Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Semigroup analysis of structured parasite populations

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then, we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In the case of a separable fertility function, we deduce a characteristic equation, and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.Comment: to appear in Mathematical Modelling of Natural Phenomen

Global Continua of Positive Equilibria for some Quasilinear Parabolic Equation with a Nonlocal Initial Condition

This paper is concerned with a quaslinear parabolic equation including a nonlinear nonlocal initial condition. The problem arises as equilibrium equation in population dynamics with nonlinear diffusion. We make use of global bifurcation theory to prove existence of an unbounded continuum of positive solutions

Enhanced diffusion due to active swimmers at a solid surface

We consider two systems of active swimmers moving close to a solid surface, one being a living population of wild-type \textit{E. coli} and the other being an assembly of self-propelled Au-Pt rods. In both situations, we have identified two different types of motion at the surface and evaluated the fraction of the population that displayed ballistic trajectories (active swimmers) with respect to those showing random-like behavior. We studied the effect of this complex swimming activity on the diffusivity of passive tracers also present at the surface. We found that the tracer diffusivity is enhanced with respect to standard Brownian motion and increases linearly with the activity of the fluid, defined as the product of the fraction of active swimmers and their mean velocity. This result can be understood in terms of series of elementary encounters between the active swimmers and the tracers.Comment: 4 pages, 2 figures in color, Physical Review Letters (in production

Pleiotropic phenotypes of a Yersinia enterocolitica flhD mutant include reduced lethality in a chicken embryo model

<p>Abstract</p> <p>Background</p> <p>The <it>Yersinia enterocolitica </it>flagellar master regulator FlhD/FlhC affects the expression levels of non-flagellar genes, including 21 genes that are involved in central metabolism. The sigma factor of the flagellar system, FliA, has a negative effect on the expression levels of seven plasmid-encoded virulence genes in addition to its positive effect on the expression levels of eight of the flagellar operons. This study investigates the phenotypes of <it>flhD </it>and <it>fliA </it>mutants that result from the complex gene regulation.</p> <p>Results</p> <p>Phenotypes relating to central metabolism were investigated with Phenotype MicroArrays. Compared to the wild-type strain, isogenic <it>flhD </it>and <it>fliA </it>mutants exhibited increased growth on purines and reduced growth on N-acetyl-D-glucosamine and D-mannose, when used as a sole carbon source. Both mutants grew more poorly on pyrimidines and L-histidine as sole nitrogen source. Several intermediates of the tricarboxylic acid and the urea cycle, as well as several dipeptides, provided differential growth conditions for the two mutants. Gene expression was determined for selected genes and correlated with the observed phenotypes. Phenotypes relating to virulence were determined with the chicken embryo lethality assay. The assay that was previously established for <it>Escherichia coli </it>strains was modified for <it>Y. enterocolitica</it>. The <it>flhD </it>mutant caused reduced chicken embryo lethality when compared to wild-type bacteria. In contrast, the <it>fliA </it>mutant caused wild-type lethality. This indicates that the virulence phenotype of the <it>flhD </it>mutant might be due to genes that are regulated by FlhD/FlhC but not FliA, such as those that encode the flagellar type III secretion system.</p> <p>Conclusion</p> <p>Phenotypes of <it>flhD </it>and <it>fliA </it>mutants are related to central metabolism and virulence and correlate with gene regulation.</p

Autoimmunenzephalitis - ein Update [Autoimmune encephalitis - an update]

Detection of autoantibodies against neurons and glia cells has brought about the early and specific diagnosis of autoimmune encephalitis in patients with variable neurological and psychiatric symptoms. Growing knowledge not only resulted in profound changes in treatment algorithms including immunotherapy but also in the understanding of disease mechanisms and etiological factors. The still increasing numbers of new autoantibodies calls for continuous updates on the state of the art in antibody diagnostics, frequencies of associated tumors and the clinical spectrum linked to each antibody, which can range from mood changes, cognitive impairment and epileptic seizures to abnormal movements, autonomic dysfunction and impaired levels of consciousness. This article summarizes the recent developments in the predominant clinical presentations of autoimmune encephalitis patients in imaging and cerebrospinal fluid diagnostics and also in prognostic markers, in the establishment of innovative immunotherapies, in the use of diagnostic pathways even before the results of the antibody tests are available and the understanding of the autoimmune etiology

Evidence that acetyl phosphate functions as a global signal during biofilm development

We used DNA macroarray analysis to identify genes that respond to the status of the intracellular acetyl phosphate (acP) pool. Genes whose expression correlated negatively with the ability to synthesize acP (i.e. negatively regulated genes) function primarily in flagella biosynthesis, a result consistent with observations that we published previously (Prüß and Wolfe, 1994, Mol Microbiol 12: 973-984). In contrast, genes whose expression correlated positively with the ability to synthesize acP (i.e. positively regulated genes) include those for type 1 pilus assembly, colanic acid (capsule) biosynthesis and certain stress effectors. To our knowledge, this constitutes the first report that these genes may respond to the status of the intracellular acP pool. Previously, other researchers have implicated flagella, type 1 pili, capsule and diverse stress effectors in the formation of biofilms. We therefore tested whether cells altered in their ability to metabolize acP could construct normal biofilms, and found that they could not. Cells defective for the production of acP and cells defective for the degradation of acP could both form biofilms, but these biofilms exhibited characteristics substantially different from each other and from biofilms formed by their wild-type parent. We confirmed the role of individual cell surface structures, the expression of which appears to correlate with acP levels, in fim or fli mutants that cannot assemble type 1 pili or flagella respectively. Thus, the information gained by expression profiling of cells with altered acP metabolism indicates that acP may help to co-ordinate the expression of surface structures and cellular processes involved in the initial stages of wild-type biofilm development

Transdiagnostic hippocampal damage patterns in neuroimmunological disorders

Hippocampal damage and associated cognitive deficits are frequently observed in neuroimmunological disorders, but comparative analyses to identify shared hippocampal damage patterns are missing. Here, we adopted a transdiagnostic analytical approach and investigated hippocampal shape deformations and associated cognitive deficits in four neuroimmunological diseases. We studied 120 patients (n = 30 in each group), including patients with multiple sclerosis (MS), neuromyelitis optica spectrum disorder (NMOSD), anti-NMDAR and anti-LGI1 encephalitis. A control group was matched to each patient sample from a pool of 79 healthy participants. We performed an MRI-based vertex-wise hippocampal shape analysis, extracted hippocampal volume estimates and scalar projection values as a measure of surface displacement. Cognitive testing included assessment of verbal memory and semantic fluency performance. Our cross-sectional analyses revealed characteristic patterns of bilateral inward deformations covering up to 32% of the hippocampal surface in MS, anti-NMDAR encephalitis, and anti-LGI1 encephalitis, whereas NMOSD patients showed no deformations compared to controls. Significant inversions were noted mainly on the hippocampal head, were accompanied by volume loss, and correlated with semantic fluency scores and verbal episodic memory in autoimmune encephalitis and MS. A deformation overlap analysis across disorders revealed a convergence zone on the left anterior hippocampus that corresponds to the CA1 subfield. This convergence zone indicates a shared downstream substrate of immune-mediated damage that appears to be particularly vulnerable to neuroinflammatory processes. Our transdiagnostic morphological view sheds light on mutual pathophysiologic pathways of cognitive deficits in neuroimmunological diseases and stimulates further research into the mechanisms of increased susceptibility of the hippocampus to autoimmunity

Relating gene expression data on two-component systems to functional annotations in Escherichia coli

<p>Abstract</p> <p>Background</p> <p>Obtaining physiological insights from microarray experiments requires computational techniques that relate gene expression data to functional information. Traditionally, this has been done in two consecutive steps. The first step identifies important genes through clustering or statistical techniques, while the second step assigns biological functions to the identified groups. Recently, techniques have been developed that identify such relationships in a single step.</p> <p>Results</p> <p>We have developed an algorithm that relates patterns of gene expression in a set of microarray experiments to functional groups in one step. Our only assumption is that patterns co-occur frequently. The effectiveness of the algorithm is demonstrated as part of a study of regulation by two-component systems in <it>Escherichia coli</it>. The significance of the relationships between expression data and functional annotations is evaluated based on density histograms that are constructed using product similarity among expression vectors. We present a biological analysis of three of the resulting functional groups of proteins, develop hypotheses for further biological studies, and test one of these hypotheses experimentally. A comparison with other algorithms and a different data set is presented.</p> <p>Conclusion</p> <p>Our new algorithm is able to find interesting and biologically meaningful relationships, not found by other algorithms, in previously analyzed data sets. Scaling of the algorithm to large data sets can be achieved based on a theoretical model.</p