Introducing molecular life science students to model building using computer simulations.

Computer simulations can facilitate the building of models of natural phenomena in research, such as in the molecular life sciences. In order to introduce molecular life science students to the use of computer simulations for model building, a digital case was developed in which students build a model of a pattern formation process in developmental biology using experimental data and computer simulations. For the development of a pedagogical approach, several design principles were used with respect to a suitable model-building method and with respect to increasing the students' understanding of (biological) systems. The case was then developed using this approach. Additional software components have been developed to provide sufficient feedback and support for students who work with the simulations. The case has been evaluated in three 3rd-year undergraduate courses at Wageningen University in the Netherlands and at the University of Zurich in Switzerland. Students appreciated working with the case and answered most exam questions about the contents of the case relatively well.

INTRODUCTION

Computer simulations can play an important role in science education. For example, they are well suited for a form of discovery learning (de Jong & van Joolingen, 1998), where the main task of the learner is to infer, through experimentation, characteristics of the model that underlie the simulation and are unknown to the learner. Scientific discovery learning with computer simulations can lead to more "intuitive" knowledge than expository teaching and it can lead to the mastery of discovery skills (de Jong & van Joolingen, 1998). However, students who employ this kind of scientific discovery learning using computer simulations do not learn how computer simulations can be applied in actual research to facilitate the building of models of natural phenomena.

The molecular life sciences constitute a research area in which computer simulations, as well as other quantitative methods, are rapidly gaining importance (Knight, 2002; Lander, 2004; Pennisi, 2003). For example, numerical simulations can be employed to discover novel biological principles (Eldar et al., 2002). In order to better prepare molecular life science students for quantitative research, curriculum adjustments that are aimed at a better integration of biology and quantitative thinking are required (Bialek & Botstein, 2004; Committee on Undergraduate Biology Education to Prepare Research Scientists for the 21st Century, 2003). For the integration of quantitative thinking into existing biology courses, it is important that the added value of quantitative thinking for biology research is illustrated, that no more mathematical knowledge is required than the current molecular life science students already have, and that students are supported in working with the quantitative methods, such that they do not get too distracted from biology (Aegerter-Wilmsen & Bisseling, 2005).

One example where numerical simulations have been employed in research to discover novel biological principles constitutes a pattern formation process during the early development of the fruit fly Drosophila, the formation of a gradient of the protein Decapentaplegic (Dpp) (Eldar et al., 2002). According to this model, a stable, dynamic Dpp gradient emerges from processes at the molecular level in combination with a specific distribution of the molecules among different regions of the embryo prior to the gradient formation. In particular, diffusion rate differences between free Dpp and a complex of Dpp and another protein, Short gastrulation (Sog), are essential for the formation of the Dpp gradient (Eldar et al., 2002).

It is worthwhile for undergraduate students who follow courses in developmental biology to become acquainted with this model for a number of reasons. First, protein gradients play a crucial role in development; therefore, it is important that students be introduced to mechanisms for the formation of a gradient. Second, diffusion rate differences are crucial in the model and diffusion rate differences are predicted to be important in other pattern forming processes (Koch & Meinhardt, 1994; Turing, 1952). Third, the Dpp gradient formation illustrates that interactions and properties at the molecular level can contribute to an emerging pattern at the embryo level. These show that emergent behavior can be important in developmental biology. Finally, the gradient forming mechanism is robust against concentration fluctuations of most of the participating proteins. This is an important biological implication of the model, since this enables embryos to develop normally even if the protein levels are not tightly controlled.

This paper describes the development and evaluation of a digital case in which students are engaged in building a model for the Dpp gradient formation using computer simulations.

DISCUSSION

Design Principles

The learning material aims to achieve several goals. Upon working with the material, students should be aware of the value that simulations add to research. Furthermore, they must know how certain biological models can be converted into a set of (partial) differential equations from a conceptual point of view (see Figure 3). For example, they must know that interactions among molecules can be represented by specific terms in (partial) differential equations, but they do not have to be able to formulate such terms themselves. Nor, do they have to be able to program anything themselves. Since experimental results are essential for model building, students should also be able to employ experimental results to test certain aspects of a model. Finally, after working with the learning material, students should understand the mechanism by which the Dpp gradient is formed. By this we mean that they should be able to describe, in their own words, how the gradient is formed under wild-type (normal) conditions as well as explain the behavior of the biological system under different experimental conditions.

In research, a rather simple model to describe the formation of the Dpp gradient was published initially (Biehs, Francois, & Bier, 1996). Later, however, it was shown that this simple model was seriously flawed (Ashe & Levine, 1999). It then took 3 years before the current, conceptually different, model was published (Eldar et al., 2002). This shows that the formulation of this new model was certainly not trivial. Compared to researchers, students have little experience with the interpretation of experimental data and building models. Therefore, in order to offer students the opportunity to participate in building a model of the gradient formation themselves, we found it necessary to offer considerable support. The cognitive apprenticeship model (Collins, Brown, & Newman, 1989) is a pedagogical model for such support. In order to structure this support, a pedagogical approach was developed based on a number of design principles with respect to a suitable general model-building method and with respect to increasing the understanding of complex biological mechanisms. These design principles will be discussed in this section.

Previously, a digital case was designed in which students build a qualitative model for another pattern forming process during Drosophila development (Aegerter-Wilmsen, Janssen, Hartog, & Bisseling, 2005). In this case, students are guided through a model-building method in which they first build a model that is as simple as possible to explain the wild-type situation. Other data are temporarily ignored. This simple model is then gradually modified to explain additional experimental data that are selectively presented to the students. After each modification step, the biological implication of the modification is analyzed. For example, students evaluate whether the newer model can generate sharper boundaries between adjacent regions; this is important to ensure that during the further development of the organism, distinct tissues are formed and the formation of some kind of intermediate tissues is prevented. There were a number of reasons for using this approach. The general structure of modifying a simple model using a step-by-step approach was chosen because expert analysis suggested that scientists who use such an approach developed models that could explain more data than scientists who attempted to build the complete model directly (Aegerter-Wilmsen, Janssen, Hartog, & Bisseling, 2005). The step of evaluating the biological implications was added, because historical studies have shown that it can be very useful to consider the biological implications of a model while building it (Resnik, 1995). The model-building method was successful to guide the design of a digital case that activates students to go through reasoning processes that are typical for model building and that indeed seems to improve students' model-building skills (Aegerter-Wilmsen, Janssen, Hartog, & Bisseling, 2005).

In order to get an indication of whether this model-building method can also be suitable to serve as a design principle for guiding students to model the formation of the Dpp gradient, the model-building stages that took place in actual research were analyzed. As was mentioned before, a rather simple model was used initially to explain the Dpp gradient formation (Biehs et al., 1996). After it was shown that this model was not valid (Ashe & Levine, 1999), a new model was developed (Eldar et al., 2002) in two stages. A core model was initially developed to explain the major characteristics of the gradient and was extended later. The extended model was used to study further properties of the network (Eldar et al., 2002). Thus, in actual research the model also went through different stages of increasing complexity before the latest version was built. Furthermore, the principle underlying the initial model, which was later rejected, is still used to explain other biological patterning mechanisms (St Johnston & Nusslein-Volhard, 1992); therefore, it is an additional advantage for students to be introduced to this principle as well. As a design principle, we thus wanted students to follow a model-building cycle in which a simple model is built first and this model is subsequently modified, step-by-step (or even conceptually changed). After each modification step, the biological implications of the adjustment are analyzed.

In order to help students to understand the specific model, a number of design principles are employed that were formulated by White and Frederiksen in the context of helping students to understand basic electricity with computer simulations (Frederiksen, White, & Gutwill, 1999; White & Frederiksen, 1989, 1990). First, students should focus on qualitative models before focusing on quantitative models. Furthermore, students should be confronted with a progression of models. For example, subsequent models can show a progression with respect to their degree of elaboration. Finally, students should make conceptual links from models with a lower level of abstraction to those with a higher level of abstraction by running a simulation of the model and reflecting on emergent behaviors (Frederiksen et al., 1999; White & Frederiksen, 1989, 1990). For example, for the specific biological system, this could be translated such that students should reflect on the effect of changes in binding affinity, diffusion rates, and synthesis rates on the properties of the emergent gradient. In addition, in the model-building cycle described above, different models are evaluated with respect to their biological implications. This should further help students to understand the different models.

Introducing biological implications could actually be seen as introducing an additional level of understanding: the first level of understanding reflects the different molecular properties, the second level reflects the properties of the emergent gradient at the embryo level, and the additional third level reflects the effects of these properties on the further development of an organism in its biological context. If the formation of the gradient is, for example, robust against changes in the values of a range of parameters, then the gradient formation could proceed similarly under different temperatures. This is an important feature for poikilothermic ("cold-blooded") organisms, such as the fruit fly, that do not maintain a constant body temperature.

Methodology

The design principles described above for different types of support served as a basis to develop the pedagogical approach that is outlined in Figure 1. Students are guided to follow the model-building cycle in a general model-building section. Whenever numerical simulations are useful to carry out a certain step of the cycle, they can enter a separate simulation environment in which they are supported in building quantitative models and running simulation experiments.

Students use the simulation environment for two (related) purposes. First, they use simulations to check whether a qualitative model that they built in the general model-building section can be converted into a quantitative model that indeed shows the desired behavior. In this way, they can verify that the qualitative model does not contradict the data relating to the behavior of the biological system. It is especially useful to do this when qualitative reasoning is not adequate to assess the behavior of a qualitative model. If there are not enough data to formulate the quantitative model directly (which is often the case in biological research), assumptions are made about the missing data, such as certain parameter values; these assumptions can then guide the formulation of future experiments. The simulation environment allows for a vast number of different models because of a large parameter space. This implies that building a quantitative model that is in agreement with certain data can require many simulation experiments if a model is only modified at random until it is indeed in agreement with the data. To ensure that students consider in advance which modification is likely to be an improvement of the model, they receive feedback immediately after each modification. This feedback supports the student in recognizing the relationship between the quantitative model, which is based on the properties and interactions of the single proteins and protein complexes, and the emergent properties of the gradient formation that can be viewed by running the simulation.

Second, related to the use described above, quantitative simulations can also be useful to check whether a quantitative model can explain new experimental data. Furthermore, properties of the quantitative model can be studied. For example, it can be determined whether the model is robust against changes in its parameter values.

This approach ensures that students follow the model-building cycle that was considered useful, that the added value of using computer simulations to build models is illustrated, and that it is an application of the design principles to help students understand the biological system (see underlined features in Figure 1).

[FIGURE 1 OMITTED]

Quantitative simulations are only employed if qualitative reasoning is insufficient. Four design principles with respect to understanding the biological model are integrated into the approach (underlined): the progression of models, the introduction of qualitative models prior to quantitative ones, the offering of conceptual links from lower-level to higher-level models, and the analysis of the biological implications of the model.

Description of the Digital Case

The digital learning material can be viewed at the following website: http://mbedu.fbt.eitn.wau.nl/demo_jcmst. The general pedagogical approach was used as a template to design the material. The material thus consists of a general model-building section and a simulation environment. Both will be discussed below.

General Model-building Section

In the general model-building section, students are guided to develop a model for the formation of the Dpp gradient. Dpp is initially distributed uniformly; later it forms a gradient. This gradient is formed as a result of complex formation between protein, specific cleavage of protein complexes, differences in diffusion rates among different components, and different initial localization of the participating proteins (Eldar et al., 2002). In particular, the diffusion rate of free Dpp is lower than that of a complex between Dpp and Sog.

In order that the students work with numerical simulations themselves, it is necessary to use the computer. It was also decided to use the computer to mediate the other stages of the model building, because of the opportunity it offers to provide feedback on students' personal decisions without the requirement for intensive supervision. In addition, the material is web-based such that it can easily be distributed and thus accessed at home.

The structure of the general model-building section is outlined in Table 1. At the beginning, students can view a list that contains experimental data that will eventually be used to build the model. Situations, in which a large amount of data is already available, but no models yet created to account for the data, are likely to occur increasingly often in future research. This is because of the potentially large increase in the rate at which data will be generated and the high accessibility of such data in web-based databases.

Students essentially go through the model-building cycle in Figure 1 three times. Sometimes the computer performs certain steps if they are not considered sufficiently instructive to be performed by the students. For example, when testing whether their third model is in agreement with the experimental results that are available to them, students initially must run simulations in order to mimic experimental manipulations themselves, such that they learn how to do this. For instance, they can mimic the situation in a homozygous loss-of-function mutant of a certain protein by setting the concentration and production of this protein to zero and running the model. After they have done this a few times, they are presented with previously generated simulation results in order to save time (Figure 2) and prevent useless repetitions. The general model-building section is followed by a summary and a self-test.

[FIGURE 2 OMITTED]

The screen dump in Figure 2 shows an example of how students can evaluate the third model using previously generated simulation results.

Simulation Environment

The simulation environment implements various types of feedback and support. This helps students to use the simulation environment efficiently with their current mathematical background, ensures that students do not have to program anything themselves, and can promote the understanding of the models themselves.

Upon entering the simulation environment from the general model-building section, students receive a specific assignment. They must build a model that can generate a gradient with specific characteristics or they must perform certain tests. Having a clear goal contributes to a more efficient use of the simulation environment.

Students also get support with the building of the quantitative model itself. In order to determine the initial localizations of the proteins, students have to select a schematic figure of the embryo in which the desired region is indicated. If this localization is biologically not feasible, students are informed of this and they must select another initial localization. Students get support with setting up the partial differential equations as well. For example, when students indicate that Dpp diffusion occurs, the program shows a diffusion term in the equation that describes the Dpp concentration changes over time (Figure 3). Therefore, they can view the actual mathematical formulation and see their choices reflected in this mathematical formulation, but they do not have to give this formulation themselves. Thus, very little prior knowledge of differential equations is required.

A wide range of values can be assigned to the different parameters. In order to give students some direction, standard values are given by default (Figure 4). However, it is still necessary to change several values and, if students wish, they can change all of them.

When students want to run a simulation of the model, the program first checks whether the model is self-consistent. If the differential equation for Dpp shows a term for Dpp-Sog complex formation, for example, this term must exist in the differential equations for Sog and for the Dpp-Sog complex as well. If this is not the case, students receive feedback on how to make their model consistent. In addition, if the students have to use the simulation environment to perform specific tests, the program first tests whether the quantitative model is suitable to carry out such a test. If not, students are given information on how to change their model. For example, in order to test the robustness of a model against halving the amount of Sog, the initial Sog concentration as well as the Sog production needs to be halved. If students only halve the initial concentration, they receive feedback telling them that they need to reduce the production as well.

Upon running a quantitative simulation, students receive feedback that helps them to draw conclusions and/or consider the next steps to be taken. As an example, Figure 5 depicts a series of screen dumps of the feedback that students receive while building the second quantitative model. First, the simulation result of the student is evaluated with respect to the requirements the gradient must fulfill. In this case, the gradient is not sufficiently steep. Then the students are asked to propose a modification in their model in order to yield a steeper gradient. In this case, an increase in Sog production is suggested. The subsequent feedback informs the students whether or not this could be a useful modification based on qualitative arguments. In this example, increasing the Sog production can be useful, because it will make more Sog available to transport Dpp, which can result in a steeper gradient. Such an argumentation should help students to gain a better understanding of the model since it couples biological aspects with characteristics of the quantitative model and its behavior. When the requirements are met and/or the tests are performed and valid conclusions are drawn by the student, the student can quit the simulation environment and return to the general model-building section.

[FIGURE 3 OMITTED]

In Figure 3, initially the Dpp concentration does not change in time. If students indicate that diffusion occurs, the diffusion term is added to the differential equation that describes the changes in Dpp concentration over time.

The screen dumps in Figure 5 show an example of the feedback the students receive upon running a simulation. The first screen dump shows the simulation result. When students press "feedback," they can view whether the resulting gradient satisfies the requirements. In this case (screen dump 2), the requirements are not satisfied. In order to get support to improve the model, students can ask for more feedback. They can then propose a change to their model (screen dump 3). After submitting the change, they can read a qualitative argument as to whether or not this change is a potential improvement (screen dump 4).

Evaluation

Set-up

The material was used three times during regular 3rd year undergraduate courses on developmental biology. The first time it was used by 15 Dutch students at Wageningen University, the second time by 13 Swiss students at the University of Zurich, and the third time by 31 Dutch students, again at Wageningen University. Each time, data were collected.

[FIGURE 4 OMITTED]

In Figure 4, a wide range of different values can be entered. In order to give students some direction, standard values are already given.

[FIGURE 5 OMITTED]

In order to assess the opinion of the students, an evaluation form was handed out at the end of the sessions. As mentioned before, after working with the case, students should be aware of the value that simulations add to research. To assess the students' ideas on this issue, a question asking about added value was included in the evaluation form. Upon working with the case, students should also know how certain biological models could be converted into a set of (partial) differential equations from a conceptual point of view, they should be able to use experimental results in the context of model building, and they should understand how the Dpp gradient is formed. These aspects were tested with a number of questions that were included in the examination of the complete courses on developmental biology.

After using the case the first time, a number of significant improvements were implemented, in order to enable students to work with the case more efficiently. As a result, it took two sessions of 2-3 hours to go through the case instead of two sessions of 3-4 hours. These improvements will be discussed first. After using the case the second time, only minor improvements were implemented; these improvements did not change the overall results of the subsequent evaluation. Therefore, the results of the second and third evaluation were pooled and these combined results will be discussed.

Improvements After Initial Evaluation

After the material was used for the first time, several improvements were implemented. Most of them concerned the simulation environment. It appeared to be possible to build a model that did not yield the desired gradient, but that could not be improved with the feedback given that this would require assigning values to parameters that were outside the range the environment permits. Since the model almost fulfills the requirements at this stage and the most important features have already been implemented, students should have gained enough understanding of the model. Therefore, the feedback was adjusted such that if the proposed changes are not sufficient, students can load a preprogrammed model that does fulfill the requirements. Another improvement concerned the addition of a tutorial that can be used when students enter the simulation environment for the first time. The tutorial contains some questions about setting up partial differential equations and a short general explanation about using the simulation environment. It was added because it cost the students some time to get used to the simulation environment and to get an idea of how the partial differential equations were used during the simulations. Furthermore, exam results showed that many students did not manage to fully grasp the concept of differential equations and could not clearly distinguish between setting up differential equations and solving them. There were also some technical improvements implemented in order to limit the processing capacity required by a simulation experiment. In addition to the above improvements to the simulation environment, some relatively small improvements were implemented to the general model-building section. Most importantly, a more idealized version of an experimental result was added that could help students with the interpretation of a less idealized result.

Results of Subsequent Evaluations

The pooled results of the second and third evaluation are discussed in this section. In order to assess the students' general opinion of working with the case, answers on the evaluation forms were analyzed (35 out of 44 forms were returned). Table 2 shows that the overall evaluation of the case was 4.1 on a scale of 1-5. Furthermore, students liked working with the case (4.0 on scale of 1-5) and they thought it was instructive (4.1 on a scale of 1-5). At Wageningen University, courses are systematically evaluated with similar questions. An average appreciation of 4.0 or higher is given to about 20% of the courses. Considering the fact that at least some of the students do not have any affinity at all with quantitative thinking and mathematical language, we were very satisfied with these results.

The design of the case was aimed at illustrating the added value to students of using numerical simulations in research. To get an understanding of the students' ideas about added value upon working with the case, an open question that asks about the added value was added to the evaluation forms. Thirteen students commented that simulations could facilitate the model-building process since it can make complex networks more comprehensive. Furthermore, eight students indicated that using simulations could be helpful in formulating good hypotheses; therefore, laboratory experiments can be designed more effectively. Nine students did not mention hypotheses, but remarked more generally that simulations could save laboratory work, time, and/or money. Finally, three students mentioned a reduction in experiments with animals and three students did not give any advantage. Thus, most students could indeed give an advantage of using simulations in research upon working with the case.

In order to get an impression of the other learning outcomes, exam results were analyzed (41 out of 44 students had taken this regular exam). The questions about the contents of the case and the average scores are shown in Table 3. The first question tests whether students have enough factual knowledge of the model. Furthermore, since the students have to describe the roles of its components, it also tests whether they understand the mechanism well enough to describe the behavior of the model in qualitative terms. The second question tests whether students understand the behavior of the model sufficiently to explain why it is robust against a certain experimental manipulation, which is a biologically important feature of the model. The third question tests whether students can actively create an experiment, even though they did not have to do so in the case--they only had to interpret its results. The last question tests whether students grasped the basics of translating a qualitative model into a set of partial differential equations. In general, students score about 6-7 on a scale of 1-10 for exams. Thus, the students scored relatively high for all questions except the question about the robustness of the model. In the case, students are presented with an explanation of the cause of this robustness. In order to stimulate students to think about this robustness more actively, this explanation will be replaced by a question in the future.

SUMMARY

In this article, a digital case was described in which students develop a model of a biological process using experimental results and computer simulations. The students appreciated working with it, despite its use of mathematical language that could potentially be a negative motivating factor. The case was developed in order to make students aware of the added value of numerical simulations in the molecular life sciences. Answers on evaluation forms indicated that most students could indeed name a benefit of working with such simulations. Students also had to learn the basic principles of how a biological model can be translated into a quantitative model with partial differential equations. Furthermore, they had to be able to employ molecular biology experiments for the building of a model and they had to understand the actual biological model. Again, answers on exam questions indicated that most students did indeed attain these goals.

In the digital case, students use computer simulations in a fundamentally different way than is often used for scientific discovery learning with computer simulations (de Jong & van Joolingen, 1998), where the main task of the learner is to infer the characteristics of the model underlying the simulation, which is unknown to the learner (hereafter called "the unknown preprogrammed model"). In such a case, the learner's basic actions are changing values of input variables and observing the resulting changes in values of output variables. The outcomes of computer simulation experiments of the learners thus serve as imitations of laboratory observations that need to be accounted for by the model the learner is building. Once the learner has built a model, he or she can make predictions based on the model and use additional simulation experiments to test these predictions. However, the learner does not perform computer simulation experiments with his/her own model to check whether it indeed behaves as the unknown preprogrammed model. In the digital case described here, learners are supported in building a model that can account for real laboratory observations, instead of simulation experiments that serve as imitations of laboratory observations. Once the learner has built a qualitative model, this is used as a basis to build a quantitative model. The learner then performs simulation experiments with his/her own quantitative model to check whether it can account for the laboratory observations, since qualitative reasoning is insufficient for this purpose. Thus, in the type of scientific discovery learning where learners infer the characteristics of an unknown model underlying the simulation, learners do not use computer simulations as researchers would use them: researchers do not have to infer the characteristics of an unknown model underlying a simulation, because they generally have access to models underlying simulations and often built them on their own. In contrast, in the digital case described in this paper, learners use computer simulations as researchers can use them: to support the building of a model that can account for the experimental observations by exploiting the simulations to assess the behavior of a system based on the characteristics of its components when this cannot be achieved with qualitative reasoning.

In the case, students worked with a simulation environment in which parameters could sometimes be altered over a relatively large range. Offering a relatively large parameter space can cause the generation of feedback on specific models to be rather challenging. When building model II for example, more than [10.sup.20] different combinations of parameter values can be entered. In order to provide useful feedback that is specific to the students' choice, despite this large number of possible combinations, the fact that these combinations can only yield a limited number of qualitatively different behaviors was exploited. The feedback was then generated based on such qualitative behavior. However, since to our knowledge the set of partial differential equations cannot be solved analytically, the exact rules that determine the qualitative behavior are not clear. Moreover, it is not feasible to systematically scan the whole parameter space for the different behaviors that are generated, since this would require more than [10.sup.14] computer years if each simulation takes about 1 minute. In order to be able to generate useful feedback despite these difficulties, we generated feedback based on our own qualitative understanding of the model; this understanding was acquired by much "playing around" with the simulations. Although we cannot guarantee that the implemented feedback is appropriate for each model the students can theoretically build, in practice it appears to be sufficient for the vast majority of models the students actually generate. As a byproduct of generating the feedback as described above, our own understanding of the dynamics of the model improved to the extent that it enabled us to formulate a new model for another patterning process during Drosophila development (Ae-gerter-Wilmsen, Aegerter, & Bisseling, 2005).

In order to structure the case as a whole, a pedagogical approach was developed that combined design principles with respect to the understanding of a complex biological system and with respect to a suitable model-building approach.

Three of the principles that were used to help students understand the biological system were originally developed to help students understand basic electricity (Frederiksen et al., 1999; White & Frederiksen, 1989, 1990). They address the offering of a progression of models, the introduction of quantitative models after qualitative ones, and the making of conceptual links from lower-level models to higher-level models. When these principles were originally developed and applied, increasing the understanding of basic electricity was the main goal. Here, these principles were integrated into an approach that was not only aimed at increasing the understanding of a mechanism, but that also engages students in the scientific process of acquiring such understanding in an actual research situation.

In the case described in this paper, students are guided to build a model using a step-by-step process. In actual research, such guidance is not present. Therefore, we are planning to develop a digital case where students are not guided step-by-step, but have much more freedom to organize their model-building process themselves.

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Acknowledgements

We would like to thank Ernst Hafen and Daniel Bopp for giving us the opportunity to test the material at the University of Zurich. We would also like to thank Hylke van der Schaaf and Ayalew Kassahun for technical support.

TINRI AEGERTER-WILMSEN, DIK KETTENIS, OLIVIER SESSINK, ROB HARTOG, AND TON BISSELING

Wageningen UR

Netherlands

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FRED JANSSEN

University of Leiden

Netherlands

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Table 1 Description of the General Model-building Section. Each Step
Shows the Section of the General Model-building Cycle With Which it
Deals.

             Model-building step      Description of step

Section I
 1-2         --                       Introduction
 3           Formulate qualitative    Students are stimulated to
             model I to explain the   formulate a simple source-sink
             wild-type situation      model for the Dpp gradient
                                      formation.
 4           Access simulation        Students translate the simple
             environment: Build       qualitative source-sink model into
             quantitative model I     a quantitative model to get
             based on qualitative     acquainted with the simulation
             model I                  environment.
 5           Test main prediction     Select experimental results that
             model I                  can provide information about main
                                      prediction model I
 6           Test main prediction     Interpret selected experimental
             model I                  results: main prediction is
                                      contradicted by one of the
                                      results.
 7           Test main prediction     Interpretation of additional
             model I                  experimental result to confirm
                                      need for rejection of model I.

Section II
 1-4         Formulate qualitative    In several steps, a new
             model II                 qualitative model is built in
                                      which diffusion differences are
                                      crucial.
 5           Access simulation        Since it is hard to assess with
             environment: Build       qualitative reasoning whether the
             quantitative model II    new qualitative model can indeed
             based on qualitative     generate the observed gradient,
             model II                 students translate this model into
                                      a quantitative model.
 6           Test main prediction     Select experimental results that
             model II                 can provide information about main
                                      prediction model II: such a result
                                      is not available yet. Extend
                                      present model first before
                                      performing experiment.
 7           Access simulation        Students test whether model I
             environment: Evaluate    describes a system that is robust
             biological implications  against halving protein
             of model I               concentrations: this is not the
                                      case.
 8           Access simulation        Students test whether model II
             environment: Evaluate    describes a system that is robust
             biological implications  against halving protein
             of model II              concentrations: it does, as
                                      predicted by the data.
 9           Evaluate biological      Reasons for robustness of model
             implications of model    II are given.
             II

Section III
 1-4         Formulate qualitative    Students analyze experimental
             model III                results to implement additional
                                      proteins in their model.
 5           Access simulation        Since model III does not differ
             environment: Build       conceptually from model II
             quantitative model III   students do not build the
             based on qualitative     quantitative model themselves, but
             model III                perform a test with a
                                      preprogrammed quantitative model
                                      instead.
 6-12        Test model III (also:    All available experimental data
             with simulation          are systematically checked with
             environment)             respect to model III. Simulations
                                      and/or previously generated
                                      simulation results are used
                                      several times to facilitate this.
13           --                       Additional information: also
                                      speculation about biological
                                      implication of last extension of
                                      model

Table 2 Results From Three Questions on the Evaluation Form.

Evaluation question                        Score (n=35)

                                           scale 1-5

Give your overall impression of the case   4.1
(encircle the mark).
                                           1 (disagree)-5 (agree)

I liked working with the case              4.0
I learnt a lot from working with the case  4.1

Table 3 Average Scores on a Scale of 1-10 for Exam Questions Based on
the Case Contents.

                                                                  Score
  Question                                                        (n=41)

1 Scw, Sog, Tld, and Tsg are involved in the formation of a Dpp   7.2
  activity gradient in the dorsal part of a Drosophila embryo.
  Indicate for each of these proteins what its role is in this
  process.
2 Explain why the formation of the Dpp activity gradient is       4.7
  robust against halving the Sog concentration.
3 Describe an experiment, which can be used to determine whether  8.2
  Sog and Tsg are necessary for Dpp diffusion.
4 Assume you want to simulate the following system:               7.7
  ** B and C diffuse, whereas A and D are immobile.
  ** A and B can bind and the resulting AB complex can
     disintegrate again into A and B.
  ** (AB) and C can bind and the resulting ABC complex can
     disintegrate again into (AB) and C.
  ** Both (AB) and (ABC) diffuse.
  ** D can cleave (AB), thereby releasing A and inactive B
     fragments.
  Set up a differential equation, which describes the
  concentration changes of A in time ([delta][A]/[delta]t). Make
  thereby a selection from the terms below and make sure you use
  the correct signs (+ or -) in the equation.

  Diffusion:                            Complex disintegration:
    [D.sub.A] * [[nabla].sup.2] * [A]     [k.sub.AB disint] * [AB]
                                          [k.sub.ABC distint] * [ABC]
  Complex formation:
    [k.sub.AB form] * [A] * [B]         Cleavage by D:
    [k.sub.ABC form] * [A] * [B] * [C]    [k.sub.cl] * [D]
    [k.sub.ABC form] * [AB] * [C]         [k.sub.cl] * [D] * [AB]
                                          [k.sub.cl] * [D] * [ABC]

  [delta][A]/[delta]t =