Mathematical biophysics of color vision: III. Color constancy

A mechanism is presented which can account for certain aspects of the phenomena of color constancy. The mechanism involves interaction between a given region and the remaining field. Each region is represented by a color center having the structure previously introduced (Landahl, 1952,Bull. Math. Biophysics,14, 317–25) to account for a number of phenomena of color vision. The trichromatic, symmetric mechanism is introduced for simplicity. The interaction is such that collaterals from each of the primaries representing the background send elements to each of the centers corresponding to the primaries representing the spot. However, the collaterals impinging upon unlike centers are excitatory while the collaterals impinging on like centers, corresponding to the same primary colors, are inhibitory. With proper choice of coefficients, the result is that for small changes in illumination, the resulting apparent color is unchanged. However, for greater changes in the color of the illumination, there results a distortion of the apparent color. A number of examples are illustrated numerically. This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

Some conditions for sustained oscillations in biochemical chains with feedback inhibition

A chain ofn reactions is considered in which the last substance inhibits the production of the first with degreep, p being the order of the inhibition. Maintained oscillations are possible for certain values of the parameters under the following conditions: (1) If there is no time delay, then there must be at least three compartments (n=3) and either the degree of inhibition is sufficiently large (p>8 forn=3) or there must be enzymatic removal from the first compartment, in which casep≥1. (2) If there are time delays, but there is no enzymatic removal, the degree of the inhibition must be greater than or equal to 2 for any value ofn. (3) If there is a time delay in addition to enzymatic removal, one compartment with simple first order inhibition is sufficient. Conditions on the parameters necessary for maintained oscillations are given for many of the cases discussed.     

Note on the Donnan equilibrium

The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.     

Structural coupling of the EF hand and C‐terminal GTPase domains in the mitochondrial protein Miro

Miro is a highly conserved calcium‐binding GTPase at the regulatory nexus of mitochondrial transport and autophagy. Here we present crystal structures comprising the tandem EF hand and carboxy terminal GTPase (cGTPase) domains of Drosophila Miro. The structures reveal two previously unidentified ‘hidden’ EF hands, each paired with a canonical EF hand. Each EF hand pair is bound to a helix that structurally mimics an EF hand ligand. A key nucleotide‐sensing element and a Pink1 phosphorylation site both lie within an extensive EF hand–cGTPase interface. Our results indicate structural mechanisms for calcium, nucleotide and phosphorylation‐dependent regulation of mitochondrial function by Miro.     

On the effects of a constant sub-threshold conditioning stimulus upon the response to a constant current test stimulus

The strength of a test stimulus, which is just adequate to produce a response after a sub-threshold conditioning stimulus, is calculated on the basis of Rashevsky's two-factor theory as a function of the strength and duration of the conditioning stimulus. The results are compared with available data for one of a family of curves and found to be in satisfactory agreement.     

A mathematical model for the temporal pattern of a population structure,with particular reference to the flour beetle

Equations are derived to represent the time course of the population numbers of the various stages of the flour beetle. The assumption of constant duration of the life stages and the absence of delayed effects leads to equations from which the various population numbers can be calculated in terms of the parameters of the system. Formulae are given for the estimation of many of the latter from observations on population numbers. Calculations show that the principal features of the observed changes in population structure can be accounted for on the basis of a simple model in which it is further assumed that each interaction is proportional to the product of the numbers of the two given interacting stages. A more detailed analysis may require secondary interaction coefficients. Suggestions for estimation of such coefficients are given.     

A mathematical analysis of elongation and constriction in cell division

An equation for the rate of elongation of a dividing egg is integrated and generalized. The rates of elongation and constriction of a number of eggs under various conditions are analyzed and compared with the theoretical predictions. The theory accounts rather well for a large body of data on elongation and constriction. The general shapes of the elongation and constriction curves are predicted and the orders of magnitude of the parameters are satisfactory. One of the parameters for the elongation curves is related theoretically to the parameter of the constriction curves, and the correct order of magnitude is obtained if one parameter is predicted from the other.     

On the relationship between response time and dosage of a drug as a function of its mode of entry

Theoretical studies have been carried out to determine the effect of the route of entry and the temporal sequence of dosage on the response. On the basis of continuity equations applied to a schematized system, equations relating the dosage and response time have been derived for some special cases, and the form of this relatinship is discussed. This paper is based in part on work done for the Office of Scientific Research and Development under Contract NDCrc-132 with the University of Chicago.     

A statistical consequence of the logical calculus of nervous nets

A formal method is derived for converting logical relations among the actions of neurons in a net into statistical relations among the frequencies of their impulses.     

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.