0.6 The fluid mosaic model - determining the matrix  (Page 2/2)

A good way to visually represent the differences between these two sets of measurements is to build a histogram, a.k.a. a frequency distribution. Recall that a frequency distribution, like the one found here , is a figure relating the number of times particular observations (values or discrete traits like eye color for example) appear in a sample.

For this investigation, building two hypothetical frequency distributions one per model, will give you expected distributions of measurements to which you can compare actual measurements of inter-protein distances in order to determine whether proteins appear to be randomly or regularly distributed on the surface of a cell membrane.

4. To build a hypothetical frequency distribution, return to your sketches and two hypothetical columns of numbers. Total the number of times you observe each particular distance. For example, note the number of times you measured a distance of 1 unit between two proteins, 2 units, 3 units etc. up to a maximum number of units you observed. Finally graph these totals by placing each unit of distance (ex. 1, 2, 3, etc.) on the x-axis and number of times you expect to see each unit of distance on the y-axis. Produce one such histogram for each sketch.

Now you are prepared to compare the results you expect to see, i.e. your hypothetical frequency distributions, to the actual results from an experiment in which Nicolson, Masouredis and Singer (1971) stained the surface of human erythrocytes for the Rh protein (Figure 1).

Examine Figure 1.2. Do these proteins look randomly or regularly distributed to you? To test your opinion as well as the two models of membrane matrix structure, answer the questions below.

To determine whether Rh proteins on the surface of human erythrocytes are randomly or regularly distributed, you need to build a histogram describing the frequency with which different distances among proteins occur on this plasma membrane.

5. To do this, measure the distances between 50 pairs of proteins by choosing one protein at random and measuring the distance from this protein to all neighboring proteins for which there is a direct line of sight (i.e. you do not have to measure across an intervening protein). Repeat this process until you have recorded 50 distances. Measure distance anyway you like as long as you are consistent and do not measure the same distance twice. Record your measurements in a spread sheet like Excel.

6. Organize your data into a histogram. To do this in Excel, first create the categories (bins) that will form the x-axis. In the column next to your data, create categories that reflect the range of observations you made in one unit increments. For example, if the smallest measured distance was 1 and the largest 31, create a column of numbers 1,2,3, 4...all the way to 31. These are your bins for tallying the number of measurements of each length. Second, go to the tools menu, select the data analysis option (if not present select add-ins and highlight the analysis tool pak box), and the histogram function. Select the input range box and highlight your column of measurements, then select the bin range box and highlight the bins you composed. Finally, select the output range box and select an empty cell where you would your tallied data to appear. Highlight the chart output box at the bottom of the menu and click ok. You should see a figure titled 'histogram' and two associated columns of numbers one labeled bin, the other frequency. Click on the bars in the chart and the data columns describing the values on the x (bin) and y (frequency) axes respectively should become highlighted.

7. Write a figure legend for your histogram that describes the data illustrated in your figure. Your legend should simply relate what is shown but not interpret the data in anyway.

8. Compare your histogram to the histograms you produced for question 4. Do you think Rh proteins are randomly or regularly distributed on the surface of erythrocytes? Why or why not? Please support your explanation and conclusion with evidence.

9. Imagine you are Nicolson, Masouredis and Singer. Which model of matrix structure, lipid or protein, do you interpret your data to support? Why? Please explain.

10. Are you comfortable with the conclusion you drew in question 9 on the basis of this data? Why or why not? Please explain. If you are not, please explain one way in which you could increase your confidence in your conclusion.

Works cited

• Nicolson, G.L., S.P. Masouredis, and S.J. Singer. 1971. Quantitative two dimensional ultrastructural distribution of Rho(D) antigenic sites on human erythrocyte membranes. Proceedings of the National Academy of Sciences. 68:1416-1420.
• Singer, S.J. and G.L. Nicolson. 1972. The fluid mosaic model of the structure of cell membranes. Science. 175:720-731.