DNA block copolymers – from micelles to machines

DNA block copolymer, a new class of hybrid material composed of a synthetic polymer and an oligodeoxynucleotide segment, owns unique properties which can not be achieved by only one of the two polymers. Among amphiphilic DNA block copolymers, DNA-b-polypropylene oxide (PPO) was chosen as a model system, because PPO is biocompatible and has a Tg < 0 °C. Both properties might be essential for future applications in living systems. During my PhD study, I focused on the properties and the structures of DNA-b-PPO molecules. First, DNA-b-PPO micelles were studied by scanning force microscopy (SFM) and fluorescence correlation spectroscopy (FCS). In order to control the size of micelles without re-synthesis, micelles were incubated with template-independent DNA polymerase TdT and deoxynucleotide triphosphates in reaction buffer solution. By carrying out ex-situ experiments, the growth of micelles was visualized by imaging in liquid with AFM. Complementary measurements with FCS and polyacrylamide gel electrophoresis (PAGE) confirmed the increase in size. Furthermore, the growing process was studied with AFM in-situ at 37 °C. Hereby the growth of individual micelles could be observed. In contrast to ex-situ reactions, the growth of micelles adsorbed on mica surface for in-situ experiments terminated about one hour after the reaction was initiated. Two reasons were identified for the termination: (i) block of catalytic sites by interaction with the substrate and (ii) reduced exchange of molecules between micelles and the liquid environment. In addition, a geometrical model for AFM imaging was developed which allowed deriving the average number of mononucleotides added to DNA-b-PPO molecules in dependence on the enzymatic reaction time (chapter 3). Second, a prototype of a macroscopic DNA machine made of DNA-b-PPO was investigated. As DNA-b-PPO molecules were amphiphilic, they could form a monolayer at the air-water interface. Using a Langmuir film balance, the energy released owing to DNA hybridization was converted into macroscopic movements of the barriers in the Langmuir trough. A specially adapted Langmuir trough was build to exchange the subphase without changing the water level significantly. Upon exchanging the subphase with complementary DNA containing buffer solution, an increase of lateral pressure was observed which could be attributed to hybridization of single stranded DNA-b-PPO. The pressure versus area/molecule isotherms were recorded before and after hybridization. I also carried out a series of control experiments, in order to identify the best conditions of realizing a DNA machine with DNA-b-PPO. To relate the lateral pressure with molecular structures, Langmuir Blodgett (LB) films were transferred to highly ordered pyrolytic graphite (HOPG) and mica substrates at different pressures. These films were then investigated with AFM (chapter 4). At last, this thesis includes studies of DNA and DNA block copolymer assemblies with AFM, which were performed in cooperation with different group of the Sonderforschungsbereich 625 “From Single Molecules to Nanoscopically Structured Materials”. AFM was proven to be an important method to confirm the formation of multiblock copolymers and DNA networks (chapter 5).

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Convergence results for stochastic particle systems with social interaction

We consider stochastic individual-based models for social behaviour of groups of animals. In these models the trajectory of each animal is given by a stochastic differential equation with interaction. The social interaction is contained in the drift term of the SDE. We consider a global aggregation force and a short-range repulsion force. The repulsion range and strength gets rescaled with the number of animals N. We show that for N tending to infinity stochastic fluctuations disappear and a smoothed version of the empirical process converges uniformly towards the solution of a nonlinear, nonlocal partial differential equation of advection-reaction-diffusion type. The rescaling of the repulsion in the individual-based model implies that the corresponding term in the limit equation is local while the aggregation term is non-local. Moreover, we discuss the effect of a predator on the system and derive an analogous convergence result. The predator acts as an repulsive force. Different laws of motion for the predator are considered.

Stochastic foundations of dynamic trade and labor market models

This dissertation consists of three self-contained papers that are related to two main topics. In particular, the first and third studies focus on labor market modeling, whereas the second essay presents a dynamic international trade setup.rnrnIn Chapter "Expenses on Labor Market Reforms during Transitional Dynamics", we investigate the arising costs of a potential labor market reform from a government point of view. To analyze various effects of unemployment benefits system changes, this chapter develops a dynamic model with heterogeneous employed and unemployed workers.rn rnIn Chapter "Endogenous Markup Distributions", we study how markup distributions adjust when a closed economy opens up. In order to perform this analysis, we first present a closed-economy general-equilibrium industry dynamics model, where firms enter and exit markets, and then extend our analysis to the open-economy case.rn rnIn Chapter "Unemployment in the OECD - Pure Chance or Institutions?", we examine effects of aggregate shocks on the distribution of the unemployment rates in OECD member countries.rn rnIn all three chapters we model systems that behave randomly and operate on stochastic processes. We therefore exploit stochastic calculus that establishes clear methodological links between the chapters.