Global asymptotic stability of the size distribution in probabilistic models of the cell cycle

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for _n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, _*(x). For the special case of the transition probability model, we display _*(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).     

Transport ofl-lactate by cultured rat brain astrocytes

Several reports indicate that lactate can serve as an energy substrate for the brain. The rate of oxidation of this substrate by cultured rat brain astrocytes was 3-fold higher than the rate with glucose, suggesting that lactate can serve as an energy source for these cells. Since transport into the astrocytes may play an important role in regulating nutrient use by individuals types of brain cells, we investigated the uptake ofl-[U-¹⁴C]lactate by primary cultures of rat brain astrocytes. Measurement of the net uptake suggested two carrier-mediated mechanisms and an Eadie-Hofstee type plot of the data supported this conclusion revealing 2 Km values of 0.49 and 11.38 mM and Vmax values of 16.55 and 173.84 nmol/min/mg protein, respectively. The rate of uptake was temperature dependent and was 3-fold higher at pH 6.2 than at 7.4, but was 50% less at pH 8.2. Although the lactate uptake carrier systems in astrocytes appeared to be labile when incubated in phosphate buffered saline for 20 minutes, the uptake process exhibited an accelerative exchange mechanism. In addition, lactate uptake was altered by several metabolic inhibitors and effectors. Potassium cyanide and -cyano-4-hydroxycinnamate inhibited lactate uptake, but mersalyl had little or no effect. Phenylpyruvate, -ketoisocaproate, and 3-hydroxybutyrate at 5 and 10 mM greatly attenuated the rate of lactate uptake. These results suggest that the availability of lactate as an energy source is regulated in part by a biphasic transport system in primary astrocytes.This data was presented in part at the meeting of the Federation of American Societies for Experimental Biology in May 1989.     

Woodland canopy structure and the light response of juvenile Quercus lobata (Fagaceae)

I investigated competition for light between canopy plants and juvenile valley oaks (Quercus lobata Nee) in a mixed-broadleaf woodland of California's northern Coast Ranges. Canopy effects on understory light supply were separated among the overlying adult valley oak, the adult's woody understory, and neighboring trees and shrubs through a series of light sampling surveys and measurements of the number, size, and spatial distribution of neighboring plants. Light supply in the understory was primarily influenced by neighboring plants, with no detectable effect of the overlying adult valley oak. Light supply in the understory averaged 25% full sun due to a high frequency of canopy gaps and a typically open understory. Seedling response to understory light supply was investigated in an experimental sunfleck gradient (10%, 19%, and 100% full sun). Between 10% and 100% full sun, seedling growth increased by 90% and the shoot:∗∗∗root ratio changed from 1.561 to 0.607. Shade seedlings were also taller and produced fewer, larger, and thinner leaves than seedlings grown in full sun. A field survey of the spatial distribution and crown morphology of saplings and young adults found 1) the distance between young valley oaks and neighboring overstory trees to increase with neighbor size, and 2) crowns of the young oaks to be skewed away from neighbors. Although shading by the canopy was only moderate, canopy effects on understory light supply may restrict juvenile recruitment of valley oak in this woodland.     

Evolution of eusociality in diploid species

Haplodiploid species are naturally biased by their genetic structure toward the evolution of sterile worker castes, as shown by W. D. Hamilton (1964. J. Theoret. Biol., 7, 1–16, 17–52). Diploid species do not have this intrinsic genetic bias toward eusociality. Nonetheless, true sociality has evolved in the diploid ancestors of the modern termites, and varying degrees of quasisociality are not uncommon in diploid species, including mammals. A genetic bias toward investment in relatives rather than offspring can arise in a diploid species as a result of inbreeding. The consequences of several regular incestuous breeding systems are analyzed in detail. It is shown that, under certain conditions, there is a natural bias toward an alternation of inbred and outbred generations. As this alternation proceeds, the genetic bias toward eusociality rapidly approaches an asymptotic value of 4(1 + 2f₀)/3(1 + 3f₀), where f₀ is the average coefficient of relationship for the outbreeding pairs. For f₀ close to zero, the genetic bias toward eusociality is close to 1.33, which is even larger than the genetic bias of 1.25 in haplodiploid species. Under other conditions there may be repeated incestuous matings between successive outbreeding generations. In this case the bias toward eusociality can be as large as 2.