# Biomod/2013/Tianjin/Experiments & Results/DeliveryDevice

(Difference between revisions)

E-mail：austinamens@gmail.com | Address:Building No.20, No.92 Weijin Road, Tianjin, China | Zip-code：300072 E-mail：austinamens@gmail.com | Address:Building No.20, No.92 Weijin Road, Tianjin, China | Zip-code：300072 -

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## Current revision

Polymerizing

optimize the 1st stem-loop structure & termination

Cleavage

optimize the 2nd stem-loop structure

Delivery device

To put this track into usage, we construct walkers for this DNA track. We wanted to build a origami with trigger and see if the whole device is goanna work, but the whole project is to complicated and we don’t have instrument’s to characterize it. So we did not do further research or experiments. Instead, we do some modeling work to give it a further accurate prediction.

# Walker

We constructed 2 kinds of walkers, one is a 2-foot one, and the other is a quadruped one. And we think the 2nd one the better one. It meet the shape with the track, which means a better conduction, also it has 4 feet so that the chance of losing the walker will be lower.

Figure 3.3.1 The 2-foot walker.

# Simulation about the delivery device

We abstract the original problem into a simplified 2-dimensional problem. There are two sizes on a plane-a starting site and an ending site. The distance between the two sites is L. A chain starts from the starting site. The chain is composed of a certain number of units, whose length is r. The chains is rotatable to some extent, as shown in Figure 3.3.3. A unit can rotate freely in a certain range of degree. When the ending point of the chain is close enough to the ending site, they can be seen as successfully linked together. To guarantee successful linkage, the number of units of the chain can be too small or too big. When[[Image:#.png]] , the chain can link two site even it is stretched, as shown in Figure 3.3.4. On the contrary, when N is too large, the possibility of successful linkage is also very small.

Figure 3.3.3 The chain is rotatable.
Figure 3.3.4 Simulation Results.
Figure 3.3.5 Simulation Results.

# Monte Carlo Method [1]

We adopt Monte Carlo Method to study the influence of number of units, the value of N, on the possibility of successful linkage. And we want to find the optimal solution of N to guarantee linkage of two sites.

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; i.e., by running simulations many times over in order to calculate those same probabilities heuristically just like actually playing and recording your results in a real casino situation: hence the name. They are often used in physical and mathematical problems and are most suited to be applied when it is impossible to obtain a closed-form expression or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problems: optimization, numerical integration and generation of samples from a probability distribution.

# Algorithm

Figure 3.3.6 Algorithm Flow Chart.

# Results

Figure 3.3.7 The probability of linkage VS number of units.
Figure 3.3.8 One random test when linkage fails.
Figure 3.3.9 An example of successful linkage.

# MATLAB Code

## Code 1

function [ next] = rdp( start,r )

theta=unifrnd(-pi/2,pi/2);

next=zeros(2,1);

next(1)=start(1)+r*cos(theta);

next(2)=start(2)+r*sin(theta);

end

## Code 2

n=20;

points=zeros(2,n);

r=10;

for ii=2:n

points(:,ii)=rdp(points(:,ii-1),r);

end

plot(points(1,:),points(2,:),'-o')

hold on

plot(points(1,n),points(2,n),'ro')

thet=linspace(0,2*pi,100);

px=100+20*cos(thet);

py=20*sin(thet);

plot(px,py,'-.r')

hold off

## Code 3

function [isornot]=randtest(n)

L=100;

endp=[L,0];

crit=40;

points=zeros(2,n);

r=10;

for ii=2:n

points(:,ii)=rdp(points(:,ii-1),r);

end

%plot(points(1,:),points(2,:),'-o')

dist=sqrt((points(1,n)-endp(1))^2+(points(2,n)-endp(2))^2);

if dist<=crit

isornot=1;

else

isornot=0;

end