Ionic mechanisms underlying tonic and phasic firing behaviors in retinal ganglion cells

In the retina, the firing behaviors that ganglion cells exhibit when exposed to light stimuli are very important due to the significant roles they play in encoding the visual information. However, the detailed mechanisms, especially the intrinsic properties that generate and modulate these firing behaviors is not completely clear yet. In this study, 2 typical firing behaviors—i.e., tonic and phasic activities, which are widely observed in retinal ganglion cells (RGCs)—are investigated. A modified computational model was developed to explore the possible ionic mechanisms that underlie the generation of these 2 firing patterns. Computational results indicate that the generation of tonic and phasic activities may be attributed to the collective actions of 2 kinds of adaptation currents, i.e., an inactivating sodium current and a delayed-rectifier potassium current. The concentration of magnesium ions has crucial but differential effects in the modulation of tonic and phasic firings, when the model neuron is driven by N-methyl-D-aspartate (NMDA) -type synaptic input instead of constant current injections. The proposed model has robust features that account for the ionic mechanisms underlying the tonic and phasic firing behaviors, and it may also be used as a good candidate for modeling some other firing patterns in RGCs.     

Ionic mechanisms underlying tonic and phasic firing behaviors in retinal ganglion cells: A model study

In the retina, the firing behaviors that ganglion cells exhibit when exposed to light stimuli are very important due to the significant roles they play in encoding the visual information. However, the detailed mechanisms, especially the intrinsic properties that generate and modulate these firing behaviors is not completely clear yet. In this study, 2 typical firing behaviors—i.e., tonic and phasic activities, which are widely observed in retinal ganglion cells (RGCs)—are investigated. A modified computational model was developed to explore the possible ionic mechanisms that underlie the generation of these 2 firing patterns. Computational results indicate that the generation of tonic and phasic activities may be attributed to the collective actions of 2 kinds of adaptation currents, i.e., an inactivating sodium current and a delayed-rectifier potassium current. The concentration of magnesium ions has crucial but differential effects in the modulation of tonic and phasic firings, when the model neuron is driven by N-methyl-D-aspartate (NMDA) -type synaptic input instead of constant current injections. The proposed model has robust features that account for the ionic mechanisms underlying the tonic and phasic firing behaviors, and it may also be used as a good candidate for modeling some other firing patterns in RGCs.     

Slope-Based Stochastic Resonance: How Noise Enables Phasic Neurons to Encode Slow Signals

Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal''s rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.     

A model for repetitive firing in neurons

This paper describes a model for the generation of repetitive firing patterns in single neurons to be used as a module in large-scale network simulation studies. The model is based on the combination of extended versions of Hill's model for accomodation and of Kernell's model for adaptation. Both digital computer and electronic circuit realizations of the model are presented. The model is shown to produce strength-duration curves for accomodation which are compatible with available data from real neurons. Both “high ceiling” and “low ceiling” cell types can be matched by adjusting parameters in the model. An equation relating steady-state firing rate to amplitude of applied steady current is presented which includes the accumulation of potassium conductance changes with repetitive firing. The occurence of phasic and tonic responses to step stimulation is mapped in the parameter space of the model. Several representative response patterns to irregular inputs are presented.     

Voltage dependent activation of tonic contraction in cardiac myocytes.

Contractions of isolated single myocytes of guinea pig heart stimulated by rectangular depolarizing pulses consist of a phasic component and a voltage dependent tonic component. In this study we analyzed the mechanism of activation of the graded, sustained contractions elicited by slow ramp depolarization and their relation to the components of contractions elicited by rectangular depolarizing pulses. Experiments were performed at 37 degrees C in ventricular myocytes of guinea pig heart. Voltage-clamped myocytes were stimulated by the pulses from the holding potential of -40 to +5 mV or by ramp depolarization shifting voltage within this range within 6 s. [Ca2+]i was monitored as fluorescence of Indo 1-AM and contractions were recorded with the TV edge-tracking system. Myocytes responded to the ramp depolarization between -25 and -6 mV by the slow, sustained increase in [Ca2+]i and shortening, the maximal amplitude of which was in each cell similar to that of the tonic component of Ca2+ transient and contraction. The contractile responses to ramp depolarization were blocked by 200 microM ryanodine and Ca2+-free solution, but were not blocked by 20 microM nifedipine or 100-200 microM Cd2+ and potentiated by 5 mM Ni2+. The responses to ramp depolarization were with this respect similar to the tonic but not to the phasic component of contraction: both components were blocked by 200 microM ryanodine, and were not blocked by Cd2+ or Ni2+ despite complete inhibition of the phasic Ca2+ current. However, the phasic component but not the tonic component of contraction in cells superfused with Ni2+ was inhibited by nifedipine. Both components of contraction were inhibited by Ca2+-free solution superfused 15 s prior to stimulation. CONCLUSIONS: In myocytes of guinea pig heart the contractile response to ramp depolarization is equivalent to the tonic component of contraction. It is activated by Ca2+ released from the sarcoplasmic reticulum by the ryanodine receptors. Their activation and inactivation is voltage dependent and it does not depend on the Ca2+ influx by the Ca2+ channels or reverse mode Na+/Ca2+ exchange, however, it may depend on Ca2+ influx by some other, not yet defined route.     

Real-time decoding of dopamine concentration changes in the caudate-putamen during tonic and phasic firing

The fundamental process that underlies volume transmission in the brain is the extracellular diffusion of neurotransmitters from release sites to distal target cells. Dopaminergic neurons display a range of activity states, from low-frequency tonic firing to bursts of high-frequency action potentials (phasic firing). However, it is not clear how this activity affects volume transmission on a subsecond time scale. To evaluate this, we developed a finite-difference model that predicts the lifetime and diffusion of dopamine in brain tissue. We first used this model to decode in vivo amperometric measurements of electrically evoked dopamine, and obtained rate constants for release and uptake as well as the extent of diffusion. Accurate predictions were made under a variety of conditions including different regions, different stimulation parameters and with uptake inhibited. Second, we used the decoded rate constants to predict how heterogeneity of dopamine release and uptake sites would affect dopamine concentration fluctuations during different activity states in the absence of an electrode. These simulations show that synchronous phasic firing can produce spatially and temporally heterogeneous concentration profiles whereas asynchronous tonic firing elicits uniform, steady-state dopamine concentrations.     

Firing patterns in the adaptive exponential integrate-and-fire model

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.     

Discharge mechanism of pigeon optic tectum neurons in an in vitro preparation

The pattern of discharge of neurones of the pigeon's optic tectum to directly injected depolarizing current was investigated in in vitro slice preparation. Three patterns of discharge were found: some neurones (types I and II) give a tonic response: type I-neurones exhibited a repetitive firing whereas type II-neurones showed grouped discharges (doublets or triplets). Type III-neurones displayed a phasic response formed by a few action potentials of decreasing amplitude, triggered at the onset of the current pulse. Each pattern of response was associated with a specific shape of action potential.     

Phasic Firing in Vasopressin Cells: Understanding Its Functional Significance through Computational Models

Vasopressin neurons, responding to input generated by osmotic pressure, use an intrinsic mechanism to shift from slow irregular firing to a distinct phasic pattern, consisting of long bursts and silences lasting tens of seconds. With increased input, bursts lengthen, eventually shifting to continuous firing. The phasic activity remains asynchronous across the cells and is not reflected in the population output signal. Here we have used a computational vasopressin neuron model to investigate the functional significance of the phasic firing pattern. We generated a concise model of the synaptic input driven spike firing mechanism that gives a close quantitative match to vasopressin neuron spike activity recorded in vivo, tested against endogenous activity and experimental interventions. The integrate-and-fire based model provides a simple physiological explanation of the phasic firing mechanism involving an activity-dependent slow depolarising afterpotential (DAP) generated by a calcium-inactivated potassium leak current. This is modulated by the slower, opposing, action of activity-dependent dendritic dynorphin release, which inactivates the DAP, the opposing effects generating successive periods of bursting and silence. Model cells are not spontaneously active, but fire when perturbed by random perturbations mimicking synaptic input. We constructed one population of such phasic neurons, and another population of similar cells but which lacked the ability to fire phasically. We then studied how these two populations differed in the way that they encoded changes in afferent inputs. By comparison with the non-phasic population, the phasic population responds linearly to increases in tonic synaptic input. Non-phasic cells respond to transient elevations in synaptic input in a way that strongly depends on background activity levels, phasic cells in a way that is independent of background levels, and show a similar strong linearization of the response. These findings show large differences in information coding between the populations, and apparent functional advantages of asynchronous phasic firing.     

Tonic and phasic receptor neurons in the vertebrate olfactory epithelium

Olfactory receptor neurons (ORNs) respond to odorants with characteristic patterns of action potentials that are relevant for odor coding. Prolonged odorant exposures revealed three populations of dissociated toad ORNs, which were mimicked by depolarizing currents: tonic (TN, displaying sustained firing, 49% of 102 cells), phasic (PN, exhibiting brief action potential trains, 36%) and intermediate neurons (IN, generating trains longer than PN, 15%). We studied the biophysical properties underlying the differences between TNs and PNs, the most extreme cases among ORNs. TNs and PNs possessed similar membrane capacitances (approximately 4 pF), but they differed in resting potential (-82 versus -64 mV), input resistance (4.2 versus 2.9 G(Omega)) and unspecific current, I(u) (TNs: 0 < I(u) 1 pA/pF). Firing behavior did not correlate with differences in voltage-gated conductances. We developed a mathematical model that accurately simulates tonic and phasic patterns. Whole cell recordings from rat ORNs in fragments (approximately 4 mm(2)) of olfactory epithelium showed that such a tissue normally contains tonic and phasic receptor neurons, suggesting that this feature is common across a wide range of vertebrates. Our findings show that the individual passive electrical properties can govern the firing patterns of ORNs.     

The sensitivity of Renshaw cells to velocity of sinusoidal stretches of the triceps surae muscle.

1. The electrical activity of Renshaw cells monosynaptically excited by ventral root stimulation and disynaptically excited by electric stimulation of the group I afferents in the GS nerve has been recorded and their response to individual sinusoidal stretches of the deefferented GS muscle tested for different amplitudes and durations of the stimulus. 2. The experimental data indicate that the Rensahw cell responses are not only length dependent but also rate dependent. This finding indicates that the same Renshaw cells receive recurrent collaterals of both tonic and phasic motoneurons. 3. The observation that the discharge of Renshaw cells is particularly sensitive to the velocity of stretch suggests that the recurrent collaterals of large phasic motoneurons, which are recruited during high velocity stretches, exert a stronger excitatory action on Renshaw cells than do axon collaterals of the smaller tonic motoneurons, which are selectively stimulated during low velocity stretches.     

Unconfined compression of articular cartilage: nonlinear behavior and comparison with a fibril-reinforced biphasic model

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample's radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models.     

Cerebellar cortical activity during stretch of antagonist muscles

Single unit activity was recorded from the anterior lobe of the cerebellum during ramp and hold stretches of limb muscles in chloralose anesthetized cats. The activity of 95 "phasic" units showed a transient response during dynamic stretch of at least one muscle usually lasting for less than 350 ms following the stimulus onset. The activity of 59 phasic-tonic units was modified not only during dynamic stretch but also during the 1 s of maintained muscle length. All Purkinje cells, identified by their complex spikes, that responded to muscle stretch demonstrated exclusively phasic changes in discharge. Fourteen of 25 Purkinje cells (56%) responded to stretch of both antagonist muscles and these responses were always similar rather than reciprocal. From the 129 units without complex spikes, 70 demonstrated phasic discharge patterns whereas 59 had tonic responses. Seventy-five (59%) of these unidentified units revealed convergent responses to stretch of both antagonists, compared with 54 which responded to stretch of one muscle only. Of the unidentified units receiving convergent afferents from antagonist muscles, 62 (83%) had similar responses and only 13 (17%) had reciprocal reactions. There appeared to be no evidence that muscle afferents alone can induce reciprocal discharge patterns in Purkinje neurons of the cerebellar cortex. The firing frequency of some phasic-tonic units was correlated with both the velocity and amplitude of muscle stretch. No Purkinje cells were found with activity related to either velocity or amplitude of muscle stretch. One phasic and seven phasic-tonic unidentified units were activated at fixed latencies following trains of electrical stimulation applied to the thoracic spinal cord at frequencies exceeding 200 Hz, implying they were terminal portions of mossy fibers originating from direct spinocerebellar tracts. A few recordings of compound potentials were presumed to arise from the cerebellar glomeruli. The changing form of one of these potentials suggested that the glomerulus might be a site at which somatosensory peripheral information is modified by the cerebellar cortex.     

Methamphetamine neurotoxicity decreases phasic, but not tonic, dopaminergic signaling in the rat striatum

Neurotoxic doses of methamphetamine (METH) are known to cause depletions in striatal dopamine (DA) tissue content. However, the effects of METH-induced insults on dopaminergic neurotransmission are not fully understood. Here, we employed fast-scan cyclic voltammetry at a carbon-fiber microelectrode in the anesthetized rat striatum to assess the effects of a neurotoxic regimen of METH on phasic and tonic modes of dopaminergic signaling and underlying mechanisms of DA release and uptake. Extracellular DA was electrically evoked by stimulation of the medial forebrain bundle mimicking tonic and phasic firing patterns for dopaminergic cells and was monitored simultaneously in both the dorsomedial and dorsolateral striatum. Kinetic analysis of evoked recordings determined parameters describing DA release and uptake. Striatal DA tissue content was quantified by high performance liquid chromatography with electrochemical detection. METH-pretreatment (four doses of 7.5 or 10.0 mg/kg s.c.) induced DA depletions of ～ 40% on average, which are reported in both striatal subregions. METH pre-treatment significantly decreased the amplitude of signals evoked by phasic, but not tonic, stimulation. Parameters for DA release and uptake were also similarly reduced by ～ 40%, consistent with effects on evoked phasic-like responses and DA tissue content. Taken together, these results suggest that METH-pretreatment selectively diminishes phasic, but not tonic, dopaminergic signaling in the dorsal striatum.     

Endogenous burst capability in a neuron of the gastric mill pattern generator of the spiny lobster Panulirus interruptus

The gastric system of the lobster stomatogastric ganglion has previously been thought to include no neurons capable of endogenous bursting. We describe conditions under which one of the motorneurons, the CP cell, can burst endogenously in a free-running manner in the absence of other phasic network activity. Isolated preparations of the foregut nervous system were used, and the CP bursting was either spontaneous or was activated by continuous stimulation of an input nerve. Three criteria were applied to establish the endogenous nature of such burst generation in CP: absence of phasic input, reset of the bursting pattern by pulses of current in a characteristic phase-dependent manner, and modulation of burst rate by sustained injected current. (1) The firing of other cells which are known to be related synaptically to CP was monitored in nerve records. These other cells were either silent or fired only tonically. Cross-correlograms showed that CP bursting was not ascribable to phasic activity in these other network cells. (2) A depolarizing current pulse of sufficient strength injected intracellularly between bursts triggered a burst prematurely and reset the subsequent rhythm. A hyperpolarizing pulse during a burst terminated it and reset the subsequent rhythm. Reset behavior was similar to that described for other endogenous bursters. (3) Application of a positive-going ramp current initially caused an increase in burst rate, as described for other endogenous bursters. However, further depolarization caused a slower burst rate due to lengthening of the individual bursts, although mean firing frequency continued to increase throughout the range tested. Such free-running endogenous repetitive bursting appeared to result from the CP's ability to produce slow regenerative depolarizations (“plateau potentials”). When bursting was present, so was the plateau property, as determined by I–V analysis and by the ability of brief current pulses to trigger and terminate bursts. The previous inability to observe endogenous bursting in preparations with central input removed may be due to the usual absence of the plateau property in such preparations.     

Model of the firing frequency of the chelonian muscle spindle

A model is proposed for the frequency of firing of the chelonian muscle spindle in response to mechanical stretches. First an attempt is made to fit the response to a first and second order model and, after incorporating the encoding properties of the spindle, a simulation is obtained which predicts in terms of the instantaneous frequency of firing the response of the spindle to ramp and sinusoidal mechanical stretches.     

A model of a thalamic neuron

We modify our recent three equilibrium-point model of neuronal bursting by a means of a small deformation of the nullclines in the x-y phase plane to give a model that can have as many as five equilibrium points. In this model the middle stable equilibrium point (e.p.) is separated from the outer stable and unstable e.ps by two saddle points. If the system is started at rest at the middle stable e.p. it has the following complex properties: A short suprathreshold current pulse switches the model from a silent state to a bursting state, or to give a single burst, depending on the choice of parameters. A subthreshold depolarizing current step gives a passive response at rest, but if the model is either constantly hyperpolarized or constantly depolarized, then the same current step gives different active responses. At a hyperpolarized level this consists of a burst response that shows refractoriness. At a depolarized level it consists of tonic firing with a linear frequency--current relationship. Hyperpolarization from rest is followed by post-inhibitory rebound. The model responds in a unique and characteristic way to an applied current ramp. These properties are very similar to those that have been recently recorded intracellularly from neurons in the mammalian thalamus. In the x-y phase plane our models of the repetitively firing neuron, the bursting neuron and the thalamic neuron form a progression of models in which the y nullcline in the subthreshold region is deformed once to give the burst neuron model, and a second time to give the thalamic neuron model. Each deformation can be interpreted as corresponding to the inclusion of a slow inward current in the model. As these currents are included so the associated firing properties increase in complexity.     

Characterization of muscle spindle afferents in the adult mouse using an in vitro muscle-nerve preparation

We utilized an in vitro adult mouse extensor digitorum longus (EDL) nerve-attached preparation to characterize the responses of muscle spindle afferents to ramp-and-hold stretch and sinusoidal vibratory stimuli. Responses were measured at both room (24°C) and muscle body temperature (34°C). Muscle spindle afferent static firing frequencies increased linearly in response to increasing stretch lengths to accurately encode the magnitude of muscle stretch (tested at 2.5%, 5% and 7.5% of resting length [Lo]). Peak firing frequency increased with ramp speeds (20% Lo/sec, 40% Lo/sec, and 60% Lo/sec). As a population, muscle spindle afferents could entrain 1:1 to sinusoidal vibrations throughout the frequency (10-100 Hz) and amplitude ranges tested (5-100 μm). Most units preferentially entrained to vibration frequencies close to their baseline steady-state firing frequencies. Cooling the muscle to 24°C decreased baseline firing frequency and units correspondingly entrained to slower frequency vibrations. The ramp component of stretch generated dynamic firing responses. These responses and related measures of dynamic sensitivity were not able to categorize units as primary (group Ia) or secondary (group II) even when tested with more extreme length changes (10% Lo). We conclude that the population of spindle afferents combines to encode stretch in a smoothly graded manner over the physiological range of lengths and speeds tested. Overall, spindle afferent response properties were comparable to those seen in other species, supporting subsequent use of the mouse genetic model system for studies on spindle function and dysfunction in an isolated muscle-nerve preparation.     

High-Frequency Stimulation of Excitable Cells and Networks

High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks.     

The role of the medial preoptic area in the organization of paradoxical sleep

Influence of electrical stimulation of the medial preoptic area of cats on characteristics of paradoxical sleep and activity of medial preoptic neurons were studied in the course of sleep-waking cycle. Low-frequency stimulation of this structure in the state of slow-wave sleep evoked short-latency electrocortical desynchronization and induced transition to paradoxical sleep or paradocical sleep-like state. The same stimulation during the whole period of paradoxical sleep results in a reduction of its duration, practically complete disappearance of tonic stage, and increase in the density of rapid eye movements in phasic stage. The vast majority of meurons in the medial preoptic area decreased their firing rates during quiet waking and slow-wave sleep and dramatically increased their activity during paradoxical sleep. More than 50% of such neurons displayed activation 20-70 s prior to the appearance of electrocorticographic correlates of paradoxical sleep. Some neurons were selectively active during paradoxical sleep. Approximately 50% of cells increased their firing rates a few seconds prior to and/or during series of rapid eye movements. The results suggest that the medial preoptic area contains the units of the executive system (network) of paradoxical sleep and are involved in the mechanisms of neocortical desynchronization.