This work was funded by NIGMS Grant P50GM107618. The authors thank Zohar B. Weinstein for the insightful comments and suggestions on the manuscript.

NOTE: Any small molecule that inhibits E. coli bacteria growth can be used for the diagonal method. In this protocol, levofloxacin (LEV), nalidixic acid (NAL), and Penicillin G (PNG) will be used as an example, since these drugs show a salient three-way synergy. The workflow of this protocol is shown as Figure 6. Carry out all steps at room temperature. Use fresh aliquots of bacteria and drugs each day. Perform the experiment under biosafety levels appropriate for E. coli.
1. Preparation Steps
<ol>
	<li>Prepare Luria-Bertani (LB) media by adding 25 g of LB broth to 1 L of distilled water and mix. Autoclave at 121&#160;&#176;C for 15 min and store the autoclaved media at room temperature.</li>
	<li>Prepare E. coli glycerol stocks by mixing equal volumes of sterile 50% glycerol and bacterial cells diluted to OD600 = 1 in LB broth and freeze 150&#160;&#181;L aliquots in 1.5 mL microcentrifuge tubes at -80&#160;&#176;C.</li>
	<li>Dissolve 20 mg of antibiotics, LEV, NAL and PNG in 1 mL of dimethyl sulfoxide (DMSO) each. Dilute LEV solution 100x to 0.2&#160;&#181;g/mL by mixing 10&#160;&#181;L of LEV solution with 990&#160;&#181;L of DMSO. Use 0.2 mg/mL LEV, and 20 mg/mL NAL and PNG in the proceeding steps.</li>
	<li>Aliquot 50&#160;&#181;L of each antibiotic to 1.5 mL microcentrifuge tubes and freeze at -20&#160;&#176;C.</li>
	<li>Take one 150&#160;&#181;L aliquot of E. coli from -80&#160;&#176;C. Thaw.</li>
	<li>Add 100&#160;&#181;L of E. coli glycerol stock in 5 mL of LB media in a 14 mL culture tube.</li>
	<li>Shake the tubes in a 37&#160;&#176;C incubator overnight at 200 rpm.</li>
</ol>
2. Serial Dilution Dose-Response Experiment
<ol>
	<li>Take one aliquot of drugs LEV, NAL and PNG from -20&#160;&#176;C, leave them at room temperature for 10 min to thaw and prepare for serial dilutions of these drugs.</li>
	<li>Prepare 1100&#160;&#181;L of LB-10%sol by mixing 990&#160;&#181;L of LB media and 110&#160;&#181;L of solvent (DMSO).</li>
	<li>Prepare 500&#160;&#181;L of LB-10%LEV by mixing 450&#160;&#181;L of LB media and 50&#160;&#181;L of LEV.</li>
	<li>Vortex LB-10%sol for 5 s at the highest setting. Add 20&#160;&#181;L of LB-10%sol to the top four rows of wells in a 96-well microplate.</li>
	<li>Vortex LB-10%LEV for 5 s at the highest setting. Add 20&#160;&#181;L of LB-10%LEV to the first well in row A.</li>
	<li>Prepare two-fold serial dilution for LB-10%LEV by taking 20&#160;&#181;L from the first well, adding to the second well, pipetting up and down five times. Repeat this for all wells sequentially until the 11th well, which ends up with 40&#160;&#181;L (Figure 7A).</li>
	<li>Remove and discard 20&#160;&#181;L of the content from the 11th well, using a micropipette.</li>
	<li>Repeat steps 2.3-2.7 for the drugs NAL and PNG using the second and third rows of the microplate, respectively.</li>
	<li>Repeat steps 2.3-2.7 for the drug LEV again on fourth row as an internal positive control.</li>
	<li>Using a spectrophotometer, measure the OD600 of a 1:10 dilution of the culture (steps 1.5-1.7).</li>
	<li>Dilute the cells in 5 mL of LB media to an OD600 of 0.01. Pour into a reservoir.</li>
	<li>Using a multichannel micropipette, add 80&#160;&#181;L of the diluted cells to the drug serial dilutions prepared in step 2.4-2.9. The final drug concentrations in each well is shown in Figure 7A. Seal the plate to prevent evaporation.</li>
	<li>Incubate the plate for 16 h at 37&#160;&#176;C.</li>
	<li>Start a new bacterial culture to use in step 3 (repeat steps 1.5-1.7).</li>
</ol>
3. Linear Dilution Dose-Response Experiment
<ol>
	<li>Measure the OD600 absorbance for serial dilution dose-response plate from step 2 using a plate reader&#160;(Figure 7A right) and interpret the results based on the following steps.</li>
	<li>Normalize the growth by dividing the growth in each well with the growth in the no drug control for each row and compute percent growth by normalizing OD600to no drug condition.</li>
	<li>For each drug, locate the wells that have ~50% growth inhibition (IC50), shown in orange in Figure 7A right. Assign the concentration in these wells as &#34;serial IC50&#34; for each drug.</li>
	<li>Thaw fresh drug aliquots, prepare 1 mL of LB-10%sol by mixing LB media and solvent (DMSO) in a 9:1 ratio and LB-10%drug by mixing LB media and drug in a 9:1 ratio, where the drug&#39;s concentration is 100x of each drug&#39;s serial IC50 before adding the LB media, as chosen at step 3.3.</li>
	<li>Prepare linearly increasing doses of drugs LEV, NAL and PNG in 11 concentrations, by mixing LB-10%drug and LB-10%sol in volumes shown in Figure 7B.</li>
	<li>Prepare linearly increasing doses of LEV on fourth row as an internal positive control.</li>
	<li>Measure the OD600 of the 1:10 dilution of the culture started in step 2.14.</li>
	<li>Dilute the cells in 5 mL of LB media to an OD600 of 0.01. Pour into a reservoir.</li>
	<li>Add 80&#160;&#181;L of the diluted cells on to the drug linear dilutions prepared in step 3.6 using a multichannel micropipette. The final drug concentrations in each well is shown in Figure 7B. 
	NOTE: The middle well in the dose-response will receive the serial IC50 for this drug. Seal plate to prevent evaporation.</li>
	<li>Incubate the plate for 16 h at 37&#160;&#176;C.</li>
	<li>Start two fresh bacterial cultures to use in step 4 (repeat steps 1.5-1.7).</li>
</ol>
4. Diagonal Drug Interaction Experiment
<ol>
	<li>Measure the OD600 absorbance for linear dilution dose-response from step 3 (Figure 7B).</li>
	<li>For each drug, choose the concentration that resulted in IC50 and prepare drug LEV, NAL and PNG in 100x IC50 concentrations.</li>
	<li>Thaw fresh drugs, prepare 100x IC50 for each drug and prepare 1:1 drug mixtures by volume of LEV+NAL, LEV+PNG and NAL+PNG and 1:1:1 drug mixture by volume of LEV+NAL+PNG.</li>
	<li>Prepare two plates for drug interaction experiments as shown in Figure 8.</li>
	<li>Measure the OD600 of the 1:10 dilution of the cultures started in step 3.11.</li>
	<li>Prepare OD600 = 0.01 dilutions of two cultures in two 10&#160;mL of LB media.</li>
	<li>Add 80&#160;&#181;L of the cells from culture 1 and 2 on plates 1 and 2, respectively. Seal the plates to prevent evaporation. Incubate the plates for 16 h at 37&#160;&#176;C.</li>
</ol>
5. Diagonal Drug Interaction Scores
<ol>
	<li>Measure the OD600 absorbance for diagonal drug interaction experiment plates from step 4.</li>
	<li>Normalize the growth by dividing the growth in each well with the growth in the no drug control well for each row.</li>
	<li>For each row, locate the column that has growth inhibition closest to IC50, shown in orange in Figure 8 right. Assign IC50 based on the relative concentration of drug in this well.</li>
	<li>For LEV+NAL, LEV+PNG and NAL+PNG and LEV+NAL+PNG dose-responses, calculate expected IC50 by averaging the IC50 of the single drugs in each combination. Note that averaging is a simple approximation for exact expected IC50 calculation as described before12.</li>
	<li>Compute Fractional Inhibitory Concentration (FIC) scores by dividing the observed IC50 by the expected IC50 in each combination.</li>
</ol>

<ol>
	<li>Zimmermann, G. R., Lehar, J., Keith, C. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Multi-target+therapeutics:+when+the+whole+is+greater+than+the+sum+of+the+parts.">Multi-target therapeutics: when the whole is greater than the sum of the parts.</a> Drug Discovery Today. 12 (1), 34-42 (2007).</li><li>Berenbaum, M. C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=What+is+synergy?.">What is synergy?.</a> Pharmacological Reviews. 41 (2), 93-141 (1989).</li><li>Cokol, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Drugs+and+their+interactions.">Drugs and their interactions.</a> Current Drug Discovery Technologies. 10 (2), 106-113 (2013).</li><li>Yeh, P. J., Hegreness, M. J., Aiden, A. P., Kishony, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Drug+interactions+and+the+evolution+of+antibiotic+resistance.">Drug interactions and the evolution of antibiotic resistance.</a> Nature Reviews Microbiology. 7 (6), 460-466 (2009).</li><li>Leh&#225;r, J., Krueger, A., Zimmermann, G., Borisy, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=High-order+combination+effects+and+biological+robustness.">High-order combination effects and biological robustness.</a> Molecular Systems Biology. 4 (1), 215 (2008).</li><li>Loewe, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+problem+of+synergism+and+antagonism+of+combined+drugs.">The problem of synergism and antagonism of combined drugs.</a> Arzneimittelforschung. 3 (6), 285-290 (1953).</li><li>Foucquier, J., Guedj, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Analysis+of+drug+combinations:+current+methodological+landscape.">Analysis of drug combinations: current methodological landscape.</a> Pharmacology Research &amp; Perspectives. 3 (3), (2015).</li><li>Wood, K. 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The authors have nothing to disclose.

The use of drug combinations against pathogens or tumors is an attractive prospect, especially under the circumstances of the drying antibiotic pipeline. However, this potential is hampered by at least two difficulties. The first difficulty is the astronomical number of possible combinations. There are, for example, 4950 possible pairwise combinations among 100 antibiotics. All possible combinations among 100 antibiotics (2100) is on the same order of magnitude with the number of bacteria on Earth (~1030). How to predict strongly synergistic combinations among these possibilities has been the subject of numerous computational studies. The second difficulty is the measurement of high-order drug interactions. Consider that a computational platform may suggest that a certain 10-drug combination is strongly synergistic against a certain pathogen. Traditional methods to test drug interactions is too costly to verify or refute this hypothesis, therefore the study of synergy among many drugs has been outside the boundaries of scientific inquiry. The diagonal method, which was first proposed almost 30 years ago and was used in a few recent synergy screens provide a strong foundation for the first problem, by allowing testing of the interaction among many pairs. It solves the second problem by an informative sampling of the traditional assays and allows the study of high-order drug interactions.
We importantly note that our protocol uses a linear dosing for drug interaction measurements, to provide the sensitivity for detecting even weak interactions. Establishing the right concentration range for linear dosing is a challenging task. By first performing a serial dilution, we make an informed decision about the search space for linear dosing. However, the protocol can be modified to use 2-fold or higher serial dilutions for drug interaction testing. Such a modification would shorten the experiment time and allow the testing of more interactions; however, it would have sensitivity to detect only strongly synergistic or antagonistic interactions.
The protocol we described shows the measurement of pairwise or three-way interactions. A critical aspect of the protocol is that single agents are on the same plate as the combination, to minimize bias due to plate variations. Therefore, the protocol can be adjusted to measure interactions up to 7-way combinations by trivial modifications. Combinations of more than 7 drugs will require more than one 96-well microplate and additional considerations must be taken to ensure correct data integration, such as inter-plate replicates.
A notable limitation of the diagonal method is the restriction that each drug in the assay must inhibit the phenotype of interest. Therefore, the diagonal method is not useful for understanding the interactions among active agents and inert adjuvants. Such &#39;potentiating&#39; interactions may be studied under alternative models such as Bliss or Highest Single Agent models.
An important consideration for the analysis of high-order drug interactions is the null model choice for the &#34;expected IC50.&#34; When two drugs are combined, the combination&#39;s effect can only be compared to the single drug effects. When three drugs are combined, the combination&#39;s effect can be compared to the single effects or pairwise effects. For example, if all pairwise combinations of three drugs are synergistic, then it may be expected that these drugs will show a three-way synergy. A three-way interaction&#39;s deviation from what is expected from pairwise interactions has been recently dubbed &#34;emergent interaction&#34;16,17. For simplicity, our protocol describes the measurement of the three-way combination&#39;s &#34;net interaction,&#34; which defines the null model as single drug effects. However, the data that is obtained from the protocol may also be used to compute the emergent interaction of the three-way combination. In our analysis, we defined the expected IC50 of the three-way combination as the average of the single drug IC50s. Alternatively, the expected IC50 can be defined as the average of the IC50s of pairwise combinations (~1.1-1.2). When the observed IC50 is divided by this alternative expected IC50, the obtained FIC provides the emergent FIC for the three-way combination, as previously described12. This consideration reveals that LEV+NAL+PNG is more synergistic than what would be expected from the pairwise interactions among three drugs, demonstrating that LEV+NAL+PNG has emergent synergy.

Drug combinations may exhibit surprisingly high or low effect on a phenotype given the effects of constituent drugs, corresponding to synergistic or antagonistic drug interactions, respectively1,2,3. The use of synergistic combinations may allow dose-escalation for efficacy increase and dose-reduction for side-effect relief. Combination treatments may also apply multiple setbacks to cellular machinery, thereby blocking potential evolutionary escape mechanisms to resistance4. Therefore, combinations of three or more drugs are routinely used in pathogen or cancer treatment5.
Synergy and antagonism are defined by a comparison between the observed effect of a combination versus an expected effect given individual drug effects. Among the models for drug interactions, Loewe additivity is the most stringent and has a well-defined null model (Figure 1)6, and the inferred synergy/antagonism interaction is independent of the drug concentration used6,7. However, the Loewe model is experimentally costly even for a pairwise interaction test. Drug interaction assays traditionally comprise of a 2D matrix of drug concentration combinations (a checkerboard assay) (Figure 2). If 5 doses are used for each drug, then 25 combinations are required, corresponding to one half of a microplate if experiments are conducted in replicate. The cost of this approach prohibits synergy measurement by the Loewe additivity model for multi-drug combinations (Figure 3). For example, to test a 10-way interaction, traditional methods would require more than 100 thousand microplates, barring experimental measurement of high-order synergies by the stringent, well-theorized and concentration-independent Loewe additivity model8.
Current clinical treatments utilize only a fraction of possible drug combinations. For example, the standard treatment of active tuberculosis is a combination of three antibiotics. There are approximately 20 antibiotics used in Mycobacterium tuberculosis (Mtb) treatment. There are 1140 possible 3-way combinations among 20 drugs, each with the potential to have a strong synergy against Mtb. As there has been no cost-effective method to measure drug interactions among many drugs, potentially life-saving synergistic combinations remain untested.
Here, we describe a simple protocol to measure pairwise and three-way drug interactions by sampling only the diagonal of a checkerboard assay (Figure 4 and Figure 5). The underlying concept of sampling the diagonal of a checkerboard experiment was theorized by Berenbaum in his seminal work in 19789. Yet, this approach has only recently been applied to drug synergy screens10,11,12. We present our protocol with Escherichia coli (E. coli) and the growth phenotype. However, we note that the protocol is independent of the biological species and phenotype of interest, and hence may be applied to the measurement of high-order drug synergy in other biological contexts.

<table border="0" cellpadding="0" cellspacing="0" width="528">
	<tbody>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">1.5 mL Semi Micro Cuvette&#160;</td>
			<td style="width:125px;">VWR</td>
			<td style="width:119px;">97000-586</td>
			<td style="width:63px;"></td>
		</tr>
		<tr height="40">
			<td height="40" style="height:40px;width:223px;">1.5 mL &#160;Eppendorf&#160;Microcentrifuge Tubes</td>
			<td style="width:125px;">USA Scientific</td>
			<td>4036-3204</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">1000 &#181;L Tips</td>
			<td style="width:125px;">Geneseesci</td>
			<td>24830</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">14 mL Breathable Cell Culture Tube</td>
			<td style="width:125px;">VWR</td>
			<td>60819-761</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">20 &#181;L Tips</td>
			<td style="width:125px;">Geneseesci</td>
			<td>24804</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">200 &#181;L Tips</td>
			<td style="width:125px;">Geneseesci</td>
			<td>24815</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">37 &#176;C Incubator</td>
			<td style="width:125px;">Panasonic</td>
			<td>MIR-262-PA</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">37 &#176;C Shaker Incubator</td>
			<td style="width:125px;">Thermo Scientific</td>
			<td>SHKE8000</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">5 mL Cell Culture Serological Pipette</td>
			<td style="width:125px;">VWR</td>
			<td>53300-421</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">96-well Microplates</td>
			<td style="width:125px;">VWR</td>
			<td>15705-066</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Breathable Sealing Film</td>
			<td>USA Scientific</td>
			<td>2920-0010</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">DMSO</td>
			<td style="width:125px;">Sigma</td>
			<td>41647</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">Escherichia coli</td>
			<td style="width:125px;">ATCC</td>
			<td>700926</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">Glycerol</td>
			<td style="width:125px;">Sigma</td>
			<td>G9012</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">LB Broth Powder</td>
			<td style="width:125px;">RPI</td>
			<td style="width:119px;">L24065</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">Levofloxacin</td>
			<td style="width:125px;">Sigma</td>
			<td style="width:119px;">28266</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Micropipette</td>
			<td style="width:125px;">GILSON</td>
			<td style="width:119px;">PIPETMAN Classic</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">Microplate reader</td>
			<td style="width:125px;">BioTek</td>
			<td style="width:119px;">Synergy H1</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Multichannel micropipette</td>
			<td style="width:125px;">VistaLab</td>
			<td style="width:119px;">1060</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">Nalidixic acid</td>
			<td style="width:125px;">Sigma</td>
			<td style="width:119px;">N8878</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:223px;">Penicillin G</td>
			<td style="width:125px;">Sigma</td>
			<td>P3032</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Pipette Pump</td>
			<td>Drummond&#160;</td>
			<td>4-000-501</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Reagent Reservoir</td>
			<td style="width:125px;">VWR</td>
			<td>89094-658</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Spectrophotometer</td>
			<td style="width:125px;">BIO-RAD</td>
			<td>1702525</td>
			<td></td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;">Vortex Mixer</td>
			<td>Fisher Scientific</td>
			<td>10-320-807</td>
			<td></td>
		</tr>
	</tbody>
</table>

diagonal method to measure synergy among any number of drugs

A synergistic drug combination has a higher efficacy compared to the effects of individual drugs. Checkerboard assays, where drugs are combined in many doses, allow sensitive measurement of drug interactions. However, these assays are costly and do not scale well for measuring interaction among many drugs. Several recent studies have reported drug interaction measurements using a diagonal sampling of the traditional checkerboard assay. This alternative methodology greatly decreases the cost of drug interaction experiments and allows interaction measurement for combinations with many drugs. Here, we describe a protocol to measure the three pairwise interactions and one three-way interaction among three antibiotics in duplicate, in five days, using only three 96-well microplates and standard laboratory equipment. We present representative results showing that the three-antibiotic combination of Levofloxacin + Nalidixic Acid + Penicillin G is synergistic. Our protocol scales up to measure interactions among many drugs and in other biological contexts, allowing for efficient screens for multi-drug synergies against pathogens and tumors.

Previously, we have reported the pairwise interactions among three drugs: LEV, NAL and PNG based on testing in miniaturized checkerboard assays, where two drugs were combined in a 4 x 4 matrix13,14. While NAL and LEV were synergistic, PNG was reported to be antagonistic with both LEV and NAL13,14. Here, we verified these pairwise interactions and measured the three-way interaction among these three drugs using a diagonal assay. Our results demonstrate that LEV+NAL+PNG is a synergistic 3-way antibiotic combination. Schematic representations for the results of the individual experimental procedure sections were given on the right side of Figure 7 and Figure 8. Here, we present and interpret representative raw results from three plate readings, which are given in Figure 9. The top plate reading corresponds to serial and linear dilution experiments conducted in steps 2 and 3. The bottom two plate readings are duplicate interaction plates conducted in step 4.
The raw data in Figure 9 shows that top growth is around 0.55, but there is a 0.05 optical density of the media itself, as observed in the OD600 of the high drug concentrations where there is no growth. Therefore, we define IC50 as (0.55-0.05)/2 = 0.25. For each dose-response, the wells located closest to this value are shown with orange.
The upper half of Figure 9A shows the results from step 2, serial dose-response experiment. The IC50 wells for LEV is at column 10 in two replicates, which correspond to 4 ng/mL. The IC50 for NAL and PNG are at 3 &#181;g/mL and 25 &#181;g/mL, respectively. These concentrations correspond to the 1x concentration shown in Figure 7B. The lower half of Figure 9B shows the results from step 3, linear dose-response experiments. LEV, NAL and PNG&#39;s IC50 are found at 0.4x, 0.8x and 1.2x, respectively. These concentrations are assigned as the 1X IC50 for step 4.
Two plates corresponding to two replicate experiments are shown in Figure 9B, where the IC50 wells are shown with orange. In plate 1, all single drugs have their IC50 at 1x concentration. The expected IC50 for the pairwise or three-way combination is calculated by the arithmetic mean of constituent drugs, making expected IC50 for all combinations also 1x concentration. In plate 2, LEV and PNG have their IC50 at the 1x concentration, but NAL IC50 is at 1.2x. The expected IC50 for each combination is defined using the arithmetic means of these IC50 values. For example, the expected IC50 for LEV+NAL and NAL+PNG is 1.1x. The drug interaction score (FIC) for each combination is calculated by dividing observed IC50 with the expected IC50, as shown on the right side of the plates. Inspection of the FIC scores of the two plates demonstrates that LEV+NAL and LEV+NAL+PNG are synergistic, while LEV+PNG and NAL+PNG are antagonistic. FIC scores obtained in the two plates are in agreement, supporting the reliability of the protocol.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/57713/57713fig1.jpg" /> 
Figure 1: Null model definition for Loewe additivity drug interaction model. Two 5 x 5 matrices on a microplate, where drug A is linearly increased in one axis as shown at left, and a top concentration of drug inhibits a quantifiable phenotype (top right). The addition of these matrices is shown in the middle, where the lines connecting equipotent drug A concentrations in each single drug have the same concentration as drug A. When cells are added on this &#34;checkerboard&#34; of drug concentration combinations, it is expected that the recorded phenotype on this line will be equivalent for the wells it connects. In this self-self drug interaction experiment, the isobole depicting a phenotype (shown with a dashed green line) is expected to be linear, defining the additivity null model. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/57713/57713fig2.jpg" /> 
Figure 2: Pairwise drug interactions according to Loewe additivity drug interaction model. When two drugs are combined in a checkerboard assay as in Figure 1, the observed isophenotypic contour may be straight, convex or concave. At right, possible isophenotypic contours (dashed green lines) are superimposed on checkerboard assays. Drug combinations with straight isophenotypic contours are Loewe-additive, as the contours are not different from a self-self drug interaction, which is Loewe-additive by definition. When the isophenotypic contour is significantly concave or convex, the combination is synergistic or antagonistic, respectively. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/57713/57713fig3.jpg" /> 
Figure 3: Three-way drug interactions according to Loewe additivity drug interaction model. Similar to the checkerboard assay for pairwise interactions, three-drugs are combined in a 3D grid (a &#34;checkercube&#34;), where each drug is linearly increased in one axis. If the three drugs were identical, the isophenotypic surface is expected to be flat, defining the additivity for three drug combinations. If the surface is more concave or convex than this Loewe-additive null model, drug combinations are synergistic or antagonistic, respectively. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/57713/57713fig4.jpg" /> 
Figure 4: Diagonal method to measure pairwise drug interactions. For each checkerboard assay, only the regions shown in magenta rectangles are measured. i and ii are linearly increasing single drug concentrations. iii is assessed by making a 1:1 mixture of two drugs and linearly titrating this mixture as if it was a single drug. The FIC is equal to the observed IC50 in the combination divided by the expected IC50 of two single drugs. For the Loewe additivity model, the expected IC50 is approximated by the average IC50 of the two single drugs. A FIC value is 1 for Loewe-additive pairs and is lower or higher than 1 for synergistic or antagonistic pairs, respectively2,12. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/57713/57713fig5.jpg" /> 
Figure 5: Diagonal method to measure three-way drug interactions. For each checkercube assay, only the regions shown are measured. i, ii and iii are linearly increasing single drug concentrations. iv is measured by making a 1:1:1 mixture of three drugs and linearly titrating this mixture as if it were a single drug. The Fractional Inhibitory Concentration is equal to the observed IC50 in the combination divided by the expected IC50 given three single drugs. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/57713/57713fig6.jpg" /> 
Figure 6: Workflow for the diagonal method protocol described herein and the setup details for each microplate. The plate shown in Day 4 is conducted in duplicate. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 7" class="xfigimg" src="/files/ftp_upload/57713/57713fig7.jpg" /> 
Figure 7: Serial and linear dilution dose-response experiments. (A) Preparation of serial dilution dose-response for one drug and corresponding final drug concentrations. E. coli cells are added to the plate; growth is recorded after 16 h. Serial IC50, shown in orange, is selected for each drug for use in the following day&#39;s linear dilution dose-response experiments. (B) Preparation of linear dilution dose-response for one drug and corresponding final drug concentrations. E. coli cells are added to the plate; growth is recorded after 16 h. For each drug, the selected IC50s that will be used in the following day&#39;s drug interaction experiments are shown in orange. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig7large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 8" class="xfigimg" src="/files/ftp_upload/57713/57713fig8.jpg" /> 
Figure 8: Drug interaction experiments. Preparation of interaction experiments is similar to single drug linear dose-responses, except that a 1:1 or 1:1:1 mixture of drugs is used for two or three drug dose-responses, respectively. Observed IC50s for each dose-response, depicted in orange, are used to calculate FIC scores. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig8large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 9" class="xfigimg" src="/files/ftp_upload/57713/57713fig9.jpg" /> 
Figure 9: Representative experiment results. Representative results obtained using the described protocol are shown, with details provided in the main text. <a href="https://www.jove.com/files/ftp_upload/57713/57713fig9large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Watch this Scientific Journal Video about Diagonal Method to Measure Synergy Among Any Number of Drugs at JoVE.com

Diagonal Method to Measure Synergy Among Any Number of Drugs

In this protocol, we describe how to make Loewe additivity-based drug interaction measurements for pairwise and three-way drug combinations.

A synergistic drug combination has a higher efficacy compared to the effects of individual drugs. Checkerboard assays, where drugs are combined in many ...

diagonal-method-to-measure-synergy-among-any-number-of-drugs

Nanyang Technological University

Research

JoVE Journal

Biology

18.2K Views.  Sabanci University. In this protocol, we describe how to make Loewe additivity-based drug interaction measurements for pairwise and three-way drug combinations.

Video: Diagonal Method to Measure Synergy Among Any Number of Drugs

A Behavioral Assay to Measure Responsiveness of Zebrafish to Changes in Light Intensities 

The optokinetic reflex (OKR) is a basic visual reflex exhibited by most vertebrates and plays an important role in stabilizing the eye relative to the visual scene. However, the OKR requires that an animal detect moving stripes and it is possible that fish that fail to exhibit an OKR may not be completely blind. One zebrafish mutant, the no optokinetic response c (nrc) has no OKR under any light conditions tested and was reported to be completely blind. Previously, we have shown that OFF-ganglion cell activity can be recorded in these mutants. To determine whether mutant fish with no OKR such as the nrc mutant can detect simple light increments and decrements we developed the visual motor behavioral assay (VMR). In this assay, single zebrafish larvae are placed in each well of a 96-well plate allowing the simultaneous monitoring of larvae using an automated video-tracking system. The locomotor responses of each larva to 30 minutes light ON and 30 minutes light OFF were recorded and quantified. WT fish have a brief spike of motor activity upon lights ON, known as the startle response, followed by return to lower-than baseline activity, called a freeze. WT fish also sharply increase their locomotor activity immediately following lights OFF and only gradually (over several minutes) return to baseline locomotor activity. The nrc mutants respond similarly to light OFF as WT fish, but exhibit a slight reduction in their average activity as compared to WT fish. Motor activity in response to light ON in nrc mutants is delayed and sluggish. There is a slow rise time of the nrc mutant response to light ON as compared to WT light ON response. The results indicate that nrc fish are not completely blind. Because teleosts can detect light through non-retinal tissues, we confirmed that the immediate behavioral responses to light-intensity changes require intact eyes by using the chokh (chk) mutants, which completely lack eyes from the earliest stages of development. In our VMR assay, the chk mutants exhibit no startle response to either light ON or OFF, showing that the lateral eyes mediate this behavior. The VMR assay described here complements the well-established OKR assay, which does not test the ability of zebrafish larvae to respond to changes in light intensities. Additionally, the automation of the VMR assay lends itself to high-throughput screening for defects in light-intensity driven visual responses.

A Behavioral Assay to Measure Responsiveness of Zebrafish to Changes in Light Intensities

We developed the Visual-Motor Response to quantitate the motor output of larval zebrafish in response to light increments and decrements. We also examined zebrafish vision mutants, including the no optokinetic response (nrc) mutants, which were thought to be completely blind when tested by another vision assay, the optokinetic reflex.

The optokinetic reflex (OKR) is a basic visual reflex exhibited by most vertebrates and plays an important role in stabilizing the eye relative to the ...

Photobleaching Assays (FRAP &amp; FLIP) to Measure Chromatin Protein Dynamics in Living Embryonic Stem Cells

Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Loss In Photobleaching (FLIP) enable the study of protein dynamics in living cells with good spatial and temporal resolution. Here we describe how to perform FRAP and FLIP assays of chromatin proteins, including H1 and HP1, in mouse embryonic stem (ES) cells. In a FRAP experiment, cells are transfected, either transiently or stably, with a protein of interest fused with the green fluorescent protein (GFP) or derivatives thereof (YFP, CFP, Cherry, etc.). In the transfected, fluorescing cells, an intense focused laser beam bleaches a relatively small region of interest (ROI). The laser wavelength is selected according to the fluorescent protein used for fusion. The laser light irreversibly bleaches the fluorescent signal of molecules in the ROI and, immediately following bleaching, the recovery of the fluorescent signal in the bleached area - mediated by the replacement of the bleached molecules with the unbleached molecules - is monitored using time lapse imaging. The generated fluorescence recovery curves provide information on the protein's mobility. If the fluorescent molecules are immobile, no fluorescence recovery will be observed. In a complementary approach, Fluorescence Loss in Photobleaching (FLIP), the laser beam bleaches the same spot repeatedly and the signal intensity is measured elsewhere in the fluorescing cell. FLIP experiments therefore measure signal decay rather than fluorescence recovery and are useful to determine protein mobility as well as protein shuttling between cellular compartments. Transient binding is a common property of chromatin-associated proteins. Although the major fraction of each chromatin protein is bound to chromatin at any given moment at steady state, the binding is transient and most chromatin proteins have a high turnover on chromatin, with a residence time in the order of seconds. These properties are crucial for generating high plasticity in genome expression1. Photobleaching experiments are therefore particularly useful to determine chromatin plasticity using GFP-fusion versions of chromatin structural proteins, especially in ES cells, where the dynamic exchange of chromatin proteins (including heterochromatin protein 1 (HP1), linker histone H1 and core histones) is higher than in differentiated cells2,3.

Photobleaching Assays FRAP & FLIP to Measure Chromatin Protein Dynamics in Living Embryonic Stem Cells

We describe photobleaching methods including Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Loss In Photobleaching (FLIP) to monitor chromatin protein dynamics in embryonic stem (ES) cells. Chromatin protein dynamics, which is considered to be one of the means to study chromatin plasticity, is enhanced in pluripotent cells.

Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Loss In Photobleaching (FLIP) enable the study of protein dynamics in living cells with ...

Insulin Injection and Hemolymph Extraction to Measure Insulin Sensitivity in Adult Drosophila melanogaster

Conserved nutrient sensing mechanisms exist between mammal and fruit fly where peptides resembling mammalian insulin and glucagon, respectively function to maintain glucose homeostasis during developmental larval stages 1,2. Studies on largely post-mitotic adult flies have revealed perturbation of glucose homeostasis as the result of genetic ablation of insulin-like peptide (ILP) producing cells (IPCs) 3. Thus, adult fruit flies hold great promise as a suitable genetic model system for metabolic disorders including type II diabetes. To further develop the fruit fly system, comparable physiological assays used to measure glucose tolerance and insulin sensitivity in mammals must be established. To this end, we have recently described a novel procedure for measuring oral glucose tolerance response in the adult fly and demonstrated the importance of adult IPCs in maintaining glucose homeostasis 4,5. Here, we have modified a previously described procedure for insulin injection 6 and combined it with a novel hemolymph extraction method to measure peripheral insulin sensitivity in the adult fly. Uniquely, our protocol allows direct physiological measurements of the adult fly's ability to dispose of a peripheral glucose load upon insulin injection, a methodology that makes it feasible to characterize insulin signaling mutants and potential interventions affecting glucose tolerance and insulin sensitivity in the adult fly.

Insulin Injection and Hemolymph Extraction to Measure Insulin Sensitivity in Adult Drosophila melanogaster

Conserved insulin signaling pathways found in the fruit fly Drosophila melanogaster make this organism a potential tool for modeling metabolic disorders including type II diabetes. To this end, it is critical to establish physiological assays to effectively measure systemic insulin action in peripheral glucose disposal in the adult fly.

Conserved nutrient sensing mechanisms exist between mammal and fruit fly where peptides resembling mammalian insulin and glucagon, respectively function ...

Array Comparative Genomic Hybridization (Array CGH) for Detection of Genomic Copy Number Variants

Array CGH for the detection of genomic copy number variants has replaced G-banded karyotype analysis. This paper describes the technology and its application in a clinical diagnostic service laboratory. DNA extracted from a patient&#8217;s sample (blood, saliva or other tissue types) is labeled with a fluorochrome (either cyanine 5 or cyanine 3). A reference DNA sample is labeled with the opposite fluorochrome. There follows a cleanup step to remove unincorporated nucleotides before the labeled DNAs are mixed and resuspended in a hybridization buffer and applied to an array comprising ~60,000 oligonucleotide probes from loci across the genome, with high probe density in clinically important areas. Following hybridization, the arrays are washed, then scanned and the resulting images are analyzed to measure the red and green fluorescence for each probe. Software is used to assess the quality of each probe measurement, calculate the ratio of red to green fluorescence and detect potential copy number variants.

Array Comparative Genomic Hybridization Array CGH for Detection of Genomic Copy Number Variants

Array CGH for the detection of genomic copy number variants has replaced G-banded karyotype analysis. This paper describes the technology and its application in a diagnostic service laboratory.

Array CGH for the detection of genomic copy number variants has replaced G-banded karyotype analysis. This paper describes the technology and its ...

Quantitative Immunofluorescence Assay to Measure the Variation in Protein Levels at Centrosomes

Centrosomes are small but important organelles that serve as the poles of mitotic spindle to maintain genomic integrity or assemble primary cilia to facilitate sensory functions in cells. The level of a protein may be regulated differently at centrosomes than at other .cellular locations, and the variation in the centrosomal level of several proteins at different points of the cell cycle appears to be crucial for the proper regulation of centriole assembly. We developed a quantitative fluorescence microscopy assay that measures relative changes in the level of a protein at centrosomes in fixed cells from different samples, such as at different phases of the cell cycle or after treatment with various reagents. The principle of this assay lies in measuring the background corrected fluorescent intensity corresponding to a protein at a small region, and normalize that measurement against the same for another protein that does not vary under the chosen experimental condition. Utilizing this assay in combination with BrdU pulse and chase strategy to study unperturbed cell cycles, we have quantitatively validated our recent observation that the centrosomal pool of VDAC3 is regulated at centrosomes during the cell cycle, likely by proteasome-mediated degradation specifically at centrosomes.

Here, a novel quantitative fluorescence assay is developed to measure changes in the level of a protein specifically at centrosomes by normalizing that protein&#8217;s fluorescence intensity to that of an appropriate internal standard.

Centrosomes are small but important organelles that serve as the poles of mitotic spindle to maintain genomic integrity or assemble primary cilia to ...

Using plusTipTracker Software to Measure Microtubule Dynamics in Xenopus laevis Growth Cones

Microtubule (MT) plus-end-tracking proteins (+TIPs) localize to the growing plus-ends of MTs and regulate MT dynamics1,2. One of the most well-known and widely-utilized +TIPs for analyzing MT dynamics is the End-Binding protein, EB1, which binds all growing MT plus-ends, and thus, is a marker for MT polymerization1. Many studies of EB1 behavior within growth cones have used time-consuming and biased computer-assisted, hand-tracking methods to analyze individual MTs1-3. Our approach is to quantify global parameters of MT dynamics using the software package, plusTipTracker4, following the acquisition of high-resolution, live images of tagged EB1 in cultured embryonic growth cones5. This software is a MATLAB-based, open-source, user-friendly package that combines automated detection, tracking, visualization, and analysis for movies of fluorescently-labeled +TIPs. Here, we present the protocol for using plusTipTracker for the analysis of fluorescently-labeled +TIP comets in cultured Xenopus laevis growth cones. However, this software can also be used to characterize MT dynamics in various cell types6-8.

Using plusTipTracker Software to Measure Microtubule Dynamics in Xenopus laevis Growth Cones

The MATLAB-based, open source software package, plusTipTracker, can be used to analyze image series of fluorescently-labeled +TIPs to quantify microtubule dynamics.

Microtubule (MT) plus-end-tracking proteins (+TIPs) localize to the growing plus-ends of MTs and regulate MT dynamics1,2. One of the most well-known and ...

In Vitro Assay to Measure Phosphatidylethanolamine Methyltransferase Activity

Phosphatidylethanolamine methyltransferases are biosynthetic enzymes that catalyze the transfer of one or more methyl group(s) from S-adenosyl-L-methionine onto phosphatidylethanolamine, monomethyl-phosphatidylethanolamine, or dimethyl-phosphatidylethanolamine to give either monomethyl-phosphatidylethanolamine, dimethyl-phosphatidylethanolamine or phosphatidylcholine. These enzymes are ubiquitous in animal cells, fungi, and are also found in approximately 10% of bacteria. They fulfill various important functions in cell physiology beyond their direct role in lipid metabolism such as in insulin resistance, diabetes, atherosclerosis, cell growth, or virulence. The present manuscript reports on a simple cell-free enzymatic assay that measures the transfer of tritiated methyl group(s) from S-[Methyl-3H]adenosyl-L-methionine onto phosphatidylethanolamine using whole cell extracts as an enzyme source. The resulting methylated forms of phosphatidylethanolamine are hydrophobic and thus, can be separated from water soluble S-[Methyl-3H]adenosyl-L-methionine by organic extraction. This assay can potentially be applied to any other cell types and used to test inhibitors/drugs specific to a phosphatidylethanolamine methyltransferase of interest without the need to purify the enzyme.

In Vitro Assay to Measure Phosphatidylethanolamine Methyltransferase Activity

The present report describes an in vitro enzymatic assay to measure phosphatidylethanolamine methyltransferase activity using Leishmania cell extracts. This assay is based on the transfer of a radioactive methyl group from S-[Methyl-3H]adenosyl-L-methionine onto endogenous phosphatidylethanolamine.

Phosphatidylethanolamine methyltransferases are biosynthetic enzymes that catalyze the transfer of one or more methyl group(s) from ...

Using Microfluidic Devices to Measure Lifespan and Cellular Phenotypes in Single Budding Yeast Cells

Budding yeast Saccharomyces cerevisiae is an important model organism in aging research. Genetic studies have revealed many genes with conserved effects on the lifespan across species. However, the molecular causes of aging and death remain elusive. To gain a systematic understanding of the molecular mechanisms underlying yeast aging, we need high-throughput methods to measure lifespan and to quantify various cellular and molecular phenotypes in single cells. Previously, we developed microfluidic devices to track budding yeast mother cells throughout their lifespan while flushing away newborn daughter cells. This article presents a method for preparing microfluidic chips and for setting up microfluidic experiments. Multiple channels can be used to simultaneously track cells under different conditions or from different yeast strains. A typical setup can track hundreds of cells per channel and allow for high-resolution microscope imaging throughout the lifespan of the cells. Our method also allows detailed characterization of the lifespan, molecular markers, cell morphology, and the cell cycle dynamics of single cells. In addition, our microfluidic device is able to trap a significant amount of fresh mother cells that can be identified by downstream image analysis, making it possible to measure the lifespan with higher accuracy.

This article presents a protocol optimized for the production of microfluidic chips and the setup of microfluidic experiments to measure the lifespan and cellular phenotypes of single yeast cells.

Budding yeast Saccharomyces cerevisiae is an important model organism in aging research. Genetic studies have revealed many genes with conserved effects ...

High-resolution Respirometry to Measure Mitochondrial Function of Intact Beta Cells in the Presence of Natural Compounds

High-resolution respirometry allows for the measurement of oxygen consumption of isolated mitochondria, cells and tissues. Beta cells play a critical role in the body by controlling blood glucose levels through insulin secretion in response to elevated glucose concentrations. Insulin secretion is controlled by glucose metabolism and mitochondrial respiration. Therefore, measuring intact beta cell respiration is essential to be able to improve beta cell function as a treatment for diabetes. Using intact 832/13 INS-1 derived beta cells we can measure the effect of increasing glucose concentration on cellular respiration. This protocol allows us to measure beta cell respiration in the presence or absence of various compounds, allowing one to determine the effect of given compounds on intact cell respiration. Here we demonstrate the effect of two naturally occurring compounds, monomeric epicatechin and curcumin, on beta cell respiration under the presence of low (2.5 mM) or high glucose (16.7 mM) conditions. This technique can be used to determine the effect of various compounds on intact beta cell respiration in the presence of differing glucose concentrations.

The goal of this protocol is to measure the effect of glucose-mediated changes to mitochondrial respiration in the presence of natural compounds on intact 832/13 beta cells using high-resolution respirometry.

High-resolution respirometry allows for the measurement of oxygen consumption of isolated mitochondria, cells and tissues. Beta cells play a critical role ...

Using a Thermal Camera to Measure Heat Loss Through Bird Feather Coats

Feathers are essential to insulation, and therefore to the cost of thermoregulation,&#160;in birds. There is robust literature on the energetic cost of thermoregulation in birds across a variety of ecological circumstances. However, few studies characterize the contribution of the feathers alone to thermoregulation. Several previous studies have established methods for measuring the insulation value of animal pelts, but they require destructive sampling methods that are problematic for birds, whose feathers are not distributed evenly across the skin. More information is needed about 1) how the contribution of feathers to thermoregulation varies both across and within species and 2) how feather coats may change over space and time. Reported here is a method for rapidly and directly measuring the thermal performance of feather coats and the skin using dried whole skin specimens, without the need to destroy the skin specimen. This method isolates and measures the thermal gradient across a feather coat in a way that measurements of heat loss and metabolic cost in live birds, which use behavioral and physiological strategies to thermoregulate, cannot. The method employs a thermal camera, which allows the rapid collection of quantitative thermal data to measure heat loss from a stable source through the skin. This protocol can easily be applied to various research questions, is applicable to any avian taxa, and does not require destruction of the skin specimen. Finally, it will further the understanding of the importance of passive thermoregulation in birds by simplifying and accelerating the collection of quantitative data.

This protocol describes the quantification of heat transmission through a flat skinned avian specimen using a thermal camera and hot water bath. The method allows obtaining of quantitative, comparative data about the thermal performance of feather coats across species using dried flat skin specimens.

Feathers are essential to insulation, and therefore to the cost of thermoregulation,&#160;in birds. There is robust literature on the energetic cost of ...