Result:
Click here to view!

1. First off, we start with a new canvas, and I'm going to use the sizes 640*480. And press D and then X. After that get your elliptical marquee tool (m) and make circle and then fill it with black.
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2. Now stay with the selection of the circle and with your tool and click on the 'Subtract from selection' tool.
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3. Now subtract from the circle you made, leaving about 20 pixels thick of the circle you made and the rest, press delete to delete it. Make your circle similar to this:
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4. Next, make a new layer and get your rectangular marquee tool (m). And make a square similar to this:
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5. Now select the circle layer and hold ctrl+I and now go to your square layer and get your eraser and erase ONLY the inside parts inside the circle of the square.
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6. Your logo design is almost coming together, yours should look somewhat similar to this:
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7. Next make a new layer and get your rectangular marquee tool (m) and make a rectangle filled with black.
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8. Now go to Filter > Distort > Shear... and a window will pop up, now make shearize the line to make it look like the following:
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9. Now hold ctrl+T to transform it and make it smaller to fit the size of your circle.
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10. If it some of the parts of the curved line still sticks out, you can always use the eraser tool to erase it.
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11. Now duplicate the curved line by holding ctrl+J or right clicking on the layer and clicking on Duplicate Layer when the drop-down menu comes up. Once you've duplicated the layer, click on the duplicated layer and go to Edit > Transform > Flip Horizontal. And there you have 2 DNA outlines.
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12. Now get your Single Row Marquee Tool.
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13. And with a new layer start making lines starting from the bottom of the circle and going upwards.
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14. Now, its up to you how you want to go upwards, I'm going to go upwards by every 5 pixels but its all up to you. The less space in between the more work you have to do. So when your done about half of your circle line up, it should look somewhat similar to this:
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15. Now get your eraser tool and erase all of the line parts OUTSIDE of the circle.
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16. Now erase all the line parts INSIDE the circle but NOT inside the space between the curved lines.
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17. Once you've completed this process move on to lining up the top half of the circle and viola!
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This concludes our tutorial, you should have something similar to this:
Click here to view!

Download this tutorials .PSD file here.