In this thesis, phylogenomic and comparative structural analyses of several widespread energy converting enzymes were performed. The focus was on the major subfamilies of the enzymes that process nucleoside triphosphates (ATP and GTP) and on some key enzymes of the electron transfer chains. First, we analyzed the P-loop GTPases, RadA/RecA recombinases, chaperone GroEL, branched-chain α-ketoacid dehydrogenase kinases, chaperone Hsc70, actins, and membrane pyrophosphatases. In the each inspected family we could identify (1) members which were potassium-dependent and/or contained K+ ions in the active site, and (2) potassium-independent enzymes with lysine or arginine residues as catalytic groups that occupy the positions of potassium ions in the homologous, K+-dependent enzymes. Based on the results of our analyses, we suggest that the appearance of the K+-binding sites could precede in evolution the recruitment of positively charged residues (lysine or arginine "fingers") with the latter providing more possibilities to control the enzyme reactions. Second, we have described the distinctive features of a phylogenetically separated subfamily of rotary membrane ATPases which we named N-ATPases. The N-ATPases have a specific operon organization with two additional subunits, absent in other rotary ATPases, and a complete set of Na+-binding ligands in the membrane c-subunits. We made a prediction, which was later confirmed, that these enzymes are capable of Na+ translocation across the membrane and may confer salt tolerance on marine prokaryotes. Third, phylogenomic analysis of the cytochrome bc complexes suggests that these enzyme complexes initially emerged within the bacteria and were then transferred to archaea via lateral gene transfer on several independent occasions. Our analysis indicates that the ancestral form of the cytochrome bc complex was a b6f-type complex; the fusion of the cytochrome b6 and the subunit IV to a "long" cytochrome b of the cytochrome bc1 complexes could have happened in different lineages independently. Fourth, our phylogenomic and comparative structural analyses of the cytochrome bc1 complex and of cytochrome c allowed us to trace how these enzymes became involved in triggering of apoptosis in Metazoa. We could trace the emergence of a specific cardiolipin-binding site within the cytochrome bc complex and the evolution of structural traits that account for the involvement of the cytochrome c as a trigger of apoptosis in vertebrates.

Cellular automata (CA) are fully discrete dynamical systems. Space is represented by a regular lattice while time proceeds in finite steps. Each cell of the lattice is assigned a state, chosen from a finite set of "values". The states of the cells are updated synchronously according to a local interaction rule, whereby each cell obeys the same rule. Formal definitions of deterministic, probabilistic and lattice-gas CA are presented. With the so-called mean-field approximation any CA model can be transformed into a deterministic model with continuous state space. CA rules, which characterise movement, single-component growth and many-component interactions are designed and explored. It is demonstrated that lattice-gas CA offer a suitable tool for modelling such processes and for analysing them by means of the corresponding mean-field approximation. In particular two types of many-component interactions in lattice-gas CA models are introduced and studied. The first CA captures in abstract form the essential ideas of activator-inhibitor interactions of biological systems. Despite of the automaton´s simplicity, self-organised formation of stationary spatial patterns emerging from a randomly perturbed uniform state is observed (Turing pattern). In the second CA, rules are designed to mimick the dynamics of excitable systems. Spatial patterns produced by this automaton are the self-organised formation of spiral waves and target patterns. Properties of both pattern formation processes can be well captured by a linear stability analysis of the corresponding nonlinear mean-field (Boltzmann) equations.