Origin of the Electrophoretic Force on DNA in a Nanopore

Transcription

1 Origin of the Electrophoretic Force on DNA in a Nanopore Stijn van Dorp 1 Ulrich F. Keyser 2, *Nynke H. Dekker 1, Cees Dekker 1, Serge G. Lemay 1 1 Kavli Institut of Nanoscience, Delft University of Technology, NL 2 Institut für Experimentelle Physik I, Universität Leipzig, D *Present Address: Cavendish Lab, University of Cambridge, UK

2 Outline Early experiments revisited (Nature Physics (2006)) Force on DNA in nanopores: numerical modeling and new experiments

3 DNA Tug of War Idea: put DNA in a nanopore and pull on it how cool is that? U. F. Keyser et al., Nature Physics (2006)

4 U. F. Keyser et al. Nature Physics 2, 473 (2006) First Measurements 40 Time (ms) 30 DNA in Pore Current (na) Position (µm) F = k ( Z 1 Z0) Controlled insertion of DNA strands one by one Exact number of DNA in the nanopore is known from ionic current measurement

5 Time-Resolved Events Conductance step indicates capture of DNA in nanopore Only when DNA is pulled taut the force changes Time to pull taut t is consistent with translocation of DNA

6 Force on DNA Linear force-voltage characteristic Force does not depend on distance nanopore-trap Extract the gradient and vary salt concentration

7 Salt Dependence of Force Slope (pn/mv) Nanopore diameter around ~6-10 nm KCl concentration (M) See e.g. Manning Q Rev Biophys 11, (1978), Laue et al. J.Pharm. Sci. 85, (1996), Long, Viovy, and Ajdari Biopolymers (1996), Keyser et al. Nature Physics 2, 473 (2006) Force is constant as ionic strength is varied From literature force is expected to decrease with increasing salt concentration Force/voltage conversion 0.23±0.02 pn/mv

8 Effective Charge Potential drops over nanopore Force on DNA F F q eff = ( q = ( q eff V = E( z) dz eff / a) E( z) dz / a) V effective charge/bp Slope effective charge Yes but

9 U. F. Keyser et al., Nature Physics 2, 473 (2006) What is missing here? The role of the nanopore (walls)...

10 Lots of Interest Recently Analytical calculations S. Ghosal Phys. Rev. E 74, (2006) Phys. Rev. E 76, (2007) Phys. Rev. Lett. 98, (2007) Molecular dynamics simulations A. Aksimentiev et al. Phys. Rev. E (2008) in press Talk yesterday

11 Vary Nanopore Diameter Task: increase nanopore diameter by at least a factor of ten

12 Increase Nanopore Diameter relative DNA area ~ 1:25 relative DNA area ~ 1: nm 80 nm DNA Detection of a single DNA molecule still possible? Yes should be at low salt concentration see Smeets PNAS (2008)

13 applied voltage (mv) DNA in a D=80 nm Nanopore current (na) time (s) Nanopore diameter ~80 nm Salt concentration M KCl current (na) data 20 point average time (s)

14 Force Measurements pn/mv 0.24 pn/mv 0.11 pn/mv 11 pn/mv 2in force (pn) 8 4 1in voltage (mv) Force on two DNA strands is doubled as expected DNA strands do not interact in large pores R > 15 nm

15 Change in Conductance G Nanopore diameter ~80 nm Salt concentration M KCl Usually 100 events are measured

16 Change in Conductance G Pore radius varied from 3 nm 45 nm Large pores: G is constant and lower Consistent with free translocation (open symbols )

17 Forces Dependence on Radius Force is proportional to voltage as expected For larger nanopore force is roughly halfed

18 Numerical Modeling Solve Poisson-Boltzmann equation numerically in 1D Electrostatic potential Φ and distribution of ions n ± : with as reduced potential Boundary conditions: insulating nanopore walls (uncharged) on DNA surface Simplification: access resistance is neglected

19 Potential Distribution Potential depends on radius of nanopore Calculated for bare charge of DNA 2e/bp In small nanopores a finite potential is observed despite boundary condition of zero charge

20 Co- and Counter-ion Distribution Counter-ions accumulate near DNA In small nanopores counter-ion cloud is compressed Co-ions are almost completely depleted In large nanopore almost bulk numbers

21 Flow Velocity We assume a no-slip boundary conditions Nanopore wall is uncharged Maximum flow velocity depends on distance between nanopore wall and DNA Drag force depends on nanopore radius F mech =-F elec =F bare -F drag depends on pore radius R

22 Relating Model to Experiments Combining Poisson Boltzmann and Stokes equation: Potential Φ(a) on DNA surface, Φ(R) Nanopore wall S. Ghosal PRE 76, (2007) Logarithmic dependence of F mech on nanopore radius explains slow variation with pore diameter

23 Nanopore Diameter Matters Force on DNA depends on pore diameter Change in pore diameter by factor 10 increases drag by a factor of two

24 Main Conclusion Potential on DNA surface and pore wall depend on pore radius R although DNA charge remains constant

25 Comparison: Model Data Force depends on nanopore radius R Our full PB model fits data when ion mobility is reduced

26 Summary Experimental prove that force on DNA depends on geometry of nanopore Hydrodynamic interactions have to be considered Numerical model qualitatively explains experiments For quantitative fitting mobility of counter ions have to be known MD simulations Aksimentiev et al.

27 1/f-Noise Sources in Nanopores Not only one origin of 1/f noise in nanopores Identified Nanobubbles (de-wetting) as ONE source of 1/f a -noise Smeets et al. PRL 2006 General Hooge relation for 1/f noise holds in nanopores Smeets et al. PNAS (2008) Sources of 1/f-noise see webpage with collection of papers

28 Funding Delft University of Technology FOM NWO DFG Emmy Noether Program Universität Leipzig