John Prothero

Methodological aspects of scaling in biology

Interest in the scaling approach to problems of biological design has increased dramatically in the past few years. But thus far no systematic attempt has been made to review the possible pitfalls attendant upon this approach. As a beginning, the problems which can arise from rounding exponents, or taking standard errors at face value, or expressing dependent variables in ratio form are discussed. There follows a discussion of fitting specific functions to scaling data, of the special needs for documentation and of the potential value to be derived from suitable computer programs in scaling studies. Finally, the possible difficulties of demonstrating global optimization in biological systems, the risks of dimensional analysis and the value and nature of scaling models are discussed.

Scaling of blood parameters in mammals

Abstract 1. 1. Values for blood plasma and red cell volumes, as well as hematocrit and half-saturation (T 50 ) values in male and female mammals, both aquatic and terrestrial, are submitted to linear (log-log) regression analysis. 2. 2. The slope of the regression lines for blood and plasma volumes is identically one. The slope (0.97) of the red cell regression is probably not significantly different from one ( df = 71, t = 2, P 3. 3. The slope (− 0.01) of the hematocrit regression line is, statistically speaking, different from zero ( df = 87, t = 4.7, P 4. 4. The slope (− 0.03) of the half-saturations ( T 50 ) values is also, statistically, different from zero ( df = 89, t = 4.1, P 5. 5. No statistically significant differences were found in any of the above blood parameters as between either male and female animals or aquatic and terrestrial mammals.

Three-dimensional reconstruction from serial sections. IV. The reassembly problem

In many fields of biology and medicine there is a pressing need for quantitative descriptions of biological structures at a resolution of micrometers. This need is currently met best by three-dimensional reconstruction from serial sections. The preliminary steps in three-dimensional reconstruction include fixation, embedding in plastic, introduction of fiducials, serial sectioning, and staining. At the light microscope level, with which we are chiefly concerned, one will usually want to do photomicrography (or videomicrography) of adjacent fields within individual tissue sections. The resultant images are projected onto a digitizer pad and the contours of interest manually digitized. From the digitized coordinates generated thereby, one wishes to generate a likeness of the original object, using computer graphic displays, and to then do interactive morphometrics. The problem of combining the digitized coordinates so as to produce a numerically faithful representation of the original object (i.e., the reassembly problem) is, as a practical matter, nontrivial. A technical description of the reassembly problem is presented. The main factors entering into a solution of the problem are discussed and a mathematical statement of the solution is given.

Organ scaling in mammals: The liver

1. Values for liver weight, in growing and adult male and female mammals, both terrestrial and aquatic, as well as values for hepatic blood flow, blood volume and oxygen consumption are submitted to linear (log-log) regression analysis. 2. The slope of the regression line for liver weight on adult body weight in adult mammals was found to be 0.886. No statistically significant difference was found between male and female, nor between terrestrial and aquatic mammals (at the 1% confidence level). 3. Over about four orders of magnitude there is (on present evidence) a tendency for the mammalian liver to grow as about the 0.94 power of body weight (pre- and post-natal). 4. The slopes of the regression lines for hepatic blood flow, blood volume and oxygen consumption were found to be 0.91, 0.86 and 0.69, respectively. 5. The mean hepatocyte size in fixed tissue of rats was found to be 7400 micrometers 3. 6. It is argued that the slope of the regression line for hepatic oxygen consumption in mammals generally is likely to fall in the range of 0.67-0.77.

Evidence for clonal attenuation of growth potential in hela cells

SummaryThe growth of primary clones and serial subclones of HeLa cells and of diploid human fibroblast-like cells were compared both in the presence and absence of feeder layers; the latter had no significant effects upon the results. Clones and subclones of both cell types displayed great heterogeneity in growth rates, typically with a bimodality of growth distributions. Serial passages of clones selected on the basis of superior rates of proliferation showed attentuation of growth potentials; the extent of such attentuations was much less in the case of HeLa cells, suggesting at least one possible basis for the differences in long-term growth potential between these two classes of cell lines.

Scaling of maximal lifespan in bats

1. Values for maximal lifespan in heterothermic and homeothermic bats as a function of body weight, brain weight and lifetime basal energy consumption were submitted to linear (log-log) and multiple regression analysis. 2. The results of the regression analyses of maximal lifespan in bats were compared with those reported for non-flying mammals based on both narrow and wide weight ranges. 3. It was found that the regression lines (linear or multiple) for maximal lifespan in bats (heterothermic or homeothermic) lie well above the regression lines for non-flying mammals. 4. Predictions of maximal lifespan in heterothermic bats based on estimated lifetime basal energy consumption and body weight are in reasonable agreement with observed values when torpor and hibernation behaviour are taken into account. 5. But observed values of maximal lifespan in homeothermic bats were found to lie substantially above the regression lines derived for non-flying mammals. 6. It was concluded that existing hypotheses do not account for the long lifespan observed in bats generally.

Scaling of Maximal Lifespan in Mammals: A Review

The study of maximal lifespan in mammals is a topic of considerable interest. Recent comparative studies have demonstrated a correlation between efficiency of DNA repair and maximal lifespan 1, an inverse correlation between cytochrome P-448 content and maximal lifespan2, a correlation between the ratio of superoxide dismutase to specific energy metablism and maximal lifespan3, and a correlation between in vitro cellular proliferative potential and maximal lifespan4. Another well known example is the maximal lifespan-brain weight correlation discussed by Sacher5. Such correlations may serve to stimulate the formulation of hypotheses as to the nature of the factors influencing maximal lifespan.

Visualization-Based Mapping of Language Function in the Brain

Cortical language maps, obtained through intraoperative electrical stimulation studies, provide a rich source of information for research on language organization. Previous studies have shown interesting correlations between the distribution of essential language sites and such behavioral indicators as verbal IQ and have provided suggestive evidence for regarding human language cortex as an organization of multiple distributed systems. Noninvasive studies using ECoG, PET, and functional MR lend support to this model; however, there as yet are no studies that integrate these two forms of information. In this paper we describe a method for mapping the stimulation data onto a 3-D MRI-based neuroanatomic model of the individual patient. The mapping is done by comparing an intraoperative photograph of the exposed cortical surface with a computer-based MR visualization of the surface, interactively indicating corresponding stimulation sites, and recording 3-D MR machine coordinates of the indicated sites. Repeatability studies were performed to validate the accuracy of the mapping technique. Six observers-a neurosurgeon, a radiologist, and four computer scientists, independently mapped 218 stimulation sites from 12 patients. The mean distance of a mapping from the mean location of each site was 2.07 mm, with a standard deviation of 1.5 mm, or within 5.07 mm with 95% confidence. Since the surgical sites are accurate within approximately 1 cm, these results show that the visualization-based approach is accurate within the limits of the stimulation maps. When incorporated within the kind of information system envisioned by the Human Brain Project, this anatomically based method will not only provide a key link between noninvasive and invasive approaches to understanding language organization, but will also provide the basis for studying the relationship between language function and anatomical variability.

Organ scaling in mammals: The kidneys

Values of kidney weight in adult male and female mammals, both terrestrial and aquatic, as well as values for renal blood flow and glomerular number and diameter, were submitted to linear (log-log) regression analysis. The slope of the regression line for kidney weight in 63 species of adult terrestrial mammals was 0.85 %/- 0.01. No statistically significant difference was found between the slopes of the regression lines for male and female terrestrial mammals. The slope of regression line for kidney weight in eight species of adult aquatic mammals was 0.92 +/- 0.01. Again, no statistically significant difference was found between the slopes for males and females. However, the slope (0.92) of the regression line for aquatic mammals was significantly different from the slope (0.85) for terrestrial mammals (P much less than 0.001). The slope of the regression of renal blood flow on body weight was 0.82 +/- 0.01. This value is consistent with the hypothesis that renal blood flow represents a constant fraction of cardiac output (over about 3.4 orders of magnitude in body weight). The slopes of the regression lines for glomerular number (per kidney) and mean glomerular diameter were 0.59 +/- 0.02 and 0.11 +/- 0.01, respectively. A schematic model representing the scaling of energy-partitioning in mammals is introduced.

Three-dimensional reconstruction from serial sections. I. A portable microcomputer-based software package in Fortran

Abstract A software package is described that is designed to simplify the collection, storage, and processing of data to be used for three-dimensional reconstruction from serial sections. The package, called MORPHO, consists of four independent programs, all written in FORTRAN, running under CP M , and called ISPY, DMPSPY, EDSPY, and STATSPY. The function of ISPY is to guide the user in the documentation, digitization, and storage of data derived from serial section images. The serial sections may be at any level of resolution: ultrastructural, microscopic, or macroscopic. DMPSPY allows the user to display and to make hard copies of the digitized contours. EDSPY allows any and all errors in data entry to be rectified simply and directly. STATSPY carries out statistical calculations, such as cross-sectional areas and volumes. A useful feature of STATSPY is the provision for easy insertion of additional subroutines to compute special statistics not currently provided.