A meta-analysis on association between CSN3 gene variants and milk yield and composition in cattle.

A meta-analysis on the effects of A and B alleles, the most frequent alleles of CSN3 gene, on milk yield and composition traits was conducted by pooling a large dataset consisting of 30 471 genotyped cattle. Four genetic models, comprising dominant (AA + AB vs. BB), recessive (AA vs. AB + BB), additive (AA vs. BB) and co-dominant (AA + BB vs. AB), were employed to analyze data. Standardized mean difference (SMD) was used to measure the size of the effects of A and B alleles of CSN3 on studied traits. Effect sizes of 0.2, 0.5 and 0.8 represent small, medium and large effects, respectively. The results indicate that B allele, in the form of BB genotype, has a significant, but medium effect on lactation yield under dominant (SMD = 0.259, P-value = 0.006) and additive (SMD = 0.279, P-value = 0.035) models. Moreover, a small decrease in the fat percentage occurred in cows having A allele under dominant (SMD = -0.077, P-value = 0.006) and additive (SMD = -0.106, P-value = 0.035) models. Furthermore, CSN3 variants significantly but slightly affect protein percentage under dominant (SMD = -0.146, P-value = 0.000), recessive (SMD = -0.077, P-value = 0.000) and additive (SMD = -0.219, P-value = 0.000) models, showing the negative effect of A allele on this trait. Meta-analysis results reveal that daily milk yield is slightly affected by CSN3 variants under recessive (SMD = 0.056, P-value = 0.033) and additive (SMD = 0.061, P-value = 0.013) genetic models. There is no effect of CSN3 variants on either protein or fat yield. In addition, the effects of CSN3 variants on milk-related traits were not observed under the co-dominant model. Sensitivity and publication bias analyses were carried out to confirm the stability of meta-analyses results.

Effect of chain stiffness on the entropic segregation of chain ends to the surface of a polymer melt.

Entropic segregation of chain ends to the surface of a monodisperse polymer melt and its effect on surface tension are examined using self-consistent field theory (SCFT). In order to assess the dependence on chain stiffness, the SCFT is solved for worm-like chains. Our focus is still on relatively flexible polymers, where the persistence length of the polymer, ℓ p , is comparable to the width of the surface profile, ξ, but still much smaller than the total contour length of the polymer, ℓ c . Even this small degree of rigidity causes a substantial increase in the level of segregation, relative to that of totally flexible Gaussian chains. Nevertheless, the long-range depletion that balances the surface excess still exhibits the same universal shape derived for Gaussian chains. Furthermore, the excess continues to reduce the surface tension by one unit of k B T per chain end, which results in the usual N -1 reduction in surface tension observed by experiments. This enhanced segregation will also extend to polydisperse melts, causing the molecular-weight distribution at the surface to shift towards smaller N n relative to the bulk. This provides a partial explanation for recent quantitative differences between experiments and SCFT calculations for flexible polymers.

Entropic segregation of short polymers to the surface of a polydisperse melt.

Chain ends are known to have an entropic preference for the surface of a polymer melt, which in turn is expected to cause the short chains of a polydisperse melt to segregate to the surface. Here, we examine this entropic segregation for a bidisperse melt of short and long polymers, using self-consistent field theory (SCFT). The individual polymers are modeled by discrete monomers connected by freely-jointed bonds of statistical length a , and the field is adjusted so as to produce a specified surface profile of width [Formula: see text]. Semi-analytical expressions for the excess concentration of short polymers, [Formula: see text], the integrated excess, [Formula: see text] , and the entropic effect on the surface tension, [Formula: see text], are derived and tested against the numerical SCFT. The expressions exhibit universal dependences on the molecular-weight distribution with model-dependent coefficients. In general, the coefficients have to be evaluated numerically, but they can be approximated analytically once [Formula: see text]. We illustrate how this can be used to derive a simple expression for the interfacial tension between immiscible A- and B-type polydisperse homopolymers.

Segregation of chain ends to the surface of a polymer melt: Effect of surface profile versus chain discreteness.

Silberberg has argued that the surface of a polymer melt behaves like a reflecting boundary on the random-walk statistics of the polymers. Although this is approximately true, independent studies have shown that violations occur due to the finite width of the surface profile and to the discreteness of the polymer molecule, resulting in an excess of chain ends at the surface and a reduction in surface tension inversely proportional to the chain length, N . Using self-consistent field theory (SCFT), we compare the magnitude of these two effects by examining a melt of discrete polymers modeled as N monomers connected by Hookean springs of average length, a , next to a polymer surface of width [Formula: see text]. The effects of the surface width and the chain discreteness are found to be comparable for realistic profiles of [Formula: see text] ∼ a. A semi-analytical approximation is developed to help explain the behavior. The relative excess of ends at the surface is dependent on the details of the model, but in general it decreases for shorter polymers. The excess is balanced by a long-range depletion that has a universal shape independent of the molecular details. Furthermore, the approximation predicts that the reduction in surface energy equals one unit of kBT for every extra chain end at the surface.

Segregation of chain ends to the surface of a polymer melt.

Self-consistent field theory (SCFT) is used to examine the surface of an incompressible polymer melt of freely jointed chains, each consisting of N discrete monomers connected by bonds of an arbitrary potential. As a result of entropic considerations, the end monomers tend to accumulate in a narrow region next to the surface (on the monomer scale), which causes a slight depletion of ends further into the melt (on the molecular scale). Due to the reduced configurational entropy available to polymers in the vicinity of a surface, we find an entropic contribution to the surface tension that increases with the degree of polymerization, N. While many quantities are dependent on the precise bond potential connecting the monomers, the excess of ends at the surface in the limit of infinite N, the functional form of the long-range depletion of ends, and the N dependence of the surface tension turn out to be universal.