Comparative studies of Hox genes in mammalian limb and vertebral pattern formation

Divergence of anterior-posterior (AP) limb pattern and differences in vertebral column morphology are the two main examples of mammalian evolution. The Hox genes (homeobox containing gene) have been implicated in driving evolution of these structures. However, regarding Hox genes, how they contribute to the generation of mammalian morphological diversities, is still unclear. Implementing comparative gene expression and phenotypic rescue studies for different mammalian Hox genes could aid in unraveling this mystery. In the first part of this thesis, the expression pattern of Hoxd13 gene, a key Hox gene in the establishment of the limb AP pattern, was examined in developing limbs of bats and mice. Bat forelimbs exhibit a pronounced asymmetric AP pattern and offer a good model to study the molecular mechanisms that contribute to the variety of mammalian limbs. The data showed that the expression domain of bat Hoxd13 was shifted prior to the asymmetric limb plate expansion, whereas its domain in mice was much more symmetric. This finding reveals a correlation between the divergence of Hoxd13 expression and the AP patterning difference in limb development. The second part of this thesis details a phenotypic rescue approach by human HOXB1-9 transgenes in mice with Hoxb1-9 deletion, The mouse mutants displayed homeosis in cervical and anterior thoracic vertebrae. The human transgenes entirely rescued the mouse mutants, suggesting that these human HOX genes have similar functions to their mouse orthologues in anterior axial skeletal patterning. The anterior expressing human HOXB transgenes such as HOXB1-3 were expressed in the mouse embryonic trunk in a similar manner as their murine orthologues. However, the anterior boundary of human HOXB9 expression domain was more posterior than that of the mouse Hoxb9 by 2-3 somites. These data provide the molecular support for the hypothesis that Hox genes are responsible for maintaining similar anterior axial skeletal architectures cervical and anterior thoracic regions, but different architectures in lumbar and posterior thoracic regions between humans and mice. ^

Comparison of particle dispersion obtained with simple stochastic models and les in pipe flow

A hybrid Eulerian-Lagrangian approach is employed to simulate heavy particle dispersion in turbulent pipe flow. The mean flow is provided by the Eulerian simulations developed by mean of JetCode, whereas the fluid fluctuations seen by particles are prescribed by a stochastic differential equation based on normalized Langevin. The statistics of particle velocity are compared to LES data which contain detailed statistics of velocity for particles with diameter equal to 20.4 µm. The model is in good agreement with the LES data for axial mean velocity whereas rms of axial and radial velocities should be adjusted.

Pattern formation of parametrically driven surface waves induced by vibration

Esta tesis se centra en la generación de ondas superficiales subarmónicas en fluidos sometidos a vibración forzada en el régimen gravitatorio capilar con líquidos de baja viscosidad. Tres problemas diferentes han sido estudiados: un contenedor rectangular con vibración horizontal, la misma geometría pero con una combinación de vibración vertical y horizontal y un obstáculo completamente sumergido vibrado verticalmente en un contenedor grande. Se deriva una ecuación de amplitud desde primeros principios para describir las ondas subarmónicas con forzamiento parámetrico inducido por la vibración. La ecuación es bidimensional mientras que el problema original es tridimensional y admite un forzamiento espacial no uniforme. Usando esta ecuación los tres sistemas han sido analizados, centrándose en calcular la amplitud crítica, la orientación de los patrones y el carácter temporal de los patrones espaciotemporales, que pueden ser estrictamente subarmónicos o cuasiperiodicos con una frecuencia de modulación temporal. La dependencia con los parámetros adimensionales también se considera. La teoría será comparada con los experimentos disponibles en la literatura. Abstract This thesis focus on the generation of subharmonic surface waves on fluids subject to forced vibration in the gravity-capillary regime with liquids of small viscosity. Three different problems have been considered: a rectangular container under horizontal vibration; the same geometry but under a combination of horizontal and vertical vibration; and a fully submerged vertically vibrated obstacle in a large container. An amplitude equation is derived from first principles that fairly precisely describes the subharmonic surfaces waves parametrically driven by vibration. That equation is two dimensional while the underlying problem is three-dimensional and permits spatially nonuniform forcing. Using this equation, the three systems have been analyzed, focusing on the calculation of the threshold amplitude, the pattern orientation, and the temporal character of the spatio-temporal patterns, which can be either strictly subharmonic or quasi-periodic, showing an additional modulation frequency. Dependence on the non-dimensional parameters is also considered. The theory is compared with the experiments available in the literature.

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.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Trans-cis Isomerism and acylimine formation in DsRed chromophore models: Intrinsic rotation barriers

The chromophore of the red fluorescent protein DsRed contains an acylimine substituent to a GFP-like chromophore structure. The acylimine is formed from the trans peptide linkage between residues F65 and Q66 in immature DsRed, but has a cis configuration in the mature protein. The relationship between acylimine formation and trans–cis isomerization is unresolved. We have calculated bond rotation profiles for models of mature and immature DsRed chromophores using B3LYP DFT. The isomerization barrier is substantially reduced in acylimine-substituted models, providing prima facie evidence that acylimine formation precedes trans–cis isomerization in DsRed chromophores.