Design considerations for two-stage enrichment clinical trials

When there is a predictive biomarker, enrichment can focus the clinical trial on a benefiting subpopulation. We describe a two-stage enrichment design, in which the first stage is designed to efficiently estimate a threshold and the second stage is a “phase III-like” trial on the enriched population. The goal of this paper is to explore design issues: sample size in Stages 1 and 2, and re-estimation of the Stage 2 sample size following Stage 1. By treating these as separate trials, we can gain insight into how the predictive nature of the biomarker specifically impacts the sample size. We also show that failure to adequately estimate the threshold can have disastrous consequences in the second stage. While any bivariate model could be used, we assume a continuous outcome and continuous biomarker, described by a bivariate normal model. The correlation coefficient between the outcome and biomarker is the key to understanding the behavior of the design, both for predictive and prognostic biomarkers. Through a series of simulations we illustrate the impact of model misspecification, consequences of poor threshold estimation, and requisite sample sizes that depend on the predictive nature of the biomarker. Such insight should be helpful in understanding and designing enrichment trials.     

Environmental conditions during glycerol bioconversion affect 3-hydroxypropionic acid bioproduction by Limosilactobacillus reuteri DSM 17938

3-Hydroxypropionic acid (3-HP) is a platform molecule whose biological production was carried out by the bacterium Limosilactobacillus reuteri according to a two-step process: first, a growth phase in batch mode on glucose, then a glycerol bioconversion into 3-HP in fed-batch mode. With the objective of improving 3-HP bioproduction, this study aimed at defining the operating conditions during the bioconversion phase that increases the bioproduction performance. A central composite rotatable design allowed testing various pH levels and specific glycerol feeding rates. By establishing response surfaces, optimal conditions have been identified that were different depending on the considered output variable (final 3-HP quantity, 3-HP production yield and production rate). Of them, 3-HP final quantity and 3-HP production yield were maximized at pH 6.0 and at specific glycerol feeding rates of 60 and 55 mg_gly g_CDW⁻¹ h⁻¹, respectively. The specific 3-HP production rate was the highest at the upper limit of the specific substrate feeding rate (80 mg_gly g_CDW⁻¹ h⁻¹) but was not affected by the pH. An additional experiment was carried out at pH 6.0 and a specific glycerol feeding rate of 80 mg_gly g_CDW⁻¹ h⁻¹ to validate the previous observations. In conclusion, the results showed a significant improvement of 3-HP concentration by 13%, of specific production rate by 34% and of 3-HP volumetric productivity by 39%, as compared to the initial values.     

Effect of exogenous gibberellin A4/7 on tracheid production, longitudinal growth and the levels of indole‐3‐acetic acid and gibberellins A4, A7 and A9 in the terminal shoot of Pinus sylvestris seedlings

Synchronously dividing cultures of the unicellular green alga Scenedesmus obtusiusculus were cultivated for 24 or 70 h in medium high (1000 μM) or low (60 μM) in phosphorus. Aliquots of AlCl₃ (0, 37, 74, 111, 148, 185, or 222 μmol) were added daily to 1 l cell suspension at the end of the cell division phase. Algae were also grown in media with different pH, adjusted with HCl, in the absence of AlCl₃.
Effects of Al on cell metabolism vary with the intracellular Al concentration and with the concentration of Al available per cell. When the concentration of phosphorus is low, internal concentrations of Al are high and the chlorophyll content and the net dry matter production per cell increase, whereas the photosynthesis and the cell division are increased. Presence of Al in a low P medium decreases the pH of the medium down to 4.5. There are only small effects of Al in the presence of P, due to precipitation of most of the Al with P in the medium.
Despite the Al-induced decrease of the pH of the culture medium, effects caused by Al cannot be explained as a pH effect. Instead, the Al effect may, at least to some extent, be related to a decrease in availability of P in the metabolism, due to formation of aluminium phosphate inside the cell.     

LIFE CYCLE OF A STEPHANODISCUS SP. (BACILLARIOPHYTA)1

Studies of the life cycle of a centric diatom, tentatively identified as Stephanodiscus neoastraea Håkansson & Hickel, showed that sexual reproduction occurred every year in a freshwater lake (Lough Neagh, Northern Ireland). Male and female gametes were produced in cells below 55% of the maximum diameter during a 3–4-week period in late summer, following the return of nitrate concentrations above 10 μM NO_3-N. The frequency of sexual reproduction was linked to the cycle of diameter size reduction and regeneration. The times of largest decreases in cell diameter were during nutrient stress in summer and low light conditions in late autumn, rather than during the main spring growth period. So, environmental conditions (combined with the limited life-spans of individual cells) affected the rate of diameter reduction and, therefore, the length of the life cycle (3–4 years).     

The role of meiofauna in the marine ecosystem: evolutionary considerations*

The meiobenthos are regarded as the first metazoans to appear on earth This paper considers some aspects of their role in the marine ecosystem over evolutionary time. It is speculatively suggested that they have had a profound influence on many structural and functional attributes of the marine ecosystem as we see it today, both in the benthic and pelagic realms. Certain features such as size spectra, the life-history characteristics of the macrobenthos, and the energetic balance between ecological compartments of the marine ecosystem are considered to result from evolution away from negative interactions with the meiobenthos.     

Effects of asexual reproduction on the neighborhood area of cyclical parthenogens

The habitat occupied by a subpopulation and withinwhich there is random mating is known as itsneighborhood area. Neighborhood area is dependenton dispersal rates and organisms with low rates ofdispersal are expected to have small neighborhoodareas. In the absence of evolutionary forces,neighborhood areas under sexual reproduction will beconstant in size as long as dispersal patterns do notchange. This scenario differs when reproduction is bycyclical parthenogenesis since recombination anddispersal may occur in different generations. Ingeneral, dispersal distances increase with the numberof parthenogenetic generations. We show that cyclicalparthenogenesis increases neighborhood area which,concomitantly, decreases the potential for geneticsubdivision. It is noteworthy, however, that theincrease in neighborhood area is a decreasing functionof the number of parthenogenetic generations.This mechanism may have important implications for thepopulation structure of planktonic rotifers living ina horizontally undifferentiated habitat. In suchhabitats organisms are effectively unrestricted intheir lateral movements. Because rotifers typicallyhave low dispersal rates spatial geneticdiscontinuities may develop that divide the populationinto genetically distinct subpopulations. Counteringthis tendency is the increased neighborhood areaproduced by dispersal during the parthenogeneticphase. Thus cyclical parthenogenesis in organismslike rotifers may have important and previouslyunreported effects on the population's geneticstructure.     

Assembly of local communities: consequences of an optimal body size for the organization of competitively structured communities

Much empirical evidence suggests that there is an optimal body size for mammals and that this optimum is in the vicinity of l00g. This presumably reflects an underlying fitness function that is greatest at this mass. Here, I combine such a fitness function with an equilibrium model of competitive character displacement to assess the potential influence of a globally optimal body size in structuring local ecological communities. The model accurately predicts the range of body sizes and the average difference in size for species in communities of varying species richness. The model also predicts a uniform spacing of body sizes, rather than the gaps and clumps in the sizes of coexisting species observed in real communities. Alternative explanations for this phenomenon are discussed. The allometric relationships that result in a body size optimum subsume a large number of characteristics associated with the physiological, behavioral, demographic, and evolutionary dynamics of the species. Further integration of the underlying dynamics (e.g. individual energetics) of these relationships into all hierarchical levels of ecology will have to incorporate multiple interactive sites, spatial heterogeneity, and phylogenetic structure, but it has the potential to provide important discoveries into the means by which natural selection operates.