Design of Bio-Chips from Theory and Multiscale Simulation

1. Design of Bio-Chips from Theoryand MultiscaleSimulation

3. Prominent Technologies DNA and Peptide/protein

4. DNA & Protein Microarraysare useful for a variety of tasks • Genetic analysis • Disease detection • Synthetic Biology • Computing

5. What tools are required? • $1000 Genome at birth • $100 Diagnostic exam • Proteome at birth? • Universal standards

6. Cross platform comparisons Controls Validation Data bases for comparisons Nearly impossible due differences in the physics and chemistry at the surface Problems in Surface Mounted technologies: Microarrays, Next-gen …

7. Binding (recognition) is different in the presence of a surface than in homogeneous solution. The surface determines: Polarization fields Ionic screening layers Ultimately: Device response A Central Theoretical Issue:

8. T - - G A - C - - - - C - - G G G T C - A A - T - - - Salt Water - - - - - - - - - - - - Targets - GC - TA - - - - - AT - - - - - 5nm - - - - CG - Probes - - - - - - - GC - - - - - AT - Prepared Hard Surface

9. Materials, Preparation and Size Matter • DNA prep 10nm 100nm 10 μm to bulk solid

10. What length scales are required? • Solid Substrate Roughness • Linkers • Surface Probes • Targets • Solution Correlations

11. Chemistry Na Cl .1 to .8 M Probe Target

12. Simulations and Theories of Bio Chips Set up must include • Substrate (Au, Si, SiO2 …) • Electrostatic fields • Surface modifications • Spacers (organic) • Probe and Target Bio (DNA or peptide) strands • Salt and lots of Water • Force field, … Wong & Pettitt CPL 326, 193 (2000) Wong & Pettitt TCA 106, 233 (2001) Wong & Pettitt Biopoly 73, 570 (2004) Pettitt, Vainrub, Wong NATO ASI (2005) Qamhieh, Wong Lynch Pettitt IJNAM (2009)

13. Simulate a simple classical force field Model the interactions between atoms • Bonds - 2 body term • harmonic, Hooke's law spring • Angles -3 body term • Dihedrals -4 body term Source: http://www.ch.embnet.org/MD_tutorial/

14. Nonbonded Terms • 2 body terms • van der Waals (short range) & Coulomb (long range) • Coulomb interaction consumes > 90% computing time Ewald Sum electrostatics to mimic condensed phase screening • Periodic Boundary Conditions Electrostatic Forces Dominate Behavior

15. F = ma or With a classical Molecular Mechanics potential, V(r) These potentials have only numerical solutions. t must be small, 10-15s

18. Correlations • Neither Vertical nor Flat on surface (tilt) • Nonuniform Structures • Linker/spacer effects Wong & Pettitt CPL 326, 193 (2000) Wong & Pettitt TCA 106, 233 (2001)

19. Implications • Colloidal behavior affects • synthesis / fabrication • and binding • Tilt restricts possible geometries of pairing • Affinity and specificity G & G

20. – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – ± ± ± ± ± ± ± ± ± ± Forces: Surface and Solution Water +[salt] ± ± Substrate ± ± ±

21. Theory Calculate the free energy difference of hybridization between that in solution and on a surface Gsol-hybrid -Gsur-hybrid= Gss-att-Gdup-att Gsol-hybrid Target + Probe Target : Probe Gdup-attach Gss-attach Gsur-hybrid Target :Probe:Surface Target + Probe:Surface

22. Theory To get the work to form a single duplex on the surface we need: • ΔGsolwhich we can take from thermodynamic tables: solution reference state (John Santa-Lucia). • ΔGatt from a consideration of the surface effects (chemistry and physics)

23. Coarse graining DNA electrostatic field(Poisson-Boltzmann) J. Ambia-Garrido Vainrub, Pettitt, Chem. Phys. Lett. 323 160 (2000) Ambia-Garrido, Pettitt, Comp Phys Com 3, 1117 (2008)

24. The ions and water penetrate the grooves. Na+ Cl- H2O Feig & Pettitt BJ 77, 1769 (1999)

26. A Simple Model • Ion permeable, 20 Å sphere over a plane/surface • 8 bp in aqueous saline solution over a surface • Linear Poisson-Boltzmann has an analytic solution h DNA - Vainrub and Pettitt, CPL ’00 Ellipse - Garrido and Pettitt, CPC, 08

27. The shift of the dissociation free energy or temperature for an immobilized 8 base pair oligonucleotide duplex at 0.01M NaCl as a function of the distance from a charged dielectric surface q=0 or  0.36e-/nm2 linker Vainrub and Pettitt, CPL ’00 Vainrub and Pettitt, Biopoly ’03

28. Surface at a constant potential for a metal coated substrate @ .01 M NaCl Vainrub and Pettitt, CPL ’00 Vainrub and Pettitt, Biopoly ’03

29. Response to E-fields Salt and Substrate Material Effects on 8-bp DNA Vainrub & Pettitt, Biopoly 2004

30. Finite Concentration and Coverage 2f = k2f outside the sphere and plane, 2f = k2f - (r/ee0) inside the sphere, f|r =a+ = f|r =a- , r f|r =a+ = rf|r =a- on the sphere, f|z =0+ = f|r =0- , z f|z =0+ - rf|z =0- = -s/ee0 on the plane. Different from O & K h Vainrub and Pettitt, Biopolymers 2003 Vainrub & Pettitt et al , NATO Sci , 2005

31. Coulomb Blockage Dominates Optimum DNA spacing Langmuir High negative charge density repels target surface binding On Chip Binding Target Conc hybridization efficiency θ (0 θ1) target concentration C0 Vainrub &Pettitt, PRE (2002) Vainrub &Pettitt, JACS (2003) Probe surface density

32. Experimental Isotherm for perfectly matched lengths Explains some experiments: • Low on-array hybridization efficiency on glass (Guo et al 1994, Shchepinov et al 1995) • Broadening and down-temperature shift of melting curve (Forman et al 1998, Lu et al 2002) • Surface probe density effects (Peterson et al 2001, Steel et al 1998, Watterson 2000)

33. Melting curve temperature and widthAnalytic wrt surface probe density (coverage) W+ DW W In solution Tm = DH0/ (DS0 – R ln C) W = 4RTm2/DH0 On-array: Isotherms *1012 nP probes/cm2 dA20 /dT20 duplex Tm - DTm Tm Critical for SNP detection design Pettitt et al NATO Sci 206, 381 (2005)

34. Strength and linearity of hybridization signal x1012 Vainrub and Pettitt JACS (2003); ibid Biopolymers, (2004)

35. Peak of sensitivity Vainrub and Pettitt, JACS (2003)

36. Linear range of hybridization Non-linear error is below Beyond the linear range use the on-array binding isotherm

38. Probe vs. Target lengths often mismatch in various ways . . . vs.

39. Longer sequences are the expected and require true mesoscale models Perfect pairing Pairing w/ an overhang Garrido Vainrub &Pettitt CPC ‘10

40. To Accommodate Longer Sequences and Secondary Structure Near a Surface

41. Mesoscale: Allow for variations inLinker chemistryOver-hangUnder-hangon probesand targetsin all combinations.Parameterize ssDNAas well as dsDNA. Garrido Vainrub &Pettitt JPCM submitted

42. DNA Entropic contributions • Sample with Monte-Carlo • via Meirovitch (hypothetical scan) • via Quasi Harmonic • Correlations of sequence mismatch with physical corrections • Data mining for equilibrium thermodynamics

43. ΔG

44. ΔG

45. Information vs efficiency • ssDNA has the same spatial average as dsDNA but not fluctuations. • Longer strands have more information 4n. • Kinetic problem • Shorter strands pair more efficiently. • Kinetic balance

46. High Salt is Far Beyond Analytic PB (Mean Field) Electrostatics Gouy-Chapman ~1910 Double layer at charged interfaces. How good is this? Add all the atoms via integral equations in 3D (renorm.- HNC)

47. Solvent and ion charge densities MF-PB HNC-IE H2O ε=80 w/ Ions

48. Charge-Charge correlations • Multi Layer effects not Bilayer • Dominate at interfaces • Determine the thermodynamics • Change the kinetics

49. To design for Affinity and Specificity Coverage and Surface effects • Use Electric fields • Effects of DNA with poly cations • Use surface effects • Layered hard materials • Use quantitative theories • Explicit polymer entropy • Non m.f. coverage and electrostatics