Refine
Has Fulltext
- no (5) (remove)
Year of publication
- 2020 (5) (remove)
Document Type
- Doctoral Thesis (5) (remove)
Language
- English (5)
Is part of the Bibliography
- yes (5)
Keywords
- Bayesian inference (1)
- L-edge spectroscopy (1)
- Migration (1)
- Moonlets (1)
- Propellers (1)
- Resonances (1)
- Rings (1)
- Saturn (1)
- anomalous diffusion (1)
- biophysics (1)
Institute
- Institut für Physik und Astronomie (5) (remove)
The development of methods such as super-resolution microscopy (Nobel prize in Chemistry, 2014) and multi-scale computer modelling (Nobel prize in Chemistry, 2013) have provided scientists with powerful tools to study microscopic systems. Sub-micron particles or even fluorescently labelled single molecules can now be tracked for long times in a variety of systems such as living cells, biological membranes, colloidal solutions etc. at spatial and temporal resolutions previously inaccessible. Parallel to such single-particle tracking experiments, super-computing techniques enable simulations of large atomistic or coarse-grained systems such as biologically relevant membranes or proteins from picoseconds to seconds, generating large volume of data. These have led to an unprecedented rise in the number of reported cases of anomalous diffusion wherein the characteristic features of Brownian motion—namely linear growth of the mean squared displacement with time and the Gaussian form of the probability density function (PDF) to find a particle at a given position at some fixed time—are routinely violated. This presents a big challenge in identifying the underlying stochastic process and also estimating the corresponding parameters of the process to completely describe the observed behaviour. Finding the correct physical mechanism which leads to the observed dynamics is of paramount importance, for example, to understand the first-arrival time of transcription factors which govern gene regulation, or the survival probability of a pathogen in a biological cell post drug administration. Statistical Physics provides useful methods that can be applied to extract such vital information. This cumulative dissertation, based on five publications, focuses on the development, implementation and application of such tools with special emphasis on Bayesian inference and large deviation theory. Together with the implementation of Bayesian model comparison and parameter estimation methods for models of diffusion, complementary tools are developed based on different observables and large deviation theory to classify stochastic processes and gather pivotal information. Bayesian analysis of the data of micron-sized particles traced in mucin hydrogels at different pH conditions unveiled several interesting features and we gained insights into, for example, how in going from basic to acidic pH, the hydrogel becomes more heterogeneous and phase separation can set in, leading to observed non-ergodicity (non-equivalence of time and ensemble averages) and non-Gaussian PDF. With large deviation theory based analysis we could detect, for instance, non-Gaussianity in seeming Brownian diffusion of beads in aqueous solution, anisotropic motion of the beads in mucin at neutral pH conditions, and short-time correlations in climate data. Thus through the application of the developed methods to biological and meteorological datasets crucial information is garnered about the underlying stochastic processes and significant insights are obtained in understanding the physical nature of these systems.
One of the tremendous discoveries by the Cassini spacecraft has been the detection of propeller structures in Saturn's A ring. Although the generating moonlet is too small to be resolved by the cameras aboard Cassini, its produced density structure within the rings, caused by its gravity can be well observed. The largest observed propeller is called Blériot and has an azimuthal extent over several thousand kilometers. Thanks to its large size, Blériot could be identified in different images over a time span of over 10 years, allowing the reconstruction of its orbital evolution. It turns out that Blériot deviates considerably from its expected Keplerian orbit in azimuthal direction by several thousand kilometers. This excess motion can be well reconstructed by a superposition of three harmonics, and therefore resembles the typical fingerprint of a resonantly perturbed body. This PhD thesis is directed to the excess motion of Blériot. Resonant perturbations are a known for some of the outer satellites of Saturn. Thus, in the first part of this thesis, we seek for suiting resonance candidates nearby the propeller, which might explain the observed periods and amplitudes. In numeric simulations, we show that indeed resonances by Prometheus, Pandora and Mimas can explain the libration periods in good agreement, but not the amplitudes. The amplitude problem is solved by the introduction of a propeller-moonlet interaction model, where we assume a broken symmetry of the propeller by a small displacement of the moonlet. This results in a librating motion the moonlet around the propeller's symmetry center due to the non-vanishing accelerations. The retardation of the reaction of the propeller structure to the motion of the moonlet causes the propeller to become asymmetric. Hydrodynamic simulations to test our analytical model confirm our predictions. In the second part of this thesis, we consider a stochastic migration of the moonlet, which is an alternative hypothesis to explain the observed excess motion of Blériot. The mean-longitude is a time-integrated quantity and thus introduces a correlation between the independent kicks of a random walk, smoothing the noise and thus makes the residual look similar to the observed one for Blériot. We apply a diagonalization test to decorrelated the observed residuals for the propellers Blériot and Earhart and the ring-moon Daphnis. It turns out that the decorrelated distributions do not strictly follow the expected Gaussian distribution. The decorrelation method fails to distinguish a correlated random walk from a noisy libration and thus we provide an alternative study. Assuming the three-harmonic fit to be a valid representation of the excess motion for Blériot, independently from its origin, we test the likelihood that this excess motion can be created by a random walk. It turns out that a non-correlated and correlated random walk is unlikely to explain the observed excess motion.
Cells and tissues are sensitive to mechanical forces applied to them. In particular, bone forming cells and connective tissues, composed of cells embedded in fibrous extracellular matrix (ECM), are continuously remodeled in response to the loads they bear. The mechanoresponses of cells embedded in tissue include proliferation, differentiation, apoptosis, internal signaling between cells, and formation and resorption of tissue.
Experimental in-vitro systems of various designs have demonstrated that forces affect tissue growth, maturation and mineralization. However, the results depended on different parameters such as the type and magnitude of the force applied in each study. Some experiments demonstrated that applied forces increase cell proliferation and inhibit cell maturation rate, while other studies found the opposite effect. When the effect of different magnitudes of forces was compared, some studies showed that higher forces resulted in a cell proliferation increase or differentiation decrease, while other studies observed the opposite trend or no trend at all.
In this study, MC3T3-E1 cells, a cell line of pre-osteoblasts (bone forming cells), was used. In this cell line, cell differentiation is known to accelerate after cells stop proliferating, typically at confluency. This makes this cell line an interesting subject for studying the influence of forces on the switch between the proliferation stage of the precursor cell and the differentiation to the mature osteoblasts.
A new experimental system was designed to perform systematic investigations of the influence of the type and magnitude of forces on tissue growth. A single well plate contained an array of 80 rectangular pores. Each pore was seeded with MC3T3-E1 cells. The culture medium contained magnetic beads (MBs) of 4.5 μm in diameter that were incorporated into the pre-osteoblast cells. Using an N52 neodymium magnet, forces ranging over three orders of magnitude were applied to MBs incorporated in cells at 10 different distances from the magnet. The amount of formed tissue was assessed after 24 days of culture. The experimental design allowed to obtain data concerning (i) the influence of the type of the force (static, oscillating, no force) on tissue growth; (ii) the influence of the magnitude of force (pN-nN range); (iii) the effect of functionalizing the magnetic beads with the tripeptide Arg-Gly-Asp (RGD). To learn about cell differentiation state, in the final state of the tissue growth experiments, an analysis for the expression of alkaline phosphatase (ALP), a well - known marker of osteoblast differentiation, was performed.
The experiments showed that the application of static magnetic forces increased tissue growth compared to control, while oscillating forces resulted in tissue growth reduction. A statistically significant positive correlation was found between the amount of tissue grown and the magnitude of the oscillating magnetic force. A positive but non-significant correlation of the amount of tissue with the magnitude of forces was obtained when static forces were applied. Functionalizing the MBs with RGD peptides and applying oscillating forces resulted in an increase of tissue growth relative to tissues incubated with “plain” epoxy MBs. ALP expression decreased as a function of the magnitude of force both when static and oscillating forces were applied. ALP stain intensity was reduced relative to control when oscillating forces were applied and was not significantly different than control for static forces.
The suggested interpretation of the experimental findings is that larger mechanical forces delay cell maturation and keep the pre-osteoblasts in a more proliferative stage characterized by more tissue formed and lower expression of ALP. While the influence of the force magnitude can be well explained by an effect of the force on the switch between proliferation and differentiation, the influence of force type (static or oscillating) is less clear. In particular, it is challenging to reconcile the reduction of tissue formed under oscillating forces as compared to controls with the simultaneous reduction of ALP expression. To better understand this, it may be necessary to refine the staining protocol of the scaffolds and to include the amount and structure of ECM as well as other factors that were not monitored in the experiment and which may influence tissue growth and maturation.
The developed experimental system proved well suited for a systematic and efficient study of the mechanoresponsiveness of tissue growth, it allowed a study of the dependence of tissue growth on force magnitude ranging over three orders of magnitude, and a comparison between the effect of static and oscillating forces. Future experiments can explore the multiple parameters that affect tissue growth as a function of the magnitude of the force: by applying different time-dependent forces; by extending the force range studied; or by using different cell lines and manipulating the mechanotransduction in the cells biochemically.
The electronic charge distributions of transition metal complexes fundamentally determine their chemical reactivity. Experimental access to the local valence electronic structure is therefore crucial in order to determine how frontier orbitals are delocalized between different atomic sites and electronic charge is spread throughout the transition metal complex. To that end, X-ray spectroscopies are employed in this thesis to study a series of solution-phase iron complexes with respect to the response of their local electronic charge distributions to different external influences. Using resonant inelastic X-ray scattering (RIXS) and X-ray absorption spectroscopy (XAS) at the iron L-edge, changes in local charge densities are investigated at the iron center depending on different ligand cages as well as solvent environments. A varying degree of charge delocalization from the metal center onto the ligands is observed, which is governed by the capabilities of the ligands to accept charge density into their unoccupied orbitals. Specific solvents are furthermore shown to amplify this process. Solvent molecules of strong Lewis-acids withdraw charge from the ligand allowing in turn for more metal charge to be delocalized onto the ligand. The resulting local charge deficiencies at the metal center are, however, counteracted by competing electron-donation channels from the ligand towards the iron, which are additionally revealed. This is interpreted as a compensating effect which strives to maintain local charge densities at the iron center. This mechanism of charge density preservation is found to be of general nature. Using time-resolved RIXS and XAS at the iron L-edge, an analogous interplay of electron donation and back-donation channels is also revealed for the case of charge-transfer excited states. In such transient configurations, the electronic occupation of iron-centered frontier orbitals has been altered by an optical excitation. Changes in local charge densities that are expected to follow an increased or decreased population of iron-centered orbitals are, however, again counteracted. By scaling the degree of electron donation from the ligand onto the metal, local charge densities at the iron center can be efficiently maintained. Since charge-transfer excitations, however, often constitute the initial step in many electron transfer processes, these findings challenge common notions of charge-separation in transition metal dyes.
Small moonlets or moons embedded in dense planetary rings create S-shaped density modulations called propellers if their masses are smaller than a certain threshold, alternatively they create a circumferential gap in the disk if the embedded body’s mass exceeds this threshold (Spahn and Sremčević, 2000). The gravitational perturber scatters the ring particles, depletes the disk’s density, and, thus, clears a gap, whereas counteracting viscous diffusion of the ring material has the tendency to close the created gap, thereby forming a propeller. Propeller objects were predicted by Spahn and Sremčević (2000) and Sremčević et al. (2002) and were later discovered by the Cassini space probe (Tiscareno et al., 2006, Sremčević et al., 2007, Tiscareno et al., 2008, and Tiscareno et al., 2010). The ring moons Pan and Daphnis are massive enough to maintain the circumferential Encke and Keeler gaps in Saturn’s A ring and were detected by Showalter (1991) and Porco (2005) in Voyager and Cassini images, respectively. In this thesis, a nonlinear axisymmetric diffusion model is developed to describe radial density profiles of circumferential gaps in planetary rings created by embedded moons (Grätz et al., 2018). The model accounts for the gravitational scattering of the ring particles by the embedded moon and for the counteracting viscous diffusion of the ring matter back into the gap. With test particle simulations it is shown that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich and Tremaine (1980). This is especially significant for the modeling of the Keeler gap. The model is applied to the Encke and Keeler gaps with the aim to estimate the shear viscosity of the ring in their vicinities. In addition, the model is used to analyze whether tiny icy moons whose dimensions lie below Cassini’s resolution capabilities would be able to cause the poorly understood gap structure of the C ring and the Cassini Division. One of the most intriguing facets of Saturn’s rings are the extremely sharp edges of the Encke and Keeler gaps: UVIS-scans of their gap edges show that the optical depth drops from order unity to zero over a range of far less than 100 m, a spatial scale comparable to the ring’s vertical extent. This occurs despite the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Borderies et al. (1982, 1989) have shown that this striking feature is likely related to the local reversal of the usually outward-directed viscous transport of angular momentum in strongly perturbed regions. We have revised the Borderies et al. (1989) model using a granular flow model to define the shear and bulk viscosities, ν and ζ, in order to incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model for circumferential gaps presented in this thesis (Grätz et al., 2019). The sharp Encke and Keeler gap edges are modeled and conclusions regarding the shear and bulk viscosities of the ring are discussed. Finally, we explore the question of whether the radial density profile of the central and outer A ring, recently measured by Tiscareno and Harris (2018) in the highest resolution to date, and in particular, the sharp outer A ring edge can be modeled consistently from the balance of gravitational scattering by several outer moons and the mass and momentum transport. To this aim, the developed model is extended to account for the inward drifts caused by multiple discrete and overlapping resonances with multiple outer satellites and is then used to hydrodynamically simulate the normalized surface mass density profile of the A ring. This section of the thesis is based on studies by Tajeddine et al. (2017a) who recently discussed the common misconception that the 7:6 resonance with Janus alone maintains the outer A ring edge, showing that the combined effort of several resonances with several outer moons is required to confine the A ring as observed by the Cassini spacecraft.