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1.  High-resolution dynamic atomic force microscopy in liquids with different feedback architectures 
The recent achievement of atomic resolution with dynamic atomic force microscopy (dAFM) [Fukuma et al., Appl. Phys. Lett. 2005, 87, 034101], where quality factors of the oscillating probe are inherently low, challenges some accepted beliefs concerning sensitivity and resolution in dAFM imaging modes. Through analysis and experiment we study the performance metrics for high-resolution imaging with dAFM in liquid media with amplitude modulation (AM), frequency modulation (FM) and drive-amplitude modulation (DAM) imaging modes. We find that while the quality factors of dAFM probes may deviate by several orders of magnitude between vacuum and liquid media, their sensitivity to tip–sample forces can be remarkable similar. Furthermore, the reduction in noncontact forces and quality factors in liquids diminishes the role of feedback control in achieving high-resolution images. The theoretical findings are supported by atomic-resolution images of mica in water acquired with AM, FM and DAM under similar operating conditions.
PMCID: PMC3596120  PMID: 23503468
atomic force microscopy; dAFM; high-resolution; liquids
2.  Interpreting motion and force for narrow-band intermodulation atomic force microscopy 
Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip–surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip–surface force that are in-phase with the tip motion (F I) and quadrature to the motion (F Q). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F I and F Q actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F I and F Q from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F I and F Q, providing deeper insight into the tip–surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.
PMCID: PMC3566785  PMID: 23400552
atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency
3.  Repulsive bimodal atomic force microscopy on polymers 
Bimodal atomic force microscopy can provide high-resolution images of polymers. In the bimodal operation mode, two eigenmodes of the cantilever are driven simultaneously. When examining polymers, an effective mechanical contact is often required between the tip and the sample to obtain compositional contrast, so particular emphasis was placed on the repulsive regime of dynamic force microscopy. We thus investigated bimodal imaging on a polystyrene-block-polybutadiene diblock copolymer surface and on polystyrene. The attractive operation regime was only stable when the amplitude of the second eigenmode was kept small compared to the amplitude of the fundamental mode. To clarify the influence of the higher eigenmode oscillation on the image quality, the amplitude ratio of both modes was systematically varied. Fourier analysis of the time series recorded during imaging showed frequency mixing. However, these spurious signals were at least two orders of magnitude smaller than the first two fundamental eigenmodes. Thus, repulsive bimodal imaging of polymer surfaces yields a good signal quality for amplitude ratios smaller than A 01 /A 02 = 10:1 without affecting the topography feedback.
PMCID: PMC3388370  PMID: 23016150
bimodal AFM imaging; diblock copolymer; polybutadiene; polystyrene
4.  Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy 
The noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) consists of cantilever thermal noise, tip–surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density d z at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d Δ f at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip–surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d z, we predict d Δ f for specific filter settings, a given level of detection-system noise spectral density d z ds and the cantilever-thermal-noise spectral density d z th. We find an excellent agreement between the calculated and measured values for d Δ f. Furthermore, we demonstrate that thermal noise in d Δ f, defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.
PMCID: PMC3566860  PMID: 23400758
Cantilever; feedback loop; filter; noncontact atomic force microscopy (NC-AFM); noise
5.  Force to Rebalance Control of HRG and Suppression of Its Errors on the Basis of FPGA 
Sensors (Basel, Switzerland)  2011;11(12):11761-11773.
A novel design of force to rebalance control for a hemispherical resonator gyro (HRG) based on FPGA is demonstrated in this paper. The proposed design takes advantage of the automatic gain control loop and phase lock loop configuration in the drive mode while making full use of the quadrature control loop and rebalance control loop in controlling the oscillating dynamics in the sense mode. First, the math model of HRG with inhomogeneous damping and frequency split is theoretically analyzed. In addition, the major drift mechanisms in the HRG are described and the methods that can suppress the gyro drift are mentioned. Based on the math model and drift mechanisms suppression method, four control loops are employed to realize the manipulation of the HRG by using a FPGA circuit. The reference-phase loop and amplitude control loop are used to maintain the vibration of primary mode at its natural frequency with constant amplitude. The frequency split is readily eliminated by the quadrature loop with a DC voltage feedback from the quadrature component of the node. The secondary mode response to the angle rate input is nullified by the rebalance control loop. In order to validate the effect of the digital control of HRG, experiments are carried out with a turntable. The experimental results show that the design is suitable for the control of HRG which has good linearity scale factor and bias stability.
PMCID: PMC3252009  PMID: 22247692
Hemispherical Resonator Gyro (HRG); force-to-rebalance control; FPGA; quadrature error; rate sensor
6.  A measurement of the hysteresis loop in force-spectroscopy curves using a tuning-fork atomic force microscope 
Measurements of the frequency shift versus distance in noncontact atomic force microscopy (NC-AFM) allow measurements of the force gradient between the oscillating tip and a surface (force-spectroscopy measurements). When nonconservative forces act between the tip apex and the surface the oscillation amplitude is damped. The dissipation is caused by bistabilities in the potential energy surface of the tip–sample system, and the process can be understood as a hysteresis of forces between approach and retraction of the tip. In this paper, we present the direct measurement of the whole hysteresis loop in force-spectroscopy curves at 77 K on the PTCDA/Ag/Si(111) √3 × √3 surface by means of a tuning-fork-based NC-AFM with an oscillation amplitude smaller than the distance range of the hysteresis loop. The hysteresis effect is caused by the making and breaking of a bond between PTCDA molecules on the surface and a PTCDA molecule at the tip. The corresponding energy loss was determined to be 0.57 eV by evaluation of the force–distance curves upon approach and retraction. Furthermore, a second dissipation process was identified through the damping of the oscillation while the molecule on the tip is in contact with the surface. This dissipation process occurs mainly during the retraction of the tip. It reaches a maximum value of about 0.22 eV/cycle.
PMCID: PMC3323909  PMID: 22496993
atomic force microscopy; energy dissipation; force spectroscopy; hysteresis loop; PTCDA/Ag/Si(111) √3 × √3
7.  Thermal Actuation Based 3-DoF Non-Resonant Microgyroscope Using MetalMUMPs 
Sensors (Basel, Switzerland)  2009;9(4):2389-2414.
High force, large displacement and low voltage consumption are a primary concern for microgyroscopes. The chevron-shaped thermal actuators are unique in terms of high force generation combined with the large displacements at a low operating voltage in comparison with traditional electrostatic actuators. A Nickel based 3-DoF micromachined gyroscope comprising 2-DoF drive mode and 1-DoF sense mode oscillator utilizing the chevron-shaped thermal actuators is presented here. Analytical derivations and finite element simulations are carried out to predict the performance of the proposed device using the thermo-physical properties of electroplated nickel. The device sensitivity is improved by utilizing the dynamical amplification of the oscillation in 2-DoF drive mode using an active-passive mass configuration. A comprehensive theoretical description, dynamics and mechanical design considerations of the proposed gyroscopes model are discussed in detail. Parametric optimization of gyroscope, its prototype modeling and fabrication using MetalMUMPs has also been investigated. Dynamic transient simulation results predicted that the sense mass of the proposed device achieved a drive displacement of 4.1μm when a sinusoidal voltage of 0.5V is applied at 1.77 kHz exhibiting a mechanical sensitivity of 1.7μm /°/s in vacuum. The wide bandwidth frequency response of the 2-DoF drive mode oscillator consists of two resonant peaks and a flat region of 2.11 kHz between the peaks defining the operational frequency region. The sense mode resonant frequency can lie anywhere within this region and therefore the amplitude of the response is insensitive to structural parameter variations, enhancing device robustness against such variations. The proposed device has a size of 2.2 × 2.6 mm2, almost one third in comparison with existing M-DoF vibratory gyroscope with an estimated power consumption of 0.26 Watts. These predicted results illustrate that the chevron-shaped thermal actuator has a large voltage-stroke ratio shifting the paradigm in MEMS gyroscope design from the traditional interdigitated comb drive electrostatic actuator. These actuators have low damping compared to electrostatic comb drive actuators which may result in high quality factor microgyroscopes operating at atmospheric pressure.
PMCID: PMC3348830  PMID: 22574020
Finite element method; micromachined gyroscope; MEMS; thermal V shaped actuator; chevron-shaped actuator
8.  Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case 
This paper presents experiments on Nafion® proton exchange membranes and numerical simulations illustrating the trade-offs between the optimization of compositional contrast and the modulation of tip indentation depth in bimodal atomic force microscopy (AFM). We focus on the original bimodal AFM method, which uses amplitude modulation to acquire the topography through the first cantilever eigenmode, and drives a higher eigenmode in open-loop to perform compositional mapping. This method is attractive due to its relative simplicity, robustness and commercial availability. We show that this technique offers the capability to modulate tip indentation depth, in addition to providing sample topography and material property contrast, although there are important competing effects between the optimization of sensitivity and the control of indentation depth, both of which strongly influence the contrast quality. Furthermore, we demonstrate that the two eigenmodes can be highly coupled in practice, especially when highly repulsive imaging conditions are used. Finally, we also offer a comparison with a previously reported trimodal AFM method, where the above competing effects are minimized.
PMCID: PMC4142983  PMID: 25161847
amplitude modulation; bimodal; multifrequency atomic force microscopy; indentation depth modulation; Nafion; open loop; proton exchange membranes; trimodal
9.  Determining cantilever stiffness from thermal noise 
We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f n, quality factor Q n and specifically the stiffness k n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.
PMCID: PMC3628876  PMID: 23616942
AFM; cantilever; noncontact atomic force microscopy (NC-AFM); Q-factor; thermal excitation; resonance; spectral analysis; stiffness
10.  Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case 
We present an overview of the bimodal amplitude–frequency-modulation (AM-FM) imaging mode of atomic force microscopy (AFM), whereby the fundamental eigenmode is driven by using the amplitude-modulation technique (AM-AFM) while a higher eigenmode is driven by using either the constant-excitation or the constant-amplitude variant of the frequency-modulation (FM-AFM) technique. We also offer a comparison to the original bimodal AFM method, in which the higher eigenmode is driven with constant frequency and constant excitation amplitude. General as well as particular characteristics of the different driving schemes are highlighted from theoretical and experimental points of view, revealing the advantages and disadvantages of each. This study provides information and guidelines that can be useful in selecting the most appropriate operation mode to characterize different samples in the most efficient and reliable way.
PMCID: PMC3628543  PMID: 23616939
amplitude-modulation; atomic force microscopy; frequency-modulation; phase-locked loop; spectroscopy
11.  Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops 
BMC Research Notes  2012;5:287.
Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs.
We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case.
The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.
PMCID: PMC3532088  PMID: 22694947
12.  Increased imaging speed and force sensitivity for bio-applications with small cantilevers using a conventional AFM setup 
Micron (Oxford, England : 1993)  2012;43(12):1399-1407.
► Development of small cantilever. ► Speed increase by a factor of ten using small cantilevers on a commercial AFM. ► Force sensitivity increase by a factor of five using small cantilever prototypes for force spectroscopy measurements.
In this study, we demonstrate the increased performance in speed and sensitivity achieved by the use of small AFM cantilevers on a standard AFM system. For this, small rectangular silicon oxynitride cantilevers were utilized to arrive at faster atomic force microscopy (AFM) imaging times and more sensitive molecular recognition force spectroscopy (MRFS) experiments. The cantilevers we used had lengths between 13 and 46 μm, a width of about 11 μm, and a thickness between 150 and 600 nm. They were coated with chromium and gold on the backside for a better laser reflection. We characterized these small cantilevers through their frequency spectrum and with electron microscopy. Due to their small size and high resonance frequency we were able to increase the imaging speed by a factor of 10 without any loss in resolution for images from several μm scansize down to the nanometer scale. This was shown on bacterial surface layers (s-layer) with tapping mode under aqueous, near physiological conditions and on nuclear membranes in contact mode in ambient environment. In addition, we showed that single molecular forces can be measured with an up to 5 times higher force sensitivity in comparison to conventional cantilevers with similar spring constants.
PMCID: PMC3430863  PMID: 22721963
Small cantilever; High resolution imaging; Fast AFM imaging; Ultra-sensitive molecular recognition force spectroscopy
13.  Multi-frequency tapping-mode atomic force microscopy beyond three eigenmodes in ambient air 
We present an exploratory study of multimodal tapping-mode atomic force microscopy driving more than three cantilever eigenmodes. We present tetramodal (4-eigenmode) imaging experiments conducted on a thin polytetrafluoroethylene (PTFE) film and computational simulations of pentamodal (5-eigenmode) cantilever dynamics and spectroscopy, focusing on the case of large amplitude ratios between the fundamental eigenmode and the higher eigenmodes. We discuss the dynamic complexities of the tip response in time and frequency space, as well as the average amplitude and phase response. We also illustrate typical images and spectroscopy curves and provide a very brief description of the observed contrast. Overall, our findings are promising in that they help to open the door to increasing sophistication and greater versatility in multi-frequency AFM through the incorporation of a larger number of driven eigenmodes, and in highlighting specific future research opportunities.
PMCID: PMC4222484  PMID: 25383276
amplitude-modulation; bimodal; frequency-modulation; multi-frequency atomic force microscopy; multimodal; open loop; trimodal
14.  Feedback between p21 and reactive oxygen production is necessary for cell senescence 
The sustained activation of CDKN1A (p21/Waf1/Cip1) by a DNA damage response induces mitochondrial dysfunction and reactive oxygen species (ROS) production via signalling through CDKN1A-GADD45A-MAPK14- GRB2-TGFBR2-TGFbeta in senescing primary human and mouse cells in vitro and in vivo.Enhanced ROS production in senescing cells generates additional DNA damage. Although this damage is repairable and transient, it elevates the average levels of DNA damage response permanently, thus forming a positive feedback loop.This loop is necessary and sufficient to maintain the stability of growth arrest until a ‘point of no return' is reached during establishment of senescence.
The phenomenon of cellular ‘senescence'—the permanent arrest of division in normally proliferating mammalian cells such as fibroblasts—is thought to be a central component of the ageing process. Senescence contributes both to age-related loss of tissue homeostasis, as the loss of division capacity leads to impaired cell renewal, and also to protect against cancer, because it acts to block the uncontrolled proliferation of cells that may give rise to a malignant tumour. Replicative senescence is triggered by uncapped telomeres or by ‘unrepairable' non-telomeric DNA damage. Both lesions initiate the same canonical DNA damage response (DDR) (d'Adda di Fagagna, 2008). This response is characterized by activation of sensor kinases (ATM/ATR, DNA-PK), formation of DNA damage foci containing activated H2A.X (γH2A.X) and ultimately induction of cell cycle arrest through activation of checkpoint proteins, notably p53 (TP53) and the CDK inhibitor p21 (CDKN1A). This signalling pathway continues to contribute actively to the stability of the G0 arrest in fully senescent cells long after induction of senescence (d'Adda di Fagagna et al, 2003). However, senescence is more complex than mere CDKI-mediated growth arrest. Senescent cells alter their expression of literally hundreds of genes (Shelton et al, 1999), prominent among these being pro-inflammatory secretory genes (Coppe et al, 2008) and marker genes for a retrograde response induced by mitochondrial dysfunction (Passos et al, 2007a).
There is a growing evidence that multiple mechanisms interact to underpin ageing at the cellular level (Kirkwood, 2005; Passos et al, 2007b) necessitating a systems biology approach if the complex mechanisms of ageing are to be understood (Kirkwood, 2008). With respect to cell senescence, the two major unanswered questions are (i) How does a DNA lesion that can be repaired, at least in principle, induce and maintain irreversible growth arrest? and (ii) How does a growth arrest trigger a completely different cellular phenotype as soon as it becomes irreversible?
To understand those questions, we performed a kinetic analysis of the establishment phase of senescence initiated by DNA damage or telomere dysfunction, focussing on pathways downstream of the classical DDR. Using an approach that combined (i) in-silico interactome analysis, (ii) functional target gene inhibition, (iii) stochastic modelling, and (iv) live cell microscopy, we identified a positive feedback loop between DDR and mitochondrial production of reactive oxygen species (ROS) as necessary and sufficient for long-term maintenance of growth arrest. Using pathway log likelihood scores calculated by a quantitative in-silico interactome analysis to guide siRNA and small molecule inhibition experiments, and using results of sequential and combined inhibition experiments to refine the predictions from the interactome analysis, we found that DDR triggered mitochondrial dysfunction leading to enhanced ROS activation through a linear signal transduction through TP53, CDKN1A, GADD45A, p38 (MAPK14), GRB2, TGFBR2 and TGFβ(Figure 2D). We hypothesized that these ROS stochastically generate novel DNA damage in the nucleus, thus forming a positive feedback loop contributing to the long-term maintenance of DDR (Figure 3A). First confirmation came from static inhibitor experiments as before, showing that nuclear DNA damage foci frequencies in senescent cells were reduced if feedback signalling was suppressed. To formally establish the existence of a feedback loop and its relevance for senescence, we used live cell microscopy in combination with quantitative modelling.
We transformed the conceptual model shown in Figure 3A into a stochastic mechanistic model of the DDR feedback loop by extending the previously published model of the TP53/Mdm2 circuit (Proctor and Gray, 2008) to include reactions for synthesis/activation and degradation/deactivation/repair of CDKN1A, GADD45, MAPK14, ROS and DNA damage. The model replicated very precisely the kinetic behaviour of activated TP53, CDKN1A, ROS and DNA damage foci after initiation of senescence by irradiation. Having established its concordance with the experimental data, the model was then used to predict the effects of intervening in the feedback loop. The model predicted that any intervention reducing ROS levels by about half would decrease average DNA damage foci frequencies from six to four foci/nucleus within about 15 h. It further predicted that this would be sufficient to reduce CDKN1A to basal levels continuously for at least 6 h in about 20% of the treated cells, thus allowing a significant fraction of cells to escape from growth arrest and to resume proliferation. This should happen even if the intervention into the feedback loop was started at a late time point (e.g. 6 days) after induction of senescence.
To analyse DNA damage foci dynamics we used a reporter construct (AcGFP–53BP1c) that quantitatively reports single DNA damage foci kinetics in time-resolved live cell microscopy (Nelson et al, 2009). Foci frequency measurements quantitatively confirmed the prediction from the stochastic model. More importantly, we found that many individual foci in both telomere- and stress-dependent senescence had short lifespans with half-lives below 15 h. Feedback loop inhibition reduced only the frequencies of short-lived DNA damage foci in accordance with the hypothesis that ROS production contributed to DDR by constant replenishment of short-lived DNA damage foci.
Finally, we inhibited signalling through the loop at different time points after induction of senescence by ionizing radiation and measured ROS levels, DNA damage foci frequencies and proliferation markers. Treatments with the MAPK14 inhibitor SB203580 or the free radical scavenger PBN were used to block the loop. The results quantitatively confirmed the model prediction and indicated that the feedback loop between DDR and ROS production was both necessary and sufficient to maintain cell cycle arrest for at least 6–10 days after induction of senescence. Interestingly, the loop was still active at later time points and in deep senescence, but proliferation arrest was then stabilized by additional factor(s). This indicated that certain features of the senescent phenotype-like ROS production that might be responsible for the negative impact of senescent cells into their tissue environment can be successfully inhibited even in deep senescence. This may prove relevant for novel therapeutic studies aiming to modulate intracellular ROS levels in both aging and cancer.
Cellular senescence—the permanent arrest of cycling in normally proliferating cells such as fibroblasts—contributes both to age-related loss of mammalian tissue homeostasis and acts as a tumour suppressor mechanism. The pathways leading to establishment of senescence are proving to be more complex than was previously envisaged. Combining in-silico interactome analysis and functional target gene inhibition, stochastic modelling and live cell microscopy, we show here that there exists a dynamic feedback loop that is triggered by a DNA damage response (DDR) and, which after a delay of several days, locks the cell into an actively maintained state of ‘deep' cellular senescence. The essential feature of the loop is that long-term activation of the checkpoint gene CDKN1A (p21) induces mitochondrial dysfunction and production of reactive oxygen species (ROS) through serial signalling through GADD45-MAPK14(p38MAPK)-GRB2-TGFBR2-TGFβ. These ROS in turn replenish short-lived DNA damage foci and maintain an ongoing DDR. We show that this loop is both necessary and sufficient for the stability of growth arrest during the establishment of the senescent phenotype.
PMCID: PMC2835567  PMID: 20160708
aging; cell senescence; DNA damage foci; mitochondria; reactive oxygen
15.  Development of a Prototype Miniature Silicon Microgyroscope 
Sensors (Basel, Switzerland)  2009;9(6):4586-4605.
A miniature vacuum-packaged silicon microgyroscope (SMG) with symmetrical and decoupled structure was designed to prevent unintended coupling between drive and sense modes. To ensure high resonant stability and strong disturbance resisting capacity, a self-oscillating closed-loop circuit including an automatic gain control (AGC) loop based on electrostatic force feedback is adopted in drive mode, while, dual-channel decomposition and reconstruction closed loops are applied in sense mode. Moreover, the temperature effect on its zero bias was characterized experimentally and a practical compensation method is given. The testing results demonstrate that the useful signal and quadrature signal will not interact with each other because their phases are decoupled. Under a scale factor condition of 9.6 mV/°/s, in full measurement range of ± 300 deg/s, the zero bias stability reaches 15°/h with worse-case nonlinearity of 400 ppm, and the temperature variation trend of the SMG bias is thus largely eliminated, so that the maximum bias value is reduced to one tenth of the original after compensation from -40 °C to 80 °C.
PMCID: PMC3291928  PMID: 22408543
silicon microgyroscope (SMG); self-oscillating; dual-channel closed-loop; scale factor; zero bias stability; temperature compensation; miniature prototype
16.  Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy 
In frequency-modulation atomic force microscopy the direct observable is the frequency shift of an oscillating cantilever in a force field. This frequency shift is not a direct measure of the actual force, and thus, to obtain the force, deconvolution methods are necessary. Two prominent methods proposed by Sader and Jarvis (Sader–Jarvis method) and Giessibl (matrix method) are investigated with respect to the deconvolution quality. Both methods show a nontrivial dependence of the deconvolution quality on the oscillation amplitude. The matrix method exhibits spikelike features originating from a numerical artifact. By interpolation of the data, the spikelike features can be circumvented. The Sader–Jarvis method has a continuous amplitude dependence showing two minima and one maximum, which is an inherent property of the deconvolution algorithm. The optimal deconvolution depends on the ratio of the amplitude and the characteristic decay length of the force for the Sader–Jarvis method. However, the matrix method generally provides the higher deconvolution quality.
PMCID: PMC3323913  PMID: 22496997
frequency-modulation atomic force microscopy; force deconvolution; numerical implementation
17.  A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli 
Combining in vivo FRET with time-varying stimuli, such as steps, ramps, and sinusoids allowed deduction of the molecular mechanisms underlying cellular signal processing.The bacterial chemotaxis pathway can be described as a two-module feedback circuit, the transfer functions of which we have characterized quantitatively by experiment. Model-driven experimental design allowed the use of a single FRET pair for measurements of both transfer functions of the pathway.The adaptation module's transfer function revealed that feedback near steady state is weak, consistent with high sensitivity to shallow gradients, but also strong steady-state fluctuations in pathway output.The measured response to oscillatory stimuli defines the frequency band over which the chemotaxis system can compute time derivatives.
In searching for better environments, bacteria sample their surroundings by random motility, and make temporal comparisons of experienced sensory cues to bias their movement toward favorable directions (Berg and Brown, 1972). Thus, the problem of sensing spatial gradients is reduced to time-derivative computations, carried out by a signaling pathway that is well characterized at the molecular level in Escherichia coli. Here, we study the physiology of this signal processing system in vivo by fluorescence resonance energy transfer (FRET) experiments in which live cells are stimulated by time-varying chemoeffector signals. By measuring FRET between the active response regulator of the pathway CheY-P and its phosphatase CheZ, each labeled with GFP variants, we obtain a readout that is directly proportional to pathway activity (Sourjik et al, 2007). We analyze the measured response functions in terms of mechanistic models of signaling, and discuss functional consequences of the observed quantitative characteristics.
Experiments are guided by a coarse-grained modular model (Tu et al, 2008) of the sensory network (Figure 1), in which we identify two important ‘transfer functions': one corresponding to the receptor–kinase complex, which responds to changes in input ligand concentration on a fast time scale, and another corresponding to the adaptation system, which provides negative feedback, opposing the effect of ligand on a slower time scale. For the receptor module, we calibrate an allosteric MWC-type model of the receptor–kinase complex by FRET measurements of the ‘open-loop' transfer function G([L],m) using step stimuli. This calibration provides a basis for using the same FRET readout (between CheY-P and CheZ) to further study properties of the adaptation module.
It is well known that adaptation in E. coli's chemotaxis system uses integral feedback, which guarantees exact restoration of the baseline activity after transient responses to step stimuli (Barkai and Leibler, 1997; Yi et al, 2000). However, the output of time-derivative computations during smoothly varying stimuli depends not only on the presence of integral feedback, but also on what is being integrated. As this integrand can in general be any function of the output, we represent it by a black-box function F(a) in our model, and set out to determine its shape by experiments with time-varying stimuli.
We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, ac that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of ac versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.
To obtain the feedback transfer function, F(a), we apply a simple coordinate transformation, identified using our model, to the same ramp-response data (Figure 5B). This function reveals how the temporal rate of change of the feedback signal m depends on the current output signal a. The shape of this function is analyzed using a biochemical reaction scheme, from which in vivo kinetic parameters of the feedback enzymes, CheR and CheB, are extracted. The fitted Michaelis constants for these enzymatic reactions are small compared with the steady-state abundance of their substrates, thus indicating that these enzymes operate close to saturation in vivo. The slope of the function near steady state can be used to assess the strength of feedback, and to compute the relaxation time of the system, τm. Relaxation is found to be slow (i.e. large τm), consistent with large fluctuations about the steady-state activity caused by the near-saturation kinetics of the feedback enzymes (Emonet and Cluzel, 2008).
Finally, exponential sine-wave stimuli are used to map out the system's frequency response (Figure 5C). The measured data points for both the amplitude and phase of the response are found to be in excellent agreement with model predictions based on parameters from the independently measured step and ramp responses. No curve fitting was required to obtain this agreement. Although the amplitude response as a function of frequency resembles a first-order high-pass filter with a well-defined cutoff frequency, νm, we point out that the chemotaxis pathway is actually a low-pass filter if the time derivative of the input is viewed as the input signal. In this latter perspective, νm defines an upper bound for the frequency band over which time-derivative computations can be carried out.
The two types of measurements yield complementary information regarding time-derivative computations by E. coli. The ramp-responses characterize the asymptotically constant output when a temporal gradient is held fixed over extended periods. Interestingly, the ramp responses do not depend on receptor cooperativity, but only on properties of the adaptation system, and thus can be used to reveal the in vivo adaptation kinetics, even outside the linear regime of the kinase response. The frequency response is highly relevant in considering spatial searches in the real world, in which experienced gradients are not held fixed in time. The characteristic cutoff frequency νm is found by working within the linear regime of the kinase response, and depends on parameters from both modules (it increases with both cooperativity in the receptor module, and the strength of feedback in the adaptation module).
Both ramp responses and sine-wave responses were measured at two different temperatures (22 and 32°C), and found to differ significantly. Both the slope of F(a) near steady state, from ramp experiments, and the characteristic cutoff frequency, from sine-wave experiments, were higher by a factor of ∼3 at 32°C. Fits of the enzymatic model to F(a) suggest that temperature affects the maximal velocity (Vmax) more strongly than the Michaelis constants (Km) for CheR and CheB.
Successful application of inter-molecular FRET in live cells using GFP variants always requires some degree of serendipity. Genetic fusions to these bulky fluorophores can impair the function of the original proteins, and even when fusions are functional, efficient FRET still requires the fused fluorophores to come within the small (<10 nm) Förster radius on interactions between the labeled proteins. Thus, when a successful FRET pair is identified, it is desirable to make the most of it. We have shown here that combined with careful temporal control of input stimuli, and appropriately calibrated models, a single FRET pair can be used to study the structure of multiple transfer functions within a signaling network.
The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22°C and below 0.018 Hz at 32°C. Our results show how dynamic input–output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.
PMCID: PMC2913400  PMID: 20571531
adaptation; feedback; fluorescence resonance energy transfer (FRET); frequency response; Monod–Wyman–Changeux (MWC) model
18.  Measurement of Mechanical Properties of Cantilever Shaped Materials 
Sensors (Basel, Switzerland)  2008;8(5):3497-3541.
Microcantilevers were first introduced as imaging probes in Atomic Force Microscopy (AFM) due to their extremely high sensitivity in measuring surface forces. The versatility of these probes, however, allows the sensing and measurement of a host of mechanical properties of various materials. Sensor parameters such as resonance frequency, quality factor, amplitude of vibration and bending due to a differential stress can all be simultaneously determined for a cantilever. When measuring the mechanical properties of materials, identifying and discerning the most influential parameters responsible for the observed changes in the cantilever response are important. We will, therefore, discuss the effects of various force fields such as those induced by mass loading, residual stress, internal friction of the material, and other changes in the mechanical properties of the microcantilevers. Methods to measure variations in temperature, pressure, or molecular adsorption of water molecules are also discussed. Often these effects occur simultaneously, increasing the number of parameters that need to be concurrently measured to ensure the reliability of the sensors. We therefore systematically investigate the geometric and environmental effects on cantilever measurements including the chemical nature of the underlying interactions. To address the geometric effects we have considered cantilevers with a rectangular or circular cross section. The chemical nature is addressed by using cantilevers fabricated with metals and/or dielectrics. Selective chemical etching, swelling or changes in Young's modulus of the surface were investigated by means of polymeric and inorganic coatings. Finally to address the effect of the environment in which the cantilever operates, the Knudsen number was determined to characterize the molecule-cantilever collisions. Also bimaterial cantilevers with high thermal sensitivity were used to discern the effect of temperature variations. When appropriate, we use continuum mechanics, which is justified according to the ratio between the cantilever thickness and the grain size of the materials. We will also address other potential applications such as the ageing process of nuclear materials, building materials, and optical fibers, which can be investigated by monitoring their mechanical changes with time. In summary, by virtue of the dynamic response of a miniaturized cantilever shaped material, we present useful measurements of the associated elastic properties.
PMCID: PMC3675557
Microcantilever; mechanics; ageing; environment; stress; gas; materials; sensor; pressure; temperature
19.  Synergistic Interactions between the Molecular and Neuronal Circadian Networks Drive Robust Behavioral Circadian Rhythms in Drosophila melanogaster 
PLoS Genetics  2014;10(4):e1004252.
Most organisms use 24-hr circadian clocks to keep temporal order and anticipate daily environmental changes. In Drosophila melanogaster CLOCK (CLK) and CYCLE (CYC) initiates the circadian system by promoting rhythmic transcription of hundreds of genes. However, it is still not clear whether high amplitude transcriptional oscillations are essential for circadian timekeeping. In order to address this issue, we generated flies in which the amplitude of CLK-driven transcription can be reduced partially (approx. 60%) or strongly (90%) without affecting the average levels of CLK-target genes. The impaired transcriptional oscillations lead to low amplitude protein oscillations that were not sufficient to drive outputs of peripheral oscillators. However, circadian rhythms in locomotor activity were resistant to partial reduction in transcriptional and protein oscillations. We found that the resilience of the brain oscillator is depending on the neuronal communication among circadian neurons in the brain. Indeed, the capacity of the brain oscillator to overcome low amplitude transcriptional oscillations depends on the action of the neuropeptide PDF and on the pdf-expressing cells having equal or higher amplitude of molecular rhythms than the rest of the circadian neuronal groups in the fly brain. Therefore, our work reveals the importance of high amplitude transcriptional oscillations for cell-autonomous circadian timekeeping. Moreover, we demonstrate that the circadian neuronal network is an essential buffering system that protects against changes in circadian transcription in the brain.
Author Summary
Circadian clocks allow organisms to predict daily environmental changes. These clocks time the sleep/wake cycles and many other physiological and cellular pathways to 24hs rhythms. The current model states that circadian clocks keep time by the use of biochemical feedback loops. These feedback loops are responsible for the generation of high amplitude oscillations in gene expression. Abolishment of circadian transcriptional oscillations has been shown to abolish circadian function. Previous studies addressing this issue utilize manipulations in which the abolishment of the transcriptional oscillations is very dramatic and involves strong up or down-regulation of circadian genes. In this study we generated fruit flies in which we diminished the amplitude of circadian oscillations in a controlled way. We found that a decrease of more than 50% in the amplitude of circadian oscillations leads to impaired function of circadian physiological outputs in the periphery but does not significantly affect circadian behavior. This suggests that the clock in the brain has a specific compensatory mechanism. Moreover, we found that flies with reduced oscillation and impaired circadian neuronal communication display aberrant circadian rhythms. These finding support the idea of network buffering mechanisms that allows the brain to produce circadian rhythms even with low amplitude molecular oscillations.
PMCID: PMC3974645  PMID: 24698952
20.  Synthetic in vitro transcriptional oscillators 
A fundamental goal of synthetic biology is to understand design principles through engineering biochemical systems.Three in vitro synthetic transcriptional oscillators were constructed and analyzed: a two-node-negative feedback oscillator, an amplified negative-feedback oscillator, and a three-node ring oscillator.The in vitro oscillators are governed by similar design principles as previous theoretical studies and synthetic oscillators in vivo.Because of unintended reactions that arise even without the complexity of living cells, several challenges remain for predictive and robust oscillator performance.
Fundamental goals for synthetic biology are to understand the principles of biological circuitry from an engineering perspective and to establish engineering methods for creating biochemical circuitry to control molecular processes—both in vitro and in vivo (Benner and Sismour, 2005; Adrianantoandro et al, 2006). Here, we make use of a previously proposed class of in vitro biochemical systems, transcriptional circuits, that can be modularly wired into arbitrarily complex networks by changing the regulatory and coding sequence domains of DNA templates (Kim et al, 2006; Subsoontorn et al 2011). Using design motifs for inhibitory and excitatory regulations, three different oscillator designs were constructed and characterized: a two-switch negative-feedback oscillator, loosely analogous to the p53–Mdm2-feedback loop (Bar-Or et al, 2000); the same oscillator augmented with a positive-feedback loop, loosely analogous to a synthetic relaxation oscillator (Atkinson et al, 2003); and a three-switch ring oscillator analogous to the repressilator (Elowitz and Leibler, 2000).
DNA and RNA hybridization reactions (Figure 1B) can be assembled to create either an inhibitable switch (Figure 1A, right and bottom) with a threshold set by the total concentration of its DNA activator strand (Figure 1C, bottom), or an activatable switch (Figure 1A, left and top) with a threshold set by its DNA inhibitor strand concentration (Figure 1C, top). This threshold mechanism is analogous to biological threshold mechanisms such as ‘inhibitor ultrasensitivity' (Ferrell, 1996) and ‘molecular titration' (Buchler and Louis, 2008). Using these design motifs, we constructed a two-switch negative-feedback oscillator (Figure 1A, inset): RNA activator rA1 activates the production of RNA inhibitor rI2 by modulating switch Sw21, while RNA inhibitor rI2, in turn, inhibits the production of RNA activator rA1 by modulating switch Sw12. A total of seven DNA strands are used, in addition to the two enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H. The fact that such a negative-feedback loop can lead to temporal oscillations can be seen from a mathematical model of transcriptional networks. Experimental results showed qualitative agreement with predicted oscillator behavior from simple model simulations.
The fully optimized system revealed five complete oscillation cycles with a nearly 50% amplitude swing (Figure 3A) until, after ∼20 h, the production rate could no longer be sustained in the batch reaction. Gel measurements verified oscillations in RNA concentrations and switch states (Figure 3B and C). However to our surprise, rather than oscillations with constant amplitude and constant mean, the RNA inhibitor concentration builds up after each cycle. An extended mathematical model that incorporated an interference reaction from ‘waste' product (Figure 3B and C) could qualitatively capture this behavior.
Using a new autoregulatory switch Sw11, we added a positive-feedback loop to the two-node oscillator to make an amplified negative feedback oscillator (Design II, Figure 1D). Further, we replaced the excitatory connection of Sw21 by a chain of two inhibitory connections, Sw23 and Sw31, to construct a three-switch ring oscillator (Design III, Figure 1D). All three oscillator designs could be tuned to reach the oscillatory regime in parameter space.
Reassuringly, our in vitro oscillators exhibit several design principles previously observed in vivo. (1) Introducing delay in a simple negative-feedback loop can help achieve stable oscillation (Novák and Tyson, 2008; Stricker et al, 2008). (2) The addition of a positive-feedback self-loop to a negative-feedback oscillator provides access to rich dynamics and improved tunability (Tsai et al, 2008). (3) Oscillations in biochemical ring oscillators (such as the repressilator) are sensitive to parameter asymmetry among individual components (Tuttle et al, 2005). (4) The saturation of degradation machinery and the management of waste products could play an important role.
However, several significant difficulties remain for predictive and robust oscillator performances: limited lifetime of closed batch reactions, interference from waste products, and asymmetry of switch components make quantitative modeling and predictio difficult. As a complementary approach to top-down view of systems biology, cell-free in vitro systems offer a valuable training ground to create and explore increasingly interesting and powerful information-based chemical systems (Simpson, 2006). In vitro oscillators could be used to orchestrate other chemical processes such as DNA nanomachines (Dittmer and Simmel, 2004) and to provide embedded controllers within prototype artificial cells (Noireaux and Libchaber, 2004; Griffiths and Tawfik, 2006).
The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells.
PMCID: PMC3063688  PMID: 21283141
cell free; in vitro; oscillation; synthetic biology; transcriptional circuits
21.  Intrinsically High-Q Dynamic AFM Imaging in Liquid with a Significantly Extended Needle Tip 
Nanotechnology  2012;23(23):235704.
Atomic force microscope (AFM) probe with a long and rigid needle tip was fabricated and studied for high Q factor dynamic (tapping mode) AFM imaging of samples submersed in liquid. The extended needle tip over a regular commercially-available tapping mode AFM cantilever was sufficiently long to keep the AFM cantilever from submersed in liquid, which significantly minimized the hydrodynamic damping involved in dynamic AFM imaging of samples in liquid. Dynamic AFM imaging of samples in liquid at an intrinsic Q factor of over 100 and an operation frequency of over 200 kHz was demonstrated. The method has the potential to be extended to acquire viscoelastic materials properties and provide truly gentle imaging of soft biological samples in physiological environments.
PMCID: PMC3401635  PMID: 22595833
22.  Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model 
Integrating molecular time-series data resulted in a more robust model of the plant clock, which predicts that a wave of inhibitory PRR proteins controls the morning genes LHY and CCA1.PRR5 is experimentally validated as a late-acting component of this wave.The family of sequentially expressed PRR proteins allows flexible entrainment of the clock, whereas a single protein could not, suggesting that the duplication of clock genes might confer this generic, functional advantage.The observed post-translational regulation of the evening protein TOC1 by interaction with ZTL and GI remains consistent with an indirect activation of TOC1 mRNA expression by GI, which was previously postulated from modelling.
Circadian rhythms are present in most eukaryotic organisms including plants. The core genes of the circadian clock are very important for plant physiology as they drive the rhythmic expression of around 30% of Arabidopsis genes (Edwards et al, 2006; Michael et al, 2008). The clock is normally entrained by daily environmental changes in light and temperature. Oscillations also persist under constant environmental conditions in a laboratory. The clock gene circuit in Arabidopsis is based on multiple interlocked feedback loops, which are typical of circadian genetic networks in other organisms (Dunlap and Loros, 2004; Bell-Pedersen et al, 2005). Mechanistic, mathematical models are increasingly useful in analysing and understanding how the observed molecular components give rise to the rhythmic behaviour of this dynamic, non-linear system.
Our previous model of Arabidopsis circadian clock (Locke et al, 2006) presented the core, three-loop structure of the clock, which comprised morning and evening oscillators and coupling between them (Figure 1). The morning loop included the dawn-expressed LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) genes, which negatively regulate their expression through activation of the inhibitor proteins, PSEUDO-RESPONSE REGULATOR 9 (PRR9) and PRR7. These were described by a single, combined model component, PRR9/7. The evening loop included the dusk-expressed gene TIMING OF CAB EXPRESSION 1 (TOC1), which negatively regulates itself through inhibition of a hypothetical activator, gene Y. The evening-expressed gene GIGANTEA (GI) contributes to Y function. The morning and evening loops were connected through inhibition of the evening genes by LHY/CCA1 and activation of LHY/CCA1 expression by a hypothetical evening gene X. Here, we extend the previous model of circadian gene expression (Locke et al, 2006) based on recently published data (Figure 1). The new model retains the good match of our previous model to the large volume of molecular time-series data, and improves the behaviour of the model clock system under a range of light conditions and in a wider range of mutants.
The morning loop was extended by adding a hypothetical clock component, the night inhibitor (NI), which acts together with PRR9 and PRR7 to keep the expression of LHY and CCA1 at low levels over a broad interval spanning dusk. This regulation is important to set the phase of LHY/CCA1 expression at dawn. Data from the literature suggested that the PRR5 gene was a candidate for NI, leading us to predict that the sequentially expressed PRR9, PRR7 and PRR5 proteins together formed a wave of inhibitors of LHY and CCA1. This hypothesis was tested under discriminating light conditions, in which the light interval is replaced with the dawn and dusk pulses of light to form a ‘skeleton photoperiod'. Combining this protocol with mutation of the PRR7 and/or PRR5 genes, our new experimental results validated the model predictions and confirmed that PRR5 contributes to the function that we modelled as NI. During revision of this paper, that result received further experimental support (Nakamichi et al, 2010).
Model simulations revealed the functional importance of the inhibitor wave in entraining the clock to the light/dark cycle. Separating PRR9 from the other inhibitors in the model showed how the strong light activation observed for this gene contributes to more rapid entrainment. The observed, post-translation regulation of all three inhibitor proteins by light (Farre and Kay, 2007; Ito et al, 2007; Kiba et al, 2007) was also included in the model. Light-regulated degradation provides a molecular mechanism to explain the later phase of LHY and CCA1 expression under long photoperiods compared with short photoperiods, in line with experimental observations.
The connection between evening and morning loops was revised by including the inhibition of the morning gene PRR9 by the evening component TOC1, based on the data on TOC1-overexpressing plants (Makino et al, 2002; Ito et al, 2005). This inhibition causes a delay of PRR9 expression relative to LHY/CCA1, which allows LHY/CCA1 to reach a higher expression level at dawn. Our simulations showed that a partial mutant that lacks this inhibition of PRR9 by TOC1 is sufficient to cause the higher level of PRR9 and the short circadian period observed in toc1 mutant plants.
The evening loop was extended by introducing the observed, post-translational regulation of the TOC1 protein by the F-box protein ZEITLUPE (ZTL) and stabilization of ZTL by its interaction with GI in the presence of light (Kim et al, 2007). GI's function in the clock model has thus been revised according to the data: GI promotes an inhibition of TOC1 protein function through positive regulation of ZTL. This results, together with negative regulation of Y by TOC1, in indirect activation of TOC1 mRNA expression by GI, which agrees with our earlier experimental data (Locke et al, 2006). Simulations showed that the post-translational regulation of TOC1 by ZTL and GI results in the observed long period of the ztl mutant and fast dampening of rhythms in the lhy/cca1/gi triple mutant.
This is the first mathematical model that incorporates the observed post-translational regulation into the genetic network of the Arabidopsis clock. In addition to specific, mechanistic insights, the model shows a generic advantage from the duplication of clock genes and their expression at different phases. Such clock gene duplications are observed in eukaryotes with larger genomes, such as the mouse. Analogous, functional duplication can be achieved by differential regulation of a single clock gene in distinct cells, as in Drosophila.
Circadian clocks generate 24-h rhythms that are entrained by the day/night cycle. Clock circuits include several light inputs and interlocked feedback loops, with complex dynamics. Multiple biological components can contribute to each part of the circuit in higher organisms. Mechanistic models with morning, evening and central feedback loops have provided a heuristic framework for the clock in plants, but were based on transcriptional control. Here, we model observed, post-transcriptional and post-translational regulation and constrain many parameter values based on experimental data. The model's feedback circuit is revised and now includes PSEUDO-RESPONSE REGULATOR 7 (PRR7) and ZEITLUPE. The revised model matches data in varying environments and mutants, and gains robustness to parameter variation. Our results suggest that the activation of important morning-expressed genes follows their release from a night inhibitor (NI). Experiments inspired by the new model support the predicted NI function and show that the PRR5 gene contributes to the NI. The multiple PRR genes of Arabidopsis uncouple events in the late night from light-driven responses in the day, increasing the flexibility of rhythmic regulation.
PMCID: PMC2964123  PMID: 20865009
Arabidopsis thaliana; biological clocks; circadian rhythms; mathematical model; systems biology
23.  Noncontact microrheology at acoustic frequencies, using frequency-modulated atomic force microscopy 
Nature methods  2010;7(8):650-654.
We report an atomic force microscopy (AFM) method for assessing elastic and viscous properties of soft samples at acoustic frequencies under non-contact conditions. The method can be used to measure material properties via frequency modulation and is based on hydrodynamics theory of thin gaps we developed here. A cantilever with an attached microsphere is forced to oscillate tens of nanometers above a sample. The elastic modulus and viscosity of the sample are estimated by measuring the frequency-dependence of the phase lag between the oscillating microsphere and the driving piezo at various heights above the sample. This method features an effective area of pyramidal tips used in contact AFM but with only piconewton applied forces. Using this method, we analyzed polyacrylamide gels of different stiffness and assessed graded mechanical properties of guinea pig tectorial membrane. The technique enables the study of microrheology of biological tissues that produce or detect sound.
PMCID: PMC3508509  PMID: 20562866
24.  Apertureless scanning near-field optical microscopy of sparsely labeled tobacco mosaic viruses and the intermediate filament desmin 
Both fluorescence imaging and atomic force microscopy (AFM) are highly versatile and extensively used in applications ranging from nanotechnology to life sciences. In fluorescence microscopy luminescent dyes serve as position markers. Moreover, they can be used as active reporters of their local vicinity. The dipolar coupling of the tip with the incident light and the fluorophore give rise to a local field and fluorescence enhancement. AFM topographic imaging allows for resolutions down to the atomic scale. It can be operated in vacuum, under ambient conditions and in liquids. This makes it ideal for the investigation of a wide range of different samples. Furthermore an illuminated AFM cantilever tip apex exposes strongly confined non-propagating electromagnetic fields that can serve as a coupling agent for single dye molecules. Thus, combining both techniques by means of apertureless scanning near-field optical microscopy (aSNOM) enables concurrent high resolution topography and fluorescence imaging. Commonly, among the various (apertureless) SNOM approaches metallic or metallized probes are used. Here, we report on our custom-built aSNOM setup, which uses commercially available monolithic silicon AFM cantilevers. The field enhancement confined to the tip apex facilitates an optical resolution down to 20 nm. Furthermore, the use of standard mass-produced AFM cantilevers spares elaborate probe production or modification processes. We investigated tobacco mosaic viruses and the intermediate filament protein desmin. Both are mixed complexes of building blocks, which are fluorescently labeled to a low degree. The simultaneous recording of topography and fluorescence data allows for the exact localization of distinct building blocks within the superordinate structures.
PMCID: PMC3778390  PMID: 24062977
apertureless scanning near-field optical microscope; atomic force microscopy; fluorescence microscopy
25.  Frequency Function in Atomic Force Microscopy Applied to a Liquid Environment 
Sensors (Basel, Switzerland)  2014;14(6):9369-9379.
Scanning specimens in liquids using commercial atomic force microscopy (AFM) is very time-consuming due to the necessary try-and-error iteration for determining appropriate triggering frequencies and probes. In addition, the iteration easily contaminates the AFM tip and damages the samples, which consumes probes. One reason for this could be inaccuracy in the resonant frequency in the feedback system setup. This paper proposes a frequency function which varies with the tip-sample separation, and it helps to improve the frequency shift in the current feedback system of commercial AFMs. The frequency function is a closed-form equation, which allows for easy calculation, as confirmed by experimental data. It comprises three physical effects: the quasi-static equilibrium condition, the atomic forces gradient effect, and hydrodynamic load effect. While each of these has previously been developed in separate studies, this is the first time their combination has been used to represent the complete frequency phenomenon. To avoid “jump to contact” issues, experiments often use probes with relatively stiffer cantilevers, which inevitably reduce the force sensitivity in sensing low atomic forces. The proposed frequency function can also predict jump to contact behavior and, thus, the probe sensitivity could be increased and soft probes could be widely used. Additionally, various tip height behaviors coupling with the atomic forces gradient and hydrodynamic effects are discussed in the context of carbon nanotube probes.
PMCID: PMC4118394  PMID: 24865882
frequency shift function; jump to contact; liquid environment; atomic force microscopy

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