Review of the monograph by S.I. Fokin “Mathematical model of a neuron. Derivation of the basic psychophysical law for the receptor level”

In the monograph reviewed, S.I. Fokin’s mathematical model is presented which characterizes quantitative relationships between stimuli and responses values during the transition from the macro level of the whole organism to the micro level of a sensation forming. A stimulus transformation into a frequency of primary receptor neurons action potentials is described mathematically. Moreover, the model explains differences between stimulus-sensory curves in individuals with strong and weak nervous systems to be due to differences in physiological properties of their primary neuron receptors. Fokin’s calculation formulas have been confirmed in experiments made in the auditory sensory modality. The model suggested has an undeniable novelty for psychophysics and psychophysiology. It deserves the attention of a wide range of scientists.

Introduction

In psychophysics, functions are known that describe quantitative relationships between stimuli and responses values. They are: G.T. Fechner’s logarithmic law, S.S. Stevens’ power law and the variants of the generalized psychophysical law (Ekman, 1959; Zabrodin, 1976). In the S.I. Fokin’s monograph the author’s attempt is made to characterize such relationships during the transition from the macro level of the whole organism to the micro level of a sensation forming. In this sense, the book reflects an important stage of such a transition and has an undeniable novelty. The stage of a stimulus transformation into a sensation at the level of primary receptor neurons, which takes place in sensory system of any modality, is considered. Therefore, the new theoretical regularities obtained by the author can manifest themselves in various sensory systems to one degree or another.

When developing his model, the author uses the known mechanisms of action potential formation in a nerve cell and the electrical circuit of its membrane, proposed by A. Hodgkin and A. Huxley (Hodgkin, Huxley, 1952). However, their empirical formulas, which describe the electrical parameters of the action potential in the general form, are not used by the author. Instead, Fokin derives his formulas for the special case of a psychophysical experiment and physiological parameters of a neuron. At the same time, it turns out that the relationship between the magnitude of the stimulus and the frequency of action potentials, generally speaking, is not monotonic and may have a maximum under certain neuron parameters, which are typical for individuals with a weak nervous system. The author shows experimental confirmations of the sensation magnitude encoding by the frequency of action potentials registrated in primary receptor neurons (Ratanova, 2008).

However, it should be noted that such “additive” coding (when the sensation magnitude increases during the stimulus magnitude increasing) is observed not for all object features (types of stimuli), but for most of them which Stevens called “quantitative” (“prothetic”) ones. These are: intensities (brightness, loudness, heaviness, strength of smell or taste), as well as a number of spatial and temporal characteristics. In contrast, in the case of “qualitative” (“metathetic”) features (color, pitch, line orientation and some others), the coding occurs according to the “substitution” principle: by channel number (when the stimulus magnitude changes, the previous neural elements are replaced by others). With regard to “quantitative” types of stimuli, Fokin reasonably assumes that the “saturation effect” in individuals with a weak nervous system, discovered in numerous psychophysical experiments by foreign and domestic researchers (Petrie, 1960; Ilyin, 2004; Ratanova, 2008), can be formed at the receptor level initially, but not in the higher parts of the brain, as previously proposed in A. Petrie’s “filter theory” (Petrie, 1960). Experimental confirmation of this hypothesis can be obtained by comparing the dynamics of action potentials frequency, registrated in receptors of “quantitative” sensory modalities primary neurons, with evoked potentials in the corresponding areas of the cerebral cortex.

The adequacy of the author’s mathematical model is also supported by the results of calculations, which explain the psychophysical phenomenon described by “cross” behavior of stimulus-sensory curves in individuals with strong and weak nervous systems (according to I. P. Pavlov’s classification), due to differences in the physiological properties of their primary neuron receptors. Thus, there is a suggestion that there is a physiological basis for psychological manifestations of strength or weakness in the nervous system. This would be a significant interdisciplinary scientific achievement if experimentally confirmed at the microscopic level. Fokin’s calculation formulas describing the relationship between stimulus intensity and the frequency of action potentials recorded in primary receptor neurons have been experimentally confirmed at the macro-level of the body through psychophysical dependences “stimulus intensity-strength of sensation”, which were obtained, in particular, for the auditory sensory system. A characteristic “cross” behavior of the corresponding curves has been found in both the strong and weak nervous systems, both in theory and in experiment (Ratanova, 2008).

I have repeatedly gotten acquainted with S.I. Fokin’s main works on the topic of his monograph and, for good reason, expressed my opinion on the possibility of presenting them at conferences and seminars held afterwards. The materials in Fokin’s monograph are presented consistently and logically, and deserve the attention of a wide range of scientists. I can say this first of all in relation to psychophysics, a the field I know professionally.

References

1. Ekman, G. (1959). Weber’s law and related functions. The Journal of Psychology, 47(1), 343–352.
2. Fechner, G. T. (1860). Elemente der Psychophysik. Breitkopf und Härtel.
3. Fokin, S. I. (2024). Mathematical model of a neuron. Derivation of the basic psychophysical law for the receptor level. MAKS Press.
4. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500–544. https://doi.org/10.1113/jphysiol.1952.sp004764
5. Ilyin, E. P. (2004). Psikhologiya individual’nykh razlichiy [Psychology of individual differences]. Piter.
6. Petrie, A., Collins, W., & Solomon, P. (1960). The tolerance for pain and for sensory deprivation. The American Journal of Psychology, 73(1), 80–90. https://doi.org/10.2307/1419118
7. Ratanova, T. A. (2008). Psikhofizicheskoe shkalirovanie. Sil’ oshchushcheniy, sila nervnoy sistemy i chuvstvitel’nost’ [Psychophysical scaling. Strength of sensations, strength of the nervous system and sensitivity] (2nd ed.). Moscow Psychological and Social Institute; MODEK.
8. Stevens, S. S. (1957). On the psychophysical law. Psychological Review, 64(3), 153–181.
9. Zabrodin, Y. M. (1976). On the scope of psychophysics: Some methodological considerations. In H.-G. Geissler & Y. M. Zabrodin (Eds.), Advances in psychophysics (pp. 15–42). VEB Deutscher Verlag der Wissenschaften.