Unsolved morphogenesis problems and the hidden order.

In this work, the morphogenesis mechanisms are considered from the complexity perspective. It is shown that both morphogenesis and the functioning of organs should be unstable in the case of short-range interaction potentials. The repeatability of forms during evolution is a strong argument for its directionality. The formation of organs during evolution can occur only in the presence of a priori information about the structure of such an organ. The focus of the discussion is not merely on constraining potential possibilities but on the concept of directed evolution itself. A morphogenesis model was constructed based on nontrivial quantum effects. These interaction effects between biologically important molecules ensure the accurate synthesis of cells, tissues, and organs.

Aging and group selection: New arguments in favor of partially directed evolution.

In this study, theories of aging and its mechanisms under various environmental conditions were analyzed. The analysis of published data suggested that aging is a controlled process. It is known that many mathematical algorithms utilize an analogy of aging. However, this is possible only when a "target set" is known in advance. Various forms of selection in relation to aging were analyzed both collectively and separately. The general conclusion is that aging is one of the mechanisms of directed evolution. A model was constructed, which shows how aging is integrated into partially directed evolution.

Mutations, sex, and genetic diversity: New arguments for partially directed evolution.

A review of the theories of the existence of sexes, genetic diversity, and the distribution of mutations among organisms shows that all these concepts are not a product of random evolution and cannot be explained within the framework of Darwinism. Most mutations are the result of the genome acting on itself. This is an organized process that is implemented very differently in different species, in different places in the genome. Because of the fact that it is not random, this process must be directed and regulated, albeit with complex and not fully understood laws. This means that an additional reason must be included in order to model such mutations during evolution. The assumption of directionality must not only be explicitly included in evolutionary theory but must also occupy a central place in it. In this study an updated model of partially directed evolution is constructed, which is capable of qualitatively explaining the indicated features of evolution. Experiments are described that can confirm or disprove the proposed model.

Mechanisms and models of movement of protocells and bacteria in the early stages of evolution.

A review of the physicochemical models of the movement of protocells and bacteria was performed. The mechanisms of gliding and movement based on flagella are considered. Based on the models, the average speed of movement of protocells and bacteria was calculated. A physicochemical model of bacterial gliding was constructed. The efficiency of the process of converting the energy of ATP into the energy of motion is estimated. A review of models of movement with the help of flagella was performed. A model has been constructed for converting ATP energy into proton and sodium motive forces, which, in turn, are converted into energy of rotor rotation. The problem of the accuracy of operation of nanomachines, on the basis of which the directed movement of bacteria occurs, is discussed. The considered models can be applied to create nanomotors for medical purposes.

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.

Nonlinear optimal control for the synchronization of biological neurons under time-delays.

The article proposes a nonlinear optimal control method for synchronization of neurons that exhibit nonlinear dynamics and are subject to time-delays. The model of the Hindmarsh-Rose (HR) neurons is used as a case study. The dynamic model of the coupled HR neurons undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure relies on Taylor series expansion of the model and on computation of the associated Jacobian matrices. For the approximately linearized model of the coupled HR neurons an H-infinity controller is designed. For the selection of the controller's feedback gain an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The stability properties of the control loop are proven through Lyapunov analysis. First, it is shown that the H-infinity tracking performance criterion is satisfied. Moreover, it is proven that the control loop is globally asymptotically stable.

A Model of Isotope Separation in Plants.

A model representing isotope separation during water evaporation in plants was constructed. The model accounts for substance diffusion, convective transfer and evaporation from the surface of the leaves. The dependence of the system's separation and enrichment coefficients on various parameters (liquid velocity, diffusion coefficient, and potential barriers for molecules and their thermal velocities) was determined. A comparison was made between the enrichment coefficients calculated from experimental data from different plants and those based on the model. Qualitative agreement between the experimental and theoretical values was obtained for the case of [Formula: see text], where u is the average velocity of water in the plant, h is the height of the plant, and D is the diffusion coefficient of the substance.

Adaptive Heat Engine.

A major limitation of many heat engines is that their functioning demands on-line control and/or an external fitting between the environmental parameters (e.g., temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence, no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that make the bath temperatures closer. We determine resources of adaptation and relate them to the prior information available about the environment.

A Model of Isotope Separation in Cells at the Early Stages of Evolution.

The separation of the isotopes of certain ions can serve as an important criterion for the presence of life in the early stages of its evolution. A model of the separation of isotopes during their transport through the cell membrane is constructed. The dependence of the selection coefficient on various parameters is found. In particular, it is shown that the maximum efficiency of the transport of ions corresponds to the minimum enrichment coefficient. At the maximum enrichment, the efficiency of the transport system approaches ½. Calculated enrichment coefficients are compared with experimentally obtained values for different types of cells, and the comparison shows a qualitative agreement between these quantities.

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.

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.

[A model of active transport of ions in hepatocytes].

A mathematical model of the transport of basic ions (K+, Na+, Cl-) across the hepatocyte membrane has been created using the previously constructed models of active ion transport in biomembranes. The dependence of the resting potential on extracellular ion concentration has been established. Using the model, it is possible to independently calculate the resting potential at the biomembrane and the concentrations of sodium, potassium, and chlorine ions in the cell. The calculated internal concentrations of the ions are in good agreement with the corresponding experimental values.

Model of active transport of ions in archaea cells.

A mathematical model of the active transport of main ions in cells of archaebacteria has been constructed. A set of equations has been developed and solved for ion fluxes through the bacterium membrane. The model is based on the principle "one ion-one transport system." Considering experimental data, the major transport mechanism was determined for each ion and the balance equation was written on the basis of this mechanism in the stationary state. This allowed calculating values of the membrane potential and intracellular concentrations of the ions independently. The calculated values of the intracellular concentrations and resting potential are in qualitative agreement with the corresponding experimental values for cells of extremely halophilic archaea.

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.

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

Requirements on models of the active transport of ions in biomembranes have been formulated. The basic requirements include an explicit dependence of the resting potential and intracellular concentrations of ions on the difference of ATP-ADP chemical potentials, a consideration of the reversibility of the ionic pump operation, a correlation between theoretical and experimental data on the resting potential and intracellular concentrations of ions for different types of cells, the pump efficiency approaching 100%, and a tendency of the resting potential to the Donnan potential if the active transport is blocked. A model satisfying the aforementioned requirements has been proposed by the authors as an example.

[Could life evolve by random mutations?].

The problem of the rate and mechanisms of evolution was considered. It was shown that organisms could not be formed by random mutations during real times of about one million years. It was concluded that deterministic models are necessary for the description of evolution.

[Can an organism select new valuable information from environment]. / Mozhet li organizm otbirat' novuiu tsennuiu informatsiiu iz okruzhaiushchei sredy?

The process of selecting new information by the organism ("learning") was studied. To take a decision, key patterns have to be set a priori, and so knowledge accumulation (learning) based on pattern recognition is impossible. It was shown that the only physical process that, takes place during the emergence of an external signal is the triggering of a priori programmes. An equivalent biophysical scheme of pattern recognition and taking the decisions by the organism was developed in which a signal received by the receptor leads to the synthesis of one of possible catalysts. The catalyst starts up the corresponding thermodynamic process. The information contained in the organism does not change during this process.

[Model for the cell biomembrane electric potential during active transport of various ions]. / Model' élektrokineticheskogo potentsiala na biomembrane kletki pri perenose neskol'kikh ionov sistemoi aktivnogo transporta.

A model of a stationary electrical potential on biomembrane was created. This model takes into account conformational changes in transport ATPase. N positive ions are transported simultaneously by the system of active transport. The model allows one to determine independently ion concentrations inside the cell and membrane electrical potential. It is shown that, to obtain the electrical potential, it is necessary to take into account organic negative intracellular ions. The effect of positive ions that are not transported by active transport systems on the potential value is discussed. The results obtained are in a good agreement with experimental data for various cells.

[On the mechanism of generation of electrical potential differences in cell biomembranes]. / K voprosu o mekhanizme vozniknoveniia raznosti élektricheskikh potentsialov na biomembrane kletok.

A statistical model of active ion transport in biomembranes was developed. The model makes it possible to calculate both the value of membrane potential phi zero and the rate of ion concentrations inside and outside the cell. These values depend on the difference of chemical potentials of the ATP-ADP system and the permeability of the biomembrane for ions being transported. The calculated phi zero value approximately 200-250 mV is consistent with the data on proton pumps.