Pattern formation in cell-sized membranes

The research presented in this dissertation follows in the tradition of experimental membrane biophysics. Our goal is to study the physical mechanisms underlying organization in the plasma membrane of living cells by using model systems. The central result from our experiments is that mixed-lipid membrane vesicles that are adhered by proteins to a solid-supported lipid membrane can dynamically form long-lived holes at the adhesion interface between the membranes. The first set of experiments we discuss exhibit the stable persistence of static patterns. The patterns are formed by adhering ternary-lipid vesicle membranes to a planar membrane supported on a solid, glass substrate \textit{via} biotin-avidin binding. The membrane and avidin are marked with spectrally distinct fluorescent dyes. We use fluorescence microscopy to acquire data. Adhesion causes half of adhered vesicles to form rough annular patterns with a central region that is devoid of membrane dye and protein binders. The peripheral region is dense in proteins and enriched in dye compared to the free, non-adhered portion of the same membrane. We measure the volume V and surface area A of adhered membranes. Using the measure 6[square root of pi]V/A[superscript 3/2] we find 0.84 for patterned and 0.98 for non-patterned membranes. Thus, adhered vesicles have two equilibrium states, one with annular patterns and one without, and the transition between them involves a loss of internal volume. Collectively our results suggest the annular patterns are holes. Finally, we report on a dynamic pattern that occurs in binary-lipid membranes adhered to a supported lipid bilayer. The pattern consists of finger-shaped holes that invade the protein-bound region. We show the characteristics of the fingers depend on the density [rho] of the protein binders in the adhered region: the width of static fingers [lambda] scales as [lambda] \sim\ [rho] and the rate of finger formation r, defined as the number of fingers that branch off from a boundary per unit time, scales as ln [r] \sim\ [rho]. Theoretically, we treat the formation of a finger as a thermally activated event occurring in a tense elastic film. The activation energy required to form a finger is approximately 3.5 kT, a biologically relevant energy scale.Physic

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

Using Experimentally Calibrated Regularized Stokeslets to Assess Bacterial Flagellar Motility Near a Surface

The presence of a nearby boundary is likely to be important in the life cycle and evolution of motile flagellate bacteria. This has led many authors to employ numerical simulations to model near-surface bacterial motion and compute hydrodynamic boundary effects. A common choice has been the method of images for regularized Stokeslets (MIRS); however, the method requires discretization sizes and regularization parameters that are not specified by any theory. To determine appropriate regularization parameters for given discretization choices in MIRS, we conducted dynamically similar macroscopic experiments and fit the simulations to the data. In the experiments, we measured the torque on cylinders and helices of different wavelengths as they rotated in a viscous fluid at various distances to a boundary. We found that differences between experiments and optimized simulations were less than 5% when using surface discretizations for cylinders and centerline discretizations for helices. Having determined optimal regularization parameters, we used MIRS to simulate an idealized free-swimming bacterium constructed of a cylindrical cell body and a helical flagellum moving near a boundary. We assessed the swimming performance of many bacterial morphologies by computing swimming speed, motor rotation rate, Purcell’s propulsive efficiency, energy cost per swimming distance, and a new metabolic energy cost defined to be the energy cost per body mass per swimming distance. All five measures predicted that the optimal flagellar wavelength is eight times the helical radius independently of body size and surface proximity. Although the measures disagreed on the optimal body size, they all predicted that body size is an important factor in the energy cost of bacterial motility near and far from a surface

Universality in Kinetic Models of Circadian Rhythms in \u3cem\u3eArabidopsis thaliana\u3c/em\u3e

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

Tobramycin and Bicarbonate Synergise to Kill Planktonic Pseudomonas Aeruginosa, but Antagonise to Promote Biofilm Survival

We thank Marvin Whiteley (The University of Texas at Austin) for his gift of CF clinical isolates and scientific discussions, Andreas Matouschek (The University of Texas at Austin) for use of his laboratory equipment and Kendra Rumbaugh (Texas Tech Health Sciences Center) for scientific input. We thank the Statistical Consulting Group (The University of Texas at Austin) and Biswanadham Sridhara and Dennis Wylie (bioinformatics consultants at The University of Texas at Austin) for discussion of response surface fitting and analysis, and Kanishk Jain for suggestions on fitting. This work was supported by start-up funds from The University of Texas at Austin to V.D.G., a gift from ExxonMobile to V.D.G., and a Microbiology Summer Merit Award from UT Austin to K.S.K. The funders had no role in the study design, data collection and interpretation, or the decision to submit the work for publication.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.Center for Nonlinear Dynamic

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