Circuit Topology for Bottom-Up Engineering of Molecular Knots

The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide them with thermal and kinetic stability. Yet, little is known about the design principles of naturally evolved molecular knots. Intra-chain contacts and chain entanglement contribute to the folding of knotted proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized to account for chain entanglement. This generalization is unique to circuit topology and not motivated by other theories. In this conceptual paper, we systematically analyze the circuit topology approach to a description of linear chain entanglement. We utilize a bottom-up approach, i.e., we express entanglement by a set of four fundamental structural units subjected to three (or five) binary topological operations. All knots found in proteins form a well-defined, distinct group which naturally appears if expressed in terms of these basic structural units. We believe that such a detailed, bottom-up understanding of the structure of molecular knots should be beneficial for molecular engineering.

Investigation of an embedded closed-loop stimulation current control principle based on the use of nonlinear ceramic capacitors

Over the years, a constant progress in the development of implantable medical devices (IMD’s) can be observed. On one hand, the advanced implantable electronics enable the implementation of numerous smart functionalities, on the other hand, the variety of electronic components including sensors and a bulky battery severely restrict their degree of miniaturization and reliability. To overcome this limitation, our approach is to realize smart functionalities in leadless and battery-free IMD’s emerging from frugal innovation by exploiting the intrinsic nonlinear properties of the components to be used anyway. The aim of this work is to deepen the understanding of the dynamic behavior of circuit topologies of nonlinear ferroelectric ceramic capacitors and to investigate their potential use for an embedded closed-loop control of the stimulation current. We characterized a selection of 40 commercial ceramic capacitors by measurement and simulation. The degree of nonlinearity resulting from a circuit topology consisting of one, two series and two parallel connected nonlinear capacitors was modeled and evaluated in Mathcad. We present a model with parameterized nonlinear capacitors to simulate the dynamic behavior of an inductively coupled implantable system. The stabilization and amplitude of the stimulation current is controlled by two features. These features are in turn controlled by the circuit topology and the degree of nonlinearity of the capacitors. We found that a high degree of nonlinearity allows the stimulation current to be stabilized within a reasonable range, but it makes the system more prone to instability. However, our model needs to include the dynamic behavior of ferroelectric materials used as dielectric in ceramic capacitors to extend the current investigations and to deepen the understanding of the physics behind the nonlinear properties of ferroelectric capacitors.

Polynomial Invariant of Molecular Circuit Topology

The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain entanglements and local or global structural symmetries stabilised by formation contacts between different parts of the chain. Circuit topology captures the arrangements of intra-chain contacts within a given folded linear chain and allows for the classification and comparison of chains. Contacts keep chain segments in physical proximity and can be either mechanically hard attachments or soft entanglements that constrain a physical chain. Contrary to knot theory, which offers many established knot invariants, circuit invariants are just being developed. Here, we present polynomial invariants that are both efficient and sufficiently powerful to deal with any combination of soft and hard contacts. A computer implementation and table of chains with up to three contacts is also provided.

Automated design of a linear microwave monolithic distributed amplifier

Microwave integrated circuit (IC) design tends to become more efficient and less expensive which leads to emerging the circuit topology and layout synthesis software. In the paper we present a technique and an algorithm for microwave distributed amplifier (DA) automated synthesis based on requirements to linear characteristics. The technique feature is the using of active and passive element’s models for a chosen IC process. This allow the technique to generate circuit topology which can be manufactured using a given IC process. The proposed DA automated design technique work was demonstrated with preamplifier stage design for 20–30 GHz buffer amplifier MMIC based on the 0.25um GaAs pHEMT process of Svetlana-Rost foundry in Saint-Petersburg.