APPENDIX A
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`APPENDIX A
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` ie
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`The ability to measure multiple targets simultaneously (multiplexing) within every
`partition of a digital PCR system is often limited by the detection approach. Commonly one
`measures fluorescenceto classify partitions as positive (if the measured fluorescenceis
`high) or negative (if the measured fluorescence is low). Some chemistries, such as TaqMan,
`allow measurementsof several targets simultaneously by utilizing target-specific probes
`labeled with different dyes. If the detector can measurethe fluorescence emitted by N
`different dyes, then the digital PCR system is effectively capable of measuring N different
`targets. Typically, instruments that are capable of detecting more colors are more
`expensive than those with fewer colors. Increasing the number of detectable dyesis
`expensive and is impractical beyond a certain number. On the other hand, many
`applications especially where sampleis limited could benefit greatly from higher degrees of
`multiplexing.
`
`Here wepresentan approachthat, given an instrument capable of detecting multiple
`colors, can dramatically increase the number of simultaneously measured targets without
`requiring any changes to the instrument. The standard approachof designing assaysis that
`a given target is assessed based on fluorescence produced fromasingle probe with a single
`dye. Thus, if the instrument is capable of detecting two colors such as FAM andVIC, one
`measures the concentration of one target by counting the numberofpartitions with
`positive FAM signals and anothertarget by counting the numberof partitions with positive
`VIC signals.
`
`The core of this invention is that one can design assays that producefluorescence on
`multiple channels simultaneously. If processed on a digital PCR platform with a large
`number of partitions these assays can be multiplexed together with single channel assays
`and can be measured by counting the number of partitions with fluorescence on both
`channels.
`
`
`
`Assuming weare lookingat two unlinked loci (target 1 and target 2), and given some
`number of FAM-only droplets as well as some number of VIC-only droplets, we can
`estimate how many FAM-VIC droplets we expect. If we are operating at low concentrations
`this number should be small and can be worked outin a straightforward fashion.
`
`If we set up a third assay (target 3) such thatit has two additional probes — one labeled
`with FAM and one labeled with VIC, we can estimate the concentration of this third target
`
`1
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`Appendix A
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`locus by how many excess FAM-VIC droplets we have compared to the expectation. This
`would reduce the overall precision but not much,and basically notat all if we are operating
`ina dilute regime (i.e., the total numberof partitions is much larger than the number of
`positive partitions). Below is an example of an algorithm that can be used todeterminethe
`concentration of the excess FAM-VIC species.
`
`The use of multiple probes labeled with the samedye will increase the fluorescence of the
`negative droplets, which can presenta challenge in extremecasesif fluorescence of the
`negative droplets starts approachingthat of the positive droplets. This challenge can be
`addressed effectively by using sufficiently robust assays. One can also use commonprobes
`and avoid the elevation of negative fluorescence altogether. For the above example, we can
`consider using acommon FAMprobe for target 1 and target 3 and a commonVIC probe for
`target 2 and target 3 byutilizing tailed primers or LNA probes.
`
`
`
`One gains an ever-larger advantage from this approach when one uses four or morecolors.
`There are six combinations of twocolors if one has four to choose from. Together with
`single colors, this would give a total of ten reporters. If we go further and use triplets of
`colors we would end up with 13 reporters.
`
`Another important point is that the advantage of using this multi-color scheme becomes
`more pronouncedwith higher numbersof partitions. For that reason, this approachis of
`particular utility when combined with more recent implementations of digital PCR such as
`droplet digital PCR where thousandsor millions of partitions can be produced in an easy
`and cost effective manner.
`
`Several assay schemes can be employed to assess a target with multiple colors
`simultaneously. One could design a multi-labeled probe -i.e., a single probe can be labeled
`with FAM and VIC. Alternatively, in a TaqMan assay, two separate probes can be designed
`to bind to the same amplicon:
`
`\ FAM-------~-MGB VIC-------MGB
`
`Or, to increase signal-to-noise ratiothe probes can be put on opposite strands (to position
`the dyes away from the quenchersandfacilitate the fluorescence increase from the bound
`probes):
`
`This approachis general and can be used with a range of chemistries including: ligation
`chain reaction, molecular beacons, scorpion probes, molecular inversion probes.
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`2
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`Appendix A
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`
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`The following is an example of an algorithm that can be used to estimate concentrations of
`a joint FAM-VIC species.
`* Get 2x2 table of FAM versus VIC counts
`* Compute concentration of distinct FAM and joint FAM-VIC asif there are 1 species
`* Compute concentration of distinct VIC and joint FAM-VIC asif there are 1 species
`¢
`Try out different concentrationsof joint FAM-VIC (from which concentration of
`distinctFAM and distinct VIC can be found), and find the bestfit of the probability
`table with the observed counts:
`
`
`
`vic
`
`¥.
`(+f) (ev) (-c}
`
`Ftv) (-o)
`
`Below is an example of a matlab implementationofthe algorithm.
`
`Note that the algorithm can be expandedin a straightforward fashion to high order
`multiplexes.
`
`%. Consider three types of DNA fragments. Fam-Vic together,
`% Fam fragment, Vic fragment. We observe some probabilities (counts in
`% FAM-VIC cross plot), and goal is to infer the concentrations.
`
`% First let us do forward. Given concentrations, compute counts. Then to ds
`% inverse; we simply try <1 different values of concentrations and select
`% one which gives actual counts.
`
`20000:
`{O000;
`20600:
`B=10000: % Joined together
`
`NA BA
`
`CAB = ABIN;
`
`forintf(:, “Sof Sof %An’, CAB, cA, cB);
`
`pA = 4- exp(-cA);
`pB = -1- exp(-cB);
`pAB = 1
`- exp(-cAB);
`
`‘A is X and B is ¥ in cross plot
`
`p(2,1) = ( - pA) * (4 - pB)* Cl -pAB); % Bottom left
`p(2.2) = pA * (1 = pB) * (= pAB): % Bottom tight
`p(t,1) = G- pA) * pB* (1 -pAB); % Top Left
`p(1.2) = 1- p(2,1) - pC.2) - p(1,1); % Top Right
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`3
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`Appendix A
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`disp(round(p * N));
`
`% Also. compute marginals directly
`cAorAB = (A+ ABV/N; % = cA +cAB:
`cBorAB = (B+ AB)/N; % =cB +cAB;
`
`pAorAB = 1 - exp(-cAorAB); % Can be computed from p too
`pBorAB = 4:= exp(-cBorAB);
`
`% Inverse
`H='p* Nj-% We are given somehits
`
`oH = (68000;20000];
`
`% Compute prob
`estN:= sum(H()):
`ip = H/estN;
`ipAorAB =ip(t, 2) +bple; 2);
`L-pBorAB = ip(t) FEpc, 2);
`
`i: CAorAB = -log(7- i: pAorAB):
`i CBorAB = -log(}:- - pBorAB);
`
`maxVal =:min(icAorAB, i:cBorAB);
`delta = maxVal/iGQ0;
`
`errArr = [];
`gcABArr = [];
`
`JorgcAB = 0:delta:maxVal
`gcA =i: CAorAB = gcAB:
`gcB: =i: cBorAB = qeAB;
`
`- expCgcA),
`gpA = 1
`- exp(-gcB),
`gpB = 7
`gpAB = 4+: - exp-qcAB);
`
`gp@,t)=(1- gpA):*:(4-- gpB):*: (4 - gpAB); % Bottom left
`gp, 2) = gpA * (1 - gpB) * (= gpAB); % Bottom right
`apt, 1) = (1- apA)* opB * (4 - gpAB); % Top Left
`gp(i,2) = 4 - ap(2,4) - gp(2.2) - ap(t, 1); % Top Right
`
`gH = gp * estN;
`
`err = sart(sum((H(:) -gH(:)).42));
`
`errArr: = [errArr; err];
`gcABArr = [gcABArr: gcAB];
`
`end
`
`figure; plot(gcABArr; errArr);
`minidx = find(errArr == min(errArr(:)));
`minidx = minidx(?);
`estAB = gqcABArr(minidx);
`estA = 1 cAorAB - estAB:
`estB = 1 cBorAB-- estAB:
`forinti() ; Yef Yok Yofin’, estAB, estA; estB);
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`Appendix A
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`- exp-estA);
`gpA = 1
`gpB = 3- exp(-estB):
`gpAB = 7-- exp(-estAB);
`
`go(2; tt) = (= gpA)* (4 = gpB):* (= gpAB): % Bottom left
`gp@.2) = gpA * (b= 9gpB) *-(1- gpAB); % Bottom right
`gp(1, 1) = (1- gpA)* gpB * (4 - gpAB); % Top Left
`gp(,2)= 1 - gp,1) - gp(24.2) - gp(t, 1), % Top Right
`
`gH:= gp:*:estN:
`
`disp(round(gH));
`
`% Confirm the results using simulation
`
`numMolA = round(estA * estN):
`numMolB: = round(estB * estN):
`humMolAB = round(estAB * estN);
`
`A= unique(randsample(estN; numMolA;7);
`B= unique(randsample(estN, numMolB; ? ));
`AB = unique(randsample(estN, numMolAB, 74):
`
`U = trestN;
`notA = setdiff(U; A);
`notB = setdiff(U; B);
`notAB = setdiff(U; AB);
`AorBorAB =anies(A, usios(B; AB)):
`none = setdiff(U; AorBorAB);
`
`simcount(2,;1) = length(none);
`simcount(2 2) = length(intersect(A, intersect(notB,; notAB)));
`simcount(1;1):= lenqth(intersect(B; intersect(notA, notAB)));
`simcount(7;2) = length(AorBorAB):- simcount(Z;2) - simcount(t; 3);
`
`disp(simcount);
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`Appendix A
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