Mathematical biophysics of color vision

A neural mechanism is studied in which three primary receptors interact in such a manner that only a small region is in activity for a given colored stimulus. The similarity to the color triangle is noted. The introduction of an additional primary receptor may or may not change the dimensionality of sensation space in this mechanism. Problems of discrimination of color, absolute judgment of saturation, and hue are discussed.     

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.     

On the biophysics and kinetics of toehold-mediated DNA strand displacement

Dynamic DNA nanotechnology often uses toehold-mediated strand displacement for controlling reaction kinetics. Although the dependence of strand displacement kinetics on toehold length has been experimentally characterized and phenomenologically modeled, detailed biophysical understanding has remained elusive. Here, we study strand displacement at multiple levels of detail, using an intuitive model of a random walk on a 1D energy landscape, a secondary structure kinetics model with single base-pair steps and a coarse-grained molecular model that incorporates 3D geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Two factors explain the dependence of strand displacement kinetics on toehold length: (i) the physical process by which a single step of branch migration occurs is significantly slower than the fraying of a single base pair and (ii) initiating branch migration incurs a thermodynamic penalty, not captured by state-of-the-art nearest neighbor models of DNA, due to the additional overhang it engenders at the junction. Our findings are consistent with previously measured or inferred rates for hybridization, fraying and branch migration, and they provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.     

On the vision of insects

Summary The resolving power of the insect eye in both time and space, as well as the perception of wavelength and plane of polarization, have been the topics of numerous investigations employing diverse methods. Here we sketch some milestones on the path to our present knowledge.Dedicated to Prof. H. Autrum, on the occasion of his 70th birthday Acknowledgement: Many of us are grateful for the collaboration ofCalliphora erythrocephala in answering so many of our countless questions     

Leukocyte biophysics

The biophysical properties of leukocytes in the passive and active state are discussed. In the passive unstressed state, leukocytes are spherical with numerous membrane folds. Passive leukocytes exhibit viscoelastic properties, and the stress is carried largely by the cell cytoplasm and the nucleus. The membrane is highly deformable in shearing and bending, but resists area expansion. Membrane tension can usually be neglected but plays a role in cases of large deformation when the membrane becomes unfolded. The constant membrane area constraint is a determinant of phagocytic capacity, spreading of cells, and passage through narrow pores. In the active state, leukocytes undergo large internal cytoplasmic deformation, pseudopod projection, and granule redistribution. Several different measurements for assessment of biophysical properties and the internal cytoplasmic deformation in form of strain and strain rate tensors are presented. The current theoretical models for active cytoplasmic motion in leukocytes are discussed in terms of specific macromolecular reactions.     

Mathematical biophysics of color vision II: Theory of color changes induced by the alternation of colors at various frequencies.

A model previously introduced to account for a number of phenomena of color vision is studied for the conditions in which the alternation of colors is periodic. The case of three primary receptors having no differences in their time constants is considered for the situations such as the temporal alternation of two primaries, a primary and a neighboring binary, a primary and white, a binary and white, etc. Using the same mathematical model which was used to account for the enhancement effect of interrupted illumination, it is found possible to account for observed changes in hue in a qualitative manner. A method is suggested for measuring the color changes quantitatively. This method is readily adapted for demonstration purposes. The model shows that there should be differences between “primaries” and “binaries” with respect to change in hue. In principle, therefore, comparison between theory and experiment should yield information regarding the physiological primaries. 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.     

On the work of the developmental biophysics laboratory of the embryology department of Moscow State University

The laboratory is engaged in morphomechanics—the study of self-organization of mechanical forces that create the shape and structure of the embryonic primordia. As part of its work, the laboratory described pulsating modes of mechanical stresses in hydroids, identified and mapped mechanical stresses in the tissues of amphibian embryos, and studied morphogenetic reorganization caused by the relaxation and reorientation of tensions. The role of mechanical stresses in maintaining the orderly architectonics of the embryo is shown. Mechano-dependent genes are detected. Microstrains of embryonic tissues and stress gradients associated with them are described. A model of hyper-recovery of mechanical stresses as a possible driving force of morphogenesis is proposed.     

Mathematical biophysics of growth

The rate of growth of a tissue is studied mathematically in its dependence on the metabolism of the cells. A high glycolytic coefficient, which facilitates cell division, as has been shown before, does in this way also increase indirectly the rate of growth of the tissue. There is however also a possible direct effect of glycolysis on the rate of growth, which is also studied analytically. Equations are derived, giving the total rate of growth of a tissue in its dependence on the glycolytic coefficient.     

Mathematical biophysics of the galvanic skin response

Beginning with Rashevsky's equation for the development of the excitatory state in a nerve fiber, an equation for the change in skin resistance upon the presentation of an instantaneous stimulus is derived. The mechanism assumed is in conformity with the existing evidence of neuro-physiology. Certain deductions from the equations are made and experimental problems suggested for testing the theory.     

On the biophysics of cathodal galvanotaxis in rat prostate cancer cells: Poisson-Nernst-Planck equation approach

Rat prostate cancer cells have been previously investigated using two cell lines: a highly metastatic one (Mat-Ly-Lu) and a nonmetastatic one (AT-2). It turns out that the highly metastatic Mat-Ly-Lu cells exhibit a phenomenon of cathodal galvanotaxis in an electric field which can be blocked by interrupting the voltage-gated sodium channel (VGSC) activity. The VGSC activity is postulated to be characteristic for metastatic cells and seems to be a reasonable driving force for motile behavior. However, the classical theory of cellular motion depends on calcium ions rather than sodium ions. The current research provides a theoretical connection between cellular sodium inflow and cathodal galvanotaxis of Mat-Ly-Lu cells. Electrical repulsion of intracellular calcium ions by entering sodium ions is proposed after depolarization starting from the cathodal side. The disturbance in the calcium distribution may then drive actin polymerization and myosin contraction. The presented modeling is done within a continuous one-dimensional Poisson-Nernst-Planck equation framework.