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The New Concept of Brain Functions, Abridged

Summary

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A new concept of brain functions is proposed. According to it, the brain is a hierarchy of neural optimal control systems where each level possesses a dynamic model of its controlled object; this can be a lower control level in the CNS or an executive organ. The new concept of brain functions is based on the solution of the problem of central pattern generators and on the neural network computational principle. Contemporary data on the cerebellum, cortico-basal ganglia-thalamo-cortical loops (the structural/ functional basis of the highest brain levels), Parkinson’s disease, and methods of its treatment (including deep brain stimulation) are analyzed from the point of view of the new concept of brain functions. These examples demonstrate the universal applicability of the new concept in the investigation of the physiology and pathophysiology of neural networks and the respective clinical effects.

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Keywords: new concept of brain functions, optimal control, central pattern generator, neural network computational principle, cerebellum, basal ganglia, parkinsonism, deep brain stimulation.

Contents 

Introduction

Drawbacks of the classical concept of brain functions

New concept of brain functions

Solution of the problem of functional

organization of central pattern generators

Neural optimal control systems (NOCSs)

Types of afferent signals

Neural network computational principle

Interaction of various NOCSs

Examples of applications of the new concept

Physiology of neural networks

Cerebellum

Cortico- basal ganglia-thalamo-cortical loops

Pathophysiology of neural networks

Parkinson’s disease

Clinical phenomena

Levodopa therapy in parkinsonism

Partial lesions of the basal ganglia and thalamic nuclei in motor disorders

Deep brain stimulation: Mechanisms, prospects, and limitations

Conclusions

 

INTRODUCTION

According to the classical concept of brain functions described in all textbooks on neurobiology, to understand how the brain controls behavior, it is necessary to know in detail the structure and properties of the elements of that part of the neural network under study that is active during certain types of behavior, and the activity of the elements of this neural network during such behavior.

Synthesis of these two types of knowledge, their superposition, leads to an adequate understanding of the work of the system. It is the essence of classical understanding of the relationship between structure and function in neurobiology. This algorithm of brain exploration is adopted from technical field where it appeared to be rather effective for analysis of simple systems. This is what we are taught in schools and universities, and it is the approach we would use in reverse-engineering a thermostat, a refrigerator, or a frequency generator.

When we read a description of the mechanisms of simplest behavioral reactions, like flexor and extensor reflexes, withdraw and escape reactions, or a simple neuronal rhythm, there is an impression of successful understanding, and there is no thought about the inadequacy of this brain exploration algorithm. When we become acquainted with the results of application of this algorithm for the analysis of more complex brain parts, e.g., the highest brain levels in mammals, the impression of “understanding” disappears, and we should admit that we do not know how the brain works. However, thoughts about the inadequacy of the classical concept of brain functions still do not come to mind. According to the widespread opinion, the classical concept is correct. The system is simply too big and complex, and we at present do not possess the necessary tools for its analysis. New superior methods will be found, and mysteries of the brain will then be revealed. This logic is the basis of the methodical orientation of neurosciences, when methods determine the formulation of experimental problems.

When one scientific view or another that has become a classical part of textbooks and has been repeated for many generations is proven incorrect, the acceptance of new views can take a number of generations. The history of natural sciences knows such examples, and neurosciences, neurobiology in particular, are not an exception to the rule. A little bit more than two decades ago, some discoveries were made in neurosciences and some adjacent disciplines, which radically change the conceptual views on the brain and on how it should be studied. The new concept of brain functions is so unusual for scientists and specialists with “classical” biological and/or medical education that full mastery of this concept to make it applicable in systemic neurobiology will require learning new fields of knowledge. In this article, we analyze the drawbacks of the classical concept of brain functions, discuss why it is inadequate, and describe the basics of the new concept of brain functions.

The problem of organization of central pattern generators (CPGs) is the basis for this analysis. The strategy of CPG investigation based on the classical concept is described, and it is shown why the CPG problem cannot be solved within the framework of classical views. After this, the solution of the CPG problem obtained as a result of the analysis of the interaction between CPGs and afferent flow is described. New notions, like the neural optimal control system (NOCS) and the neural network computational principle, are introduced for the purpose of building the new concept of brain functions. Examples demonstrating the applicability of the new concept in the explanation of physiology, pathophysiology, and clinical phenomena are presented. Corollaries of the new concept of brain functions are discussed in the Conclusion.

The review is written in response to numerous requests to publish this new concept of brain functions in Russian. Only basic ideas of the new concept of brain functions are described in this communication because of space limitations. The topic is so broad that citation of many thousands of the respective scientific publications is not expedient. Only references that are necessary to understand the material are given in the text. Additional information can be found in the cited literature and on the web site neurallaws.com. The article is written for various specialists whose work is related to the brain, neurobiologists, neurosurgeons, neurologists, psychiatrists, and psychologists; it will help them to better understand the place of their research activity in the general picture of exploration of the brain. Completion of a university neurobiology course should be sufficient to understand the basic ideas of the new concept of brain functions.

DRAWBACKS OF THE CLASSICAL CONCEPT OF BRAIN FUNCTIONS

The term CPG defines brain systems capable of producing complex repeated efferent commands even in the absence of peripheral afferent feedback. Precisely the latter feature became the basis for the term. Locomotion, scratching, swallowing, or breathing are typical examples of behaviors controlled by generators.

The CPG problem was formulated in the 1960–1970s. Its ideological clarity and formulation simplicity were very attractive. How is a generator built? The general belief was that the solution of the generator problem would be a great success in neurobiology and bring about the long-awaited understanding of how the brain controls behaviors. This hope was based on two important factors. A number of effective experimental models for studying the generators in various animal species have been developed. The models used the fact that, as a rule, generators are activated by a rather simple commands. For example, even in vertebrates generators can be activated under certain conditions in decerebrated, spinal, and immobilized animals, or even in the isolated spinal cord. It can be provided by tonic stimulation of certain regions of the nervous systems or by the addition of mediators to the solution surrounding an isolated brain tissue. In this case, the higher the stimulation frequency or concentration of the mediator, the more intense the rhythm. These models made experimental tasks significantly easier by making the object well and easily observable. The second factor, the success achieved by the microelectrode technique at that time, gave one hope for rapid solution of the problem by using the well-known strategy of brain exploration. This strategy was built on the classical concept whose foundation was laid down by Decartes and later developed by Sherrington [1].

Intense studies of central generators were carried out in various animal species. The most attractive objects for application of the classical concept were such generators in invertebrates. Such generators, however, may include only a few neurons (e.g., the generator in the sea slug consists only of twelve neurons, six on each side). Despite the simplicity of these generators, they illustrate the flaws in the classical approach well.
    Getting [2], the first scientist who applied the classical strategy successfully to study the swimming generator in the sea slug (Tritonia diomedea) by giving a complete description of the generator circuitry, defined the strategy as mechanistic and subdivided it into eight steps:
    1. Description of behavior.
    2. Characterization of the motor pattern and efferent commands produced by the generator.
    3. Identification of motoneurons and interneurons. Getting did not consider motoneurons components of the generator.
    4. Identification of pattern-generating neurons. Changes in the activity of a generator neuron should be accompanied by changes in the rhythm pattern at all levels, interneuronal, motoneuronal, and behavioral.
    5. Mapping of the synaptic connectivity between generator neurons.
    6. Characterization of properties of the cells composing the generator.
    7. Manipulations of network, synaptic, or cellular properties to identify the role of individual cells, synapses, or cellular properties in the generation of the overall motor pattern.
    8. Reconstruction of the pattern generator, its motor output, and the corresponding behavior. At this final step, the description may be qualitative and verbal or look like a quantitative computer simulation.

Getting successfully passed all eight steps, including computer simulation, which coincided well with the behavior of the real generator network. At that time, these studies were considered a great success, and many other scientists joined CPG studies. However, nobody succeeded in passing all the above eight steps while studying more complex generators in vertebrates. Thousands of publications are dedicated to the generators. Considering the purpose of the current review, it is possible to summarize all these studies in the following way: There is no single circuitry solution of construction of the generators. Neural circuits and networks turned out to be different in different species. There is no single general mechanism of rhythm generation even in invertebrates. Network, synaptic, and cellular mechanisms all provide the generator activity. Generators adapted for long-lasting activity include pacemaker neurons. Generators that are used rarely and for a short time usually rely on a balance of synaptic excitation and inhibition. It was also found that the more complex the executive organ (e.g., a limb), the more complex the generated pattern and the more complex the construction of the generator.

The activity of generators is subjected to corrective (descending and/or peripheral) influences, which help to adjust movements to environmental conditions. Generator responses to peripheral and descending signals depend on the level and phase of its activity. Thus, if we want to understand how generators control behavior in different animal species, in addition to studying generators in these species of animals we should also investigate the dependence of the corresponding reflexes and descending influences on the level and phase of generator activity.

Therefore, the essence of the classical concept consists of selecting the neural networks and circuits specific for definite functions from the structure and functions of a bigger neural network. This means that when we want to understand how the brain functions, it is necessary to find and investigate circuits that are specific for each form of behavior in each animal species that we want to study. It is unclear how to do this even at some of the lowest CNS levels. Neural circuits of different generators, e.g, spinal generators for locomotion and scratching in cats, significantly overlap with each other. Reflex arcs also overlap. This means that one generator can be located within another one. Moreover, each spinal generator includes neurons of a few reflex arcs. Finally, how does one select specific circuits from the brain while analyzing its functions? Nobody has succeeded in doing this, and, as will be substantiated later, nobody can succeed in principle. Later on, it will become clear why. In addition, as we know, a surprisingly great number of animal species and their forms of behavior do exist, especially in higher vertebrates. In humans, the number of forms of behavior is so large that such a way of brain exploration seems to be unreal. However, the systems neurobiology went this way and continues to go this way.

Several questions that the classical concept never answered (and some of them did not even address) should be added to the above-mentioned.
    1. Why are biological neural networks built the way they are?
    2. Is it correct to select a specific neural network from a bigger one to explain one type of behavior or another?
    3. Is it adequate to use diagrams where functionally similar groups of neurons are presented as a single element to explain the respective functions and perform computer simulations?
    4. Why can one and the same neuron be a component of different specific circuits?
    5. What is the role of convergence and divergence in neural networks, and what is the role of parallel circuits?
    6. What is the role of neuronal dendritic trees?

NEW CONCEPT OF BRAIN FUNCTIONS

Solution of the problem of functional organization of central pattern generators (CPGs). In his own time, the author paid tribute to the classical approach and published in the 1970–1980s many articles on the CPG problem before it became clear how this problem should be resolved. The solution was obtained in experiments on cats while studying the interaction of locomotor and scratching CPGs with afferent flow. Experiments were carried out on animals performing real and fictive movements [3, 4]. Statistical dependences of reorderings of the generators related to stimulation of various peripheral nerves were studied during fictive movements (in immobilized preparations). The phase distribution of afferent signals in the motor cycle was studied during real movements. These experiments were based on the earlier found fact of modulation of presynaptic inhibition by the activity of spinal CPGs [5-8]. Due to this mechanism, spinal CPGs perform active selection of afferent information so that they are poorly sensitive or completely insensitive to external signals within certain phases of their activity.

It was found that spinal generators for locomotion and scratching include a dynamic model of the controlled object (the term “forward model” is more often used in the English scientific literature). There is parity interaction between the model and actual flows; in other words, the model flow can be considered a component of the afferent flow, and the above-mentioned modulation of presynaptic inhibition by generators is a reflection of the activity of the internal model. The internal model predicts what will be received from the periphery in the absence of perturbation in response to a command sent to the executive organ. Therefore, reverberation of the activity via the loop that includes the internal model is the basis for rhythm generation by CPGs after deafferentation (Fig. 1). This generation is not based on reverberation between flexor and extensor half-centers, as was suggested according to classical views [9]. However, modifications of the latter idea about half-centers and the classical approach to the generator problem can still be found in the scientific literature [10-13].

Fig. 1

Fig. 1. Major functional subdivisions of a neural optimal control system (NOCS). Informational and initiating signals are shown by filled and open arrows, respectively. See the text for explanations.

Several conclusions suggest themselves at once.

Generators in all animal species are built according to the same principle; they all contain a dynamic model of their controlled object. At the same time, the schematic solution of these generators can be dissimilar because of the phenomenon of optimization (see below, the neural network computational principle).

If lower levels of the CNS contain the model of the controlled object, then higher-located control centers should possess predictive mechanisms even more so. The CNS is a hierarchical control system in which each higher level considers the lower one its controlled object. Consequently, the former contains the model of the latter.

From the point of view of the control theory, the presence of the controlled object model in the controlling system means that the latter is optimal. Therefore, all controlling levels in the CNS are optimal, and we can introduce the notion of the neural optimal control system (NOCS) for the purpose of future analysis.

Neural optimal control systems (NOCSs). The NOCS of any level includes two major functional blocks, a controller and an internal model of the dynamics of the controlled object (CO). The controller utilizes information on the current state of the CO to compute the control signal that will move the CO from its initial point to its destination point along the optimal (or quasi-optimal) trajectory. The internal model predicts the next most probable state of the CO after the latter receives the controlling signal. The NOCS uses the internal model for a few purposes. One of those is to determine the CO current state. Special mechanisms of integration of model and afferent flows are used for this purpose (the afferent information processing block in Fig. 1). These mechanisms allow NOCS to pay more attention to more active (more intense) inputs and consider them as being more “reliable.” Low-activity or “silent” channels are considered by NOCS poorly reliable or nonreliable. In the spinal cord, the above-mentioned modulation of presynaptic inhibition is an important mechanism of such distribution of “attention.” In other parts of the brain, this function can be performed by complex synapses, for instance, by glomeruli. This mechanism of “attention” distribution gives an afferent system the holographic property, the ability to function after partial damage (elimination) of some afferent inputs. Another purpose for using the model is comparison of the model and actual afferent flows to compute the mismatch (error) signal that is necessary for tuning the model to the object (see below).

Incomplete observability and controllability are major reasons for having a model in the NOCS. Sensory systems, e.g., visual, transmit to the brain information on only a portion of the environment. The environment has its own dynamics and can interact with the CO in an unpredictable way (in other words, perturbations can occur). Control of the CO is always performed with some error (see Neural network computational principle), and this, in turn, can be a reason for perturbations. Finally, incomplete controllability also means that the CO cannot be moved to a desired state in one control step. Many steps require intermediate computations with the involvement of the model.

Types of afferent signals. The NOCS receives two types of afferent signals, initiating and informational ones. There is only one difference between these two types of afferent signals. The NOCS tries to minimize initiating signals during the process of control; more exactly, the NOCS uses the informational context to compute such control output that minimizes the integral measure of initiating signals. Initiating signals can be considered “energetic” ones. They activate automatisms stored in the NOCS. Reflex- and generator-provided controls are typical examples of automatisms. For instance, the limb withdraw reflex and escape reaction with subsequent locomotion minimize any harmful influence on the organism. A mismatch signal (or error) between the model and real flows is another example of the initiating signal. This signal should also be minimized during the control (during tuning the model to the object). It initiates the learning process. The easiest way to imagine this process is its presentation as continuous learning to imitate the afferent flow as precisely as possible.

In control theory, it is customary to use such terms as “state space” and “control space” to describe the behavior of a control system or a process. The first determination is a generalization of the term “phase space.” The dimensionality of these spaces is determined by the complexity of a particular system or a process. Within this framework, the task of control consists of moving the CO within the state space from an initial point to a destination point along an optimal or a quasi-optimal trajectory. It is worth mentioning that the state of a neural network itself can be considered a point in a definite state space, and the process of computation can be considered motion from one point to another one.

The NOCSs are multifunctional by their nature. Any automatism is started by the corresponding simple initiating command. The NOCS receives information on the state space coordinates of the CO at a destination point. All other operations are performed by the NOCS autonomously, determining the current state of the CO, the optimal or quasi-optimal trajectory, and moving the CO along this trajectory to the destination point. It becomes clear that there is no principal difference between rhythmic and phasic movements. During rhythmic movements, a nonzero velocity is set at the destination point, while during phasic movements the velocity is set to zero. Initiating signals can be descending, generated at the same hierarchical level, or arriving in the NOCS from its CO. For example, a painful stimulus can evoke a flexor reflex or locomotion. Consequently, the CPGs and reflexes are simply dissimilar regimes of work of the NOCS and have only functional differences within the new concept of brain functions. They are not definite anatomical structures, as it was implied within the framework of the classical brain concept.

Any perturbation should be considered in the following way. Any NOCS attempts to perform optimal operations after a perturbation, i.e., it will try to move the CO along an optimal trajectory from the new initial state in which its CO appears after this perturbation. This scenario is known in mathematics as Bellman’s principle (see [14]).

Continuous learning is the foundation for multifunctionality of the NOCSs. It is realized during the whole ontogenesis. It is enough to remember the embryonic motility that starts in vertebrates when the spinal cord establishes the first synaptic connections with the limb muscles [15-17]. The embryonic motility is a reflection of realization of the trial-and-error method that is used to tune the model to the CO. The controller also learns how to move the CO (in this case, the limb) from the initial point to any destination point in its state space. It becomes obvious why many animal species are capable of performing complex movements immediately after birth. Learning that continues from birth till death at all levels allows us to understand how such complex movements, like playing the piano, playing tennis, gymnastic exercises, and so on are mastered. The NOCS hierarchy and the basic principle of learning will be described below.

Fig. 2

Fig. 2. Pacemaker neuron that controls muscle contraction, as an example of the neural optimal control system (NOCS). A) “Classical” diagram; B) diagram within the framework of N OCS notion; PN is impulse activity of the pacemaker neuron, RPR is activity of the relaxation position receptor, MF is change in the muscle force, and MC is change in muscle contraction.

Functional subdivisions (blocks) of the NOCS can be anatomically inseparable. For instance, in generators built on the basis of a single pacemaker neuron, the latter can be a substrate for both the controller and the model (Fig. 2). The membrane and intracellular properties of this neuron play a key role in the given realization of the controlling system. This example shows how the idea of NOCS can be applied to simple neural networks, like those of the autonomic nervous system. In more complex systems (e.g., in the highest brain levels, see below), functional subdivisions can be anatomically separated to a considerable degree. However, it is understandable that one functional block does not make sense without the presence of the other.

The term “optimization” requires explanation. In everyday life, the term “optimal” just means that the object or the process is better than other objects and processes; the term lacks a constructive meaning. In the technical field, however, the term “optimization” has such a meaning. The adding of an optimization criterion to a system of equations allows one to find a solution that satisfies this criterion. Shapes of modern airplanes and cars are well known examples of drag optimization (minimization). There are various criteria of optimization, namely minimization of energy consumption, minimization of distance, maximization of output power, etc. Life itself is the best example of optimization. Each animal species is optimally adapted to its ecological niche, starting from the body shape and ending with the construction of the nervous system. Biological optimization is optimization in a broad sense; everything that can be optimized inevitably undergoes the process of optimization by using genetic, molecular, cellular, and system mechanisms. The scheme of learning described below is an example of optimization in neural networks. Optimization in the technical field is optimization in a narrow sense, when one parameter or only a few parameters are optimized. Limitations of technical capabilities are the reason for such a situation.

Neural network computational principle. The nervous system performs information processing, and, from the point of view of mathematics, any information processing is computation. Knowledge of how biological neural networks perform computations came from neurocomputing. Let us consider the following mathematical construction, the three-layer unidirectional neural network (Fig. 3), proposed by Kolmogorov [18]. The first (input) layer consists of n units that distribute, in a fan-like manner, signals to the second hidden layer (2n+1 elements). The processing elements of the hidden layer are not directly connected to the outside world. They send signals to the output layer. The output processing elements (m neurons) send an output vector to the outside world. Neurons of the hidden and output layers perform linear and nonlinear summation of their input signals, respectively. Kolmogorov proved the theorem that such a three-layer neural network can implement any continuous function of many variables if its synaptic weights are adjusted properly (an existence theorem). Later on, many algorithms were developed in neurocomputing that showed how to build such a network by adjusting synaptic weights during the learning procedure. One of them is a back-propagation algorithm.

Fig. 3

Fig. 3. Architecture of a Kolmogorov neural network. See the text for explanations.

The importance of these artificial neural networks to neurobiology cannot be overestimated. Despite simplification, they provide a very good analogy of how actual biological neural networks perform approximation of functions of many variables. At the same time, the role of convergence and divergence in biological neural networks becomes obvious. The existence of almost complete convergence and divergence in neuronal functional modules has been experimentally proven for certain neuronal systems. For example, a single motoneuron receives projections from all of the spindles of the muscle it innervates. Conversely, each Ia afferent fiber sends its terminals to all of the motoneurons supplying the muscle of origin [19, 20].

Actual biological neural networks are much more complex than the above-mentioned artificial ones. Their architecture is more complex. They can have more layers, be recurrent, i.e., include positive and negative feedbacks, and their individual neurons can possess various features, in particular they can be pacemakers or generate plateau potentials and afterspike hyperpolarization. This distinguishes them from artificial neurons with very simple transfer functions. Finally, real neurons can have dendritic trees that significantly surpass the size of the cell soma. All these differences show that real neural networks are capable of performing very complex computations; a single neuron with its dendritic tree can be equivalent to a huge network of artificial neurons.

Based on the neural network computational principle, it is easy to conceptualize learning in biological neural networks. It is a process of adjustment of network parameters (first of all, of weights of synaptic connections between neurons; at the same time, changes in other parameters of the neurons and surrounding elements can also be a part of this process). As the result of this process, the network becomes capable of computing a new function minimizing the signal that initiated this learning. The temporal sequence of events during basic, the most primitive, and, evolutionary, the earliest learning can be imagined in the following way (Fig. 4). An informational context (conditioning stimulus) is used to compute the function that minimizes the initiating signal (unconditioned stimulus); in other words, the new function should lead to generation of the control signal before the arrival of the initiating one. The latter evokes fluctuations (increase or decrease) in the weights of informational synapses that were active during a certain time window preceding the initiating signal. The amplitude of fluctuations decreases with decrease in the magnitude of the initiating signal. It is easy to show that such a system converges to the solution minimizing the initiating signal, even if the number of iterations is very large [21]. This strategy of random search is the only available one when a correct solution is not known a priori. It is obvious that it is possible to make maximization the purpose of learning by inverting the initiating signal.

Fig. 4

Fig. 4. Simplest learning scheme providing minimization of the initiating signal. CO) Controlled object, IC) informational context, IS) initiating (“harmful”) signal, M) movement that moves away the CO from the harmful stimulus, A, B, and C) Beginning, middle, and end of the learning process, respectively. At the end of learning, the NOCS generates the control signal evoking the movement, which moves away the CO from the harmful influence, and the initiating signal is not generated.

Several conclusions concerning evolutionary improvements of this type of learning arise from the described strategy. This scheme is based on the presence of a time window directed backwards and pointing at those synapses that require “adjustments.” The duration of this time window is determined by the molecular mechanisms of memory. The respective mechanisms can be quite simple for short time intervals. For instance, even trace processes in neurons can last tens of milliseconds. Longer time windows, e.g., at the highest levels of the CNS, are certainly based on more complex mechanisms. It is also clear that the capability of an individual neuron to determine the direction of change in a single synapse leading to minimization of the initiating signal can crucially increase the rate of learning. Other types of learning are derivatives of this primitive one.

The network computational principle gives the system several extremely important features. First of all, this is mulifunctionality; numerous functions can be stored within one network, and the accuracy of the approximations performed by each function degrades slowly as the number of stored functions increases. Networks having different architectures can approximate the same functions. Then follows the holographic property: Any network can in principle continue to function after partial loss of its neuronal elements but only with less precision. Further, follows the capability of forming numerous attractors, i.e., stable states in the state space. There can be different attractors, point, ring, cyclic, or chaotic (the name originates from the behavior of the system at the attractor point). They can be the basis for memory, pattern generation, and many other functions.

Taking into account the network computational principle, it becomes clear why schematic implementations of CPGs are different in different animal species. All of them are NOCSs, but differences in the COs and element basis (properties of neuronal elements) led to different optimal solutions in the course of evolution.

Interaction of various NOCSs. Coordinated activity of the nervous system requires interaction between various NOCSs. This interaction should be realized horizontally (interaction between NOCSs of the same hierarchical level) and vertically (interaction between NOCSs of different hierarchical levels). In the first case, any NOCS should receive information from other NOCSs with which it coordinates its activity (information about their state). For the NOCS, this is afferent information, and its internal model will try to predict this information as precisely as possible. Also, like any other informational context, this information can be used to minimize initiating signals according to the scheme described above. It is necessary to note that “higher” NOCSs can send to “lower” ones both types of signals, informational (e.g., information from distant receptors can be sent to low-level NOCSs in the simplest animals) and initiating, i.e., signals about errors. The latter considerably broadens the behavioral repertoire of “lower” NOCSs.

To understand the hierarchical interaction between various NOCSs, let us remember how generators are activated. This, as a rule, is provided by a simple tonic command. This means that the initiating system is in a point of its state space, while the generator (the “lower” NOCS) moves along a closed trajectory in its state space, i.e., generates cyclic motor commands. When the “higher” level “jumps” to another point, the “lower” level changes its trajectory. Lower NOCSs are the COs for higher NOCSs. In the described case, a “higher” NOCS receives from its CO (“lower” NOCS, i.e., the, generator) rather simply organized tonic afferent signals (if the generator activity is stable). These signals contain information on the frequency and intensity of movements performed by the “lower” level. Hence, the internal model of the initiating NOCS is simpler than a dynamic limb model included in the generator (“lower” NOCS). There is no necessity for the initiating NOCS to “know” all the details of the limb control by the “lower” NOCS; this significantly simplifies the construction of such “higher” initiating NOCS. This example demonstrates the major advantage of hierarchy, namely abstraction of the state space when we move from lower NOCSs to higher ones. During motor control, higher-located NOCSs can work with such parameters as the speed of locomotion, direction of the movement, location in the environment, etc. Neurons reacting to the direction of movement and place in space have been found at higher brain levels [22-26].

The hierarchy is also important for the functioning of the sensory systems. In these systems, higher NOCSs tune lower ones to specific features. Primary, secondary, and so on detectors are created this way. Mismatch signals generated by a lower level move higher and higher until they reach a competent level capable of minimizing it by tuning lower levels.

EXAMPLES OF APPLICATIONS OF THE NEW CONCEPT

In this section, brief descriptions of examples of application of the new concept of brain functions are given. These examples are the result of reinterpretation of literature data by using the new concept. Detailed descriptions can be found in the cited references.

PHYSIOLOGY OF NEURAL NETWORKS

Fig. 5

Fig. 5. Semantics of the cerebellar inputs. CFs and MFs) Climbing and mossy fiber systems, respectively; SOCT) spino- olivo-cerebellar tract; SRCT) spino-reticulo-cerebellar tract; VSCT) ventral spino-cerebellar tract; DSCT) dorsal spino- cerebellar tract. 

Cerebellum. The cerebellum is a uniform structure that has only two afferent inputs, mossy and climbing fiber systems. Figure 5 shows the semantics of signals coming to the cerebellum from other NOCSs [27, 28]. Results of analysis of ascending spino- cerebellar and descending cerebro-spinal tracts during fictive and real locomotion and scratching [29] are the basis for this semantics. Model and real afferent flows enter through the mossy fiber system. The cerebellum does not need its own model, because it uses models from other NOCSs. Information from complex detectors and cortical motor areas also enters through this input. This information enriches substantially the informational context coming to the cerebellum. The inferior olive is a part of the error distribution system. The error signals come from lower and higher NOCSs. It is understandable that the construction should be modular; in other words, a cerebellar module receiving an error signal from a lower NOCS or its part should send descending commands to the addressee that made the error.

Let us recall the learning scheme shown in Fig. 4. The neural network uses any available informational context to compute the output controlling signal that minimizes the initiating signal, i.e., the error signal. Similarly to the scheme shown in Fig. 4, the error signal coming through the inferior olive reaches Purkinje cells via climbing fibers 10-15 msec later than the mossy-fiber information arrives [30]. Therefore, the cerebellum supplied with an additional informational context (vestibular, visual, auditory, and other information) during the whole ontogenesis learns to correct numerous NOCSs by producing control signals sent to the spinal cord via rubro-, reticulo-, and vestibulo-spinal tracts. This conceptual view of the cerebellar functions explains well why control of movements remains possible after cerebellectomy, though the movements become poorly coordinated.

Cortico-basal ganglia-thalamo-cortical loops. Cortico-basal ganglia-thalamo-cortical loops are the structural basis of the highest brain levels. At present, five loops are usually distinguished, namely the motor (or skeletomotor), oculomotor, dorsolateral prefrontal, lateral orbitofrontal, and anterior cingulate (or limbic) loops [31, 32]. The similarities between these loops led long ago to the opinion that similar neuronal operations are performed at comparable stages in each of the five mentioned loops. But what operations? Let us analyze the motor loop.

The motor loop, as other loops, is built as a combination of closed and open loops (Fig. 6). Information from vast, usually functionally interconnected, cortical areas enters the basal ganglia and is progressively integrated in the course of its passage through the loop. In closed loops, the target cortical area sends projections to the basal ganglia, but this is not the case for open loops.

Fig. 6

 Fig. 6. Functional organization of the skeletomotor loop. DNs) Dopaminergic neurons; SMA) supplementary motor area; PMC) premotor cortex; MC) motor cortex; APA) arcuate premotor area; SSC) somatosensory cortex; GPi) internal segment of the globus pallidus; SNr) substantia nigra, pars reticulata; TNs) thalamic nuclei; CO) controlled object.

Analysis of the semantics of the corresponding signals revealed two interesting facts [33-35]. “Predictive” neurons have been found in the striatum; these are neurons that in trained animals fire before presentation of a stimulus that can be predicted based on previous signals. Dopaminergic neurons react to an error, to a mismatch between the predicted and real events. Dopaminergic neurons of the substantia nigra, pars compacta and the adjacent mesocorticolimbic group project to the striatum and the cortex and receive inputs from these structures and other areas. Therefore, dopaminergic neurons are a part of the error distribution system forming an initiating input to the motor loop. Undoubtedly, there are other initiating inputs, but they await discovery.

Consequently, in the motor loop, as in the other loops, the basal ganglia are the substrate for the model [27, 36-38]. The body of the animal and the environment are the CO for the motor loop, but at a more abstract level. The motor loop controls the animal’s behavior by initiating automatisms of the lower NOCSs, and it is not necessary for it to take care of the control of single muscles. At this level, the system works with velocities and directions of movements, place in space, etc. The model is tuned to changes in the CO very rapidly (within several tens of milliseconds). For example, in the case of driving, the model predicts not only the state of the driver, but also the position of static and moving objects on the road at the next moment in time.

PATHOPHYSIOLOGY OF NEURAL NETWORKS

Parkinson’s disease. The death of dopaminergic neurons of the substantia nigra, pars compacta, the cause of which is unknown, leads to the development of Parkinson’s disease. Manifestation of the symptoms usually starts when less than 15% of dopaminergic neurons remain alive. From the point of view of the new concept, Parkinson’s disease should be considered a disease of the error distribution system within the motor loop [27, 36-39]. The process, undoubtedly, involves other loops, but this issue will not be broached in this review.

It follows from the neural network computational principle that biological neural networks cannot function with 100% accuracy. Hence, in the case of the motor loop, prediction of the CO state is always made with some error; instead of a point in the CO state space we should consider a certain region where the CO most probably should occur based on the prediction by the model. Similarly, concerning afferent information coming from the CO, we should also consider a certain region in the state space where the controlled object is most probably located. If the predicted and actual regions of the state space completely or partially overlap, the NOCS considers them as coinciding; in other words, the NOCS does not react to an error if it does not reach a certain threshold. Therefore, in normal subjects the predicted and actual states overlap in the absence of external perturbations (Fig. 7A). In Parkinson’s disease, the system generating predictions cannot function with the necessary precision, because it does not receive accurate information on errors; naturally, it cannot be properly tuned to the object. This results in the absence of coincidence between the predicted and real states (Fig. 7B), and the NOCS, i.e., the motor loop, will try to correct the situation in each subsequent control step. This is manifested in the form of parkinsonian symptoms. For instance, setting of incorrect parameters at the destination point for lower NOCSs may be the basis for the tremor phenomenon.

Clinical phenomena. The above-described view on Parkinson’s disease allows us to propose a new interpretation for the mechanisms of its treatment. It is well known that, at early stages of the disease, pharmacotherapy amplifying the dopaminergic influences is effective. Drugs containing precursors of dopamine synthesis or slowing its decay in the synaptic cleft are examples of such drugs. As the disease progresses, an increase in the dose of these drugs is necessary, and this is accompanied by side effects like dyskinesias. When medication leads to dyskinesias, the only treatments left are functional neurosurgical procedures, like partial lesion or stimulation of several nuclei that are components of the skeletomotor loop.

Fig. 7

Fig. 7. Simplified scheme of the processes developing during tuning the model to 2 the controlled object in normal (A) and parkinsonian (B) subjects, and an error profile (C). S and S ) Coordinates of the state space (two-dimensional case is shown); I) intensity of the error signal; S) state of the modeling network. See the text for further explanations.

Targets for functional neurosurgical procedures in Parkinson’s disease were found empirically many decades ago. The most accepted targets for surgical interventions are the globus pallidus, pars interna, subthalamic nucleus, and ventral intermediate thalamic nucleus. The first two belong to the basal ganglia. The third one is a relay nucleus through which the cerebellum transmits its information to the cortical centers responsible for motor control. Partial lesions of these nuclei are known under the names of pallidotomy, subthalamotomy, and thalamotomy. Chronic stimulation of these nuclei received the name deep brain stimulation (DBS), e.g., DBS of the subthalamic nucleus. It is necessary to note that the same nuclei are the targets for many other motor disorders, in particular, essential tremor and dystonias. There is no explanation within the framework of the classical concept of brain functions why stimulation or lesions of the above- mentioned nuclei exert positive clinical effects. We shall analyze DBS mechanisms after describing the mechanisms of drug therapy and partial lesions of the basal ganglia nuclei.

Levodopa therapy in parkinsonism. Under normal conditions, an error signal is delivered to the part of the network that made the error, and each time the model is tuned to the CO, the error should be minimized (Fig. 7C); in other words, the system should descend to the global minimum. Parkinson’s disease is a progressive disorder; dopaminergic neurons continue to die, sprouting takes place, signals on errors are delivered less and less precisely in the course of the disease, and it becomes more and more difficult for the system to “slide” to the global minimum. The system more and more tends to get “stuck” in local minima (C). Drugs that amplify the dopamine action, e.g., levodopa, work like amplifiers of error signals helping the system to slide to the global minimum. However, at later stages of the disease, when only a small number of dopaminergic neurons are left relatively intact (error signals are delivered to those parts of the system whose tuning cannot remove the causes of the errors), the dose increase can only worsen the situation, which leads to dyskinesias. Adjustments of the synaptic weights become inadequately large, and the system “jumps” from one local minimum to another bypassing the global minimum (e.g., from minimum 1 to minimum 2, C).

Partial lesions of the basal ganglia and thalamic nuclei in motor disorders. Let us go back to the neural network computational principle to understand why partial lesion of the skeletomotor loop nuclei alleviate parkinsonian symptoms. A holographic property, the tolerance to partial lesions, is one of the features of the network systems. After a partial lesion, a neural network continues to function, but with a lesser accuracy of approximation. In Parkinson’s disease, 25-35% of the mentioned earlier nuclei are destroyed. Depending on the site of the lesion, in the model-generating system (the globus pallidus, pars interna or the subthalamic nucleus), or in the system delivering information on the actual state of the CO (the ventral intermediate thalamic nucleus), such lesion will result, correspondingly, in increases in the regions of predicted or actual states of the CO and, therefore, in partial overlapping of the predicted and real states (Fig. 8B, C). The decrease in working precision will also help in easier descent of the system to the global minimum.

It is noteworthy that, under conditions of realization of the network computational principle, a decrease in precision is a very effective strategy of functional improvement in a situation where the system of error distribution undergoes substantial degradation and cannot provide the necessary accuracy of local delivery of error signals. It is well known from the technical field that a control task is much easier when the requirements for accuracy become lower (e.g., in the case of aiming at a target).

Deep brain stimulation: Mechanisms, prospects, and limitations. At present, DBS as a method of treatment is at a unique stage of its development. On the one hand, the method has proven itself well in movement disorders, like Parkinson’s disease and essential tremor. On the other hand, there are tendencies to broaden its applications without a clear understanding of how the method works. The latter process led to the situation where the scientific literature is full of articles that describe well-known results or results and successes that nobody can repeat, or it simply advertises DBS by comparing it to “brain pacemaker,” “brain massage,” etc. It is obvious that understanding the DBS mechanisms is a necessary step in defining the limits of using this method.

A typical clinical DBS system (e.g., that manufactured by Medtronic, USA) consists of two components, the electrode set and the stimulator. The active part of the electrode set implanted in the brain has four concentric electrodes (diameter 1.27 mm, height 1.5 mm, distance between the proximal and distal electrodes about 10 mm). The programmable stimulator is usually implanted in the subclavicular area. Stimulation can be done through any pair of the electrodes or monopolarly, when the stimulator case is an indifferent electrode. Typical parameters of stimulation are the following, frequency 100-180 sec–1, stimulus duration about 0.1 msec, and amplitude around several (1 to 4) volts.

It is obvious that two processes occur around the electrode tip under such stimulation parameters depending on the distance from the electrode; these are stimulation and functional blocking of neurons and axons surrounding the electrode site. The blocking effect is more pronounced during increase, and the stimulating effect is greater during decrease, in the stimulation frequency. The mechanism of the blocking effect is an equivalent of the above- described partial lesion. Concerning the stimulating effect, it is nothing more than noise injection into the controlling system. Incoming signals do not carry any meaningful information. It is known, however, from neurocomputing that adding noise helps the process of neural network learning. The systems go through local minima much easier and reach the global minimum faster. The noise also has another effect; it decreases the resolving power of the network, i.e., decreases the accuracy of the computations performed. This double effect of DBS is shown in Fig. 8D.

ig. 8

Fig. 8. Predicted and actual state of the CO in parkinsonian patients after various functional neurosurgical procedures. Coordinates are the same as in Fig. 7A. A) Before treatment; B) after partial lesion of the modeling network; C) after partial lesion of the system transmitting real afferent information on the CO; D) after deep brain stimulation (DBS) of the network that generates the prediction.

What part of the controlling system is affected by stimulation? Estimates performed have shown that DBS significantly affects 30-35% of the stimulated nucleus [40, 41]. Let us consider the subthalamic nucleus an example in which the density of information passing through the cortico- basal ganglia-thalamo-cortical loop is maximal. In humans, the volume of this nucleus is about 240 mm3 and it contains about 560,000 neurons. Thus, around 180,000 neurons, their dendrites, and axons are affected by DBS and excluded from the normal process of computation. And if we take into account the number of affected synapses, whose number exceeds by thousands of times the number of neurons and where almost all the computations occur, then the scale of DBS influences on the controlling system becomes even more immense. These facts emphasize again the holographic properties of the nervous system and its tolerance to noise during computations.

 Hence, DBS has numerous advantages in comparison with partial lesions. A functional block, the analog of a lesion, is reversible, and its scale can be varied by changing the stimulation parameters. The noise injected into the system (the component that is absent in the case of lesions, i.e., pallidotomy, thalamotomy, etc.) can also be varied, and its optimal parameters can be found.

The described mechanisms of DBS immediately allow understanding the prospects and limitations of this method. DBS should be considered as a trade- off between symptom alleviation and the decrease in resolving capabilities of the stimulated system. It is understandable that the decrease in approximation accuracy and the addition of noise to alleviate symptoms in various disorders of the nervous system can only be done within certain limits, dissimilar for different NOCSs. The substantial decrease in the approximation accuracy is the cause of confusion and unclear thinking; these are symptoms of involvement of the prefronatal and frontal loops, described after DBS of the subthalamic nucleus and pallidum. Undoubtedly, if the NOCS has been significantly impaired during the disease, and there is a substantial loss of the capability to perform accurate computations, DBS cannot alleviate symptoms in this disorder. Huntington’s disease, in which degeneration in the striatum occurs, is an example. It is well known that DBS is not effective in this disorder.

The fact that there is a decrease in the resolving capability of the controlling system is not easily acceptable psychologically by many people. In this connection, it is appropriate to draw analogies with other treatment methods, which also rely on decreases in resolving power of the affected neural networks. Electroconvulsive therapy, insulin shock therapy, the sorrowfully referred-to lobotomy, some “softer” methods (like transcranial magnetic stimulation), and others are examples. It is necessary to note that many neurotropic drugs can also act by decreasing the precision of work of certain neural networks. Nobody has analyzed their mechanisms from this aspect. The action of such a substance as ethyl alcohol, is, however, extensively known. The following conclusion suggests itself: If the symptoms of a disease can be alleviated by the above-mentioned shock therapies or other methods decreasing the resolving power of neural networks, then the probability that the disease can be treated with DBS is high. At present, such disorders as Tourette’s syndrome, obsessive- compulsive disorder, intractable depression, and even Alzheimer ’s disease are considered candidates for effective application of DBS. The first three disorders respond positively to shock therapy, but Alzheimer ’s disease does not.

Within the framework of the new concept of brain functions, Tourette’s syndrome, obsessive- compulsive disorder, and intractable depression may be considered the results of formation of pathological attractors within different cortico- basal ganglia-thalamo-cortical loops [27]. From a theoretical standpoint, partial decrease in the resolving power and noise injection in the system can help it to more easily leave the attractor states. Concerning Alzheimer ’s disease, numerous neurodegenerative changes in the brain are observed during this disorder, among which most authors mention degeneration in the nucl. basalis of Meynert, entorhinal cortex, and hippocampus. The Meynert’s nucleus is a part of the error distribution system. Its neurons react to novelty [42]. The entorhinal cortex and hippocampus may be considered networks working primarily with the informational context (however, it is understandable that they also compute and transmit initiating signals). Therefore, the computing neural network in Alzheimer ’s disease is already incapable of precisely computing, and the respective symptoms (in particular, memory loss) reflect this incapability. It is hard to imagine how DBS, which leads to even greater decrease in the resolving power of the neural network and injects noise in it, can alleviate symptoms of Alzheimer ’s disease.

CONCLUSIONS

It is impossible to discuss all corollaries of the new concept of brain functions in this short review. Only major logical questions arising from the above- stated considerations are broached below:

Why did the classical concept of brain functions survive for so long?

What are the nearest objectives of switching system neurobiology to the new concept of brain functions?

How do we understand the relationship between the structure and function in systems that are multifunctional by their nature and possess such a unique feature as multiple realizability?


It is probably better to leave a detailed answer to the first question to historians. In this paper, it is only necessary to note that the creation of the new concept of brain functions required putting together many notions like the model, the controller, initiating and informational signals, the hierarchy, the network computational principle, learning, optimality, etc. Exclude one of these notions, and the new concept of brain functions cannot be built as a unified complete system. Several good ideas like “acceptor of action,” re-efference, and model of the result, which were pioneering for their times but did not lead to the creation of a new integral system of views on the brain, are examples of this [43-45]. It is also necessary to add to the above that the creation of the new concept required analysis of a large volume of new scientific data that simply did not exist several decades ago.

To answer the second question, let us go back to the examples of applications of the new concept of brain functions described in the “Examples of applications of the new concept” section. Those applications resulted from reinterpretation of the existing scientific data. It gives hope that, using this approach and taking into account the huge volume of already accumulated information, we will be able to make significant progress in our understanding of the brain without conducting additional experiments. Those examples show what should be the focus of attention in a theoretical analysis of various brain systems. Identification of the NOCSs, their COs, and the semantics of signals arriving at the system and leaving it are the starting point for such analysis. At the same time, it is necessary to recognize that a part of the accumulated information (probably, quite substantial) will turn out to be uninterpretable. I came across this while working on the above-mentioned examples, and am writing about this for those who decide to conduct such theoretical analysis. They should also be ready for this. Knowing what to pay attention to, while working with the literature, will allow one to separate effectively useful information from a byproduct. The reason for this is the fact that the experimental problems were formulated within the framework of the classical concept of brain functions, and the results obtained may not contain the information necessary for applying the new concept.

Among the immediate goals of theoretical analysis, the creation of simplified computer simulations to explain the basic principles of functioning and pathology of neural networks should be mentioned. Complex computer models based on the new concept of brain functions are not possible yet and even seem unnecessary. The respective models can demonstrate simple analogies of how brain phenomena should be interpreted based on the new concept. For example, well-systematized symptoms of various brain disorders are the foundation of neurology and psychiatry. This foundation is broadly used for differential diagnostics, while the mechanisms of the symptoms remain mostly unknown. Only computer simulations can bring an understanding of the symptom mechanisms in brain pathology.

The majority of scientists working in the field of system neurobiology are experimentalists, and it is very important for them to realize what makes and what does not make sense in continuing studies in behavioral experiments within the framework of the new concept of brain functions. To give a universal recommendation for this issue is impossible, although it is possible to give examples of what problems are correct, what problems are incorrect within the framework of the new concept, and what can be achieved with mild modifications of the experiments. Minor complications of the experimental paradigms allowing one to analyze neuronal activity in the studied system during behavioral errors evoked by perturbations induced by the experimenter make sense within the framework of the new concept of brain functions, because the obtained data will allow one to reveal the semantics of signals and the part of the system that processes error signals. The latter is necessary for subsequent studies of learning mechanisms in this system.

On the contrary, investigation of neuronal populations during one behavior or another and performing various mathematical operations with the parameters of their activity to reveal correlations between the population behavior and behavior of the CO may be of doubtful value within the framework of the new concept of brain functions. The following is the reason for this. It is known from neurocomputing that knowledge of behavior of neuronal elements does not allow researchers to make conclusions about functions computed by the system. The relationship between micro- and macro- parameters in the network structures has not been found yet, and there is no hope that this relationship will be found (if we take into account the multiple realizability in neural systems; see below). It is necessary to add to the above that an animal in behavioral experiments usually performs a certain fixed learned function, and this function is only a small part of the possible behavioral repertoire of the studied animal (in other words, only one of a huge set of functions computed by a given NOCS). Population studies give information on localization of the function in the brain; however, such information can quite often be more easily obtained.

The answer to the third question, how to understand the relationship between the structure and function within the framework of the new concept of brain functions, is the most unexpected and shocking to specialists with classical medical or biological education. But before switching to it, let us go back to the earlier-mentioned term “multiple realizability.” This term means that the same computation may be implemented in different ways within the same network. There are many proofs of multiple realizability in the brain. For instance, the locomotor rhythm generation in the spinal cord of the chick embryo can be based on different mediator mechanisms [46]. A spontaneous locomotor rhythm disappears after blocking one type of mediator transmission or another, but it reappears in 30 to
90 min despite the fact that the blocking agents are still doing their job. In philosophy, multiple realizability is used as an argument in favor of the point of view that the brain is not completely cognizable. Supporters of the opposite point of view, which got the name “ruthless reductionism,” believe that the phenomena of memory, consciousness, and attention should be described in the terms of cellular and molecular mechanisms [47].

Let us remember what is any NOCS that we want to study. Its functioning results from continuous learning in the course of ontogenesis, i.e., from optimization. It is also necessary to add that any NOCS of interest in each animal species underwent the process of structural optimization in the course of phylogensis. A “well-learned” automatism is optimal or suboptimal. The studied NOCS stores information on how to execute one or another automatism from a quite large set of those already learned. Therefore, knowing that the NOCS moves its CO along an optimal trajectory, it is possible to formulate an inverse problem. Based on the CO properties and its optimization criteria, it is possible to compute the optimal trajectories for this object and the necessary controls. It is understandable that the CO may not necessarily be a physical object. It can be abstract and move in an abstract state space, which occurs during planning and thinking. Knowledge of the optimal trajectories and controls for the CO will allow one to study what computations should be performed by NOCS and its functional blocks to move the CO along optimal trajectories. Only after this it is possible to analyze what neural networks, and with what architectures, are able to perform the necessary computations and work with corresponding classes of functions, and whether the networks of interest are capable of performing these computations or not. Analysis of this type will give answers to questions related to encoding of the CO state, role of the network topology, and properties of individual neurons and other parameters of the network in its capability of performing necessary computations. This approach to understanding the structure through the function will require very intense theoretical analysis and computer simulations. New branches of mathematics will be created, and special attention will be paid to revealing properties of the COs at various levels (in other words, to revealing with what abstractions one hierarchical level or another in the nervous system is working and what optimization criteria are applicable to these COs). It is obvious that this new approach might become possible only after corresponding changes in education and financing in neurosciences.

Undoubtedly, a “bottom-up” approach will be also used to understand the computational capabilities of biological neural networks. A very simple logic may be behind this. If we know the components, we can put together the entire picture. For example, EPSPs and IPSPs are the simplest operations of summation and subtraction. Axo-axonal synapses responsible for presynaptic inhibition can be considered the basis for multiplication and division, and the analysis of dendritic bifurcations makes it possible to find analogies for logical operations “and,” “or,” etc. A network reconstructed this way may then be analyzed for the purpose of revealing its computational capabilities by using computer simulations. However, it is necessary to note that this approach, most probably, is destined to fail. In the case of complex networks, there are always numerous unaccounted parameters, and everyone who carries out computer simulation experiments knows well that unaccounted parameters lead to serious errors. The incomplete observability of biological neural networks is the main reason for the existence of unaccounted parameters. For instance, a prevailing part of computations in biological neural networks is realized at the level of dendrites and synapses localized on the latter. Such structures (cellular compartments), because of their colossal number, are a typical example of an incompletely observable object. Let us add to this the above- mentioned neural network properties, namely multifunctionality and multiple realizability, and it will become once and for all clear why it is necessary to be very cautious with the “bottom-up” analysis. However, elements of this analysis may be useful for the “top-down” analysis, by helping to better understand what computations can be performed by individual subnets of the network of interest.

It is obvious that the basic ideas of the new concept of brain functions are applicable to other systems built according to the network principle. Examples of such systems can be found everywhere, from molecular networks of intracellular control to social systems. But these applications await further research.

My primary thanks go to P. Pomeroy, Vice-President of Neurosciences at the St. Joseph’s Hospital and Medical Center, for his support of my theoretical research. I am also very grateful to collaborators of my former Department of Physiology of the Spinal Cord in the Bogomolets Institute of Physiology of the National Academy of Sciences of Ukraine (Kyiv), with whom experimental studies on the CPG problem were carried out until 1992, and whose contribution led to solution of this problem. Furthermore, I am grateful to Dr. V.K. Berezovskii and Dr. R. Dhall for their useful comments during the preparation of this manuscript.

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