MA 61 Precalculus for Biology Majors
Lab III: Modeling Data Using Regression – Photosynthesis
The primary source of energy for nearly all life is the Sun. The energy in sunlight is introduced into the
biosphere by a process known as photosynthesis, which occurs in plants, algae and some types of bacteria.
Photosynthesis can be defined as the physico-chemical process by which photosynthetic organisms use light
energy to drive the synthesis of organic compounds. The photosynthetic process depends on a set of complex
protein molecules that are located in and around a highly organized membrane. Through a series of energy
transducing reactions, the photosynthetic machinery transforms light energy into a stable form that can last for
hundreds of millions of years.
6CO2 + 6H2O + sunlight ---> 6O 2 + C6 H12O 6
or...
carbon dioxide + water + sunlight ---> oxygen + carbohydrate (sugar)
This lab focuses on showing how mathematical models can be used to study the structure of the photosynthetic
machinery and the reactions essential for transforming light energy into chemical energy.
To produce photosynthetic reactions plants absorb energy from sunlight. A graph of the visible spectrum of
light at different wavelengths and colors is provided below:
Introductory Task: Understand the Problem to be Modeled
Open and view the first 20 or so slides of the Photosynthesis_self_study_exercise PowerPoint slide show
presentation in the Lab 3 folder on the CD. This is a long and thorough description of photosynthesis that
you may wish to view in its entirety at a later time for your biology class.
Lab Assignment Part 1: Interpreting Graphs
Task I: Plotting and Interpreting an Absorbance Curve
Sample Absorbance versus Wavelength data is provided in an Excel spreadsheet (Photosynthesis.xls). Open
the Photosynthesis.xls Excel spreadsheet and plot the Absorbance data using what you have previously
learned with the Chart Wizard and then answer the following questions:
1. What wavelengths give you the higher absorbance levels? What color/colors are these wavelengths
associated with?
2. What wavelengths give you the lower absorbance levels? What color/colors are these wavelengths
associated with?
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3. What are plants green in color?
Lab Assignment Part 2: Constructing a Model I
How do we measure photosynthesis? Well, obviously from the chemical reaction above, if we can measure the
amount of oxygen produced, then we also know how much carbohydrates or sugars are also produced. A
measure of how much oxygen is produced and, therefore the level of photosynthesis, can be determined from an
O2 evolution curve.
O2 evolution curves
A light response curve is an example of something called a "second-order" graph, since the rate of
photosynthesis first must be determined by plotting O2 evolution versus time at different light levels. The rates
calculated from each O2 evolution curve are then plotted against light level. For example, the figure below
shows O2 evolution curves when photosynthesis was allowed to occur in the presence of two different light
levels.
Notice that there is a time period (called the lag period) between the time the lights are turned on and when
photosynthesis reaches steady state.
Task II: Modeling Oxygen Evolution
Open the Photosynthesis.xls spreadsheet and plot the five sets of oxygen production data at the various light
intensities, i.e. 50, 100, 200, 300 and 400 m/(m2 s). Find the “best-fitting” curve and write down the
associated regression curve equation.
O2 evolution rates
The rate of photosynthesis is calculated from the slope of the linear part of the O2 evolution curve. This figure
shows regression lines drawn through the steady-state regions of the O2 evolution curves.
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In experimental setups, O2 and light levels are monitored automatically by sensors. The O2 sensor is calibrated
to measure "partial pressure" of O2-- the amount of O2 relative to other gases in the atmosphere. Since the units
of partial pressure are %O2, the slope of the line will have units of %O2 / min. This value can be used to
calculate a photosynthesis rate with units of 'umole O2 / m2 / min' by factoring in leaf area and using proper
conversion factors.
The Photosynthesis Light Response Curve
When photosynthesis rates from several experiments are plotted against light intensity, the result is a
photosynthesis light response curve, such as the one shown below.
Interpreting the photosynthesis light response curve
Different plants (even different leaves on the same plant) show differences in the shape of their light response
curves, which reveals characteristics of the underlying photosynthesis processes including the light-dependent
and light-independent reactions, the efficiency at which light is utilized by photosynthesis, and even the rate of
O2 uptake. The response curve can be divided into two phases. Notice that under low-light levels, the rate of
photosynthesis increases as the irradiance level is increased.
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The Light Saturation Point
At a particular light intensity, the so-called "light saturation point", the rate of O2 evolution levels off. Any
further increase in the amount of light striking the leaf does not cause an increase in the rate of photosynthesis-the amount of light is said to be 'saturating' for the photosynthetic process.
Task III: Modeling a Light Response Curve
From the graphs in Task II above, you can determine the photosynthetic rate for each of the five intensities
by taking the slope of each line. Once you have done this, prepare a second graph plotting photosynthetic
rate versus light intensity. Use this curve to approximate the Light Saturation Point.
The Light Compensation Point
Notice that when extrapolated down, the light response curve does not pass through the origin of the graph. The
light value on the X-axis through which the line passes is called the "light compensation point." As you can see,
at light levels below this, there is no net O2 evolution. Do not misinterpret this to mean that photosynthesis does
not occur at light levels below this point, there is a better explanation.
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You should note that this line does not pass through the origin. Instead, it crosses the x-axis at what is called the
photosynthetic compensation point. The photosynthetic compensation point is the intensity of light required
for no net carbon assimilation, meaning that the CO2 consumed by photosynthesis is exactly the same amount
produced by respiration. At light intensities above the photosynthetic compensation point, the plant is taking in
more carbon that it is producing as a waste product by its metabolism. At light intensities below the
photosynthetic compensation point, the plant is actually losing carbon!
Task IV: Determine the Light Compensation Point
In this task we will determine the photosynthetic compensation point. Use the light Response Curve from
Task III above and find the appropriate equation of the line for this curve (see figure above). Then set y = 0
in the resulting equation and solve for x. The x value is the compensation point.
Note: There is no such thing as a negative compensation point (this would imply that the plant is gaining
energy from photosynthesis in total darkness). This lab sometimes doesn't work for one reason or another and
when you solve for x in the above equation, you may find that the compensation point is negative. You should
interpret this as an illogical result and simply state that you cannot determine the compensation point with your
dataset and recommend that you perform the experiment again
Photosynthetic Efficiency
The slope of the linear phase of the response curve is a measure of "photosynthetic efficiency" -- how
efficiently solar energy is converted into chemical energy.
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The photosynthesis apparatus we use is not designed to directly measure the amount of light absorbed by the
leaf. Nevertheless, the light response curves that the class produces do allow comparisons in photosynthetic
efficiency between plants.
Task V: Determine Photosynthetic Efficiency
Use the models created above to determine the photosynthetic efficiency of the data set.
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