Traveling wave solutions for a one-dimensional crawling nematode sperm cell model

In this paper, we proved that the one-dimensional crawling nematode sperm cell model proposed by Mogilner and Verzi (2003) supports traveling wave solutions if there is no disassembly of unbundled filaments in the cell. Uniqueness of traveling wave is established under additional assumptions and numerical examples are also given in the paper. Mathematical methods used include dynamical system techniques, implicit function theorem and global bifurcation theory.Revised version: 16 September 2003     

From macroscopic measurements to microscopic mechanisms of protein aggregation

The ability to relate bulk experimental measurements of amyloid formation to the microscopic assembly processes that underlie protein aggregation is critical in order to achieve a quantitative understanding of this complex phenomenon. In this review, we focus on the insights from classical and modern theories of linear growth phenomena and discuss how theory allows the roles of growth and nucleation processes to be defined through the analysis of experimental in vitro time courses of amyloid formation. Moreover, we discuss the specific signatures in the time course of the reactions that correspond to the actions of primary and secondary nucleation processes, and outline strategies for identifying and characterising the nature of the dominant process responsible in each case for the generation of new aggregates. We highlight the power of a global analysis of experimental time courses acquired under different conditions, and discuss how such an analysis allows a rigorous connection to be established between the macroscopic measurements and the rates of the individual microscopic processes that underlie the phenomenon of amyloid formation.     

Traveling wave solutions in a two-group SIR epidemic model with constant recruitment

Journal of Mathematical Biology - Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves...     

Traveling wave solutions in a plant population model with a seed bank

We propose an integro-difference equation model to predict the spatial spread of a plant population with a seed bank. The formulation of the model consists of a nonmonotone convolution integral operator describing the recruitment and seed dispersal and a linear contraction operator addressing the effect of the seed bank. The recursion operator of the model is noncompact, which poses a challenge to establishing the existence of traveling wave solutions. We show that the model has a spreading speed, and prove that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions by using an asymptotic fixed point theorem. Our numerical simulations show that the seed bank has the stabilizing effect on the spatial patterns of traveling wave solutions.     

Linking microscopic interactions with macroscopic effects

Understanding how biotic interactions impact plant community assembly is a long‐standing goal in ecology, but studies of biotic interactions in this context are often limited to macro‐interactions. In this issue of Journal of Vegetation Science, Sonkoly et al. synthesize current knowledge regarding the impact of cyanobacteria on terrestrial plants and show that cyanotoxins can alter germination and establishment success in grassland communities.     

Traveling wave solutions of a reaction diffusion model for competing pioneer and climax species

Presented is a reaction-diffusion model for the interaction of pioneer and climax species. For certain parameters the system exhibits bistability and traveling wave solutions. Specifically, we show that when the climax species diffuses at a slow rate there are traveling wave solutions which correspond to extinction waves of either the pioneer or climax species. A leading order analysis is used in the one-dimensional spatial case to estimate the wave speed sign that determines which species becomes extinct. Results of these analyses are then compared to numerical simulations of wave front propagation for the model on one and two-dimensional spatial domains. A simple mechanism for harvesting is also introduced.     

Long range intermolecular forces between macroscopic bodies: macroscopic and microscopic approaches.

Van der Waals energies of interaction are calculated by two methods, the macroscopic method of Lifshitz and the microscopic method of London-Casimir and Polder-Hamaker for the case of two semi-infinite slabs separated by a thin film. When retardation effects may be neglected, the London-Hamaker approach yields values of dispersion interactions which almost coincide with those of the Lifshitz approach, the magnitude of the former values being larger by approximately 10–25%, which is attributed to the effect of the molecular environment in condensed media. At 50–100 Å film thicknesses where retardation effects are small, dispersion terms are generally the major part of van der Waals forces in the Lifshitz formulation. Hence, for 50–100 Å film thicknesses the Hamaker approach, which only includes dispersion interactions is generally adequate. By accounting for retardation effects, which significantly reduce the magnitude of dispersion interactions at several hundred Å, there is a reasonable agreement between the values obtained by the macroscopic and microscopic approaches. When polar substances are present and for film thicknesses of several hundred Å, where dispersion interactions are significantly reduced, the major contribution to van der Waals forces may arise from orientation and induction terms. For such cases the Hamaker approach may lead to critical underestimates of the calculated magnitude of van der Waals forces. An ad hoc way to overcome this difficulty which is applicable to any geometry is proposed. This study presents a simple procedure for the determination of free energies of interaction between macroscopic bodies of various shapes. The procedure, which is applicable when the molecules of bodies and surrounding medium are isotropic, yields results which closely approximate those obtained with the Lifshitz theory.     

Navigating through models of chemotaxis

Chemotaxis in eukaryotic cells involves the coordination of several related but separable processes: motility, polarization, and gradient sensing. Mathematical models that have been proposed to explain chemotaxis typically focus on only one of these processes. We summarize the strengths and weaknesses of the models and point out the need for an integrated model.     

Osmosis: a macroscopic phenomenon,a microscopic view

At present, physical chemistry employs the tools of thermodynamics to treat osmosis across a semipermeable membrane. We propose a model in terms of momentum transfer, the inherent asymmetry of which leads quantitatively to the van't Hoff relationship; qualitatively, the solute molecules can be looked upon as micropumps that suck solvent through the pores in the membrane.     

Distinct macroscopic structures developed from solutions of chemical compounds and periodic proteins

By controlling the growth of inorganic crystals, macro-biomolecules, including proteins, play pivotal roles in modulating biomineralization. Natural proteins that promote biomineralization are often composed of simple repeats of peptide sequences; however, the relationship between these repetitive structures and their functions remains largely unknown. Here we show that an artificial protein containing a repeated peptide sequence allows NaCl, KCl, CuSO₄ and sucrose to form a variety of macroscopic structures, as represented by their dendritic configurations. Mutational analyses revealed that the physicochemical characteristics of the protein, not the peptide sequence per se, were responsible for formation of the dendritic structures. This suggests that proteins that modulate crystal growth may have evolved as repeat-containing forms at a relatively high rate. These observations could serve as the basis for developing new genetic programming systems for creation of artificial proteins able to modulate crystal growth from inorganic compounds, and may thus provide a new tool for nano-biotechnology.     

Relating microscopic charge movement to macroscopic currents: the Ramo-Shockley theorem applied to ion channels

Since the discovery of gating current, electrophysiologists have studied the movement of charged groups within channel proteins by changing potential and measuring the resulting capacitive current. The relation of atomic-scale movements of charged groups to the gating current measured in an external circuit, however, is not obvious. We report here that a general solution to this problem exists in the form of the Ramo-Shockley theorem. For systems with different amounts of atomic detail, we use the theorem to calculate the gating charge produced by movements of protein charges. Even without calculation or simulation, the Ramo-Shockley theorem eliminates a class of interpretations of experimental results. The theorem may also be used at each time step of simulations to compute external current.     

Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions

To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.     

Properties of solutions for a chemotaxis system

 We investigate mathematically the system of equations proposed by Chaplain and Stuart [2], to describe the chemotactic response of endothelial cells under the angiogenesis stimulus. In particular, we characterize the steady state endothelial cell density function, and give conditions on the chemotactic parameter k and cell proliferation parameter b that ensure that migration/ proliferation either does or does not occur in steady state. The time dependent problem is also treated. Received 12 September 1995; received in revised form 6 August 1996     

Species of the Bacillus strain: macroscopic and microscopic morphology

Between October 2001 and January 2002, the Microbiology Group of the Instituto Nacional de Salud processed 705 envelopes under suspicion of harboring anthrax spores. We present photographs of cultures and slides prepared from them of Bacillus species to be used as reference material for the accurate macroscopic and microscopic identification of the agent found in samples.     

Effects of cadmium chloride administration on the macroscopic and microscopic characteristics of ejaculates from Chios ram-lambs

The effects of cadmium chloride on the volume of the ejaculate, semen density, total number of spermatozoa per ejaculate, viability, grade of motility, and morphological abnormalities were studied in 3-month-old ram-lambs of the Chios breed. Two groups of seven animals each were used. For a period of 7 months, one group was treated with a daily oral dose (3 mg/kg b.w.) of cadmium chloride and the other group received the corresponding volume of doubly distilled water. Blood samples were collected for cadmium determinations, whereas semen was collected weekly. In the cadmium-treated animals, cadmium concentration in the whole blood was increased and the testes weight was lower. The volume of the ejaculate, the semen density and the total number of spermatozoa were significantly reduced by the administration of cadmium chloride. No differences were observed in the viability, the grade motility of spermatozoa, or the percentage of dead and morphologically abnormal spermatozoa between the control and the cadmium-treated animals. Histopathological examination in the cadmium-treated animals revealed the presence of lesions in the Sertoli cells, the seminiferous tubules, the primary and the secondary spermatocytes and the spermatides, whereas in the Leydig cells no significant lesions were evident.     

Development of macroscopic and microscopic characteristics of ejaculates from Chios, Serres and Karaguniki breed lambs

The developmental characteristics in the volume of the ejaculate, motility (percentage of motile spermatozoa) and grade of motility (vitality), density, total number of spermatozoa per ejaculate and percentage of dead (stained) and of morphologically abnormal spermatozoa were studied in 14-to 46-week-old lambs of the Chios (n=10), Serres (=10) and Karaguniki (n=10) breeds, born in October 1984. The first appearance of spermatozoa in the ejaculate of the Chios, Serres and Karaguniki lambs occurred at 20.1+/-0.31 (x +/-SEM), 20.4+/-0.37 and 20.6+/-0.54 weeks of age, respectively, when the lambs had attained a body weight of 36.4+/-, 36.5+/-0.70 and 34.9+/-0.99 Kg, respectively. The volume of the ejaculate, the motility and the grade of motility of spermatozoa increased at a rapid rate up to the age of 32 weeks, when the relevant values were the same as those found in the adult animal. Density of the semen and the total number of spermatozoa per ejaculate increased at a slower rate up to the age of 46 weeks, while the percentages of dead (stained) and of morphologically abnormal spermatozoa decreased significantly between 20 and 32 weeks of age. It is concluded that the quality of the semen at the time when the first spermatozoa appear in the ejaculate is not satisfactory, but it improves in the course of the ensuing 2 to 3 months. The optimal age at which the lambs may be used for artificial insemination are 32, 36 and 34 weeks for the Chios, Serres and Karaguniki breeds, respectively.