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Ton Bisseling and Tinri Aegerter-Wilmsen are in the Laboratory of Molecular Biology, Wageningen University and Research Centre, Wageningen, the Netherlands.

An online educational module introduces students to concepts of quantitation and numerical simulations in developmental biology.

As an example of the integration of quantitative teaching and cutting edge biology, we have implemented an educational module in which numerical simulations are used in an existing course on developmental biology (

First, we wanted to illustrate to students the value of using numerical simulations to study a developmental process. Therefore, a pattern-forming mechanism was selected that can initially be rather hard to understand: the generation of the morphogen gradient formed by the extracellular signalling molecule decapentaplegic (Dpp) early during

Second, we designed the simulation environment in such a way that biology students with their existing mathematical background can build quantitative models and run numerical simulations themselves. In this environment (

After several minutes, Dpp forms one peak in the centre of the dorsal region, as in the wild type. The various elements of the quantitative model can be entered under “protein conc. changes”, “initial localizations”, “values of constants”, and “initial concentrations”. The numerical simulation itself shows the dynamic behaviour of the designed quantitative model.

If a student indicates that Dpp diffusion occurs, a diffusion term is added to the differential equation that describes the changes in Dpp concentration.

Third, we wanted to make sure that students would use the simulation environment effectively. Therefore, a clear goal is formulated when students enter the simulation environment. For example, they are asked to make a model that generates a Dpp gradient that fulfills a number of specific criteria, or simulates certain mutants. After running a simulation, students can view feedback that helps them draw conclusions or consider the next step to be taken. If a student's model, for example, generates a gradient that is too shallow, the student has to indicate which change in the model he expects to be useful for generating a steeper gradient. The student then receives an intuitive explanation of the usefulness of the given suggestion. If an increase in the synthesis of one of the proteins, Short gastrulation, is proposed, for example, feedback is given that this could indeed be useful, since there would then be more Short gastrulation available to transport Dpp, such that the gradient can become steeper. In this way, the student is stimulated to carefully consider each step and is provided with sufficient support to decide which is a useful step to follow. In addition, with this type of feedback, explanations are given that relate quantitative changes in the model to qualitative changes in its behaviour, which should increase the student's understanding of the behaviour of the biological model.

We consider it important that students, while using the module, are not distracted too much by quantitative issues from the actual biological principles and facts. These have to be mastered in order to obtain a strong biological background. If students want to learn more advanced quantitative skills, they can still follow courses that are specifically aimed at this aspect.

Quantitative analysis is already gaining importance in molecular life sciences. Therefore, it is desirable that curriculum changes are implemented in the short term. This poses challenges to faculties, especially to those whose members do not have much, if any, experience with the application of quantitative tools in their own research. Therefore, it may be useful to initially focus on the development of learning materials that are rather self-contained, such that their application requires relatively little competence in quantitative analysis from the teaching staff. If these materials are openly available they can be incorporated rapidly into existing courses, such that even the current generation of students may be better prepared to integrate quantitative thinking and biology in their future research.

We would like to thank Rob Hartog, Fred Janssen, Dik Kettenis, and Olivier Sessink for their contribution to the development of the educational material and Christof Aegerter for helpful discussions.

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