I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. EXPERIMENTAL METHODSIII. RESULTSIV. DISCUSSIONV. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCESMicrofluidics has played a pivotal role in illuminating the polymer physics of DNA molecules in flow,11. L. Rems, D. Kawale, L. J. Lee, and P. E. Boukany, “Flow of DNA in micro/nanofluidics: From fundamentals to applications,” Biomicrofluidics 10, 043403 (2016). https://doi.org/10.1063/1.4958719 including the dynamics of tethered polymers,2–42. T. T. Perkins, D. E. Smith, R. G. Larson, and S. Chu, “Stretching of a single tethered polymer in a uniform flow,” Science 268, 83–87 (1995). https://doi.org/10.1126/science.77013453. P. S. Doyle, B. Ladoux, and J. L. Viovy, “Dynamics of a tethered polymer in shear flow,” Phys. Rev. Lett. 84, 4769–4772 (2000). https://doi.org/10.1103/PhysRevLett.84.47694. C. M. Schroeder, R. E. Teixeira, E. S. Shaqfeh, and S. Chu, “Characteristic periodic motion of polymers in shear flow,” Phys. Rev. Lett. 95, 018301 (2005). https://doi.org/10.1103/PhysRevLett.95.018301 the coil–stretch transition,55. T. T. Perkins, D. E. Smith, and S. Chu, “Single polymer dynamics in an elongational flow,” Science 276, 2016–2021 (1997). https://doi.org/10.1126/science.276.5321.2016,66. C. M. Schroeder, H. P. Babcock, E. S. G. Shaqfeh, and S. Chu, “Observation of polymer conformation hysteresis in extensional flow,” Science 301, 1515–1519 (2003). https://doi.org/10.1126/science.1086070 elongation of DNA for flow-based mapping,77. E. Y. Chan, N. M. Goncalves, R. A. Haeusler, A. J. Hatch, J. W. Larson, A. M. Maletta, G. R. Yantz, E. D. Carstea, M. Fuchs, G. G. Wong, S. R. Gullans, and R. Gilmanshin, “DNA mapping using microfluidic stretching and single-molecule detection of fluorescent site-specific tags,” Genome Res. 14, 1137–1146 (2004). https://doi.org/10.1101/gr.1635204,88. J. W. Griffis, E. Protozanova, D. B. Cameron, and R. H. Meltzer, “High-throughput genome scanning in constant tension fluidic funnels,” Lab Chip 13, 240–51 (2013). https://doi.org/10.1039/c2lc40943g and other fundamental questions.99. D. J. Mai, C. Brockman, and C. M. Schroeder, “Microfluidic systems for singe DNA dynamics,” Soft Matter 8, 10560–10572 (2012). https://doi.org/10.1039/c2sm26036k The appeal of DNA for studying the dynamics of polymers in flow is threefold. First, owing to its biological origin, DNA is available as a monodisperse system, which greatly simplifies data analysis when compared to polydisperse samples produced by conventional polymer synthesis. Second, bright dyes such as YOYO1010. H. S. Rye, S. Yue, D. E. Wemmer, M. A. Quesada, R. P. Haugland, R. A. Mathies, and A. N. Giazer, “Stable fluorescent complexes of double-stranded DNA with bis-intercalating asymmetric cyanine dyes: Properties and applications,” Nucleic Acids Res. 20, 2803–2812 (1992). https://doi.org/10.1093/nar/20.11.2803 allow visualizing single DNA molecules with readily available microscopy equipment on time scales well suited to videomicroscopy frame rates. Third, the length scales of DNA are commensurate with microfluidic technologies, with typical radii of gyration ranging from hundreds of nanometers to several micrometers.1111. D. E. Smith, T. T. Perkins, and S. Chu, “Dynamical scaling of DNA diffusion coefficients,” Macromolecules 29, 1372–1373 (1996). https://doi.org/10.1021/ma951455p Taken together, these properties make DNA an attractive model system for studying the properties of polymers in the complex flow fields available in microfluidic devices.One important challenge in using long DNA as a model polymer is that it is relatively easy to break the molecule in flow. Indeed, even the shear produced by pipetting1212. H. R. Reese and B. H. Zimm, “Fracture of polymer chains in extensional flow: Experiments with DNA, and a molecular-dynamics simulation,” J. Chem. Phys. 92, 2650–2662 (1990). https://doi.org/10.1063/1.457960,1313. T. T. Perkins, S. R. Quake, D. E. Smith, and S. Chu, “Relaxation of a single DNA molecule observed by optical microscopy,” Science 264, 822–826 (1994). https://doi.org/10.1126/science.8171336 is sufficient to fragment long DNA, and it has been known for decades that manipulating very long molecules (e.g., megabase pair DNA) requires protecting the DNA, either in an agarose plug1414. D. C. Schwartz and C. R. Cantor, “Separation of yeast chromosome-sized DNAs by pulsed field gradient gel electrophoresis,” Cell 37, 67–75 (1984). https://doi.org/10.1016/0092-8674(84)90301-5 or converting it to a condensed form.1515. R. T. Kovacic, L. Comai, and A. J. Bendich, “Protection of megabase DNA from shearing,” Nucleic Acids Res. 23, 3999–4000 (1995). https://doi.org/10.1093/nar/23.19.3999 Unfortunately, these protection methods cannot be used for studying DNA in flow. For single-molecule studies, fragmentation of the DNA lowers the throughput, which is a frustrating but solvable problem. In contrast, breaking long DNA in flow becomes a severe issue if one wants to achieve the long-read lengths possible from nanopore sequencing1616. M. Jain, S. Koren, J. Quick, A. C. Rand, T. A. Sasani, J. R. Tyson, A. D. Beggs, A. T. Dilthey, I. T. Fiddes, S. Malla, H. Marriott, K. H. Miga, T. Nieto, J. O’Grady, H. E. Olsen, B. S. Pedersen, A. Rhie, H. Richardson, A. Quinlan, T. P. Snutch, L. Tee, B. Paten, A. M. Phillippy, J. T. Simpson, N. J. Loman, and M. Loose, “Nanopore sequencing and assembly of a human genome with ultra-long reads,” Nat. Biotechnol. 36, 338–345 (2018). https://doi.org/10.1038/nbt.4060 that were ultimately critical to producing a full human genome sequence.1717. S. Nurk, S. Koren, A. Rhie, M. Rautiainen, A. V. Bzikadze, A. Mikheenko, M. R. Vollger, N. Altemose, L. Uralsky, A. Gershman, S. Aganezov, S. J. Hoyt, M. Diekhans, G. A. Logsdon, M. Alonge, S. E. Antonarakis, M. Borchers, G. G. Bouffard, S. Y. Brooks, G. V. Caldas, N.-C. Chen, H. Cheng, C.-S. Chin, W. Chow, L. G. de Lima, P. C. Dishuck, R. Durbin, T. Dvorkina, I. T. Fiddes, G. Formenti, R. S. Fulton, A. Fungtammasan, E. Garrison, P. G. S. Grady, T. A. Graves-Lindsay, I. M. Hall, N. F. Hansen, G. A. Hartley, M. Haukness, K. Howe, M. W. Hunkapiller, C. Jain, M. Jain, E. D. Jarvis, P. Kerpedjiev, M. Kirsche, M. Kolmogorov, J. Korlach, M. Kremitzki, H. Li, V. V. Maduro, T. Marschall, A. M. McCartney, J. McDaniel, D. E. Miller, J. C. Mullikin, E. W. Myers, N. D. Olson, B. Paten, P. Peluso, P. A. Pevzner, D. Porubsky, T. Potapova, E. I. Rogaev, J. A. Rosenfeld, S. L. Salzberg, V. A. Schneider, F. J. Sedlazeck, K. Shafin, C. J. Shew, A. Shumate, Y. Sims, A. F. A. Smit, D. C. Soto, I. Sović, J. M. Storer, A. Streets, B. A. Sullivan, F. Thibaud-Nissen, J. Torrance, J. Wagner, B. P. Walenz, A. Wenger, J. M. D. Wood, C. Xiao, S. M. Yan, A. C. Young, S. Zarate, U. Surti, R. C. McCoy, M. Y. Dennis, I. A. Alexandrov, J. L. Gerton, R. J. O’Neill, W. Timp, J. M. Zook, M. C. Schatz, E. E. Eichler, K. H. Miga, and A. M. Phillippy, “The complete sequence of a human genome,” Science 376, 44–53 (2022). https://doi.org/10.1126/science.abj6987 The fragility of DNA naturally sets an upper bound for the flow phenomena that can be probed using DNA as a model polymer.The breakage of DNA in flow has been a subject of study since the discovery of DNA as the genomic carrier of information. Research dating back to the sizing of bacteriophage DNA in the 1960s indicates that (i) shear flows created by high-speed stirring tend to cut DNA close to the midpoint;1818. A. D. Hershey and E. Burgi, “Molecular homogeneity of the deoxyribonucleic acid of phage T2,” J. Mol. Biol. 2, 143–152 (1960). https://doi.org/10.1016/S0022-2836(60)80016-2,1919. E. Burgi and A. D. Hershey, “A relative molecular weight series derived from the nucleic acid of bacteriophage T2,” J. Mol. Biol. 3, 458–472 (1961). https://doi.org/10.1016/S0022-2836(61)80058-2 (ii) there is a critical shear rate for cutting DNA of a given molecular weight;1919. E. Burgi and A. D. Hershey, “A relative molecular weight series derived from the nucleic acid of bacteriophage T2,” J. Mol. Biol. 3, 458–472 (1961). https://doi.org/10.1016/S0022-2836(61)80058-2,2020. L. F. Cavalieri and B. H. Rosenberg, “Shear degradation of deoxyribonucleic acid,” J. Am. Chem. Soc. 81, 5136–5139 (1959). https://doi.org/10.1021/ja01528a029 and (iii) the probability of cutting the dsDNA is a function of the shear rate, not the shear stress.2121. R. D. Bowman and N. Davidson, “Hydrodynamic shear breakage of DNA,” Biopolymers 11, 2601–2624 (1972). https://doi.org/10.1002/bip.1972.360111217 These classic results suggest a hypothesis that, at a given shear rate γ˙, only DNA sizes M>M∗ tend to be cut, and they are cut approximately in half. However, given the precision of the tools available at the time of those experiments,18–2018. A. D. Hershey and E. Burgi, “Molecular homogeneity of the deoxyribonucleic acid of phage T2,” J. Mol. Biol. 2, 143–152 (1960). https://doi.org/10.1016/S0022-2836(60)80016-220. L. F. Cavalieri and B. H. Rosenberg, “Shear degradation of deoxyribonucleic acid,” J. Am. Chem. Soc. 81, 5136–5139 (1959). https://doi.org/10.1021/ja01528a02919. E. Burgi and A. D. Hershey, “A relative molecular weight series derived from the nucleic acid of bacteriophage T2,” J. Mol. Biol. 3, 458–472 (1961). https://doi.org/10.1016/S0022-2836(61)80058-2 the evidence to support such a model of midpoint scission in shear flow is not conclusive, and subsequent experiments in the ensuing 30 years have called this simple model into question. Most notably, experiments on DNA fragmentation in a sink flow1212. H. R. Reese and B. H. Zimm, “Fracture of polymer chains in extensional flow: Experiments with DNA, and a molecular-dynamics simulation,” J. Chem. Phys. 92, 2650–2662 (1990). https://doi.org/10.1063/1.457960 produced relatively wide molecular weight distributions that are inconsistent with the latter model. Such wide distributions could emerge from the complexity of the flow field. However, they can also arise from molecular individualism, wherein the dynamics of individual molecules in flow are highly heterogeneous despite all molecules being exposed to the same flow field.5–225. T. T. Perkins, D. E. Smith, and S. Chu, “Single polymer dynamics in an elongational flow,” Science 276, 2016–2021 (1997). https://doi.org/10.1126/science.276.5321.201622. P. G. de Gennes, “Molecular individualism,” Science 276, 1999–2000 (1997). https://doi.org/10.1126/science.276.5321.1999 In either case, the absence of midpoint scission in these later experiments1212. H. R. Reese and B. H. Zimm, “Fracture of polymer chains in extensional flow: Experiments with DNA, and a molecular-dynamics simulation,” J. Chem. Phys. 92, 2650–2662 (1990). https://doi.org/10.1063/1.457960 motivates us to revisit the problem of DNA fragmentation in shear using modern rheological and characterization methods.In the present paper, we examine DNA breakage using the simplest possible flow field: steady shear. We posit that understanding the physics of DNA breakage in this model flow is essential to modeling similar processes in the more complicated flow field possible in microfluidic devices. Indeed, theory2323. P. G. De Gennes, “Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients,” J. Chem. Phys. 5030, 5030–5042 (1974). https://doi.org/10.1063/1.1681018,2424. J. A. Odell, A. J. Muller, K. A. Narh, and A. Keller, “Degradation of polymer solutions in extensional flows,” Macromolecules 23, 3092–3103 (1990). https://doi.org/10.1021/ma00214a011 and single-molecule experiments2525. D. E. Smith, H. P. Babcock, and S. Chu, “Single-polymer dynamics in steady shear flow,” Science 283, 1724–1727 (1999). https://doi.org/10.1126/science.283.5408.1724 suggest that the coil–stretch transition driving strong chain extension,23–2623. P. G. De Gennes, “Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients,” J. Chem. Phys. 5030, 5030–5042 (1974). https://doi.org/10.1063/1.168101826. R. G. Larson and J. J. Magda, “Coil-stretch transitions in mixed shear and extensional flows of dilute polymer solutions,” Macromolecules 22, 3004–3010 (1989). https://doi.org/10.1021/ma00197a022 and ultimately chain scission, is less effective in shear flow than in the stagnation-point extensional flows that tend to produce midpoint scission.24–3027. A. Keller and J. A. Odell, “The extensibility of macromolecules in solution; A new focus for macromolecular science,” Colloid Polym. Sci. 263, 181–201 (1985). https://doi.org/10.1007/BF0141550628. J. A. Odell and A. Keller, “Flow-induced chain fracture of isolated linear macromolecules in solution,” J. Polym. Sci., Part B: Polym. Phys. 24, 1889–1916 (1986). https://doi.org/10.1002/polb.1986.09024090124. J. A. Odell, A. J. Muller, K. A. Narh, and A. Keller, “Degradation of polymer solutions in extensional flows,” Macromolecules 23, 3092–3103 (1990). https://doi.org/10.1021/ma00214a01129. T. Atkins and T. Avenue, “Elongational flow studies on DNA in aqueous solution and stress-induced scission of the double helix,” Biopolymers 32, 911–923 (1992). https://doi.org/10.1002/bip.36032080330. J. A. Odell and M. A. Taylor, “Dynamics and thermomechanical stability of DNA in solution,” Biopolymers 34, 1483–1493 (1994). https://doi.org/10.1002/bip.360341106 Moreover, recent microfluidic work on DNA scission in flow has largely focused on the design of funnel-based systems that produce complex flow fields with a mixture of shear and extensional components.31–3531. L. Shui, J. G. Bomer, M. Jin, E. T. Carlen, and A. Van Den Berg, “Microfluidic DNA fragmentation for on-chip genomic analysis,” Nanotechnology 22, 494013 (2011). https://doi.org/10.1088/0957-4484/22/49/49401332. I. V. Nesterova, M. L. Hupert, M. A. Witek, and S. A. Soper, “Hydrodynamic shearing of DNA in a polymeric microfluidic device,” Lab Chip 12, 1044–1047 (2012). https://doi.org/10.1039/c2lc21122j33. L. Shui, W. Sparreboom, P. Spang, T. Roeser, B. Nieto, F. Guasch, A. H. Corbera, A. Van Den Berg, and E. T. Carlen, “High yield DNA fragmentation using cyclical hydrodynamic shearing,” RSC Adv. 3, 13115–13118 (2013). https://doi.org/10.1039/c3ra42505c34. S. Garrepally, S. Jouenne, P. D. Olmsted, and F. Lequeux, “Scission of flexible polymers in contraction flow: Predicting the effects of multiple passages,” J. Rheol. 64, 601–614 (2020). https://doi.org/10.1122/1.512780135. S. Wu, T. Fu, R. Qiu, and L. Xu, “DNA fragmentation in complicated flow fields created by micro-funnel shapes,” Soft Matter 17, 9047–9056 (2021). https://doi.org/10.1039/d1sm00984b Engineering such devices first requires a basic model for the breakage of DNA in a simpler flow field, which has not been realized to date.

II. EXPERIMENTAL METHODS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. EXPERIMENTAL METHODS <<III. RESULTSIV. DISCUSSIONV. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCES

A. DNA preparation

The T4 GT7 DNA molecules [166 kilobase pairs (kbp), Nippon Gene] used in the DNA shear experiments were reacted with T4 ligase to repair any potential nicks along the DNA chains. The loading solution with a DNA concentration of ∼10 mg/L and 0.5× TBE buffer was prepared by first mixing 7.9 μL of the stock T4 GT7 DNA molecules from the vendor (∼760 mg/L) with 60  μL of T4 DNA ligase reaction buffer (10×, New England Biolabs), 30μL of 10× Tris base-Boric acid-Ethylenediaminetetraacetic acid (EDTA) (TBE) buffer, 0.6 μL of T4 ligase enzyme (New England Biolabs), and 501.5 μL of water (Millipore Direct-Q3, 18.2 MΩ⋅cm at 25 °C). The mixed solution was incubated at 37 °C for 2 h to perform the ligation reaction and was then heated to 65 °C for 20 min to inactivate the T4 ligase enzyme. The resulting solutions were ready to be loaded in the rheometer for the DNA shear experiments.

B. DNA shear experiments

A commercial rotational rheometer in a cone–plate geometry (DHR, TA Instruments) was used to produce a uniform shear rate for the DNA fragmentation experiments. The bottom Peltier plate was fixed and maintained the temperature of the DNA solutions at 20 °C. A rotating steel cone (40 mm diameter, 2° angle) was then equipped with a truncation gap of 50 μm. A solvent trap was applied to provide saturated water vapor and prevent solvent evaporation. To perform the DNA shear experiments, we gradually increased the shear rate from 0s−1 to the desired shear rate (1000, 3000, 5000, or 6000s−1) in less than 6 s and then maintained that shear rate for the desired time (1, 30, 60, or 120 min). Afterward, the samples were collected using pipet, with a recovery rate of around 90%, for subsequent pulsed-field gel electrophoresis (PFGE) experiments to measure the DNA molecular weight distribution. To control for the breakage of the T4 GT7 DNA molecules from pipetting, we also loaded and unloaded the original T4 GT7 DNA solutions without running the shear experiments.

C. Pulsed-field gel electrophoresis

Pulsed-field gel electrophoresis (PFGE) is a standard method for sizing long DNA and was used in previous experiments1212. H. R. Reese and B. H. Zimm, “Fracture of polymer chains in extensional flow: Experiments with DNA, and a molecular-dynamics simulation,” J. Chem. Phys. 92, 2650–2662 (1990). https://doi.org/10.1063/1.457960,2929. T. Atkins and T. Avenue, “Elongational flow studies on DNA in aqueous solution and stress-induced scission of the double helix,” Biopolymers 32, 911–923 (1992). https://doi.org/10.1002/bip.360320803,3030. J. A. Odell and M. A. Taylor, “Dynamics and thermomechanical stability of DNA in solution,” Biopolymers 34, 1483–1493 (1994). https://doi.org/10.1002/bip.360341106 on DNA fragmentation in flow. The collected DNA samples from the DNA shear experiments were first evaporated to a concentration of ∼50 mg/L prior to running the PFGE. The concentrated DNA solutions were then mixed with a gel loading dye (6×, New England Biolabs). The MidRange PFG markers (New England Biolabs) were used as the molecular weight standards for the PFGE experiments. The dyed DNA samples and the markers were loaded into agarose gels (pulsed-field certified, BioRad) prepared with 0.5× TBE buffer solution and 1% w/v agarose. The experiments were performed using a PFGE system (CHEF-DR II, BioRad) at 14 °C with a 6 V/cm electric field, 5.0 s of initial switching time, 15.0 s of final switching time, and 20 h of total run time. After running the PFGE experiments, the agarose gels were stained with a 0.5 μg/mL ethidium bromide solution (Invitrogen, Thermo Fisher Scientific), illuminated by a UV transilluminator (UVP), and then imaged by a digital camera (Canon PC1250). An example of a PFGE image is shown in Fig. 1.

D. Data processing

The PFGE images were processed by first rotating the image so that the two midrange PFG markers were aligned. The rotated image was then analyzed using a custom-written MATLAB program following the method described in Ref. 3636. K. Bomsztyk, D. Mar, Y. Wang, O. Denisenko, C. Ware, C. D. Frazar, A. Blattler, A. D. Maxwell, M. B. MacConaghy, and T. J. Matula, “PIXUL-ChIP: Integrated high-throughput sample preparation and analytical platform for epigenetic studies,” Nucleic Acids Res. 47, e69 (2019). https://doi.org/10.1093/nar/gkz222 to output normalized intensity profiles of each lane. An example of a normalized intensity profile for the control experiment in Lane 2 of the PFGE image (Fig. 1) is shown in Fig. 2(a). Since the intensity of stained DNA is proportional to the number of base pairs, the gel images correspond to the weight fraction wi of molecules with degree of polymerization (or size) Mi, where Mi was obtained through an interpolation of a calibration curve from the markers. The number fraction (xi) of molecules with size of Mi was then calculated as xi=wi/Mi to generate the distribution in Fig. 2(b). The number-averaged molecular weight, Mn, and the weight-averaged molecular weight, Mw, in a given experiment were computed as the averages of distributions of the type in Fig. 2. To provide a facile connection to the PFGE data, we will report Mn and Mw without the conversion factor of 650 g per mole of base pairs, i.e., as number-averaged and weight-averaged degrees of polymerization.The distribution for wi also was used to compute the percentage of broken DNA molecules in each lane. Since the data are somewhat noisy and contain two distributions (broken and unbroken DNA), we analyzed them using the following approach. First, the distribution for wi was transformed using a Box–Cox transformation with a constant exponent value λ=0.01; the Box–Cox transformation is a standard method to convert non-Gaussian distributions into approximately Gaussian ones.3636. K. Bomsztyk, D. Mar, Y. Wang, O. Denisenko, C. Ware, C. D. Frazar, A. Blattler, A. D. Maxwell, M. B. MacConaghy, and T. J. Matula, “PIXUL-ChIP: Integrated high-throughput sample preparation and analytical platform for epigenetic studies,” Nucleic Acids Res. 47, e69 (2019). https://doi.org/10.1093/nar/gkz222 Afterward, the transformed curves under the broken region, defined as the range of sizes between 15 and 165 kbp, and the unbroken region, defined for sizes between 165 and 209 kbp, were fitted separately using Gaussian functions. This cutoff to determine broken vs unbroken DNA was based on the band-broadening that we see for the primary band in the T4 control lane of Fig. 1. Figure 3 provides an example of a transformed weight-fraction distribution and its Gaussian fits. This approach proved to be a robust method for fitting the data across all of our experiments.To calculate the percentage of broken DNA molecules, the Gaussian fits for the transformed size were converted back to the original molecule sizes, Mi. Then, the percentage of broken DNA molecules (B%), which is the ratio of number of broken molecules to the total number of molecules in each lane, was calculated as B%=∫15165MiwfidMi∫15165MiwfidMi+∫165209MiwfidMi,(1)where wfi is the fitted weight fractions obtained from the Gaussian functions (i.e., the two fitting curves in Fig. 3).

III. RESULTS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. EXPERIMENTAL METHODSIII. RESULTS <<IV. DISCUSSIONV. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCESOur first objective is to determine whether it is even possible to fragment DNA in a steady shear flow. The theory for the coil–stretch transition2323. P. G. De Gennes, “Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients,” J. Chem. Phys. 5030, 5030–5042 (1974). https://doi.org/10.1063/1.1681018 suggests that this transition is marginal for the Couette flow, and this prediction was supported by single-molecule experimental data.2525. D. E. Smith, H. P. Babcock, and S. Chu, “Single-polymer dynamics in steady shear flow,” Science 283, 1724–1727 (1999). https://doi.org/10.1126/science.283.5408.1724 We thus probed the molecular weight distributions produced by 1 h of shearing at shear rates of γ˙=1000, 3000, 5000, and 6000s−1. To control for the DNA fragmentation due to the transfer of DNA into and out of the rheometer, as well as the post-processing of the DNA prior to PFGE, we also performed a control experiment where the DNA was loaded into the rheometer but not sheared.Figure 4 demonstrates that DNA can be significantly fragmented in a steady shear. The control experiment [Fig. 4(a)] shows a strong primary peak at the expected T4 molecular weight of 166 kbp. The breadth of that peak is indicative of the size resolution that we can obtain from PFGE. In the absence of shear, there is a faint band in the gel, corresponding to the plateau in wi (black circles) from 40 to 160 kbp, which we attribute to DNA processing. As indicated in the supplementary material, pipetting the original sample multiple times does not produce any fragmentation, and the original sample has a bright band at the expected location of 166 kbp (to within the resolution of PFGE). We suspect that the breakage observed in the control experiments arises from extensional flow created during the sample loading and unloading of the rheometer, but additional work would be required to confirm this hypothesis. The detailed mechanism of DNA breakage in the control experiment is tangential to the main focus of our manuscript, and our control experiment is a proper approach to control for the effect shearing the DNA by the rotation of the cone. As such, our discussion of the mechanism of DNA scission in flow will focus on how the primary band at 166 kbp is affected by the flow parameters, keeping in mind that some of the changes in the molecular weight distribution arise from DNA processing independent of those parameters. In particular, we want to assess whether the peak centered at 166 kbp in the control experiment, which represents those DNA that are not broken during processing in the absence of shear, is converted to a new peak at 83 kbp via midpoint scission.The peak in the number-fraction distribution xi around 40 kbp in Fig. 4(a) emerges from that plateau in wi because many small molecules are required to create a fluorescence signal of the same intensity as a few large molecules. The contrast between the control experiment in Fig. 4(a) and the data for γ˙=6000s−1 in Fig. 4(b) is stark; there is a clear loss of the primary peak at 166 kbp for γ˙=6000s−1 and a broad distribution in wi.Additional data for the lower shear rates, along with the PFGE gel image used for the data analysis, are provided in the supplementary material. The key results are summarized in Fig. 4(c), which compares the weight-averaged molecular weight Mw, the number-averaged molecular weight Mn, and the polydispersity index (PDI = Mw/Mn) for each shear rate and the control experiment, while Fig. 4(d) provides the percentage of broken molecules. At shear rates of γ˙=1000−3000s−1, there is no appreciable difference between the sheared samples and the control, and we suspect that the minimum in B% at 3000s−1 is a statistical fluctuation. Inasmuch as our focus is on cases where essentially all molecules are broken, we chose to fix the shear rate at γ˙=6000s−1 for the subsequent experiments.We then proceeded to determine the time required to fragment the DNA at a shear rate of γ˙=6000s−1, using times of 0 (control), 1, 30, 60, and 120 min. The corresponding data for the control and 60 min, which appear in the supplementary material (Figs. S3 and S4) alongside the data for 120 min, serve as replicates for the data presented in Fig. 4; the results are qualitatively the same when comparing the replicates for the controls to one another, and similar qualitative agreement is seen when comparing the replicates for 60 min of shearing to one another. For 1 min of shearing [Fig. 5(a)], the resulting molecular weight distribution is very similar to the control experiment in Fig. 4(a), as well as the additional control experiment appearing in Fig. S4(a) in the supplementary material. Once we reach 30 min of shearing at γ˙=6000s−1 in Fig. 5(b), the molecular weight distribution appears similar to the data for 60 min in Fig. 4(b) and the data for 120 min in Fig. S4(d) in the supplementary material. The resulting number-averaged and weight-averaged molecular weights [Fig. 5(c)] and percentage of sheared molecules [Fig. 5(d)] indicate that there is no significant difference between the data after a threshold of 30 min is achieved, while 1 min of shearing has no noticeable impact on the sample when compared to the control.To assess the reproducibility of the data, we also performed a set of five additional replicates at γ˙=6000s−1 for 1 h, as well as a third control experiment. The PFGE data, along with the distributions for xi and