Mechanistic equations for membrane substance transport and their identity with Kedem-Katchalsky equations

Since the physical interpretation of practical Kedem-Katchalsky (KK) equations is not clear, we consider an alternative, mechanistic approach to membrane transport generated by osmotic and hydraulic pressure. We study a porous membrane with randomly distributed pore sizes (radii). We postulate that reflection coefficient (sigma(p)) of a single pore may equal 1 or 0. From this postulate we derive new (mechanistic) transport equations. Their advantage is in clear physical interpretation and since we show they are equivalent to the KK equations, the interpretation of the latter became clearer as well. Hence the equations allow clearer and more detailed interpretation of results concerning membrane substances transport.     

Flow limits of Kedem-Katchalsky equations for fluid flux

The Kedem-Katchalsky equations for fluid flux across membranes may not be adequate for large solvent flows. In particular, for an example of two membranes in series, it is argued that they would predict physically unreasonable behavior. An alternate equation for solute flow is proposed for a simple sieving membrane. For the same example, this equation predicts more physically reasonable results.     

On the derivation of the Kargol's mechanistic transport equations from the Kedem-Katchalsky phenomenological equations

In the present article, it was demonstrated that--by starting from the so-called adjusted Kedem-Katchalsky (KK) phenomenological equations (Suchanek et al. 2004), i.e. the equations: Jv=LpDeltaP-LpDDeltaPi. JD=-LDpDeltaP+LDDeltaPi it is possible to derive practical transport equations (for the volume flow and the solute flow) in the form of the Kargol s mechanistic transport equations (Kargol and Kargol 2000, 2001, 2003a,b,c, 2004; Kargol 2002). On this basis, it has been found that the KK thermodynamic formalism for membrane transport (practical equations) is in general identical with the mechanistic equations for membrane transport.     

Some remarks on synecology

Plant Ecology - Nach einer kritischen Besprechung der begriffsmässigen Trennung zwischen Autökologie und Synökologie weist der Autor darauf hin, daß die meisten sogenannten...     

方寸天地中的昆虫百科——漫谈昆虫邮票

昆虫以六足四翅作为主要特征,数不清的种类和个体,在地球上已生存3亿多年了,一度称王称霸,还和恐龙有过很多交往,比起我们人类,它们的资格显然要古老得很多。     

Some remarks on molecular biology

The binding energy of a very long molecular chain, composed of different classes of molecules, depends in general on the order of the molecules. It is shown that under very general conditions there exists for a givenbrutto chemical composition of a chain, a class of chains which is characterized by a total binding energy which is equal to the total binding energy of any other prescribed chain of different composition within the limits of unsharpness of the energy level. This establishes a criterion formapping of a class of configurations of long chain molecules on another class. To the extent that a mapping constitutes a generalized code those results contribute to the theory of molecular codes. Applying to our results the results of a previous paper (1959,Bull. Math. Biophysics,21, 309–326), we arrive at the conclusion that the self-replication of a living molecule may be the property not of a particular structure but of classes of structures.     

Some remarks on the central nervous system

It is pointed out that the successes obtained in the mathematical biology of the central nervous system are based mostly on a number of more or less complicated neuronic circuit models, each inventedad hoc for the purpose of explaining a given phenomenon. The individual models remain disconnected from each other, however, and the unity of the CNS is not apparent. (Rashevsky,Mathematical Biophysics, 3rd Edition, Vol. II, 1960. New York, Dover Publications, Inc.) Some “field theories” of the CNS, as for example that of Griffith (Bull. Math. Biophysics,25, 111–120, 1963;27, 187–195, 1965), give more expression to this unity but lose in the explanation of specific phenomena. The present paper starts with the picture thatevery neuron in the brain isdirectly or indirectly affected to some extent byevery other neuron. This leads to a system of equations with a very large number of variables. Such a system can be replaced in the limiting case by an integral equation of the first kind. At least two specific results can be obtained with this approach and suggestions for further improvement are made.     

Some remarks on organization and structure

Self-organizing systems are defined as able to change their structure, according to need, within specific equivalence classes. Once hierarchical levels and their value functions are assigned, requirements of invariance under transformations within an equivalence class can be used as a principle to determine the population of each level. This program is carried out in complete detail, as an example, for a particular class of systems (called modular), for which it is shown that a full Thermodynamics can be constructed. Modular systems are compared with linguistic, monetary, and military organizations; they are found to describe exactly the empirical data available on monetary circulation over the world, and to offer other perhaps suggestive indications. The emerging picture is that of a development, for any such system, which alternates phases of evolution (changes of level occupation numbers) with phases of revolution (changes of level structure within the given equivalence class).