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.

Unusual Centrosome Cycle in Dictyostelium: Correlation of Dynamic Behavior and Structural Changes

Centrosome duplication and separation are of central importance for cell division. Here we provide a detailed account of this dynamic process in Dictyostelium. Centrosome behavior was monitored in living cells using a γ-tubulin–green fluorescent protein construct and correlated with morphological changes at the ultrastructural level. All aspects of the duplication and separation process of this centrosome are unusual when compared with, e.g., vertebrate cells. In interphase the Dictyostelium centrosome is a box-shaped structure comprised of three major layers, surrounded by an amorphous corona from which microtubules emerge. Structural duplication takes place during prophase, as opposed to G1/S in vertebrate cells. The three layers of the box-shaped core structure increase in size. The surrounding corona is lost, an event accompanied by a decrease in signal intensity of γ-tubulin–green fluorescent protein at the centrosome and the breakdown of the interphase microtubule system. At the prophase/prometaphase transition the separation into two mitotic centrosomes takes place via an intriguing lengthwise splitting process where the two outer layers of the prophase centrosome peel away from each other and become the mitotic centrosomes. Spindle microtubules are now nucleated from surfaces that previously were buried inside the interphase centrosome. Finally, at the end of telophase, the mitotic centrosomes fold in such a way that the microtubule-nucleating surface remains on the outside of the organelle. Thus in each cell cycle the centrosome undergoes an apparent inside-out/outside-in reversal of its layered structure.

Structural basis of an embryonically lethal single Ala → Thr mutation in the vnd/NK-2 homeodomain

The structural and DNA binding behavior is described for an analog of the vnd/NK-2 homeodomain, which contains a single amino acid residue alanine to threonine replacement in position 35 of the homeodomain. Multidimensional nuclear magnetic resonance, circular dichroism, and electrophoretic gel retardation assays were carried out on recombinant 80-aa residue proteins that encompass the wild-type and mutant homeodomains. The mutant A35T vnd/NK-2 homeodomain is unable to adopt a folded conformation free in solution at temperatures down to −5°C in contrast to the behavior of the corresponding wild-type vnd/NK-2 homeodomain, which is folded into a functional three-dimensional structure below 25°C. The A35T vnd/NK-2 binds specifically to the vnd/NK-2 target DNA sequence, but with an affinity that is 50-fold lower than that of the wild-type homeodomain. Although the three-dimensional structure of the mutant A35T vnd/NK-2 in the DNA bound state shows characteristic helix–turn–helix behavior similar to that of the wild-type homeodomain, a notable structural deviation in the mutant A35T analog is observed for the amide proton of leucine-40. The wild-type homeodomain forms an unusual i,i-5 hydrogen bond with the backbone amide oxygen of residue 35. In the A35T mutant this amide proton resonance is shifted upfield by 1.27 ppm relative to the resonance frequency for the wild-type analog, thereby indicating a significant alteration of this i,i-5 hydrogen bond.

Self-organized defensive behavior in honeybees

We investigated the defensive behavior of honeybees under controlled experimental conditions. During an attack on two identical targets, the spatial distribution of stings varied as a function of the total number of stings, evincing the classic “pitchfork bifurcation” phenomenon of nonlinear dynamics. The experimental results support a model of defensive behavior based on a self-organizing mechanism. The model helps to explain several of the characteristic features of the honeybee defensive response: (i) the ability of the colony to localize and focus its attack, (ii) the strong variability between different hives in the intensity of attack, as well as (iii) the variability observed within the same hive, and (iv) the ability of the colony to amplify small differences between the targets.

Molecular phylogenetic analysis of evolutionary trends in stonefly wing structure and locomotor behavior

Insects in the order Plecoptera (stoneflies) use a form of two-dimensional aerodynamic locomotion called surface skimming to move across water surfaces. Because their weight is supported by water, skimmers can achieve effective aerodynamic locomotion even with small wings and weak flight muscles. These mechanical features stimulated the hypothesis that surface skimming may have been an intermediate stage in the evolution of insect flight, which has perhaps been retained in certain modern stoneflies. Here we present a phylogeny of Plecoptera based on nucleotide sequence data from the small subunit rRNA (18S) gene. By mapping locomotor behavior and wing structural data onto the phylogeny, we distinguish between the competing hypotheses that skimming is a retained ancestral trait or, alternatively, a relatively recent loss of flight. Our results show that basal stoneflies are surface skimmers, and that various forms of surface skimming are distributed widely across the plecopteran phylogeny. Stonefly wings show evolutionary trends in the number of cross veins and the thickness of the cuticle of the longitudinal veins that are consistent with elaboration and diversification of flight-related traits. These data support the hypothesis that the first stoneflies were surface skimmers, and that wing structures important for aerial flight have become elaborated and more diverse during the radiation of modern stoneflies.

Structural analysis of the binding modes of minor groove ligands comprised of disubstituted benzenes

Two-dimensional homonuclear NMR was used to characterize synthetic DNA minor groove-binding ligands in complexes with oligonucleotides containing three different A-T binding sites. The three ligands studied have a C2 axis of symmetry and have the same general structural motif of a central para-substituted benzene ring flanked by two meta-substituted rings, giving the molecules a crescent shape. As with other ligands of this shape, specificity seems to arise from a tight fit in the narrow minor groove of the preferred A-T-rich sequences. We found that these ligands slide between binding subsites, behavior attributed to the fact that all of the amide protons in the ligand backbone cannot hydrogen bond to the minor groove simultaneously.

Nonlinear-dynamical arrhythmia control in humans

Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.

Linear and nonlinear pathways of spectral information transmission in the cochlear nucleus

At the level of the cochlear nucleus (CN), the auditory pathway divides into several parallel circuits, each of which provides a different representation of the acoustic signal. Here, the representation of the power spectrum of an acoustic signal is analyzed for two CN principal cells—chopper neurons of the ventral CN and type IV neurons of the dorsal CN. The analysis is based on a weighting function model that relates the discharge rate of a neuron to first- and second-order transformations of the power spectrum. In chopper neurons, the transformation of spectral level into rate is a linear (i.e., first-order) or nearly linear function. This transformation is a predominantly excitatory process involving multiple frequency components, centered in a narrow frequency range about best frequency, that usually are processed independently of each other. In contrast, type IV neurons encode spectral information linearly only near threshold. At higher stimulus levels, these neurons are strongly inhibited by spectral notches, a behavior that cannot be explained by level transformations of first- or second-order. Type IV weighting functions reveal complex excitatory and inhibitory interactions that involve frequency components spanning a wider range than that seen in choppers. These findings suggest that chopper and type IV neurons form parallel pathways of spectral information transmission that are governed by two different mechanisms. Although choppers use a predominantly linear mechanism to transmit tonotopic representations of spectra, type IV neurons use highly nonlinear processes to signal the presence of wide-band spectral features.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Mechanical behavior in living cells consistent with the tensegrity model

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.

Glucocorticoid and progestin receptors are differently involved in the cooperation with a structural element of the mouse mammary tumor virus promoter.

We have previously characterized a regulatory element located between -294 and -200 within the mouse mammary tumor virus (MMTV) long terminal repeat (LTR). This element termed AA element cooperates with the glucocorticoid response elements (GREs) for glucocorticoid activation. Here we show that in a MMTV LTR wild type context, the deletion of this element significantly reduces both glucocorticoid and progestin activation of the promoter. Deletion of the two most distal GREs forces the glucocorticoid receptor (GR) and the progestin receptor (PR) to bind the same response elements and results in a dramatic decrease in the inducibility of the MMTV promoter by the two hormones. The simultaneous deletion of the two distal GREs and of the AA element abolishes completely the glucocorticoid-induced activation of the promoter. In contrast it restores a significant level of progestin-induced activation. This different effect of the double deletion on glucocorticoid- and progestin-induced MMTV promoter activation is not cell specific because it is also observed, and is even stronger, when either GR or PR is expressed in the same cell line (NIH 3T3). This is the first description of a mutated MMTV promoter that, although retaining GREs, is activated by progestins and not by glucocorticoids. This suggests a different functional cooperation between protein(s) interacting with the AA element and GR or PR. Cotransfections with constructs containing wild-type or mutated MMTV LTR with either PR lacking its C-terminal domain or GR/PR chimeras in which the N-terminal domains have been exchanged demonstrate that the N-terminal domains of the receptors specify the different behavior of GR and PR regarding the AA element.

Structural conservation of ion conduction pathways in K channels and glutamate receptors.

Single channel recordings demonstrate that ion channels switch stochastically between an open and a closed pore conformation. In search of a structural explanation for this universal open/close behavior, we have uncovered a striking degree of amino acid homology across the pore-forming regions of voltage-gated K channels and glutamate receptors. This suggested that the pores of these otherwise unrelated classes of channels could be structurally conserved. Strong experimental evidence supports a hairpin structure for the pore-forming region of K channels. Consequently, we hypothesized the existence of a similar structure for the pore of glutamate receptors. In ligand-gated channels, the pore is formed by M2, the second of four putative transmembrane segments. A hairpin structure for M2 would affect the subsequent membrane topology, inverting the proposed orientation of the next segments, M3. We have tested this idea for the NR1 subunit of the N-methyl-D-aspartate receptor. Mutations that affected the glycosylation pattern of the NR1 subunit localize both extremes of the M3-M4 linker to the extracellular space. Whole cell currents and apparent agonist affinities were not affected by these mutations. Therefore it can be assumed that they represent the native transmembrane topology. The extracellular assignment of the M3-M4 linker challenged the current topology model by inverting M3. Taken together, the amino acid homology and the new topology suggest that the pore-forming M2 segment of glutamate receptors does not transverse the membrane but, rather, forms a hairpin structure, similar to that found in K channels.