(419m) Optimal Design of Microfluidic Capillary Networks for Rapid Gel Free DNA Separation

10 to 100 times reductions in run time over the current state-of-the-art gel electrophoresis DNA length based separation are made possible through the mathematical optimization of a novel separation technique known as micelle end-labeled free solution electrophoresis (ELFSE). In gel electrophoresis the gel sieving matrix, necessary to make DNA velocity length dependent through friction, performs at typical lab speeds of 400 bases in 1 hour. The absence of a sieving matrix in aqueous solution will ensure that DNA of all lengths will migrate at the same velocity without another friction causing agent. In micelle ELFSE this friction is generated by a dilute low viscosity solution of micelles allowing for unique, superior trade-offs in operating conditions, like electric field strength, capillary length, and micelle size, necessary for large increases in throughput. These trade-offs depend on the separation platform. Capillary arrays and microfluidic devices are examined as candidates for the fastest separation mode.

Length based separation is achieved when DNA populations of different lengths migrate at different velocities. Small deviations in DNA population velocity cause ideal Dirac-delta signals to widen into Gaussian signals which can overlap and become unresolved. These small deviations in DNA velocity are due to micelle polydispersity, diffusion, and other mass transfer effects as described by a moment analysis which renders a model similar to the Van Deemter equation in chromatography to describe the Gaussian width. Micelle polydispersity is typically the largest signal widening effect which is reduced over time by time averaging through transient binding of the micelle to the end of alkylated DNA. Because of the necessity of DNA to sample different micelles over time, fast run times and high resolution are conflicting objectives that are difficult to mitigate without a rigorous optimization approach.

Non-linear programming techniques are utilized to solve the dual objective optimization problem. The model is non-convex and requires a global optimization code like BARON to generate the pareto front. BARON identifies standard form non-convexities to relax into a convex underestimate proceeding through a spatial branch and bound to reduce the gap between the convex underestimate with the non-convex local solution to finally converge to the global optimum. The model is written to expose these standard form non-convexities (bilinear, linear fractional, and concave univate terms) for fast convergence of BARON.

Typical lab scale separations are performed using either a capillary array in a bench top system or in a curved channel in a microfluidic device. Single capillary, parallel capillaries, serpentine microfluidics, and spiral microfluidics are examined; as well as finish-line versus full channel snap shot detection modes. Snap shot is the fastest detection mode possible as every population of DNA smaller than the length of read is guaranteed to be resolved in channel once the length of read is resolved, owning to the monotonic nature of the resolution. Electric field strength and channel length are found to be strong functions of the micelle polydispersity. A reduced parameter combination of the electric field, channel length, and micelle polydispersity is used to collapse the optimization results for different levels of polydispersity onto a single curve. Minimized run times are shown to have significant improvement over gel based separations. Specifically 27%, 74%, 84%, and 90% reduction in run time out to 400 bases over gel for single capillary, 2 parallel capillaries, serpentine microfluidics, and spiral microfludics respectively. Even more improvement may be realized through the use of an electro-osmotic counter flow to slow down fast moving, hardly resolved long DNA.

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