Some further comments on the DNA-protein coding problem: A correction and a note

An error appearing in the proof of Theorem 4 of a previous paper of the author’s (1959,Bull. Math. Biophysics,21, 289–97) is pointed out, and a new proof of the theorem is supplied. We also obtain a corollary from Theorem 3 ofloc. cit. which reveals the existence of a hitherto unrecognized class of codes.     

The DNA-protein coding problem

The DNA-protein coding problem is given a general algebraic formulation, the consequences of which are then explored by standard mathematical methods. To keep the treatment self-contained, the mathematical techniques to be used are explained in detail. It is demonstrated that there exista priori a countably infinite number of different abstract DNA-protein codes, thereby showing that inductive attempts to construct such a code will most likely be fruitless. A notion of ergodicity is then introduced, which imposes a number of restrictions on the admissible codes, and, in fact, these considerations enable us toderive a small portion of a code which, if our hypothesis of ergodicity is correct, must occur in nature. Finally, we discuss briefly the problem as to whether there can exist more than one DNA-protein code in nature.     

An hypothesis of freese and the DNA-protein coding problem

Freese’s Hypothesis states that a single specific alteration in the sequence of nucleotides of an information-bearing DNA molecule results in a specific mutational effect. Within the framework of the DNA-protein coding problem developed elsewhere, and assuming the quasi-ergodicity of the general coding process, it is shown that Freese’s Hypothesis allows us to derive expressions for the length of the smallest mutable DNA molecule and to obtain a bound for the maximal number of allelic molecules of fixed length. To illustrate these ideas, calculations are carried out on appropriate data from bacternophage and man, and the results are shown to differ by a factor of 10 (modulo the rather crude approximations used). It is further shown that, if ρ(N) and ϱ(N) are respectively the number of information-bearing words of lengthN in a given code and the number of words of lengthN, then the number lim ρ(N)/ϱ(N) depends sensitively on the parameter ∈ which specifiesN→∞ the given code. The implications of this result for the spontaneous aggregation of a sufficient number of information-bearing words to characterize an organism are discussed. 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.     

Some comments on re-estalishability

The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an (ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958.     

关于生态场的几点评述

依据植物生态场的系统研究资料,对生态场的概念、场和特征函数、生态场折图形以及生态场对植物相互作用的解释进行了评述。阐明了生态场的最基本属性是物质性,目前的研究水平尚不能确定生态场是还是有别于一稻物理场的特殊形式在场,对生态场的基本特征函数－生态热模型给予了形式与模型参数体测方面的评述,表明两种生态势模型各有一定的特点与优越性。作者强调,生态场更具生态学的方法论意义,应用生态场对植物相互作用形式与过     

Some comments on activation and inhibition

A system of rate equations gives rise to a corresponding pattern of activation and inhibition between the state variables. We consider the converse question: to what extent does the specification of a pattern of activation and inhibition between interacting quantities determine the rate equations? Among other things, it is shown that in order to determine a closed set of rate equations, a set of integrability conditions among the interactions must be satisfied; hence there is a sense in which an activation-inhibition pattern is more general than systems of rate equations. Questions of the structural stability of activation-inhibition patterns, and of the time-scales determined by dynamical interactions, are briefly discussed. A comparison is made between the properties of such activation-inhibition patterns and those of neural networks, or more general modular automata.     

Some introductory comments on silver staining

Silver staining has become a versatile method for the visualization of specific cell structures and products. The similarity of the impregnation "nuclei" of reduced silver staining to the silver "specks" or "nuclei" of the latent image in photography is noted. "Physical" development (reduction of ionic silver in solution) in silver staining as compared to "chemical" development (reduction of ionic silver remaining in a silver halide crystal) in photographic procedures is briefly discussed.     

Some comments on the PAS reaction of glycogen

Synopsis The periodic acid-Schiff (PAS) reaction has been studied in sections of mouse liver using a self-assembled microspectrophotometer. Increased colour intensity was obtained up to 4 hr of oxidation with periodic acid and 2 hr treatment with Schiff's reagent. The oxidation curve showed an initial, steep increase in colouration with a levelling off afterwards, that could not be attributed to loss of aldehyde groups. The results obtained from carrying out the PAS reaction on sections pretreated with -amylase suggest that the reaction takes place in two phases in which the outer glucosyl groups of the glycogen molecule are oxidized more rapidly than the inner ones.     

Some comments on the aerobiology of fungus spores

While exposure/symptom relationships are relatively well-defined for pollen allergens, such relationships have not been clearly established for airborne fungus spores due to a lack of clearly defined seasonal patterns, prevalence of world-wide cosmopolitan fungi, and serious problems with sampling and identification. Ascospores and basidiospores have been least studied with respect to aerobiology, although both are clearly allergenic. Preliminary data on allergenicity and diurnal and seasonal prevalence patterns for selected ascospore and basidiospore types are presented.