A fibre reorientation model for orthotropic multiplicative growth

The main goal of this contribution consists in the development of a remodelling framework for orthotropic continua whereby the underlying symmetry group is incorporated via two fibre families. Special emphasis is placed on the modelling of biological tissues at finite deformations. Besides the incorporation of a referential mass source, anisotropic growth is addressed by means of a multiplicative decomposition of the overall deformation gradient into an elastic and a growth distortion. Projected quantities of a configurational growth stress tensor are advocated as driving forces for time-dependent saturation–type evolution of the principal values of the growth distortion. Moreover, the reorientation of both fibre families, which directly affects the strain energy as well as the growth distortion itself, is guided by analyzing critical energy points. In particular, a time-dependent formulation is developed which aligns the fibre directions according to the principal stretch directions. Finally, the proposed framework is embedded into a finite element context so that representative numerical examples, examining growth and resorption in volume and density together with fibre reorientation, close this study.     

A diffusion model for population growth in random environment

The growth of a population in a randomly varying environment is modeled by replacing the Malthusian growth rate with a delta-correlated normal process. The population size is then shown to be a random process, lognormally distributed, obeying a diffusion equation of the Fokker-Planck type. The first passage time p.d.f. through any arbitrarily assigned value and the probability of absorption are derived. The asymptotic behavior of the population size is investigated.     

A simple in vitro model for growth control of bacterial biofilms

The perfused biofilm fermenter was found to be unsuitable for the long-term culture and growth rate control of Staphylococcus aureus and Pseudomonas aeruginosab biofilms. In a simplified approach, biofilms of these organisms were grown within Sorbarod filter plugs which were perfused with culture medium. Pseudo-steady states were established which were stable over several days at which the growth rate of the biofilm was reproducible, measurable and significantly slower than in broth culture. Environmental scanning electron microscopy of dissected Sorbarods demonstrated an association of cells with the surfaces of individual cellulose fibres, and growth characteristic of biofilms. Relatively high cell numbers recovered from the Sorbarod model facilitated biochemical investigations of biofilm populations and cells released spontaneously from them.
SDS-PAGE demonstrated significant differences between the protein profiles of biofilm and eluted populations, which include, in Staph. aureus , the repression of a 48 kDa protein and increased expression of a 21 kDa protein relative to planktonic controls cultured at equivalent growth rates. The paper demonstrates the suitability of the approach for the culture of biofilm samples which are suitable for biochemical analysis.     

A simple in vitro model for growth control of bacterial biofilms

The perfused biofilm fermenter was found to be unsuitable for the long-term culture and growth rate control of Staphylococcus aureus and Pseudomonas aeruginosa biofilms. In a simplified approach, biofilms of these organisms were grown within Sorbarod filter plugs which were perfused with culture medium. Pseudo-steady states were established which were stable over several days at which the growth rate of the biofilm was reproducible, measurable and significantly slower than in broth culture. Environmental scanning electron microscopy of dissected Sorbarods demonstrated an association of cells with the surfaces of individual cellulose fibres, and growth characteristic of biofilms. Relatively high cell numbers recovered from the Sorbarod model facilitated biochemical investigations of biofilm populations and cells released spontaneously from them. SDS-PAGE demonstrated significant differences between the protein profiles of biofilm and eluted populations, which include, in Staph. aureus, the repression of a 48 kDa protein and increased expression of a 21 kDa protein relative to planktonic controls cultured at equivalent growth rates. The paper demonstrates the suitability of the approach for the culture of biofilm samples which are suitable for biochemical analysis.     

Monod's bacterial growth model revisited

An attempt to justify Monod's bacterial growth model is presented. The justification is based on a mechanistic approach to growth which leads to a differential equation with delay and then to Monod's model. An unexpected increase of parameterK _s with μ_m is predicted by the theory. A survey of literature shows that this effect is present in a large majority of published data.     

A bacterial artificial chromosome transgenic mouse model for visualization of neurite growth

Class III β-tubulin(Tubb3) is a component of the microtubules in neurons and contributes to microtubule dynamics that are required for axon outgrowth and guidance during neuronal development. We here report a novel bacterial artificial chromosome(BAC) transgenic mouse line that expresses Class III β-tubulin fused to m Cherry, an improved monomeric red fluorescent protein, for the visualization of microtubules during neuronal development. A BAC containing Tubb3 gene was modified by insertion of m Cherry complementary DNA downstream of Tubb3 coding sequence via homologous recombination. m Cherry fusion protein was expressed in the nervous system and testis of the transgenic animal, and the fluorescent signal was observed in the neurons that located in the olfactory bulb, cerebral cortex, hippocampal formation, cerebellum, as well as the retina. Besides, Tubb3-m Cherry fusion protein mainly distributed in neurites and colocalized with endogenous Class III β-tubulin. The fusion protein labels Purkinje cell dendrites during cerebellar circuit formation. Therefore, this transgenic line might be a novel tool for scientific community to study neuronal development both in vitro and in vivo.     

A mathematical model for the growth of bacterial microcolonies on marine sediment

Counts of bacterial microcolonies attached to deep-sea sediment particles showed 4-, 8-, 16-, and 32-celled microcolonies to be very rare. This was investigated with a mathematical model in which microcolonies grew from single cells at a constant growth rate (), detached from particles at constant rate (), and reattached as single cells. Terms for attachment of foreign bacteria (a) and death of single cells (d) were also included. The best method of fitting the model to the microcolony counts was a weighted least-squares approach by which(0.83 hour^–1) was estimated to be about 20 times greater than(0.038 hour^–1). This showed that the bacteria were very mobile between sediment particles and this mobility was explained in terms of attachment by reversible sorption. The implications of the results for the frequency of dividing cell method for estimating growth rates of sediment bacteria are discussed. The ratio of and was found to be very robust both in terms of the errors associated with the microcolony counts and the range of microcolony sizes used to obtain the solution.     

Effects of random motility on growth of bacterial populations

A spatially distributed mathematical model is developed to elucidate the effects of chemical diffusion and cell motility as well as cell growth, death, and substrate uptake on steady-state bacterial population growth in a finite, one-dimensional, nonmixed region. The situation considered is growth limited by a diffusing substrate from an adjacent phase not accessible to the bacteria. Chemotactic movement is not considered in this paper; we consider only randomwalk-type random motility behavior here. The following important general concepts are suggested by the results of our theoretical analysis: (a) The significance of random motility effects depends on the magnitude of the ratio/kL ², where is the bacterial random motility coefficient,k is the growth rate constant, andL is the linear dimension of the confined growth region. (b) In steady-state growth in a confined region, the bacterial population size decreases as increases. (c) The effect of on population size can be great; in fact, sometimes relative population sizes of two species can be governed primarily by the relative values of rather than by the relative values ofk.     

A multi-type branching model with varying environment for bacterial dynamics with postantibiotic effect

A multi-type branching process with varying environment was used to construct a pharmacokinetic/pharmacodynamic (PK/PD) model that captures the postantibiotic effect (PAE) seen in bacterial populations after exposure of antibiotics. This phenomenon of continued inhibition of bacterial growth even after removal of the antibiotic from the growth medium is of high relevance in the context of optimizing dosing regimens. The clinical implication of long PAEs lies in the interesting possibility of increasing the intervals between drug administrations.The model structure is generalizable to most types of antibiotics and is useful both as a theoretical framework for understanding the time properties of PAE and to explore optimal antibiotic dosing regimens. Data from an in vitro study with Escherichia coli exposed to different dosing regimens of cefotaxime were used to evaluate the model.     

A model for the crowding effect in the growth of tadpoles

Crowded tadpoles in a limited volume grow to divide into two groups, a normally growing group and a stunted group, even if there are a plenty of food. This phenomenon was found to be interpreted by a model involving a mutual inhibition of the growth among individuals. It was assumed that the growth curve of an individual was modelled by a Gompertz growth equation. Through mathematical analysis and computer simulation of the model, it was shown that the average growth rate of the group was a decreasing function of the population density and that the group segregated into two subgroups, a normally growing group and a stunted group in a certain range of density. A theoretical prospect that the population of normally growing group is proportionate to the volume of the aquarium was obtained.     

A flow cell photometer for bacterial growth monitoring

A flow cell photometer is described with automatic cleaning of the photometric cell, denasimetric separation of air bubbles and precipitates, and a constant sensitivity from 0 to 10 mg/ml of bacterial dry weight.     

A bacterial model system for chromosomal targeting.

A system that permits efficient site-specific chromosomal targeting of foreign DNA on the Escherichia coli chromosome has been developed, using the FLP site-specific recombination system derived from the yeast 2 mu plasmid. The system demonstrates the feasibility of using site-specific recombination for this purpose, and provides a means to gather information on parameters that may affect chromosomal targeting to guide efforts to establish similar systems in higher eukaryotes. In this model system, the efficiency of integration of foreign DNA is affected by the location of the target site in the chromosome, and the structure of the recombination sites.