Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are not taken into account in conventional knot polynomials. In this study, we develop a new class of knot polynomials specifically designed to study RNA molecules, which considers stem regions. We demonstrate that our knot polynomials have direct structural relation with RNA molecules, and can be used to classify the topology of RNA secondary structures. Furthermore, we point out that these knot polynomials can be used to model the topological effects of disulfide bonds in protein molecules.

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The insect–machine interface (IMI) is a novel approach developed for man-made air vehicles, which directly controls insect flight by either neuromuscular or neural stimulation. In our previous study of IMI, we induced flight initiation and cessation reproducibly in restrained honeybees (Apis mellifera L.) via electrical stimulation of the bilateral optic lobes. To explore the neuromechanism underlying IMI, we applied electrical stimulation to seven subregions of the honeybee brain with the aid of a new method for localizing brain regions. Results showed that the success rate for initiating honeybee flight decreased in the order: α-lobe (or β-lobe), ellipsoid body, lobula, medulla and antennal lobe. Based on a comparison with other neurobiological studies in honeybees, we propose that there is a cluster of descending neurons in the honeybee brain that transmits neural excitation from stimulated brain areas to the thoracic ganglia, leading to flight behavior. This neural circuit may involve the higher-order integration center, the primary visual processing center and the suboesophageal ganglion, which is also associated with a possible learning and memory pathway. By pharmacologically manipulating the electrically stimulated honeybee brain, we have shown that octopamine, rather than dopamine, serotonin and acetylcholine, plays a part in the circuit underlying electrically elicited honeybee flight. Our study presents a new brain stimulation protocol for the honeybee–machine interface and has solved one of the questions with regard to understanding which functional divisions of the insect brain participate in flight control. It will support further studies to uncover the involved neurons inside specific brain areas and to test the hypothesized involvement of a visual learning and memory pathway in IMI flight control.

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