^{1,a)}, Carol K. Hall

^{1,b)}and Jan Genzer

^{1}

### Abstract

We use lattice Monte Carlo simulations to study the thermodynamics of hybridization of single-stranded “target” genes in solution with complementary “probe” DNA molecules immobilized on a microarraysurface. The target molecules in our system contain 48 segments and the probes tethered on a hard surface contain 8–24 segments. The segments on the probe and target are distinct, with each segment representing a sequence of nucleotides that interacts exclusively with its unique complementary target segment with a single hybridization energy; all other interactions are zero. We examine how surface density (number of probes per unit surface area) and concentration of target molecules affect the extent of hybridization. For short probe lengths, as the surface density increases, the probability of binding long stretches of target segments increases at low surface density, reaches a maximum at an intermediate surface density, and then decreases at high surface density. Furthermore, as the surface density increases, the target is less likely to bind completely to one probe; instead, it binds simultaneously to multiple probes. At short probe lengths, as the target concentration increases, the fraction of targets binding completely to the probes (specificity) decreases. At long probe lengths, varying the target concentration does not affect the specificity. At all target concentrations as the probe length increases, the fraction of target molecules bound to the probes by at least one segment (sensitivity) increases while the fraction of target molecules completely bound to the probes (specificity) decreases. This work provides general guidelines to maximizing microarray sensitivity and specificity. Our results suggest that the sensitivity and specificity can be maximized by using probes 130–180 nucleotides long at a surface density in the range of .

We gratefully acknowledge useful discussions with Dr. Nancy Klauber-DeMore, Dr. B. Montgomery Pettitt, Dr. Erdogan Gulari, and Dr. Matthew Johnson. This work was supported by the Office of Energy Research, Basic Sciences, Chemical Science Division of the U. S. Department of Energy (DE-FG05-91ER14181) and National Science Foundation (CTS-0625888).

I. INTRODUCTION

II. MODEL AND METHOD

A. Calculation of surface density

B. Calculation of target concentration

III. RESULTS AND DISCUSSION

A. Effect of surface density on conformation of probe molecules

B. Effect of surface density on extent of hybridization

C. How probe length affects the dependence of hybridization on surface density

D. Effect of concentration of target molecules on extent of hybridization

IV. CONCLUSION

### Key Topics

- DNA
- 40.0
- BioMEMS
- 27.0
- Monte Carlo methods
- 13.0
- Nucleotides
- 12.0
- Molecular dynamics
- 7.0

## Figures

A schematic of a target molecule binding to an -segment long “end-type” probe molecule tethered to the surface.

A schematic of a target molecule binding to an -segment long “end-type” probe molecule tethered to the surface.

vs probe length for 0.000 278 (square), 0.000 625 (diamond), 0.00 111 (upward triangle), 0.0025 (downward triangle), and 0.0044 (rightsided triangle) probe on the surface for spacer length four segments and .

vs probe length for 0.000 278 (square), 0.000 625 (diamond), 0.00 111 (upward triangle), 0.0025 (downward triangle), and 0.0044 (rightsided triangle) probe on the surface for spacer length four segments and .

vs probe length for 0.000 278 (square), 0.000 625 (diamond), 0.00 111 (upward triangle), 0.0025 (downward triangle), and 0.0044 (rightsided triangle) probe on the surface for spacer length 4 segments and .

vs probe length for 0.000 278 (square), 0.000 625 (diamond), 0.00 111 (upward triangle), 0.0025 (downward triangle), and 0.0044 (rightsided triangle) probe on the surface for spacer length 4 segments and .

Probability of a contiguous stretch of segments along target binding to segments along end-type probes of length 12 segments with spacer at for 0.000 017 4 (cross), 0.000 069 4 (triangle), 0.000 278 (square), 0.000 625 (circle), 0.001 11 (inverted triangle), 0.0025 (diamond), and 0.0044 (right triangle) probe surface area.

Probability of a contiguous stretch of segments along target binding to segments along end-type probes of length 12 segments with spacer at for 0.000 017 4 (cross), 0.000 069 4 (triangle), 0.000 278 (square), 0.000 625 (circle), 0.001 11 (inverted triangle), 0.0025 (diamond), and 0.0044 (right triangle) probe surface area.

Probability (contours) of a contiguous stretch of segments along target (-axis) simultaneously binding to probe 1 , probe 2 , probe 3 , and so on, at surface , probe , spacer , and .

Probability (contours) of a contiguous stretch of segments along target (-axis) simultaneously binding to probe 1 , probe 2 , probe 3 , and so on, at surface , probe , spacer , and .

Probability of a contiguous stretch of segments along target binding to segments along end-type probes of length 8, 12, 16, 20, and 24 and spacer at at (a) low surface density (1 probe), (b) intermediate surface density (16 probes), and (c) high surface density (144 probes).

Probability of a contiguous stretch of segments along target binding to segments along end-type probes of length 8, 12, 16, 20, and 24 and spacer at at (a) low surface density (1 probe), (b) intermediate surface density (16 probes), and (c) high surface density (144 probes).

(a) Fraction of targets in the system that are bound to probes by at least one segment vs probe length, and (b) fraction of targets in the system that are bound to the probes completely at varying target concentrations of (circle), (square), (upward triangle), and (downward triangle) at intermediate surface density of and .

(a) Fraction of targets in the system that are bound to probes by at least one segment vs probe length, and (b) fraction of targets in the system that are bound to the probes completely at varying target concentrations of (circle), (square), (upward triangle), and (downward triangle) at intermediate surface density of and .

## Tables

Surface density for varying number of probes on the surface.

Surface density for varying number of probes on the surface.

Target concentration for varying number of target molecules in the system.

Target concentration for varying number of target molecules in the system.

Overlap surface density for varying probe lengths.

Overlap surface density for varying probe lengths.

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