A. Identification of oligonucleotide interactions in on-chip experiments

As shown in Fig. 1S in the supplementary material, oligonucleotide interactions occurred in the LoC system when using all of the seven oligonucleotides for the SEPT9/ACTB duplex qPCR. Therefore, qPCR reactions were performed in which the SEPT9 oligonucleotides were omitted one by one, showing that with primers and the blocker as well as with the primers and the probe, amplicons for SEPT9 and ACTB were successfully amplified. This demonstrated that only the complete mix of all types of oligonucleotides was susceptible to oligonucleotide interactions. As all components are needed for adequate qPCR performance showing high sensitivities and specificities, further effort was undertaken to find a thermal profile that allows for the amplification of SEPT9 and ACTB without the formation of oligonucleotide interactions when using the SEPT9 blocker.

B. Model-based estimation of thermal protocols

In order to identify a suitable thermal protocol with little experimental iteration, a thermal network model of the Vivalytic cartridge has been constructed and implemented in the software package Mathematica.4343. W. R. Inc., “Mathematica, Version 12.3.1,” Champaign, IL, 2021. In principle, the physical processes associated with a shuttle qPCR would justify a sophisticated scale-resolved simulation model with coupled fluid flow and heat transfer (such as in Ref. 4444. A. Naghdloo, E. Ghazimirsaeed, and A. Shamloo, Sensors Actuat. B 283, 831 (2019). https://doi.org/10.1016/j.snb.2018.12.084). However, since the focus of the present work is on the variation of thermal protocols, the computational cost of applying a detailed model has been considered too high. Though this limitation could be overcome by reduced-order methods (see, for instance, Ref. 4545. Y. Wang, H. Song, and K. Pant, Microfluid. Nanofluid. 16, 369 (2014). https://doi.org/10.1007/s10404-013-1210-0), the effort to arrive at the simple, discrete model described below is significantly less than following the path of reduced-order modeling applied to a scale-resolved simulation model.The model used in the present study is instead based on a manually defined discretization of the cartridge material (see Fig. 2), each discrete cell of which is represented by a time-dependent temperature value. Using the discretization, the thermal network can be represented by a graph data structure. Therein, the nodes (vertices) of the graph represent thermal capacities of the form Ci=(cpϱV)i for each node i, where cp indicates the material’s thermal capacity, ϱ the material’s density, and V the volume of the discretization cell. The edges of the graph represent thermal resistances Rij (or, alternatively, thermal conductances Λij=Rij−1) between two temperature states i,j of the form Rij=lij/(λijAij), where (neglecting the indices) l denotes the distance between the two states, λij the (effective) thermal conductance of the material in between the two states, and Aij the cell-to-cell interface area between the two cells i and j. Balancing thermal energy (CiTi) for all states then leads to a system of ordinary first-order differential equations, which reads [C1⋯0⋮⋱⋮0⋯Cn][T1˙⋮Tn˙]=[−(Λ12+⋯+Λ1m)Λ12⋯Λ12−(Λ21+⋯+Λ2m)⋯⋮⋮⋱Λn1Λn2⋯⋯⋯Λ1m⋯⋯Λ2m⋯⋯⋮−(Λn1+⋯+Λnm)⋯Λnm][T1⋮Tm].(2)Equation (2) contains n differential equations for each of the temperature states, and a total of m temperature variables of which the last m−n denotes the heater (input) temperatures. Additionally, the relation Rij=Rji holds because of heat flux symmetry. Heat flux between cartridge material and ambient air is included with the model in the following way. For each discretization cell i in contact with ambient air (state 0), an effective thermal resistance Ri0=(αAi0)−1 between the constant ambient air temperature (T0=40°C) and the temperature Ti is computed using a constant heat transfer coefficient of α=6.2W/(m2K) (estimated based on correlations for free convection at a horizontal flat plate, cf. Ref. 4646. W. Kast, H. Klan, and R. B. A. Thess, “F2 heat transfer by free convection: External flows,” in VDI Heat Atlas (Springer, Berlin, 2010), pp. 667–672.).In principle, Eq. (2) can now be solved after specifying initial conditions for the temperature states and time-dependent heater temperatures. However, the above system does not yet account for the fluid plug shuttling. There are several options for including the plug motion. For the present work, the fluid temperature has been included as a temperature state with its thermal relations, i.e., those values Rij involving to the fluid, changing when the fluid plug is shifted between chambers, thus changing parts of the right-hand side of Eq. (2) dynamically and making some of the coefficients Rij effectively time-dependent. The simulation setup is based on the actual control parameters used in Vivalytic actuation profiles, which are then transferred to the computational form suitable for solving Eq. (2) numerically using Mathematica’s NDSOLVE function. Figure 3 depicts a typical input–output pair of actuations and thermal responses for the thermal model.In order to validate the thermal model and assess its accuracy in predicting thermal profiles, a number of comparisons with thermal measurements were conducted. The simulation has been designed to use the same set of parameters as the experimental protocol used with the Vivalytic system. An example validation is depicted in Fig. 4 where in the right-hand side plot, the experimental settings were imitated while the left-hand side plot visualizes the effect of removing the undershoot.Within this work, the focus lies on the optimization of the annealing step, as this step is especially relevant for oligonucleotide hybridization.4747. F. Lottspeich and J. W. Engels, Bioanalytics: Analytical Methods and Concepts in Biochemistry and Molecular Biology (John Wiley & Sons, 2018).,4848. C. Mulhardt, Molecular Biology and Genomics (Elsevier, 2010). For better performance, the annealing step was divided up into two phases. In the first one, a so-called undershoot was performed in order to obtain higher cooling rates by applying temperatures lower than the final annealing temperature. In the second phase, the final annealing temperature of 56 °C was set [cf. Fig. 3(a) and Table IV in the supplementary material)].Note that the input temperatures generally deviate from the temperature experienced by the fluid plug due to thermal conduction which is one of the reasons why a thermal model is useful. Thermal actuation profiles for qPCR reactions were deduced from the simulation results and verified by thermal measurements with thermocouples (Fig. 5) build into the PCR chambers of the Vivalytic cartridge. These so-called thermocartridges were connected to an National Instruments data acquisition card and processed by the Vivalytic Analyser running the different thermal profiles.

C. Selection of thermal programs

Several thermal programs (see Table V in the supplementary material) for qPCR performance were derived from simulation results and verified by thermal measurements using integrated thermocouples (Fig. 5). Figure 6 depicts measured time series of chamber temperatures resulting from different protocols. The recorded temperature curves were used to adapt a thermal cycler-based qPCR protocol for its application within the Vivalytic LoC platform. TP2 was selected due to its long holding times of temperatures between 60 and 56 °C and a better cooling rate as with TP1 and TP5. A even higher cooling rate was achieved with TP4. TP7 and TP8 showed high cooling rates as well as long holding times. Therefore, TP2, TP4, TP7, and TP8 have been verified with the SEPT9/ACTB duplex qPCR within the Vivalyic cartridge (Fig. 7).As shown in Fig. 7, ACTB was amplified successfully with every thermal profile that was applied. The DNA methylation marker SEPT9 was successfully amplified with the thermal profile TP4. Also, with TP8, in one of the replicates, a slight amplification could be observed as well.