The size distribution of human hematogenous metastases.

The development of primary cancers and their subsequent metastases occur through a complex sequence of discrete steps. A hypothesis is proposed here whereby the time available for the growth of metastases is normally distributed, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size distribution would be lognormal; Gompertzian growth would imply a modified (Gompertz-normal) distribution, where larger metastases would occur less frequently as a consequence of a decreased growth rate. These two size distributions were evaluated against 18 human autopsy cases where precise size measurements had been collected from over 3900 macroscopic hematogenous organ metastases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to over-represent metastases greater than 10 mm diameter. The Gompertz-normal distribution provided more stringent agreement, correcting for this over-representation. These observations supported the hypothesis of normally distributed growth times, and qualified the utility of the lognormal and Gompertz-normal distributions for the size distribution of metastases.     

Segregation into separate rouleaux of erythrocytes from different species. Evidence against the agglomerin hypothesis of rouleaux formation.

Erythrocytes from one species were labelled with fluorescein isothiocyanate and mixed with unlabelled erythrocytes from another species. Albumin polymers were added to generate rouleaux. The species of origin of erythrocytes in rouleaux was determined by fluorescence microscopy. Erythrocytes from different species segregated into independent rouleaux. However, fluorescent and non-fluorescent erythrocytes from one individual were mixed randomly in rouleaux. These results confirm, using a novel experimental approach, previous observations of Sewchand & Canham [(1976) Can. J. Physiol. Pharmacol. 54, 437-442]. Since rouleaugenic agents are not species-specific, under the 'agglomerin' hypothesis of rouleau formation they would be expected to form bridges between cells from different species. It follows that either the agglomerin hypothesis is incorrect, or additional species-specific surface components are involved in the aggregation of agglomerin-cross-bridged cells.     

Mutational equilibrium model of genome size evolution

The paper describes a mutational equilibrium model of genome size evolution. This model is different from both adaptive and junk DNA models of genome size evolution in that it does not assume that genome size is maintained either by positive or stabilizing selection for the optimum genome size (as in adaptive theories) or by purifying selection against too much junk DNA (as in junk DNA theories). Instead the genome size is suggested to evolve until the loss of DNA through more frequent small deletions is equal to the rate of DNA gain through more frequent long insertions. The empirical basis for this theory is the finding of a strong correlation and of a clear power-function relationship between the rate of mutational DNA loss (per bp) through small deletions and genome size in animals. Genome size scales as a negative 1.3 power function of the deletion rate per nucleotide. Such a relationship is not predicted by either adaptive or junk DNA theories. However, if genome size is maintained at equilibrium by the balance of mutational forces, this empirilical relationship can be readily accommodated. Within this framework, this finding would imply that the rate of DNA gain through large insertions scales up a quarter-power function of genome size. On this view, as genome size grows, the rate of growth through large insertions is increasing as a quarter power function of genome size and the rate of DNA loss through small deletions increases linearly, until eventually, at the stable equilibrium genome size value, rates of growth and loss equal each other. The current data also suggest that the long-term variation is genome size in animals is brought about to a significant extent by changes in the intrinsic rates of DNA loss through small deletions. Both the origin of mutational biases and the adaptive consequences of such a mode of evolution of genome size are discussed.     

The geographic distribution of mammal body size in Europe

Aims  To describe the pattern of mean body size of native mammals in Europe, and to investigate its relationships with environmental predictors related to four hypotheses: (1) dispersal; (2) heat conservation; (3) heat dissipation; and (4) resource availability.
Location  Continental western Europe and Great Britain.
Methods  We used range maps to estimate the mean body size (average log mass) of mammals in 386 cells of 12,100 km² each. Environmental conditions in each cell were quantified using nine historical, climatic and primary production variables. We attempted to tease apart the effects of these variables using correlation, multiple regression and spatial autocorrelation analyses.
Results  In the part of the continent covered by ice during the Pleistocene, body mass decreases southwards, and annual average temperature explains 73% of the variance in body size, consistent with the heat-conservation hypothesis. However, in warmer, non-glaciated areas the best predictor is an estimate of seasonality in plant production, but it explains only 18% of the variance. Carnivores, omnivores and herbivores show similar relationships, but the pattern for herbivores is substantially weaker than for the other groups.
Main conclusions  Overall, the relationship between mean body size and temperature is non-linear, being strong in cold environments but virtually disappearing above a temperature threshold.     

Rheological behaviors of bovine blood forming artificial rouleaux

A purpose of the present study is to make an artificial rouleau of bovine red blood cells which is not capable of rouleau formation under physiological condition. Rheological behaviors of bovine blood forming artificial rouleaux were examined. The modification of cell surface by enzyme trypsin induced rouleau formation, whereas the modification of cell surface by neuraminidase did not cause any aggregate formation. The drastic elevation of the fibrinogen content in bovine red blood cells suspension also brought about the formation of rouleau. The value of dynamic rigidity modulus G' of bovine red blood cells in saline solution containing high concentration of fibrinogen is somewhat smaller than that of trypsin treated bovine red blood cells in plasma. The value of G' of trypsin treated bovine red blood cells in plasma first increased to a maximum value and then decreased with the time. It is supposed that the removal of macro-molecules from the cell surface facilitates the mutual approach of cells and causes the formation of rouleau which seems to be the same as that of human and horse bloods.     

Time-dependent changes in the size distribution of distearoylphosphatidylcholine vesicles.

The results of transmission electron microscopic and ultracentrifugal studies of the size distributions of sonicated distearoylphosphatidylcholine vesicles are reported. Small vesicles (d approximately 300 A) were prepared by sonication of pure 1,2-distearoyl-3-sn-phosphatidylcholine in water and incubated at 4, 21, 40, 53, and 65 degrees C. The vesicle size distributions changed as a function of time at all temperatures below the phase-transition temperature but remained constant at the transition temperature and above. The sizes of structures to which the small vesicles are converted are the same at all temperatures, although the rates of conversion differ. The primary structures formed are identified as larger vesicles. The rate of loss of small vesicles is found to increase with decreasing temperature. At 4 and 21 degrees C small vesicles are converted to amorphous material, possibly irregular fragments of neat phase, in addition to being converted to larger vesicles. Trace amounts of an impurity commonly produced in the synthesis of 1,2-distearoyl-3-sn-phosphatidylcholine, 1,3-distearoyl-2-sn-phosphatidylcholine, are found to dramatically reduce the rate of loss of small vesicles at 21 degrees C.     

Stochastic kinetic models for small reversible systes; The equilibrium distribution

The equilibrium probability distribution of the process level is studied for a general class of reversible stochastic reactions. A calculationally convenient approximation for equilibrium probabilities is derived and its accuracy is investigated over a range of values of the equilibrium constant. A method of approximating the equilibrium means and variance is developed and illustrated forQ ^th-order processes.     

Determination of size distribution of elliptical microvessels from size distribution measurement of their section profiles

In transmission electron microscopy, microvessels (MVs) are studied as profiles on ultrathin sections. To determine MV sizes from measurements made on MV profiles, an assumption must be made about MV shape, a circular cylinder being used to approximate the latter on limited lengths. However, this model is irrelevant in case MVs have some flatness. The elliptical cylinder model is preferable, although relationships between the cylinder profile (two-dimensional; 2D) and its true (three-dimensional; 3D) sizes are not yet known. We have obtained the 2D/3D functions that express the relationships between such profile sizes as the minor radius (Y), major radius (X), axial ratio (X/Y), area (S), and perimeter (P) on the one hand, and the corresponding MV sizes (Y(0), X(0), X(0)/Y(0), S(0), and P(0)) on the other. The 2D/3D functions make it possible to derive elliptical MV sizes from section profile size distributions, probability density functions (PDFs) for the latter being determined. We have applied the 2D/3D functions in studying axial ratios of thyroid hemocapillaries. A factual X/Y frequency histogram has been constructed and fitted by theoretical X/Y PDFs plotted for different sets of capillary sizes. The thyroid capillaries have been revealed to be clustered, 72.7% of them having X(0)/Y(0) approximately 1.6, 17.6%, X(0)/Y(0) approximately 1.0, and 9.7%, X(0)/Y(0) approximately 3.2. The proposed technique is instrumental in precise modeling of microcirculatory network geometry.     

The relationship between ostracod distribution and sediment grain size

Sediment samples from an area seaward of the River Crouch in the Thames estuary have been analysed for their particle size distribution and later picked over for ostracods. The sediments were classified into sediment types and three depositional sub-environments were recognised, viz. Intertidal Flat, Sandbank and Tidal Channel. Study of the ostracods showed that three distinct faunas characterise the same three environments. Log grain size/probability plots have been used to show a relationship between ostracod distribution and sediment grain size.     

The influence of pH on the equilibrium distribution of iron between the metal-binding sites of human transferrin.

The dependence of the metal-binding properties of transferrin on pH in the pH 6--9 range was investigated by urea/polyacrylamide-gel electrophoresis. Equations are presented for calculating the relative values of the four conditional site constants for the stepwise binding of iron to the two sites of transferrin and for calculating the equilibrium distribution of the protein among the four principal forms, apotransferrin, the C-terminal and N-terminal monoferric transferrins and diferric transferrin. The relative affinity of iron for the two sites and the co-operativity of iron-binding follow characteristic "pH titration' curves. A mathematical model that can account for the former behaviour is presented. In both cases the metal-binding sites are affected by the ionization of functional groups with apparent pKa values near physiological pH approx. 7.4. There is strong positive co-operatively in the release of protons from these groups. The results indicate that pH must be accurately controlled in studies of the differential properties of the two sites of the transferrin molecule.     

A model for rouleaux pattern formation of red blood cells

Human red blood cells (RBCs) in a solution form rouleaux patterns under various conditions. The degree of rouleaux formation depends on, for example, the concentration and molecular weight of added large molecules. We present a two-dimensional discrete cellular space model in which an RBC is represented by a rectangle and differential adhesion is assumed among the longer (a-site), the shorter (b-site) sides of the rectangle and the solvent. The total sum of the adhesion energy is assumed to guide the step-by-step change of the model cell configuration and also define absolutely stable patterns. We compare the set of absolutely stable patterns and cell aggregate patterns for both actual and computer-simulated cases to obtain the basic validity of our framework. Then we proceed to assess the effects of added high polymers to the adhesion parameters. We first note that under suitable conditions, decrease in a-site-solvent affinity is necessary to have complex patterns rather than increase of a-a affinity. The hypothesis that addition of high polymers reduce the a-site-solvent affinity is concomitant with a newly proposed osmotic stress theory. The parameter fitting results for the experimental phase change curves can also be interpreted as supporting more the new theory than existing traditional explanations.     

The distribution of species range size: a stochastic process

The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date.     

On the equilibrium distribution of population in space

Spatial equilibrium distributions of population are derived from the spatial distribution of net rates of reproduction, and from a relationship between migratory flow and gradients of population density and of locational “attractiveness.” Conditions are discussed for which population approaches a uniform spatial density. Under certain conditions a particularly simple statement of the equilibrium conditions is possible in terms of the “potential of population,” a concept introduced by demographers (J. Q. Stewart,Geographical Review,37, 46–85, 1947) to measure the proximity of a point to people. This paper was first written at the Center for Advanced Study in the Behavioral Sciences.