Requirements on models and models of active transport of ions in biomembranes

From leaves to roots: Biophysical models of transport of substances in plants

The transport processes of substances in various plant tissues are extremely diverse. However, models aimed at elucidating the mechanisms of such processes are almost absent in the literature. A unified view of all these transport processes is necessary, considering the laws of statistical physics and thermodynamics. A model of active ion transport was constructed based on the laws of statistical physics. Using this model, we traced the entire pathway of substances and energy in a plant. The pathway included aspects of the production of energy in the process of photosynthesis, consumption of energy to obtain nutrients from the soil, transport of such substances to the main organelles of all types of plant cells, the rise of water with dissolved substances along the trunk to the leaves, and the evaporation of water, accompanied by a change in the percentage of isotopes caused by different rates of evaporation. Models of ion transport in the chloroplasts and mitochondria of plant cells have been constructed. A generalized model comprising plant cells and their vacuoles was analyzed. A model of the transport of substances in the roots of plants was also developed. Based on this model, the problem of transport of substances in tall trees has been considered. The calculated concentrations of ions in the vacuoles of cells and resting potentials agreed well with the experimental data.

Active ion transport as the basis for water movement in plants

A model of active ion transport in plant root hair cells was built and can be used to independently calculate the concentration of ions inside plant cells and the resting potential on its membrane. Using the model, the maximum height to which water can be transported in plants was calculated.

Intra- and intercellular transport of substances: Models and mechanisms

Non-equilibrium-statistical models of intracellular transport are built. The most significant features of these models are microscopic reversibility and the explicit considerations of the driving forces of the process - the ATP-ADP chemical potential difference. In this paper, water transport using contractile vacuoles, the transport and assembly of microtubules and microfilaments, the protein distribution within a cell, the transport of neurotransmitters from the synaptic cleft and the transport of substances between cells using plasmodesmata are discussed. Endocytosis and phagocytosis models are considered, and transport tasks and information transfer mechanisms inside the cell are explored. Based on an analysis of chloroplast movement, it was concluded that they have a complicated method of influencing each other in the course of their movements. The role of quantum effects in sorting and control transport mechanisms is also discussed. It is likely that quantum effects play a large role in these processes, otherwise reliable molecular recognition would be impossible, which would lead to very low intracellular transport efficiency.

Protocells and LUCA: Transport of substances from first physicochemical principles

Models of the transport of substances in protocells are considered from first physicochemical principles. Functional similarities and differences in the transport systems of archaea, cyanobacteria, E. coli, and diatoms have been analyzed. Based on the selection of the most important transport systems, a model of transport of substances through the membrane of the last universal common ancestor, LUCA, was constructed. Models of isotope separation in protocells were considered. Based on the proposed models, the difference in isotope concentrations in rocks can be predicted, which can serve as an indicator of the presence of life in the early stages of evolution. Mechanisms of energy conversion for the simplest forms of directed motion in protocells are considered. A special stage in the evolution of protocells is proposed - the minimal mobile cell.

Nontrivial quantum and quantum-like effects in biosystems: Unsolved questions and paradoxes

Non-trivial quantum effects in biological systems are analyzed. Some unresolved issues and paradoxes related to quantum effects (Levinthal's paradox, the paradox of speed, and mechanisms of evolution) are addressed. It is concluded that the existence of non-trivial quantum effects is necessary for the functioning of living systems. In particular, it is demonstrated that classical mechanics cannot explain the stable work of the cell and any over-cell structures. The need for quantum effects is generated also by combinatorial problems of evolution. Their solution requires a priori information about the states of the evolving system, but within the framework of the classical theory it is not possible to explain mechanisms of its storage consistently. We also present essentials of so called quantum-like paradigm: sufficiently complex bio-systems process information by violating the laws of classical probability and information theory. Therefore the mathematical apparatus of quantum theory may have fruitful applications to describe behavior of bio-systems: from cells to brains, ecosystems and social systems. In quantum-like information biology it is not presumed that quantum information bio-processing is resulted from quantum physical processes in living organisms. Special experiments to test the role of quantum mechanics in living systems are suggested. This requires a detailed study of living systems on the level of individual atoms and molecules. Such monitoring of living systems in vivo can allow the identification of the real potentials of interaction between biologically important molecules.

Origin of the directed movement of protocells in the early stages of the evolution of life

The origin of the directed motion of protocells during the early stages of evolution was discussed. The expenditures for movement, space orientation, and reception of information about the environment were taken into consideration, and it was shown that directed movement is evolutionarily advantageous in the following cases: when opposite gradients of different resources (for example, matter and energy) are great enough and when there is a rapid change in environmental parameters. It was also shown that the advantage of directed movement strategies depends greatly on how information about the environment is obtained by a protocell.

Algorithms for optimization of the transport system in living and artificial cells

An optimization of the transport system in a cell has been considered from the viewpoint of the operations research. Algorithms for an optimization of the transport system of a cell in terms of both the efficiency and a weak sensitivity of a cell to environmental changes have been proposed. The switching of various systems of transport is considered as the mechanism of weak sensitivity of a cell to changes in environment. The use of the algorithms for an optimization of a cardiac cell has been considered by way of example. We received theoretically for a cell of a cardiac muscle that at the increase of potassium concentration in the environment switching of transport systems for this ion takes place. This conclusion qualitatively coincides with experiments. The problem of synthesizing an optimal system in an artificial cell has been stated.

Analytical model of ion transport and conversion of light energy in chloroplasts

An analytical model, which describes the stationary transformation of light energy to the energy of pigment electronic excitation, has been constructed. A proton pump of the thylakoid membrane has been considered as a two-level conformon. The difference between the energies of the excited and ground states of both the pigment and the protein complex is assumed to be the energy of an absorbed photon. It has been found how the concentration of ions in a lumen and the potential across the thylakoid membrane depend on the concentration of ions in the stroma and the brightness temperature of absorbed radiation. Conditions for the maximum efficiency of the photosynthesis process have been analyzed. This model has been used to determine the electric potential (phi approximately 6.7mV) at the chloroplast thylakoid membrane. The calculated value of the electric potential is in good agreement with the experimental data. A limitation on the stoichiometric coefficient of the proton transport through ATP-synthase, m>3, has been found theoretically.

Model of active transport of ions through diatom cell biomembrane

A model of the active transport of ions in the Cascinodiscus wailesii diatom cell is constructed taking into account the transport of H(+), Na(+), K(+), Ca(+2), NO(3)(-), Cl(-), and NH(4)(+) ions. This model allows calculating intracellular concentrations of basic ions and the biomembrane resting potential. A hierarchical algorithm "one ion--one transport system" is used in the model. The dependence of the resting potential on the extracellular concentration of potassium is plotted in terms of the model. The calculated values are in good agreement with the corresponding experimental data.

Early stages of the evolution of life: a cybernetic approach

Early stages of the evolution of life are considered in terms of control theory. A model is proposed for the transport of substances in a protocell possessing the property of robustness with regard to changes in the environmental concentration of a substance.

Model of active transport of ions in cardiac cell

A model of the active transport of ions in a cardiac muscle cell, which takes into account the active transport of Na(+), K(+), Ca(2+), Mg(2+), HCO(3)(-) and Cl(-) ions, has been constructed. The model allows independent calculations of the resting potential at the biomembrane and concentrations of basic ions (sodium, potassium, chlorine, magnesium and calcium) in a cell. For the analysis of transport processes in cardiac cell hierarchical algorithm "one ion-one transport system" was offered. The dependence of the resting potential on concentrations of the ions outside a cell has been established. It was shown, that ions of calcium and magnesium, despite their rather small concentration, play an essential role in maintenance of resting potential in cardiac cell. The calculated internal concentrations of ions are in good agreement with the corresponding experimental values.

Nonequilibrium statistical model of active transport of ions and ATP production in mitochondria

A model of the active transport of ions through internal membranes of mitochondria is proposed. If concentrations of ions in a cell are known, this model allows calculating concentrations of all main ions (H(+), Ca(+2), K(+), Mg(2+), Na(+), Cl(-)) in the mitochondrion matrix and the resting potential across the membrane. The theoretical values satisfactorily agree with available experimental data on the concentrations and the potentials, including different operating regimes of the adenosine triphosphate (ATP) synthetase (the main regime, short circuiting or ATP synthetase blocking). The active transport of Mg(2+) ions in exchange for protons was assumed. In accordance with the model, the ATP synthetase operation is possible only if the stoichiometric coefficient of protons is 3.

Models of active transport of neurotransmitters in synaptic vesicles

Models of the active transport of neurotransmitters in synaptic vesicles were constructed. The models were used to determine the resting potential at membranes of synaptic vesicles: 40mV (monoamines and acetylcholine) and -40mV (glutamate). The potential at the membrane of a synaptic vesicle was almost absent for the transport of GABA and glycine. The neurotransmitter concentration of a cell was 0.1-18mM at the concentration of neurotransmitters in a vesicle equal to 0.5M. This result is in qualitative agreement with the relevant experimental data.

Model of active transport of ions in biomembranes based on ATP-dependent change of height of diffusion barriers to ions

A closed model of the active transport was constructed taking into account ATP-dependent opening and closing of barriers to ions and the relationship between the membrane potential and the work of ionic pumps under the condition of electroneutrality inside the cell. The internal consistency of the model was verified by the fulfillment of Onsager's reciprocity relation. It was demonstrated that at the limit of large energy barriers the operation of the system of the active transport is equivalent to the "turning segment" model, which was proposed by the authors earlier. Values of the resting potential and the intracellular concentration of ions were obtained for different types of cells. These results were in qualitative agreement with relevant experimental data.