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.

Abscisic acid-induced stomatal closure mediated by cyclic ADP-ribose

Abscisic acid (ABA) is a plant hormone involved in the response of plants to reduced water availability. Reduction of guard cell turgor by ABA diminishes the aperture of the stomatal pore and thereby contributes to the ability of the plant to conserve water during periods of drought. Previous work has demonstrated that cytosolic Ca2+ is involved in the signal transduction pathway that mediates the reduction in guard cell turgor elicited by ABA. Here we report that ABA uses a Ca2+-mobilization pathway that involves cyclic adenosine 5′-diphosphoribose (cADPR). Microinjection of cADPR into guard cells caused reductions in turgor that were preceded by increases in the concentration of free Ca2+ in the cytosol. Patch clamp measurements of isolated guard cell vacuoles revealed the presence of a cADPR-elicited Ca2+-selective current that was inhibited at cytosolic Ca2+ ≥ 600 nM. Furthermore, microinjection of the cADPR antagonist 8-NH2-cADPR caused a reduction in the rate of turgor loss in response to ABA in 54% of cells tested, and nicotinamide, an antagonist of cADPR production, elicited a dose-dependent block of ABA-induced stomatal closure. Our data provide definitive evidence for a physiological role for cADPR and illustrate one mechanism of stimulus-specific Ca2+ mobilization in higher plants. Taken together with other recent data [Wu, Y., Kuzma, J., Marechal, E., Graeff, R., Lee, H. C., Foster, R. & Chua, N.-H. (1997) Science 278, 2126–2130], these results establish cADPR as a key player in ABA signal transduction pathways in plants.

Non-Arrhenius kinetics for the loop closure of a DNA hairpin

Intramolecular chain diffusion is an elementary process in the conformational fluctuations of the DNA hairpin-loop. We have studied the temperature and viscosity dependence of a model DNA hairpin-loop by FRET (fluorescence resonance energy transfer) fluctuation spectroscopy (FRETfs). Apparent thermodynamic parameters were obtained by analyzing the correlation amplitude through a two-state model and are consistent with steady-state fluorescence measurements. The kinetics of closing the loop show non-Arrhenius behavior, in agreement with theoretical prediction and other experimental measurements on peptide folding. The fluctuation rates show a fractional power dependence (β = 0.83) on the solution viscosity. A much slower intrachain diffusion coefficient in comparison to that of polypeptides was derived based on the first passage time theory of SSS [Szabo, A., Schulten, K. & Schulten, Z. (1980) J. Chem. Phys. 72, 4350–4357], suggesting that intrachain interactions, especially stacking interaction in the loop, might increase the roughness of the free energy surface of the DNA hairpin-loop.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Disruption of the MacMARCKS gene prevents cranial neural tube closure and results in anencephaly.

MacMARCKS is a member of the MARCKS family of protein kinase C (PKC) substrates. Biochemical evidence demonstrates that these proteins integrate calcium and PKC-dependent signals to regulate actin structure at the membrane. We report here that deletion of the MacMARCKS gene prevents cranial neural tube closure in the developing brain, resulting in anencephaly. This suggests a central role for MacMARCKS and the PKC signal transduction pathway in the folding of the anterior neural plate during the early phases of brain formation, and supports the hypothesis that actin-based motility directs cranial neural tube closure.

Earliest evolution associated with closure of the Tropical American Seaway.

Oceanographic changes caused by the emerging Central American isthmus, which completely severed connections between the Caribbean Sea and tropical Pacific Ocean about 3.5 million years ago, began to stimulate evolution of Caribbean reef corals and benthic foraminifera in the Late Miocene. At that time, first appearances of benthic foraminifera increased, especially those species strongly associated with carbonate-rich substrata; reef corals diversified dramatically; and the carbonate content of southern Caribbean deep-sea sediments increased. We suggest that the changes in marine environments caused by the constricting seaway and resulting in increasing carbonate content of sediments induced accelerated origination in reef corals and carbonate-associated benthic foraminifera.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.

Premature suture closure and ectopic cranial bone in mice expressing Msx2 transgenes in the developing skull.

The coordinate growth of the brain and skull is achieved through a series of interactions between the developing brain, the growing bones of the skull, and the fibrous joints, or sutures, that unite the bones. These interactions couple the expansion of the brain to the growth of the bony plates at the sutures. Craniosynostosis, the premature fusion of the bones of the skull, is a common birth defect (1 in 3000 live births) that disrupts coordinate growth and often results in profoundly abnormal skull shape. Individuals affected with Boston-type craniosynostosis, an autosomal dominant disorder, bear a mutated copy of MSX2, a homeobox gene thought to function in tissue interactions. Here we show that expression of the mouse counterpart of this mutant gene in the developing skulls of transgenic mice causes craniosynostosis and ectopic cranial bone. These mice provide a transgenic model of craniosynostosis as well as a point of entry into the molecular mechanisms that coordinate the growth of the brain and skull.