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MS SPIDOC is a novel sample delivery system designed for single (isolated) particle imaging at X-ray Free-Electron Lasers that is adaptable towards most large-scale facility beamlines. Biological samples can range from small proteins to MDa particles. Following nano-electrospray ionization, ionic samples can be m/z-filtered and structurally separated before being oriented at the interaction zone. Here, we present the simulation package developed alongside this prototype. The first part describes how the front-to-end ion trajectory simulations have been conducted. Highlighted is a quadrant lens; a simple but efficient device that steers the ion beam within the vicinity of the strong DC orientation field in the interaction zone to ensure spatial overlap with the X-rays. The second part focuses on protein orientation and discusses its potential with respect to diffractive imaging methods. Last, coherent diffractive imaging of prototypical T = 1 and T = 3 norovirus capsids is shown. We use realistic experimental parameters from the SPB/SFX instrument at the European XFEL to demonstrate that low-resolution diffractive imaging data (q < 0.3 nm⁻¹) can be collected with only a few X-ray pulses. Such low-resolution data are sufficient to distinguish between both symmetries of the capsids, allowing to probe low abundant species in a beam if MS SPIDOC is used as sample delivery.

This booklet was written to give an idea about how errors propagate in physical measurements. For this purpose we will first discuss what a measurement of a physical quantity means and where errors come from. Then we will show how to write down the result in a proper way, using a scientific notation. We then discuss how to compute errors in different cases, in direct and indirect measurements. Finally, we give an example that explicitly shows how to use the methods.

The booklet can be useful for students who do laboratory work in physics. It might be used as a reference source for data reduction and propagation of errors.

Proteins can, without any exaggeration, be called the "building blocks of life". Their physical properties depend not only on the chemical structure but also on their geometric shape. In this thesis, I investigate protein geometry using several different methods.

We start with a coarse-graining model to study the general behavior of polymers. For this reason, we utilize an effective Hamiltonian that can describe the thermodynamic properties of polymer chains and reproduce secondary and tertiary structures. To investigate this model, I perform classical Monte Carlo simulations using my software package.

Another problem we address in this thesis is how to distinguish thermodynamic phases of proteins. The conventional definition of phases of polymer systems uses scaling laws. However, this method needs the chain's length to be varied, which is impossible to do with heteropolymers where the number of sites is one of the system's characteristics. We will apply renormalization group (RG) theory ideas to overcome this difficulty. We present a scaling procedure and an observable through which RG flow can define a certain polymer chain's phase.

Another part of the thesis is dedicated to the method of molecular dynamics. Our focus is on a novel experimental technique called Single Particle Imaging (SPI). The spatial orientation of the sample in this method is arbitrary. Scientists proposed to use a strong electric field to fix the orientation since most biological molecules have a non-zero dipole moment. Motivated by this, we investigate the influence of a strong electric field's ramping on the orientation of protein ubiquitin. For the same question of SPI and using the same protein, we study the reproducibility of unfolding it in a strong electric field. With the help of a new graph representation, I show different unfolding pathways as a function of the electric field's value and compare them with thermal and mechanical unfolding. I show that the RG flow observable can also detect the different ubiquitin unfolding pathways more simply.

The study described in this thesis has two types of results. One is a very concrete type, which can be utilized right away in the SPI experiments, like MS SPIDOC on the European XFEL. The other type of results are more theoretical and opens up a new field for further research. However, all of them contribute to protein science, an area vital for humanity's ability to protect us from threats such as the current COVID-19 pandemic.

I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules. There are two crucial differences from other smoothing methods that make the algorithm unique: data compression and recursive implementation. One of the simplest forms of the method that is described in this article has only one free parameter - the number of iterative steps. This means that hardware implementation should be relatively easy because each loop is simple and strictly defined. The method could be beneficially applied to pattern recognition and data compression in future studies.

The emergence of ultra-fast X-ray free-electron lasers opens the possibility of imaging single molecules in the gas phase at atomic resolution. The main disadvantage of this imaging technique is the unknown orientation of the sample exposed to the X-ray beam, making the three-dimensional reconstruction not trivial. The induced orientation of molecules prior to X-ray exposure can be highly beneficial, as it significantly reduces the number of collected diffraction patterns whilst improving the quality of the reconstructed structure. We present here the possibility of protein orientation using a time-dependent external electric field. We used ab initio simulations on Trp-cage protein to provide a qualitative estimation of the field strength required to break protein bonds, with 45 V/nm as a breaking point value. Furthermore, we simulated, in a classical molecular dynamics approach, the orientation of ubiquitin protein by exposing it to different time-dependent electric fields. The protein structure was preserved for all samples at the moment orientation was achieved, which we denote `orientation before destruction'. Moreover, we find that the minimal field strength required to induce orientation within ten ns of electric field exposure was of the order of 0.5 V/nm. Our results help explain the process of field orientation of proteins and can support the design of instruments for protein orientation.

Proteins often have nonzero electric dipole moments, making them interact with external electric fields and offering a means for controlling their orientation. One application that is known to benefit from orientation control is single-particle imaging with x-ray free-electron lasers, in which diffraction is recorded from proteins in the gas phase to determine their structures. To this point, theoretical investigations into this phenomenon have assumed that the field experienced by the proteins is constant or a perfect step function, whereas any real-world pulse will be smooth. Here, we explore the possibility of orienting gas-phase proteins using time-dependent electric fields. We performed ab initio simulations to estimate the field strength required to break protein bonds, with 45 V/nm as a breaking point value. We then simulated ubiquitin in time-dependent electric fields using classical molecular dynamics. The minimal field strength required for orientation within 10 ns was on the order of 0.5 V/nm. Although high fields can be destructive for the structure, the structures in our simulations were preserved until orientation was achieved regardless of field strength, a principle we denote "orientation before destruction."

The dynamics of proteins are crucial for their function. However, commonly used techniques for studying protein structures are limited in monitoring time-resolved dynamics at high resolution. Combining electric fields with existing techniques to study gas phase proteins, such as Single Particle Imaging using Free-electron Lasers and gas phase Small Angle X-ray Scattering, has the potential to open up a new era in time-resolved studies of gas phase protein dynamics. Using molecular dynamics simulations, we identify well-defined unfolding pathways of a protein, induced by experimentally achievable external electric fields. Our simulations show that strong electric fields in conjunction with short pulsed X-ray sources such as Free-electron Lasers can be a new path for imaging dynamics of gas-phase proteins at high spatial and temporal resolution.

Chiral heteropolymers such as large globular proteins can simultaneously support multiple length scales. The interplay between the different scales brings about conformational diversity, determines the phase properties of the polymer chain, and governs the structure of the energy landscape. Most importantly, multiple scales produce complex dynamics that enable proteins to sustain live matter. However, at the moment there is incomplete understanding of how to identify and distinguish the various scales that determine the structure and dynamics of a complex protein. Here we address this impending problem. We develop a methodology with the potential to systematically identify different length scales, in the general case of a linear polymer chain. For this we introduce and analyze the properties of an order parameter that can both reveal the presence of different length scales and can also probe the phase structure. We first develop our concepts in the case of chiral homopolymers. We introduce a variant of Kadanoff's block-spin transformation to coarse grain piecewise linear chains, such as the C alpha backbone of a protein. We derive analytically, and then verify numerically, a number of properties that the order parameter can display, in the case of a chiral polymer chain. In particular, we propose that in the case of a chiral heteropolymer the order parameter can reveal traits of several different phases, contingent on the length scale at which it is scrutinized. We confirm that this is the case with crystallographic protein structures in the Protein Data Bank. Thus our results suggest relations between the scales, the phases, and the complexity of folding pathways.

Nuclear magnetic resonance spectroscopy is used routinely for studying the three-dimensional structures and dynamics of proteins. Structure determination is usually done by adding restraints based upon NMR data to a classical energy function and performing restrained molecular simulations. Here we report on the implementation of a script to extract NMR restraints from a NMR-STAR file and export it to the GROMACS software. With this package, it is possible to model distance restraints, dihedral restraints, and orientation restraints. The output from the script is validated by performing simulations with and without restraints, including the ab initio refinement of one peptide.