476 CHAPTER 10. GEL ELECTROPHORESIS 1. Field gradients and dsDNA gel electrophoresis. We consider gel electrophoresis of double-stranded DNA (dsDNA). One way to fit more DNA bands on a gel is to use a field gradient. Our sample has three DNA molecules with sizes M = 5 kbp, 40 kbp and 41 kbp. The gel is L = 24 cm long. At time t = 0, we load our mixed sample at a distance x = 1 cm from the end of the gel. We stop the experiment when the 5 kbp molecule reaches x5 = 23 cm to use most of the gel. At the same time, we want to optimize the distance between the two other DNA bands. The mobility of our molecules can be well described by the relation (kbp = kilo-basepair) 1 kbp M μ(M, E) = 3 × 10-4 cm² Х V sec (¹ (10.34) CHAPTER 10. GEL ELECTROPHORESIS We can neglect the effects of diffusion. V ст (a) If I use a uniform field intensity E = 5 how long is the separation and what are the final positions x40 and x41 of the two largest molecules? (b) I now use a non-uniform field given by E. for 0 < x < 4 cm and E(x) = E。 × [1 − (x-4)] for 10 cm x 24 cm. (10.35) (b1) What value of E, do I need to keep the same mean field intensity? (b2) Plot E(x) and describe what you expect in terms of electrophoresis. (b2) How much time will the 5 kbp molecule need to reach the final position x5 = 23 cm? (b3) What will be the final positions of the other two molecules? (b4) Did this non-uniform field increase the final separation x40 — x41? (c) We used eq 10.34: what gel electrophoresis regime is this? (d) Can you estimate the mean pore size given eqs 10.34, 10.1 and 10.11? 477 478 1 cm t=0 X41 X 40 CHAPTER 10. GEL ELECTROPHORESIS 24 cm direction of motion 1 cm X5 CHAPTER 10. GEL ELECTROPHORESIS 2. Electrophoretic regime of a large globular biomolecule A spherical molecule of radius R = 4 nm in an aqueous buffer (Debye length XD carries a charge Q = 3e. (a) Estimate its diffusion coefficient D. (b) Estimate its electrophoretic mobility µ. (c) Are you in the Hückel or Schmoluchowski limit? (d) Is the fluctuation-dissipation theorem satisfied? = 10 nm) 479