Biomolecular motors (kinesin-protein process and bacterial flagellar motor) transport substance at the nanoscale level within biological cells, and the motor-cargo connected tether is elastic allowing the motor to defuse rapidly. The energy is stored by the high-energy chemical bonds (proton gradient across the cell's inner membrane). The goal of this paper is to address the critical needs for synergistic science and engineering research and developments in nanoscale to devise the fundamental understanding and apply resulting technological advances arising from the developed theoretical and applied results. Novel phenomena and processes have been observed at the nanoscale, e.g., the Brownian motor direction of displacement does not compline with the applied force. Significant challenges remain in the areas of fundamental understanding, modeling, analysis, and simulation the Brownian motor as well as other nanobiosystems and biostructures dynamics. Other problems which must be addressed is the relationship between functionality, operation, actuation and sensing, feedback mechanism, etc. Research in these areas supports the development of a fundamental understanding of nanobiostructures and processes, nanobiotechnology, and techniques for a broad range of applications in biomaterials, biosystem-based electronics, agriculture, energy, medicine, and health. The goal is to thoroughly study biological and biologically inspired systems in which nanoscale phenomena and effects play important roles. This includes developing an understanding of the relationships among biochemical, electromagnetic, and mechanical processes. This research will allow to synthesize, design, manufacture novel high-performance nanostructures, nanodevices (nanoscale actuators and sensors), and nanoelectromechanical systems.
The ability to find equations (mathematical models), which adequately describe nanosystems properties, phenomena and effects, is a key problem in modeling, analysis, synthesis, and optimization of nanoelectromechanical systems [1-3]. In this paper, we developed the approach to model, analyze, and simulate Brownian Molecular Motors. The reported developments support the existing setups in modeling, analysis, and design of nanoelectromechanical systems. The proposed fundamental results allow us to solve a broad spectrum of problems compared with currently existing methods. The reported results are verified to demonstrated. The parameters of the mathematical model are identified, and the feasibility of the derived equations which model the Brownian motor dynamic and steady-state responses is documented. This research is critical to overcome current obstacles in complete understanding of processes and phenomena in nanoscale, with long-standing goal to develop fundamental and experimental tools to design and fabricate nanostructures. In fact, the devised mathematical models and parameters allow us to understand the operating principles and embedded mechanism to study the motor functionality.
S. E. Lyshevski, Nano- and Microelectromechanical System: Fundamentals of Nano- and Microengineering, CRC Press, FL, 2000.
H. Risken, The Fokker-Plank Equation, Springer, New York, 1984.
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