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1.  Noise performance of frequency modulation Kelvin force microscopy 
Noise performance of a phase-locked loop (PLL) based frequency modulation Kelvin force microscope (FM-KFM) is assessed. Noise propagation is modeled step by step throughout the setup using both exact closed loop noise gains and an approximation known as “noise gain” from operational amplifier (OpAmp) design that offers the advantage of decoupling the noise performance study from considerations of stability and ideal loop response. The bandwidth can be chosen depending on how much noise is acceptable and it is shown that stability is not an issue up to a limit that will be discussed. With thermal and detector noise as the only sources, both approaches yield PLL frequency noise expressions equal to the theoretical value for self-oscillating circuits and in agreement with measurement, demonstrating that the PLL components neither modify nor contribute noise. Kelvin output noise is then investigated by modeling the surrounding bias feedback loop. A design rule is proposed that allows choosing the AC modulation frequency for optimized sharing of the PLL bandwidth between Kelvin and topography loops. A crossover criterion determines as a function of bandwidth, temperature and probe parameters whether thermal or detector noise is the dominating noise source. Probe merit factors for both cases are then established, suggesting how to tackle noise performance by probe design. Typical merit factors of common probe types are compared. This comprehensive study is an encouraging step toward a more integral performance assessment and a remedy against focusing on single aspects and optimizing around randomly chosen key values.
PMCID: PMC3896264  PMID: 24455457
dynamic; frequency noise; Kelvin force microscopy; noise performance; phase noise; thermal excitation
2.  Amplitude Demodulation of Entrained Sway to Analyze Human Postural Control 
This paper presents an innovative technique to study postural control. Our translating platform, the Sliding Linear Investigative Platform For Analyzing Lower Limb Stability and Simultaneous Tracking, EMG and Pressure mapping (SLIP-FALLS-STEPm), makes precise, vibration movements under controlled conditions. We look at the psychophysical thresholds to the perception of a sinusoidally induced sway. In the Sine Lock experiments described, an induced sinusoidal perturbation locks the subject's natural sway pattern at the frequency of the perturbation. The input / output system is treated as an Amplitude Shift Key (ASK) modulated signal modulating a carrier frequency (at or about a subject's natural sway frequency). The Position signal (input) and the Anterior-Posterior Center of Pressure (APCOP) signal (output) or the ankle angle are demodulated by mixing them with the pure sine wave carrier at the frequency of underlying oscillation and then low-pass filtering it to detect the amplitude envelope. These detected envelopes elucidate that the square pulse increase in the position sine wave amplitude yields a triangular increase in APCOP demodulated signal.
PMCID: PMC2261375  PMID: 18003110
3.  A Low-Noise Delta-Sigma Phase Modulator for Polar Transmitters 
The Scientific World Journal  2014;2014:521717.
A low-noise phase modulator, using finite-impulse-response (FIR) filtering embedded delta-sigma (ΔΣ) fractional-N phase-locked loop (PLL), is fabricated in 0.18 μm CMOS for GSM/EDGE polar transmitters. A simplified digital compensation filter with inverse-FIR and -PLL features is proposed to trade off the transmitter noise and linearity. Experimental results show that the presented architecture performs RF phase modulation well with 20 mW power dissipation from 1.6 V supply and achieves the root-mean-square (rms) and peak phase errors of 4° and 8.5°, respectively. The measured and simulated phase noises of −104 dBc/Hz and −120 dBc/Hz at 400-kHz offset from 1.8-GHz carrier frequency are observed, respectively.
PMCID: PMC3956518  PMID: 24719578
4.  Single-Chip Fully Integrated Direct-Modulation CMOS RF Transmitters for Short-Range Wireless Applications 
Sensors (Basel, Switzerland)  2013;13(8):9878-9895.
Ultra-low power radio frequency (RF) transceivers used in short-range application such as wireless sensor networks (WSNs) require efficient, reliable and fully integrated transmitter architectures with minimal building blocks. This paper presents the design, implementation and performance evaluation of single-chip, fully integrated 2.4 GHz and 433 MHz RF transmitters using direct-modulation power voltage-controlled oscillators (PVCOs) in addition to a 2.0 GHz phase-locked loop (PLL) based transmitter. All three RF transmitters have been fabricated in a standard mixed-signal CMOS 0.18 μm technology. Measurement results of the 2.4 GHz transmitter show an improvement in drain efficiency from 27% to 36%. The 2.4 GHz and 433 MHz transmitters deliver an output power of 8 dBm with a phase noise of −122 dBc/Hz at 1 MHz offset, while drawing 15.4 mA of current and an output power of 6.5 dBm with a phase noise of −120 dBc/Hz at 1 MHz offset, while drawing 20.8 mA of current from 1.5 V power supplies, respectively. The PLL transmitter delivers an output power of 9 mW with a locking range of 128 MHz and consumes 26 mA from 1.8 V power supply. The experimental results demonstrate that the RF transmitters can be efficiently used in low power WSN applications.
PMCID: PMC3812584  PMID: 23917260
CMOS; direct-modulation; phase-locked loop (PLL); radio frequency (RF); short-range; voltage-controlled oscillator (VCO); wireless transmitter
5.  Polynomial Method for PLL Controller Optimization† 
Sensors (Basel, Switzerland)  2011;11(7):6575-6592.
The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach.
PMCID: PMC3231652  PMID: 22163973
non-linear systems; phase-locked loop; optimization
6.  In vivo Conditions Induce Faithful Encoding of Stimuli by Reducing Nonlinear Synchronization in Vestibular Sensory Neurons 
PLoS Computational Biology  2011;7(7):e1002120.
Previous studies have shown that neurons within the vestibular nuclei (VN) can faithfully encode the time course of sensory input through changes in firing rate in vivo. However, studies performed in vitro have shown that these same VN neurons often display nonlinear synchronization (i.e. phase locking) in their spiking activity to the local maxima of sensory input, thereby severely limiting their capacity for faithful encoding of said input through changes in firing rate. We investigated this apparent discrepancy by studying the effects of in vivo conditions on VN neuron activity in vitro using a simple, physiologically based, model of cellular dynamics. We found that membrane potential oscillations were evoked both in response to step and zap current injection for a wide range of channel conductance values. These oscillations gave rise to a resonance in the spiking activity that causes synchronization to sinusoidal current injection at frequencies below 25 Hz. We hypothesized that the apparent discrepancy between VN response dynamics measured in in vitro conditions (i.e., consistent with our modeling results) and the dynamics measured in vivo conditions could be explained by an increase in trial-to-trial variability under in vivo vs. in vitro conditions. Accordingly, we mimicked more physiologically realistic conditions in our model by introducing a noise current to match the levels of resting discharge variability seen in vivo as quantified by the coefficient of variation (CV). While low noise intensities corresponding to CV values in the range 0.04–0.24 only eliminated synchronization for low (<8 Hz) frequency stimulation but not high (>12 Hz) frequency stimulation, higher noise intensities corresponding to CV values in the range 0.5–0.7 almost completely eliminated synchronization for all frequencies. Our results thus predict that, under natural (i.e. in vivo) conditions, the vestibular system uses increased variability to promote fidelity of encoding by single neurons. This prediction can be tested experimentally in vitro.
Author Summary
The vestibular system senses the motion of the head in space and is vital for gaze stability, posture control, and the computation of spatial orientation during everyday life. The activities of single vestibular neurons recorded in the brains of awake behaving animals show that they can accurately transmit information about the time course of head motion, which is necessary for several behaviors such as the vestibulo-ocular reflex required for gaze stabilization. In contrast, this is not the case when the same neurons are recorded in isolation and sensory stimulation is mimicked experimentally. We investigated the cause for this discrepancy by studying how a mathematical model of vestibular neuron activity responds to mimics of sensory stimulation under different conditions. We found that the differences in the activities of vestibular neurons recorded in awake behaving animals and in isolation can be explained by the addition of synaptic noise, which in turn, increases the variability of action potential firing that is seen in more natural conditions. Our modeling results make a clear prediction that can be tested experimentally.
PMCID: PMC3140969  PMID: 21814508
7.  Designing a Ring-VCO for RFID Transponders in 0.18 μm CMOS Process 
The Scientific World Journal  2014;2014:580385.
In radio frequency identification (RFID) systems, performance degradation of phase locked loops (PLLs) mainly occurs due to high phase noise of voltage-controlled oscillators (VCOs). This paper proposes a low power, low phase noise ring-VCO developed for 2.42 GHz operated active RFID transponders compatible with IEEE 802.11 b/g, Bluetooth, and Zigbee protocols. For ease of integration and implementation of the module in tiny die area, a novel pseudodifferential delay cell based 3-stage ring oscillator has been introduced to fabricate the ring-VCO. In CMOS technology, 0.18 μm process is adopted for designing the circuit with 1.5 V power supply. The postlayout simulated results show that the proposed oscillator works in the tuning range of 0.5–2.54 GHz and dissipates 2.47 mW of power. It exhibits a phase noise of −126.62 dBc/Hz at 25 MHz offset from 2.42 GHz carrier frequency.
PMCID: PMC3919089  PMID: 24587731
8.  Intrinsic and Extrinsic Neuronal Mechanisms in Temporal Coding: A Further Look at Neuronal Oscillations 
Neural Plasticity  1999;6(4):173-189.
Many studies in recent years have been devoted to the detection of fast oscillations in the Central Nervous System (CNS), interpreting them as synchronizing devices. We should, however, refrain from associating too closely the two concepts of synchronization and oscillation. Whereas synchronization is a relatively well-defined concept, by contrast oscillation of a population of neurones in the CNS looks loosely defined, in the sense that both its frequency sharpness and the duration of the oscillatory episodes vary widely from case to case. Also, the functions of oscillations in the brain are multiple and are not confined to synchronization. The paradigmatic instantiation of oscillation in physics is given by the harmonic oscillator, a device particularly suited to tell the time, as in clocks. We will thus examine first the case of oscillations or cycling discharges of neurones, which provide a clock or impose a “tempo” for various kinds of information processing. Neuronal oscillators are rarely just clocks clicking at a fixed frequency. Instead, their frequency is often adjustable and controllable, as in the example of the “chattering cells” discovered in the superficial layers of the visual cortex. Moreover, adjustable frequency oscillators are suitable for use in “phase locked loops” (PLL) networks, a device that can convert time coding to frequency coding; such PLL units have been found in the somatosensory cortex of guinea pigs. Finally, are oscillations stricto sensu necessary to induce synchronization in the discharges of downstream neurones? We know that this is not the case, at least not for local populations of neurones. As a contribution to this question, we propose that repeating patterns in neuronal discharges production may be looked at as one such alternative solution in relation to the processing of information. We review here the case of precisely repeating triplets, detected in the discharges of olfactory mitral cells of a freely breathing rat under odor stimulation.
PMCID: PMC2565318  PMID: 10714268
9.  Modeling and Development of INS-Aided PLLs in a GNSS/INS Deeply-Coupled Hardware Prototype for Dynamic Applications 
Sensors (Basel, Switzerland)  2015;15(1):733-759.
A GNSS/INS deeply-coupled system can improve the satellite signals tracking performance by INS aiding tracking loops under dynamics. However, there was no literature available on the complete modeling of the INS branch in the INS-aided tracking loop, which caused the lack of a theoretical tool to guide the selections of inertial sensors, parameter optimization and quantitative analysis of INS-aided PLLs. This paper makes an effort on the INS branch in modeling and parameter optimization of phase-locked loops (PLLs) based on the scalar-based GNSS/INS deeply-coupled system. It establishes the transfer function between all known error sources and the PLL tracking error, which can be used to quantitatively evaluate the candidate inertial measurement unit (IMU) affecting the carrier phase tracking error. Based on that, a steady-state error model is proposed to design INS-aided PLLs and to analyze their tracking performance. Based on the modeling and error analysis, an integrated deeply-coupled hardware prototype is developed, with the optimization of the aiding information. Finally, the performance of the INS-aided PLLs designed based on the proposed steady-state error model is evaluated through the simulation and road tests of the hardware prototype.
PMCID: PMC4327046  PMID: 25569751
GNSS/INS deeply-coupled integration; INS-aided PLLs; PLL tracking error; steady state error model; hardware prototype
10.  The neuromagnetic response to spoken sentences: Co-modulation of theta band amplitude and phase 
NeuroImage  2012;60(4):2118-2127.
Speech elicits a phase-locked response in the auditory cortex that is dominated by theta (3–7 Hz) frequencies when observed via magnetoencephalography (MEG). This phase-locked response is potentially explained as new phase-locked activity superimposed on the ongoing theta oscillation or, alternatively, as phase-resetting of the ongoing oscillation. The conventional method used to distinguish between the two hypotheses is the comparison of post- to prestimulus amplitude for the phase-locked frequency across a set of trials. In theory, increased amplitude indicates the presence of additive activity, while unchanged amplitude points to phase-resetting. However, this interpretation may not be valid if the amplitude of ongoing background activity also changes following the stimulus. In this study, we employ a new approach that circumvents this problem. Specifically, we utilize a fine-grained time–frequency analysis of MEG channel data to examine the co-modulation of amplitude change and phase coherence in the post-stimulus theta-band response. If the phase-locked response is attributable solely to phase-resetting of the ongoing theta oscillation, then amplitude and phase coherence should be uncorrelated. In contrast, additive activity should produce a positive correlation. We find significant positive correlation not only during the onset response but also throughout the response period. In fact, transient increases in phase coherence are accompanied by transient increases in amplitude in accordance with a “signal plus background” model of the evoked response. The results support the hypothesis that the theta-band phase-locked response to attended speech observed using MEG is dominated by additive phase-locked activity.
PMCID: PMC3593735  PMID: 22374481
Auditory; Speech; MEG; Evoked; Phase; Amplitude
11.  Entrainment by an Extracellular AC Stimulus in a Computational Model of Cardiac Tissue 
Cardiac tissue can be entrained when subjected to sinusoidal stimuli, often responding with action potentials sustained for the duration of the stimulus. To investigate mechanisms responsible for both entrainment and extended action potential duration, computer simulations of a two-dimensional grid of cardiac cells subjected to sinusoidal extracellular stimulation were performed.
Methods and Results
The tissue is represented as a bidomain with unequal anisotropy ratios. Cardiac membrane dynamics are governed by a modified Beeler-Reuter model. The stimulus, delivered by a bipolar electrode, has a duration of 750 to 1,000 msec, an amplitude range of 800 to 3,200 μA/cm, and a frequency range of 10 to 60 Hz. The applied stimuli create virtual electrode polarization (VEP) throughout the sheet. The simulations demonstrate that periodic extracellular stimulation results in entrainment of the tissue. This phase-locking of the membrane potential to the stimulus is dependent on the location in the sheet and the magnitude of the stimulus. Near the electrodes, the oscillations are 1:1 or 1:2 phase-locked; at the middle of the sheet, the oscillations are 1:2 or 1:4 phase-locked and occur on the extended plateau of an action potential. The 1:2 behavior near the electrodes is due to periodic change in the voltage gradient between VEP of opposite polarity; at the middle of the sheet, it is due to spread of electrotonic current following the collision of a propagating wave with refractory tissue.
The simulations suggest that formation of VEP in cardiac tissue subjected to periodic extracellular stimulation is of paramount importance to tissue entrainment and formation of an extended oscillatory action potential plateau.
PMCID: PMC2837923  PMID: 11699528
defibrillation; AC stimulation; entrainment; action potential duration; computer simulation; virtual electrode polarization
We examined changes in the motor organization of postural control in response to continuous, variable amplitude oscillations evoked by a translating platform and explored whether these changes reflected implicit sequence learning. The platform underwent random amplitude (maximum ± 15 cm) and constant frequency (0.5 Hz) oscillations. Each trial was composed of three 15-second segments containing seemingly random oscillations. Unbeknownst to participants, the middle segment was repeated in each of 42 trials on the first day of testing and in an additional seven trials completed approximately 24 hours later. Kinematic data were used to determine spatial and temporal components of total body centre of mass (COM) and joint segment coordination. Results showed that with repeated trials, participants reduced the magnitude of horizontal body COM displacement, shifted from a COM phase lag to a phase lead relative to platform motion and increased correlations between ankle/platform motion and hip/platform motion as they evolved from an ankle strategy to a multi-segment control strategy involving the ankle and hip. Maintenance of these changes across days provided evidence for learning. Similar improvements for the random and repeated segments, however, indicate that participants did not exploit the sequence of perturbations to improve balance control. Rather, the central nervous system (CNS) may have been tuning into more general features of platform motion. These findings provide important insight into the generalizabilty of improved compensatory balance control with training.
PMCID: PMC2855617  PMID: 18327574
platform translation; balance; learning; continuous perturbation; postural coordination; implicit sequence learning
13.  Specific Entrainment of Mitral Cells during Gamma Oscillation in the Rat Olfactory Bulb 
PLoS Computational Biology  2009;5(10):e1000551.
Local field potential (LFP) oscillations are often accompanied by synchronization of activity within a widespread cerebral area. Thus, the LFP and neuronal coherence appear to be the result of a common mechanism that underlies neuronal assembly formation. We used the olfactory bulb as a model to investigate: (1) the extent to which unitary dynamics and LFP oscillations can be correlated and (2) the precision with which a model of the hypothesized underlying mechanisms can accurately explain the experimental data. For this purpose, we analyzed simultaneous recordings of mitral cell (MC) activity and LFPs in anesthetized and freely breathing rats in response to odorant stimulation. Spike trains were found to be phase-locked to the gamma oscillation at specific firing rates and to form odor-specific temporal patterns. The use of a conductance-based MC model driven by an approximately balanced excitatory-inhibitory input conductance and a relatively small inhibitory conductance that oscillated at the gamma frequency allowed us to provide one explanation of the experimental data via a mode-locking mechanism. This work sheds light on the way network and intrinsic MC properties participate in the locking of MCs to the gamma oscillation in a realistic physiological context and may result in a particular time-locked assembly. Finally, we discuss how a self-synchronization process with such entrainment properties can explain, under experimental conditions: (1) why the gamma bursts emerge transiently with a maximal amplitude position relative to the stimulus time course; (2) why the oscillations are prominent at a specific gamma frequency; and (3) why the oscillation amplitude depends on specific stimulus properties. We also discuss information processing and functional consequences derived from this mechanism.
Author Summary
Olfactory function relies on a chain of neural relays that extends from the periphery to the central nervous system and implies neural activity with various timescales. A central question in neuroscience is how information is encoded by the neural activity. In the mammalian olfactory bulb, local neural activity oscillations in the 40–80 Hz range (gamma) may influence the timing of individual neuron activities such that olfactory information may be encoded in this way. In this study, we first characterize in vivo the detailed activity of individual neurons relative to the oscillation and find that, depending on their state, neurons can exhibit periodic activity patterns. We also find, at least qualitatively, a relation between this activity and a particular odor. This is reminiscent of general physical phenomena—the entrainment by an oscillation—and to verify this hypothesis, in a second phase, we build a biologically realistic model mimicking these in vivo conditions. Our model confirms quantitatively this hypothesis and reveals that entrainment is maximal in the gamma range. Taken together, our results suggest that the neuronal activity may be specifically formatted in time during the gamma oscillation in such a way that it could, at this stage, encode the odor.
PMCID: PMC2760751  PMID: 19876377
14.  Coupling governs entrainment range of circadian clocks 
Circadian clock oscillator properties that are crucial for synchronization with the environment (entrainment) are studied in experiment and theory.The ratio between stimulus (zeitgeber) strength and oscillator amplitude, and the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity.Uncoupled lung clocks entrain to extreme zeitgeber cycles, whereas the coupled oscillator system in the suprachiasmatic nucleus (SCN) does not; however, when coupling in the SCN is inhibited, larger ranges of entrainment can be achieved.
Daily rhythms in physiology, metabolism and behavior are controlled by an endogenous circadian timing system, which has evolved to synchronize an organism to periodically recurring environmental conditions, such as light–dark or temperature cycles. In mammals, the circadian system relies on cell-autonomous oscillators residing in almost every cell of the body. Cells of the SCN in the anterior hypothalamus are able to generate precise, long-lasting self-sustained circadian oscillations, which drive most rhythmic behavioral and physiological outputs, and which are believed to originate from the fact that the SCN tissue consists of tightly coupled cells (Aton and Herzog, 2005). In contrast, peripheral oscillators, such as lung tissue, exhibit seemingly damped and usually less precise oscillations, which are thought to be brought about by the lack of intercellular coupling.
Precise synchronization of these rhythms within the organism, but also with the environment (so-called entrainment), is an essential part of circadian organization. Entrainment is one of the cornerstones of circadian biology (Roenneberg et al, 2003). In evolution, the phase of a rhythmic variable is selective rather than its endogenous period. Thus, the synchronization of endogenous rhythms to zeitgeber cycles of the environment (resulting in a specific phase of entrainment) is fundamental for the adaptive value of circadian clocks. In this study, we systematically investigated the properties of circadian oscillators that are essential for entrainment behavior and describe coupling as a primary determinant.
As an experimental starting point of this study, we found that the circadian oscillators of lung tissue have a larger range of entrainment than SCN tissue—they readily entrained to extreme experimental temperature cycle of 20 or 28 h, whereas SCN tissue did not (Figure 4). For this purpose, we cultured SCN and lung slices derived from mice that express luciferase as fusion protein together with the clock protein PERIOD2 (Yoo et al, 2004). The detection of luciferase-driven bioluminescence allowed us to follow molecular clock gene activity in real-time over the course of several days.
In theoretical analyses, we show that both the ratio of amplitude and zeitgeber strength and, importantly, inter-oscillator coupling are major determinants for entrainment. The reason for coupling being critical is twofold: (i) Coupling makes an oscillatory system more rigid, i.e., it relaxes faster in response to a perturbation, and (ii) coupling increases the amplitude of the oscillatory system. Both of these consequences of coupling lead to a smaller entrainment range, because zeitgeber stimuli affect the oscillatory system less if the relaxation is fast and the amplitude is high (Figure 1). From these theoretical considerations, we conclude that the lung clock probably constitutes a weak oscillatory system, likely because a lack in coupling leads to a slow amplitude relaxation. (Circadian amplitude is not particularly low in lung (Figure 4).) In contrast, the SCN constitutes a rigid oscillator, whereby coupling and its described consequences probably are the primary causes for this rigidity. We then tested these theoretical predictions by experimentally perturbing coupling in the SCN (with MDL and TTX; O'Neill et al, 2008; Yamaguchi et al, 2003) and find that, indeed, reducing the coupling weakens the circadian oscillatory system in the SCN, which results in an enlargement of the entrainment range (Figure 6).
Why is the SCN designed to be a stronger circadian oscillator than peripheral organs? We speculate that the position of the SCN—as the tissue that conveys environmental timing information (i.e., light) to the rest of the body—makes it necessary to create a circadian clock that is robust against noisy environmental stimuli. The SCN oscillator needs to be robust enough to be protected from environmental noise, but flexible enough to fulfill its function as an entrainable clock even in extreme photoperiods (i.e., seasons). By the same token, peripheral clocks are more protected from the environmental zeitgebers due to intrinsic homeostatic mechanisms. Thus, they do not necessarily need to develop a strong oscillatory system (e.g., by strengthening the coupling), rather they need to stay flexible enough to respond to direct or indirect signals from the SCN, such as hormonal, neural, temperature or metabolic signals. Such a design ensures that only robust and persistent environmental signals trigger an SCN resetting response, while SCN signals can relatively easily be conveyed to the rest of the body. Thus, the robustness in the SCN clock likely serves as a filter for environmental noise.
In summary, using a combination of simulation studies, analytical calculations and experiments, we uncovered critical features for entrainment, such as zeitgeber-to-amplitude ratio and amplitude relaxation rate. Coupling is a primary factor that governs these features explaining important differences in the design of SCN and peripheral oscillators that ensure a robust, but also flexible circadian system.
Circadian clocks are endogenous oscillators driving daily rhythms in physiology and behavior. Synchronization of these timers to environmental light–dark cycles (‘entrainment') is crucial for an organism's fitness. Little is known about which oscillator qualities determine entrainment, i.e., entrainment range, phase and amplitude. In a systematic theoretical and experimental study, we uncovered these qualities for circadian oscillators in the suprachiasmatic nucleus (SCN—the master clock in mammals) and the lung (a peripheral clock): (i) the ratio between stimulus (zeitgeber) strength and oscillator amplitude and (ii) the rigidity of the oscillatory system (relaxation rate upon perturbation) determine entrainment properties. Coupling among oscillators affects both qualities resulting in increased amplitude and rigidity. These principles explain our experimental findings that lung clocks entrain to extreme zeitgeber cycles, whereas SCN clocks do not. We confirmed our theoretical predictions by showing that pharmacological inhibition of coupling in the SCN leads to larger ranges of entrainment. These differences between master and the peripheral clocks suggest that coupling-induced rigidity in the SCN filters environmental noise to create a robust circadian system.
PMCID: PMC3010105  PMID: 21119632
circadian clock; coupling; entrainment; mathematical modeling; oscillator
15.  Asymmetric Sensory Reweighting in Human Upright Stance 
PLoS ONE  2014;9(6):e100418.
To investigate sensory reweighting as a fundamental property of sensor fusion during standing, we probed postural control with simultaneous rotations of the visual scene and surface of support. Nineteen subjects were presented with pseudo-random pitch rotations of visual scene and platform at the ankle to test for amplitude dependencies in the following conditions: low amplitude vision: high amplitude platform, low amplitude vision: low amplitude platform, and high amplitude vision: low amplitude platform. Gain and phase of frequency response functions (FRFs) to each stimulus were computed for two body sway angles and a single weighted EMG signal recorded from seven muscles. When platform stimulus amplitude was increased while visual stimulus amplitude remained constant, gain to vision increased, providing strong evidence for inter-modal reweighting between vision and somatosensation during standing. Intra-modal reweighting of vision was also observed as gains to vision decreased as visual stimulus amplitude increased. Such intra-modal and inter-modal amplitude dependent changes in gain were also observed in muscular activity. Gains of leg segment angle and muscular activity relative to the platform, on the other hand, showed only intra-modal reweighting. That is, changing platform motion amplitude altered the responses to both visual and support surface motion whereas changing visual scene motion amplitude did not significantly affect responses to support surface motion, indicating that the sensory integration scheme between somatosensation (at the support surface) and vision is asymmetric.
PMCID: PMC4069006  PMID: 24959665
16.  Influence of Feedback Parameters on Performance of a Vibrotactile Balance Prosthesis 
We investigated the influence of feedback conditions on the effectiveness of a balance prosthesis. The balance prosthesis used an array of 12 tactile vibrators (tactors) placed on the anterior and posterior surfaces of the torso to provide body orientation feedback related to several different combinations of angular position and velocity of body sway in the sagittal plane. Control tests were performed with no tactor activation. Body sway was evoked in subjects with normal sensory function by rotating the support surface upon which subjects stood with eyes closed. Body sway was analyzed by computing root-mean-square sway measures and by a frequency-response function analysis that characterized the amplitude (gain) and timing (phase) of body sway over a frequency range of 0.017 to 2.2 Hz. Root-mean-square sway measures showed a reduction of surface stimulus evoked body sway for most vibrotactile feedback settings compared to control conditions. However, frequency-response function analysis showed that the sway reduction was due primarily to a reduction in sway below about 0.5 Hz, whereas there was actually an enhancement of sway above 0.6 Hz. Finally, we created a postural model that accounted for the experimental results and gave insight into how vibrotactile information was incorporated into the postural control system.
PMCID: PMC2726898  PMID: 19497820
Balance Prosthesis; Feedback Control Model; Posture control; Sensorimotor Integration
17.  Dominant side in single-leg stance stability during floor oscillations at various frequencies 
We investigated lateral dominance in the postural stability of single-leg stance with anteroposterior floor oscillations at various frequencies.
Thirty adults maintained a single-leg stance on a force platform for 20 seconds per trial. Trials were performed with no oscillation (static condition) and with anteroposterior floor oscillations (2.5-cm amplitude) at six frequencies: 0.25, 0.5, 0.75, 1.0, 1.25 and 1.5 Hz (dynamic condition). A set of three trials was performed on each leg in each oscillation frequency in random order. The mean speed of the center of pressure in the anteroposterior direction (CoPap) was calculated as an index of postural stability, and frequency analysis of CoPap sway was performed. Footedness for carrying out mobilizing activities was assessed with a questionnaire.
CoPap speed exponentially increased as oscillation frequency increased in both legs. The frequency analysis of CoPap showed a peak <0.3 Hz at no oscillation. The frequency components at 0.25-Hz oscillation included common components with no oscillation and those at 1.5-Hz oscillation showed the maximum amplitude among all conditions. Postural stability showed no significant difference between left- and right-leg stance at no oscillation and oscillations ≤1.25 Hz, but at 1.5-Hz oscillation was significantly higher in the right-leg stance than in the left-leg stance. For the lateral dominance of postural stability at individual levels, the lateral difference in postural stability at no oscillation was positively correlated with that at 0.25-Hz oscillation (r = 0.51) and negatively correlated with that at 1.5-Hz oscillation (r = -0.53). For 70% of subjects, the dominant side of postural stability was different at no oscillation and 1.5-Hz oscillation. In the subjects with left- or right-side dominance at no oscillation, 94% or 38% changed their dominant side at 1.5-Hz oscillation, with a significant difference between these percentages. In the 1.5-Hz oscillation, 73% of subjects had concordance between the dominant side of postural stability and that of mobilizing footedness.
In static conditions, there was no lateral dominance of stability during single-leg stance. At 1.5-Hz oscillation, the highest frequency, right-side dominance of postural stability was recognized. Functional role in supporting leg may be divided between left and right legs according to the change of balance condition from static to dynamic.
PMCID: PMC4146446  PMID: 25127541
Dynamic balance; Lateral dominance; Single-leg stance; Static balance
18.  Head sway response to optic flow: effect of age is more important than the presence of unilateral vestibular hypofunction 
The purpose of this study was to examine how older adults with vestibular impairment use sensory feedback for postural control.
Nine older adult subjects with unilateral vestibular hypofunction (UVH, mean age 69 y) and 14 older (mean age 70 y) and 8 young adult controls (CON, mean age 28 y) viewed full-field optic flow scenes while standing on a fixed or sway-referenced support surface. The subjects with UVH had 100% caloric asymmetry. Optic flow consisted of sinusoidal anterior-posterior movement of the visual surround at three frequencies and three amplitudes of stimulation. The anterior-posterior head sway was measured. The number of head sway responses that were coupled to the optic flow and magnitude of head sway during optic flow relative to during quiet stance on fixed floor was quantified.
The number of trials in which the head sway response was significantly coupled to the optic flow was significantly greater in the Older UVH and Older CON subjects compared with the Young CON subjects. Furthermore, the magnitude of head sway was two to three times greater in Older UVH and CON compared with Young CON subjects. There was no difference in coupling or magnitude of head sway between Older UVH and Older CON subjects. The amplitude of sway was also dependent on the amount of surface support, stimulus frequency, and stimulus amplitude.
Older adults with unilateral vestibular hypofunction who are able to effectively compensate show no difference in postural responses elicited by optic flow compared with age-matched controls.
PMCID: PMC4166515  PMID: 17312341
balance; vision; posture; optic flow
19.  Contribution of vision to postural behaviors during continuous support-surface translations 
Experimental brain research  2013;232(1):169-180.
During standing balance, kinematics of postural behaviors have been previously observed to change across visual conditions, perturbation amplitudes, or perturbation frequencies. However, experimental limitations only allowed for independent investigation of such parameters. Here, we adapted a pseudorandom ternary sequence (PRTS) perturbation previously used in rotational support-surface perturbations (Peterka 2002) to a translational paradigm, allowing us to concurrently examine the effects of vision, perturbation amplitude, and frequency on balance control. Additionally, the unpredictable PRTS perturbation eliminated effects of feedforward adaptations typical of responses to sinusoidal stimuli. The PRTS perturbation contained a wide spectral bandwidth (0.08-3.67 Hz) and was scaled to 4 different peak-to-peak amplitudes (3-24 cm). Root-mean-square (RMS) of hip displacement and velocity increased relative to RMS ankle displacement and velocity in the absence of vision across all subjects, especially at higher perturbation amplitudes. Gain and phase lag of CoM sway relative to the perturbation also increased with perturbation frequency; phase lag further increased when vision was absent. Together, our results suggest that visual input, perturbation amplitude, and perturbation frequency can concurrently and independently modulate postural strategies during standing balance. Moreover, each factor contributes to the difficulty of maintaining postural stability; increased difficulty evokes a greater reliance on hip motion. Finally, despite high degrees of joint angle variation across subjects, CoM measures were relatively similar across subjects, suggesting that the CoM is an important controlled variable for balance.
PMCID: PMC4065169  PMID: 24132526
Balance; posture; kinematics; kinetics; perturbation response
20.  Nonvisual Complex Spike Signals in the Rabbit Cerebellar Flocculus 
The Journal of Neuroscience  2014;34(9):3218-3230.
In addition to the well-known signals of retinal image slip, floccular complex spikes (CSs) also convey nonvisual signals. We recorded eye movement and CS activity from Purkinje cells in awake rabbits sinusoidally oscillated in the dark on a vestibular turntable. The stimulus frequency ranged from 0.2 to 1.2 Hz, and the velocity amplitude ranged from 6.3 to 50°/s. The average CS modulation was evaluated at each combination of stimulus frequency and amplitude. More than 75% of the Purkinje cells carried nonvisual CS signals. The amplitude of this modulation remained relatively constant over the entire stimulus range. The phase response of the CS modulation in the dark was opposite to that during the vestibulo-ocular reflex (VOR) in the light. With increased frequency, the phase response systematically shifted from being aligned with contraversive head velocity toward peak contralateral head position. At fixed frequency, the phase response was dependent on peak head velocity, indicating a system nonlinearity. The nonvisual CS modulation apparently reflects a competition between eye movement and vestibular signals, resulting in an eye movement error signal inferred from nonvisual sources. The combination of this error signal with the retinal slip signal in the inferior olive results in a net error signal reporting the discrepancy between the actual visually measured eye movement error and the inferred eye movement error derived from measures of the internal state. The presence of two error signals requires that the role of CSs in models of the floccular control of VOR adaption be expanded beyond retinal slip.
PMCID: PMC3935084  PMID: 24573280
accessory optic system; climbing fiber; complex spike; inferior olive; prepositus hypoglossi; Purkinje cell
21.  Theoretical foundations of the sound analog membrane potential that underlies coincidence detection in the barn owl 
A wide variety of neurons encode temporal information via phase-locked spikes. In the avian auditory brainstem, neurons in the cochlear nucleus magnocellularis (NM) send phase-locked synaptic inputs to coincidence detector neurons in the nucleus laminaris (NL) that mediate sound localization. Previous modeling studies suggested that converging phase-locked synaptic inputs may give rise to a periodic oscillation in the membrane potential of their target neuron. Recent physiological recordings in vivo revealed that owl NL neurons changed their spike rates almost linearly with the amplitude of this oscillatory potential. The oscillatory potential was termed the sound analog potential, because of its resemblance to the waveform of the stimulus tone. The amplitude of the sound analog potential recorded in NL varied systematically with the interaural time difference (ITD), which is one of the most important cues for sound localization. In order to investigate the mechanisms underlying ITD computation in the NM-NL circuit, we provide detailed theoretical descriptions of how phase-locked inputs form oscillating membrane potentials. We derive analytical expressions that relate presynaptic, synaptic, and postsynaptic factors to the signal and noise components of the oscillation in both the synaptic conductance and the membrane potential. Numerical simulations demonstrate the validity of the theoretical formulations for the entire frequency ranges tested (1–8 kHz) and potential effects of higher harmonics on NL neurons with low best frequencies (<2 kHz).
PMCID: PMC3821005  PMID: 24265616
phase-locking; sound localization; auditory brainstem; periodic signals; oscillation; owl
22.  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
23.  Practice-related improvements in posture control differ between young and older adults exposed to continuous, variable amplitude oscillations of the support surface 
Healthy older adults were repeatedly exposed to continuous, variable amplitude oscillations of the support surface to determine 1) whether age affects the capacity for postural motor learning under continuous perturbation conditions with limited predictability and 2) whether practice leads to modifications in the control strategy used to maintain balance in older adults. During training, a translating platform underwent 45-second trials of constant frequency (0.5 Hz) and seemingly random amplitude oscillations (range ± 2 to 15 cm). The middle 15 seconds of each trial contained the same sequence of oscillation amplitudes. This repeated middle segment was used for analyses because young adults in Van Ooteghem et al (2008) experienced the same segment, allowing group comparisons to be made in the present study. To examine learning, participants performed a retention test following a 24-hour delay. Kinematic data were used to derive spatial and temporal measures of whole body centre of mass (COM), trunk, thigh, and shank segment orientation, and ankle and knee angle from performance during the repeated middle segment. Results showed that with training, older adults maintained the capacity to learn adaptive postural responses in the form of improved temporal control of the COM and minimization of trunk instability at a rate comparable to young adults. With practice however, older adults maintained a more rigid, ‘platform-fixed’ control strategy which differed from young adults who shifted toward ‘gravity-fixed’ control that minimized their COM motion. This study provides important insight into the ability of older adults to demonstrate longer-term improvements in postural regulation.
PMCID: PMC2855625  PMID: 19756552
aging; balance control; platform translation; learning; continuous perturbation; postural coordination
24.  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
25.  Age-Related Changes in the Relationship Between Auditory Brainstem Responses and Envelope-Following Responses 
Hearing thresholds and wave amplitudes measured using auditory brainstem responses (ABRs) to brief sounds are the predominantly used clinical measures to objectively assess auditory function. However, frequency-following responses (FFRs) to tonal carriers and to the modulation envelope (envelope-following responses or EFRs) to longer and spectro-temporally modulated stimuli are rapidly gaining prominence as a measure of complex sound processing in the brainstem and midbrain. In spite of numerous studies reporting changes in hearing thresholds, ABR wave amplitudes, and the FFRs and EFRs under neurodegenerative conditions, including aging, the relationships between these metrics are not clearly understood. In this study, the relationships between ABR thresholds, ABR wave amplitudes, and EFRs are explored in a rodent model of aging. ABRs to broadband click stimuli and EFRs to sinusoidally amplitude-modulated noise carriers were measured in young (3–6 months) and aged (22–25 months) Fischer-344 rats. ABR thresholds and amplitudes of the different waves as well as phase-locking amplitudes of EFRs were calculated. Age-related differences were observed in all these measures, primarily as increases in ABR thresholds and decreases in ABR wave amplitudes and EFR phase-locking capacity. There were no observed correlations between the ABR thresholds and the ABR wave amplitudes. Significant correlations between the EFR amplitudes and ABR wave amplitudes were observed across a range of modulation frequencies in the young. However, no such significant correlations were found in the aged. The aged click ABR amplitudes were found to be lower than would be predicted using a linear regression model of the young, suggesting altered gain mechanisms in the relationship between ABRs and FFRs with age. These results suggest that ABR thresholds, ABR wave amplitudes, and EFRs measure complementary aspects of overlapping neurophysiological processes and the relationships between these measurements changes asymmetrically with age. Hence, measuring all three metrics provides a more complete assessment of auditory function, especially under pathological conditions like aging.
PMCID: PMC4141432  PMID: 24845405
frequency-following response; colliculus; aging; brainstem; auditory; ASSR; AMFR; inhibition; central gain; synaptopathy; neuropathy; evoked potential

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