Cell Size

Biology Cells Day 5 Cell Size Science Probe 10, Chapter 15, pp. 352-253 Themes: Observation and interpretation. How and why things change over time. PLO addressed: �describe the factors that limit cell size� Objectives: To learn about some physical processes very important for living things. To become familiar with using deduction from mathematical models of natural processes. To become familiar with interpreting observations. Materials: Potatoes (one per four students), knives, iodine or dye, droppers, petri dishes (two per student). Teacher�s Background Info: All cells need to obtain nutrients from and transport wastes to their surroundings. Diffusion is responsible for much of the movement of molecules involved. When particles are not being forced to move in a particular way, the move by �Brownian Motion.� That is, they move randomly as heat-excited water molecules hit them. Although this motion is random, we can make general predictions about it. If there are two joining areas in which a particular kind of molecule is found, and if there is no boundary between the two areas, the particles from one side will inevitably flow into the other side. If there is a greater concentration of those particles on one of the sides, more random motion on that side will lead to particles traveling to the other side. Due to this trend, the concentrations the two sides will equalize. Cells often depend on this trend when its cellular concentration of waste is higher or of nutrients is lower than the surroundings. Cells also make use of osmosis, a specialized form of diffusion. In osmosis, water molecules are the particles that move randomly and that will become equal in concentration everywhere unless acted on by some directional force. As cells become larger, the area across which molecules can flow, the cells surface area, increases. However, the volume of the cell that requires nutrients, the cytoplasm (cytosol + organelles), increases at a higher rate. So as a cell grows, its surface-to-volume ratio (calculated by dividing surface area by volume) decreases. A larger cell will have a higher concentration gradient of nutrients and wastes between itself and the surroundings. This will increase the rate of diffusion up to a point, but the latter will level off when the cell gets too large. A cell that does not slow its growth or divide at this point will not get enough nutrients and will not get rid of wastes. This cell will not thrive and may even die. In this lesson, a mathematical model and a lab will be used to show some of these facts. Estimated Time for Activity: 55 min Content: Students do a mathematical model and an experiment showing how cells run into problems when they grow too large. At the beginning of the class, the teacher will introduce diffusion, asking students to explain why an open perfume bottle on the other side of a room will eventually be smelled. The concept should be explained with use of the perfume analogy and should be kept very simple. Osmosis can also be discussed: it may be introduced as a special form of diffusion. Use the action of a sponge as an analogy for this process. Teacher will then lead a discussion about how an objects surface area and volume change with change in the linear dimension of the object. The formulas governing these changes will likely be arrived at by the student if the teacher reminds them of area and volume formulas. The formulas for this lesson are: Surface Area = SA = 6(width)2 Volume = V = (width)3 The teacher should not explain what these equations mean for a living cell, as the purpose of this exercise is for the students to discover the implications themselves. Two stations will be set up in the class: one is the Potato Station, the other is the Math Station. Students should be told that the findings they make at one station will not be used at the other station, though of course ideas developed at one station are applicaple to the other. At the Potato Station, students will cut up potatoes into cubes of different sizes and measure one side of each cube. Very small and perfectly cuboidal cubes work best for this lab. The cubes should be arranged from smallest to largest. Iodine, or a dye, should be poured into a petri dish. Students will stick toothpicks into the cubes and will submerge them in the iodine or dye. After a defined period of time, the submerged cube should be removed and cut in half. Students will record whether the colour penetrated to the center of the cube. If it does not in a particular cube, that �cell� is declared �dead.�cut the potato cubes into thirds a fixed period of time after the iodine was applied. width     dead/alive     The teacher should spend most of his/her time at the Math Station. There, students will graph surface area vs. width and volume vs. width on the same axis, using the two formulas (ya=x2) and (yv=x3), where ya is surface area, yv is volume, and x is the measured side of the cube. The scales of the two measurements will have to be adjusted so that the trends of the lines are directly comparable. Students should also plot SA vs. V. The graphs should look something like this:                       Notice that the lower line in the first graph, representing surface area vs. width, is lower increases more slowly than the volume vs. width line. The teacher can provide values for the linear dimensions of a variety of cells and organelles and ask students to plot the points on the graph. � 100 nm Large Virus � 1 - 10 um Prokaryotes � 2 um E.coli - a bacterium � 3 um Mitochondrion � 5 um length of chloroplast � 6 um (3 - 10 micrometers) the Nucleus � 9 um Human red blood cell � (10 - 30 um) Most Eukaryotic animal cells � 90 um Amoeba � 100 um Human Egg This will allow them to enter a discussion or answer questions about cell size and cell adaptation. Students will be given 15 minutes at each station. Closure: A class discussion will be held. Students can report their findings and develop ideas about how the math/theory part connected with the lab part. Teacher should ask students to think about how cells could grow very large without having the SA-to-V ratio get too low. (Students may suggest that a cell could grow in a shape that maximizes SA, such as having outgrowths or an irregular shape.) Assessment: Assign questions about diffusion and osmosis (Questions 2,3, and 7 in Review 15.2 on page 340 of Science Probe 10) and have the students prepare a brief report comparing their findings at the two stations.

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