Contributions to the theory of active transport

A system consisting of two solutions separated by a membrane may be in one of four possible states: (1) transient, (2) steady, (3) equilibrium, or (4) pseudo-equilibrium. The latter state denotes that in the solutions the net flow of all components is zero but at least one of the components is not in thermodynamic equilibrium. Transient and steady-state systems may or may not have active transport. Thus only systems in either equilibrium or pseudo-equilibrium are considered in this paper, since the former indicates that there is no active transport, whereas in the latter case there always is active transport. This simplifies the problem of finding whether a system does or does not have an active transport mechanism, since it is frequently fairly easy to determine experimentally whether a system is in equilibrium or pseudo-equilibrium. The assumption that electric neutrality exists within very thin membranes is shown not to be valid. However, electric neutrality does exist in the solutions in a system in a pseudo-equilibrium state with fixed charges and impermeative ions. It is then shown how the presence and sign of an electric potential may be found by use of electroneutrality. The mechanism of active transport may be due to a general force acting on all particles of a particular component or to an individual force acting on the individual particles of a particular component. A general solvent flow or a diffusion drag force illustrates the first mechanism while the second is accomplished by either a carrier or a Maxwell Demon. The general type of active transport has been extensively treated in the literature, while the individual type has not been treated in a generalized form. Therefore, the individual type of active transport is discussed at length, and a simple illustrative model is intensively analyzed. Following this, there is a discossion of the Maxwell Demon and some models of it are presented. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600) 1454.     

A model for conditioning and the effect of spaced trials in learning

A mechanism is suggested in which a postulated substance can enter a synaptic region only during the simultaneous action of a conditioned and an unconditioned stimulus. If this substance remains and produces a physico-chemical change, then a consequence is that the degree of learning will depend on the spacing of conditioning trials and the time constant of the process will be related to the rate of diffusion or transport of the substance along the axon. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF 49(638)-414.     

On the interpretation of the effect of area on the critical flicker frequency

The effects of area and intensity on the critical flicker frequency, threshold, and reaction time are considered in terms of neural net theory. An attempt is made to develop a mechanism which can account for the phenomena associated with the empirically observed laws of Ricco, Granit, Talbot, and Ferry-Porter as well as observations on reaction time and threshold. A simple model gives results which are substantially in agreement with observation except for a few apparent discrepancies. Experimental procedures are suggested which can determine whether these are apparent or real. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

The derivation of D’Arcy Thompson’s theory of transformations from the theory of optimal design

It is shown informally that Cohn’s theory of Optimal Forms can be construed as a comparative theory, and that when this is done the celebrated theory of transformations of D’Arcy Thompson follows as a consequence. The implications of this type of theoretical foundation for the Thompson theory with regard to problems of comparative morphology are discussed, and some suggestions for the further implementation of the theory are described. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

On the biophysics of vision

A photochemical system is considered which is similar to that of S. Hecht but which includes an intermediate substance between visual purple and visual white. This intermediate is assumed to change the embrane voltage of the photoreceptors. A simple model is presented from which one may calculate the frequency of the impulses resulting from the application of light. It is found that this physicochemicai model enables one to account for a considerable number of physiological phenomena of vision. Among these are the light and dark adaptation phenomena. By introducing a simple assumption regarding spatial interaction one can account for some psychological phenomena such as the effect of intensity, light-dark ratio, shape, and area on the critical flicker frequency. A number of other phenomena are discussed in terms of the model. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Factors in visual acuity: I. Neural inhibition and the visual perception of contours

Interpretations of the mechanisms of perception of contours or of Mach bands have stressed either the role of various spatial derivatives of light intensity at the retina or the importance of various forms of inhibitory effects between neighboring retinal elements. Evidence is presented here in support of the latter type of interpretation. It is considered that the brightness contrast and perceived contours arise from neural elements, each of which is stimulated in proportion to the intensity of photo-receptor excitation at a point of the retina and inhibited in proportion to the mean intensity in some neighborhood of that point. The role of the spatial derivatives is best seen as a particular manifestation of the inhibitory mechanism. Predictions based upon this hypothesis appear to be consistent with experimentally observed evidence. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18(600)-1454. Reproduction in while or in part is permitted for any purpose of the United States Government.     

On visual adaptation: I. Photochemistry

Quantitative aspects of the photochemistry of visual adaptation are considered. A simplied model is given that fits data on changes of rhodopsin concentration during and following strong illumination. A variation on Wald’s compartment hypothesis is shown to fit the quasilinear dependence of log threshold upon pigment concentration. Finally, there is a brief review of pertinent data on cone pigments. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414, and in part by the United States Public Health Service Training Grant 2G-833.     

On visual adaptation: II. The electroretinogram and the bipolar cells

First a model for theb-wave of the electroretinogram is given. The essential part of the model is the diffusion into the rod-bipolar synapse of a transmitter substance, followed by the induction of an inhibitor. Making use of this model, adaptation to an illumination too weak to cause of significant decrease in the concentration of visual pigment is interpreted as due to a decreased effectiveness of the rod impulse in exciting the bipolar cell. The disparity between threshold changes for very small test spots and for relatively large spots is explained simply, without invoking any additional physiological mechanisms. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414 and in part by the United States Public Health Service Training Grant 2G-833.     

A neural net model for escape learning

An escape learning situation is discussed in terms of a neural model in which a stimulus can result in a conditioned excitement and a specific conditioned response. By using the simplest relations between the strengths of conditioning and the number of reinforcements and by introducing a distribution of fluctuations occurring regularly in time, one can calculate the probabilities of various responses, as well as the various latencies, in successive trials. The results are in moderately satisfactory agreement with the data of R. L. Solomon and L. C. Wynne (Psychol. Monogr.,67, No. 4, 1953). Consequences of the model for various experimental situations are discussed. This research was supported in part by the United States Public Health Service Grant RCA GM K6 18,420 and in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Grant No. AF AFOSR 370-64.     

An avoidance learning situation. A neural net model

A simple avoidance situation is considered in terms of a neural net learning model. Data for the control situation can be represented by an expression having three parameters which determine the initial and the steady state activities together with the transient aspects. The introduction of a learning parameter then allows one to calculate satisfactorily the results obtained in the experimental situation in which shock is applied. This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Grant No. AF AFOSR 370-63 and in part by the United States Public Health Service Grant RCA GM K6 18,420.     

A mathematical interpretation of motor reactions to fixed and moving stimulation of the eye

The results of experiments performed by L.S. Stone and by R. W. Sperry on vision in salamanders are analyzed. A summary of Reichardt's theory, which originated in the researches of B. Hassenstein on insects, is given, and an application to salamanders is carried out. Introducing a simpler mathematical development based on the onefactor theory of excitation, the same formal results are obtained. A complete model, which includes those results and tries to fit the salamander behavior described by stone, is elaborated and translated into Boolean terms. As a complementary consideration, it is pointed out that the functional rigidity of the visuomotor system, deriving from a biological molecular hysteresis, could be framed in theneuro-affinity principle, the spatial expression of which would turn out to be abiological field. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Decision equation for binary systems. Application to neuronal behavior

Summary The exact mathematical treatment is given for a non linear equation describing the delayed yes-or-no response to a binary system to external stimulations, in some typical cases of interest. Comparison is made with neurophysiological data on the frequency rate of firings of stimulated neurons; the same equation, however, can be conceivably applied to a vast variety of phenomena. The procedures followed to solve the problems that arise in connection with this equation could be extended to more general types of non linear equations.The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research under Contract no. AF EOAR 65-44 through the European Office of Aerospace Research, OAR, United States Air Force.     

Representation of modality in cutaneous sensibility

Morphologically identical nerve endings subserve more than one sensory modality. Two possible explanations are: such endings are functionally different, responding to one type of physical excitation only, or such endings are capable of responding to more than one type of physical stimulus, but central mechanisms discriminate between different stimuli. A simple network is described to illustrate how thermal receptors could discriminate between thermal and mechanical stimuli. This research was supported in part by the United States Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

On the role of chemical systems in the microphysical aspects of primary genetic mechanisms

It is pointed out that two fundamentally different views of primary genetic processes occur in the literature which are frequently confused. The first is a true communication-theoretic view, which regards the genetic apparatus as containing a real information-source and a transducer which converts that information to useful form. The second view is generally expressed as a template scheme based on the Watson-Crick model; it is shown that in this model there is actually no such thing as genetic information in a communication-theoretic sense. Both views are then discussed on the basis of microphysical principles developed in previous work of the author (Bull. Math. Biophysics,22, 227–255, 1960) in an attempt to find which approach is in closer accord with the biological facts. It is shown that, if the communication-theoretic view is correct, then the information-bearing object must act as a “catalyst,” but it is pointed out that the type of catalysis involved must be of a fundamentally different nature than that occurring in familiar enzyme-catalyzed reactions. On the basis of general considerations of irreversible changes in microphysical measuring systems, it is shown that any type of template must suffer a gradual and irreversible denaturation, which seems to make it unlikely that a template could play a primary role in fundamental genetic processes. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract AF 49(638)-917.     

Man/machine interaction in adaptively controlled experimental conditions

Systems in which a human subject interacts with an adaptive control mechanism through display and response facilities are examined. A cybernetic model is discussed, together with supporting experimental data. The research reported in this paper has been supported by the Air Force Office of Scientific Research, under Contract AF. 61.052.640. (for Cybernetic models for learning) and by the Aerospace Medical Research Laboratories A.F.C.S., under contract AF. 61.052.402. (for adaptive teaching systems), through the European Office for Aerospace Research.     

Brain and physics of many-body problems

Summary On the basis of a recent physical theory of many-body problems developped in our Institute, a model of the brain is formulated, and it is shown how some of its typical features, such as learning and memory processes, find therein a natural and simple explanation. In the Appendix a short surview of the necessary mathematical formalism is finally given.A brief outline of the model presented in this paper was unformally given by one of the authors (L.M.R.) at the I.S.P. Neurosciences Research Program; Boulder Colorado, in July 1966.This work has been sponsored in part by: Air Force Avionics Lab., Research and Technology Div., Wright Patterson Air Force, Air Force System Commend-U.S.A.F.-Government of United States of America. Contract No. AF 33(615)-2786.     

A contribution to the study of diffusion of neutral particles through pores

Diffusion through a flat pore into a large open region is proportional to the linear dimension of the pore and not to its area. This was first explained by Brown and Escombe (1900) for a circular pore and is here generalized, by means of a dimensional argument, to include any type of regular opening. The problem is further generalized to include diffusion through pores of finite thickness, finite distance apart, and into finite regions. Since this problem cannot be solved exactly, an approximation method is introduced. Reasons for the credibility of the approximation are presented. It is then shown, by means of the approximation method, that the diffusive flow through a pore is equal to the total concentration difference divided by the resistance of the system. The resistance, in turn, is the sum of the resistances of all portions of the system, each of which is calculated. The result is compared with results which have been calculated exactly for limiting cases and found to agree very well. The results are then applied to a standard method of computing pore size in membranes, and it is shown that the correction factor is negligible. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 49(638)-414. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Electron microscopic observations on the reactional changes occurring in insect nerve fibers after transection

Summary An electron microscopic study of the interganglionic connectives of an orthopteran (Laplatacris dispar) demonstrated that a reaction starts in the sectioned fibers very soon after transection (30 minutes). This reaction is closely similar to that observed in sectioned nerves of vertebrates and consists in the appearance of microvesicles and the proliferation of mitochondria. Sectioned connectives were studied from 30 minutes to 88 hours after section. The reaction mentioned increases progressively during the indicated lapse of time.This research was supported by the United States Air Force under Contract No AF 49 (638) 585 and Grant Af 61-64, monitored by the Air Force Office of Scientific Research, Air Force Research Division of the Air Research and Development Command.     

On some distribution functions for non-linear switching elements with finite dead time

Summary The output distribution function of a non-linear switching element with a Poissonian sequence of impulses at the input is calculated by a straightforward method. The dead time of the element is taken into account. Some limiting properties of this distribution and its mean value are studied.The present research has been sponsored in part by the Air Force Avionics Lab., Research and Technology Div., Wright-Patterson Air Force, Air Force System Command — U.S.A.F. — Government of United States of America, Contract no. AF 33(615)-2786.     

Color perception using a single cone type with distributed maximum sensitivity

This paper proposes a model for color perception which accounts for variations in the dimension of the space of perceived colors. The model assumes that there is only one type of cone with only one shape of response curve, but that different cone's response curves differ by translation. It also assumes that the final discrimination system, learned from originally random connections, maximizes discrimination in the normal visual environment. Learning mechanisms are discussed, and the form which the final discrimination system ought to take is plausibly derived. An algorithm for the tristimulus curves is obtained from this model, and it is shown that a good fit of the empirical data can be obtained. This work was supported by the Air Force Systems Command, United States Air Force, Contract No. AF33(657)-8681.