Metabolism to a response pathway selective retinoid ligand during axial pattern formation

We report identification of 9-cis-4-oxo-retinoic acid (9-cis-4-oxo-RA) as an in vivo retinoid metabolite in Xenopus embryos. 9-Cis-4-oxo-RA bound receptors (RARs) α, β, and γ as well as retinoid X receptors (RXRs) α, β, and γ in vitro. However, this retinoid displayed differential RXR activation depending on the response pathway used. Although it failed to activate RXRs in RXR homodimers, it activated RXRs and RARs synergistically in RAR-RXR heterodimers. 9-Cis-4-oxo-RA thus acted as a dimer-specific agonist. Considering that RAR-RXR heterodimers are major functional units involved in transducing retinoid signals during embryogenesis and that 9-cis-4-oxo-RA displayed high potency for modulating axial pattern formation in Xenopus, metabolism to 9-cis-4-oxo-RA may provide a mechanism to target retinoid action to this and other RAR-RXR heterodimer-mediated processes.

Molecular genetics of pattern formation in the inner ear: Do compartment boundaries play a role?

The membranous labyrinth of the inner ear establishes a precise geometrical topology so that it may subserve the functions of hearing and balance. How this geometry arises from a simple ectodermal placode is under active investigation. The placode invaginates to form the otic cup, which deepens before pinching off to form the otic vesicle. By the vesicle stage many genes expressed in the developing ear have assumed broad, asymmetrical expression domains. We have been exploring the possibility that these domains may reflect developmental compartments that are instrumental in specifying the location and identity of different parts of the ear. The boundaries between compartments are proposed to be the site of inductive interactions required for this specification. Our work has shown that sensory organs and the endolymphatic duct each arise near the boundaries of broader gene expression domains, lending support to this idea. A further prediction of the model, that the compartment boundaries will also represent lineage-restriction compartments, is supported in part by fate mapping the otic cup. Our data suggest that two lineage-restriction boundaries intersect at the dorsal pole of the otocyst, a convergence that may be critical for the specification of endolymphatic duct outgrowth. We speculate that the patterning information necessary to establish these two orthogonal boundaries may emanate, in part, from the hindbrain. The compartment boundary model of ear development now needs to be tested through a variety of experimental perturbations, such as the removal of boundaries, the generation of ectopic boundaries, and/or changes in compartment identity.

Synaptic pattern formation during cellular recognition

Cell–cell recognition often requires the formation of a highly organized pattern of receptor proteins (a synapse) in the intercellular junction. Recent experiments [e.g., Monks, C. R. F., Freiberg, B. A., Kupfer, H., Sciaky, N. & Kupfer, A. (1998) Nature (London) 395, 82–86; Grakoui, A., Bromley, S. K., Sumen, C., Davis, M. M., Shaw, A. S., Allen, P. M. & Dustin, M. L. (1999) Science 285, 221–227; and Davis, D. M., Chiu, I., Fassett, M., Cohen, G. B., Mandelboim, O. & Strominger, J. L. (1999) Proc. Natl. Acad. Sci. USA 96, 15062–15067] vividly demonstrate a complex evolution of cell shape and spatial receptor–ligand patterns (several microns in size) in the intercellular junction during immunological synapse formation. The current view is that this dynamic rearrangement of proteins into organized supramolecular activation clusters is driven primarily by active cytoskeletal processes [e.g., Dustin, M. L. & Cooper, J. A. (2000) Nat. Immunol. 1, 23–29; and Wulfing, C. & Davis, M. M. (1998) Science 282, 2266–2269]. Here, aided by a quantitative analysis of the relevant physico-chemical processes, we demonstrate that the essential characteristics of synaptic patterns observed in living cells can result from spontaneous self-assembly processes. Active cellular interventions are superimposed on these self-organizing tendencies and may also serve to regulate the spontaneous processes. We find that the protein binding/dissociation characteristics, protein mobilities, and membrane constraints measured in the cellular environment are delicately balanced such that the length and time scales of spontaneously evolving patterns are in near-quantitative agreement with observations for synapse formation between T cells and supported membranes [Grakoui, A., Bromley, S. K., Sumen, C., Davis, M. M., Shaw, A. S., Allen, P. M. & Dustin, M. L. (1999) Science 285, 221–227]. The model we present provides a common way of analyzing immunological synapse formation in disparate systems (e.g., T cell/antigen-presenting cell junctions with different MHC-peptides, natural killer cells, etc.).

Auxin as a positional signal in pattern formation in plants.

By using a novel, extremely sensitive and specific gas chromatography-mass spectrometry technique we demonstrate in Pinus sylvestris (L.) trees the existence of a steep radial concentration gradient of the endogenous auxin, indole-3-acetic acid, over the lateral meristem responsible for the bulk of plant secondary growth, the vascular cambium. This is the first evidence that plant morphogens, such as indole-3-acetic acid, occur in concentration gradients over developing tissues. This finding gives evidence for a regulatory system in plants based on positional signaling, similar to animal systems.

Models for stochastic climate prediction

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more sophisticated models beyond stable linear Langevin equations. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. The strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta-plane with topography and a mean flow. In this example, the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom.

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

Complex formation between stage-specific oocyte factors and a Xenopus mRNA localization element

It is a long-standing proposal that localization of maternal factors in eggs can provide the basis for pattern formation in the early embryo. The localized information can be stored as RNA, one example being Vg1 RNA, which is localized exclusively to the vegetal hemisphere of Xenopus oocytes and eggs. Localization of Vg1 mRNA is directed by a 340-nt sequence element contained within its 3′ untranslated region. To understand the mechanism of localization, I have tested whether factors from the oocyte interact specifically with the RNA localization sequence. Results presented here show that a set of oocyte proteins form complexes with the localization element both in vitro and in vivo. These proteins are specifically enriched in the stages of oogenesis during which localization occurs and recognize sub-elements of the RNA localization element that are essential for localization in vivo. These data suggest that formation of a localization-specific RNA–protein complex may be the first step in directing Vg1 mRNA to its subcellular destination.

Abnormal skeletal patterning in embryos lacking a single Cbp allele: A partial similarity with Rubinstein–Taybi syndrome

CBP is a transcriptional coactivator required by many transcription factors for transactivation. Rubinstein–Taybi syndrome, which is an autosomal dominant syndrome characterized by abnormal pattern formation, has been shown to be associated with mutations in the Cbp gene. Furthermore, Drosophila CBP is required in hedgehog signaling for the expression of decapentapleigic, the Drosophila homologue of bone morphogenetic protein. However, no direct evidence exists to indicate that loss of one copy of the mammalian Cbp gene affects pattern formation. Here, we show that various abnormalities occur at high frequency in the skeletal system of heterozygous Cbp-deficient mice resulting from a C57BL/6-CBA × BALB/c cross. In support of a conserved signaling pathway for pattern formation in insects and mammals, the expression of Bmp7 was found to be reduced in the heterozygous mutants. The frequency of the different abnormalities was significantly lower in a C57BL/6-CBA background, suggesting that the genetic background is an important determinant of the variability and severity of the anomalies seen in Rubinstein–Taybi syndrome patients.

Dissociation of HIV-1 from follicular dendritic cells during HAART: Mathematical analysis

Follicular dendritic cells (FDC) provide a reservoir for HIV type 1 (HIV-1) that may reignite infection if highly active antiretroviral therapy (HAART) is withdrawn before virus on FDC is cleared. To estimate the treatment time required to eliminate HIV-1 on FDC, we develop deterministic and stochastic models for the reversible binding of HIV-1 to FDC via ligand–receptor interactions and examine the consequences of reducing the virus available for binding to FDC. Analysis of these models shows that the rate at which HIV-1 dissociates from FDC during HAART is biphasic, with an initial period of rapid decay followed by a period of slower exponential decay. The speed of the slower second stage of dissociation and the treatment time required to eradicate the FDC reservoir of HIV-1 are insensitive to the number of virions bound and their degree of attachment to FDC before treatment. In contrast, the expected time required for dissociation of an individual virion from FDC varies sensitively with the number of ligands attached to the virion that are available to interact with receptors on FDC. Although most virions may dissociate from FDC on the time scale of days to weeks, virions coupled to a higher-than-average number of ligands may persist on FDC for years. This result suggests that HAART may not be able to clear all HIV-1 trapped on FDC and that, even if clearance is possible, years of treatment will be required.

AP-2-null cells disrupt morphogenesis of the eye, face, and limbs in chimeric mice

The homozygous disruption of the mouse AP-2 gene yields a complex and lethal phenotype that results from defective development of the neural tube, head, and body wall. The severe and pleiotropic developmental abnormalities observed in the knockout mouse suggested that AP-2 may regulate several morphogenic pathways. To uncouple the individual developmental mechanisms that are dependent on AP-2, we have now analyzed chimeric mice composed of both wild-type and AP-2-null cells. The phenotypes obtained from these chimeras indicate that there is an independent requirement for AP-2 in the formation of the neural tube, body wall, and craniofacial skeleton. In addition, these studies reveal that AP-2 exerts a major influence on eye formation, which is a critical new role for AP-2 that was masked previously in the knockout mice. Furthermore, we also have uncovered an unexpected influence of AP-2 on limb pattern formation; this influence is typified by major limb duplications. The range of phenotypes observed in the chimeras displays a significant overlap with those caused by teratogenic levels of retinoic acid, strongly suggesting that AP-2 is an important component of the mechanism of action of this morphogen.

A model for individual and collective cell movement in Dictyostelium discoideum

The cellular slime mold Dictyostelium discoideum is a widely used model system for studying a variety of basic processes in development, including cell–cell signaling, signal transduction, pattern formation, cell motility, and the movement of tissue-like aggregates of cells. Many aspects of cell motion are poorly understood, including how individual cell behavior produces the collective motion of cells observed within the mound and slug. Herein, we describe a biologically realistic model for motile D. discoideum cells that can generate active forces, that interact via surface molecules, and that can detect and respond to chemotactic signals. We model the cells as deformable viscoelastic ellipsoids and incorporate signal transduction and cell–cell signaling by using a previously developed model. The shape constraint restricts the admissible deformations but makes the simulation of a large number of interacting cells feasible. Because the model is based on known processes, the parameters can be estimated or measured experimentally. We show that this model can reproduce the observations on the chemotactic behavior of single cells, streaming during aggregation, and the collective motion of an aggregate of cells driven by a small group of pacemakers. The model predicts that the motion of two-dimensional slugs [Bonner, J. T. (1998) Proc. Natl. Acad. Sci. USA 95, 9355–9359] results from the same behaviors that are exhibited by individual cells; it is not necessary to invoke different mechanisms or behaviors. Our computational experiments also suggest previously uncharacterized phenomena that may be experimentally observable.

Simple mechanochemistry describes the dynamics of kinesin molecules

Recently, Block and coworkers [Visscher, K., Schnitzer, M. J., & Block, S. M. (1999) Nature (London) 400, 184–189 and Schnitzer, M. J., Visscher, K. & Block, S. M. (2000) Nat. Cell Biol. 2, 718–723] have reported extensive observations of individual kinesin molecules moving along microtubules in vitro under controlled loads, F = 1 to 8 pN, with [ATP] = 1 μM to 2 mM. Their measurements of velocity, V, randomness, r, stalling force, and mean run length, L, reveal a need for improved theoretical understanding. We show, presenting explicit formulae that provide a quantitative basis for comparing distinct molecular motors, that their data are satisfactorily described by simple, discrete-state, sequential stochastic models. The simplest (N = 2)-state model with fixed load-distribution factors and kinetic rate constants concordant with stopped-flow experiments, accounts for the global (V, F, L, [ATP]) interdependence and, further, matches relative acceleration observed under assisting loads. The randomness, r(F,[ATP]), is accounted for by a waiting-time distribution, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{1}^{+}}}\end{equation*}\end{document}(t), [for the transition(s) following ATP binding] with a width parameter ν ≡ 〈t〉2/〈(Δt)2〉≃2.5, indicative of a dispersive stroke of mechanicity ≃0.6 or of a few (≳ν − 1) further, kinetically coupled states: indeed, N = 4 (but not N = 3) models do well. The analysis reveals: (i) a substep of d0 = 1.8–2.1 nm on ATP binding (consistent with structurally based suggestions); (ii) comparable load dependence for ATP binding and unbinding; (iii) a strong load dependence for reverse hydrolysis and subsequent reverse rates; and (iv) a large (≳50-fold) increase in detachment rate, with a marked load dependence, following ATP binding.

Impact of vaccination on the spatial correlation and persistence of measles dynamics.

The onset of measles vaccination in England and Wales in 1968 coincided with a marked drop in the temporal correlation of epidemic patterns between major cities. We analyze a variety of hypotheses for the mechanisms driving this change. Straightforward stochastic models suggest that the interaction between a lowered susceptible population (and hence increased demographic noise) and nonlinear dynamics is sufficient to cause the observed drop in correlation. The decorrelation of epidemics could potentially lessen the chance of global extinction and so inhibit attempts at measles eradication.

A rice homeobox gene, OSH1, is expressed before organ differentiation in a specific region during early embryogenesis.

Homeobox genes encode a large family of homeodomain proteins that play a key role in the pattern formation of animal embryos. By analogy, homeobox genes in plants are thought to mediate important processes in their embryogenesis, but there is very little evidence to support this notion. Here we described the temporal and spatial expression patterns of a rice homeobox gene, OSH1, during rice embryogenesis. In situ hybridization analysis revealed that in the wild-type embryo, OSH1 was first expressed at the globular stage, much earlier than organogenesis started, in a ventral region where shoot apical meristem and epiblast would later develop. This localized expression of OSH1 indicates that the cellular differentiation has already occurred at this stage. At later stages after organogenesis had initiated, OSH1 expression was observed in shoot apical meristem [except in the L1 (tunica) layer], epiblast, radicle, and their intervening tissues in descending strength of expression level with embryonic maturation. We also performed in situ hybridization analysis with a rice organless embryo mutant, orl1, that develops no embryonic organs. In the orl1 embryo, the expression pattern of OSH1 was the same as that in the wild-type embryo in spite of the lack of embryonic organs. This shows that OSH1 is not directly associated with organ differentiation, but may be related to a regulatory process before or independent of the organ determination. The results described here strongly suggest that, like animal homeobox genes, OSH1 plays an important role in regionalization of cell identity during early embryogenesis.

4-Oxoretinol, a new natural ligand and transactivator of the retinoic acid receptors.

All-trans-retinoic acid (at-RA) induces cell differentiation in a wide variety of cell types, including F9 embryonic teratocarcinoma cells, and can influence axial pattern formation during embryonic development. We now identify a novel retinoid synthetic pathway in differentiating F9 cells that results in the intracellular production of 4-oxoretinol (4-oxo-ROL) from retinol (vitamin A). Approximately 10-15% of the total retinol in the culture is metabolized to 4-hydroxyretinol and 4-oxo-ROL by the at-RA-treated, differentiating F9 cells over an 18-hr period, but no detectable metabolism of all-trans-retinol to at-RA or 9-cis-retinoic acid is observed in these cells. Remarkably, we show that 4-oxo-ROL can bind and activate transcription of the retinoic acid receptors whereas all-trans-retinol shows neither activity. Low doses of 4-oxo-ROL (e.g., 10(-9) or 10(-10 M) can activate the retinoic acid receptors even though, unlike at-RA, 4-oxo-ROL does not contain an acid moiety at the carbon 15 position. 4-oxo-ROL does not bind or transcriptionally activate the retinoid X receptors. Treatment of F9 cells with 4-oxo-ROL induces differentiation without conversion to the acid and 4-oxo-ROL is active in causing axial truncation when administered to Xenopus embryos at the blastula stage. Thus, 4-oxo-ROL is a natural, biologically active retinoid that is present in differentiated F9 cells. Our data suggest that 4-oxo-ROL may be a novel signaling molecule and regulator of cell differentiation.