Modelling the biological invasion of Carcinus maenas (the European green crab)

This paper proposes a system of integro-difference equations to model the spread of Carcinus maenas, commonly called the European green crab, that causes severe damage to coastal ecosystems. A model with juvenile and adult classes is first studied. Here, standard theory of monotone operators for integro-difference equations can be applied and yields explicit formulas for the asymptotic spreading speeds of the juvenile and adult crabs. A second model including an infected class is considered by introducing a castrating parasite Sacculina carcini as a biological control agent. The dynamics are complicated and simulations reveal the occurrence of periodic solutions and stacked fronts. In this case, only conjectures can be made for the asymptotic spreading speeds because of the lack of mathematical theory for non-monotone operators. This paper also emphasizes the need for mathematical studies of non-monotone operators in heterogeneous environments and the existence of stacked front solutions in biological invasion models.     

Score Tests for Exploring Complex Models: Application to HIV Dynamics Models

In biostatistics, more and more complex models are being developed. This is particularly the case in system biology. Fitting complex models can be very time‐consuming, since many models often have to be explored. Among the possibilities are the introduction of explanatory variables and the determination of random effects. The particularity of this use of the score test is that the null hypothesis is not itself very simple; typically, some random effects may be present under the null hypothesis. Moreover, the information matrix cannot be computed, but only an approximation based on the score. This article examines this situation with the specific example of HIV dynamics models. We examine the score test statistics for testing the effect of explanatory variables and the variance of random effect in this complex situation. We study type I errors and the statistical powers of this score test statistics and we apply the score test approach to a real data set of HIV‐infected patients.     

Nonparametric estimation in a cure model with random cure times

Acute respiratory distress syndrome (ARDS) is a life-threatening acute condition that sometimes follows pneumonia or surgery. Patients who recover and leave the hospital are considered to have been cured at the time they leave the hospital. These data differ from typical data in which cure is a possibility: death times are not observed for patients who are cured and cure times are observed and vary among patients. Here we apply a competing risks model to these data and show it to be equivalent to a mixture model, the more common approach for cure data. Further, we derive an estimator for the variance of the cumulative incidence function from the competing risks model, and thus for the cure rate, based on elementary calculations. We compare our variance estimator to Gray's (1988, Annals of Statistics 16, 1140-1154) estimator, which is based on counting process theory. We find our estimator to be slightly more accurate in small samples. We apply these results to data from an ARDS clinical trial.     

Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells

 In the presence of stimulatory concentrations of glucose, the membrane potential of pancreatic β-cells may experience a transition from periods of rapid spike-like oscillations alternating with a pseudo-steady state to spike-only oscillations. Insulin secretion from β-cells closely correlates the periods of spike-like oscillations. The purpose of this paper is to study the mathematical structure which underlines this transitional stage in a pancreatic β-cell model. It is demonstrated that the transition can be chaotic but becomes more and more regular with increase in glucose. In particular, the system undergoes a reversed period-doubling cascade leading to the spike-only oscillations as the glucose concentration crosses a threshold. The transition interval in glucose concentration is estimated to be extremely small in terms of the rate of change for the calcium dynamics in the β-cells. The methods are based on the theory of unimodal maps and the geometric and asymptotic theories of singular perturbations. Received: 25 October 1996/Revised version: 18 August 1997     

Expression of functional recombinant human lysozyme in transgenic rice cell culture

Using particle bombardment-mediated transformation, a codon-optimized synthetic gene for human lysozyme was introduced into the calli of rice (Oryza sativa) cultivar Taipei 309. The expression levels of recombinant human lysozyme in the transformed rice suspension cell culture approached approximately 4% of total soluble protein. Recombinant human lysozyme was purified to greater than 95% homogeneity using a two-step chromatography process. Amino acid sequencing verified that the N-terminus of the mature recombinant human lysozyme was identical to native human lysozyme. This indicates that the rice RAmy3D signal peptide was correctly cleaved off from the human lysozyme preprotein by endogenous rice signal peptidase. Recombinant human lysozyme was found to have the same molecular mass, isoelectric point and specific activity as native human lysozyme. The bactericidal activity of recombinant human lysozyme was determined by turbidimetric assay using Micrococcus lysodeikticus in 96-well microtiter plates. The bactericidal activity of lysozyme on Gram-negative bacteria was examined by adding purified lysozyme to mid-log phase cultures of E. coli strain JM109. In this study, significant bactericidal activity was observed after E.coli cells were exposed to recombinant human lysozyme for 60min. Both native and recombinant human lysozyme displayed the same thermostability and resistance to degradation by low pH. The potential for using rice-derived lysozyme as an antimicrobial food supplement, particularly for infant formula and baby foods, is discussed.