A Three-Tiered Study of Differences in Murine Intrahost Immune Response to Multiple Pneumococcal Strains

We apply a previously developed 4-variable ordinary differential equation model of in-host immune response to pneumococcal pneumonia to study the variability of the immune response of MF1 mice and to explore bacteria-driven differences in disease progression and outcome. In particular, we study the immune response to D39 strain of bacteria missing portions of the pneumolysin protein controlling either the hemolytic activity or complement-activating activity, the response to D39 bacteria deficient in either neuraminidase A or B, and the differences in the response to D39 (serotype 2), 0100993 (serotype 3), and TIGR4 (serotype 4) bacteria. The model accurately reproduces infection kinetics in all cases and provides information about which mechanisms in the immune response have the greatest effect in each case. Results suggest that differences in the ability of bacteria to defeat immune response are primarily due to the ability of the bacteria to elude nonspecific clearance in the lung tissue as well as the ability to create damage to the lung epithelium.     

Models for contact-mediated pattern formation: cells that form parallel arrays

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.     

An adaptive model for synchrony in the firefly Pteroptyx malaccae

We describe a new model for synchronization of neuronal oscillators that is based on the observation that certain species of fireflies are able to alter their free-running period. We show that by adding adaptation to standard oscillator models it is possible to observe the frequency alteration. One consequence of this is the perfect synchrony between coupled oscillators. Stability and some analytic results are included along with numerical simulations.This work was partially supported by NSF Grant DMS9002028 and the Mathematical Research Branch of The National Institutes of Health     

Temporal oscillations in neuronal nets

Summary A model for the interactions of cortical neurons is derived and analyzed. It is shown that small amplitude spatially inhomogeneous standing oscillations can bifurcate from the rest state. In a periodic domain, traveling wave trains exist. Stability of these patterns is discussed in terms of biological parameters. Homoclinic and heteroclinic orbits are demonstrated for the space-clamped system.The research reported in this paper was supported in part by NIH GM2037     

Model for Transition from Waves to Synchrony in the Olfactory Lobe of Limax

A biophysical model for the interactions between bursting (B) cells and nonbursting (NB) cells in the procerebral lobe of Limax is developed and tested. Phase-sensitivity of the NB cells is exhibited due to the strong inhibition from the rhythmically bursting B cells. Electrical and chemical junctions coupled with a parameter gradient lead to sustained periodic waves in the lobe. Excitatory interactions between the NB cells, which rarely fire, lead to stimulus evoked synchrony in the lobe oscillations. A novel calcium current is suggested to explain the effects of nitric oxide (NO) on the lobe. Gap junctions are shown both experimentally and through simulations to be required for the oscillating field potentials.     

Models for the length distributions of actin filaments: I. Simple polymerization and fragmentation

We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.     

Seroprevalence of <Emphasis Type="Italic">Borrelia burgdorferi</Emphasis> sensu lato and <Emphasis Type="Italic">Anaplasma phagocytophilum</Emphasis> in Danish horses

Background

Borrelia burgdorferi sensu lato and Anaplasma phagocytophilum are able to infect horses. However, the extend to which Danish horses are infected and seroconvert due to these two bacteria is unknown. The aim of the present study was to evaluate the seroprevalence of B. burgdorferi sensu lato and A. phagocytophilum in Danish horses.

Methods

A total of 390 blood samples collected from all major regions of Denmark and with a geographical distribution corresponding to the density of the Danish horse population were analyzed. All samples were examined for the presence of antibodies against B. burgdorferi sensu lato and A. phagocytophilum by the use of the SNAP^®4DX ^® ELISA test.

Results

Overall, 29.0% of the horses were seropositive for B. burgdorferi sensu lato whereas 22.3% were seropositive for A. phagocytophilum.

Conclusions

Antibodies against B burgdorferi sensu lato and A. phagocytophilum are commonly found among Danish horses thus showing that Danish horses are frequently infected by these organisms.

     

The variance of phase-resetting curves

Phase resetting curves (PRCs) provide a measure of the sensitivity of oscillators to perturbations. In a noisy environment, these curves are themselves very noisy. Using perturbation theory, we compute the mean and the variance for PRCs for arbitrary limit cycle oscillators when the noise is small. Phase resetting curves and phase dependent variance are fit to experimental data and the variance is computed using an ad-hoc method. The theoretical curves of this phase dependent method match both simulations and experimental data significantly better than an ad-hoc method. A dual cell network simulation is compared to predictions using the analytical phase dependent variance estimation presented in this paper. We also discuss how entrainment of a neuron to a periodic pulse depends on the noise amplitude.