Coelenterazine is the most common substrate for light-emitting reactions identified in luminous marine organisms. Among bioluminescent proteins engaging coelenterazine as a luciferin, Ca2+-regulated photoproteins form stable enzyme-substrate complexes offering thereby a unique opportunity to study their bioluminescence reactions in detail. Here, we used stopped-flow kinetics to investigate the formation of the emitters of recombinant aequorin, obelin, and W92F obelin activated with coelenterazine, as well as aequorin activated with coelenterazine-e. Based on the presence of up to four different spectral components, a modified unanimous kinetic model describing the bioluminescence reaction of Ca2+-regulated photoproteins is presented. The neutral, amide anionic, and phenolate anionic excited states of coelenteramide are proposed to originate from different pathways of dioxetanone decomposition with competing rates of proton transfer, radiation, and population and consequently to act as independent emitters in photoprotein bioluminescence.

Generalization as the use of past experience to solve new problems is realized through the formation of internal representations of the external world, which can also be called reflection in a broad sense. A suitable model object for studying reflection is the simplest recurrent neural networks (RNN). We assume that agents capable of reflection can demonstrate a universal reflection skill, which means that after training on one reflection task, the agent solves another, previously unknown (test) task better than one who has not been trained at all. If such an effect is observed for different primary and test tasks, then we can confirm the presence of reflexive equifinality. In this paper, we test the presence of reflexive equifinality by considering two reflection tasks: reflexive games (even-odd, rock-paper-scissors) and responding to fixed time series of stimuli according the mentioned game rules. The formation of a universal reflexive skill was not observed, since the trained RNN coped with new tasks as well or worse than the untrained ones. However, responding to fixed time series allowed the RNN to maintain its ability to adapt to new conditions better than the reflexive game, which was also shown from the point of view of the structural characteristics of the RNN. Therefore, in order to form internal representations, subjects need regular changes in environmental conditions. The obtained results help us to systematize our understanding of reflection and simplify the choice of environmental conditions, i.e. tasks, for further research of this cognitive phenomenon.

Representation in a broad sense is how a particular object is presented in the space of internal states of the perceiving subject. Inspired by the works of V.A. Lefebvre, we call the formation and use of representations “reflection in a broad sense”. We study representations in extremely simple model objects – recurrent neural networks of small size (30 neurons). One of the simplest tasks that requires the presence of representations for solution is responding to fixed time series of stimuli, in which the neural network should recognize the series feeding to the input and thereby predict the next stimulus it will receive. The representation of a series is considered as a dynamic pattern of neural activity distinguishable from representations of other series. This pattern can be decoded, i.e., based on its type, it is possible to define the certain series fed to the input of the neural network. In this paper, we check whether there are differences in decoding of homogeneous and heterogeneous recurrent neural networks’ neural activity, considering decoding using feedforward networks and the K-nearest neighbors method. Configurations with temporal heterogeneity (DTRNN) demonstrate differences from homogeneous ones, while configurations with functional heterogeneity (RefNet) behave similarly to homogeneous configurations. This result is consistent with the literature data on the significance of temporal coding obtained on more complex systems. In the future, we plan to continue working models that have temporal heterogeneity in order to formulate a mathematically and neurobiologically substantiated measure of the neural activity decodability.

The paper provides a brief overview of the available facts and ideas about the nature of climate change. Theproblems of ecological research, which are becoming more acute in relation to biosphere research, are considered: this is the problem of data deficit and the problem of the uniqueness of ecosystems. The key difference between the biosphere and natural ecosystems is highlighted, which ensures the long-term, in the ultimate perspective infinite, existence of the biosphere – the existence of a balance of biogen cycles or the closure of the flows of substances. The advantages of laboratory closed ecological systems (CES) as tools for experimental and theoretical study of the biosphere are considered. The contribution of the most well-known CES (BIOS-3, Folsom microcosms, Biosphere-2, micro-CES) to the understanding of biospheric processes is discussed. The problems and paradoxes identified in the mathematical modeling of CESs (Vernadsky-Darwin paradox, limitations of models of rigid metabolism), which are closely related to the well-known ecological paradoxes of May and Hutchinson, are discussed. A flexible metabolism approach is proposed to reduce the severity of these paradoxes. The measures proposed within the framework of so-called “green initiative” are discussed from the position of “biosphere as a CES”. Among these measures are reducing the carbon footprint of pets, migration to electric vehicles and renewable energy sourcesб and carbon sequestration by trees. The seriousness of biosphere-climatic changes problem is emphasized, which cannot be resolved without accounting the closure of substance flows in the biosphere.

The functioning of a subject in a changing environment is most effective from the point of view of survival if the subject can form, maintain and use internal representations of the external world for decision-making. These representations are also called reflection in a broad sense. Using it, one can win in reflexive games since an internal representation of the enemy allows predicting their future moves. The goal is to assess the reflexive potential of heuristic model objects – artificial neural networks – in the reflexive games “Even-Odd” (or “Matching pennies”) and “Rock-Paper-Scissors”. We used homogeneous fully connected neural networks of small sizes (from 8 to 45 neurons). Games were played between neural networks with different configurations and parameters (size, step size for modifying weight coefficients). A set of reflexivity criteria is presented, corresponding to different levels of consideration: neuronal, behavioral, formal. The transitivity of formal success in the game is shown. The most successful configurations, however, may not meet other criteria of reflexivity. We hypothesize that the best compliance with the criteria and, as a consequence, universal success in reflection tasks is achievable for heterogeneous configurations with a structure in which the formation of hierarchical systems of attractors is possible.

In accordance with the ideas of V.I. Vernadsky, the Earth’s biosphere can exist only because of the high degree of closure of the cyclic matter transformations carried out by all living organisms by using the energy from the Sun. In the course of its evolution, the Earth’s biosphere has undergone a number of cardinal transformations, but, at least for the last 20 million years, the gas composition of the atmosphere, and primarily the concentration of carbon dioxide, has remained practically unchanged. Nevertheless, the high degree of closure of material flows in the Earth’s biosphere seems paradoxical, since closure is not an adaptive feature of an individual undergoing natural selection for traits that give an advantage here and now (the Vernadsky–Darwin paradox). The stages in the formation of the closure of the Earth’s biosphere are considered in the context of four epochs that differ in the energy available to living organisms: (1) geochemical energy; (2) solar energy; (3) energy of oxidative phosphorylation; and (4) consumption of living flesh, predation. The paper considers possible options for resolving the VD paradox using as the example models of closed ecological systems (CES) with low species diversity. The fundamental inapplicability of ecological models with rigid metabolism for the description of CES is shown. Three mechanisms for resolving the VD paradox are proposed and the conditions for their implementation are assessed: (1) a stochastic mechanism: random selection of closing organisms (decomposers) with the corresponding stoichiometric ratios; (2) changing the consumption stoichiometry by switching catabolic pathways to different types of substances (proteins, fats, carbohydrates); and (3) changing the consumption stoichiometry by choosing food, depending on the state of internal nutrient pools. The present study leads to the conclusion that the Vernadsky–Darwin paradox can be resolved in nature by combining the mechanisms that simultaneously provide both a current competitive advantage and the ability to close trophic chains with a wide variation in the composition of material flows.

Functioning in the flow of events is possible since the subject recognizes current events as familiar and acts in accordance with the representation of ​​them. The presence of internal representations is called reflection in a broad sense and can be regarded as a requirement for effective solving of some tasks, for example, winning in a reflexive game. We consider tasks that imitate Even-odd and Rock-scissors-paper games by replacing a playmate with fixed sequences of moves. In this paper, we investigate the question whether it is possible to identify which of the available fixed sequences of moves is currently receiving by model object – a simple recurrent neural network, by decoding signals on its neurons. We show that neural-network based decoding method allows recognizing the current sequence of moves by the neural activity of the playing network, separating data that does not correspond to any of the known sequences. Therefore, simple recurrent neural networks can form stable recognizable representations associated with fixed sequences of game events in the imitation of reflexive games. This result indicates that these model objects implement reflexive processing of information and can be used for studying reflection phenomenon.

The light emitted by a luminescent bacterium serves as a unique native channel of information regarding the intracellular processes within the individual cell. In the presence of highly sensitive equipment, it is possible to obtain the distribution of bacterial culture cells by the intensity of light emission, which correlates with the amount of luciferase in the cells. When growing on rich media, the luminescence intensity of individual cells of brightly luminous strains of the luminescent bacteria Photobacterium leiognathi and Ph. phosporeum reaches 104–105 quanta/s. The signal of such intensity can be registered using sensitive photometric equipment. All experiments were carried out with bacterial clones (genetically homogeneous populations). A typical dynamics of luminous bacterial cells distributions with respect to intensity of light emission at various stages of batch culture growth in a liquid medium was obtained. To describe experimental distributions, a phenomenological model that links the light of a bacterial cell with the history of events at the molecular level was constructed. The proposed phenomenological model with a minimum number of fitting parameters (1.5) provides a satisfactory description of the complex process of formation of cell distributions by luminescence intensity at different stages of bacterial culture growth. This may be an indication that the structure of the model describes some essential processes of the real system. Since in the process of division all cells go through the stage of release of all regulatory molecules from the DNA molecule, the resulting distributions can be attributed not only to luciferase, but also to other proteins of constitutive (and not only) synthesis.

At the beginning of the paper, the level of necessary phenomenology of complex models is discussed. When working with complex systems, which of course include living organisms and ecological systems, it is necessary to use a phenomenological description. An illustration of the phenomenological approach is given, which captures the most significant general principles or patterns of interactions; the specific values of the parameters cannot be calculated from the first principles, but are determined empirically. An appropriate interpretation is also chosen empirically and pragmatically. However, in order to simulate a wider range of situations, it becomes necessary to lower the level of phenomenology, switch to a more detailed description of the system, introducing interaction between selected elements of the system. The requirements for a system model combining ecological, metabolic and genetic levels of cell culture description are formulated. A mathematical model of quorum sensing dynamics during the growth of batch culture of luminescent bacteria at different concentrations of the nutrient substrate has been developed. The model contains four blocks describing ecological, energy, quorum and luminescent aspects of bacterial culture growth. The model demonstrated good agreement with the experimental data obtained. When analyzing the model, three oddities in the behavior of the culture were noted, which presumably can change the idea of some processes taking place during the development of a culture of luminescent bacteria. The results obtained suggest the presence of some additional control system for the luminescent reaction via the synthesis pathways of FMN · Н2 or aliphatic aldehyde. In this case, the generalized description of the contribution of energy metabolism to luminescence only through ATP is too strong a simplification. As a result of comparing the model dynamics with the experiment, a discrepancy arose between the concentration of the substrate (peptone) measured in the experiment and its effective influence on the bacterial population growth. This discrepancy seems to indicate peptone is not the leading substrate, and growth is limited by nutrients contained in the yeast extract, the concentration of which did not change in these experiments. The discrepancies noted between the expectations and the results of experimental data processing, together with the assumptions about the causes of these discrepancies, set the direction for further experimental and theoretical studies of quorum sensing mechanisms in a culture of luminescent bacteria.

The paper reports the assessment of the possibility to recover information obtained using an artificial neural network via inspecting neural activity patterns. A simple recurrent neural network forms dynamic excitation patterns for storing data on input stimulus in the course of the advanced delayed match to sample test with varying duration of pause between the received stimuli. Information stored in these patterns can be used by the neural network at any moment within the specified interval (three to six clock cycles), whereby it appears possible to detect invariant representation of received stimulus. To identify these representations, the neural network-based decoding method that shows 100% efficiency of received stimuli recognition has been suggested. This method allows for identification the minimum subset of neurons, the excitation pattern of which contains comprehensive information about the stimulus received by the neural network.

The study is concerned with question whether it is possible to identify the specific sequence of input stimuli received by artificial neural network using its neural activity pattern. We used neural activity of simple recurrent neural network in course of “Even-Odd” game simulation. For identification of input sequences we applied the method of neural network-based decoding. Multilayer decoding neural network is required for this task. The accuracy of decoding appears up to 80%. Based on the results: 1) residual excitation levels of recurrent network’s neurons are important for stimuli time series processing, 2) trajectories of neural activity of recurrent networks while receiving a specific input stimuli sequence are complex cycles, we claim the presence of neural activity attractors even in extremely simple neural networks. This result suggests the fundamental role of attractor dynamics in reflexive processes.

We tested the ability of simple recurrent neural networks to use the reflection of playmate during the “Even-Odd” reflexive game. Reflection is understood as an internal representation of an external environment. To determine if subject uses reflection in the game, three criteria were proposed and applied: formal, neuronal, behavioral. The formal criterion is a win in the game, the neuronal one is a dynamic attractor’s formation of the player’s neural activity, the behavioral one is the deviation of a move sequence from the natural strategy “win-stay, lose-shift”. Three configurations of simple recurrent neural networks were used: 1) the basic one; 2) the one with an additional input which receives information about the success of the last game move, 3) the one which has off-game cycles for processing the received stimulus and making instant decision. We considered the following game conditions: 1) round-robin tournaments of various neural network configurations with modifiable and fixed synapses, 2) playing against fixed sequences of moves. It was found that the simplest neural network model is able to play as good as and, in some cases, better than neural networks of a more complex configuration. The off-game cycles for processing the received stimuli contribute to the non-reflexive behavior of the neural network. The performance of neural networks in a reflexive game correlates 1) with the presence of a self-sustaining dynamic attractor and 2) with the use of moves other than the natural strategy.

We demonstrate the possibility of identification of certain stimuli time series, which is received by simple recurrent neural network while playing a reflexive game “Even-Odd” (Matching Pennies), using its neural activity patterns. For successful identification by the method of neural network-based decoding, a non-linear decoder with at least 6 neurons on the hidden layer is required. This result indicates the presence of attractors of neural activity, which allow the trained recurrent neural network to determine the type of the received stimuli sequence and form the right response.

The influence of ryanodine channels on the cytosole Ca2+ dynamics was studied. We added the equations for ryanodine receptors and voltage-gated calcium channels into the original De Pitta et al. model of Ca2+. The derived model was shown to have significantly wider range of predictions: we derived the frequency of cytosole calcium spontaneous oscillations (which are absent in the original De Pitta et al. model) for various existing models of Ca2+ signalling in astrocytes. Particularly, the initial De Pitta et al. results can be converted to either Lavrentovich and Hemkin model or in the Dupont et al model predictions. The absence of the Ca2+ oscillations in astrocytes with the active ryanodine channels only was recently reported. This behaviour can be achieved in our model predictions for the certain values of parameters, which are supposedly responsible for the bifurcation landscape between the oscillatory and non-oscillatory dynamics of cytosol Ca2+ in astrocytes. We also investigated the interplay between the spontaneous and glutamate-triggered oscillations.

In 2012, the Convergent Cross Mapping method for finding a causal relationship between system variables from their time series was published. This method is widely used in the study of systems of various nature - from assessing the effect of cosmic radiation on the climate, to the study of cerebral activity. The relevance and prospects of using this method prompted us to master it and to apply it to identifying causal relationships between the variables of the “biosphere-climate” system. The obtained results seemed suspicious and forced us to check carefully the adequacy of the CCM conclusions in relation to various model systems. This paper presents examples of model situations when the method gives false estimates of the presence of causal relationships and offers a possible explanation for the causes of false estimates appearance.

Reflection, that in a general sense means internal representation of the external world, refers to one of awareness levels observed in animals. In this paper we demonstrate the ability of a homogeneous recurrent neural network to solve a problem that requires a reflection. The delayed matching to sample test was chosen as a task which is impossible to pass without an internal representation of an external world. Experiments showed that simple recurrent neural networks can form these representations and store them as neuron firing patterns for several clock cycles. Although the trained network was able to distinguish these patterns easily, the identification of certain stimulus by neuron firing was not practically possible due to minor differences in the level of synchronous firing of a given neuron for different stimuli. Neural networks were shown to be applicable for modeling reflexive abilities, so these simple models may also be used for creation of general technique that ultimately can be applied to recognizing neural correlates of human consciousness.

The study is concerned with the comparison of two methods for identification of stimulus received by artificial neural network using neural activity pattern that corresponds to the period of storing information about this stimulus in the working memory. We used simple recurrent neural networks learned to pass the delayed matching-to-sample test. Neural activity was detected at the period of pause between receiving stimuli. The analysis of neural excitation patterns showed that neural networks encoded variables that were relevant for the task during the delayed matching-to-sample test, and their activity patterns were dynamic. The method of centroids allowed identifying the type of the received stimuli with efficiency up to 75% while the method of neural network-based decoder showed 100% efficiency. In addition, this method was applied to determine the minimal set of neurons whose activity was the most significant for stimulus recognition.

Enzymes activity in a cell is determined by many factors, among which viscosity of the microenvironment plays a significant role. Various cosolvents can imitate intracellular conditions in vitro, allowing to reduce a combination of different regulatory effects. The aim of the study was to analyze the media viscosity effects on the rate constants of the separate stages of the bacterial bioluminescent reaction. Non-steady-state reaction kinetics in glycerol and sucrose solutions was measured by stopped-flow technique and analyzed with a mathematical model developed in accordance with the sequence of reaction stages. Molecular dynamics methods were applied to reveal the effects of cosolvents on luciferase structure. We observed both in glycerol and in sucrose media that the stages of luciferase binding with flavin and aldehyde, in contrast to oxygen, are diffusion-limited. Moreover, unlike glycerol, sucrose solutions enhanced the rate of an electronically excited intermediate formation. The MD simulations showed that, in comparison with sucrose, glycerol molecules could penetrate the active-site gorge, but sucrose solutions caused a conformational change of functionally important αGlu175 of luciferase. Therefore, both cosolvents induce diffusion limitation of substrates binding. However, in sucrose media, increasing enzyme catalytic constant neutralizes viscosity effects. The activating effect of sucrose can be attributed to its exclusion from the catalytic gorge of luciferase and promotion of the formation of the active site structure favorable for the catalysis.

Since introduction of neural networks into remote sensing they demonstrate good efficiency in remote sensing data analysis. This work is devoted to processing of multispectral (12 bands) images from Sentinel-2(A, B) satellites. Satellite images of areas in Krasnoyarsk Region and Khakassia with known vegetation types are used as task books to train neural networks. Trained neural networks have been reduced to determine which bands are significant for vegetation type identification. Reduction of trained neural network show that vegetation type can be determined from only four infrared bands without significant loses in performance in comparison with non-reduced neural network.