conformational changes of macromolecules.     

Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies

This article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity. Following Cochran (1937, Journal of the Royal Statistical Society 4(Supple), 102-118; 1954, Biometrics 10, 101-129; 1980, in Proceedings of the 25th Conference on the Design of Experiments in Army Research, Development and Testing, 21-33) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with unequal within-group variances. A reparametrization of the likelihood leads to simplified computations, easier identification and interpretation of multimodality of the likelihood, and (through a non-informative-prior Bayesian approach) approximate confidence regions for the mean and between-group variance.