What mathematical subjects (e.g.: Operations Research, Statistics) are used as a tool to investigate scientific areas within DNA Nanotechnology for a research aimed at developing technologies such as - DNA Computing, DNA Robotics, DNA Self Assembly, and DNA Manufacturing etc.?
Since so many properties of DNA are sequence dependent I would stress that probability theory and especially conditional probability theory, combinatorics, and the theory of permutations are important areas in which to develop some working knowledge. We showed many years ago that one could use experimental nearest neighbor frequencies (conditional base sequence probabilities) to predict pyrimidine tract distributions ["The distribution of pyrimidine tracts in DNA can be calculated from nearest neighbor frequencies;" J. Texter and J.C. Sutherland, J. Theor. Biol., 75, 263–269 (1978).], and then we showed how to use such techniques to model various photochemical processes using Monte Carlo methods [(1) "Saturation photodimerization of thymines in DNA;" J. Texter, Biopolymers, 30, 797–802 (1990); (2) "Quantum yield for preferential photodimerization in long pyrimidine tracts;" J. Texter, Biopolymers, 32, 53–59 (1992); (3) "Alternate solution to a discrete car-parking problem;" J. Texter, J. Chem. Phys., 91, 6295–6301 (1989).].
Respected Sir (Dr. John Texter) - Thank you for your answer and the attachment. Let me try to understand the material deeply and if I have question(s) regarding the concerned matter, I'll get back to you. Meanwhile, could you please comment on the role (if any) of Complex and Real Analysis AND Linear and Abstract Algebra in DNA Nanotechnology research?
Complex and real analysis is fundamental to developing a good base in mathematics. I believe it significantly impacts almost every other filed of mathematics, particularly in any area that expresses or requires a measure or some sort of quantification. It provides basis for contour integration, needed in Fourier and Laplace analyses, which bridges to linear algebra. You should study linear algebra before getting too involved in probability theory. Linear algebra provides means to model many systems and to obtain solutions to many problems, including many nonlinear problems (that can be cast as a sequence of linear ones). There are many types of physico-chemical models of DNA (melting, binding) that would benefit from a practical understanding of linear algebra.
Thank you for your last reply (mentioned above). I'll have to work based on the guidance provided by you and as I progress in my studies pursuing a research work, I think I'll have to get back to you for more help. Best Compliments...
if computational and information storage devices (DNA-based computers) are goals of these efforts, I suggest proficiency in Boolean Algebra, Logic Gates and Binary Arithmetic would be invaluable. I recommend studying relevant portions of Computer Science and Electrical Engineering curricula.
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