A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach

A maximum likelihood estimator based on the coalescent for unequal migration rates and different subpopulation sizes is developed. The method uses a Markov chain Monte Carlo approach to investigate possible genealogies with branch lengths and with migration events. Properties of the new method are shown by using simulated data from a four-population n-island model and a source–sink population model. Our estimation method as coded in migrate is tested against genetree; both programs deliver a very similar likelihood surface. The algorithm converges to the estimates fairly quickly, even when the Markov chain is started from unfavorable parameters. The method was used to estimate gene flow in the Nile valley by using mtDNA data from three human populations.

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.

Sequence analysis of the cis-regulatory regions of the bithorax complex of Drosophila.

The bithorax complex (BX-C) of Drosophila, one of two complexes that act as master regulators of the body plan of the fly, has now been entirely sequenced and comprises approximately 315,000 bp, only 1.4% of which codes for protein. Analysis of this sequence reveals significantly overrepresented DNA motifs of unknown, as well as known, functions in the non-protein-coding portion of the sequence. The following types of motifs in that portion are analyzed: (i) concatamers of mono-, di-, and trinucleotides; (ii) tightly clustered hexanucleotides (spaced < or = 5 bases apart); (iii) direct and reverse repeats longer than 20 bp; and (iv) a number of motifs known from biochemical studies to play a role in the regulation of the BX-C. The hexanucleotide AGATAC is remarkably overrepresented and is surmised to play a role in chromosome pairing. The positions of sites of highly overrepresented motifs are plotted for those that occur at more than five sites in the sequence, when < 0.5 case is expected. Expected values are based on a third-order Markov chain, which is the optimal order for representing the BXCALL sequence.

Tertiary structure of an amyloid immunoglobulin light chain protein: a proposed model for amyloid fibril formation.

An immunoglobulin light chain protein was isolated from the urine of an individual (BRE) with systemic amyloidosis. Complete amino acid sequence of the variable region of the light chain (VL) protein established it as a kappa I, which when compared with other kappa I amyloid associated proteins had unique residues, including Ile-34, Leu-40, and Tyr-71. To study the tertiary structure, BRE VL was expressed in Escherichia coli by using a PCR product amplified from the patient BRE's bone marrow DNA. The PCR product was ligated into pCZ11, a thermal-inducible replication vector. Recombinant BRE VL was isolated, purified to homogeneity, and crystallized by using ammonium sulfate as the precipitant. Two crystal forms were obtained. In crystal form I the BRE VL kappa domain crystallizes as a dimer with unit cell constants isomorphous to previously published kappa protein structures. Comparison with a nonamyloid VL kappa domain from patient REI, identified significant differences in position of residues in the hypervariable segments plus variations in framework region (FR) segments 40-46 (FR2) and 66-67 (FR3). In addition, positional differences can be seen along the two types of local diads, corresponding to the monomer-monomer and dimer-dimer interfaces. From the packing diagram, a model for the amyloid light chain (AL) fibril is proposed based on a pseudohexagonal spiral structure with a rise of approximately the width of two dimers per 360 degree turn. This spiral structure could be consistent with the dimensions of amyloid fibrils as determined by electron microscopy.

A general model of invariant chain association with class II major histocompatibility complex proteins.

The binding of invariant chain to major histocompatibility complex (MHC) proteins is an important step in processing of MHC class II proteins and in antigen presentation. The question of how invariant chain can bind to all MHC class II proteins is central to understanding these processes. We have employed molecular modeling to predict the structure of class II-associated invariant chain peptide (CLIP)-MHC protein complexes and to ask whether the predicted mode of association could be general across all MHC class II proteins. CLIP fits identically into the MHC class II alleles HLA-DR3, I-Ak, I-Au, and I-Ad, with a consistent pattern of hydrogen bonds, contacts, and hydrophobic burial and without bad contacts. Our model predicts the burial of CLIP residues Met-91 and Met-99 in the deep P1 and P9 anchor pockets and other detailed interactions, which we have compared with available data. The predicted pattern of I-A allele-specific effects on CLIP binding is very similar to that observed experimentally by alanine-scanning mutations of CLIP. Together, these results indicate that CLIP may bind in a single, general way across products of MHC class II alleles.