Mikael Cronhjort

Cluster compartmentalization may provide resistance to parasites for catalytic networks

Abstract We have performed calculations on reaction-diffusion equations with an aim to study two-dimensional spatial patterns. The systems explicitly studied are three different catalytic networks: a 4-component network displaying chaotic dynamics, a 5-component hypercycle network and a simple 1-component system. We have obtained cluster states for all these networks, and in all cases the clusters have the ability to divide. This contradicts recent conclusions that only systems with chaotic dynamics may give cluster states. On the contrary, we think that any network architecture may display cluster formation and cluster division. Our conclusion is in agreement with experimental results reported for an inorganic system corresponding to the simple 1-component system studied in this paper. In a partial differential equations model, the clusters do not provide resistance to parasites, which are assumed to arise by mutations. Parasites may spread from one cluster to another, and eventually kill all clusters. However, by combinding the partial differential equations with a suitable cut-off rule, we demonstrate a system of partly isolated clusters that is resistant against parasites. The parasites do not infect all clusters, and when the infected clusters have decayed, they are replaced by new ones, as neighbouring clusters divide.

Hypercycles versus parasites in the origin of life: model dependence in spatial hypercycle systems

Spatial hypercycle systems can be modelled by means of cellular automata or partial differential equations. In either model, two dimensional spirals or clusters can be formed. Different models give rise to slightly different spatial structures, but the response to parasites is fundamentally different: In cellular automata the hypercycle is resistant to parasites that are fatal in a partial differential equations model. In three dimensions scroll rings correspond to the two dimensional spirals. Numerical simulations on a partial differential equations model indicate that the scroll rings are unstable: The contract by a power law and disappear. Therefore, in three dimensions clusters seem to be the best candidate for the hypercycle resistant to parasites.

Intron evolution : a statistical comparison of two models

The two most frequently occurring explanations for the existence and distribution of introns in the genes of different species are: (1) introns are remnants of the original genetic material. (2) Introns were introduced during evolution. We construct mathematical models corresponding to these two explanations, and calculate the probabilities that the intron distribution in genes from different species coding for actin, alpha-tubulin, triosephosphate isomerase and superoxide dismutase are described by these models. In both models, the branch lengths as well as the structure of the corresponding evolutionary tree is taken into account. Every branch in the evolutionary tree is assumed to have its own individual rate of loss of introns for the first model and rate of gain of introns for the second model. These rate constants are estimated from the actual number of introns. Using the rate constants we stimulate the intron evolution and calculate the probabilities that the actual intron arrangements are produced. The results for actin and alpha-tubulin, which are the two genes we have the most data for, favor the model corresponding conjecture (1), i.e. the idea that introns are old. This contradicts the results from an earlier attempt to model intron evolution where almost the same data was used (Dibb & Newman, 1989, EMBO J. 8, 2015-2021).

3D hypercycles have no stable spatial structure

Abstract Two-dimensional (2D) hypercycles have been shown to generate spiral patterns, which may protect the hypercycle from parasites that would be fatal to the hypercycle in a homogeneous spatial distribution. We perform numerical experiments on a partial differential equations hypercycle model and show that scroll rings are formed and are not stable: They contract by a power law and disappear within finite time. Similar results are obtained with a 3D cellular automaton hypercycle model. For the 3D hypercycle the final state is homogeneously oscillating, except with initial conditions creating plane waves or 2D spirals. This indicates that the mechanism which may protect the 2D hypercycle from parasites is not applicable to 3D hypercycles. The contraction of the scroll rings is analogous to what has been observed and calculated for other phenomena and models, of which one is the Belousov-Zhabotinsky reaction, described by several mathematical models.

Engineering students’ experiences of interactive teaching in calculus

ABSTRACT This study reports on an educational development initiative where peer instruction was used instead of traditional lectures in a calculus course for first-year engineering students. The aim of the study was to explore students’ experiences of this method. Data were collected by means of an open-ended questionnaire on two occasions: early and late in the course. The data were analyzed with an inductive content analysis. The findings comprise three qualitatively different ways to experience the interactive teaching method in calculus: (1) enthusiasm, (2) nuanced skepticism and (3) aversion. The categories differed regarding emotional reactions to the teaching, experiences of learning, conceptions of teaching and learning, and experiences of meaningfulness. Many students expressed enthusiasm for learning with peer instruction and noted that the method gave both teachers and students feedback on what students have difficulties with. These students perceived that they were responsible for their own learning. Other students experienced that peer instruction had some advantages and disadvantages, and preferred a mix between traditional lectures and peer instruction sessions. They seemed to believe that teachers and students share responsibility for learning. Some students expressed an aversion for peer instruction and the method seemed to challenge their beliefs of how teaching and learning is best conducted. Our study illustrates that educational development initiatives, even though based on research on student learning, do not benefit all students. One of the major obstacles seems to be that students’ underlying beliefs regarding teaching and learning may be counterproductive to the ideas behind the educational initiative. We suggest that beliefs regarding teaching and learning need to be addressed when introducing new teaching and learning methods.