Ring theory

In what follows we demonstrate that the minimum requirement for the formation of a DNA ring is a pair of ordinary (ABC … ABC) or inverted (ABC … C′B′A′) repetitions. DNA fragments that are partly degraded from their ends by a 3′ (or 5′) specific exonuclease such as exonuclease III (or λ exonuelease) produce resected fragments that can only form rings by virtue of ordinary repetitions.Next we analyze how random fragments cut from DNA molecules containing ordinary repetitions would be expected to form rings. Since longer fragments (>5 to 10 μm) cyclize less efficiently than do shorter ones (2 μm), we are led to the view that the chromatid is composed of thousands of distinctive regions, called g-regions, within which characteristic repetitious sequences are clustered in an intermittent or tandem fashion. Mathematical expressions are derived that allow one to measure the length and number of these g-regions from the ring frequency, R, and its dependence on the length of the fragment.The interior organization of the g-regions is considered in terms of two models and their variants: intermittent repetition and tandem repetition. These are depicted in Figure 2. The objective of this effort is to calculate the frequency of rings that can be generated from these two models, and to explain the “shortside fall-off”, that is, the decrease in ring frequency as the fragment length becomes shorter. This could not be due to the stiffness of the DNA double helix and must reflect a distribution of spacing of the repetitious sequences within the g-regions. Mathematical expressions are obtained that allow one to estimate the average values of the repetitive or partly repetitive unit. These estimates may be obtained from the dependence of ring frequency on the extent of resection, and from the dependence of ring frequency on the length of shorter fragments.The mathematical expressions derived here are employed in the previous papers of this group, and lead to the conclusion that the g-regions are composed of tandemly repeating sequences.     

Deactivation theory

A general model of enzyme deactivations involving unimolecular processes is introduced. For most mechanisms of this type, the parameters of the general model can be expressed in terms of actual physical parameters. The number of physical parameters that can be determined from the deactivation data cannot exceed the number of independent constants in the general model. When there is an excess of physical parameters, then some parameters must be determined from independent methods of analysis. If this is not possible, then some parameters must be left as lumped parameters or global parameters. The general form of the model can be useful in determining the number of independent, potentially active forms of the enzyme present during deactivation. Some exceptions to the general model are due to higher-order processes such as dissociation, autolysis, and biological contamination.     

Testcross selection theory

Summary The purpose of this paper is to extend the theoretical basis for testcross selection theory from models assuming two alleles per locus to a model which is general for number and frequency of alleles. The expectations of genetic variances expressed among and within testcross families is presented for both inbred and population testers. Predicted change due to selection in testcross, non-inbred and selfed population performance with testcross selection are derived. Expected changes in testcross heterosis and inbreeding depression in the population are also derived. Approximate confidence intervals for predicted selection response are developed and appropriate sets of progeny to evaluate in order to estimate parameters of interest are identified.Contribution from the Missouri Agricultural Experiment Station. Journal Series No. 10063     

Gene-culture coevolutionary theory

Gene-culture coevolutionary theory is a branch of theoretical population genetics that models the transmission of genes and cultural traits from one generation to the next, exploring how they interact. These models have been employed to examine the adaptive advantages of learning and culture, to investigate the forces of cultural change, to partition the variance in complex human behavioral and personality traits, and to address specific cases in human evolution in which there is an interaction between genes and culture.