Three-Step Approach to Solving Linear Gradient Problems in Photosynthesis - Prof. Douglas , Study notes of Cellular and Molecular Biology

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THREE STEPS TO “GETTING”

LINEAR GRADIENT PROBLEMS

There are only three archetypes of linear gradient problems possible for the light reactions of photosynthesis:

1. [H+]STROMA > [H+]THYLAKOID LUMEN
2. [H+]STROMA = [H+]THYLAKOID LUMEN
3. [H+]STROMA < [H+]THYLAKOID LUMEN These problem types are listed above in order of decreasing difficulty. Luckily, no matter how seemingly difficult the problem, it can be solved like all others using three simple steps. Before we define the steps, lets think back and try to recall information about your best light reactions resource, the “movie” from the course website. Do you remember any specific numbers resulting from actions in the movie? Electrons moved? Photons used? Water molecules split? Could you list them all? If you’re drawing a blank, watch the movie again and check to see if this list makes sense: That last number is especially important. Because every action in the movie sums to produce a single molecule of O 2 gas, for the purposes of this class, the movie can be considered the least amount of work the light reaction system is capable of performing (we have no idea how to produce 3/8ths of an oxygen molecule, so don’t try it! Just round up ). This means that the “movie cycle” has now become your basal unit for gradient problems. Whenever you are confronted with a gradient problem, you should immediately ask yourself the question “How many full movie cycles do I need to perform to solve this?” Now, you may have realized “Wait… that movie cycle list doesn’t even talk about protons, and I know they move around a lot!” You would be right on both counts. The net movement of protons per movie cycle is so important that it will be though of as separate from our list of other numbers. Do you know the changes in proton concentration on both sides of the thylakoid membrane during a movie cycle? If not, watch the movie again while looking at the simplified figure on the next page to see if the numbers make sense:

Let’s take an example from the most difficult archetype of linear gradient problem to put our new knowledge to the test: “With an initial proton gradient of 200H+^ in the stroma and 100 H+^ in the thylakoid lumen, how many photons of light are necessary to produce 3ATP?” (assuming linear electron transport) STEP #1: Find The Gradient We Must Develop to Produce Our Product Every gradient problem will provide you with an “initial condition.” If none is explicitly stated, you should assume that both sides of the thylakoid membrane begin the problem in a state of proton equilibrium (there are the same number of protons on both sides). This problem’s initial condition, highlighted yellow, reveals that we initially have more protons in the stroma than in the thylakoid lumen. This is the opposite of the concentration difference necessary to produce ATP through the ATP synthase ([H+] thylakoid lumen > [H+] stroma), so our first job is to get the two sides back to equilibrium. We do this by moving protons from the stroma to the thylakoid lumen – just as a plant cell would. How many protons would we need to move through the membrane to equilibrate both sides? Fifty. Remember those fifty protons; this is the first part of the gradient we must develop. Every gradient problem will also contain a “product” (ours is highlighted in blue). This product will almost always be a number of ATP or sugar molecules – indirectly made by ATP and NADPH – that we are required to produce via proton motive force through ATP synthase. Now that we have equilibrated the membrane, we must move the number of protons required to produce our product through the same process: Remember though, protons only run through ATP synthase to reestablish equilibrium. This means that only half of those nine protons would actually feel like moving. We would need to double the amount of protons required to 18H+^ to actually produce our 3ATP product. So, the true gradient we must develop in this problem is 50 H+^ (establish equilibrium) plus 18 H+^ (make product), which equals 68 H+. This is the answer for Step #1.

STEP #2: Determine the Lowest Whole Number of Movie Cycles Required to Produce Our Product This step is easy. You know the total gradient you need to develop to produce your product (68 H+) and you know what gradient you can develop per movie cycle (14 H+), so just divide them! Remember, we don’t want to deal with fractional cycles, so just round up 4.86 movie cycles to 5. This is the answer for Step #2. STEP #3: Answer Your Original Question Using the Movie Cycle Chart The wording of a gradient problem contains one final element ‐ the actual question, duh! Don’t think we forgot about that. The question posed in this gradient problem (highlighted green) asks for the number of photons required to make our product. We just discovered in Step #2 that we need to run five movie cycles to make 3ATP. If only we had some tool to relate movie cycles to photons… oh, wait! We have that old list! In fact, the list doesn’t just help us convert to photons; it can and should be used to solve any kind of question a gradient problem may dish out. A simple word change from “photons” to “water molecules” in the question of this gradient problem could have completely thrown off an unprepared student, but someone reading this guide would have merely pulled a different number from their list. Crisis averted  Back to our example problem. To finish up, just multiply the number of movie cycles necessary to make our product (five cycles) by the number of photons per movie cycle (eight photons). This gives us our final answer to the question posed in this gradient problem.