Mean Branch Length Research Articles

Development of the anterior olfactory nucleus in normal and unilaterally odor deprived rats

The development of a second order structure in the olfactory pathway, the anterior olfactory nucleus, was examined in both normal rat pups and in subjects which underwent unilateral naris closure on postnatal day 1 (P1). Naris occlusion in neonatal rats produces a constellation of changes within the first relay in the pathway, the olfactory bulb, including a 25% reduction in total volume. Such large changes suggest that higher order structures might also be affected. Anterior olfactory nucleus development was quantified in several ways. Laminar volumes were computed by using serial section planimetry. In control animals differential development was observed, with regions extending most rostrally (e.g., pars externa and pars lateralis) exhibiting the least growth. The anterior olfactory nucleus on the "deprived" side of subjects with a single naris occluded was identical in size to that observed in controls, development within the pars lateralis was examined in control animals at P10, P20, P30, and adults. Developmental increases in numbers of both branches per cell and spines were noted, but mean branch length remained relatively constant. Finally, the effects of naris occlusion on histological patterns of succinate dehydrogenase (SDH) staining and 2-deoxyglucose uptake within pars lateralis were examined at P20 to test for more subtle effects of naris occlusion. SDH staining was quite similar in deprived and control rats at P20. However, 3H-2-DG uptake was decreased in rostral areas of the anterior olfactory nucleus ipsilateral to the deprived olfactory bulb, suggesting that naris closure does affect the structure.

A multiple scaled fractal tree

In a study of two species of oak tree, the distribution and arrangement of branch lengths are found to be governed by a simple algorithm. The algorithm which has its footing in a type of fractal self-similarity observed in other physiological structures ( West et al., 1986 . J. appl. Physiol. 60, 189–197; Goldberger & West, 1987 . Yale J. biol. Med. 60, 421–435), reproduces the observed power-law behaviour of mean branch length with order. Furthermore, the high degree of intra-order variability is accounted for as a natural consequence of the superposition of a multiplicity of scales in the structure. The conclusions of this study point to a genetic rather than environmental origin for the design.

Postnatal development of cell columns and their associated dendritic bundles in the lumbosacral spinal cord of the rat. I. The ventrolateral cell column.

The postnatal development of the ventrolateral dendrite bundle (LDB) in the rat lumbosacral cord was studied quantitatively with Golgi-Cox impregnation. At birth, motoneuronal perikarya and their dendrites were not fully developed, and had not begun to form bundles; varicose dendritic shafts radiated symmetrically from motoneurons. Dendrites contained numerous spines and growth cones. At 5 days, dendritic shafts began to arrange themselves longitudinally, and by 10 days of age, dendrite bundling was apparent. Dendritic growth and bundling appeared complete by two months of age. LDB formation was a dynamic process; rapid dendritic growth occurred in discrete phases with brief intervals of slower dendritic development between them. The mean number of secondary and tertiary dendrites, and the mean branch length of all orders progressively increased. Motoneurons of the LDB primarily innervate the pelvic musculature. Selective horizontal orientation of dendrites into discrete compact bundles suggests that the LDB may serve as a specialized receiving and integrating system for autonomic control over excretory and reproductive functions. It is interesting to note that in patients suffering from amyotrophic lateral sclerosis, motoneurons in the LDB are resistant to destruction. This finding suggests that motoneurons in the LDB may express unique features that protect them from certain disease processes. A better understanding of the developmental anatomical, physiological and biochemical properties of the LDB may provide insight into the treatment of patients with disease processes involving spinal cord and brainstem lower motoneurons.

Sizes of long branches in low density polyethylenes

Abstract13C‐NMR spectroscopy and size exclusion chromatography have been used to determine the mean length of long branches in a number of high pressure process low density polyethylenes (LDPEs). 13C‐NMR analyses count all branches longer than C5 as “long.” The polyethylenes studied all had 2–3 long branches per 1000 carbons. The mean branch length was of the order of 200–300 carbons in length. The size of long branches increases with increasing M̄n of the parent polyethylene, but the size of long branches relative to the overall macromolecular size decreases with increasing M̄n. The mean molecular weight of the long branches is some 5–20% of M̄n of the particular polymer and decreases as M̄n increases. Both autoclave and tubular reactor products were studied.

Does Horton's law of branch length apply to open branching systems?

Horton analysis has been applied to colonies of mycelial fungi and the mean branch lengths of branches per branch order tend to form a direct arithmetical, not geometric, series with branch order. Data for two botanical trees also show the arithmetical relationship. It is argued, from simulation models, that for branching systems showing outward unconstrained growth an arithmetical relationship results when linear growth rate of the elements is constant, but that a geometric relationship may result when linear growth rate shows a progressive decline.

Application of Horton's first and second laws of branching to fungi

A total of 183 colonies representing 14 species of fungi were examined for their agreement with Horton's laws of branch number and of branch length. Most conformed to the law of branch number, an inverse regression of logarithm of branch number per order on branch order. Only a minority of the colonies conformed to the law of branch length, a direct regression of logarithm of mean branch length per order on branch order. More of the colonies were well described by the regression of mean branch length on branch order, and more still by the regression of mean branch length on logarithm of branch order. Branch ratios for colonies were found to vary widely within an isolate and the value of single determinations is questioned. The calculation of length ratios for growing fungal colonies is considered to be valueless. The significance of these findings is discussed in relation to stage of colony development and differentiation.