Design
of Bio-Chips from
Theory
and Multiscale
Simulation
Prominent Technologies
DNA and Peptide/protein
DNA & Protein Microarrays
are useful for a variety of tasks
• Genetic analysis
• Disease detection
• Synthetic Biology
• Computing
What tools are required?
• $1000 Genome at birth
• $100 Diagnostic exam
• Proteome at birth?
• Universal standards
Problems in Surface Mounted
technologies: Microarrays, Next-gen
…
Cross platform comparisons
• Controls
• Validation
• Data bases for comparisons
Nearly impossible due differences in the
physics and chemistry at the surface
A Central Theoretical
Issue:
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
Salt Water
TG
A
C C
G G G -T
C
A
TA
5nm
-
-
- --
---
-GC
-TAAT
- CG
-GC
AT
Targets
- - - --
Prepared Hard Surface
Probes
Materials, Preparation
and Size Matter
• DNA prep
10nm
100nm
10 μm to bulk solid
What length scales are
required?
• Solid Substrate Roughness
• Linkers
• Surface Probes
• Targets
• Solution Correlations
Chemistry
Na Cl .1 to .8 M
Probe
Target
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
Wong & Pettitt CPL 326, 193 (2000)
Wong & Pettitt TCA 106, 233 (2001)
Force field, …
Wong & Pettitt Biopoly 73, 570 (2004)
Pettitt, Vainrub, Wong NATO ASI (2005)
Qamhieh, Wong Lynch Pettitt IJNAM (2009)
Simulate a simple classical force field
Model the interactions between atoms
• Bonds - 2 body term
– harmonic, Hooke's law spring
2
K
(
r

r
)
 b e
bonds
• Angles - 3 body term
2
K
(



)
 
e
angles
• Dihedrals - 4 body term
 K 1  cos(n   )
torsions
Source: http://www.ch.embnet.org/MD_tutorial/
Nonbonded Terms
• 2 body terms
• van der Waals (short range) & Coulomb (long range)

Nonbonded
pairs of atoms
   ij 12   ij 6  qi q j
4 ij        
 r 
r  
r



• Coulomb interaction consumes > 90% computing time
Ewald Sum electrostatics to mimic condensed phase
screening
• Periodic Boundary Conditions
Electrostatic Forces Dominate Behavior
F = ma
or
 V (r )  mr
With a classical Molecular Mechanics
potential, V(r)
These potentials have only numerical solutions.
r (t   t)  r (t )  r(t )t  r(t )t  0(t )
1
2!
t must be small, 10-15s
2
3
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)
Implications
• Colloidal behavior affects
– synthesis / fabrication
– and binding
• Tilt restricts possible geometries of pairing
• Affinity and specificity
G & G
Forces: Surface and Solution
––
––
––
––
–
–
–
–
–
–
–
–
–
– – –
–
–
– –
––
––
–
– –
– –
–
–
–
Water
+[salt]
±
±
±
±
±
Substrate
Theory
Calculate the free energy difference of
hybridization between that in solution
and on a surface
Target + Probe
Gsol-hybrid
Target : Probe
Gdup-attach
Gss-attach
Gsur-hybrid
Target + Probe:Surface
Target :Probe:Surface
Gsol-hybrid -Gsur-hybrid= Gss-att-Gdup-att
Theory
To get the work to form a single duplex on the
surface we need:
• ΔGsol which we can take from thermodynamic
tables: solution reference state (John SantaLucia).
• ΔGatt from a consideration of the surface effects
(chemistry and physics)
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)
The ions and water penetrate the grooves.
Na+
Cl-
H2O
Feig & Pettitt BJ 77, 1769 (1999)
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
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
Tm 
H
S
linker
Vainrub and Pettitt, CPL ’00
Vainrub and Pettitt, Biopoly ’03
Surface at a constant potential for
a metal coated substrate @ .01 M NaCl
Vainrub and Pettitt, CPL ’00
Vainrub and Pettitt, Biopoly ’03
Response to E-fields
Salt and Substrate Material Effects on 8-bp DNA
0.001M
0.01M
0.1M
1M
o
Shift of melting temperature T ( C)
0
-50
DIELECTRIC
=0
-100
0.1
1
10
DIELECTRIC
 = -25 mV
0.1
1
10
DIELECTRIC
 = +25 mV
0.1
1
10
200
METAL
=0
150
METAL
 = -25 mV
METAL
 = +25 mV
100
50
0
0.1
1
10
Vainrub & Pettitt, Biopoly 2004
0.1
1
10
Distance from surface h (nm)
0.1
1
10
Finite Concentration and Coverage
 2   k2 
outside the sphere and plane,
2  k2  r/0
inside the sphere,
|r =a+ = |r =a- , r |r =a+ = r |r =aon the sphere,
|z =0+ = |r =0- , z |z =0+ - r |z =0- = -/0
on the plane.
Different from O & K
h
Vainrub and Pettitt, Biopolymers 2003
Vainrub & Pettitt et al , NATO Sci , 2005
Coulomb Blockage Dominates
Optimum DNA spacing
High negative charge
density repels target
surface binding
Langmuir
On Chip
Target Conc
θ
 H 0  TS0   wn P Z P ( Z P  ZT  

exp
C0
 exp


RT
1 θ
RT

 
Probe surface density
hybridization efficiency θ (0 θ 1)
target concentration C0
Vainrub &Pettitt, PRE (2002)
Vainrub &Pettitt, JACS (2003)
Experimental Isotherm for perfectly
matched lengths
-11
ln[(1-)C/]
-12
-13
-14
-15
0
5x10
12
1x10
13
2x10
13
(1+)Np
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)
Melting curve temperature and width
Analytic wrt surface probe density (coverage)
W + W
In solution
Tm = H0/ S0 – R ln C)
1.0
4RTm2/H0
On-array: Isotherms
Tm 
3wZ2 n p
2H 0  3wZ n p
2
W  Tm
3
12 10 8
0.8
2
Hybridization efficiency
W=
W
6
4
210
*1012 nP
probes/cm2
0.6
0.4
dA20 /dT20
duplex
0.2
Parameter:
[(Vd-Vp)/RT0]*qp*Np
0.0
200
250
350
Temperature (K)
Tm - Tm
Critical for SNP detection design
300
Tm
Pettitt et al NATO Sci 206, 381 (2005)
Strength and linearity of hybridization signal
12
2
Hybrids density (1/cm )
10
1
10
10
2
4
6
8
0.1 x1012
11
2x10
10
10
0
0
10
9
5x10
12
1x10
13
2
Probe density (1/cm )
10
-2
10
-1
10
0
10
1
2
10
10
3
10
4
Target concentration (*exp[G0/RT0] Moles)
Vainrub and Pettitt JACS (2003); ibid Biopolymers, (2004)
Peak of sensitivity
RT
np 
2
wZ P
Normalized hybridization signal
1.0
T = 330 K
0.8
T = 332 K
0.6
T = 334 K
0.4
T = 340 K
0.2
T = 360 K
0.0
0.0
12
2.0x10
12
4.0x10
-2
Probe surface density (cm )
Vainrub and Pettitt, JACS (2003)
Linear range of hybridization
0
10
Non-linear error is below
1 2
 wn Z Z θ (1  θ )  RT
 wn Z Z θ  
δ P P T 2
exp P P T   1
RT
(1  θ ) RT

 

 H 0  TS 0  wn P Z P2
 exp
RT





Hybridization efficiency
3
10
1 2 3 4
-1
4
10
-2
10
-3
1 2
3
4
12
10
3
4
-4
-13
10
-11
10
-9
1x10
-7
1x10
-5
1x10
Target concentration (mol/L)
Beyond the linear range use the on-array binding isotherm
n P S
C0 
N V
A

θ
 H 0  TS 0 
 wn P Z P ( Z P  Z T   
exp
 exp

1 θ
RT
RT




-3
1x10
Probe vs. Target lengths often
mismatch in various ways
...
vs.
Longer sequences are the expected
and require true mesoscale models
Perfect pairing
Garrido Vainrub &Pettitt CPC ‘10
Pairing w/ an overhang
To Accommodate Longer
Sequences and Secondary
Structure Near a Surface
Mesoscale:
Allow for variations in
Linker chemistry
Over-hang
Under-hang
on probes
and targets
in all combinations.
Parameterize ssDNA
as well as dsDNA.
Garrido Vainrub &Pettitt JPCM submitted
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
ΔG
ΔG
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
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)
Solvent and ion charge densities
MF-PB
H2 O
w/ Ions
ε=80
HNC-IE
Charge-Charge correlations
•
•
•
•
Multi Layer effects not Bilayer
Dominate at interfaces
Determine the thermodynamics
Change the kinetics
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
Arnold Vainrub
Clem Wong
Joaquin Ambia-Garrido
Jesse Howard
Khawla Qamhieh
Alex Micu
Keck Center for Computational Biology
Mike Hogan, Lian Gao,
Rosina Georgiadis,
Yuri Fofanov
Thanks to NIH, NASA, DOE,
Welch Foundation, ARP
&SDSC, PNNL, PSC, NCI, MSI