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The interest in DNA research has escalated in recent years due to the properties of DNA. High specificity in the self-assembly of DNA, rigidity, and the ability to create arbitrary sequences of DNA has allowed researches to consider it as a platform in the creation of new technological devices and circuit boards.1,7,8 These devices could have new properties that current devices are unable to combine8 such as an “easy-to-read test for the presence of a genetic sequence” and cantilevers that can scan biological samples for a genetic sequence.9 However, in order to be used as scaffolding, DNA rafts must be able to bind in predictable ways. If DNA raft chains form according to a pattern, then what is the pattern and does it follow any rule? Through seeking the answer to this question, a model may be drawn from the data in order to forecast the number of DNA rafts per chain, and the number of chains. This, then, is one step closer to the creation of DNA platforms.
 * Deposition of DNA Rafts on Mica Resulting in Polymerization **
 * Rationale and Purpose of Research **

Research in this field of study has been active. A research group at the University of Notre Dame published a paper explaining the effects of DNA oligonucleotides assembling into rafts and binding on silicon wafers with trenches. APTES (aminopropyltriethoxysilane), a substance that binds the DNA to the silicon surface, was deposited in these trenches. The DNA did, indeed, bind to the “stripes” of APTES, resulting in a patterning of the silicon surface. 1 Additionally, a research team at Duke University explains the significance of using computer science in the development of nanostructures. Using computer science, DNA can be “patterned’ in order to have other specifically designated materials bind to it. This, then, creates a program from which DNA platforms can be mass-produced. 2 However, another model was developed by a separate group of scientists, in which 2-D structures were created through folding single stranded DNA. This “origami” of DNA can then be combined with other techniques, such as self-assembly, to create more complex structures that can have additional, selected components programmed to bind to it.3 Mathematical literature on condensation polymerization, too, is crucial to this area of research. Algorithmic self-assembly has been explored recently; however, limitations include errors in growth processes and control of variables .4 Within the laboratory, research has been conducted to identify the relationships between DNA plasmids and APTES on mica and silicon before identifying the relationship between DNA rafts and silicon or mica. Additionally, other monolayers have been used to supply another method to bind DNA to silicon, in order to loosen the DNA for the purpose of arranging it. Furthermore, the use of gold particles to add to the DNA scaffolding is being explored. The use of top-down methods to pattern a surface, and in particular, electron-beam lithography (EBL), is also being used to explore ways of patterning surfaces. In short, it is an interdisciplinary field, involving the use of the Atomic Force Microscope (AFM), Scanning Tunneling Microscope (STM), EBL, spectroscopy and quantitative analysis.
 * Pertinent Scientific Literature **
 * Prior Works and Contributions of Others on This Project **

In order to conduct the research, I had full access to a lab and the guidance of mentors. Therefore, I was fortunate to be able to obtain and use a lab and any necessary materials for my project, which included DNA strands, buffer solutions, nitrogen gas, mica chips, desiccators, and an AFM and its software, which was the Nanoscope IIIa Multimode instrument. In order to create my samples, the ds (double-stranded) DNA had to be ordered. Figure 1, below, shows the structure of the raft
 * Methodology **

**Figure 1**. Each Red, Green, Blue, and Yellow strands in the A, B, C, and D tiles are separate. Below are the sequences of the tiles. The 5’ end on the B’ tile and the 5’ end on the C’ tile on separate rafts bind together to form a chain of rafts. A Tile 4RedA 5’ ACT GGT GGA AGGTTT AAG GTG AAA CTC GAC CTC TAT TCC CTG GCG ATG 3’ 4YellowA 5’ CAT CGC CAC CAC CAG TGA GAT 3’ 4BlueA 5’ CAG AGG TCT TTC ACC TTA AAC CTT GGG AAT AGA GGT CGA GAC AAG TCG 3’ 4GreenA 5’ CGA CTT GTG ACC TCT GTC TTG 3’ B’Tile 4RedB 5’ AGT GAG GAC AGG CAA CGA AGC ATC TC 3’ 4YellowB 5’ GCT TCG TTC CCA CGA ACC TAC AGC AAG CCA CGA TAG CTC AGC CTG TCC 3’ 4BlueB 5’ GAC CGA GGT GAA GTG C 3’ 4GreenB 5’ GTT GTG TGG A GCA CTT CAG CTG TAG GTT CGT GGG TGA GCT ATC GTG GCT TCC TCG GTC 3’ C’Tile 4RedC 5’GGC AAT CCA CAA CCGG C 3’ 4YellowC 5’ TCC ACA CAA C GCG GTT GTC CAA CTT ACC AGA TCC ACA AGC CGA CGT TAC AGG ATT GCC 3’ 4BlueC 5’GTA TGG CGA ACG GTG TAG AGC CAA GA 3’ 4GreenC 5’ GCT CTA CAG CAT CTG GTA AGT TGG TGT AAC GTC GGC TTG TCC GTT CGC 3’ D Tile 4RedD 5’ CAT TCT GGA CGC CAT AAGA ATA GCA CCT CGA CTC ATT TGC CTG CGG TAG 3’ 4YellowD 5’ TCA CTC TAC CGC ACC AGA ATG 3’ 4BlueD 5’ CAG TAG CCT GCT ATC TTA TGG CGT GGC AAA TGA GTC GAG GAC GGA TCG 3’ 4GreenD 5’ CAT ACC GAT CCG TGG CTA CTG 3’ To create the DNA solution, 5 ul of each of the 16 oligonucleotides (short portions of DNA, and in this case, the 16 strands) were individually mixed with 45 ul of dH2O in 16 different Eppendorff tubes. These tubes were stored in a freezer until further use. Therefore, when the stock solution was made, a vortex was employed to liquefy each oligonucleotide solution. To create the stock solution, then, 5 ul of each of the 16 oligonucleotides was added to 20 ul of Mg 2+/TAE (Tri-acetate) 10x buffer (which balanced the pH of the negative solution) and to 100 ul of 18 mega ohm (de-ionized) H20. After the stock solution was created, it was annealed in the thermal cycler for 12 hours, so this procedure was executed overnight. The thermal cycler heats the solution to 90 degrees Celsius, and then cools it to 20 degrees Celsius, over the course of 12 hours. The annealing process allows for the complementary strands to bind together, via the polymerase chain reaction (PCR) process. When the annealing process was complete, 2 ul of the stock solution and 8 ul of the Mg 2+/TAE (1x) buffer were pippetted into an Eppendorff tube, for a total volume of 10 ul. This mixture was gently mixed using the index finger. The remaining stock solution was stored in a refrigerator if it was going to be used within 1-3 days. If not, then it was placed in the freezer. Next, the approximately 1 cm2 mica was cleaned by peeling off 2 surface layers with single-sided tape, a process termed “cleaving” the mica. After this, it was “vigorously” rinsed (i.e. rinsed with about 20 drops of H20) with 18 mega ohm H20 and then dried completely with nitrogen gas. Next, the 10 ul of the DNA solution was deposited onto the surface, with a deposition time of 3 minutes. After the allotted time, the sample was “vigorously” rinsed with 18 mega ohm water and dried thoroughly with nitrogen gas. The sample was then placed on a puck that had a piece of double-sided tape attached to it. Next, the sample was viewed under the AFM in tapping mode. When an area appeared to have DNA rafts, images were captured of a 5um2, a 2 um2, and a 1 um2 region at 256 pixels. The scan rate varied between 1.246-1.299 Hz/second. If, however, the sample was not going to be viewed the same day it was created, it was placed in a desiccator until use. The desiccator helps to prevent the creation of moisture-induced contaminants. Obtaining the right mixture of DNA and the buffer solution was a matter of trial and error. At first, the stock solution contained 80 ul of DNA, 10 ul of Mg2+/TAE (10x) buffer, and 10 ul of 18 mega ohm water. The resulting images under the AFM produced networks and web-like structures, and no clear images of DNA were identified. In essence, the solution was too concentrated, even when the buffer solution was added and the deposition time decreased. Images such as the following were obtained. **Figure 2.** (a) 20 ul of 0.1mM solution on mica, 5 minute deposition time; (b) 10 ul of 0.1 mM solution on mica, 3 minute deposition time; (c) 5 ul of solution + 5 ul of Mg 2+/TAE 1x buffer, 3 minute deposition time.

So, when a new, diluted stock solution, a 0.05mM solution, was created, the large clumps of DNA were eliminated. However, a different problem arose in the formation of network and web-like structures on the sample surface. Some examples are presented in the following images. **Figure 3- Samples with web-like structures.** (a) 10 ul 0.05 mM solution; 3 minute deposition time; (b) 10 ul 0.05 mM solution; 3 minute deposition time Eventually, these networks were eliminated by rinsing the mica with 18 mega ohm water and drying it completely in the cleaning process before the deposition of DNA. So, from this point onward, every mica sample was “vigorously” rinsed with water before DNA deposition. The next variable that was altered was the mixture of different levels of DNA and the buffer in a homogenous solution before deposition on the mica surface.

0.05 mM solution further diluted- this is 3 ul of DNA solution + 7 ul of Mg 2+/TAE 1x buffer. 3 minute deposition time. *Made a homogenous solution before deposition. After obtaining this image, and seeing structures resembling DNA chains, or necklaces, I decided to dilute the solution further, with hopes to spread the molecules farther apart. Therefore, for the next set of samples, I made a new 0.05 mM stock solution, and created the samples using 2 ul of the new stock solution and 8 ul of the buffer. The following images were obtained.
 * Figure 5.**

**Figure 6- DNA Rafts** (a) 0.05 mM solution further diluted- this is 2 ul of DNA solution + 8 ul Mg 2+/TAE 1x buffer. 3 minute deposition time; (b) Same preparation- zoomed in to 1 um2; (c) Same preparation- another image in 1 um2

These images yielded much more promising results. However, in order to verify that the particles in these images were, indeed, DNA rafts, section analysis was conducted on the lengths and heights of the DNA rafts using the software for the AFM. Length and height measurements were conducted on 102 particles. The horizontal measurements added up to a total of ~3780 nm. This was then divided by 102 to obtain ~37 nm, which is the accepted length of a DNA raft.5 The vertical distance measurements added to ~132 nm, when, divided by 102, equals ~1.3 nm, which, too, is within the range of the accepted height.5 Therefore, upon certifying this information, I was able to plot the length of the DNA raft chains formed v. the number of chains. The histogram for the aggregated data is as follows: **Figure 7.** Plotting the relationship between the number of chains v. the number of DNA rafts/chain provides some clues as to how we can predict the average number of DNA rafts/chain for a given sample.

From the data, it is evident that the number of rafts peaks between 2-3 DNA Rafts per chain. When an average of the chain length is taken, however, the result is about 3.53 rafts per chain. Given this, then, when the data is plugged into the Carothers Equation, where chain length, Xn = 1/(1-P), where “P” is the extent of reaction, the result should be close to this average. 6 However, the result is an average of 20.54 rafts per chain, when the degree of conversion is 95.1%. Therefore, another equation must be used, and in this case, the modified Carothers Equation for step polymerization with only a monofunctional component was used. 6 Using the modified equation, then, of Xn = {1+ (39/801)}/{1-(762/801)+(39/801)} yields an average chain length of 10.77 rafts/chain.
 * Results**

The Carothers Equation explains the relationship between the degree of conversion in the reaction and the average chain length in a sample. The higher the degree of conversion, the higher the predicted average chain length. 6 Since the original Carothers Equation produced a number that was outside a rational average, the modified equation was used because it takes into account whether one of the “sticky-ends” was not functioning. The rafts having a monofunctional component was supported with the Polydispersity Index (PDI) explained below.

This index describes the spread of molecular mass in a sample containing polymers. All values are greater than 1, but values approach 1 if the polymer chains are of uniform length. 6 This is not necessarily the case with these data, and fitting the data into the PDI = Mw/Mn, where Mw= {Mo (1+P)}/(1-P) and is the weight average molecular weight, and Mn = Mo/(1-P) is the number average molecular weight. 6 “P” in the equation is the extent of reaction, as in the Carothers’ Equation. 6

The PDI for these data equals 1.951, which is close to a value of 2 that indicates step polymerization. 6 Step polymerization is the condition of having multifunctional components that have an equal chance of reacting**.** 6 In this case, there are two “sticky-ends” that have an equal chance of reacting with other monomers or chains. It is irrelevant whether one “sticky-end” is already bonded to a chain; the other “sticky-end” has an equal chance of binding to either a monomer or another chain. 6

So, one of the main questions that arose is why my predicted chain length using the modified Carothers Equation for step-growth polymerization with a monofunctional unit was much higher than the average chain length, which came out to be ~3.53 rafts/chain, or about 4 rafts/chain. If this number is instead put in place of Xn in the equation, than (1-P) will be designated as “x” in order to find what the number of monomers in the data would have been. So, the equation looks like the following: 3.53 = (1+x)/{1-(1-x)+x}, where “x” comes to be ~0.165. So, to find the number of un-reacting monomers, multiply 0.165 by 801, which yields approximately 132 monomers. That is a difference of 93 monomers from the data obtained.
 * Discussion**

Reasons for this discrepancy are usually due to defective rafts. Given the yield obtained, the predicted average chain length is higher than the average chain length. Therefore, there could have been “sticky-ends” that were deactivated in some way, either through bacteria that may have damaged the rafts or through decomposition of the monomer. Since DNA is a biological material, it is subject to many external forces that may inhibit self-assembly or functionality.10

Another possible reason for this discrepancy may be due to inability to count the number of rafts in every chain on a sample’s image. Some of the chains had indistinguishable rafts, and therefore could not be complied into the aggregate data. The data, then, may have had a higher average chain length and may have matched more closely to the predicted value from the Carothers Equation.

Initially, the data was thought to follow chain-growth polymerization, which is the most common for polymers. Chain-growth polymerization occurs on an active site on a growing polymer. It also yields a PDI of between 10 and 20. 6 However, since the PDI of the data yielded a value close to 2, the idea of chain-growth polymerization was eliminated.

The ideal situation would have chain-growth polymerization because in the creation of circuit boards, and the utilization of DNA rafts as a platform, having one active site where the other rafts fall into place would be easier to predict and mass produce. The data, however, indicates step-growth polymerization, which, because of the two reactive sites, proves harder to determine what the spread of the chain length will be. Therefore, if step-growth is the mode of polymerization for these specific rafts, greater care must be taken to evaluate whether the rafts are defective or not, in order to mass produce DNA platforms for nanotechnology. Once that is overcome, and degrees of conversion for polymerization are similar, then the predicted chain length of polymers using the Carothers Equation can be used to plan DNA platforms for nanotechnology.
 * Conclusions**