On system-spanning demixing properties of cell polarization

Nonreciprocal Cahn-Hilliard Model Emerges as a Universal Amplitude Equation

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatiotemporal pattern formation. Starting from a linear large-scale oscillatory instability-a conserved-Hopf instability-that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs small-scale instability, stationary vs oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.

Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling

We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well-known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis, we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.

On the influence of cell shape on dynamic reaction-diffusion polarization patterns

The distribution of signaling molecules following mechanical or chemical stimulation of a cell defines cell polarization, with regions of high active Cdc42 at the front and low active Cdc42 at the rear. As reaction-diffusion phenomena between signaling molecules, such as Rho GTPases, define the gradient dynamics, we hypothesize that the cell shape influences the maintenance of the “front-to-back” cell polarization patterns. We investigated the influence of cell shape on the Cdc42 patterns using an established computational polarization model. Our simulation results showed that not only cell shape but also Cdc42 and Rho-related (in)activation parameter values affected the distribution of active Cdc42. Despite an initial Cdc42 gradient, the in silico results showed that the maximal Cdc42 concentration shifts in the opposite direction, a phenomenon we propose to call “reverse polarization”. Additional in silico analyses indicated that “reverse polarization” only occurred in a particular parameter value space that resulted in a balance between inactivation and activation of Rho GTPases. Future work should focus on a mathematical description of the underpinnings of reverse polarization, in combination with experimental validation using, for example, dedicated FRET-probes to spatiotemporally track Rho GTPase patterns in migrating cells. In summary, the findings of this study enhance our understanding of the role of cell shape in intracellular signaling.

Pattern selection in reaction diffusion systems

Turing's theory of pattern formation has been used to describe the formation of self-organized periodic patterns in many biological, chemical, and physical systems. However, the use of such models is hindered by our inability to predict, in general, which pattern is obtained from a given set of model parameters. While much is known near the onset of the spatial instability, the mechanisms underlying pattern selection and dynamics away from onset are much less understood. Here, we provide physical insight into the dynamics of these systems. We find that peaks in a Turing pattern behave as point sinks, the dynamics of which is determined by the diffusive fluxes into them. As a result, peaks move toward a periodic steady-state configuration that minimizes the mass of the diffusive species. We also show that the preferred number of peaks at the final steady state is such that this mass is minimized. Our work presents mass minimization as a potential general principle for understanding pattern formation in reaction diffusion systems far from onset.

Evidence for disruption of diurnal salivary cortisol rhythm in childhood obesity: relationships with anthropometry, puberty and physical activity

Background

The aim of this study was to examine the characteristics of diurnal cortisol rhythm in childhood obesity and its relationships with anthropometry, pubertal stage and physical activity.

Methods

Thirty-five children with obesity (median age: 11.80[interquartile range 10.30, 13.30] and median BMI z-score: 3.21[interquartile range 2.69, 3.71]) and 22 children with normal weight (median age: 10.85[interquartile range 8.98, 12.13] and median BMI z-score: − 0.27[interquartile range − 0.88, 0.35]) were recruited. Saliva samples were collected at 08:00, 16:00 and 23:00 h. Cortisol concentrations at 3 time points, corresponding areas under the curve (AUCs) and diurnal cortisol slope (DCS) were compared between the two groups. Anthropometric measures and pubertal stage were evaluated, and behavioural information was obtained via questionnaires.

Results

Children with obesity displayed significantly lower cortisol_08:00 (median [interquartile range]: 5.79[3.42,7.73] vs. 8.44[5.56,9.59] nmol/L, P = 0.030) and higher cortisol_23:00 (median [interquartile range]: 1.10[0.48,1.46] vs. 0.40[0.21,0.61] nmol/L, P < 0.001) with a flatter DCS (median [interquartile range]: − 0.29[− 0.49, 0.14] vs. -0.52[− 0.63, 0.34] nmol/L/h, P = 0.006) than their normal weight counterparts. The AUC increased with pubertal development (AUC_{08:00–16:00}:P = 0.008; AUC_{08:00–23:00}: P = 0.005). Furthermore, cortisol_08:00 was inversely associated with BMI z-score (β = − 0.247, P = 0.036) and waist-to-height ratio (WHtR) (β = − 0.295, P = 0.027). Cortisol_23:00 was positively associated with BMI z-score (β = 0.490, P<0.001), WHtR (β = 0.485, P<0.001) and fat mass percentage (FM%) (β = 0.464, P<0.001). Absolute values of DCS were inversely associated with BMI z-score (β = − 0.350, P = 0.009), WHtR (β = − 0.384, P = 0.004) and FM% (β = − 0.322, P = 0.019). In multivariate analyses adjusted for pubertal stage and BMI z-score, Cortisol_08:00, AUC_{08:00–16:00} and absolute values of DCS were inversely associated with the relative time spent in moderate to vigorous intensity physical activity (P < 0.05). AUC_{16:00–23:00} was positively associated with relative non-screen sedentary time and negatively associated with sleep (P < 0.05).

Conclusions

The disorder of diurnal salivary cortisol rhythm is associated with childhood obesity, which is also influenced by puberty development and physical activity. Thus, stabilizing circadian cortisol rhythms may be an important approach for childhood obesity.

Universal aspects of collective behavior in chemotactic systems

We investigate the collective dynamics of particles (e.g., microorganisms) interacting via chemotactic gradients. Specifically, we focus on continuum models for chemotaxis that include a damping of the chemical production with increasing local particle density and/or systems where the chemotactic sensitivity is reduced with increasing local concentration of the chemical. Using a recently introduced perturbative method [Phys. Rev. E 98, 020603 (2018)10.1103/PhysRevE.98.020603], we show that the onset of particle clustering in these systems is described by the universal Cahn-Hilliard (CH) model. On the one hand, this establishes particle-conserving models for chemotaxis as a further example for the universal class of nonequilibrium demixing phenomena we call active phase separation. On the other hand, the reduction to the CH model allows an analytical determination of suitable parameter ranges wherein, e.g., the transition to spatial density modulations is continuous and/or undesired blow-up solutions can be avoided. A comparison between the numerical solutions of the chemotaxis model and the derived CH model also provides the parameter range where the basic chemotaxis model behaves like other systems showing active phase separation, including the coarsening behavior in two spatial dimensions. Our approach highlights how basic principles of pattern formation theory allow the identification of common basic properties in different chemotaxis models.