Figure 4 – a) Heat map of normalized sfGFP yield from BL21 DE3 Star cell extracts prepared at different volumes and total energies, with z-axis color bar presenting relative amounts of expression (replotted from (Kwon & Jewett, 2015)). Thick dashed lines depict temperatures (K) at these sonication conditions obtained by the finite element simulation. Thin solid lines indicate energy density values (J/mL). b) The same normalized yield data plotted in a more generalized fashion as power density vs. total energy; dashed lines again show temperatures estimated by simulation.
These modeled temperatures allow us to observe the effect of temperature on different yields. From the graph, it can be observed that the yield is > 90% relative yield in regions where temperature is below 305K; beyond 320K the yield reduces below 50% relative yield. Our finding that protein yield is influenced by temperature is well supported by cell free literature (Kigawa et al., 2004). We also observe from the Kwon data that increased energy at larger volume has little effect on yield; this is again attributed to temperature effect as we see from the model that the mixture reaches a steady state temperature below the 305K limit. Again, the steady state is reached when the heat added by sonication and removed by cooling is equal, which depends on rate of energy supplied, as we discuss next.
In the Kwon et al. study, a linear equation is presented that determines total energy needed based on sample volume to optimize protein yield, but this is only at a set specific amplitude and pulse on/off times. It makes intuitive sense that the yield is not only dependent on total energy supplied per volume (energy density), but also the rate at which energy is supplied per unit volume (power density and pulsing times). In the Kown et al. framework a certain amount of energy has to be given per volume for optimal lysing. However, the energy could be supplied slowly (less power density and short pulse on time) or quickly (more power density long pulse on time). Intuitively, if the energy is supplied too fast the temperature would rise above an undesired point, and the yield should fall. This power density effect can be studied with the heat transfer model. For example, the optimum energy for a 1000 μL sample according to the Kwon et al. equation is (1000-33.4) \(\times\)1.8-1 = 553 Joules. If this 553 Joules is supplied using 15 Watt power corresponding to 0.015 W/μL power density with 20 second on-off pulse, it would take only two bursts to supply the required energy and the total processing time required would be one minute; however, the final temperature would be above 340K and yield would suffer despite use of the optimal energy density.
Thus, to observe the role of power density more clearly, we transform the same data into another contour plot (Fig 4b). Here the y-axis is changed from volume to power density by dividing the tip input power at that liquid volume (empirically derived – Supplement figure 7) by the volume. The x and z-axis are kept the same as before (energy and yield, temperature values respectively). At these sonication conditions (50% amplitude and 10 s pulse settings) the relative yield is above 90% in the small window of power densities between 0.005 to 0.01 W/μL and 200 to 1000 J total energy. If the power density is more than 0.015 W/μL, the yield is low (<60%) regardless of energy input and the modeled temperature increases above 320K for total energies above 100 J. Another interesting observation from inspecting the data in terms of power density, is that at each power density the temperature rises to a steady state very quickly (horizontal isotherms). This means that at each sonication setting (under active cooling, ice bath) the steady state temperature can be determined by the finite element heat transfer model. In other words, the maximum temperature that can be reached in a sonication system can be tuned using the heat transfer model by altering power density and pulsing.