The comprehension of chromosome movement during mitosis and meiosis is essential for understanding genetic transmission, but students often find this process difficult to grasp in a classroom setting. I propose a “double-spring model” that incorporates a physical demonstration and can be used as a teaching tool to help students understand this process, particularly the energy changes that occur during different stages of the cell cycle. My teaching experience has demonstrated that this model is very effective, and it has been favorably received by numerous students.

Models are useful in classroom settings because they allow the investigator (or student) to easily examine processes that are difficult to learn exclusively from books. In the past, various conceptual models have been extensively used in the field of chemistry. Such models are also important tools in the biological sciences, where they can enhance students' understanding and problem-solving ability (Chinnici et al., 2004).

The comprehension of the chromosome movement involved in mitosis and meiosis is essential to understanding transmission genetics, but this is often challenging for students in the classroom, especially for students who lack a strong scientific background. The main reason for this conceptual difficulty, in our experience, is the complexity of the forward and reverse movements involved: equator-ward migration from prophase to metaphase, and then pole-ward migration from metaphase to anaphase. Scientists have documented that chromosome movement depends on motor complexes, especially actin and myosin in the cytoplasm (Chuang et al., 2006). A number of researchers have outlined models to explain the actual mechanisms underlying chromosome movement (Garel et al., 1987; Grancell & Sorger, 1998; Banks & Heald, 2001; Rath et al., 2009; Shtylla & Keener, 2010), and they mainly focused on the details of specific processes of mitosis or meiosis, such as how many genes or proteins are taking part in the process and how these genes or proteins act within the process. Therefore, these models have failed to assist in students' learning in the classroom because they fail to look at the big picture. Some instructors have attempted to construct learning aids to allow students to achieve a better understanding of mitosis and meiosis (Mathis, 1979; Kindfield, 1994; Clark & Mathis, 2000; Chinnici et al., 2004), but such models remain ineffective in facilitating learning and understanding of the process of chromosome movement without conveying the innate logic of these processes.

Development of Materials

As part of a general genetics course, I have developed a simple model with two springs. The spindles, which come from the two poles of a cell when a cell enters mitosis or meiosis, are similar to two springs, each of which has its own polar-ejection forces because it gains energy during interphase. The two opposite poles of the cell are classified as the minus end and plus end (Goshima et al., 2005). Likewise, within the paired kinetochores, one kinetochore represents the plus face (depicted in black in Figures 1 and 2), while the other represents the minus face (shown in red). For ease of illustration, in the establishment of chromosomal bi-orientation, the spindle ejected from the minus end can only attach to the minus face (in red) kinetochore, whereas that from the plus pole can only attach to the plus face (in black).

Figure 1.

Double-Spring Model for demonstrating mitosis in the classroom. (A) Prophase in the cell: bi-oriented, replicated chromosomes that are contacted by two springs from opposite poles will move to the equator because of the different lengths of the two springs. (B) Metaphase: the replicated chromosomes are at the equator of the cell with the springs at equal lengths. (C) Anaphase: the sister chromatids physically separate and move toward opposite poles, which is caused by the shrinkage of the springs. (D) Telophase: the chromosomes move to the poles when the springs shrink to their natural lengths.

Figure 1.

Double-Spring Model for demonstrating mitosis in the classroom. (A) Prophase in the cell: bi-oriented, replicated chromosomes that are contacted by two springs from opposite poles will move to the equator because of the different lengths of the two springs. (B) Metaphase: the replicated chromosomes are at the equator of the cell with the springs at equal lengths. (C) Anaphase: the sister chromatids physically separate and move toward opposite poles, which is caused by the shrinkage of the springs. (D) Telophase: the chromosomes move to the poles when the springs shrink to their natural lengths.

Figure 2.

Double-Spring Model for demonstrating meiosis in the classroom. (A) Prophase of the cell: co-orientation of homologous chromosomes contacted with two springs from opposite poles, which will move to the equator because of the different lengths of the two springs. (B) Metaphase: the homologous chromosomes are at the equator of the cell with equal lengths of the springs. (C) Anaphase: the homologous chromosome pairs physically separate and move toward opposite poles, which is caused by shrinkage of the springs. (D) Telophase: the chromosomes move to the poles when the springs shrink to their natural lengths.

Figure 2.

Double-Spring Model for demonstrating meiosis in the classroom. (A) Prophase of the cell: co-orientation of homologous chromosomes contacted with two springs from opposite poles, which will move to the equator because of the different lengths of the two springs. (B) Metaphase: the homologous chromosomes are at the equator of the cell with equal lengths of the springs. (C) Anaphase: the homologous chromosome pairs physically separate and move toward opposite poles, which is caused by shrinkage of the springs. (D) Telophase: the chromosomes move to the poles when the springs shrink to their natural lengths.

The Model

Accurate chromosome segregation requires that chromosomes be bi-oriented, so we begin testing the model by attempting to describe the orientation of the sister chromatids in mitosis and that of the two synapsed chromosomes in meiosis.

In prophase, the mono-oriented chromosome exhibits oscillatory movements over nearly the entire range that can be reached by the chromosome before the establishment of bi-orientation. Once the bi-oriented configuration has been achieved, the oscillatory movements result in a centering effect because the two springs have different lengths, and the configuration reaches the middle plate (Figures 1A and 2A). We assumed that the natural lengths of the springs are short but that they are also flexible enough that their maximum length (with its associated potential energy) is large enough to cover the entire cell.

During the prophase of meiosis I, the synapsed chromosomes form a bivalent structure that also has one exposed minus-face kinetochore and one exposed plus-face kinetochore. This demonstration further reinforces the idea that the synapse of homologous chromosomes is a hallmark of meiosis because the bi-orientation of nonsister kinetochores (two kinetochores from homologous chromosomes) results in the physical separation of the homologous chromosomes (Luo, 2009).

Logically, the two forces produced by the two springs coming from two opposite poles are equal when the two springs have equal lengths; this stage represents metaphase (Figures 1B and 2B). The magnitude of the two forces acts as a signal; reaching the same magnitude results in the onset of anaphase. This finding is in agreement with the conclusion that the counter-tension produced by the cleavage of the kleisin subunit of cohesin observed when all sister chromatids are in mitosis (Jones, 2010) or all bivalents are in meiosis (Dumont et al., 2010) follows the alignment of the chromosomes at the equator. Next, the chromosomes exhibit pole-ward migration from metaphase to anaphase because of the inherent tendency of the springs to shorten when they are not under tension (Figures 1C and 2C). Finally, either the chromatids in mitosis or the chromosomes in meiosis I reach the polar state caused by the shrinkage of the spring to its natural length and the diminishing energy of the spring (Figures 1D and 2D).

Evaluation & Discussion

This model offers an active, exciting, and logical demonstration of these processes while engaging students and allowing them to learn and logically appreciate the details of chromosome movement rather than simply memorizing the sequences of events. Many students find these models engaging, as they are required to actively think about these processes.

Prior to the formation of bi-oriented chromosomes, the chromosomes exhibit only oscillatory movement. However, after the establishment of the bi-oriented configuration, the chromosome movement becomes equator-oriented between prophase and metaphase because the two springs have different lengths, and the longer spring generates more force. This description makes it easy for students to understand the forward and reverse movements that occur during the cell cycle. Finally, the model shows that the springs represent the spindle and that spindle lengths are controlled by numerous microtubules through changes in chemical energy caused by the actions of various proteins, such as actin and myosin. Additionally, this conceptual model encourages students to find recent data in the literature to support or modify the model. This research is beneficial because the teaching of science to college students has made parallel gains with the stunning success of recent scientific research.

We could also explain how certain abnormalities in mitosis and meiosis occur with this model. For instance, the sister chromatids do not separate at the anaphase stage of mitosis in the case of mutants that fail to undergo cleavage of cohesion (Hodges et al., 2005); similarly, chromosomes do not separate at anaphase of meiosis I in some mutants with abnormalities of both formation and distribution of the synaptonemal complex (Tsubouchi et al., 2006). In these mutant cases, we assume that the force between sister chromatids or between homologous chromosomes does not decrease, whereas this force is expected to decrease when a normal cell goes into anaphase of mitosis or meiosis I. Therefore, we further assume that the force between sister chromatids, homologous chromosomes before mitosis metaphase, sister chromatids, or homologous chromosome is larger than the maximal of the spring. As a result, some springs would break during anaphase, causing sister chromatids or paired chromosomes to go into a polar state instead of two opposite poles; this irregular process is called disjunction.

During the past year, I have developed and implemented the new and effective teaching model described above, and this Double-Spring Model has been favorably received by almost all of my students. More than 1000 students have provided unsolicited comments on the teaching of the model and of the course in which it is included. All the student feedback related to this teaching experience has been positive, and >99% of students have provided highly favorable responses. For example, “The process of chromosome movement in mitosis and meiosis became very easy to understand both physically and logically after the demonstration using the Double-Spring Model”; and “I am surprised that the complicated processes of mitosis and meiosis can be simplified by only two springs and a little knowledge about magnets, and this fact gives us enough confidence to study genetics well” were stated by two students who enjoyed the teaching. I feel that this model is highly effective, illustrative, and heuristic, and it has also been favorably received by other teachers who have been exposed to it. I hope that this new model will be introduced into additional genetics classrooms in the future.

Acknowledgments

I am grateful for financial support from the National Natural Science Foundation of China (no. 30971787), the Provincial Science and Technology Foundation for Young Scientists of Sichuan, China (2010JQ0042), and the Foundation of Major Comprehensive Reform of Sichuan Provincial Education Department.

References

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