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Knowledge of intrinsic neuronal firing dynamics is a critical first step to establishing an accurate biophysical model of any neuron. In this study we examined cerebellar Purkinje cells to determine the bifurcations likely to underlie firing dynamics within a biophysically realistic and experimentally supported model. We show that Purkinje cell dynamics are consistent with a system undergoing a saddle-node bifurcation of fixed points in the transition from rest to firing and a saddle homoclinic bifurcation from firing to rest. Our analyses account for numerous observed Purkinje cell firing properties that include bistability, plateau potentials, specific aspects of the frequency–current (F–I) relationship, first spike latency, and the ability for climbing fiber input to induce state transitions in the bistable regime. We also experimentally confirm new properties predicted from our model and analysis that include the presence of a depolarizing afterpotential (DAP), the ability to fire at low frequencies (<50 Hz) and with a high gain in the F–I relationship, and a bistable region limited to low-frequency firing. Purkinje cell dynamics, including bistability, prove to arise from numerous biophysical factors that include the DAP, fast refractory dynamics, and a long membrane time constant. A hyperpolarizing activated cation current (IH) is shown not to be directly involved in establishing bistable dynamics but rather reduces the range for bistability. A combined electrophysiological and modeling approach thus accounts for several properties of Purkinje cells, providing a firm basis from which to assess Purkinje cell output patterns.
It has become clear that identifying the intrinsic dynamics of neurons is a critical step in the process of understanding network behavior, synaptic integration, and information processing in the brain (Izhikevich 2000, 2007; Izhikevich et al. 2003; Rinzel and Ermentrout 1998). Consequently, gaining a biophysical and dynamical systems perspective of intrinsic neuronal firing behavior is important. From both an electrophysiological and dynamical systems perspective cerebellar Purkinje cells possess complex intrinsic firing behaviors, which include bistability, hysteresis, and plateau potentials (Hounsgaard and Midtgaard 1988; Llinas and Sugimori 1980b; Loewenstein et al. 2005). Given that Purkinje cells integrate numerous synaptic inputs and are the sole output of the cerebellar cortex, an understanding of intrinsic Purkinje cell dynamics is critical to comprehending cerebellar function.
Previous work in vitro has identified numerous intrinsic electrophysiological behaviors of Purkinje cells that are conserved across different species (Hounsgaard and Midtgaard 1988; Llinas and Sugimori 1980a,b; Loewenstein et al. 2005; Williams et al. 2002). Properties that have received particular attention are bistability and the generation of plateau potentials. Recent work has shown that intrinsic membrane bistability allows climbing fiber (CF) input to transition the cell between a rest and firing state (Loewenstein et al. 2005; McKay et al. 2007; Williams et al. 2002). Central to this are plateau potentials that allow an excitatory stimulus to generate a depolarization that outlasts the original stimulus (Llinas and Sugimori 1980a). Other characteristic features of Purkinje cells are a linear frequency–current (F–I) relationship with a minimum firing frequency between 40 and 70 Hz and the ability to sustain tonic firing frequencies in excess of 150 Hz (Khaliq et al. 2003; Llinas and Sugimori 1980b; Martina et al. 2003; McKay and Turner 2004, 2005; Williams et al. 2002). Electrophysiological studies have identified many of the ion conductances that contribute to these different aspects of Purkinje cell output (Hounsgaard and Midtgaard 1988; Llinas and Sugimori 1980a,b; Raman and Bean 1999a,b).
Previous modeling studies in Purkinje cells have emphasized how the distribution of ion channels or morphological features of the dendritic tree shape synaptic integration (De Schutter and Bower 1994a,b; Santamaria and Bower 2005; Santamaria et al. 2002) or spike backpropagation (Vetter et al. 2001), or were used to explain a specific property of Purkinje cell firing (Genet and Delord 2002; Khaliq et al. 2003; Loewenstein et al. 2005). We sought a more general firing model based on an understanding from dynamical systems theory that could account for as many properties of Purkinje cells as possible within a realistic biophysical framework. Using a combined electrophysiological, modeling, and dynamical systems analysis we show that Purkinje cell firing dynamics are consistent with a system undergoing a saddle-node bifurcation in the transition from rest to firing and a saddle homoclinic bifurcation from firing to rest [for a review of these concepts and bifurcation theory as applied to intrinsic neuronal biophysics see Izhikevich (2007) or Rinzel and Ermentrout (1998)]. Within this framework we illustrate that numerous aspects of Purkinje cell firing are fundamentally related to the underlying bifurcation structure and further reveal previously unrecognized firing properties of these neurons.
Animal care
Sprague–Dawley rats [postnatal day 17 to 25] were obtained from Charles River Laboratories (Quebec, Canada) and procedures were conducted according to guidelines approved by the local Animal Care Committee and the Canadian Council for Animal Care.
All chemicals were obtained from Sigma (St. Louis, MO) unless otherwise noted. Whole cell current and voltage-clamp recordings were obtained using a 700A amplifier (Axon Instruments) and data collected with pCLAMP 8.1 software (Axon Instruments). Tissue slices of cerebellum were prepared as detailed in McKay and Turner (2005). Briefly, artificial cerebrospinal fluid (aCSF) was composed of (in mM): NaCl (125), KCl (3.25), CaCl2 (1.5), MgCl2 (1.5), NaHCO3 (25), and d-glucose (25) preoxygenated by carbogen (95% O2-5% CO2) gas. Rats were anesthetized with sodium pentobarbital (MTC Pharmaceuticals, Cambridge, Ontario, Canada). Parasagittal tissue slices (300-μm thickness) were cut and subsequently transferred to the recording chamber of a Zeiss Axioskop FS-2 microscope and maintained at 34°C as a submerged preparation. Neurons were visualized using differential interference contrast optics and infrared light transmission (DIC-IR). All current-clamp recordings were carried out in synaptic blockers that were bath applied after obtaining the initial seal: picrotoxin (50 μM; Tocris Cookson, Ellisville, MO) for γ-aminobutyric acid type A (GABAA) receptors, dl-2-amino-5-phosphonopentanoic acid (d-AP5, 25 μM; Tocris Cookson) for N-methyl-d-aspartate receptors, 6,7-dinitroquinoxolinedione (DNQX, 10 μM; Tocris Cookson) for α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors, and (2S)-3-[[(1S)-1-(3,4-dichlorophenyl)ethyl]amino-2-hydroxypropyl] (phenylmethyl)phosphinic acid (CGP 55845, 1 μM; Tocris Cookson) for GABAB receptors. Pipettes had a resistance of 5–8 MΩ with access resistance of 6–15 MΩ (80–90% compensation in voltage clamp). The internal solution for current-clamp recordings consisted of (in mM): K-gluconate (130), EGTA (0.1), HEPES (10), NaCl (7), MgCl2 (0.3), di-tris-creatine phosphate (5), Tris-ATP (2), and Na-GTP (0.5) (pH 7.3 with KOH). For outside-out voltage-clamp recordings of K+ current the internal solution consisted of (in mM): KCl (140), EGTA (5), HEPES (10), and MgCl2 (2.5), with CsCl (2) in the external bath to block the hyperpolarizing activated cation current IH.
Antidromic stimulations were conducted with a concentric bipolar electrode placed in the white matter region of the folia in the presence of synaptic blockers. Stimuli were delivered by a stimulus isolation unit (DS2 isolation stimulator, Digitimer, Hertfordshire, UK).
Analysis of current-clamp data was accomplished using custom software written in MatLab 7.1 (The MathWorks, Natick, MA). Spike threshold was determined through analysis of the voltage derivative. A calculated junction potential of 11 mV was subtracted from all current-clamp recordings. In voltage-clamp recordings the junction potential was not subtracted because the value was small (∼2 mV) for internal KCl.
ZAP protocol
A ZAP protocol consisted of a time-varying current stimulus of 6 s duration generated by the following equations where I(t) is current stimulus, IE is electrode holding current, and fstart and frate are the initial frequency and rate of change in frequency (in Hz), respectively.
Simulations were constructed in MatLab 7.1 using a fourth-order Runge–Kutta algorithm with a time step (dt) of 0.001 ms. Models were formulated using Hodgkin–Huxley formalism. Bifurcation and phase-plane analyses were carried out in XPPAUT v 5.85 (Ermentrout 2002).
Five-equation model
Somatic voltage
Dendritic voltage
Na+ activation
The h variable represents a merged refractory variable (Na+ inactivation and K+ activation).
IH activation
Slow K+ activation Cs = 1.5 μF/cm2, Cd = 1.5 μF/cm2, R = 3/4, gNa = 40 mS/cm2, gKs = 8.75 mS/cm2, gIH = 0.03 mS/cm2, gKd(slow) = 12 mS/cm2, and gleak = 0.032 mS/cm2.
Testing model robustness
To test for the robustness of the five-equation model individual parameters (maximum conductances, coupling coefficient between compartments, and time constants) were independently varied by as much as 20% from the default values. Under all cases the model retained the key characteristics described in this study provided that the bias current (IE) was adjusted to compensate for small changes in threshold. Properties tested include a substantial bistable range (>0.15 μA/cm2), the ability to generate a long delay to first spike relative to the subsequent ISI, the generation of a DAP, and the ability for a unipolar input to switch between a rest and firing state.
Reduced two-equation model
K+ activation
C = 1.5 μF/cm2, gNa = 20 mS/cm2, gK = 4.2 mS/cm2, and gleak = 0.05 mS/cm2.
For all simulations reversal values were set to: ENa+ = 45 mV, EK+ = −95 mV, EIH = −20 mV, and Eleak = −77 mV.
Threshold dynamics in Purkinje cells are consistent with a saddle-node bifurcation of fixed points
Understanding the dynamics governing the transition from rest to firing is critical because it will largely set the dynamical framework from which many properties of Purkinje cell firing may be accounted for. We started by considering the type of bifurcation underlying Purkinje cell spike threshold. In brief, a bifurcation can often consist of a qualitative change in the system dynamics (e.g., transition from rest to firing) that involves the creation or elimination of fixed points or limit cycles. A neuronal resting state is an example of a stable fixed point and a spiking state a limit cycle (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998; Strogatz 1994). The type of bifurcation that the Purkinje cell undergoes at threshold will largely determine the potential nature of a plateau potential and bistability (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998).
The two principal types of bifurcation governing thresholds in neurons are a Hopf bifurcation and a saddle-node bifurcation (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998). An important criteria for identifying the type of bifurcation underlying spike threshold are steady-state current–voltage (I–V) relationship and the voltage trajectory in the subthreshold range (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998). These two factors can be used to differentiate whether a cell undergoes a saddle-node bifurcation of fixed points or a Hopf bifurcation when driving current is the sole bifurcation parameter. In essence, the presence of a highly nonlinear I–V relationship with an abrupt increase in membrane voltage deflections (resistance) near threshold is consistent with a saddle-node bifurcation. The ability to generate long delays to first spike is also consistent with a saddle-node bifurcation. Finally, an approach to spike threshold with no fast subthreshold or damped oscillations in membrane voltage, combined with long first delays to the first spike, are also consistent with a saddle-node bifurcation (Izhikevich 2000, 2007). Thus we evaluated the I–V relationship and subthreshold voltage trajectory to distinguish which bifurcation was consistent with the activity of Purkinje cells.
To evaluate the steady-state I–V relationship the membrane potential was held near −71 mV and stepped to voltages ranging from −74 to −64 mV in 10 pA increments for 350 ms. Membrane voltage was measured at 275 ms, which provided sufficient time for the IH-mediated sag in the voltage response to equilibrate. As previously shown (Llinas and Sugimori 1980a,b), Purkinje cells showed a highly nonlinear I–V relationship for depolarizations greater than −70 mV (Fig. 1, A and B). Application of TTX resulted in a linear I–V relationship, indicating a steady-state activation of Na+ current that increased the slope of the I–V relationship and thus the input resistance in this voltage region (Fig. 1, A and B). This occurs because a steady-state negative conductance acts to increase the amplitude of positive and negative voltage deflections by increasing the inward current with depolarization (amplifying a depolarization) and decreasing inward current with hyperpolarization (amplifying a hyperpolarization) (Stafstrom et al. 1982). From a dynamical systems perspective the rapid increase in membrane input resistance can represent a nonmonotonic relationship in the steady-state I–V relationship. This nonmonotonicity is critical for producing the fold associated with the coalescing of a node and saddle point, and thus a saddle-node bifurcation (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998). Purkinje cells thus satisfy the criterion of exhibiting a nonlinear steady-state I–V relationship with a dramatic increase in input resistance near threshold necessary for a saddle-node bifurcation of fixed points.
We next tested whether Purkinje cells could generate long first spike latency times. To accomplish this we held Purkinje cells at −70 mV and provided a weak depolarizing input (usually <50 pA). Under these conditions all Purkinje cells tested could generate first spike latencies in excess of 150 ms (Fig. 1C). Furthermore, in the subthreshold voltage trajectory leading up to the first spike there was a clear absence of damped or sustained fast oscillatory activity, as predicted for a saddle-node bifurcation. Note that although the initial first spike latency was long, the subsequent interspike intervals (ISIs) were always shorter than the initial spike delay. Although this trajectory is often attributed to a subthreshold inactivating K+ current (IA), we and others find no evidence for this current in outside-out patches obtained from mature Purkinje cells (Supplementary Fig. 1)1 (Martina et al. 2003; McKay and Turner 2004). Previous work in mouse Purkinje cells has shown evidence for a subthreshold inactivating K+ current (Sacco and Tempia 2002). These experiments, however, were carried out in postnatal day 3 to 9 animals. Their results are thus consistent with immunohistochemical data that indicate only a transient early developmental expression of channels contributing to the A-type current (Hsu et al. 2003). Thus our data support previous conclusions that A-type currents are absent in mature rat Purkinje cells.
As a final test for the type of bifurcation governing threshold dynamics in Purkinje cells we applied a ZAP protocol. A ZAP protocol provides a simple method to assess the subthreshold impedance of neurons by stimulating the neuron with sinusoidal current with a slowly increasing frequency (Hutcheon and Yarom 2000). Neurons that undergo a Hopf bifurcation have a dampening conductance active below threshold that acts similar to an inductor (Izhikevich 2007). Consequently, when combined with the membrane resistance and capacitance, neurons undergoing a Hopf bifurcation resonate at intermediate frequencies of subthreshold stimulation, which produces a band-pass impedance profile. Conversely, neurons undergoing a saddle-node bifurcation have no resonance behavior and thus have a low-pass impedance profile associated with the membrane resistance and capacitance (Izhikevich 2007). As shown in Fig. 1D, application of a ZAP protocol produced no resonance behavior in the Purkinje cell membrane voltage response and also produced a monotonic membrane impedance profile (n = 8).
In summary, these simple experiments provide evidence that Purkinje cell spike threshold dynamics are consistent with a saddle-node bifurcation of fixed points. They also confirm that a steady-state Na+ current is the principal determinant of the nonlinearities in the subthreshold range of the I–V curve. Thus as the membrane voltage approaches threshold, more net inward current with a negative conductance is activated. Consequently, from a dynamical systems perspective any model of Purkinje cell firing and bistability must incorporate a saddle-node bifurcation of fixed points to account for the physiological properties apparent during the transition from rest to firing.
Purkinje cells respond nonmonotonically to climbing fiber–like stimuli
Previous work has established that Purkinje cells have the ability to switch from rest to firing as well as from firing to rest in response to a strong unipolar current input (Fig. 2 A) (Loewenstein et al. 2005). Consequently, bistability in Purkinje cells occurs between a fixed point and a limit cycle. This differs from some neurons that have been shown to be bistable in which the two stable states are represented by a hyperpolarized or depolarized resting state (Crunelli et al. 2005; Williams et al. 1997). Physiologically such a unipolar input can be provided by climbing fiber (CF) activation, which induces a strong synaptic current lasting about 15 ms (Schmolesky et al. 2002). Therefore in the next set of experiments we focused on the intrinsic dynamics of Purkinje cell firing in the context of postsynaptic CF-like stimuli. In particular, we were interested in whether the membrane voltage response of Purkinje cells to CF-like stimuli could further constrain our identification of dynamics underlying spike firing (Fig. 1).
We regarded the large complex spike depolarization triggered by CF input as a strong perturbation comparable to changing the initial conditions of a model. To facilitate analysis of Purkinje cell dynamics and modeling we used square intracellular current steps of varying amplitude and fixed duration (0.25 to >5 nA; 15 ms) to simulate the depolarization associated with a complex spike. For these experiments Purkinje cells were held at −68 mV with approximately −50 pA. As shown in Fig. 2B, the ability to switch from rest to firing depended on the amplitude of the stimulus. As expected, weak stimulation (0.25 nA) had a very low probability of inducing a state transition to firing (0.22 ± 0.10; n = 5), although it could produce a prolonged (100 ms) subthreshold plateau depolarization after the end of the current step (Fig. 2C). We also found that very strong stimulations (>5 nA) were relatively unsuccessful in inducing transitions to the firing state (0.04 ± 0.04; n = 5). In these cases membrane voltage rapidly returned to rest after stimulation and was often followed by a transient hyperpolarization. Intermediate-size stimuli (0.5–2 nA) were the most successful in inducing a transition from the rest to firing state (Fig. 2C; 0.96 ± 0.04; n = 5).
A simple explanation for the nonmonotonicity in the relationship between CF-like stimulus magnitude and state transition probability is that stronger stimulation recruits a greater amount of K+ current activation or Na+ current inactivation. This in turn brings about a failure to transition to the firing state and a rapid return to the rest state. In fact, this can be observed in the rate of repolarization after different magnitudes of CF-like stimuli. To test this we held cells at a slightly more negative membrane potential (−74 mV) so that the cell did not transition to the firing state and the rate of repolarization after stimulation could be observed. We used three different strengths of CF-like stimuli (1, 2, and 5 nA). As expected, the membrane potential returned more quickly to baseline voltage after stronger stimulation (Fig. 2D), which suggested the recruitment of a K+ current or inactivation of Na+ current.
An interesting aspect of Purkinje cell state transitions is that the same magnitude depolarizing pulse can induce transitions both from rest to firing and from firing back to rest (Fig. 2A) (Loewenstein et al. 2005). The ability for such a unipolar and fixed input (i.e., complex spike depolarization) to toggle the cell between firing and rest states may also be accounted for in terms of the relative activation of K+ and Na+ currents. Thus the firing state recruits more net K+ current or Na+ inactivation than at rest, allowing a CF-like stimulus to switch the cell to the rest state. If this scenario is valid it would be expected that the rate of repolarization after a square-step depolarization that induced a moderate rate of firing would be greater than a similar step that is slightly subthreshold because, during the firing state, more K+ current activation or Na+ inactivation would be present. Once again we held cells at a sufficiently negative membrane voltage to avoid state transitions and observed the rate of repolarization after the step pulse. We used a 200 ms step depolarization of either 100 pA (subthreshold) or 175 pA (suprathreshold and firing at ∼80 Hz) from a holding potential of −75 mV. As shown in Fig. 2, E and F, the rate of repolarization after a step depolarization was faster if the cell membrane potential returned to baseline from a firing state rather than a depolarized but subthreshold state.
Because of the absence of spiking in the presence of TTX we could measure the I–V relationship over a wider range of membrane voltages. In particular, we were interested in the conductance behavior at increasingly depolarized membrane voltages. We reasoned that if increasing depolarization induces a faster rate of repolarization to the rest state, then the I–V relationship should indicate a strong saturation (decrease in input resistance) at more depolarized membrane potentials. Furthermore, if the rate of repolarization in the presence of TTX is greater when preceded by a stronger depolarization it indicates that depolarization activates a K+ conductance that facilitates repolarization on cessation of the current step. This prediction was borne out in the steady-state I–V relationship of Purkinje cells, which began to saturate at membrane voltages greater than −50 mV in the presence of TTX (Fig. 2, G and H). This was also accompanied by an increase in the rate of repolarization after cessation of stronger depolarizing steps (Fig. 2G). These results are consistent with an increased activation of K+ current during the firing state that deactivates slowly enough to influence the rate of repolarization at the end of the current step. Thus the same depolarizing stimulus that switched a cell to the firing state can be used to switch the cell back to the rest state through the additional activation of K+ current.
A model of Purkinje cells indicates the dynamical basis of bistability
To gain greater insight into Purkinje cell firing dynamics we constructed a firing model. We used the data on threshold dynamics, which indicated the presence of a saddle-node bifurcation, and the membrane voltage response to CF-like stimuli as a general framework for the model's dynamics and biophysics. We also considered experimental results from previous electrophysiological studies of Purkinje cells. We started by incorporating the essential elements required to reproduce basic properties of Purkinje cell behavior, including a somatic and dendritic compartment and conductances required to generate spike firing.
Previous work has shown that a portion of Purkinje cells can produce a three-stage trimodal firing pattern that arises when cells fire at sufficiently high frequencies (McKay and Turner 2004; Womack and Khodakhah 2002). In our experiments we found that approximately half of Purkinje cells at the age examined could develop a trimodal firing pattern. Recent in vitro work, however, reveals that reintroducing low-frequency (∼1 Hz) CF activation or strong depolarization inhibits trimodal firing and stabilizes Na+ spike output at a new lower-frequency level (McKay et al. 2007), whereas the removal of CF inputs in vivo leads to trimodal-like activity (Cerminara and Rawson 2004). This suggests that the tonic firing behavior is most likely the normal firing mode for Purkinje cells in vivo. For these reasons we did not incorporate trimodal firing dynamics in our model.
We first considered the addition of a dendritic compartment given the important role this can have in establishing spike firing behavior (Doiron et al. 2001; Fernandez et al. 2005; Mainen and Sejnowski 1996). It has been established that Purkinje cell dendrites do not generate active regenerative events (Na+ or Ca2+ spikes) during tonic repetitive Na+ spiking at the soma (McKay and Turner 2004; Stuart and Hausser 1994). Consequently, the charging of the dendritic compartment draws current away from the active zone in the soma/axon hillock, raising current threshold at the active zone. Once charged, however, the relative absence of fast voltage-gated Na+ and K+ conductances in dendrites prevents the dendritic membrane voltage from equilibrating at the same time as the somatic compartment. This causes the dendritic membrane potential to remain positive relative to the somatic compartment for a substantial period of time during an ISI. This behavior is in fact consistent with dual-patch recordings from Purkinje cell soma and dendrite, where dendritic membrane voltage remains at a more depolarized level during the somatic afterhyperpolarization (AHP) (McKay and Turner 2004; Stuart and Hausser 1994). This property has also been recognized as important in previous models of Purkinje cells (Jaeger et al. 1997). To simplify the model as well as facilitate analysis we used a reduction approach developed by Pinsky and Rinzel (1994). With this reduction the two compartments influence each other through a current term that is proportional to the difference in voltage between the two compartments and scaled by a term representing the resistance between the compartments (Pinsky and Rinzel 1994). In our model we used a coupling resistance between the two compartments that reproduced the delay and voltage drop observed in dual soma-dendritic recordings (see methods) (McKay and Turner 2004; Stuart and Hausser 1994).
The somatic compartment contains a transient Na+ current and a noninactivating K+ current. The dendritic compartment contains a slow K+ current subsequently described. To reduce the dimensionality of the model we set Na+ activation to equilibrate instantaneously with voltage and described Na+ inactivation and K+ activation as h and 1 − h, respectively (Rinzel 1985). Furthermore, to take into account the fast refractory dynamics observed in Purkinje cells, we made the time constant of the refractory variable (h) relatively fast (0.1–0.9 ms) to permit the model to fire at frequencies >150 Hz. This is consistent with previous work in Purkinje cells that established that fast activating and deactivating K+ currents as well as a resurgent Na+ current enable high-frequency firing by contributing to a greater net depolarization between spikes (Khaliq et al. 2003; Martina et al. 2003; McKay and Turner 2004; Raman and Bean 1999a,b, 2001; Swensen and Bean 2003). More recent work has shown that Purkinje cells express exceptionally fast K+ currents with activation and deactivation time constants ranging from 0.2 to 2.5 ms when measured at room temperature (Martina et al. 2007). Finally, we selected a leak conductance density that produced an approximate membrane time constant of 90 ms, which is within the range measured in previous studies (Rapp et al. 1994; Roth and Hausser 2001).
The TTX-sensitive Na+ current that contributes to a nonlinear increase in membrane voltage at depolarized potentials (Fig. 1B) may arise through a steady-state Na+ window current or a persistent (noninactivating) Na+ current (Stafstrom et al. 1982). To incorporate this in the model we set Na+ conductance to have a window current by providing an overlap in the steady-state activation and inactivation variables. The model also includes a greater Na+ current density relative to K+ and leak current. In doing so we ensure that more net Na+ current activates at subthreshold membrane voltages (−70 to −65 mV) than K+ or leak current, which reproduces the nonlinearity in voltage response in the subthreshold region (Fig. 3 B). A persistent Na+ current is not included because the Na+ window current is sufficient to reproduce the experimentally observed I–V relationship. In Fig. 3A we have calculated the steady-state I–V relationship as a function of membrane voltage for the entire model—both the total current and each individual active conductance. As expected, the steady-state I–V relationship for the total current is nonmonotonic with a fold region corresponding to the increase in input resistance during the approach to threshold (Fig. 3A). Consequently, the steady-state I–V relationship for the model as a function of current is nonlinear with increasing input resistance at depolarized membrane potentials similar to that observed in Purkinje cells (cf. Figs. 1B and 3B).
The time course of the membrane voltage response of Purkinje cells to step depolarizations in the presence or absence of TTX suggested the expression of an additional slower K+ current (Fig. 1A). Greater depolarization was also associated with a faster rate of repolarization on cessation of a depolarizing current step (Fig. 2, E and G). Although the fast K+ current in the model can account for the saturation in the steady-state I–V plot in the presence of TTX, it cannot reproduce the faster repolarization after strong depolarization (Fig. 3C). In essence, the short time constant for the fast K+ current causes it to turn off too quickly to influence the time course of repolarization. To reproduce this behavior in the model requires the addition of a slower K+ current with a time constant of 15 ms (Fig. 3Cii). This slow K+ conductance could arise from an interaction between internal Ca2+ and Ca2+-activated K+ channels (Hounsgaard and Midtgaard 1989). However, we did not model Ca2+-dependent K+ currents explicitly because of the increase in dimensionality this approach requires and the lack of experimental data on the specific biophysics governing intracellular Ca2+ dynamics in Purkinje cells. This does not affect the fundamental formulation of the model because, from a dynamical systems perspective, it is not critical whether the K+ conductances are voltage-gated indirectly through voltage-gated Ca2+ channels or directly through an intrinsic voltage sensor. Finally, we incorporated IH into the model using parameters established by previous experimental studies (Roth and Hausser 2001; Williams et al. 2002), which reproduced the typical sag in the membrane voltage associated with hyperpolarization (Fig. 3B).
To establish the performance of our model to Purkinje cells we began by comparing the responses evoked by step depolarizations of 250 ms. Purkinje cells were held at −74 mV and depolarized with a maximum of 200 pA (Fig. 4 Ai). In comparison, our model is able to reproduce the major characteristics associated with Purkinje cell depolarization in the subthreshold range, including a long first spike latency relative to the subsequent ISI and an absence of damped oscillatory activity (Fig. 4Aii). The model also accurately reproduces the slow decaying plateau potential subsequent to cessation of the depolarizing current (Fig. 4A, i and ii). Like the Purkinje cell, the decay rate of the plateau potential is faster after greater depolarization and firing frequency (Fig. 4A, i and ii).
As noted previously, Purkinje cells responded to a moderate step depolarization by producing a long first spike latency that was followed by shorter ISIs (Fig. 4Ai). Although this behavior is similar to that of neurons expressing IA, we established that mature rat Purkinje cells lack IA (Supplementary Fig. 1). Rather, the IA-like voltage trajectory in the model is explained by the fast refractory dynamics governing high-frequency firing. These dynamics can be viewed as factors equivalent to dendritic feedback, fast K+ currents, and resurgent Na+ current that all help maintain a depolarization after each spike. Thus by reducing the duration of the ISI, rather than lengthening the first spike latency with IA, both Purkinje cells and the model produce a voltage trajectory similar to one with IA.
In terms of the bistable dynamics the model is also successful in reproducing the nonmonotonic relationship between CF-like stimulation strength and state transition probability. Consequently, an intermediate stimulus of 15 ms and 3 μA/cm2 is successful in mediating state transitions from rest to firing, whereas weaker (1.4 μA/cm2) or stronger (7 μA/cm2) stimuli are unsuccessful (Fig. 4B). Note that a weak stimulus (brief subthreshold current step) generates a substantial plateau potential lasting >100 ms (Fig. 4B). This is a result of the model having a saddle-node bifurcation and the corresponding steady-state Na+ conductance in the subthreshold range required to establish the bifurcation.
Like the cell, the model is able to switch from rest to firing and from firing to rest using a strong unidirectional input (15 ms and 4.2 μA/cm2) (Fig. 4C). This behavior in the model depends critically on the presence of the slow K+ current. Thus in the presence of slow K+ current, stimuli of intermediate strength from the rest state can transition the model to the firing state (Fig. 4C). Stimuli of the same strength delivered from the firing state recruits a greater amount of the slow K+ current, which then mediates the repolarization back to the rest state (Fig. 4C). By comparison, without slow K+ current a depolarizing input can transition the model only from rest to firing (not shown). Note also in Fig. 4C that after the initial transition from rest to spiking the onset of tonic spike firing is delayed immediately after the CF-like stimulus. A similar observation has been made in the Purkinje cell by both ourselves and others (Fig. 2A) (Hounsgaard and Midtgaard 1989; Williams et al. 2002). In the model this is caused by an increased activation of the slow K+ current after the first CF-like stimulus, which is sufficient to delay the onset of tonic spike firing (Fig. 4C).
To understand the dynamical and biophysical basis of bistability in the model we began by performing a single-parameter bifurcation using driving current as the bifurcation parameter. As expected, with increasing driving current the node (rest state) and saddle point coalesce at the fold (Fig. 5 A) in a saddle-node bifurcation of fixed points. With the elimination of the rest state the system jumps onto a limit cycle attractor. Note, however, that the limit cycle exists before the coalescing of the fixed points. Within a range of driving current (Fig. 5Aii) the rest state is only locally stable with perturbations (such as a CF-like stimulus) capable of transitioning the system from the node to the limit cycle. If the system is already on the limit cycle, however, it remains on a periodic solution past the fold region where both a node and saddle point exist. Analysis of the frequency–current (F–I) relationship of the model indicates a discontinuity associated with the bistable region if the system is driven from rest to spike firing (Fig. 5B). Thus the lowest possible firing frequency attainable in the model if the system is driven from rest to firing is about 43 Hz. This is consistent with previous work, which has shown that the F–I relationship of Purkinje cells is linear and discontinuous if measured using square-wave current steps that evoke spike output ranging from threshold to high-frequency firing (Llinas and Sugimori 1980b; McKay and Turner 2005; Williams et al. 2002). If the system is driven from spike firing to rest, however, the model F–I relationship is continuous, albeit with a very high gain in the low-frequency range. Furthermore, our analysis indicates that bistability in the model is limited to the low-frequency and higher-gain region of the F–I relationship.
The bifurcation analysis and F–I relationship suggest that the transition from the limit cycle to the rest state is mediated by a saddle homoclinic bifurcation (as compared with a saddle-node on an invariant cycle bifurcation). In particular, the extremely high gain in the low-frequency firing range is consistent with a saddle homoclinic bifurcation (Izhikevich 2007; Rinzel and Ermentrout 1998). Also consistent with this bifurcation is the discontinuity in the F–I relationship when transitioning from rest to firing. Finally, a saddle homoclinic bifurcation is consistent with a bistable system that produces long first spike latencies in the absence of fast subthreshold oscillations (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998). In essence a model with a saddle homoclinic bifurcation can be viewed as a system with an extremely high gain compared with one with a saddle node on an invariant cycle bifurcation. The high gain is caused by a large amount of positive feedback after a spike. If the feedback is sufficiently high (biophysically this can be generated by factors contributing to a DAP or inhibiting an AHP) any input that crosses threshold and generates a spike will cause strong positive feedback driving an additional spike and thus lead to a permanent spiking state. Under these conditions the system will be bistable and undergo a saddle homoclinic bifurcation. The saddle homoclinic bifurcation will occur when the system is taken from firing to rest with negative driving current (the bifurcation parameter). Furthermore, the gain of the F–I relationship in the transition from firing to rest will be extremely high.
Given that a saddle homoclinic bifurcation can be produced in a two-equation firing model (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998), we proceeded to investigate whether this type of reduced model and bifurcation could account for the general behavior of Purkinje cell firing and CF-induced state transitions.
A saddle homoclinic bifurcation with a nonmonotonic separatrix can account for Purkinje cell dynamics
We started by constructing a model of two dynamical variables undergoing a saddle homoclinic bifurcation of the limit cycle. This permits phase-plane analysis such that the stable manifold of the saddle point associated with spike threshold can be visualized. Note that this is not possible with the five-dimensional model. The phase-plane analysis also allows one to more easily discern the key biophysical features required to establish a saddle homoclinic bifurcation. In addition, it allows visualization of a separatrix, which is often associated with a bistable system. Consequently, the key requirements that control the presence and shape of the separatrix can be considered.
The two-equation model contained only a Na+, K+, and leak conductance. To retain the basic biophysics of spike firing using only two equations we let Na+ conductance activation equilibrate instantaneously with membrane voltage and modeled Na+ inactivation and K+ activation using the same variable (Rinzel 1985). Consequently, the two dynamical variables are membrane voltage and refractoriness (representing both K+ activation and Na+ inactivation). Previous work has established that a saddle homoclinic bifurcation and the resulting bistability can be achieved using a refractory time constant that is small relative to the membrane time constant (Izhikevich 2000, 2007; Rinzel and Ermentrout 1998). We manipulated leak conductance density (to adjust the membrane time constant) and the refractory time constant to establish a saddle homoclinic bifurcation. We set the default value for the refractory time constant at 0.6 ms. Although this value suggests a very fast K+ current, recent voltage-clamp data from Purkinje cell nucleated patches has measured and confirmed the presence of a fast and prominent K+ conductance (Martina et al. 2007).
In Fig. 6 A we show the phase-plane projection of the model for three different time constants of the refractory variable. When the model has a large time constant for the refractory variable (1.2 ms) the transition from the limit cycle to the stable fixed point is mediated by a saddle node on an invariant cycle bifurcation. As a consequence the system has no bistable dynamics and the stable manifold (dashed line) of the saddle point connects to the unstable point on its right (Fig. 6Ai). As the refractory time constant is reduced to an intermediate value (0.6 ms), however, the system undergoes a saddle homoclinic bifurcation of the limit cycle. Under this condition the stable manifold becomes a separatrix, which separates two regions in phase space that correspond to the two possible steady-state solutions (rest and firing) of the model (Fig. 6Aii). A separatrix can be viewed as a line in phase space corresponding to a demarcation of a hard threshold. Thus any perturbation that crosses the separatrix in a bistable system will result in a transition to the firing or rest state depending on the current state of the model. In a nonbistable system undergoing a saddle-node bifurcation the stable manifold simply demarcates the firing threshold of the model. Note that with a saddle homoclinic bifurcation a single spike is capable of generating a large depolarizing afterpotential (DAP) as a consequence of the fast refractory dynamics (Fig. 6B). Also important is the shape of the separatrix. Because the separatrix is nonmonotonic, such that it surrounds the limit cycle, a unipolar input can be used to switch between the stable point and the limit cycle (Fig. 6C). For this reason intermediate inputs can switch the model from the rest state to the firing state, whereas excessively strong inputs fail because they cross the separatrix twice, bypassing the firing state and returning the system to the rest state. This provides a dynamical systems explanation of the restricted range of CF-like stimuli that are able to induce state transitions in the bistable region. If the refractory time constant is further reduced (0.2 ms) the model retains the saddle homoclinic bifurcation and bistability but the separatrix becomes monotonic (Fig. 6Aiii). Thus switching from the rest state to the limit cycle can be done with a positive current input, whereas switching from the limit cycle to the rest state requires a negative current input. Note that when the model has a saddle homoclinic bifurcation it generates a long first spike latency relative to the subsequent ISI (Fig. 6E). This is a consequence of the fast refractory dynamics, which actively shorten the ISI relative to the first spike latency, and is consistent with our previous interpretation of the five-equation model.
Our two-equation model indicates that, from a biophysical perspective, any factors that provide a net depolarizing influence after spike generation can potentially establish a saddle homoclinic bifurcation and bistability. In effect, the bistability emerges because spike generation is followed by a depolarization or weak hyperpolarization, which locks the system into a spike firing solution. As a result, over a range of current input, spike firing becomes self-generating once threshold is crossed. In the two-equation model the primary cause of bistability is the fast deactivation of the K+ conductance, which prevents the system from fully resetting once threshold is crossed. Also important is the membrane time constant. A comparatively long membrane time constant acts in a manner similar to that of a fast deactivating K+ conductance because it prevents the membrane from fully resetting after spike generation by retaining membrane charge for a long duration. An intermediate refractory time constant, however, is required for state transitions to be mediated by a unipolar input. This is similar to the addition of a slow K+ current in the five-equation model, which permits a CF-like stimulus to mediate state transitions.
Biophysical basis for bistability in the five-equation model
In the five-equation model dynamics similar to those present in the two-equation model should establish bistability, although additional factors will be important. The two-equation model, however, predicts that the presence of conductances that slow membrane repolarization and increase the membrane time constant will establish a saddle homoclinic bifurcation and bistability. Thus we predict that removing the dendritic compartment and reducing Na+ conductance will eliminate bistability by removing a spike-dependent depolarizing factor (dendritic feedback) and decreasing the membrane time constant (Na+ conductance removal). Alternatively, increasing the K+ conductance and leak conductance will eliminate bistability by producing a strong and long-duration hyperpolarization after a spike and decreasing the membrane time constant (arising from the increased leak conductance).
To test these predictions in the five-equation model we proceeded to manipulate the components predicted to establish a saddle homoclinic bifurcation and control the bistable range. We performed a bifurcation analysis under each manipulation to evaluate overall system dynamics. We considered four factors: the dendritic compartment, refractory dynamics, leak conductance, and the Na+ window current. For each parameter we considered the scenario that would be predicted to reduce the bistable range. Thus we removed the dendritic compartment, slowed the refractory variable, increased somatic leak conductance, and reduced the Na+ window current (through a −6 mV shift in the steady-state inactivation parameter). As shown in Fig. 7, A–E each of the manipulations reduces or eliminates the bistable range of the model (indicated by a reduced overlap between the limit cycle and node across different current values). Under the control condition (Figs. 5 and 7A) the bistable range occurs over 0.26 μA/cm2 of driving current. Under each of the four manipulations the bistable range is either eliminated or reduced to <0.03 μA/cm2 range of driving current (Fig. 7, B–E).
To further illustrate the effects of these four manipulations on bistability we considered the DAP after a single spike. As stated previously, the factors analyzed here contribute to bistability by providing a depolarization after each spike, which locks the system into a spike firing solution. Below the bistable range (when the model is slightly hyperpolarized), however, it is expected that the model will generate a DAP before returning to the rest state and that any of the four manipulations described earlier will reduce the size of the DAP. As shown in Fig. 7Fi, the control model (black line) produces a large DAP after a brief current step. Conversely, any of the manipulations that reduce the bistable range also reduce or eliminate the DAP (Fig. 7Fi). Furthermore, when the model is held at a more depolarized membrane potential (−70 mV, within the bistable region) the ability to switch from rest to firing is eliminated with any of the four manipulations (Fig. 7Fii).
The five-equation model can account for previous experimental results
As a test of the validity of our model we sought to examine whether it could reproduce previous experimental results related to bistability that remain unexplained. In particular, we were interested in the effects of changing the density of Na+ current on plateau potentials and the density of IH on the bistability range.
Previous work has established that a small reduction of Na+ conductance with TTX in Purkinje cells can reduce the duration of spiking plateau potentials with no effect on spike parameters (Williams et al. 2002). We proceeded to reduce the Na+ conductance density (gNamax) and test the ability of the model to generate plateau potentials in response to a brief current step. We note that in the model the plateau potential is generated by the same factors that sustain the DAP. For these simulations the model was held at −73 mV with 0.023 μA/cm2. As shown in Fig. 7, a small reduction in gNamax that reduces the DAP shortens the duration of the spiking plateau potential (Fig. 7G, i and ii). Because the plateau potential is caused by a balance of inward and outward currents, a small change in gNamax has a dramatic effect on its duration, eventually eliminating the ability to generate a plateau potential and bistability. In contrast, during the spike upstroke membrane permeability is dominated by Na+ conductance. As a result, a small change in gNamax has no effect on spike parameters (Fig. 7Gii). Thus our model can accurately reproduce these experimental observations within the biophysical context described previously to establish a saddle homoclinic bifurcation.
We next examined the effects of IH on the bistable range of the model. The effect of IH on bistability remains somewhat controversial. Experimental results indicate that removal of IH with pharmacological blockers or modulators does not inhibit bistability (Williams et al. 2002). In fact, the overall effect of IH block is to increase the observation of bistability in Purkinje cells (Williams et al. 2002). Modeling data from a more recent study, however, place IH as the critical conductance underlying bistability in Purkinje cells (Loewenstein et al. 2005). Given that only modeling data suggest a critical role for IH in sustaining bistability (Loewenstein et al. 2005), we carried out experiments to examine the effects of removing IH with 20 μM 4-(N-ethyl-N-phenylamino)-1,2-dimethyl-6-(methylamino) pyridinium chloride (ZD7288) on bistability. To test for bistability cells were held at −68 mV and given two 15 ms duration 2 nA current steps of positive and then negative polarity spaced 500 ms apart (Fig. 8 Ai). In all cells tested (n = 8) blockade of IH did not prevent state transitions between rest and firing (Fig. 8Ai). Thus bistability was not blocked by the removal of IH, confirming previous results by Williams et al. (2002). An effective block of IH was confirmed by delivering a negative 2 nA current pulse (15 ms), which under control conditions produced a voltage overshoot and dampening (indicating deactivation of IH) that was abolished in the presence of 20 μM ZD7288 (Fig. 8Aii).
To examine the role of IH in the model we changed the IH conductance density and measured the bistable range using a bifurcation analysis. In Fig. 8B we show the effects of four different IH conductance densities [0.03 (control), 0, 0.06, and 0.3 mS/cm2] on the bistable range of the model. With the complete removal of IH the bistable range increases by a small amount relative to the control case (Fig. 8Bii), whereas an increase in IH decreases the bistable range (Fig. 8B, iii and iv). We followed by plotting the bistable range of the model as a function of IH density (Fig. 8C). As indicated, the effect of adding IH is to decrease the bistable range of the model over a large range of conductance densities (Fig. 8C).
Although IH might be expected to increase the bistable range of the neuron by contributing to the DAP (by rebounding membrane voltage during the spike AHP), its major contribution to membrane dynamics comes about through a decrease in input resistance and the membrane time constant. This occurs because the time constant of IH activation and deactivation is too large for any dynamic contribution during a single spike cycle. Consequently, only the steady-state activation of IH contributes to the bistable dynamics by decreasing the membrane time constant and decreasing the amplitude and duration of the DAP (Fig. 8D). In fact, data in support of this have been reported, in that blockade of IH with ZD7288 has been shown to increase input resistance and the membrane time constant (Williams et al. 2002). Thus within the context of the saddle homoclinic bifurcation the addition of IH is equivalent to an increase in leak conductance and a shorter membrane time constant.
Testing model predictions in Purkinje cells
To further evaluate the validity of our model we proceeded to test some of the predictions made by the model. We considered the following qualitative behaviors: the presence of a DAP during antidromic stimulation, high gain in the low-frequency firing region of the F–I relationship, and a bistable range limited to the low-frequency firing range.
A critical feature to establishing a saddle homoclinic bifurcation in our model is the presence of a long DAP. To test whether Purkinje cells produce a DAP similar to that observed in the model we used antidromic stimulation to elicit a single spike during whole cell Purkinje cell recordings. Cells were held between −80 and −65 mV and stimulated antidromically with a bipolar electrode in the white matter region of the folia in the presence of synaptic blockers (see methods). All Purkinje cells tested produced a substantial DAP lasting between 50 and 100 ms and ranging in amplitude from 3 to 7 mV (Fig. 9 Aii; n = 4). The voltage trajectory of the Purkinje cell DAP thus compared favorably with that of the model when driven with a brief 2 ms current step.
A second prediction made by the model is that Purkinje cells should be able to fire at low firing frequencies and that the gain (slope) of the F–I relationship should be significantly higher at low frequencies. In the model this occurs because the system undergoes a saddle homoclinic bifurcation, which produces a high-gain region in the bistable range of the neuron. To test this we applied a ramp protocol that carried the cell from rest to firing and back to rest. The total duration of the ramp was 4 s with a slope of 100 pA/s (cells were initially held at approximately −75 mV). As shown in a previous study (Williams et al. 2002), Purkinje cells respond to a ramp protocol with strong hysteresis (Fig. 9Bi). Thus all cells tested were able to fire spikes at lower current inputs on the downstroke than on the upstroke of the ramp. To measure the gain of the cell during the ramp we constructed an F–I relationship from the instantaneous firing frequency during the protocol (Fig. 9B, ii and iii). In all cells tested, the lowest attainable frequency was lower on the downstroke than on the upstroke of the ramp protocol (Fig. 9B, ii and iii; n = 7). Indeed, in many cases Purkinje cells could be made to fire at a frequency <20 Hz on the downstroke of the ramp protocol when the same cells would typically begin to fire between 60 and 70 Hz on the upstroke. Note that the lower frequency value obtained during the downstroke is also significantly lower than the onset frequency reported by previous studies, which normally measure the F–I relationship using current steps that take the cell from rest to firing (Llinas and Sugimori 1980b; McKay and Turner 2005; Womack and Khodakhah 2002). Furthermore, a measurement of the gain of the F–I relationship using a linear fit indicated that gain was significantly higher at lower firing frequencies (<50 Hz) (Fig. 9, C and D; P < 0.01, n = 7), a result consistent with our model. A recent study has also shown that evoked or simulated parallel fiber excitatory postsynaptic potentials (EPSPs) have a higher gain (produce a larger change in firing frequency) when applied at low firing frequencies (<60 Hz) relative to those applied at high firing frequencies (>60 Hz) in Purkinje cells (McKay et al. 2007).
Another key property in our model is that bistability is limited to the low frequency firing region (<43 Hz). With increased driving current and firing frequency, the stable rest state (node) disappears by a saddle-node bifurcation, leaving the limit cycle as the globally stable solution. Consequently, Purkinje cells should be able to transition between the firing and rest state only at low firing frequencies. We tested this by holding Purkinje cells at two different ranges of firing frequency and using an inhibitory current step that hyperpolarized the cell to −90 mV (n = 6). We used inhibitory rather than excitatory current steps to induce the transition from firing to rest because it was easier to control the final membrane voltage (we defined a low firing frequency as <50 Hz). When Purkinje cells fired at low frequencies a hyperpolarizing step of 85 ms duration was sufficient to transition the cell from firing to rest (Fig. 10). Conversely, when Purkinje cells were held at high firing frequencies a similar step (we increased the size of the inhibitory current step to take the cell to the same final membrane voltage) was insufficient to transition the system from firing to rest. We also carried out these experiments with positive current steps (5 nA) and found that bistability was limited to the low firing frequency range (data not shown). Thus these tests validate the basic dynamics of our model and provide novel information on Purkinje cell firing behavior.
The current study identifies two different bifurcations that can account for several established properties of cerebellar Purkinje cell firing. Although in this study we do not indicate all the precise factors likely to contribute to Purkinje cell bistability, we delineate the basic biophysical and dynamical mechanisms by which it is achieved. In doing so we provide a general framework from which future studies can determine all the possible contributing factors. Within this framework we account for previous observations and reproduce them accurately using our model. Furthermore, we use our model, dynamic systems analysis, and experimental data to demonstrate and explain important and even previously unrecognized aspects of Purkinje cell firing behavior. These include the following properties: a narrow range of a CF-like stimulus is capable of transitioning Purkinje cells to the firing state, spike firing at frequencies <40 Hz, a nonlinear F–I relationship with a high gain in the low frequency region, and that the bistable region is limited to the low-frequency firing range. These findings are significant because they indicate that numerous properties of Purkinje cell firing are fundamentally linked to the type of bifurcation underlying threshold transitions in the cell. As a result, we find that bistability is one of many properties associated with the presence of a saddle homoclinic bifurcation in Purkinje cells.
Biophysical basis of bistability in Purkinje cells
Because bistable dynamics in Purkinje cells emerge through a saddle homoclinic bifurcation, the basic factors controlling bistability are the membrane time constant and the spike refractory dynamics that generate a DAP. Within the bistable range the DAP provides sufficient depolarization after the spike to generate an additional spike and permanently stabilize tonic firing. In essence, the DAP can be viewed as equivalent to the excitatory feedback used in some models of network activity that produce bistability and persistent activity (Li et al. 2006; Seung et al. 2000). Consequently, any factors that decrease the membrane time constant and/or slow the refractory dynamics will reduce or eliminate the DAP and bistability. In Purkinje cells a major contributing factor to bistability is the long membrane time constant, which is likely to result from a large specific membrane resistance (Rapp et al. 1994; Roth and Hausser 2001). The long membrane time constant acts to slow the final repolarization after a spike and thus contributes to the DAP. Similarly, a fast refractory variable contributes to a DAP by turning off sufficiently fast as to permit a depolarization to dominate the postspike period. Numerous factors can contribute to a fast refractory variable. These include fast deactivating K+ currents or resurgent Na+ current. A resurgent Na+ current could support a DAP because this type of conductance activates during the repolarizing phase of a spike. Consequently, the presence of a resurgent Na+ current can be viewed as similar to a fast deactivating K+ current because both types of currents can shorten the effective refractory period and support a DAP. Although we did not include a resurgent Na+ current in any of our models, its presence would accentuate the dynamics described in this study and would thus contribute to establishing a saddle homoclinic bifurcation. In support of this, previous studies have shown that Purkinje cells express both of these types of currents (Martina et al. 2003; McKay and Turner 2004; Raman and Bean 2001).
As indicated by our model, Purkinje cell dendrites should also contribute to the DAP. Because dendritic voltage is more positive than the soma immediately after a Na+ spike (McKay and Turner 2004; Stuart and Hausser 1994), current can flow into the soma and contribute to a late depolarization. As a result, when combined with a long membrane time constant and fast refractory dynamics, a dendritic compartment contributes to establishing bistability.
A past study on the development of Purkinje cell morphology and in vitro electrophysiological properties is also consistent with our interpretation and model (McKay and Turner 2005). In particular, this study showed that the ability to generate a discontinuous F–I relationship, a first spike latency longer than the subsequent ISI, and bistability develops in parallel with the generation of a narrower somatic Na+ spike and larger dendritic arbor. This suggests that the development of a dendritic arbor and fast refractory dynamics contribute to establishing properties associated with a saddle homoclinic bifurcation.
Although Purkinje cell dendrites have been shown to generate Ca2+ spikes and Ca2+-dependent plateau potentials (Llinas and Sugimori 1980a), dual recordings from soma and dendrite indicate a lack of Ca2+ spike activity during tonic somatic Na+ spike firing (0–200 Hz) (McKay and Turner 2004; Stuart and Hausser 1994; Williams et al. 2002). This is also consistent with dendritic recordings from Llinas and Sugimori (1980b), which show Ca2+ spikes only during burst firing or with strong local depolarization of the dendrite with current steps. Furthermore, previous work has indicated that blocking voltage-gated Ca2+ conductances does not decrease bistability (Williams et al. 2002). Consequently, Ca2+ spikes and Ca2+-mediated plateau potentials may represent a local dendritic phenomenon required for synaptic integration, but have less influence on the intrinsic somatic firing dynamics within the tonic firing range.
A previous reduced model of Purkinje cells used an IH conductance measured in entorhinal cortical stellate cells to reproduce membrane voltage bistability associated with CF-like stimulation (Loewenstein et al. 2005). Although this model captures some of the elements of Purkinje cell dynamics, such as switching with a unipolar current input, it fails to account for experiments that indicate that block of IH does not eliminate bistability and can actually augment the bistable range (Williams et al. 2002). Because the Loewenstein model has no spiking dynamics, bistability results from a relatively slow variable (IH activation and deactivation) and INa. It is assumed in this model that the introduction of fast spiking dynamics will not change this and that spikes will ride on top of the INa- IH-mediated plateau potential. Consequently, bistability in the Loewenstein model is between two different rest states (hyperpolarized and depolarized).
Both models presented in the current study differ critically in this respect. First, bistability is between a rest state and a firing state. Second, bistability depends on the fast variables in the model that are within the timescale of a single spike. The following information, however, supports our current models. Most important is the fact that IH block does not eliminate bistability in Purkinje cells, but rather can increase the observation of bistability in these cells. Purkinje cell bistability has been shown to be eliminated with TTX (Williams et al. 2002), thus supporting the conclusion that bistability is between a rest state and a firing state. We should also note that we observed no bistability in membrane voltage (between two rest states) once spiking had been abolished with 1 μM TTX. Finally, Purkinje cells have been shown to have fast refractory dynamics consistent with our biophysical and dynamical interpretation. Thus we feel that our current models represent a more biophysically and dynamically accurate explanation of Purkinje cell firing behavior.
Spontaneous activity in vitro
Previous studies in vitro have delineated two types of spontaneous activity in Purkinje cells. The first type is tonic firing, which can vary in frequency from 70 to 200 Hz (Williams et al. 2002). The second type is a trimodal burst firing pattern, which consists of a three-stage cycle: tonic firing, burst firing, and quiescence (McKay and Turner 2004; Womack and Khodakhah 2002). In our present work we found that more than half the cells expressed a trimodal firing pattern, whereas the rest of the cells fired tonically with no indication of trimodal activity. Details on the prevalence and development of intrinsic trimodal activity in Purkinje cells were recently described (McKay and Turner 2005). In the current study the trimodal pattern was sidestepped for the duration of experiments by applying a slightly negative bias current to reduce the rate of Na+ spike firing. Given the exceedingly complex nature of the dynamics associated with trimodal burst firing we did not include them in our model. Moreover, we recently showed that reintroducing a physiological rate of CF-like stimuli and complex spike depolarizations in vitro rapidly blocks trimodal activity and slows Na+ spike frequency to the range necessary to observe bistable behavior and the associated change in gain now explained mechanistically here (McKay et al. 2007).
Low firing frequency
Previous in vitro work on Purkinje cells has established that the F–I relationship is linear and discontinuous with a minimal firing frequency ranging from 40 to 70 Hz using standard current step protocols (Llinas and Sugimori 1980b; McKay and Turner 2005; Williams et al. 2002). Our model and data indicate that the F–I relationship of Purkinje cells is nonlinear and has a firing frequency range substantially <40 Hz. The low frequency firing range, however, occurs largely within the bistable range. As a consequence the only way to attain low firing frequencies is to impose a hyperpolarizing shift (i.e., with negative current) once the cell has already attained a high frequency firing state. Alternatively, CF-like stimuli at rest can transition the system to the low frequency firing range because bistability is limited to that range of frequencies.
Comparison to in vivo Purkinje cell firing behavior
Recent work in rat cerebellum has shown that bistability can be observed in vivo (Loewenstein et al. 2005), although there is controversy as to whether CF-induced toggling between states reflects natural or experimental conditions (Schonewille et al. 2006). Our analysis of Purkinje cell dynamics indicates that only intermediate-strength CF-like stimuli can mediate state transitions. In this regard, direct recordings in vitro indicate a substantial variation in the net current evoked during a CF-evoked complex spike depolarization between different Purkinje cells, suggesting that CF-induced toggling may be more prevalent in cells receiving CF postsynaptic currents in the appropriate range (McKay et al. 2005). Additionally, the bistable area of Purkinje cells is limited to the low frequency firing region. Thus the restrictions placed by the requirement of a complex spike of the correct magnitude and a limited bistable range may render state transitions induced through CF activation less likely to be encountered in awake animals, but still potentially active when the appropriate conditions are met.
Our analysis further indicates that switching between the two states is only one of many features associated with intrinsic Purkinje cell dynamics. Although bistability is the most obvious of characteristics with a potential functional significance associated with a saddle homoclinic bifurcation, many of the other properties associated with this bifurcation may also be important. First spike latencies longer than the subsequent ISI, plateau potentials (both spiking and nonspiking), and a discontinuous F–I relationship in the slow transition from rest to firing are also a consequence of a saddle homoclinic bifurcation. Some, if not all, these features may be important for in vivo Purkinje cell function even under conditions in which CF activation remains unable to toggle between a rest and firing state. For example, the high gain at lower firing frequencies would still be influential in vivo, a condition that could be established when tonic CF activation reduces Purkinje cell firing rate (Cerminara and Rawson 2004; Colin et al. 1980; McKay et al. 2007; Montarolo et al. 1982). This has previously been suggested to reflect the activation of Ca2+-dependent K+ channels by the complex spike depolarization (Cerminara and Rawson 2004; Hounsgaard and Midtgaard 1989; McKay et al. 2007), indicating that the history of CF input will be important in actively regulating the gain of the cell. Indeed, work in vivo has shown that Purkinje cell responsiveness to excitatory and inhibitory stimuli is increased after CF activation (Ebner and Bloedel 1981, 1984). The dynamical and biophysical basis for bistability in Purkinje cells delineated here may then be important to understanding multiple aspects of Purkinje cell output.
This work was supported by a Canadian Institutes of Health Research (CIHR) Doctoral Studentship to F. R. Fernandez and CIHR operating grant and Alberta Heritage Foundation for Medical Research Scientist Award to R. W. Turner.
We gratefully acknowledge the technical assistance of M. Kruskic, M. L. Molineux, and B. E. McKay and comments on the manuscript by W. H. Mehaffey.
↵1 The online version of this article contains supplemental data.
- Copyright © 2007 by the American Physiological Society


text:
D.C. police on Thursday arrested a 36-year-old suspect in the stabbing death of a man who was found Saturday lying behind a strip of rowhouses on Georgia Avenue in Northwest Washington.
Officer Araz Alali, a department spokesman, said Marvin Moore of Northwest Washington was charged with second-degree murder while armed. He has not been arraigned.
Police said a patrol officer found the victim, Timothy Benjamin, 58, lying on his back about 12:40 a.m. The victim was pronounced dead at an area hospital. Police said he had been stabbed several times.
Authorities did not comment on a possible motive.

subset: commoncrawl


text:
This is for those that have an system with UEFI and their system simply freezes on shutdown.
On shutdown the system will reach,
then freeze.
I found that it is not any module, file system or sysctl parameters.
After trying noefi, which totally disables all of the runtime services. The boot, parameter services are still active.
1. Install *buntu as you normally do.
2. Copy the /boot/efi/efi/ubuntu/grubx64.efi to /boot/efi/efi/boot/bootx64.efi
3. In the BIO's make sure that the Hard disks is first in line in boot sequence.
4. For this step first try adding noefi to the kernel that you want boot in the grub menu. ie, ESC, e - edit the menu item, then F10
if this boots successfully then Add noefi to your /etc/default/grub configuration file. GRUB_CMDLINE_LINUX="noefi"
************************************************** ********************
* If at anytime you change grub or update your system and you see that
* grub is being updated reboot and follow the first part of #4
* temporarily removing noefi to procede with the upgrade.
************************************************** ********************
5. The system should reboot and shutdown normally.
Runtime service give you the ability to get and set efi parameters, get/set time, get/set wakeup time, etc.
Some how the runtime service are not being handed over to linux?


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Cancer Council Victoria is hosting its second Creative Therapy workshop this year, which is set to take place on 13th April as part of the annual Arts Awards program.
The Cancer Council's Arts Awards program is internationally recognised and provides Australians with the opportunity to express their cancer experiences creatively. This year's theme is 'Balance' and entries are open to all Australians who have been affected by cancer – directly or indirectly.
The workshops associated with the Arts Awards will be run by Art Therapist, David Champion, and aim to provide participants with an enjoyable and enriching experience of self-expression, combining two modalities (art-making and creative writing) in a group setting.
The cost per workshop is $15, which includes all materials, a catered lunch and refreshments. Each session will start at 10am and will run for four hours.
Cancer Council Victoria spokesperson, Deb Stringer, said with 78 Victorians diagnosed with cancer every day, many of us will one day feel the impact of hearing the words, 'you have cancer'.
"Cancer can present an enormous physical and emotional challenge for all those affected including patients, family, friends and carers. It has been proven that artistic and literary expression can help many through their cancer journey and that is why we are offering Creative Therapy workshops," Ms Stringer said.
Creative Therapy workshops will be held in Melbourne on 13th April and 18th May at Cancer Council Victoria's Drummond Street premises.
If you or your family have any questions about cancer, or would like free support or information, please call a cancer nurse on 13 11 20.
For further information on the workshops or visit the Arts Awards website, or call 1300 65 65 85.
Entries for Arts Awards close on 29th July 2013 and categories include Visual Art, Poetry, Short Story, Film, Aboriginal and Torres Strait Islander Visual Art, Children's Art, Children's Writing, Youth Writing and Youth Art.


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Index provider MSCI has launched a new emerging market index that excludes the 'Bric' countries of Brazil, Russia, India and China .
The MSCI EM Beyond BRIC index has been launched following a sustained period of underperformance from the four Bric stock markets, which comprise more than 40 per cent of the MSCI Emerging Markets index, in recent years.
Of the 17 countries in the new index, Korea, South Africa and Taiwan occupy the highest weightings, although MSCI said it will cap the weightings of the bigger markets at 15 per cent of the value of the index.


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AN ANIMAL lover is distraught after she believes a tree housing rare baby woodpeckers was cut down by the council.
But officers at Bracknell Forest Council said that they thoroughly checked the tree in Longhill Park, Winkfield, for any signs of the lesser spotted woodpecker.
Wildlife enthusiast, Leanne Dawson, from Priestwood, Bracknell, said: "I go past that tree every day and hear the babies chirping. But then on Friday morning it had been cut down.
"They are protected birds and the council need to stop chopping down trees this time of year." However, the council insists that the park ranger and tree surgeons that they hire are experienced and always check trees for nesting birds and that they were confident there were none nesting in what they considered a dying tree.
Richard Walton, Bracknell Forest Council's head of parks and countryside, said: "We have looked into the resident's concerns thoroughly and we are as confident as we can be there were no nesting birds in the tree.
"The contractor is very competent with many years of experience and followed clear guidance in regards to wildlife in these circumstances.
"The contractor carried out all the necessary checks before starting work and would not have begun work if there had been any sign of nesting birds." The woodpeckers, which are about 100 times rarer than their relative, the greater spotted woodpecker, tend to make their nests in the holes of dead or dying trees.
A spokesman for the Royal Society Protection of Birds said: "The lesser spotted is a protected species which has suffered an amazing and astonishing decline in recent years.
"During breeding season our advice to councils and residents is to minimise the amount of cutting of trees.
"If you have to cut them down check that there are not breeding birds in the tree and protect yourself from breaking the law." The council said that the trees in the area where Miss Dawson said she saw the woodpeckers posed a risk.
Sue Boyce, spokeswoman for the council, said: "As a rule we wouldn't do that this time of year, but the trees were dead and dying and deemed to be dangerous as they were hanging over a path."


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I actually find this news depressing. Out of all the Law & Order shows, my favorite has always been SVU. Because of reruns, I've literally watched every episode at least four or five times.
A little while ago, it was reported that Mariska Hargitay, who has starred on SVU for 12 years, was going to be appearing part-time for the next season. She will reportedly be appearing in the first 13 episodes of the season and then appearing in a part-time capacity for the remainder of the season.
Now it's been reported that Chris Meloni – who has played Elliot Stabler for 12 seasons – is leaving the show.
As in, no part-time. No 13 episodes. Nada.
Apparently Meloni was not able to reach a contract agreement with NBC for the show and has elected to depart. When it returns in the fall for its thirteenth season, Law & Order: SVU will be the only remaining Law & Order show on television, as Law & Order: LA was canceled by NBC and another spin-off (Law & Order: Criminal Intent) is currently ending its run this season.
I have no idea who they might bring in to replace Meloni. Rumors were swirling that Jennifer Love Hewitt (who I thought was fantastic in her guest appearance earlier this season) might come in as a new police officer to help fill the void left by the part-time Hargitay. But that's still just a rumor and hasn't been confirmed. And as of right now, there's no indication who else might be added to the cast of SVU.
Yes, other Law & Order shows have been able to handle some pretty significant cast changes, but Hargitay and Meloni have been the stars of the show since the very beginning, so we don't know how much longer SVU will be able to go once they depart.
clarissa @ tvovermind.com


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In Jonathan Kellerman's gripping novels, the city of Los Angeles is as much a living, breathing character as the heroes and villains who roam its labyrinthine streets. Sunny on the surface but shadowy beneath, this world of privilege and pleasure has a dark core and a dangerous edge. In True Detectives, Kellerman skillfully brings his renowned gifts for breathless suspense and sharp psychological insight to a tale that resonates on every level and satisfies at… (more)
Publisher: Ballantine Books (March 24, 2009)
Format: EPUB
File size: 2 MB
Protection: DRM
Language: English


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Hello everyone!
I am having trouble adding the featured slider (image slider to display image slidshow) of the Sight theme to the front page of my web page (or any other page).
I have created a static web page, as I do not wish to have a blog, but a regular web page. I've read that I'll need to create a sticky post to add the featured slider, but I don't want posts, I want a web page.
Can anyone help? Please make you reply detailed... Thank you! :)
The blog I need help with is saschkeramik.wordpress.com.


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Women's Metallic Lentil 24k Yellow Gold Mini Station Necklace
From the Lentil Collection. This 18k yellow gold chain necklace is delicately dotted with drops in hammered 24k and secured with a clasp in 18k, creating a chic yet minimalist accent that complements any ensemble. 18k, 22k and 24k yellow gold. Length, about 18". Lobster clasp. Color: metallic


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New York vs Atlanta Recap - Thrashers Win 2-1
The Islanders came up short Sunday against the Thrashers, falling 2-1.
Atlanta was favored by -190 and came through for bettors backing them. The game went UNDER the consensus closing total of 5.5.
Atlanta got goals from Nik Antropov and Dustin Byfuglien in the victory. Antropov opened the scoring at 2:25 of the third period.
Ondrej Pavelec turned in a 28-save effort for the Thrashers.
Michael Grabner scored for the Islanders, finding the net behind Ondrej Pavelec.
Rick DiPietro stopped 33 of 35 shots for the Islanders, but it wasn't enough to earn the victory.
On the power play, Atlanta went 1-for-4, while the Islanders were 0-for-4 with the man advantage.
New York lost the shots on goal battle to Atlanta by a margin of 35-29.
Next game, Atlanta takes its act home to face Detroit looking for another win. For New York, they head home to face Columbus.


text:
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Sleek and sculpting! This slimming pair of long legged girdle panties is made by the Playtex label in their infamous "Double Diamonds" style (style #2834), of a pale ivory white nylon/spandex. The long legged panties have an elastic waistband, front "Diamond" patterned contouring panel, side & rear shaping panels, four hidden garters and a soft cotton lined crotch.MEASUREMENTS: Labeled as a size 2XL... waist fits 33 - 36 inches and the panty is 15 inches in length. CONDITION: Excellent condition. SHIPPING: Canada/USA $5.50. INTERNATIONAL $7.00. accessories are not included, unless stated. *********************** I LOVE TO COMBINE shipping! $2 for each additional item shipped within CANADA and the UNITED STATES. $3 for each additional item shipped INTERNATIONALLY (anyw outside of North America). *******************************
Payment:Your bid is a contract - Please do not bid if you don't intend to pay. Payment is accept via PAYPAL only. DUE TO NEW EBAY POLICY, I CAN NO LONGER ACCEPT ANY Thank you. Payment is expected within 7 days. If you would like to run a tab with me, just let me know. I will gladly run a tab for a week but after a week, payment in full is required. Shipping: Everything is shipped via Airmail. ... read more


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UND VOLLEYBALL: North Dakota earns Big Sky title
UND was a so-so team during the 2012 Big Sky Conference volleyball season, finishing 10-10 in league play. In its first year as a Big Sky member, North Dakota qualified for the league's postseason tournament, but Ellen Krueger knew there was so much more potential for the program.
"It was a big deal making it to the conference tournament last year," said Krueger, a UND senior. "But we all knew at the end of the season we could have done better."
UND did much better this season; much, much better.
The North Dakota volleyball team made history Saturday at the Betty Engelstad Sioux Center, beating Southern Utah 25-13, 25-16, 25-12 before 1,193 fans to earn the school's first regular-season championship as a Big Sky member.
UND earned a share of the Big Sky title with Portland State, which beat Idaho State on Saturday night. Both finished 17-3. Portland, however, has the tie-breaker and will take the No. 1 seed into the into next weekend's Big Sky postseason tournament in Portland. UND will be the No. 2 seed and will receive a first-round bye.
In Year No. 2 as a Big Sky member, UND established itself as a league power and North Dakota may be in that position for a while as the program loses only three seniors.
"It was a heck of a deal, to win a title in our second year," said UND coach Ashley Hardee. "Going forward, we don't have to talk anymore about getting over the hump. We proved ourselves."
UND didn't mess around with Southern Utah, controlling play throughout.
"We knew we had to go out and execute," said Hardee. "We always talk about proving ourselves, respecting our opponent and enjoying volleyball. We did that."
Krueger finished with 11 kills, as did freshman Anna Pioske. Lexi Robinson added eight kills, while Lisa Parlich and Ronni Munkeby finished with seven and six, respectively. Parlich and Munkeby are the program's two other seniors.
"We knew we'd get a lot of emotion from our six seniors," said Hardee. "Our quick start was important."
UND didn't take its foot off the gas at all. North Dakota held Southern Utah to a negative hitting percentage (-.028).
"That's quite a task, to do that," Hardee said.
After the match, UND honored its three seniors. And the team also posed for a photo in front of a Big Sky Conference championship banner.
"We wanted a good start on Senior Night," said Krueger. "Everyone was a little anxious for the win. You could feel it in the air. We had a couple of ups and downs but we fought through it."
Now, UND's focus turns toward the Big Sky tournament.
"This year, we exceeded everyone's expectations," said Krueger. "Coach has high expectations for us."
With its finish, UND earned a first-round bye and will play in Friday night's semifinals. The program also is now two wins away from qualifying for the NCAA tournament.
UND averaged 1,130 fans this season -- a program record. Also, UND's average attendance was the highest in the Big Sky since the 2006 season.


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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $16.99Edition: 2ndCopyright year: 2009Publisher: Indiana University PressPublication date: 8/20/2009Binding: PaperbackPages: 424Size: 6.00" wide x 9.25" long x 1.00" tall Weight: 1.584Language: English
Manuel G. Gonzales is Professor of History at Diablo Valley College and adjunct professor of history at California State University, East Bay. He has also been a visiting professor of Chicano history at the University of California, Berkeley. His publications include Andrea Costa and the Rise of Socialism in the Romagna (Rowman and Littlefield, 1981) and Mexicanos: A History of Mexicans in the United States (University Press of America, 1980).
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All quotes tagged Six
(2113 quotes found)
"Out started six officers, seized my bridle, put their pistols to my breast, ordered me to dismount, which I did. One of them, who appeared to have the command there, and much of a gentleman, asked me where I came from; I told him. He asked what time I left . I told him, he seemed surprised, said ''Sir, may I crave your name?'' I answered ''My name is Revere."
"My doctor gave me six months to live, but when I couldn't pay the bill he gave me six months more."
"How tall are you big boy?
Six foot nine inches!
Let's go up to my place and talk about the nine inches!"
"Magnetism is one of the Six Fundamental Forces of the Universe, with the other five being Gravity, Duct Tape, Whining, Remote Control, and The Force That Pulls Dogs Toward The Groins Of Strangers."
"In spite of the six thousand manuals on child raising in the bookstores, child raising is still a dark continent and no one really knows anything. You just need a lot of love and luck -- and, of course, courage."
"Learn one thing from a lion; one from a crane; four a cock; five from a crow; six from a dog; and three from an ass."
"I'm a Gemini, and I get so bored so easily. I mean, I have moved six times in the last eight years."


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Words, letters, and/or numbers in stylized form
Personalized memorial in the nature of a photograph frame of non-precious metal containing a place to incorporate a photograph of a deceased person
Business in Danville, IL


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Scammer Yana Zharova
|Add comments >>>
|Report scammer >>>
|First name:
|Last name:
|Oksana Shestakova, Irina Zarubina, Oksana Vylegzhanina, Oksana Kolpakova, Julia Kovtyn, Nadezhda
|Name aliases:
|Iana, Ianusha, Ianushenka, Ira, Irchonka, Irchushka, Irena, Irene, Irinka, Irinuska, Irisha, Irishik, Irishka, Irka, Irocha, Irochka, Iroschka, Irushka, Irusichka, Irusik, Irusya, Irwinka, Iryna, Iryush, Iulia, Iuliia, Iuliya, Iyana, Jana, Janna, Janny, Jule, Julechka, Julenka, Julichka, Julie, Juliya, Julusha, Julya, Julye, Kensij, Ksusha, Ksushka, Ksyusha, Ksyushka, Nada, Nadejda, Nadenka, Nadia, Nadiya, Naduha, Nadusha, Nadushok, Nady, Nadya, Oksanka, Oksanochka, Oksanushka, Oksusha, Oksy, Oxana, Susha, Trishka, Ulenka, Ulia, Uliya, Yanka, Yanna, Yanochka, Yanusia, Ylia, Yliya, Ylya, Yryna, Yula, Yulchika, Yulchona, Yulechka, Yulenka, Yulia, Yuliah, Yulichka, Yulija, Yuliy, Yuliya, Yulosha, Yulosha, Yulusha, Yuly, Yulya, Yulyasha
|Kirov (Russia); Kramatorsk (Ukraine); Lugansk (Ukraine); Ternopol (Ukraine); Vinnitsa (Ukraine)
Ukraine, 91000, Lugansk, Solnechnyi block, 4/16
Russia, 613000, Kirov, Shorina str., 30-28
Ukraine, 21000, Vinnitsa, Architektora Artunova str., 4
|Phone number(s):
|E-mail address(es):
|Operates on site(s):
|Lava Life, Mate 1, RBrides, Russian Euro, Singles Net, Site 2 Date
|Scam media:
|Fake documents:
Report N1 (added on June, 6, 2006)
I have her photos and letter listing costs with the agency!
Randy (USA)
Report N2 (added on January, 16, 2007)
Translation scam.
Isaac (Canada)
Report N3 (added on February, 2, 2007)
Scammer had an account on the singles web site of RussianEuro under the name: Oksana, with a member number: 179225. Scammer utilizes email to contact older men. Then seeks to develop trust, by claiming she is planning on visiting the USA and asks to stay with the man. Email contact continues to the point of eventually seeking financial aid while claiming hardship in Moscow.
Douglas (USA)
Report N4 (added on July, 25, 2007)
I have been and I still am in corespondence with this woman. I have 27 emails from her at this time and have used a private agency to check her out which has led me to this site. She has asked me for money for visa/travel docs and I did not send it as of yet I have been stalling for some time and she is still playing along. The address of her residence did not check out and now she has given me an address for her work which will most likely be wrong. I have received one phone call from her only 2 days ago and the number she used did not show up on my phone so I cannot supply it. It showed up as Unknown. I have approximatley 20 photos from her so far and 2 media voice files. I am convinced this is the same woman due to the fact that some of the letters that Hugh has posted are exact carbon copies of some of the letters I have received. Let me know what you want me to submit and I will send it to you asap.
Iver (Canada)
Report N5 (added on July, 25, 2007)
Simple and easy on this one: 3rd letter i am her darling, 4rth letter i am her destiny and her love, and 5th letter is the best.
Nick (Canada)
Report N6 (added on November, 22, 2007)
Same old story.... wanna find a man, but doesn't speak english, so she needs money for translation.... and blah blah blah.... just another stupid scammer!!!
Gianluca (Italy)
Report N7 (added on June, 19, 2008)
Translation scammer; received the customary 4 letters then this:
"Dear Sir, Thank You for the letter. Your Lady Yulya is still interested in Youand we are very happy that You have the same feelings. So this is the needed information for making transfer. Receiver: Yulya KovtynAddress: Vinnitsa, Street Architektora Artunova, 4, 21000 You can make a transfer money through the Western Union. After these You should send us the information about Your transfer:Money Transfer Control Number (10 points), amount of money You sent toYour Lady, full name of the sender and the country where from themoney is sent. This is our price list. You can choose any post You want"
Don (Canada)
Report N8 (added on August, 8, 2008)
She, as several women that i have talked to.. after a few letters i get an email from a translator service wanting me to send money to fill up her account and that she is still interested in me.. they want anywhere from$200.00 to $500.00 to re establish contact with the woman.
Ed (USA)
Report N9 (added on February, 17, 2010)
Jean-Pierre (France)


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Sold in 1lb. Bags/Units
Ingredients: Roasted Oats,* Roasted Sunflower Seed Kernels, Cranberries (sunflower oil, sugar), Sunflower Oil, Honey, Roasted Pumpkin Seeds, Roasted Brown Flax Seed. *certified Gluten Free produced by Gluten Free Harvest Co.
IMPORTANT NOTE: Although we are a dedicated no-nuts equipment facility, if you have allergies to any Gerbs Allergy Friendly products (chocolate, grains, seeds, fruits, rice or oats), please eMail us first before ordering: email@example.com
All of our raw ingredients are processed, packaged, handled, stored, and shipped by trained staff in our family owned & operated facility in Johnston, Rhode Island on dedicated Non-GMO, Vegan, and Kosher Equipment. No Co-packers. No Co-manufacturers. For anyone with a mild to severe food allergy or a family with one, we wish to assure you that this is why Gerbs handles all aspects of production & operation, and we are among a handful of companies in the world who can state this.
This product was sourced by the Buyers at Gerbs who partner with the world's top dedicated Natural, non-GMO, and Organic farms that harvest in dedicated facilities on dedicated equipment so there is no risk of the top food allergen's and/or cross -contamination. Our goal is to give the Allergy Community relief in the battle of living with food allergies.
Gluten Free (including Wheat Free)
Peanut Free
Tree Nut Free
Legume Free
Egg Free
Soy Free
Dairy Free
Fish Free
Shellfish Free
Mustard Free
Sesame Free
NOTE: Orders 10 lbs. & greater will (at Gerbs discretion) ship in one large Bulk bag/package. Please eMail us prior to placing your order, with special requests to avoid bulk shipments (additional charges applicable). The buyer will assume all return shipping fee's back to Gerbs and from Gerbs to the original shipping address. email@example.com
Eating granola may help lower your cholesterol and prevent certain chronic diseases, such as heart disease and cancer. It's a type of breakfast cereal consisting of whole grain oats, nuts and dried fruits. The oats are commonly toasted with a small amount of oil and sweetener, giving the cereal a crunchy texture. Each variation of granola has a slightly different nutritional value. Some may have more sugar, fat, calories or protein, depending on the ingredients.
•Contains Fiber
Whole grain oats and SEEDS, two main ingredients in most granola, contain dietary fiber. From just 1/3 cup of granola, you'll get about 4 grams of fiber. Although it's indigestible by your body, fiber helps to regulate digestion and prevent constipation. It may also help control your blood sugar and promote a feeling of fullness after eating, allowing you to cut calories with less hunger. Soluble fiber found in oats is particularly helpful for lowering bad cholesterol levels. The soluble fiber binds to bile acids, which contain cholesterol, in your digestive tract and removes them from your body.
•Provides Beneficial Fats
Granola is a good source of healthy fats, which come from the nuts, seeds and oils it contains. A serving of granola gives you about 4 grams of monounsaturated fatty acids and about 4 grams of polyunsaturated fatty acids. These two forms of fat may help lower cholesterol and blood pressure, and reduce inflammation. Among other things, these effects can help to prevent or manage heart disease, diabetes, cancer and inflammatory conditions. Omega-3 fatty acids, a type of polyunsaturated fatty acid, in granola are essential for proper brain function.
•Supplies Vitamins
Whole grain foods, such as granola, generally contain more vitamins and minerals per serving than refined cereals. Vitamin E, thiamin and folate are all found in significant amounts in granola. The oils, nuts and seeds in granola provide vitamin E, which acts as an antioxidant in your body to protect from damaging free-radical compounds. It also plays a part in maintaining the health of your heart, skin and nervous system. Thiamin and folate are B vitamins that aid in energy metabolism, nerve function, cell growth and the prevention of certain neural tube birth defects.
•A Good Source of Minerals
Granola contains almost every mineral essential to your health. Magnesium, phosphorus, zinc, copper, manganese and selenium are present in the highest percent of your daily needs. Magnesium plays a part in more than 300 enzyme reactions in your body, including energy production, calcium use and maintenance of healthy bones. Phosphorus aids in acid-base balance in your body and production of some proteins. Selenium, zinc, copper and manganese, although needed in only small amounts by your body, are essential for the formation of connective tissues, red blood cells and bones. They also help to maintain healthy immune, nervous and cardiovascular system function; aid in regulating the thyroid; and contribute to proper healing.
If properly stored, our Products will stay fresh so that you can enjoy them for an average 6-8 months. We strongly recommend storing in an airtight (dark colored/opaque) container in a cool, dark environment like a pantry or kitchen cabinet, away from direct exposure to sunlight or excessive heat like an oven. The amount of times you open the container and let in the harmful effects of oxygen will only increase the likelihood of rancidity; thus we encourage you do not empty more than 1 pound of product at a time, and to enjoy at least 1-3 ounces per day for optimal health benefits.
|1 lbs
|1 x 1 x 1 in
|Frequency (how many times a month)
1 x a month, 2 x a month, 3 x a month, 4 x a month, One Time Order
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