Organisms use cell division to replicate, grow, and, in the case of a process called meiosis, to make gametes for reproduction. This lab explores the processes of mitosis and meiosis through both physical and mathematical modeling.

Importance & Means of Cell Division

An important part of any organism’s life cycle is reproduction and growth. Not only does reproduction enable us to take pictures of cute animals to post online, it also, of course, ensures survival of the species.

Reproduction and growth are possible in both animals and plants because of cell division, the process by which new cells are created. Eukaryotes, that is, organisms that have nucleated cells, use two types of cell division during their life cycles: mitosis, the process by which a nucleated cell divides into two equal (sometimes called ‘daughter’) cells, and meiosis, the process of cell division that creates reproductive cells called gametes. Remember, this lesson’s material won’t apply to prokaryotes, like bacteria, because their method of cell division doesn’t involve a nucleus.

Mitosis & Chi-Square Analysis

Let’s begin by reviewing mitosis. First, it’s important to recognize that mitosis is only one part of a larger process called the cell cycle. Ninety percent of a cell’s time is spent in a phase called interphase. Interphase is subdivided into three parts: G1, in which the cell prepares to replicate its genetic material; S, in which the DNA is ‘synthesized,’ or duplicated; and G2, in which the cell prepares to divide. Mitosis, which takes place in a series of steps described next, follows interphase.

In prophase, the nuclear envelope breaks down, and the cell’s duplicated genetic material, present in the nucleus in a diffuse structure called chromatin, condenses into visible bodies called chromosomes. These are the familiar X structures you see in drawings; each half of a duplicated chromosome is called a sister chromatid. Next, the chromosomes align themselves across the cell’s ‘equator’ in a step called metaphase, with one sister chromatid on either side of the equator. In anaphase, the sister chromatids split and begin to move to opposite poles of the cell. Finally, in telophase, the chromosomes arrive at opposite ends of the cell, and the nuclear envelope reforms. Cytokinesis, the equal distribution of the cytoplasm into two new cells, completes the cycle, and two identical daughter cells are formed.

The cell cycle is under the control of proteins called cyclins and cyclin-dependent kinases, or CDKs. When a CDK interacts with its complementary cyclin, the cell cycle either proceeds or is halted. In this way, the cell cycle passes through a series of ‘checkpoints,’ each of which ensures that everything is in place for cell division. If, for example, a part of the mitotic machinery is not properly assembled, the cell cycle will halt so that a defective cell will not be produced. Mutations, changes in DNA that code for these regulatory proteins, can result in the uncontrolled cell division that we call cancer.

An experiment can be done by introducing a compound called lectin to the roots of soybean plants. Lectins encourage cell division, and therefore, root growth. Thinking about the number of cells in mitosis and interphase, what would you expect to see when comparing a root tip treated with lectin to one not treated with lectin? You’re probably thinking ‘Simple! More cells will be dividing in the one with lectin.’ You’d probably be right, but science asks for a little more.

In science, we use statistics as an agreed-upon way to determine significance – that is, if there’s really something going on in an experiment. In this case, we can use a simple statistical test called chi-square (X^2) analysis. There are whole courses on statistics, so we won’t be able to cover every aspect of this test. But briefly, chi-square analysis compares the observed results of an experiment with those that are expected. Based on the outcome of this test, we should be able to determine if that difference is small and likely due to chance or large and likely due to something other than chance. In general, the hypothesis used for chi-square analysis is ‘there will be no difference between the observed and expected; any difference that does exist is due to chance.’

The process to complete chi-square is shown in the table. Numbers represent 100 cells in an untreated root tip. The expected values were calculated based on the fact that a cell spends 90% of its cycle in interphase.

Cell cycle Stage Observed (O) Expected (E) (OE) (OE)^2 (OE)^2 / E
Interphase 92 90 2 4 0.04
Mitosis 8 10 -2 4 0.9
Chi square value: 0.94

Our value, 0.94, we compare to a standard statistical table:

Degrees of Freedom Reject hypothesis if X^2 value is greater than:
1 3.841
2 5.991
3 7.815

The degrees of freedom in this type of analysis are determined by the number of categories minus 1. Here, our choices were either interphase or mitosis (2 categories). Our degrees of freedom equals 1. Since 0.94 is much less than 3.841, we accept our null hypothesis: there is statistically no difference between the observed and expected values. In this example, that outcome makes sense; since there was no treatment to these cells, we would not expect to see a large difference between our observed and expected values.

Let’s compare that to some data from a root tip treated with lectin:

Cell cycle Stage Observed (O) Expected (E) (OE) (OE)^2 (OE)^2 / E
Interphase 60 90 – 30 900 10
Mitosis 40 10 30 900 90
Chi square value: 100

Clearly, 100 is much greater than 3.841; in this instance, the null hypothesis must be rejected. The results are due to something beyond chance. This makes sense as well given that lectin encourages mitotic division.

Let’s do one more: let’s compare the treated and untreated conditions. In this case, the expected is the control (untreated) values.

Treatment Observed (O) Expected (E) (OE) (OE)^2 (OE)^2 / E
Interphase 60 92 – 32 1024 11.1
Mitosis 40 8 32 1024 128
Chi square value: 139.1

Again, as in the treated example, the chi square value is much greater than 3.841, indicating that the results are due to something beyond chance and that the null hypothesis should be rejected.

Meiosis & Crossing Over

As a process of cell division, meiosis has one outcome: gametes – sperm and egg cells in animals and spores in organisms like protists and mosses. As such, to prevent multiple chromosomes in a new organism, the four (instead of two) daughter cells that result from meiosis have half the number of chromosomes as the initial cell. Also, unlike mitosis, which results in identical daughter cells, meiosis results in genetically-different cells. These differences result from three processes: crossing over, segregation, and independent assortment. We’ll look at these in the context of meiotic division.

First, it’s important to clarify the term homologous chromosomes. These are chromosomes that are similar in size and genetic content. You can think of them as a pair of socks that are identical in every way except for color. Homologous pairs of chromosomes are made of one chromosome from each parent. For example, a homologous pair might be made of chromosome 12 from the mother organism and chromosome 12 from the father organism.

The process of meiosis begins much like mitosis. In prophase I, genetic material is replicated and condenses from chromatin into the familiar X shape used to represent two identical sister chromatids joined at their centers. Prophase I also includes crossing over, the process in which homologous chromosomes align with one another and physically touch, exchanging genetic material. In metaphase I, the duplicated chromosomes align across from their homologue on the equator. The chromosomes align randomly, increasing genetic variability through what’s called ‘independent assortment.’

The chromosomes move apart from one another in anaphase I in segregation, the separation of identical genes. Telophase I finds the duplicated chromosomes in opposite ends of the cell; cytokinesis completes this process. Each of the two cells formed by meiosis I undergoes a process that looks very similar to mitosis in a series of steps called meiosis II. At the end of meiosis II, four genetically distinct daughter cells are formed, each containing half of the amount of genetic material of the original organism.

You can concretely view the results of crossing over in a genus of fungus called Sordaria. The result of meiosis in this organism is eight gametes called ‘spores.’ If an organism that has black spores is genetically crossed with one that has tan spores, it’s expected to yield four black spores and four tan spores. If this pattern doesn’t occur, it’s due to exchange of genetic material in crossing over.

Lesson Summary

Let’s review what we’ve covered in this lesson. Reproduction and growth are possible in both animals and plants because of cell division, the process by which new cells are created. Eukaryotes, organisms that have nucleated cells, use two types of cell division during their life cycles: mitosis, the process by which a nucleated cell divides into two identical daughter cells, and meiosis, the process of cell division that creates genetically different reproductive cells called gametes – egg and sperm in animals and spores in organisms like protists and fungi.

Mitosis takes up only about ten percent of the cell cycle. During the steps of prophase, metaphase, anaphase, and telophase, replicated chromosomes are equally distributed into two new cells. Mutations in genes that create proteins essential to the cell cycle control can lead to cancer.

Chi-square analysis is one statistical method used by scientists to determine if there are significance in data collected during an experiment. The formula is (the sum of the observed – expected squared/by the expected). By comparing the chi-square value to a reference number, we can tell if there is a significant difference between the observed and expected data. If there is, the null hypothesis, which states ‘there is no significance,’ can be rejected.

Meiosis results in genetically different cells thanks to crossing over, independent assortment, and segregation. In this process, replicated chromosomes line up across with their homologue, or chromosome similar in size and genetic content. Meiosis consists of two series of prophase, metaphase, anaphase, and telophase steps and results in four genetically-different daughter cells that contain half of the number of chromosomes of the initial cell.

Learning Outcomes

After you’ve completed this lesson, you’ll be able to:

  • Define cell division and identify the two types of cell division in Eukaryotes
  • Describe the processes of mitosis and meiosis
  • Explain what chi-square analysis is and how it is conducted
  • Recall how mutations can lead to cancer