Pauline Hogeweg

Spiral breakup in a modified FitzHugh-Nagumo model

In a modified FitzHugh-Nagumo model for excitable tissue a spiral wave is found to break up into an irregular spatial pattern. The main difference between our equations and the standard FitzHugh-Nagumo model is that we use two different time constants: one for the relative refractory period and another for the absolute refractory period. Breakup occurs when the relative refractory period is short. The effect is numerically stable at least for a five-fold decrease in the space integration step.

Evolutionary consequences of spiral waves in a host—parasitoid system

In a spatial model host—parasitoid interactions have been shown to generate spiral waves and spiral chaos. We demonstrate that this spatial self-structuring has far-reaching evolutionary consequences. It turns out that the selection of mutants is determined by the physical process of expansion of a faster rotating spiral. This selection at the level of entire spirals replaces selection at the level of individuals. This change in the level of selection leads to selection for less efficient parasitoids.

Predator—prey coevolution: interactions across different timescales

Using a simple predator—prey model we studied the consequences of interlocking processes that occur on ecological and evolutionary timescales. Various evolutionary attractors are shown, one of which is a system of two prey and two predator quasi-species packed in an alternating pattern. This pattern, which proves to be very robust, is studied in more detail to investigate the interaction between evolutionary and population dynamics. The evolutionary and the population dynamics both show complex periodic behaviour, with the same two dominant periods. The two prey quasi-species as well as the two predator ‘quasi-species’ oscillate synchronously, albeit out of phase. It is this temporal pattern in the population dynamics which drives the evolutionary dynamics and evolutionary dynamics which force the population dynamics to periodic behaviour with much shorter periods than if there were no evolution. This mutual influencing of the periodic behaviour is an interesting consequence of the interaction across different timescales. It is further shown that the evolutionary dynamics are essential for the maintenance of different species in the system.

Memory but no suppression in low-dimensional symmetric idiotypic networks

We present a new symmetric model of the idiotypic immune network. The model specifies clones of B-lymphocytes and incorporates: (1) influx and decay of cells; (2) symmetric stimulatory and inhibitory idiotypic interactions; (3) an explicit affinity parameter (matrix); (4) external (i.e. non-idiotypic) antigens. Suppression is the dominant interaction, i.e. strong idiotypic interactions are always suppressive. This precludes reciprocal stimulation of large clones and thus infinite proliferation. Idiotypic interactions first evoke proliferation, this enlarges the clones, and may in turn evoke suppression. We investigate the effect of idiotypic interactions on normal proliferative immune responses to antigens (e.g. viruses).A 2-D, i.e. two clone, network has a maximum of three stable equilibria: the virgin state and two asymmetric immune states. The immune states only exist if the affinity of the idiotypic interaction is high enough. Stimulation with antigen leads to a switch from the virgin state to the corresponding immune state. The network therefore remembers antigens, i.e. it accounts for immunity/memory by switching beteen multiple stable states. 3-D systems have, depending on the affinities, 9 qualitatively different states. Most of these also account for memory by state switching.Our idiotypic network however fails to account for the control of proliferation, e.g. suppression of excessive proliferation. In symmetric networks, the proliferating clones suppress their anti-idiotypic suppressors long before the latter can suppress the former. The absence of proliferation control violates the general assumption that idiotypic interactions play an important role in immune regulation. We therefore test the robustness of these results by abandoning our assumption that proliferation occurs before suppression. We thus define an “escape from suppression” model, i.e. in the “virgin” state idiotypic interactions are now suppressive. This system erratically accounts for memory and never for suppression. We conclude that our “absence of suppression from idiotypic interactions” does not hinge upon our “proliferation before suppression” assumption.

Simulating the growth of cellular forms

The computer simulation enterprise has undergone successive waves of transformation (one might even say revolution) in its short existence. From the analog modelling of aircraft control systems and the Monte Carlo simulation of neutron beam trajectories to the comprehensive ambitions of &dquo;world simulationists&dquo; stretches a tremendous span of quantitative and qualitative technological developments. Indeed, rapid expansion of the domain of application of simulation has been accompanied by steady progress in the

Spatial gradients enhance persistence of hypercycles

Abstract In this paper we study a partial differential equation model of cyclic catalysis of replicating entities (i.e. a hypercycle). In the presence of a spatial gradient in the decay rate of molecules we observe spiral drift towards the region of faster rotating spirals. On a radial gradient one spiral anchors in the region of fasterst rotation. If the drop in the gradient is large enough, this spiral will break up in the periphery and form new spiral centres. The system settles in a dynamic equilibrium. This equilibrium turns out to be persistent even against strong parasites, i.e., molecules that receive increased catalysis but do not give any catalysis. If just one peripheral spiral manages to escape the first attacking wave of the parasite, this spiral will gradually push out the parasites and in the long run the dynamic equilibrium will be completely restored. We conclude that a gradient can supply regenerative power to the hypercycle.

Patterns in vegetation succession, an ecomorphological study

Traditionally there are two largely independent sets of concepts for the description of assemblages of plants: those pertaining to ‘populations’ and those pertaining to ‘vegetation’. To bridge the gap between them, we cannot confine ourselves to the original sets of concepts because each represents a different and incompatible global description, obtained by different ways of averaging. Nevertheless they describe the same ‘object’. Relating population and vegetation concepts can be done via a microscopic description sufficient to generate this object, which in turn can be described (amongst others) in terms of populations and/or vegetation by appropriate methods of averaging. The relations between descriptions in terms of populations and in terms of vegetation are shown to depend on variation in the microscopic structure of plant assemblages, which should be defined in terms of local interactions between local entities such as individual plants or small areas. The concepts ‘scale’ and ‘detail’ are important in our discussion.

Equal G and C contents in histone genes indicate selection pressures on mRNA secondary structure

SummaryProtein-specific versus taxon-specific patterns of nucleotide frequencies were studied in histone genes. The third positions of codons have a (well-known) taxon-specific G+C level and a histone type-specific G/C ratio. This ratio counterbalances the G/C ratio in the first and second positions so that the overall G and C levels in the coding region become approximately equal. The compensation of the G/C ratio indicates a selection pressure at the mRNA level rather than a selection pressure or mutation bias at the DNA level or a selection pressure on codon usage. The structure of histone mRNAs is compatible with the hypothesis that the G/C compensation is due to selection pressures on mRNA secondary structure. Nevertheless, no specific motifs seem to have been selected, and the free energy of the secondary structures is only slightly lower than that expected on the basis of nucleotide frequencies.

CONCEPT ADVANTAGES OF DISCRETE EVENT FORMALISM

In this paper we study different timing regimes for a class of morpheme generating systems. These systems were previously analysed in their classical discrete time form:1 in that form they are of the type of developmental systems proposed by Lindenmayer.1,2,3By timing regime we mean rules governing activation of local transitions. The fixed limeslep, globally synchronous regime underlying L-systems are one example and the basis of our previous study. In this paper some other possibilities are considered, naturally expressable in discrete event form. Each of them involves some measure of local synchronisation and variable timing. These various timing regimes are compared with respect to the variability of the morphemes generated by them. This is done by cluster analysis.|It is shown that: (I) the generated morphemes depend more heavily on the timing regime than on the particular state transition function of the cells; (ii) local synchronisation is sufficient to reestablish the seeming complexity and the fo...

Stability of symmetric idiotypic networks-a critique of Hoffmann's analysis

Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis.