It has been known since the 1930’s that protons and neutrons, collectively called as nucleons, are not “point-like” elementary particles, but rather have a substructure. Today, we know from Quantum Chromodynamics (QCD) that nucleons are made from quarks and gluons, with gluons being the elementary force carriers for strong interactions. Quarks and gluons are collectively called as partons. The substructure of the nucleons can be described in terms of parton correlation functions such as Form Factors, (1D) Parton Distribution Functions (PDFs) and their 3D generalizations in terms of Transverse Momentum-dependent parton Distributions (TMDs) and Generalized Parton Distributions (GPDs). All these functions can be derived from the even more general Generalized Transverse Momentum-dependent Distributions (GTMDs). This dissertation promises to provide an insight into all these functions from the point of view of their accessibility in experiments, from model calculations, and from their direct calculation within lattice formulations of QCD. In the first part of this dissertation, we identify physical processes to access GTMDs. By considering the exclusive double Drell-Yan process, we demonstrate, for the very first time, that quark GTMDs can be measured. We also show that exclusive double-quarkonium production in nucleon-nucleon collisions is a direct probe of gluon GTMDs. In the second part of this dissertation, we shift our focus to the “parton quasi-distributions”. Over the last few decades, lattice QCD extraction of the full x-dependence of the parton distributions has always been prohibited by the explicit time-dependence of the correlation functions. In 2013, there was a path-breaking proposal by X. Ji to calculate instead parton quasi-distributions (quasi-PDFs). The procedure of “matching” is a crucial ingredient in the lattice QCD extraction of parton distributions from the quasi-PDF approach. We address the matching for the twist-3 PDFs gT (x), e(x), and hL(x) for the very first time. We pay special attention to the challenges involved in the calculations due to the presence of singular zero-mode contributions. We also present the first-ever lattice QCD results for gT (x) and hL(x) and we discuss the impact of these results on the phenomenology. Next, we explore the general features of quasi-GPDs and quasi-PDFs in diquark spectator models. Furthermore, we address the Burkhardt-Cottingham-type sum rules for the relevant light-cone PDFs and quasi-PDFs in a model-independent manner and also check them explicitly in perturbative model calculations. The last part of this dissertation focuses on the extraction g1T (x,~k2⊥) TMD for the very first time from experimental data using Monte Carlo techniques. This dissertation therefore unravels different aspects of the distribution functions from varied perspectives.

The oxygen that we breathe and food that we eat are products of the natural photosynthesis. Molecular oxygen is crucial for life on Earth owing to its role in the glycolysis and citric acid pathways that yield in aerobic organisms the energy-rich ATP molecules. Photosynthetic water oxidation, which produces molecular oxygen from water and sunlight, is performed by higher plants, algae and cyanobacteria. Within the molecular structure of a plant cell, photosynthesis is performed by a specific intracellular organelle – the chloroplast. Chloroplasts contain a membrane system, the thylakoid membrane, which comprises lipids, quinones and a very high content of protein complexes. The unique photosynthetic oxidation of water into molecular oxygen, protons and electrons is performed by the Mn4CaO5 cluster in photosystem II (PSII) complex. Understanding the mechanism of water oxidation by Mn4CaO5 cluster is one of the great challenges in science nowadays. When the mechanism of this process is fully understood, artificial photosynthetic systems can be designed that have high efficiencies of solar energy conversion by imitating the fundamental principle of natural system. These systems can be used in future for generation of fuels from sunlight.   In this thesis, the efficiency of water-splitting process in natural photosynthetic preparations was studied by measuring the flash-induced oxygen evolution pattern (FIOP). The overall aim is to achieve a deeper understanding of oxygen evolving mechanism of the Mn4O5Ca cluster via developing a complete kinetic and energetic model of the light-induced redox reactions within PSII complex. On the way to reach this goal, the hydrogen peroxide that is electrochemically generated on surface of Pt-cathode was discovered. The chemical effect of electrochemically produced H2O2 that can interfere in the oxygen evolution pathway or change the observed FIOP data was demonstrated. Therefore, in order to record the clean FIOP data that are further characterized by global fitting program (GFP), H2O2 has to be abolished by catalase addition and by purging the flow buffer of the Joliot-type electrode with nitrogen gas.      After FIOPs free of H2O2-induced effects were achieved, these clean data were then applied to a global fitting approach (GFP) in order to (i) result a comprehensive figure of all S-state decays whose kinetic rates were simultaneously analyzed in a high reliability and consistency, (ii) the dependence of miss parameter on S-state transitions and the oxidation state of tyrosine D (YD) can be tested, (iii) how dependent of all S-state re-combinations (to S1 state) on the various pH/pD values can be also determined in case of using Cyanidioschyzon merolae (C. merolae) thylakoids. Our data support previous suggestions that the S0 → S1 and S1 → S2 transitions involve low or no misses, while high misses occur in the S2 → S3 transition or the S3 → S0 transition. Moreover, the appearance of very slow S2 decay was clearly observed by using the GFP analysis, while there are no evidences of very slow S3 decay were recorded under all circumstances. The unknown electron donor for the very slow S2 decay which can be one of the substances of PSII-protective branch (i.e. cytochrome b559, carotenoid or ChlZ) will be determined in further researches.