Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Single-molecule fluorescence resonance energy transfer study of SNARE-mediated membrane fusion

This is a comprehensive study of protein-mediated membrane fusion through single-molecule fluorescence resonance energy transfer (smFRET). Membrane fusion is one of the important cellular processes by which two initially distinct lipid bilayers merge their hydrophobic cores, resulting in one interconnected structure. For example, exocytosis, fertilization of an egg by a sperm and communication between neurons are a few among many processes that rely on some form of fusion. Proteins called soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) play a central role in fusion processes which is also regulated by many accessory proteins, such as synaptotagmin, complexin and Munc18. By a new lipid mixing method at the single-vesicle level, we are able to accurately detect different stages of SNARE-mediated membrane fusion including docking, hemi and full fusion via FRET value of single donor/acceptor vesicle pair. Through this single-vesicle lipid mixing assay, we discovered the vesicle aggregation induced by C2AB/Ca2+, the dual function of complexin, and the fusion promotion role of Munc18/SNARE-core binding mode. While this new method provides the information regarding the extent of the ensemble lipid mixing, the fusion pore opening between two vesicular cavities and the interaction between proteins cannot be detected. In order to overcome these limitations, we then developed a single-vesicle content mixing method to reveal the key factor of pore expansion by detecting the FRET change of dual-labeled DNA probes encapsulated in vesicles. Through our single-vesicle content mixing assay, we found the fusion pore expansion role of yeast SNAREs as well as neuronal SNAREs plus synaptotagmin 1.