A contribution to the mathematical biophysics of psychophysical discrimination III

The neural mechanism previously discussed is further generalized. The case is considered in which a random variation is associated with each stimulus. The mechanism is generalized and equations are derived for discriminations between stimuli differing in several modalities. The latter indicates an analysis by the factor method. Suggestions are made in connection with the use of triads and with the problem of a multidimensional psychophysics.     

A kinetic theory of diffusion forces in metabolizing systems

The development of a molecular theory of the diffusion drag forces in liquids is attempted by considering the liquids as limiting cases of very dense gases. An expression is derived for the force on a small particle suspended in a nonuniform mixture of such gases on the basis of kinetic theory. Another expression for the order of magnitude of the force on a larger particle is obtained by introducing certain hydrodynamical considerations. These results are compared with an expression previously derived by N. Rashevsky, and estimates are made of the order of magnitude of the volume force on the granules and particles within a typical cell due to the diffusion of metabolites. It is found that the drag forces, exerted by a diffusing solute, depend to a very large extent on the physical properties of the solvent.     

A physicomathematical model of sodium balance

A model is introduced in which the reabsorption of sodium is governed by an enzymatic process. This process is in turn assumed to be influenced by the extracellular volume which depends on the amount of sodium in the body at a given time. The model allows for damped oscillations when the sodium intake lies within range of values and thus can account for observed oscillations. This investigation was supported by the U.S. Public Health Service (grants 5-K6-GM-18, 420 and A-4668), and by a grant from the Dr. Wallace C. and Clara A. Abbott Memorial Fund of the University of Chicago.     

A note on A theoretical mechanism to represent the kinetics of some alkaline phosphatases

If an enzyme acts in a manner somewhat different from that generally considered, it may appear to act as a pair of enzymes. This similarity may remain after various changes in the solution such as activation by magnesium ions. Conditions are given under which this type of activity may be differentiated from that of the enzyme pair. Some alkaline phosphatases exhibit the type of time course of hydrolysis under consideration. Available data do not eliminate the possibility that some alkaline phosphatases act in the manner here suggested.     

A note on neural nets

A neural mechanism is described which provides for a perception which is invariant with respect to movement of the stimulus.     

Equilibrium shapes in non-uniform fields of concentration

The special case of a metabolizing cell, with infinite permeability, suspended in the field of an equivalent cell is treated exactly to determine its equilibrium shape for small deformations. It is found that flattening takes place along the line of centers.     

On the spread of information with time and distance

The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.     

On the mechanism of transport of proline in the ciliary body,optic nerve and choroid plexus

An analysis of available data on proline transport in several tissues indicates that a single saturable active transport mechanism, together with a passive process, is not able to account for the data available. Introduction of a parallel transport mechanism which is not saturated below 50 mM, makes it possible to give a reasonably satisfactory account of the available data, from the three tissues, on (1) initial rate of uptake as a function of external concentration and (2) the uptake as a function of time. If the two transport mechanisms occur in two different types of cells, it is possible not only to account for the above two sets of data, but also to account reasonably well for the efflux data. While the model predicts more rapid efflux of tracer into a higher external concentration as found experimentally, an attempt was not made to account quantitatively for all four sets of experiments simultaneously. For the three tissues, the root mean square of the relative error for the 24 data points available from the three different experiments, covering a range of values of concentration of 0.1 to 50 mM, a time range of 0.17 ao 240 minutes, are respectively 5.8, 13 and 9.6%.