Arik Yochelis

Matrix GLA Protein, an Inhibitory Morphogen in Pulmonary Vascular Development

Deficiency of matrix GLA protein (MGP), an inhibitor of bone morphogenetic protein (BMP)-2/4, is known to cause arterial calcification and peripheral pulmonary artery stenosis. Yet the vascular role of MGP remains poorly understood. To further investigate MGP, we created a new MGP transgenic mouse model with high expression of the transgene in the lungs. The excess MGP led to a disruption of the pulmonary pattern of BMP-4, and resulted in significant morphological defects in the pulmonary artery tree. Specifically, the vascular branching pattern lacked characteristic side branching, whereas control lungs had extensive side branching accounting for as much as 40% of the vascular endothelium. The vascular changes could be explained by a dramatic reduction of phosphorylated SMAD1/5/8 in the alveolar epithelium, and in epithelial expression of the activin-like kinase receptor 1 and vascular endothelial growth factor, both critical in vascular formation. Abnormalities were also found in the terminal airways and in lung cell differentiation; high levels of surfactant protein-B were distributed in an abnormal pattern suggesting lost coordination between vasculature and airways. Ex vivo, lung cells from MGP transgenic mice showed higher proliferation, in particular surfactant protein B-expressing cells, and conditioned medium from these cells poorly supported in vitro angiogenesis compared with normal lung cells. The vascular branching defect can be mechanistically explained by a computational model based on activator/inhibitor reaction-diffusion dynamics, where BMP-4 and MGP are considered as an activating and inhibitory morphogen, respectively, suggesting that morphogen interactions are important for vascular branching.

Development of Standing-Wave Labyrinthine Patterns ∗

Experiments on a quasi-two-dimensional Belousov-Zhabotinsky (BZ) reaction-diffusion system, pe- riodically forced at approximately twice its natural frequency, exhibit resonant labyrinthine patterns that develop through two distinct mechanisms. In both cases, large amplitude labyrinthine patterns f orm that consist ofinterpenetrating fingers off requency-locked regions differing in phase by π. Analysis of a forced complex Ginzburg-Landau equation captures both mechanisms observed for the f ormation ofthe labyrinths in the BZ experiments: a transverse instability off ront structures and a nucleation of stripes from unlocked oscillations. The labyrinths are found in the experiments and in the model at a similar location in the forcing amplitude and frequency parameter plane.

Classification of Spatially Localized Oscillations in Periodically Forced Dissipative Systems

Formation of spatially localized oscillations in parametrically driven systems is studied, focusing on the dominant 2:1 resonance tongue. Both damped and self-excited oscillatory media are considered. Near the primary subharmonic instability such systems are described by the forced complex Ginzburg–Landau equation. The technique of spatial dynamics is used to identify three basic types of coherent states described by this equation—small amplitude oscillons, large amplitude reciprocal oscillons resembling holes in an oscillating background, and fronts connecting two spatially homogeneous states oscillating out of phase. In many cases all three solution types are found in overlapping parameter regimes, and multiple solutions of each type may be simultaneously stable. The origin of this behavior can be traced to the formation of a heteroclinic cycle in space between the finite amplitude spatially homogeneous phase-locked oscillation and the zero state. The results provide an almost complete classification of...

The formation of labyrinths, spots and stripe patterns in a biochemical approach to cardiovascular calcification

Calcification and mineralization are fundamental physiological processes, yet the mechanisms of calcification, in trabecular bone and in calcified lesions in atherosclerotic calcification, are unclear. Recently, it was shown in in vitro experiments that vascular-derived mesenchymal stem cells can display self-organized calcified patterns. These patterns were attributed to activator/inhibitor dynamics in the style of Turing, with bone morphogenetic protein 2 acting as an activator, and matrix GLA protein acting as an inhibitor. Motivated by this qualitative activator–inhibitor dynamics, we employ a prototype Gierer–Meinhardt model used in the context of activator–inhibitor-based biological pattern formation. Through a detailed analysis in one and two spatial dimensions, we explore the pattern formation mechanisms of steady state patterns, including their dependence on initial conditions. These patterns range from localized holes to labyrinths and localized peaks, or in other words, from dense to sparse activator distributions (respectively). We believe that an understanding of the wide spectrum of activator–inhibitor patterns discussed here is prerequisite to their biochemical control. The mechanisms of pattern formation suggest therapeutic strategies applicable to bone formation in atherosclerotic lesions in arteries (where it is pathological) and to the regeneration of trabecular bone (recapitulating normal physiological development).

Transition from non-monotonic to monotonic electrical diffuse layers: impact of confinement on ionic liquids

Intense investigations of room temperature ionic liquids have revealed not only their advantages in a wide range of technological applications but also triggered scientific debates about charge distribution properties within the bulk and near the solid-liquid interfaces. While many observations report on an alternating charge layering (i.e., spatially extended decaying charge density oscillations), there are recent conjectures that ionic liquids bear similarity to dilute electrolytes. Using a modified Poisson-Nernst-Planck model for ionic liquids (after Bazant et al., Phys. Rev. Lett. 2011, 106, 046102), we show that both behaviors are fundamental properties of ionic liquids. The transition from the non-monotonic (oscillatory) to the monotonic structure of electrical diffuse layers appears to non-trivially depend on ionic density in the bulk, electrostatic correlation length, confinement and surface properties. Consequently, the results not only reconcile the empirical results but also provide a powerful methodology to gain insights into the nonlinear aspects of concentrated electrolytes.

Theory of Phase Separation and Polarization for Pure Ionic Liquids.

Room temperature ionic liquids are attractive to numerous applications and particularly, to renewable energy devices. As solvent free electrolytes, they demonstrate a paramount connection between the material morphology and Coulombic interactions: the electrode/RTIL interface is believed to be a product of both polarization and spatiotemporal bulk properties. Yet, theoretical studies have dealt almost exclusively with independent models of morphology and electrokinetics. Introduction of a distinct Cahn-Hilliard-Poisson type mean-field framework for pure molten salts (i.e., in the absence of any neutral component), allows a systematic coupling between morphological evolution and the electrokinetic phenomena, such as transient currents. Specifically, linear analysis shows that spatially periodic patterns form via a finite wavenumber instability and numerical simulations demonstrate that while labyrinthine type patterns develop in the bulk, lamellar structures are favored near charged surfaces. The results demonstrate a qualitative phenomenology that is observed empirically and thus, provide a physically consistent methodology to incorporate phase separation properties into an electrochemical framework.

Self-organization of waves and pulse trains by molecular motors in cellular protrusions

Actin-based cellular protrusions are an ubiquitous feature of cells, performing a variety of critical functions ranging from cell-cell communication to cell motility. The formation and maintenance of these protrusions relies on the transport of proteins via myosin motors, to the protrusion tip. While tip-directed motion leads to accumulation of motors (and their molecular cargo) at the protrusion tip, it is observed that motors also form rearward moving, periodic and isolated aggregates. The origins and mechanisms of these aggregates, and whether they are important for the recycling of motors, remain open puzzles. Motivated by novel myosin-XV experiments, a mass conserving reaction-diffusion-advection model is proposed. The model incorporates a non-linear cooperative interaction between motors, which converts them between an active and an inactive state. Specifically, the type of aggregate formed (traveling waves or pulse-trains) is linked to the kinetics of motors at the protrusion tip which is introduced by a boundary condition. These pattern selection mechanisms are found not only to qualitatively agree with empirical observations but open new vistas to the transport phenomena by molecular motors in general.

Why Turing mechanism is an obstacle to stationary periodic patterns in bounded reaction-diffusion media with advection

Formation of stationary periodic patterns is paramount to many chemical, biological, physical, and ecological media. One of the most subtle mechanisms was suggested by Turing, who highlighted the applicability of isotropic reaction-diffusion dynamics with at least two diffusing fields. However, on finite domains with the presence of a symmetry breaking differential advection, two diffusing fields are rather disadvantageous to formation of stationary periodic patterns. We show that the criterion to stationary periodic patterns in Turing type models requires non-periodic boundary conditions and tuning of two parameters (a co-dimension-2 bifurcation in space) whereas in systems with one diffusing field (non-Turing) the bifurcation is of co-dimension 1 and thus easier to satisfy. We demonstrate this general result using spatial dynamics methods and direct numerical simulations of the canonical FitzHugh-Nagumo model.

Generation of finite wave trains in excitable media.

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end, we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory

The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and underscreening, which all impact the emergence of fluid/solid interfaces, and the transport in these systems. Because these phenomena are not captured by existing mean-field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquid mixtures. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing a free energy that consists of short- and long-range interactions, along with an energy dissipation mechanism obtained by Onsagers relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified by the free energy. The model equations not only provide insights into transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enable qualitative recovery of three distinct regions in the full range of the nonmonotonic electrical screening length that has been recently observed in experiments in which organic solvent is used to dilute ionic liquids.