Excitable cells can exhibit complex patterns of oscillations, such as spiking and bursting. In cardiac cells, pathological voltage oscillations, called early afterdepolarizations (EADs), have been widely observed under disease conditions, yet their dynamical mechanisms remain unknown. Here, we show that EADs are caused by Hopf and homoclinic bifurcations. During period pacing, chaos always occurs at the transition from no EAD to EADs as the stimulation frequency decreases, providing a novel explanation for the irregular EAD behavior frequently observed in experiments.Complex oscillatory behaviors, such as spiking and bursting dynamics in pancreatic β-cells [1], neurons [1][2][3][4][5], and optical lasers [6], are common phenomena in excitable systems. These complex dynamics are generally described by systems with fast and slow time scales, where the full system behavior can be described by slow dynamics evolving the fast subsystem through a series of bifurcations [1,2]. Cardiac myocytes can exhibit pathological excitations called early afterdepolarizations (EADs), which are voltage oscillations during the repolarizing phase of the action potential (AP). They have been implicated as a cause of lethal cardiac arrhythmias [7][8][9] and have been widely investigated in experiments [8,[10][11][12] and also in simulations [13][14][15][16]. It is commonly agreed that EADs occur when inward (depolarizing) currents are increased and/or outward (repolarizing) currents are decreased. But many such changes do not produce EADs, and the general underlying dynamical mechanism still remains unknown. In single myocytes, EADs typically occur irregularly [10][11][12], which is generally attributed to random fluctuations of the underlying ion channels [13]. In a recent study [16], we presented evidence from isolated myocyte experiments and computational simulations that irregular EAD behavior is not random, but rather dynamical chaos, and gives rise to novel tissue scale dynamics.EADs have typically been studied in computational simulations using highly detailed AP models making dynamical analysis difficult [13][14][15][16] Dynamical origin of EADsThere are typically three time scales in a normal cardiac AP. The sodium (Na) current activates very rapidly, causing the fast upstroke of the AP, and then rapidly inactivates. The L-type calcium (Ca) current activates and inactivates more slowly than the Na current, playing a key role in maintaining the long AP plateau. Time-dependent potassium (K) currents activate even more slowly and eventually overcome the inward currents, repolarizing the cell back to the resting potential. EADs have typically been studied using highly detailed AP models [13][14][15][16] where C m = 1 µF/cm 2 ; I Na is the Na current; We set E si = 80 mV and E K = −77 mV. To study the effects of the time constants for the gating variables d, f, and x on the AP dynamics, we change these time constants by multiplying them by a scalar factor, i.e.,, and τ x (V) → γτ x (V). We refer to this modified LR1 model ...
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 properties of spatially localized states within the one-dimensional forced complex Ginzburg-Landau equation as a function of the coefficients.
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 under-screening, which all impact the emergence of fluid/solid interfaces, and transport in these systems. Since 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 liquids. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing free energy that consists of short and long range interactions, together with a dissipation mechanism via 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 1
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.
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. Matrix GLA protein (MGP)2 is a known inhibitor of vascular calcification. Lack of MGP causes arterial calcification in mice (1) and the human Keutel syndrome, which is due to mutations in the MGP gene (2). The arterial calcification in mice is associated with profound changes in cell differentiation as arterial smooth muscle cells are replaced by chondrocytelike cells undergoing progressive mineralization (1). MGP deficiency also causes peripheral pulmonary artery stenosis and other morphological defects, including nasal hypoplasia and abnormal cartilage and bone calcification (2, 3). Furthermore, alterations in MGP expression has been reported in various tumors including a loss of MGP during progression of lung and colorectal carcinomas (4, 5), which may be related to tumor vascularization given that differential MGP expression has been observed in endothelial cells during angiogenesis (6).Previous work by our group and others has suggested that MGP can act as an inhibitory morphogen, acting antagonistically to bone morphogenetic proteins (BMP)-2 and -4 (7-9). Our previous studies also showed close links between BMP-4, MGP, the activin-like kinase receptor 1 (ALK1), a transforming growth factor (TGF)- receptor essential in vascular formation, and vascular endothelial growth factor (VEGF) (9). BMP-4 ...
Abstract. Experiments on a quasi-two-dimensional Belousov-Zhabotinsky (BZ) reaction-diffusion system, periodically forced at approximately twice its natural frequency, exhibit resonant labyrinthine patterns that develop through two distinct mechanisms. In both cases, large amplitude labyrinthine patterns form that consist of interpenetrating fingers of frequency-locked regions differing in phase by π. Analysis of a forced complex Ginzburg-Landau equation captures both mechanisms observed for the formation of the labyrinths in the BZ experiments: a transverse instability of front 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.
During macropinocytosis, cells remodel their morphologies for the uptake of extracellular matter. This endocytotic mechanism relies on the collapse and closure of precursory structures, which are propagating actin-based, ring-shaped vertical undulations at the dorsal (top) cell membrane, a.k.a. circular dorsal ruffles (CDRs). As such, CDRs are essential to a range of vital and pathogenic processes alike. Here we show, based on both experimental data and theoretical analysis, that CDRs are propagating fronts of actin polymerization in a bistable system. The theory relies on a novel mass-conserving reaction–diffusion model, which associates the expansion and contraction of waves to distinct counter-propagating front solutions. Moreover, the model predicts that under a change in parameters (for example, biochemical conditions) CDRs may be pinned and fluctuate near the cell boundary or exhibit complex spiral wave dynamics due to a wave instability. We observe both phenomena also in our experiments indicating the conditions for which macropinocytosis is suppressed.
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 activatorinhibitor 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).
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