Low-Power MEMS-Based Pierce Oscillator Using a 61-MHz Capacitive-Gap Disk Resonator.

A 61-MHz Pierce oscillator constructed in 0.35- [Formula: see text] CMOS technology and referenced to a polysilicon surface-micromachined capacitive-gap-transduced wine-glass disk resonator has achieved phase noise marks of -119 dBc/Hz at 1-kHz offset and -139 dBc/Hz at far-from-carrier offsets. When divided down to 13 MHz, this corresponds to -132 dBc/Hz at 1-kHz offset from the carrier and -152 dBc/Hz far-from-carrier, sufficient for mobile phone reference oscillator applications, using a single MEMS resonator, i.e., without the need to array multiple resonators. Key to achieving these marks is a Pierce-based circuit design that harnesses a MEMS-enabled input-to-output shunt capacitance more than 100× smaller than exhibited by macroscopic quartz crystals to enable enough negative resistance to instigate and sustain oscillation while consuming only [Formula: see text] of power-a reduction of  âˆ¼ 4.5× over previous work. Increasing the bias voltage of the resonator by 1.25 V further reduces power consumption to [Formula: see text] at the cost of only a few decibels in far-from-carrier phase noise. This oscillator achieves a 1-kHz-offset figure of merit (FOM) of -231 dB, which is now the best among published chip-scale oscillators to date. A complete linear circuit analysis quantifies the influence of resonator input-to-output shunt capacitance on power consumption and predicts further reductions in power consumption via reduction of electrode-to-resonator transducer gaps and bond pad sizes. The demonstrated phase noise and power consumption posted by this tiny MEMS-based oscillator are attractive as potential enablers for low-power "set-and-forget" autonomous sensor networks and embedded radios.

Metabolic photofragmentation kinetics for a minimal protocell: rate-limiting factors, efficiency, and implications for evolution.

A key requirement of an autonomous self-replicating molecular machine, a protocell, is the ability to digest resources and turn them into building blocks. Thus a protocell needs a set of metabolic processes fueled by external free energy in the form of available chemical redox potential or light. We introduce and investigate a minimal photodriven metabolic system, which is based on photofragmentation of resource molecules catalyzed by genetic molecules. We represent and analyze the full metabolic set of reaction-kinetic equations and, through a set of approximations, simplify the reaction kinetics so that analytical expressions can be obtained for the building block production. The analytical approximations are compared with the full equation set and with corresponding experimental results to the extent they are available. It should be noted, however, that the proposed metabolic system has not been experimentally implemented, so this investigation is conducted to obtain a deeper understanding of its dynamics and perhaps to anticipate its limitations. We demonstrate that this type of minimal photodriven metabolic scheme is typically rate-limited by the front-end photoexcitation process, while its yield is determined by the genetic catalysis. We further predict that gene-catalyzed metabolic reactions can undergo evolutionary selection only for certain combinations of the involved reaction rates due to their intricate interactions. We finally discuss how the expected range of metabolic rates likely affects other key protocellular processes such as container growth and division as well as gene replication.

Emergence of protocellular growth laws.

Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski 1994 Nature 369, 221; Lee et al. 1996 Nature 382, 525; Varga & Szathmáry 1997 Bull. Math. Biol. 59, 1145). We investigate a template-directed replication with a coupled template catalysed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template-container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth, and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene-container growth as conjectured by various authors (Gánti 2004 Chemoton theory). Our analysis also suggests that the exponential growth of most modern biological systems emerges from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population's generation time and not the growth law (Burdett & Kirkwood 1983 J. Theor. Biol. 103, 11-20; Novak et al. 1998 Biophys. Chem. 72, 185-200; Tyson et al. 2003 Curr. Opin. Cell Biol. 15, 221-231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al. 2000 Bull. Math. Biol. 62, 1061-1086; Stadler & Stadler 2003 Adv. Comp. Syst. 6, 47). The reported results extend these investigations. Finally, the coordinated exponential gene-container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells (Szostak 2001 et al. Nature 409, 387-390; Pohorille & Deamer 2002 Trends Biotech. 20 123-128; Rasmussen et al. 2004 Science 303, 963-965; Szathma ry 2005 Nature 433, 469-470; Luisi et al. 2006 Naturwissenschaften 93, 1-13).