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The diffusive behavior of macromolecules in solution is a key factor in the kinetics of macromolecular binding and assembly, and in the theoretical description of many experiments. Experiments on high-density protein solutions have found that a slow down of the diffusion dynamics is larger than expected from colloidal theory for non-interaction hard-spheres. It has also been shown that the rotational diffusion anisotropy in high-density protein solutions is larger than in dilute ones. High-density protein solutions are a complex fluid that is different from the neat fluid assumption used in the hydrodynamic theory. It is therefore important to have methods to accurately calculate the translational and rotational diffusion tensor from simulations as well as simulation algorithms to explore high-density solutions.
Simulations provide a powerful tool to study diffusion in complex fluids. They can be used to study the macroscopic and microscopic effects of complex fluids on the diffusive behavior. There has been already a lot of work done to accurately simulate diffusion and to determine the diffusion coefficients from simulations.
The translational diffusion of molecules in simple and complex liquids can be determined with high accuracy from simulations. This is not yet the case for rotational diffusion. Existing algorithms to calculate the rotational diffusion coefficients from simulations make assumptions about the shape of the protein or only work at short times. For the simulation of diffusive behavior of macromolecules two options exist today. An all-atom integrator with explicit solvent molecules or coarse-grained (CG) simulations with an implicit solvent. CG simulations of dynamic behavior with implicit solvent are also called Brownian dynamics (BD) simulations. For the CG simulations the Ermak-McCammon algorithm is often used to solve the underlying Langevin equation. The algorithm is an extension of the Euler-Maruyama integrator to include translation and rotation in three dimensions. This algorithm only correctly reproduces the equilibrium probability for short time-steps and the error depends linearly on the time-step. It has been shown that Monte Carlo based algorithms can produce BD for translational dynamics, when appropriately parametrized. The advantage of Monte Carlo based algorithm is that they will reproduce the correct equilibrium distribution independent of the chosen time-step. This in return allows choosing larger time-steps in simulations. The aim of this thesis is to develop novel´methods to accurately determine the rotational diffusion coefficient from simulations and extend existing Monte Carlo algorithms to include rotational dynamics.
The first project addresses the question of how to accurately determine the rotational diffusion coefficients from simulations. We develop a quaternion based method to calculate the rotational diffusion tensor from simulations and a theory for the effects of periodic boundary conditions (PBC) on the rotational diffusion coefficient in simulations.
Our method for calculating rotational diffusion coefficients is based on the quaternion covariances from Favro for a freely rotating rigid molecule. The covariances as formulated by Favro are only valid in the principal coordinate system (PCS) of the rotation diffusion tensor. The covariances can be generalized for an arbitrary reference coordinate system (RCS), i.e., a simulation, given the principle axes of the rotational diffusion tensor in the RCS. We show that no prior knowledge of the diffusion tensor and its principal axes is required to calculate the generalized covariances from simulations using common root-mean-square distance (RMSD) procedures. We develop two methods to fit the covariances calculated from simulations to our generalized equations to fit the rotational diffusion tensor. In the first method we minimize the sum of the squared error deviations between model and simulation data. For this six dimensional optimization we use a simulated annealing algorithm. Alternatively the rotational diffusion tensor can also be determined from a eigenvalue decomposition of covariance after integration. To minimize the effects of sampling noise in the integration we first apply a Laplace-transformation to smooth the covariances at large times. For ideal sampling the resulting rotational diffusion coefficient should be independent of the value of the Laplace variable. In practice, however, the best results are achieved using a value close to the inverse autocorrelation time of the rotational motion.
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The Arctic Svalbard Archipelago hosts the world’s northernmost cold-water ‘carbonate factories’ thriving here despite of presumably unfavourable environmental conditions and extreme seasonality. Two contrasting sites of intense biogenic carbonate production, the rhodolith beds in Mosselbukta in the north of the archipelago and the barnacle-mollusc dominated carbonate sediments accumulating in the strong hydrodynamic regime of the Bjørnøy-Banken south of Spitsbergen, were the targets of the RV Maria S. Merian cruise 55 in June 2016. By integrating data from physical oceanography, marine biology, and marine geology, the present contribution characterises the environmental setting and biosedimentary dynamics of these two polar carbonate factories. Repetitive CTD profiling in concert with autonomous temperature/salinity loggers on a long-term settlement platform identified spatiotemporal patterns in the involved Atlantic and Polar water masses, whereas short-term deployments of a lander revealed fluctuations of environmental variables in the rhodolith beds in Mosselbukta and at same depth (46 m) at Bjørnøy-Banken. At both sites, dissolved inorganic nutrients in the water column were found depleted (except for elevated ammonium concentrations) and show an overall increase in concentration and N:P ratios toward deeper waters. This indicates that a recycling system was fuelling primary production after the phytoplankton spring bloom at the time of sampling in June 2016. Accordingly, oxygen levels were found elevated and carbon dioxide concentrations (pCO2) markedly reduced, on average only half the expected equilibrium values. Backed up by seawater stable carbon and oxygen isotope signatures, this is interpreted as an effect of limited air-sea gas exchange during seasonal ice cover in combination with a boost in community photosynthesis during the spring phytoplankton bloom. The observed trends are enhanced by the onset of rhodophyte photosynthesis in the rhodolith beds during the polar day upon retreat of sea-ice. Potential adverse effects of ocean acidification on the local calcifier community are thus predicted to be seasonally buffered by the marked drop in pCO2 during the phase of sea-ice cover and spring phyto-plankton bloom, but this effect will diminish should the seasonal sea-ice formation continue to decline. Among the 25 macrobenthos taxa identified from images captured by the lander’s camera system, all but three species were calcifiers contributing to the carbonate production. Biodiversity was found to be much higher in Mosselbukta (21 taxa) compared to Bjørnøy-Banken (8 taxa), which is considered as a result of enhanced habitat diversity provided in the rhodolith beds by the bioengineering crustose alga Lithothamnion glaciale. Filter-feeding activity of selected key species did reveal group-specific but no common activity patterns. Biotic disturbance of the filtering activity was common, in contrast to abiotic factors, with hermit crabs representing the primary trigger. Motion tracking of rhodoliths revealed a high frequency of dislocation, triggered not by abiotic factors but by the activity of benthic invertebrates, in particular echinoids ploughing below or moving over the rhodoliths. The echinoid Strongylocentrotus sp. is the most abundant component of the associated fauna, thereby considerably contributing both to carbonate production and to grazing bioerosion. Together, these results portray a high degree of seasonal as well as short-term dynamics in environmental conditions that despite many similarities support distinctly different communities and biodiversity patterns in the calcifying macrobenthos at the two studied polar carbonate factories.