Universality in kinetic models of circadian rhythms in [Formula: see text].

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart-Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart-Landau equation to collapse the circadian oscillations onto two universal curves-one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm.

Dynamic Fingering in Adhered Lipid Membranes.

Artificial lipid membranes incorporating proteins have frequently been used as models for the dynamic organization of biological structures in living cells as well as in the development of biology-inspired technologies. We report here on the experimental demonstration and characterization of a pattern-forming process that occurs in a lipid bilayer membrane adhered via biotin-avidin binding to a second lipid membrane that is supported by a solid substrate. Adhesion regions are roughly circular with a diameter of about 25 µm. Using confocal fluorescence microscopy, we record time series of dynamic fingering patterns that grow in the upper lipid membrane and intermembrane biotin-avidin bonds. The fingers are micrometer-scale elongated pores that grow from the edge of an already-stabilized hole. Finger growth is saltatory on the scale of tens of seconds. We find that as the fingers grow and the density of adhesion proteins increases, the rate of finger growth decreases exponentially and the width of newly formed fingers decreases linearly. We show that these findings are consistent with a thermodynamic description of dynamic pore formation and stabilization.

Biofilm viscoelasticity and nutrient source location control biofilm growth rate, migration rate, and morphology in shear flow.

We present a numerical model to simulate the growth and deformation of a viscoelastic biofilm in shear flow under different nutrient conditions. The mechanical interaction between the biofilm and the fluid is computed using the Immersed Boundary Method with viscoelastic parameters determined a priori from measurements reported in the literature. Biofilm growth occurs at the biofilm-fluid interface by a stochastic rule that depends on the local nutrient concentration. We compare the growth, migration, and morphology of viscoelastic biofilms with a common relaxation time of 18 min over the range of elastic moduli 10-1000 Pa in different nearby nutrient source configurations. Simulations with shear flow and an upstream or a downstream nutrient source indicate that soft biofilms grow more if nutrients are downstream and stiff biofilms grow more if nutrients are upstream. Also, soft biofilms migrate faster than stiff biofilms toward a downstream nutrient source, and although stiff biofilms migrate toward an upstream nutrient source, soft biofilms do not. Simulations without nutrients show that on the time scale of several hours, soft biofilms develop irregular structures at the biofilm-fluid interface, but stiff biofilms deform little. Our results agree with the biophysical principle that biofilms can adapt to their mechanical and chemical environment by modulating their viscoelastic properties. We also compare the behavior of a purely elastic biofilm to a viscoelastic biofilm with the same elastic modulus of 50 Pa. We find that the elastic biofilm underestimates growth rates and downstream migration rates if the nutrient source is downstream, and it overestimates growth rates and upstream migration rates if the nutrient source is upstream. Future modeling can use our comparison to identify errors that can occur by simulating biofilms as purely elastic structures.

Tobramycin and bicarbonate synergise to kill planktonic Pseudomonas aeruginosa, but antagonise to promote biofilm survival.

Increasing antibiotic resistance and the declining rate at which new antibiotics come into use create a need to increase the efficacy of existing antibiotics. The aminoglycoside tobramycin is standard-of-care for many types of Pseudomonas aeruginosa infections, including those in the lungs of cystic fibrosis (CF) patients. P. aeruginosa is a nosocomial and opportunistic pathogen that, in planktonic form, causes acute infections and, in biofilm form, causes chronic infections. Inhaled bicarbonate has recently been proposed as a therapy to improve antimicrobial properties of the CF airway surface liquid and viscosity of CF mucus. Here we measure the effect of combining tobramycin and bicarbonate against P. aeruginosa, both lab strains and CF clinical isolates. Bicarbonate synergises with tobramycin to enhance killing of planktonic bacteria. In contrast, bicarbonate antagonises with tobramycin to promote better biofilm growth. This suggests caution when evaluating bicarbonate as a therapy for CF lungs infected with P. aeruginosa biofilms. We analyse tobramycin and bicarbonate interactions using an interpolated surface methodology to measure the dose-response function. These surfaces allow more accurate estimation of combinations yielding synergy and antagonism than do standard isobolograms. By incorporating predictions based on Loewe additivity theory, we can consolidate information on a wide range of combinations that produce a complex dose-response surface, into a single number that measures the net effect. This tool thus allows rapid initial estimation of the potential benefit or harm of a therapeutic combination. Software code is freely made available as a resource for the community.