Today you will obtain titration curves against calcium for your wild-type and mutant proteins using an automated fluorescence plate reader. This machine reads multiple samples in a standard format – in our case, a 96-well microtiter plate. The output is a grid of up to 96 fluorescence values, for rows A-G and columns 1-12, which is amenable to analysis with a program like Excel.
In order to further benefit from this high-throughput testing format, you will make friends with the multichannel pipet, a purely mechanical rather than digital aid for repetitive experiments. This tool allows you to suck up and expel equivalent volumes of multiple identical samples (usually 8-12 at a time) with just one stroke. You will use this type of pipet to fill each row of a microtiter plate with one type of protein sample, and each column with a different concentration of calcium. Although a multichannel pipet can be sufficient for a typical research lab, in pharmaceutical companies that may be assaying thousands of samples a day, yet more steps of automation and scaling up are required, such as robotic pipet arms that obviate the need for manual pipetting at all. The degree of automation commercially available, or developed ‘in-house’ in a certain lab or corporation, depends in part on the frequency with which a certain assay is used. Assays used by many different labs and companies (such as fluorescence or absorbance spectrophotometry) are likely to breed commercially available high-throughput machines.
Signal:noise in arbitrary data collection. Background measurements (open circles), sample measurements (closed circles), and average values (short horizontal lines) are shown. The short line without any data points represents the reduction in average signal when background is subtracted. All measurements are with respect to an arbitrary vertical axis; the long horizontal line represents a measurement of zero.
While the concept of scale is a pragmatic concern, a perhaps more substantive topic of interest to us today is that of confidence in our results. As you are probably well-aware, every manipulation and measurement you make in the lab has an error associated with it. For example, consider the ubiquitous P200 pipetman. According to one pipet manufacturer, its accuracy is 1% (slightly worse at the lowest volumes). So an attempt to pipet 100 μL would result in an actual volume of 99-101 μL from the error of the instrument alone, which could be further compounded by a sleepy pipet operator, say. The precision of a pipet is typically better than its accuracy, 0.25% for the example given above. Precision refers to the reproducibility of a given measurement, not its absolute accuracy. This simple example demonstrates the general principles applicable to other types of error.
You will attempt to get a sense of the overall error of today’s experiment by running your protein samples in duplicate. That is, for each protein-calcium combination, you will perform two independent measurements. These measurements can then be averaged to smooth out your data, and hopefully improve the signal to noise ratio - where signal here refers to true differences between samples mixed with different amounts of calcium, and noise means inherent fluctuations in the system due to error. Noise in this experiment can also refer to background fluorescence of the sample buffer. Thus, another way to maintain a reasonable signal:noise ratio is by keeping our protein fairly concentrated, so that the absolute fluorescence values we obtain are high compared to the background. The figure at right demonstrates the above concepts. Scatter in the data (not all of the circles are at the same height) is one kind of noise. The level of background is another kind of noise: the left-hand data has a relatively low signal and thus poor signal:noise ratio, while the right-hand data has a relatively high absolute signal and improved signal:noise ratio.
Beginning today or at a later time before your reports are due (such as next week's office hours), you will analyze the raw data obtained today. Although you should be able to produce reasonable titration curves by following the example of Nagai, the introduction/review of binding constants below may help contextualize your analysis.
Let’s start by considering the simple case of a receptor-ligand pair that are exclusive to each other, and in which the receptor is monovalent. The ligand (L) and receptor (R) form a complex (C), which reaction can be written
At equilibrium, the rates of the forward reaction (rate constant = kf) and reverse reaction (rate constant = kr) must be equivalent. Solving this equivalence yields an equilibrium dissociation constant KD, which may be defined either as kr / kf, or as [R][L] / [C], where brackets indicate the molar concentration of a species. Meanwhile, the fraction of receptors that are bound to ligand at equilibrium, often called y or θ, is C / RTOT, where RTOT indicates total (both bound and unbound) receptors. Note that the position of the equilibrium (i.e., y) depends on the starting concentrations of the reactants; however, KD is always the same value. The total number of receptors RTOT= [C] (ligand-bound receptors) + [R] (unbound receptors). Thus,
where the right-hand equation was derived by algebraic substitution. If the ligand concentration is in excess of that of the receptor, [L] may be approximated as a constant, L, for any given equilibrium. Let’s explore the implications of this result:
- What happens when L << KD?
- →Then y ~ L / KD, and the binding fraction increases in a first-order fashion, directly proportional to L.
- What happens when L >> KD?
- →In this case y ~1, so the binding fraction becomes approximately constant, and the receptors are saturated.
- What happens when L = KD?
- →Then y = 0.5, and the fraction of receptors that are bound to ligand is 50%. This is why you can read KD directly off of the plots in Nagai’s paper (compare Figure 3 and Table 1). When y = 0.5, the concentration of free calcium (our [L]) is equal to KD. This is a great rule of thumb to know.
The figures at below demonstrate how to read KD from binding curves. You will find semilog plots right particularly useful today, but the linear plot (left) can be a helpful visualization as well. Keep in mind that every L value is associated with a particular equilbrium value of y, while the curve as a whole gives information on the global equilibrium constant KD.
Simple Binding Curve
The binding fraction y
at first increases linearly as the starting ligand concentration is increased, then asymptotically approaches full saturation (y
=1). The dissociation constant KD
is equal to the ligand concentration [L]
for which y
Semilog Binding Curves
By converting ligand concentrations to logspace, the dissociation constants are readily determined from the sigmoidal curves' inflection points. The three curves each represent different ligand species. The middle curve has a KD
close to 10 nM, while the right-hand curve has a higher KD
and therefore lower affinity between ligand and receptor (vice-versa for the left-hand curve).
Of course, inverse pericam has multiple binding sites, and thus IPC-calcium binding is actually more complicated than in the example above. The KD reported by Nagai is called an ‘apparent KD’ because it reflects the overall avidity of multiple calcium binding sites, not their individual affinities for calcium. Normally, calmodulin has a low affinity (N-terminus) and a high affinity (C-terminus) pair of calcium binding sites. However, the E104Q mutant, which is the version of CaM used in inverse pericam, displays low-affinity binding at both termini. Moreover, the Hill coefficient, which quantifies cooperativity of binding in the case of multiple sites, is reported to be 1.0 for inverse pericam. This indicates that inverse pericam behaves as if it were binding only a single calcium ion per molecule. Thus, wild-type IPC is well-described by a single apparent KD.
When you write your research article, be sure to consider how changes in both binding affinity and cooperativity can affect the practical utility of a sensor.
Two groups will begin with Parts 2 to 3, while everyone else begins with Part 1.RECONSIDER
Part 1: SDS-PAGE
- Last time you prepared cell-normalized -IPTG and +IPTG samples and added Laemmli sample buffer (containing SDS, etc.) to them. Now you will complete protein denaturing in preparation for PAGE, alongside a MW ladder.
- The ladder is pre-stained and will be used to track gel progress. Unstained ladders contain a known amount of protein per band and can be used to estimate gross protein contents. We will not use one today, but they are a useful tool to be aware of.
- Boil all 7 eppendorfs (including 15 μL of ladder!) for 5 minutes in the water bath that is in the fume hood.
- You will be shown by the teaching faculty how to load your samples into the gel. You should load your samples according to the table below. Two groups will share each gel.
- Note the starting and stopping time of electrophoresis, which will be initiated by the teaching faculty at 200 V, and run for 30-45 minutes.
- Pry apart the plates using a spatula, and carefully transfer your gel to a staining box.
- Add enough distilled water to cover the gel (say, 200 mL) and rinse the gel for 5 min on the shaker in the hood.
- Repeat the rinse two more times with fresh water (~200 mL and 5 min incubation each time).
- Add ~ 50 mL of BioSafe Coomassie, and incubate for at least 1 hour.
- Empty the staining solution into the waste container in the fume hood - careful not to lose your gel!
- Add 200 mL of water to your stained gel. Replace with fresh water just before leaving the lab if you have a chance.
- Tomorrow, the teaching staff will transfer each gel to fresh water, then photograph them and post the results to the Day 6 Talk page.
Loading order and volumes
Loading volume is 10 μL for the ladder and 15 μL for your samples. Nothing goes in lane 1!
You may load your samples as -, -, -, +, +, + OR -, +, -, +, - +.
Either way, please use the order WT, E67K/T79P/M124S, X#Z.
| Sample/Lane #
|| Sample Name
|| Sample/Lane #
|| Sample Name
||Group 1, ladder
||Group 2, ladder
Part 2: Prepare samples for titration curve
Tips for Success
Take great care today to limit the introduction of bubbles in your samples. When expelling fluid, pipet slowly while touching the pipet tip against the bottom or side of the well.
When using the multichannel pipet, always check to make sure all tips are getting filled - sometimes one tip may not be on all the way, and will pull up less volume than the others. If this happens, release the fluid, adjust the tip, and try again.
Titration sample preparation
- Take a black 96-well plate, and familiarize yourself with the scheme at right: top two rows are wild-type, next two rows are one of the E67K/T79P/M124S mutants, and the final two are your own mutant.
- The dark sides of the plate reduce "cross-talk" (i.e., light leakage) between samples in adjacent wells, another potential contribution to error.
- Transfer an aliquot of wild-type protein to a plastic reservoir. Use the multichannel pipet to add 30 μL of protein (per well) to the top two rows of your plate.
- Take a fresh reservoir or use the next compartment in a divided reservoir, and repeat step 2 for your mutant proteins, adding each one to the appropriately labeled rows.
- Finally, add plain water with only BSA (no IPC) to the seventh row of the plate, using the shared dedicated reservoir. (Why do you think we are including this row of solutions?)
- Using shared reservoir #1 (lowest calcium concentration), add 30 μL to the top seven rows in the first column of the plate. Discard the pipet tips.
- Now work your way from reservoirs #2 to #12 (highest calcium concentration), and from the left-hand to the right-hand columns on your plate. Be sure to use fresh pipet tips each time! If you do contaminate a solution, let the teaching faculty know so they can put out some fresh solution. Honesty about a mistake is far preferred here to affected every downstream experiment.
- Finally, cover the plate with parafilm and wrap it in aluminum foil.
Part 3: Fluorescence assay
- BPEC (the Biological Process Engineering Center) has graciously agreed to let us use their plate reader. Walk over to the BPEC instrument room with a member of the teaching staff.
- You will be shown how to set the excitation (485 nm) and emission (515 nm) wavelength on the plate reader to assay your protein.
- Your raw data will be posted on today's Talk page; alternatively, you can bring your own flash drive to recover the data immediately.
For next time
- Extra credit, to be submitted by 4 pm Tuesday or Wednesday, respectively: Prepare a figure and caption for your SDS-PAGE, along with a paragraph of text for the associated results section. Look up the expected molecular weight using the IPC sequence document and this or a similar website. Be sure to add ~ 3 KDa for the size of the N-terminus of pRSET (His tag, etc). If you see two strong bands, what do you think the second one is?
- Module 3, Day 2 will happen in two distinct shifts. Sign up for either the 1 pm or the 3 pm Day 2 session on that day's Talk page. If your culture requires complicated preparations, you will be asked to join the second group. Be sure to tell the teaching faculty a brief description of your plans before leaving today.
- Familiarize yourself with the cell culture portion of Day 2 of this module. The better prepared we all are, the less likely it is that the day will run long. The hoods will be set up for you when you come in.
- Write a two or three sentence description of your design plan and expected assay results, and post it on the Day 2 Talk page by 6 pm Thursday or Friday, respectively. (Assay result expectations should be stated in a relative fashion: e.g., "we think [3D sample 1] will maintain a chondrocyte-like phenotype better than [3D sample 2], because..." You might also comment on cell viability, if you expect it to vary among your samples.) This posting will count for homework credit.
- Gels from Bio-Rad
- 4-15% Polyacrylamide Gels in Tris-HCl
- TGS Buffer (25 mM Tris, 192 mM glycine, 0.1% (w/v) SDS, pH 8.3)
- Kaleidoscope marker sizes here
- Calcium calibration kit from Invitrogen