Competition in notch signaling with cis enriches cell fate decisions

Notch signaling is involved in cell fate choices during the embryonic development of Metazoa. Commonly, Notch signaling arises from the binding of the Notch receptor to its ligands in adjacent cells driving cell-to-cell communication. Yet, cell-autonomous control of Notch signaling through both ligand-dependent and ligand-independent mechanisms is known to occur as well. Examples include Notch signaling arising in the absence of ligand binding, and cis-inhibition of Notch signaling by titration of the Notch receptor upon binding to its ligands within a single cell. Increasing experimental evidences support that the binding of the Notch receptor with its ligands within a cell (cis-interactions) can also trigger a cell-autonomous Notch signal (cis-signaling), whose potential effects on cell fate decisions and patterning remain poorly understood. To address this question, herein we mathematically and computationally investigate the cell states arising from the combination of cis-signaling with additional Notch signaling sources, which are either cell-autonomous or involve cell-to-cell communication. Our study shows that cis-signaling can switch from driving cis-activation to effectively perform cis-inhibition and identifies under which conditions this switch occurs. This switch relies on the competition between Notch signaling sources, which share the same receptor but differ in their signaling efficiency. We propose that the role of cis-interactions and their signaling on fine-grained patterning and cell fate decisions is dependent on whether they drive cis-inhibition or cis-activation, which could be controlled during development. Specifically, cis-inhibition and not cis-activation facilitates patterning and enriches it by modulating the ratio of cells in the high-ligand expression state, by enabling additional periodic patterns like stripes and by allowing localized patterning highly sensitive to the precursor state and cell-autonomous bistability. Our study exemplifies the complexity of regulations when multiple signalng sources share the same receptor and provides the tools for their characterization.

Spatio-temporal pattern formation in microemulsions under different physical and chemical conditions

Otto-von-Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Dissertation, 2016

Pattern formation during mesophase growth in a homologous series

Remarkable differences in the shape of the nematic-smectic-B interface in a quasi-two-dimensional geometry have been experimentally observed in three liquid crystals of very similar molecular structure, i.e., neighboring members of a homologous series. In the thermal equilibrium of the two mesophases a faceted rectanglelike shape was observed with considerably different shape anisotropies for the three homologs. Various morphologies such as dendritic, dendriticlike, and faceted shapes of the rapidly growing smectic-B germ were also observed for the three substances. Experimental results were compared with computer simulations based on the phase field model. The pattern forming behavior of a binary mixture of two homologs was also studied.

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.).

Dynamics of domain walls in pattern formation under traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Dynamics of transient pattern formation in nematic liquid crystals

We analyze the dynamics of a transient pattern formation in the Fréedericksz transition corresponding to a twist geometry. We present a calculation of the time-dependent structure factor based on a dynamical model which incorporates consistently the coupling of the director field with the velocity flow and also the effect of fluctuations. The appearance and development of a characteristic periodicity is described in terms of the time dependence of the maximum of the structure factor. We find a well-defined time for the appearance of the pattern and a subsequent stage of pattern development in which the characteristic periodicity tends to an asymptotic value.

Nonlinear effects in the dynamics of transient pattern formation in nematics

A nonlinear calculation of the dynamics of transient pattern formation in the Fréedericksz transition is presented. A Gaussian decoupling is used to calculate the time dependence of the structure factor. The calculation confirms the range of validity of linear calculations argued in earlier work. In addition, it describes the decay of the transient pattern.

Spatiotemporal Pattern Formation in the Oscillatory Electro-Oxidation of Sulfide on a Platinum Disk

Spatiotemporal pattern formation in the electrocatalytic oxidation of sulfide on a platinum disk is investigated using electrochemical methods and a charge-coupled device (CCD) camera simultaneously. The system is characterized by different oscillatory regions spread over a wide potential range. An additional series resistor and a large electrode area facilitate observation of multiple regions of kinetic instabilities along the current/potential curve. Spatiotemporal patterns on the working electrode, such as fronts, pulses, spirals, twinkling eyes, labyrinthine stripes, and alternating synchronized deposition and dissolution, are observed at different operating conditions of series resistance and sweep rate.

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.

Multimode Atomic Pattern Formation via Enhanced Light-atom Interactions

The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.

Controlling Pattern Formation in Nanoparticle Assemblies via Directed Solvent Dewetting

We have achieved highly localised control of pattern formation in two dimensional nanoparticle assemblies by direct modification of solvent dewetting dynamics. A striking dependence of nanoparticle organisation on the size of atomic force microscope-generated surface heterogeneities is observed and reproduced in numerical simulations. Nanoscale features induce rupture of the solvent-nanoparticle film, causing the local flow of solvent to carry nanoparticles into confinement. Microscale heterogeneities instead slow the evaporation of the solvent, producing a remarkably abrupt interface between different nanoparticle patterns.