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We present a new approach within mathematical formalisms for the problem of self assembly in molecular systems automation and its application in targeted drug delivery for cancer treatment. The problem under study concentrates its main focus on nano-robot control systems design including systems casualty, state notation and automata. We also describe the theory of nano-scale thermodynamically driven self assembly for collaborative information processing in a Bio-nanorobotics systems. A fuzzy shaped based approach is described in context of recognizing a single malignant cell along with its stage, as a target for medical treatment. The synthesis and imaging of magnetic nanoparticles, that can be functionally bind with the medicine and reached the effected regions for targeted drug delivery, such as in cancer treatment is also presented. A cybernetics approach for control, communication and computation in infinitesimal machinery systems with integration to complex man-machines systems in the light of general systems theory is suggested. [ABSTRACT FROM PUBLISHER]

From molecular and cellular to perception processes in biological systems, fluctuation is observed. Recently single molecule detection techniques have been developed and the dynamic changes of individual molecules can be measured and are studied in relation to the biological function. These results showed that thermal motion is biased in directional motion and reaction through the interaction with other protein molecules. When these molecules self-assemble to higher levels of hierarchic structure of biological systems, unique operations emerge to make systems function more effective and adaptable. In this paper the roles of fluctuation are described in molecular motors, protein structures and cell signal transduction. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

We study invariant manifold methods for reducing chemical master equations using the Michaelis-Menten mechanism as an example. We try Fraser’s functional iteration method first, but find that it is difficult to use for master equations of high dimension. Using the insights gained from Fraser’s method, we develop a technique to produce reduced chemical master equations directly from the eigenvectors of the state-to-state transition rate matrix. The dimension of the original chemical master equation grows quadratically with number of molecules, while the dimension of the reduced one we obtain is linear in the number of molecules. Additionally, a simple, effective way is developed to generate initial conditions for the reduced models. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]