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1.  Saccadic Burst Cell Membrane Dysfunction Is Responsible for Saccadic Oscillations 
Saccadic oscillations threaten clear vision by causing image motion on the retina. They are either purely horizontal (ocular flutter) or multidimensional (opsoclonus). We propose that ion channel dysfunction in the burst cell membrane is the underlying abnormality. We have tested this hypothesis by simulating a neuromimetic computational model of the burst neurons. This biologically realistic model mimics the physiologic properties and anatomic connections in the brainstem saccade generator. A rebound firing after sustained inhibition, called post-inhibitory rebound (PIR), and reciprocal inhibition between premotor saccadic burst neurons are the key features of this conceptual scheme. PIR and reciprocal inhibition make the circuits that generate the saccadic burst inherently unstable and can lead to oscillations unless stabilized by external inhibition. Our simulations suggest that alterations in membrane properties that lead to an increase in PIR, a reduction in external glycinergic inhibition, or both can cause saccadic oscillations.
doi:10.1097/WNO.0b013e31818eb3a5
PMCID: PMC2752370  PMID: 19145136
2.  Sustained eye closure slows saccades 
Vision research  2010;50(17):1665-1675.
Saccadic eye movements rapidly orient the line of sight towards the object of interest. Pre-motor burst neurons (BNs) controlling saccades receive excitation from superior colliculus and cerebellum, but inhibition by omnipause neurons (OPNs) prevents saccades. When the OPNs pause, BNs begin to fire. It has been presumed that part of the BN burst comes from post-inhibitory rebound (PIR). We hypothesized that in the absence of prior inhibition from OPNs there would be no PIR, and thus the increase in initial firing rate of BNs would be reduced. Consequently, saccade acceleration would be reduced. We measured eye movements and showed that sustained eye closure, which inhibits the activity of OPNs and thus hypothetically should weaken PIR, reduced the peak velocity, acceleration, and deceleration of saccades in healthy human subjects. Saccades under closed eyelids also had irregular trajectories; the frequency of the oscillations underlying this irregularity was similar to that of high-frequency ocular flutter (back-to-back saccades) often seen in normal subjects during attempted fixation at straight ahead while eyes are closed. Saccades and quick phases of nystagmus are generated by the same pre-motor neurons, and we found that the quick-phase velocity of nystagmus was also reduced by lid closure. These changes were not due to a mechanical hindrance to the eyes, because lid closure did not affect the peak velocities or accelerations of the eyes in the “slow-phase” response to rapid head movements of comparable speeds to those of saccades. These results indicate a role for OPNs in generating the abrupt onset and high velocities of saccades. We hypothesize that the mechanism involved is PIR in pre-motor burst neurons.
doi:10.1016/j.visres.2010.05.019
PMCID: PMC2929924  PMID: 20573593
Omnipause neurons; Burst neurons; Oscillations; Ballistic movement; Post-inhibitory rebound
3.  Hypothetical membrane mechanisms in essential tremor 
Background
Essential tremor (ET) is the most common movement disorder and its pathophysiology is unknown. We hypothesize that increased membrane excitability in motor circuits has a key role in the pathogenesis of ET. Specifically, we propose that neural circuits controlling ballistic movements are inherently unstable due to their underlying reciprocal innervation. Such instability is enhanced by increased neural membrane excitability and the circuit begins to oscillate. These oscillations manifest as tremor.
Methods
Postural limb tremor was recorded in 22 ET patients and then the phenotype was simulated with a conductance-based neuromimetic model of ballistic movements. The model neuron was Hodgkin-Huxley type with added hyperpolarization activated cation current (Ih), low threshold calcium current (IT), and GABA and glycine mediated chloride currents. The neurons also featured the neurophysiological property of rebound excitation after release from sustained inhibition (post-inhibitory rebound). The model featured a reciprocally innervated circuit of neurons that project to agonist and antagonist muscle pairs.
Results
Neural excitability was modulated by changing Ih and/or IT. Increasing Ih and/or IT further depolarized the membrane and thus increased excitability. The characteristics of the tremor from all ET patients were simulated when Ih was increased to ~10× the range of physiological values. In contrast, increasing other membrane conductances, while keeping Ih at a physiological value, did not simulate the tremor. Increases in Ih and IT determined the frequency and amplitude of the simulated oscillations.
Conclusion
These simulations support the hypothesis that increased membrane excitability in potentially unstable, reciprocally innervated circuits can produce oscillations that resemble ET. Neural excitability could be increased in a number of ways. In this study membrane excitability was increased by up-regulating Ih and IT. This approach suggests new experimental and clinical ways to understand and treat common tremor disorders.
doi:10.1186/1479-5876-6-68
PMCID: PMC2613385  PMID: 18990221
4.  Interplay of Intrinsic and Synaptic Conductances in the Generation of High-Frequency Oscillations in Interneuronal Networks with Irregular Spiking 
PLoS Computational Biology  2014;10(5):e1003574.
High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.
Author Summary
Neurons in the brain engage in collective oscillations at different frequencies. Gamma and high-gamma oscillations (30–100 Hz and higher) have been associated with cognitive functions, and are altered in psychiatric disorders such as schizophrenia and autism. Our understanding of how high-frequency oscillations are orchestrated in the brain is still limited, but it is necessary for the development of effective clinical approaches to the treatment of these disorders. Some neuron types exhibit dynamical properties that can favour synchronization. The theory of weakly coupled oscillators showed how the phase response of individual neurons can predict the patterns of phase relationships that are observed at the network level. However, neurons in vivo do not behave like regular oscillators, but fire irregularly in a regime dominated by fluctuations. Hence, which intrinsic dynamical properties matter for synchronization, and in which regime, is still an open question. Here, we show how single-cell damped subthreshold oscillations enhance synchrony in interneuronal networks by introducing a depolarizing component, mediated by post-inhibitory rebound, that is correlated among neurons due to common inhibitory input.
doi:10.1371/journal.pcbi.1003574
PMCID: PMC4006709  PMID: 24784237
5.  Saccades during Attempted Fixation in Parkinsonian Disorders and Recessive Ataxia: From Microsaccades to Square-Wave Jerks 
PLoS ONE  2013;8(3):e58535.
During attempted visual fixation, saccades of a range of sizes occur. These “fixational saccades” include microsaccades, which are not apparent in regular clinical tests, and “saccadic intrusions”, predominantly horizontal saccades that interrupt accurate fixation. Square-wave jerks (SWJs), the most common type of saccadic intrusion, consist of an initial saccade away from the target followed, after a short delay, by a “return saccade” that brings the eye back onto target. SWJs are present in most human subjects, but are prominent by their increased frequency and size in certain parkinsonian disorders and in recessive, hereditary spinocerebellar ataxias. Here we asked whether fixational saccades showed distinctive features in various parkinsonian disorders and in recessive ataxia. Although some saccadic properties differed between patient groups, in all conditions larger saccades were more likely to form SWJs, and the intervals between the first and second saccade of SWJs were similar. These findings support the proposal of a common oculomotor mechanism that generates all fixational saccades, including microsaccades and SWJs. The same mechanism also explains how the return saccade in SWJs is triggered by the position error that occurs when the first saccadic component is large, both in the healthy brain and in neurological disease.
doi:10.1371/journal.pone.0058535
PMCID: PMC3596296  PMID: 23516502
6.  Oculopalatal tremor explained by a model of inferior olivary hypertrophy and cerebellar plasticity 
Brain  2010;133(3):923-940.
The inferior olivary nuclei clearly play a role in creating oculopalatal tremor, but the exact mechanism is unknown. Oculopalatal tremor develops some time after a lesion in the brain that interrupts inhibition of the inferior olive by the deep cerebellar nuclei. Over time the inferior olive gradually becomes hypertrophic and its neurons enlarge developing abnormal soma-somatic gap junctions. However, results from several experimental studies have confounded the issue because they seem inconsistent with a role for the inferior olive in oculopalatal tremor, or because they ascribe the tremor to other brain areas. Here we look at 3D binocular eye movements in 15 oculopalatal tremor patients and compare their behaviour to the output of our recent mathematical model of oculopalatal tremor. This model has two mechanisms that interact to create oculopalatal tremor: an oscillator in the inferior olive and a modulator in the cerebellum. Here we show that this dual mechanism model can reproduce the basic features of oculopalatal tremor and plausibly refute the confounding experimental results. Oscillations in all patients and simulations were aperiodic, with a complicated frequency spectrum showing dominant components from 1 to 3 Hz. The model’s synchronized inferior olive output was too small to induce noticeable ocular oscillations, requiring amplification by the cerebellar cortex. Simulations show that reducing the influence of the cerebellar cortex on the oculomotor pathway reduces the amplitude of ocular tremor, makes it more periodic and pulse-like, but leaves its frequency unchanged. Reducing the coupling among cells in the inferior olive decreases the oscillation’s amplitude until they stop (at ∼20% of full coupling strength), but does not change their frequency. The dual-mechanism model accounts for many of the properties of oculopalatal tremor. Simulations suggest that drug therapies designed to reduce electrotonic coupling within the inferior olive or reduce the disinhibition of the cerebellar cortex on the deep cerebellar nuclei could treat oculopalatal tremor. We conclude that oculopalatal tremor oscillations originate in the hypertrophic inferior olive and are amplified by learning in the cerebellum.
doi:10.1093/brain/awp323
PMCID: PMC2842510  PMID: 20080879
vestibular; gap junction; connexin; motor disorders; eye movement
7.  Local Control of Postinhibitory Rebound Spiking in CA1 Pyramidal Neuron Dendrites 
The Journal of Neuroscience  2010;30(18):6434-6442.
Postinhibitory rebound spiking is characteristic of several neuron types and brain regions, where it sustains spontaneous activity and central pattern generation. However, rebound spikes are rarely observed in the principal cells of the hippocampus under physiological conditions. We report that CA1 pyramidal neurons support rebound spikes mediated by hyperpolarization-activated inward current (Ih), and normally masked by A-type potassium channels (KA). In both experiments and computational models, KA blockage or reduction consistently resulted in a somatic action potential upon release from hyperpolarizing injections in the soma or main apical dendrite. Rebound spiking was systematically abolished by the additional blockage or reduction of Ih. Since the density of both KA and Ih increases in these cells with the distance from the soma, such “latent” mechanism may be most effective in the distal dendrites, which are targeted by a variety of GABAergic interneurons. Detailed computer simulations, validated against the experimental data, demonstrate that rebound spiking can result from activation of distal inhibitory synapses. In particular, partial KA reduction confined to one or few branches of the apical tuft may be sufficient to elicit a local spike following a train of synaptic inhibition. Moreover, the spatial extent and amount of KA reduction determines whether the dendritic spike propagates to the soma. These data suggest that the plastic regulation of KA can provide a dynamic switch to unmask postinhibitory spiking in CA1 pyramidal neurons. This newly discovered local modulation of postinhibitory spiking further increases the signal processing power of the CA1 synaptic microcircuitry.
doi:10.1523/JNEUROSCI.4066-09.2010
PMCID: PMC3319664  PMID: 20445069
8.  A Multiscale Model to Investigate Circadian Rhythmicity of Pacemaker Neurons in the Suprachiasmatic Nucleus 
PLoS Computational Biology  2010;6(3):e1000706.
The suprachiasmatic nucleus (SCN) of the hypothalamus is a multicellular system that drives daily rhythms in mammalian behavior and physiology. Although the gene regulatory network that produces daily oscillations within individual neurons is well characterized, less is known about the electrophysiology of the SCN cells and how firing rate correlates with circadian gene expression. We developed a firing rate code model to incorporate known electrophysiological properties of SCN pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels.
Author Summary
Circadian rhythms are ∼24 hour cycles in biochemical, physiological and behavioral processes observed in a diverse range of organisms including Cyanobacteria, Neurospora, Drosophila, mice and humans. In mammals, the dominant circadian pacemaker that drives daily rhythms is located in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is composed of a highly connected network of ∼20,000 neurons. Within each individual SCN neuron core clock genes and proteins interact through intertwined regulatory loops to generate circadian oscillations on the molecular level. These neurons express daily rhythmicity in their firing frequency and other electrophysiological properties. The mechanisms by which the core clock produces synchronized rhythms in neural firing and gene expression are postulated to involve intracellular calcium, a second messenger that regulates many cellular processes. The interaction between the various clock components however remains unknown. In this paper, we present a single cell model that incorporates the circadian gene regulatory pathway, cellular electrophysiological properties, and cytosolic calcium dynamics. Our results suggest a possible system architecture that accounts for the robustness of the circadian clock at the single cell level. Our simulations predict a dual role for intracellular pathways instigated by intracellular calcium and VIP: maintaining the periodicity and amplitude of the core clock genes as well as the firing frequency oscillations.
doi:10.1371/journal.pcbi.1000706
PMCID: PMC2837390  PMID: 20300645
9.  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.
doi:10.1371/journal.pgen.1004252
PMCID: PMC3974645  PMID: 24698952
10.  Pharmacological Analysis of Intrinsic Neuronal Oscillations in rd10 Retina 
PLoS ONE  2014;9(6):e99075.
In the widely used mouse model of retinal degeneration, rd1, the loss of photoreceptors leads to rhythmic electrical activity of around 10–16 Hz in the remaining retinal network. Recent studies suggest that this oscillation is formed within the electrically coupled network of AII amacrine cells and ON-bipolar cells. A second mouse model, rd10, displays a delayed onset and slower progression of degeneration, making this mouse strain a better model for human retinitis pigmentosa. In rd10, oscillations occur at a frequency of 3–7 Hz, raising the question whether oscillations have the same origin in the two mouse models. As rd10 is increasingly being used as a model to develop experimental therapies, it is important to understand the mechanisms underlying the spontaneous rhythmic activity. To study the properties of oscillations in rd10 retina we combined multi electrode recordings with pharmacological manipulation of the retinal network. Oscillations were abolished by blockers for ionotropic glutamate receptors and gap junctions. Frequency and amplitude of oscillations were modulated strongly by blockers of inhibitory receptors and to a lesser extent by blockers of HCN channels. In summary, although we found certain differences in the pharmacological modulation of rhythmic activity in rd10 compared to rd1, the overall pattern looked similar. This suggests that the generation of rhythmic activity may underlie similar mechanisms in rd1 and rd10 retina.
doi:10.1371/journal.pone.0099075
PMCID: PMC4053359  PMID: 24918437
11.  The role of H-current in regulating strength and frequency of thalamic network oscillations 
Thalamus & related systems  2001;1(2):95-103.
Intrathalamic oscillations related to sleep and epilepsy depend on interactions between synaptic mechanisms and intrinsic membrane excitability. One intrinsic conductance implicated in the genesis of thalamic oscillations is the H current – a cationic current activated by membrane hyperpolarization. Activation of H current promotes rebound excitation of thalamic relay neurons and can thus enhance recurrent network activity.
We examined the effects of H current modulation on bicuculline-enhanced network oscillations (2-4 Hz) in rat thalamic slices. The adrenergic agonist norepinephrine, a known regulator of H current, caused an alteration of the internal structure of the oscillations – they were enhanced and accelerated as the interval between bursts was shortened. The acceleration was blocked by the β-adrenergic antagonist propranolol. The β agonist isoproterenol mimicked the effect of norepinephrine on oscillation frequency and truncated the responses suggesting that a β-adrenergic upregulation of H current modifies the internal structure (frequency) of thalamic oscillations. Consistent with this, we found that H channel blockade by Cs+ or ZD7288 could decelerate the oscillations and produce more robust (longer lasting) responses. High concentrations of either Cs+ or ZD7288 blocked the oscillations.
These results indicate that a critical amount of H current is necessary for optimal intrathalamic oscillations in the delta frequency range. Up- or downregulation of H current can not only alter the oscillation frequency but also retard or promote the development of thalamic synchronous oscillations. This conclusion has important implications regarding the development of epilepsy in thalamocortical circuits.
doi:10.1016/S1472-9288(01)00009-7
PMCID: PMC2222919  PMID: 18239728
H current; ZD7288; adrenergic; pacemaking
12.  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.
doi:10.1038/msb.2010.119
PMCID: PMC3063688  PMID: 21283141
cell free; in vitro; oscillation; synthetic biology; transcriptional circuits
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.
doi:10.1371/journal.pcbi.1000551
PMCID: PMC2760751  PMID: 19876377
14.  Synchronization-Induced Rhythmicity of Circadian Oscillators in the Suprachiasmatic Nucleus 
PLoS Computational Biology  2007;3(4):e68.
The suprachiasmatic nuclei (SCN) host a robust, self-sustained circadian pacemaker that coordinates physiological rhythms with the daily changes in the environment. Neuronal clocks within the SCN form a heterogeneous network that must synchronize to maintain timekeeping activity. Coherent circadian output of the SCN tissue is established by intercellular signaling factors, such as vasointestinal polypeptide. It was recently shown that besides coordinating cells, the synchronization factors play a crucial role in the sustenance of intrinsic cellular rhythmicity. Disruption of intercellular signaling abolishes sustained rhythmicity in a majority of neurons and desynchronizes the remaining rhythmic neurons. Based on these observations, the authors propose a model for the synchronization of circadian oscillators that combines intracellular and intercellular dynamics at the single-cell level. The model is a heterogeneous network of circadian neuronal oscillators where individual oscillators are damped rather than self-sustained. The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light–dark cycles. Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated. The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.
Author Summary
Circadian rhythms, characterized by a period close to 24 h, are observed in nearly all living organisms, from cyanobacteria to plants, insects, and mammals. In mammals, the central circadian clock is located in the suprachiasmatic nucleus (SCN) of the hypothalamus, where it receives light signals from the retina. In turn, the SCN controls circadian rhythms in peripheral tissues and behavioral activity. The SCN is composed of about 20,000 neurons characterized by a small size and a high density. Within each individual neuron, clock genes and proteins compose interlocked regulatory feedback loops that generate circadian oscillations on the molecular level. SCN neurons dispersed in cell cultures display cell-autonomous oscillations, with periods ranging from 20 h to 28 h. The ventrolateral part of the SCN receives light input from the retina, serving as a relay for the dorsomedial part. Coupling and synchronization among SCN neurons are ensured by neurotransmitters. A desire to understand how such a network of heterogeneous circadian oscillators achieves a synchronous and coherent output rhythm has motivated extensive experimental and theoretical work. In this paper, we present a molecular model combining intracellular and extracellular dynamics for the SCN circadian system, and propose a novel synchronization mechanism. Our results predict a dual role for the coupling factors within the SCN, both in maintaining the rhythmicity and in promoting the synchronization between the circadian oscillators.
doi:10.1371/journal.pcbi.0030068
PMCID: PMC1851983  PMID: 17432930
15.  Ocular-Motor Profile and Effects of Memantine in a Familial Form of Adult Cerebellar Ataxia with Slow Saccades and Square Wave Saccadic Intrusions 
PLoS ONE  2013;8(7):e69522.
Fixation instability due to saccadic intrusions is a feature of autosomal recessive spinocerebellar ataxias, and includes square wave intrusions (SWI) and macrosaccadic oscillations (MSO). A recent report suggested that the non-competitive antagonist of NMDA receptors, memantine, could decrease MSO and improve fixation in patients with spinocerebellar ataxia with saccadic intrusions (SCASI). We similarly tested two sisters, respectively of 58 and 60 years, with an unrecognized form of recessive, adult-onset cerebellar ataxia, peripheral neuropathy and slow saccades, who showed prominent SWI and also complained with difficulty in reading. We tested horizontal visually guided saccades (10°–18°) and three minutes of steady fixation in each patient and in thirty healthy controls. Both patients showed a significant reduction of peak and mean velocity compared with control subjects. Large SWI interrupting steady fixation were prominent during steady fixation and especially following visually guided saccades. Eye movements were recorded before and during the treatment with memantine, 20 mg/daily for 6 months. The treatment with memantine reduced both the magnitude and frequency of SWI (the former significantly), but did not modified neurological conditions or saccade parameters. Thus, our report suggests that memantine may have some general suppressive effect on saccadic intrusions, including both SWI and MSO, thereby restoring the capacity of reading and visual attention in these and in other recessive forms of ataxia, including Friedreich’s, in which saccadic intrusions are prominent.
doi:10.1371/journal.pone.0069522
PMCID: PMC3718679  PMID: 23894498
16.  Optimal Control of Saccades by Spatial-Temporal Activity Patterns in the Monkey Superior Colliculus 
PLoS Computational Biology  2012;8(5):e1002508.
A major challenge in computational neurobiology is to understand how populations of noisy, broadly-tuned neurons produce accurate goal-directed actions such as saccades. Saccades are high-velocity eye movements that have stereotyped, nonlinear kinematics; their duration increases with amplitude, while peak eye-velocity saturates for large saccades. Recent theories suggest that these characteristics reflect a deliberate strategy that optimizes a speed-accuracy tradeoff in the presence of signal-dependent noise in the neural control signals. Here we argue that the midbrain superior colliculus (SC), a key sensorimotor interface that contains a topographically-organized map of saccade vectors, is in an ideal position to implement such an optimization principle. Most models attribute the nonlinear saccade kinematics to saturation in the brainstem pulse generator downstream from the SC. However, there is little data to support this assumption. We now present new neurophysiological evidence for an alternative scheme, which proposes that these properties reside in the spatial-temporal dynamics of SC activity. As predicted by this scheme, we found a remarkably systematic organization in the burst properties of saccade-related neurons along the rostral-to-caudal (i.e., amplitude-coding) dimension of the SC motor map: peak firing-rates systematically decrease for cells encoding larger saccades, while burst durations and skewness increase, suggesting that this spatial gradient underlies the increase in duration and skewness of the eye velocity profiles with amplitude. We also show that all neurons in the recruited population synchronize their burst profiles, indicating that the burst-timing of each cell is determined by the planned saccade vector in which it participates, rather than by its anatomical location. Together with the observation that saccade-related SC cells indeed show signal-dependent noise, this precisely tuned organization of SC burst activity strongly supports the notion of an optimal motor-control principle embedded in the SC motor map as it fully accounts for the straight trajectories and kinematic nonlinearity of saccades.
Author Summary
As the fovea is the only spot on the retina with high spatial resolution, primates need to move their eyes to peripheral targets for detailed inspection. Saccades are the fastest movements of the body, and theoretical studies suggest that their trajectories are optimized to bring the fovea as fast and accurately as possible on target. Speed-accuracy optimization principles explain the stereotyped nonlinear ‘main-sequence’ relationship between saccade amplitude, duration, and peak velocity. Earlier models attributed these kinematic properties to nonlinear neural circuitry in the brainstem but this creates problems for oblique saccades. Here, we demonstrate how the brainstem can be linear, and how instead the midbrain superior colliculus (SC) could optimize saccadic speed-accuracy tradeoff. Each saccade involves the recruitment of a large population of SC neurons. We show that peak firing-rate and burst shape of the recruited cells systematically vary with their location in the SC, and that burst shapes nicely match the eye-velocity profiles. This organization of burst properties fully explains the main-sequence. Moreover, all cells synchronize their bursts, thus maximizing the total instantaneous input to the brainstem, and ensuring that oblique saccades have straight trajectories. We thus discovered a sophisticated neural mechanism underlying optimal motor control in the brain.
doi:10.1371/journal.pcbi.1002508
PMCID: PMC3355059  PMID: 22615548
17.  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.
doi:10.1038/msb.2010.92
PMCID: PMC3010105  PMID: 21119632
circadian clock; coupling; entrainment; mathematical modeling; oscillator
18.  Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops 
BMC Research Notes  2012;5:287.
Background
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.
Results
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.
Conclusion
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.
doi:10.1186/1756-0500-5-287
PMCID: PMC3532088  PMID: 22694947
19.  External Drive to Inhibitory Cells Induces Alternating Episodes of High- and Low-Amplitude Oscillations 
PLoS Computational Biology  2012;8(8):e1002666.
Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with episodes of low amplitude. Despite the widespread occurrence of amplitude fluctuations in many frequency bands and brain regions, the mechanisms by which they are generated are poorly understood. Here, we show that irregular transitions between sub-second episodes of high- and low-amplitude oscillations in the alpha/beta frequency band occur in a generic neuronal network model consisting of interconnected inhibitory and excitatory cells that are externally driven by sustained cholinergic input and trains of action potentials that activate excitatory synapses. In the model, we identify the action potential drive onto inhibitory cells, which represents input from other brain areas and is shown to desynchronize network activity, to be crucial for the emergence of amplitude fluctuations. We show that the duration distributions of high-amplitude episodes in the model match those observed in rat prefrontal cortex for oscillations induced by the cholinergic agonist carbachol. Furthermore, the mean duration of high-amplitude episodes varies in a bell-shaped manner with carbachol concentration, just as in mouse hippocampus. Our results suggest that amplitude fluctuations are a general property of oscillatory neuronal networks that can arise through background input from areas external to the network.
Author Summary
Rhythmic changes in electrical activity are observed throughout the brain, and arise as a result of reciprocal interactions between excitatory and inhibitory neurons. Synchronized activity of a large number of neurons gives rise to macroscopic oscillations in electrical activity, which can be measured in EEG recordings and are thought to have a key role in learning and memory. Interestingly, the amplitude of ongoing oscillations fluctuates irregularly, with high-amplitude episodes alternating with low-amplitude episodes. Although these amplitude fluctuations occur in many brain regions, the mechanisms by which they are generated are still poorly known. To get insight into potential mechanisms, we investigated whether such fluctuations occur in a computational model of a neuronal network. We show that the model generates amplitude fluctuations that are similar to those observed in experimental data and that external input from other brain areas to the inhibitory cells of the network is essential for their generation. This input can disrupt the synchrony of activity, causing transitions between episodes of high synchrony (high oscillation amplitudes) and episodes of low synchrony (low oscillation amplitudes). Episodes of high synchrony are relevant for brain function because they provide favorable conditions for learning.
doi:10.1371/journal.pcbi.1002666
PMCID: PMC3431298  PMID: 22956901
20.  Distinctive Features of Saccadic Intrusions and Microsaccades in Progressive Supranuclear Palsy 
The eyes do not stay perfectly still during attempted fixation; fixational eye movements and saccadic intrusions (SIs) continuously change the position of gaze. The most common type of SI, square-wave jerk (SWJ), consists of saccade pairs that appear purely horizontal on clinical inspection: the first saccade moves the eye away from the fixation target and, after a short interval, the second saccade brings it back towards the target. SWJs are prevalent in certain neurological disorders, including progressive supranuclear palsy (PSP). Here we developed an objective method to identify SWJs. We found that SWJs are more frequent, larger and more markedly horizontal in PSP patients than in healthy human subjects. Further, the loss of a vertical component in fixational saccades and SWJs was the eye movement feature that best distinguished PSP patients from controls. We moreover determined that in PSP patients and controls, the larger the saccade the more likely it was part of a SWJ. Further, saccades produced by PSP patients had equivalent properties whether they were part of a SWJ or not, suggesting that normal fixational saccades (microsaccades) are rare in PSP. We propose that fixational saccades and SIs are generated by the same neural circuit, and that, both in PSP patients and in controls, SWJs result from a coupling mechanism that generates a second corrective saccade shortly after a large fixation saccade. Due to brainstem and/or cerebellum impairment, fixational saccades in PSP are abnormally large, and thus more likely to trigger a corrective saccade, giving rise to SWJs.
doi:10.1523/JNEUROSCI.2600-10.2011
PMCID: PMC3111217  PMID: 21430139
Fixational eye movements; microsaccades; saccadic palsy; square wave jerks; parkinsonian disorders
21.  Teaching Basic Principles of Neuroscience with Computer Simulations 
It is generally believed that students learn best through activities that require their direct participation. By using simulations as a tool for learning neuroscience, students are directly engaged in the activity and obtain immediate feedback and reinforcement. This paper describes a series of biophysical models and computer simulations that can be used by educators and students to explore a variety of basic principles in neuroscience. The paper also suggests ‘virtual laboratory’ exercises that students may conduct to further examine biophysical processes underlying neural function. First, the Hodgkin and Huxley (HH) model is presented. The HH model is used to illustrate the action potential, threshold phenomena, and nonlinear dynamical properties of neurons (e.g., oscillations, postinhibitory rebound excitation). Second, the Morris-Lecar (ML) model is presented. The ML model is used to develop a model of a bursting neuron and to illustrate modulation of neuronal activity by intracellular ions. Lastly, principles of synaptic transmission are presented in small neural networks, which illustrate oscillatory behavior, excitatory and inhibitory postsynaptic potentials, and temporal summation.
PMCID: PMC3592631  PMID: 23493644
undergraduate; graduate; neurons; synapses; neural networks; modeling; SNNAP; Hodgkin-Huxley
22.  Spatiotemporal characteristics and pharmacological modulation of multiple gamma oscillations in the CA1 region of the hippocampus 
Multiple components of “γ-oscillations” between 30–170 Hz in the CA1 region of the hippocampus have been described, based on their coherence with oscillations in other brain regions and on their cross-frequency coupling with local θ-oscillations. However, it remains unclear whether the different sub-bands are generated by a single broadband oscillator coupled to multiple external inputs, or by separate oscillators that incorporate distinct circuit elements. To distinguish between these possibilities, we used high-density linear array recording electrodes in awake behaving mice to examine the spatiotemporal characteristics of γ-oscillations and their responses to midazolam and atropine. We characterized oscillations using current source density (CSD) analysis, and measured θ-γ phase-amplitude coupling by cross frequency coupling (CFC) analysis. Prominent peaks were present in the CSD signal in the mid- and distal apical dendritic layers at all frequencies, and at stratum pyramidale for γslow (30–45 Hz) and γmid (50–90 Hz), but not γfast (90–170 Hz) oscillations. Differences in the strength and timing of θ-γslow and θ-γmid cross frequency coupling, and a lack of coupling at the soma and mid-apical region for γfast oscillations, indicated that separate circuit components generate the three sub-bands. Midazolam altered CSD amplitudes and cross-frequency coupling in a lamina- and frequency specific manner, providing further evidence for separate generator circuits. Atropine altered CSD amplitudes and θ-γ CFC uniformly at all locations. Simulations using a detailed compartmental model were consistent with γslow and γmid oscillations driven primarily by inputs at the mid-apical dendrites, and γfast at the distal apical dendrite. Our results indicate that multiple distinct local circuits generate γ-oscillations in the CA1 region of the hippocampus, and provide detailed information about their spatiotemporal characteristics.
doi:10.3389/fncir.2014.00150
PMCID: PMC4290596  PMID: 25628540
current source density analysis; cross frequency coupling; midazolam; atropine; theta oscillations; gamma oscillations; compartmental modeling
23.  Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency 
Network oscillations typically span a limited range of frequency. In pacemaker-driven networks, including many Central Pattern Generators (CPGs), this frequency range is determined by the properties of bursting pacemaker neurons and their synaptic connections; thus, factors that affect the burst frequency of pacemaker neurons should play a role in determining the network frequency. We examine the role of membrane resonance of pacemaker neurons on the network frequency in the crab pyloric CPG. The pyloric oscillations (freq ~1 Hz) are generated by a group of pacemaker neurons: the Anterior Burster (AB) and the Pyloric Dilator (PD). We examine the impedance profiles of the AB and PD neurons in response to sinusoidal current injections with varying frequency and find that both neuron types exhibit membrane resonance, i.e. demonstrate maximal impedance at a given preferred frequency. The membrane resonance frequencies of the AB and PD neurons fall within the range of the pyloric network oscillation frequency. Experiments with pharmacological blockers and computational modeling show that both calcium currents ICa and the hyperpolarization-activated inward current Ih, are important in producing the membrane resonance in these neurons. We then demonstrate that both the membrane resonance frequency of the PD neuron and its supra-threshold bursting frequency can be shifted in the same direction by either DC current injection or by using the dynamic clamp technique to inject artificial conductances for Ih or ICa. Together, these results suggest that membrane resonance of pacemaker neurons can be strongly correlated with the CPG oscillation frequency.
doi:10.1523/JNEUROSCI.0545-09.2009
PMCID: PMC2716082  PMID: 19458214
Oscillation; central pattern generator; resonance; stomatogastric; model; Ih
24.  Changes in control of saccades during gain adaptation 
In a typical short-term saccadic adaptation protocol, the target moves intra-saccadically either toward (gain-down) or away (gain-up) from initial fixation, causing the saccade to complete with an endpoint error. A central question is how the motor system adapts in response to this error: are the motor commands changed to bring the eyes to a different goal, akin to a remapping of the target, or is adaptation focused on the processes that monitor the ongoing motor commands and correct them midflight, akin to changes that act via internal feedback? Here, we found that in the gain-down paradigm, the brain learned to produce a smaller amplitude saccade by altering the saccade's trajectory. The adapted saccades had reduced peak velocities, reduced accelerations, shallower decelerations, and increased durations compared to a control saccade of equal amplitude. These changes were consistent with a change in an internal feedback that acted as a forward model. On the other hand, in the gain-up paradigm the brain learned to produce a larger amplitude saccade with trajectories that were identical to those of control saccades of equal amplitude. Therefore, whereas the gain-down paradigm appeared to induce adaptation via an internal feedback that controlled saccades midflight, gain-up induced adaptation primarily via target remapping. Our simulations explained that for each condition, the specific adaptation produced a saccade that brought the eyes to the target with the smallest motor costs.
doi:10.1523/JNEUROSCI.3470-08.2008
PMCID: PMC2632981  PMID: 19091981
Saccade adaptation; saccade kinematics; forward models; optimal control; computational neuroscience; Sensorimotor
25.  Tremorgenesis: a new conceptual scheme using reciprocally innervated circuit of neurons 
Neural circuits controlling fast movements are inherently unsteady as a result of their reciprocal innervation. This instability is enhanced by increased membrane excitability. Recent studies indicate that the loss of external inhibition is an important factor in the pathogenesis of several tremor disorders such as essential tremor, cerebellar kinetic tremor or parkinsonian tremor. Shaikh and colleagues propose a new conceptual scheme to analyze tremor disorders. Oscillations are simulated by changing the intrinsic membrane properties of burst neurons. The authors use a model neuron of Hodgkin-Huxley type with added hyperpolarization activated cation current (Ih), low threshold calcium current (It), and GABA/glycine mediated chloride currents. Post-inhibitory rebound is taken into account. The model includes a reciprocally innervated circuit of neurons projecting to pairs of agonist and antagonist muscles. A set of four burst neurons has been simulated: inhibitory agonist, inhibitory antagonist, excitatory agonist, and excitatory antagonist. The model fits well with the known anatomical organization of neural circuits for limb movements in premotor/motor areas, and, interestingly, this model does not require any structural modification in the anatomical organization or connectivity of the constituent neurons. The authors simulate essential tremor when Ih is increased. Membrane excitability is augmented by up-regulating Ih and It. A high level of congruence with the recordings made in patients exhibiting essential tremor is reached. These simulations support the hypothesis that increased membrane excitability in potentially unsteady circuits generate oscillations mimicking tremor disorders encountered in daily practice. This new approach opens new perspectives for both the understanding and the treatment of neurological tremor. It provides the rationale for decreasing membrane excitability by acting on a normal ion channel in a context of impaired external inhibition.
doi:10.1186/1479-5876-6-71
PMCID: PMC2607264  PMID: 19036142

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