Mathematical Simulation of Electron Transport in the Primary Photosynthetic Processes.

Summarized results of investigation of regulation of electron transport and associated processes in the photosynthetic membrane using methods of mathematical and computer modeling carried out at the Department of Biophysics, Faculty of Biology, Lomonosov Moscow State University, are presented in this review. Detailed kinetic models of processes in the thylakoid membrane were developed using the apparatus of differential equations. Fitting of the model curves to the data of spectral measurements allowed us to estimate the values of parameters that were not determined directly in experiments. The probabilistic method of agent-based Monte Carlo modeling provides ample opportunities for studying dynamics of heterogeneous systems based on the rules for the behavior of individual elements of the system. Algorithms for simplified representation of Big Data make it possible to monitor changes in the photosynthetic apparatus in the course of culture growth in a photobioreactor and for the purpose of environmental monitoring. Brownian and molecular models describe movement and interaction of individual electron carrier proteins and make it possible to study electrostatic, hydrophobic, and other interactions leading to regulation of conformational changes in the reaction complexes. Direct multiparticle models explicitly simulate Brownian diffusion of the mobile protein carriers and their electrostatic interactions with multienzyme complexes both in solution and in heterogeneous interior of a biomembrane. The combined use of methods of kinetic and Brownian multiparticle and molecular modeling makes it possible to study the mechanisms of regulation of an integral system of electron transport processes in plants and algae at molecular and subcellular levels.

Molecular, Brownian, kinetic and stochastic models of the processes in photosynthetic membrane of green plants and microalgae.

The paper presents the results of recent work at the Department of Biophysics of the Biological Faculty, Lomonosov Moscow State University on the kinetic and multiparticle modeling of processes in the photosynthetic membrane. The detailed kinetic models and the rule-based kinetic Monte Carlo models allow to reproduce the fluorescence induction curves and redox transformations of the photoactive pigment P700 in the time range from 100 ns to dozens of seconds and make it possible to reveal the role of individual carriers in their formation for different types of photosynthetic organisms under different illumination regimes, in the presence of inhibitors, under stress conditions. The fitting of the model curves to the experimental data quantifies the reaction rate constants that cannot be directly measured experimentally, including the non-radiative thermal relaxation reactions. We use the direct multiparticle models to explicitly describe the interactions of mobile photosynthetic carrier proteins with multienzyme complexes both in solution and in the biomembrane interior. An analysis of these models reveals the role of diffusion and electrostatic factors in the regulation of electron transport, the influence of ionic strength and pH of the cellular environment on the rate of electron transport reactions between carrier proteins. To describe the conformational intramolecular processes of formation of the final complex, in which the actual electron transfer occurs, we use the methods of molecular dynamics. The results obtained using kinetic and molecular models supplement our knowledge of the mechanisms of organization of the photosynthetic electron transport processes at the cellular and molecular levels.

α-tubulin tail modifications regulate microtubule stability through selective effector recruitment, not changes in intrinsic polymer dynamics.

Microtubules are non-covalent polymers of αß-tubulin dimers. Posttranslational processing of the intrinsically disordered C-terminal α-tubulin tail produces detyrosinated and Δ2-tubulin. Although these are widely employed as proxies for stable cellular microtubules, their effect (and of the α-tail) on microtubule dynamics remains uncharacterized. Using recombinant, engineered human tubulins, we now find that neither detyrosinated nor Δ2-tubulin affect microtubule dynamics, while the α-tubulin tail is an inhibitor of microtubule growth. Consistent with the latter, molecular dynamics simulations show the α-tubulin tail transiently occluding the longitudinal microtubule polymerization interface. The marked differential in vivo stabilities of the modified microtubule subpopulations, therefore, must result exclusively from selective effector recruitment. We find that tyrosination quantitatively tunes CLIP-170 density at the growing plus end and that CLIP170 and EB1 synergize to selectively upregulate the dynamicity of tyrosinated microtubules. Modification-dependent recruitment of regulators thereby results in microtubule subpopulations with distinct dynamics, a tenet of the tubulin code hypothesis.

Mechanical properties of tubulin intra- and inter-dimer interfaces and their implications for microtubule dynamic instability.

Thirteen tubulin protofilaments, made of αß-tubulin heterodimers, interact laterally to produce cytoskeletal microtubules. Microtubules exhibit the striking property of dynamic instability, manifested in their intermittent growth and shrinkage at both ends. This behavior is key to many cellular processes, such as cell division, migration, maintenance of cell shape, etc. Although assembly and disassembly of microtubules is known to be linked to hydrolysis of a guanosine triphosphate molecule in the pocket of ß-tubulin, detailed mechanistic understanding of corresponding conformational changes is still lacking. Here we take advantage of the recent generation of in-microtubule structures of tubulin to examine the properties of protofilaments, which serve as important microtubule assembly and disassembly intermediates. We find that initially straight tubulin protofilaments, relax to similar non-radially curved and slightly twisted conformations. Our analysis further suggests that guanosine triphosphate hydrolysis primarily affects the flexibility and conformation of the inter-dimer interface, without a strong impact on the shape or flexibility of αß-heterodimer. Inter-dimer interfaces are significantly more flexible compared to intra-dimer interfaces. We argue that such a difference in flexibility could be key for distinct stability of the plus and minus microtubule ends. The higher flexibility of the inter-dimer interface may have implications for development of pulling force by curving tubulin protofilaments during microtubule disassembly, a process of major importance for chromosome motions in mitosis.

Comparative analysis of plastocyanin-cytochrome f complex formation in higher plants, green algae and cyanobacteria.

Mechanisms of the complex formation between plastocyanin and cytochrome f in higher plants (Spinacia oleracea and Brassica rapa), green microalgae Chlamydomonas reinhardtii and two species of cyanobacteria (Phormidium laminosum and Nostoc sp.) were investigated using combined Brownian and molecular dynamics simulations and hierarchical cluster analysis. In higher plants and green algae, electrostatic interactions force plastocyanin molecule close to the heme of cytochrome f. In the subsequent rotation of plastocyanin molecule around the point of electrostatic contact in the vicinity of cytochrome f, copper (Cu) atom approaches cytochrome heme forming a stable configuration where cytochrome f molecule behaves as a rather rigid body without conformational changes. In Nostoc plastocyanin molecule approaches cytochrome f in a different orientation (head-on) where the stabilization of the plastocyanin-cytochrome f complex is accompanied by the conformational changes of the G188E189D190 loop that stabilizes the whole complex. In cyanobacterium P. laminosum, electrostatic preorientation of the approaching molecules was not detected, thus indicating that random motions rather than long-range electrostatic interactions are responsible for the proper mutual orientation. We demonstrated that despite the structural similarity of the investigated electron transport proteins in different photosynthetic organisms, the complexity of molecular mechanisms of the complex formation increases in the following sequence: non-heterocystous cyanobacteria - heterocystous cyanobacteria - green algae - flowering plants.