Replication of dengue viruses in mosquito cell cultures--a model from ultrastructural observations.

Mosquito cell cultures infected with human sera from dengue-1 and dengue-2 outbreaks, started in Rio de Janerio by 1986 and 1990 respectively, were examined by electron microscopy at different times post the infection of cell cultures. More information was obtained about cell penetration of virus particles in the presence or not of antibodies, their pathway inside the cells, replication mode and exist. Infectiveness of the virus at those different stages can only be attributed to the particles appearing inside the trans-Golgi vesicles; most of all newly formed virus particles remain inside the RER-derived cell vesicles or inside lysosomes, even during cell lysis. Groups of larger particles, 65-75 nm in diameter at dengue-2 infections, persist during cell passage. The large amounts of smooth membrane structures, as vesicles or tubules inside the RER, are attributed to a cell response to viral infection.     

Mode-doubling and tripling in reaction-diffusion patterns on growing domains: A piecewise linear model

 Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system. Received: 19 December 2000 / Revised version: 24 May 2001 / Published online: 7 December 2001     

Evolution of bacteriophage T7 in a growing plaque.

The emergence of mutants during the 10(9)-fold amplification of a bacteriophage was spatially resolved in a growing plaque. When wild-type phage T7 was grown on an Escherichia coli host which expressed an essential early enzyme of the phage infection cycle, the T7 RNA polymerase, mutant phage relying on this enzyme appeared in 10(8) phage replications and outgrew the wild type. Spatial resolution of the selection process was achieved by analyzing stab samples taken along a plaque radius. Different mutants were selected at different rates along different radii of the plaque, based on host range and restriction patterns of the isolates. The mutants deleted up to 11% of their genomes, including the gene for their own RNA polymerase. They gained an advantage over the wild type by replicating more efficiently, as determined by one-step growth cultures.     

Mixed-mode pattern in Doublefoot mutant mouse limb--Turing reaction-diffusion model on a growing domain during limb development

It has been suggested that the Turing reaction-diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction-diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction-diffusion model. Finally, we make some experimentally testable predictions.     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth.     

Development of a bioartificial nerve graft. I. Design based on a reaction-diffusion model

A simple reaction-diffusion model has been developed to describe the mass transport of nutrients and nerve growth factor within a bioartificial nerve graft (BNG). The BNG consists of a porous polymer conduit that is preseeded with Schwann cells in its lumen. The Schwann cells produce growth factors to stimulate nerve regeneration within the lumen of the conduit. The model can predict the wall thickness, porosity, and Schwann cell seeding density needed to maximize the axon extension rate while ensuring that sufficient nutrients, especially oxygen, are made available to the neurons until the formation of the neovasculature. The model predicts a sixteen-fold increase in the levels of nerve growth factor by dropping the porosity from 95 to 55% but only at the expense of reducing the oxygen concentration. At higher porosities, increasing the wall thickness and increasing the Schwann cell seeding density both have the same effect of increasing the concentration of nerve growth factor within the lumen of the conduit. This model provides a simple tool for evaluating various conduit designs before continuing with experimental studies in vivo.     

Propagation of fluorescent viruses in growing plaques

To study virus propagation, we have developed a method by which the propagation of the Lambda bacteriophage can be observed and quantified. This is done by creating a fusion protein of the capsid protein gpD and the enhanced yellow fluorescent protein (EYFP). We show that this fusion allows capsid formation and that the modified viruses propagate on a surface covered with host bacteria thus forming fluorescent plaques. The intensity of fluorescence in a growing plaque determines the distribution of phages. This provides a new tool to study the propagation of infection at the microscopic level.     

Traveling waves in a piecewise-linear reaction-diffusion model of excitable medium

One-dimensional autowaves (traveling waves) in excitable medium described by a piecewise-linear reaction-diffusion system have been investigated. Two main types of wave have been considered: a single pulse and a periodic sequence of pulses (wave trains). In a two-component system, oscillations are due to the second component of the reaction-diffusion system, while in a one-component system, they are caused by external periodic excitation (forcing). Using semianalytical solutions for the wave profile, the shape and velocity of autowaves have been found. It is shown that the dispersion relation for oscillating sequences of pulses has an anomalous character.     

Attempts at growing insect viruses in microorganisms

Several attempts to grow the nuclear polyhedrosis virus of Heliothis armigera in microorganisms as suggested by Wells were unsuccessful.     

A non-linear analysis for spatial structure in a reaction-diffusion model

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on the practical Thomas reaction-diffusion mechanism which exhibits bifurcation to non-uniform states. The analytical results compare favourably with the numerical solutions. The sequential patterns generated by this model by variations in a parameter related to the reaction-diffusion domain indicate its capacity to represent certain key morphogenetic features required in a recent model by Kauffman for pattern formation in theDrosophila embryo.     

Pattern formation and morphogenesis: A reaction-diffusion model

The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.     

Replication of hepatitis A viruses with chimeric 5' nontranslated regions.

The role of the 5' nontranslated region in the replication of hepatitis A virus (HAV) was studied by analyzing the translation and replication of chimeric RNAs containing the encephalomyocarditis virus (EMCV) internal ribosome entry segment (IRES) and various lengths (237, 151, or 98 nucleotides [nt]) of the 5'-terminal HAV sequence. Translation of all chimeric RNAs, truncated to encode only capsid protein sequences, occurred with equal efficiency in rabbit reticulocyte lysates and was much enhanced over that exhibited by the HAV IRES. Transfection of FRhK-4 cells with the parental HAV RNA and with chimeric RNA generated a viable virus which was stable over continuous passage; however, more than 151 nt from the 5' terminus of HAV were required to support virus replication. Single-step growth curves of the recovered viruses from the parental RNA transfection and from transfection of RNA containing the EMCV IRES downstream of the first 237 nt of HAV demonstrated replication with similar kinetics and similar yields. When FRhK-4 cells infected with recombinant vaccinia virus producing SP6 RNA polymerase to amplify HAV RNA were transfected with plasmids coding for these viral RNAs or with subclones containing only HAV capsid coding sequences downstream of the parental or chimeric 5' nontranslated region, viral capsid antigens were synthesized from the HAV IRES with an efficiency equal to or greater than that achieved with the EMCV IRES. These data suggest that the inherent translation efficiency of the HAV IRES may not be the major limiting determinant of the slow-growth phenotype of HAV.     

Waves in a simple,excitable or oscillatory,reaction-diffusion model

A simple one variable caricature for oscillating and excitable reaction-diffusion systems is introduced. It is shown that as a parameter, , varies the system dynamics change from oscillatory ( > ₀) to excitable ( < ₀) and the frequency of the oscillation vanishes as for ₀. When such dynamics are coupled by continuous diffusion in a ring geometry (1-space dimension), propagating wave trains may be found. On an infinite ring excitable devices lead to unique solitary waves which are analogous to pulse waves. A solvable example is presented, illustrating properties of dispersion, excitability, and waves. Finally it is shown that the caricature arises in a natural way from more general excitable/oscillatory systems.     

Monotone travelling fronts in an age-structured reaction-diffusion model of a single species

 We consider a partially coupled diffusive population model in which the state variables represent the densities of the immature and mature population of a single species. The equation for the mature population can be considered on its own, and is a delay differential equation with a delay-dependent coefficient. For the case when the immatures are immobile, we prove that travelling wavefront solutions exist connecting the zero solution of the equation for the matures with the delay-dependent positive equilibrium state. As a perturbation of this case we then consider the case of low immature diffusivity showing that the travelling front solutions continue to persist. Our findings are contrasted with recent studies of the delayed Fisher equation. Travelling fronts of the latter are known to lose monotonicity for sufficiently large delays. In contrast, travelling fronts of our equation appear to remain monotone for all values of the delay. Received: 1 November 2001 / Revised version: 10 May 2002 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 35K57, 92D25 Key words or phrases: Age-structure – Time-delay – Travelling Fronts – Reaction-diffusion