This thesis introduces methods to efficiently generate and analyze time series data of many-body systems. While we have a strong focus on biomolecular processes, the presented methods can also be applied more generally. Due to limitations of microscope resolution in both space and time, biomolecular processes are especially hard to observe experimentally. Computer models offer an opportunity to work around these limitations. However, as these models are bound by computational effort, careful selection of the model as well as its efficient implementation play a fundamental role in their successful sampling and/or estimation.
Especially for high levels of resolution, computer simulations can produce vast amounts of high-dimensional data and in general it is not straightforward to visualize, let alone to identify the relevant features and processes. To this end, we cover tools for projecting time series data onto important processes, finding over time geometrically stable features in observable space, and identifying governing dynamics. We introduce the novel software library deeptime with two main goals: (1) making methods which were developed in different communities (such as molecular dynamics and fluid dynamics) accessible to a broad user base by implementing them in a general-purpose way, and (2) providing an easy to install, extend, and maintain library by employing a high degree of modularity and introducing as few hard dependencies as possible. We demonstrate and compare the capabilities of the provided methods based on numerical examples.
Subsequently, the particle-based reaction-diffusion simulation software package ReaDDy2 is introduced. It can simulate dynamics which are more complicated than what is usually analyzed with the methods available in deeptime. It is a significantly more efficient, feature-rich, flexible, and user-friendly version of its predecessor ReaDDy. As such, it enables---at the simulation model's resolution---the possibility to study larger systems and to cover longer timescales. In particular, ReaDDy2 is capable of modeling complex processes featuring particle crowding, space exclusion, association and dissociation events, dynamic formation and dissolution of particle geometries on a mesoscopic scale. The validity of the ReaDDy2 model is asserted by several numerical studies which are compared to analytically obtained results, simulations from other packages, or literature data.
Finally, we present reactive SINDy, a method that can detect reaction networks from concentration curves of chemical species. It extends the SINDy method---contained in deeptime---by introducing coupling terms over a system of ordinary differential equations in an ansatz reaction space. As such, it transforms an ordinary linear regression problem to a linear tensor regression. The method employs a sparsity-promoting regularization which leads to especially simple and interpretable models. We show in biologically motivated example systems that the method is indeed capable of detecting the correct underlying reaction dynamics and that the sparsity regularization plays a key role in pruning otherwise spuriously detected reactions.
