INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The vestibuloocular reflex (VOR) is a useful behavior with which to probe cerebellar function, primarily due to the well-defined and economical neural architecture of VOR pathways and the accessibility of these circuits for study. Modulation in the gain of this reflex (eye velocity/head velocity) represents a form of motor learning. The cerebellum is intimately involved in this process, since the cerebellar flocculus projects directly to brain stem cells that are critical participants in the VOR neuronal arcs (Langer et al. 1985), and removal or inactivation of the flocculus precludes further changes in VOR gain (Lisberger et al. 1984; Zee et al. 1981).

Ito (1972, 1982) proposed the flocculus hypothesis based on theories of cerebellar cortical function (Albus 1971; Marr 1969), wherein the flocculus is an adaptive VOR side path that inhibits the main VOR pathways. Miles and Lisberger (1981) proposed that there might be modifiable sites in both the flocculus and brain stem and that the flocculus might provide error signals to the brain stem to facilitate learning there. In support of the former proposal, Ito et al. (1974) reported changes in Purkinje cell activity of the rabbit that were coincident with changes in VOR gain, and Watanabe (1984, 1985) showed in monkey that Purkinje cells changed their response modulation during VOR following VOR gain change. Miles et al. (1980) reported that, in monkey, Purkinje cells change their firing pattern during cancellation of the VOR after learning, but argued that the direction of the change was incorrect to support the acquired VOR gain change. Lisberger et al. (1994a,b) demonstrated in monkey that both Purkinje cells and flocculus target neurons (FTNs) change their firing patterns in response to a step of head movement after learning, but that changes in the firing patterns had a latency too long to support the earliest changes in the VOR. This led them to propose the brain stem hypothesis and later the multiple site hypothesis in which the FTNs are the main adaptive site. Partsalis et al. (1995b) showed that in monkey a part of the learning remained in the FTN modulation after chemical inactivation of the flocculus, supporting the multiple site hypothesis.

Analyses of single-unit recording in relation to sensory input and/or motor output can be a powerful tool in elucidating the mechanisms of sensory-motor transformation implemented by a neuronal circuit or system. However, if the system consists of parallel and multiple stages of information processing and each stage is recursively connected by feedback loops, it is sometimes difficult to clarify the origin of the observed activity. Also when neurons receive multi-modal inputs, it may be difficult to specify which modality caused a change in neuronal activity. Floccular Purkinje cells receive vestibular and visual signals from brain stem vestibular neurons and pontine neurons, respectively, and contribute to the generation of motor commands to move the eyes. The resultant commands are fed back to flocculus as an efference copy signal. Therefore even if we see a change in the Purkinje cell firing after VOR adaptation, it may be difficult to specify the locus of the change.

One solution is to divide the neuronal circuit into subsystems that represent each stage of information processing and then identify the input-output relations of the subsystems. This system identification approach may clarify the flow of information between subsystems, and the subsystem or subsystems responsible for a behavioral change might be elucidated. Presently, we employed this approach to specify the locus of the VOR adaptation and the role of flocculus. We divided the vertical (V) VOR and optokinetic reflex (OKR) neuronal substrate into a pathway that passes through flocculus (FL pathway) and one that does not (nonFL pathway). The FL pathway was further divided into a subsystem that includes the pathway from sensory input to flocculus (preFL and FL subsystem) and a subsystem that includes the pathway from flocculus to motor output (postFL subsystem). Also, the preFL and FL subsystem and the nonFL subsystem in which multi-modal signal processing is executed were divided into subsystems, each of which represents signal processing for a single modality. Thus the information processing executed in preFL and FL vestibular, preFL and FL visual, preFL and FL efference copy, postFL, nonFL visual, and nonFL vestibular pathways could be evaluated separately.

Several similar computational studies have addressed the problem of the site of VOR motor learning. Fujita (1982) showed in his adaptive filter model that VOR adaptation could be achieved based on the framework of the flocculus hypothesis. Gomi and Kawato (1992) showed that VOR/OKR adaptation could be realized by assuming the flocculus hypothesis in their model adopting a feedback error learning scheme. Lisberger and Sejnowski (1992) and Lisberger (1994) suggested that changes in the flocculus together with those in FTNs are required to achieve stability in the VOR circuitry. The simulations of Quinn et al. (1998) suggested that both FTNs and flocculus Purkinje cells change their characteristics after VOR learning, supporting the multiple site hypothesis.

In contrast to these computational approaches in which model parameters were determined heuristically, there has been no study employing system identification techniques that used real experimental data to determine characteristics of the subsystems that compose the VOR. Our method can identify the transfer function of each of the subsystems described using experimental data. No presumption for adaptability of any of the subsystems was made, and thus all subsystems were free to change their characteristics in parallel with VOR gain adaptation.

The results illustrate that characteristics of the preFL and FL subsystems related to head movement change with VVOR adaptation while those of other preFL and FL subsystems remain stable. In keeping with our previous work, the characteristics of the nonFL subsystem related to head movement that includes the Y-group and FTNs also change with the learning. With the use of this information, a role for the cerebellar flocculus in VOR adaptation is discussed. Preliminary reports have appeared (Hirata et al. 1999). A glossary of terms used for experimental paradigms is provided in Table 1.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Description of the model

Figure 1A is a diagram of the known synaptic linkage within the VVOR/VOKR pathways, and Fig. 1B is the model. In Fig. 1A, input to the circuit arises from motion of the head, the visual surround, or both. The output is an eye movement. Eye movements are fed back via an external physical feedback loop to a summing junction where they are combined with visual movements and head movements computed as retinal inputs. Head velocity and acceleration are decoded by the vestibular organ and act as inputs to superior vestibular nucleus (SVN) and position vestibular pause (PVP) neurons in medial vestibular nucleus (MVN) (McCrea et al. 1987; Mitsacos et al. 1983). The flocculus receives head motion information via the floccular projecting neurons (FPNs) (Zhang et al. 1993) that modulate exclusively to head motion, not eye motion at the 0.5-Hz sinusoidal stimuli applied. Signals similar to those on FPNs reflecting head motion have also been recorded as input elements within the primate flocculus (Lisberger and Fuchs 1978; Miles et al. 1980). Retinal slip information arrives as mossy fiber inputs at the flocculus via the middle temporal area (MT)/medial superior temporal area (MST)/dorsolateral pontine nucleus (DLPN) or nucleus reticularis tegmenti pontis (NRTP) circuit (Kawano et al. 1992, 1994). An efference copy of ascending eye movement commands is relayed, e.g., via axon collaterals of the ascending vestibular nucleus neurons terminating in the midline paramedian tract (PMT) cells that are prefloccular nuclei (Blanks et al. 1983; Buttner-Ennever et al. 1989; McCrea et al. 1987). The output of these midline PMT nuclei provides a mossy fiber input that reflects an efference copy of ascending oculomotor commands (Buttner-Ennever et al. 1989; McCrea et al. 1987). Signals reflecting a copy of the ascending oculomotor commands present on vestibular nuclear neurons have also been recorded in primate flocculus as input elements (Lisberger and Fuchs 1978; Miles et al. 1980). Another candidate source for an efference copy signal might be the prepositus hypoglossi. The Y group receives head motion information via SVN interneurons reflecting both anterior and posterior canal input (Blazquez et al. 1994, 2000) and Y-group and SVN-FTNs receive the terminals of floccular Purkinje cells (Langer et al. 1985; Partsalis et al. 1995a; Zhang et al. 1995). FTN and Y group outputs project to the extraocular motor neurons that send the final command to move the eyes. This diagram does not include the OKN indirect pathway because the stimulus currently employed was outside of the frequency range in which the OKN indirect pathway is activated. Further, signals carried on climbing fibers to the flocculus have not been addressed in the present experiments. VOR gain change or motor learning within the context of the VOR implies that the brain's assessment of the magnitude of head motion is the variable that is reevaluated or learned. This head motion signal is carried by mossy fibers. Climbing fiber signals might be more related to underlying mechanisms that achieve VOR learning and are not addressed here. This diagram does not show visual pathways that do not pass through the flocculus to avoid complexity of the diagram, but these are included in the model in Fig. 1B.

View larger version (43K): [in this window] [in a new window]   Fig. 1. Vertical vestibuloocular reflex (VOR) and optokinetic reflex (OKR) neuronal circuit (A) and model (B). In A, FPN and FTN are the floccular projecting neurons and the floccular target neurons in superior vestibular nuclei (SVN), respectively, Y is dorsal Y group, Int. is the inter-neurons in SVN projecting to Y group. P is a floccular Purkinje cell, and g is a granule cell. PVP is position vestibular pause neurons in medial vestibular nuclei (MVN). MT, MST and DLPN are the middle temporal visual area, the medial superior temporal area, and the dorsolateral pontine nuclei, respectively. MN, extraocular motor neurons; LTN, lateral terminal nucleus of the accessory optic system. Colors in the background in A correspond to colors of the blocks in B. In B, G(s), G(s), and G(s) are prefloccular/floccular subsystems each of which represents a transfer function of prefloccular/floccular efference copy pathway, vestibular pathway, and visual pathway, respectively. The 3 components are added in the flocculus and form the Purkinje cell simple spike (SS) output. GpostFL(s) represents a transfer function of postfloccular pathway, which transfers the Purkinje cell SS activity to a part of the motor command. G(s) and G(s) represent transfer functions of nonfloccular visual and vestibular pathways, respectively. Corresponding neuronal circuit to G(s) is not shown in A. The block on the left hand side of G(s) represents a nonlinear transformation of retinal slip to linearize its relationship to Purkinje cell activity. h(t), d(t), r(t), f(t), ecopy(t), and x(t) are head movement, optokinetic stimulus movement, retinal slip movement, floccular Purkinje cell SS activity, efference copy signal, and eye movement, respectively.

Figure 1B is a block diagram of the VVOR/VOKR system configured around the flocculus reflecting the pathways in Fig. 1A. This model consists of three components, namely 1) prefloccular/floccular (preFL and FL), 2) postfloccular (postFL), and 3) nonfloccular (nonFL) systems. The preFL and FL system includes signal processing executed in prefloccular pathways and in the flocculus itself, and its output is indicated as floccular Purkinje cell simple spike (SS) activity. In the current study, only SS firing was analyzed as mentioned above. For this reason, Fig. 1B does not include a pathway from the inferior olive to flocculus (in this report the term flocculus should be understood to mean both the true flocculus and the ventral paraflocculus). The three kinds of mossy fiber input to the flocculus are explicitly described as separate pathways in the preFL and FL system. In each pathway, the sensory or original efference copy signal is processed by a subsystem G(s), G(s), or G(s) for vestibular, visual, or efference copy signals, respectively, and is converted into floccular Purkinje cell SS activity. The postFL system G_postFL(s) and subsequent oculomotor muscle plant transfer Purkinje cell activity into eye movements. The nonFL system consists of two pathways, each processing vestibular or visual sensory signals and converting them into eye movements. Signal processing executed in the nonFL visual and vestibular pathways are described by the transfer functions G(s) and G(s), respectively.

The following assumptions were made for the model structure based on previous physiological evidence. 1) The interaction of vestibular, visual, and efference copy signals in the flocculus is linear in the stimulus range employed (Lisberger and Fuchs 1978; Miles and Fuller 1975). 2) Interaction between signals from floccular and nonfloccular pathways is linear in the stimulus range employed (Robinson 1977). The plausibility of these assumptions was tested by predicting system outputs in response to unknown inputs (cf. Evaluation of model adequacy and estimated parameters).

The following system identification technique was developed to identify characteristics of each subsystem by using sensory input, motor output signals, and floccular Purkinje cell activity.

System identification technique

One direct method to identify a system's characteristics is to measure the input and output of a system simultaneously. In biological systems, however, this direct approach is not always possible due to technical difficulties and to the structural complexity of the system. Thus we embarked on the following approach to identify each subsystem in the model. The method consists of four steps.

Presently only slow phase eye movements and corresponding Purkinje cell SS activity were studied, assuming that slow phase and quick phase eye movements are generated by independent mechanisms. Also it was assumed that each subsystem is time invariant during one recording set that consists of about 5 min of several visual-vestibular mismatch paradigms.

IDENTIFICATION OF THE PRE-FLOCCULAR/FLOCCULAR SUBSYSTEMS: G(s), G(s), G(s). The system equation for the preFL and FL system in the Laplace transform domain is expressed as follows
where s denotes the Laplace operator while F(s), H(s), R(s), and E(s) denote Laplace transforms of floccular Purkinje cell SS firing rate f(t)¹, vertical head movement h(t) (head position), retinal slip r(t) (retinal slip position), and efference copy ecopy(t), respectively. Position, velocity, and acceleration of the eye, head, and retinal slip movements are vertical unless otherwise specified. G(s) is a transfer function of the semicircular canals, and since it can be assumed that its characteristics are not affected by the gain of VOR (Miles et al. 1980), it is incorporated into G(s) hereafter. G_r(s) is a transfer function of the retina. We also assume that its characteristics are not affected by the gain of the VOR and incorporate it into G(s). Therefore the above equation becomes

(1)

If it is assumed that 1) head velocity and acceleration signals, 2) retinal slip velocity and acceleration signals contribute to Purkinje cell firing modulation, and that 3) efference copy signals convey eye velocity information, the system equation in the time domain can be expressed as the following multiple linear regression model

(2)

where _h [spk/s per deg/s²], _h [spk/s per deg/s], _r [spk/s per deg/s²], _r [spk/s per deg/s], _e [spk/s per deg/s], and  [spk/s] are regression coefficients and denote sensitivities of Purkinje cell firing to head acceleration acc_h(t), velocity vel_h(t), retinal slip acceleration acc_r(t), velocity vel_r(t), efference copy signals ecopy(t), and the dc component of Purkinje cell firing, respectively. _h [s], _r [s], and _e [s] denote delays between head movement and Purkinje cell activity, retinal slip and Purkinje cell activity, and efference copy signals and Purkinje cell activity, respectively. (t) is the error term whose mean is 0. The assumptions made above are plausible if we consider that 1) the vestibular nerve signal conveys mainly head velocity and acceleration (Goldberg and Fernandez 1971), 2) the contribution of retinal slip position was significant only in the very low-frequency range (Kobayashi et al. 1998) that was not presently used, and 3) mossy fibers convey an efference copy of oculomotor motor commands to the flocculus predominantly as an eye velocity signal (Miles et al. 1980; Stone and Lisberger 1990).

Step 1: identification of G(s), G(s).

(3)

Step 2: identification of G(s).

IDENTIFICATION OF POST-FLOCCULAR AND NON-FLOCCULAR SUBSYSTEMS: G_postFL(s), G(s), G(s). The system equation for the postFL and nonFL systems in the Laplace domain is expressed as follows
where G_m(s) and X(s) denote a transfer function of the ocular muscle plant and a Laplace transform of eye movement (eye position), respectively. Since it is assumed that the characteristics of G_m(s) as well as G(s) and G_r(s) do not change with VOR gain change, they were incorporated into G(s), G(s), or G_postFL(s). Thus the above equation becomes

(5)

This can be rewritten as
It has been shown that Purkinje cell firing encodes a part of eye movement inverse-dynamics in terms of a linear combination of eye acceleration, velocity, and position (Shidara et al. 1993). This means that the postFL pathway can be described by a second-order linear system. If we assume that nonFL subsystems can also be characterized by a second-order linear system within the input range currently employed, the above equation can be expressed in the time domain as follows

(6)

where a_x [spk/s per deg/s²], b_x [spk/s per deg/s], c_x [spk/s per deg] denote sensitivities of Purkinje cell firing rate to eye acceleration acc_x(t), velocity vel_x(t), and position pos_x(t), respectively while _x [s] denotes a delay time between Purkinje cell activity and eye movement.  is the dc term and (t) is the error term whose mean is 0. a_r, b_r, a_h, _r, and _h together with a_x, b_x, c_x, and _x determine the second-order transfer functions of nonFL subsystems and postFL subsystem as follows


Thus identifying each nonFL subsystem and postFL system results in determining the regression coefficients in Eq. 6.

Step 3: identification of G_postFL(s) and G(s).

(7)

Step 4: identification of G(s).

(8)

Evaluation of model adequacy and estimated parameters

The model adequacy was checked by examining the residual of Purkinje cell firing following the regressions executed in steps 1, 2, 3, and 4 (residual check), and the predictions of Purkinje cell firing in response to visual-vestibular mismatch stimuli (prediction check) such as VOR_e, VOR_r, VOR_s (see Experimental paradigms below for stimulus condition), which were not used to determine the model parameters. The amplitude distribution and autocorrelation function of the residual were compared with those of Purkinje cell firing rate during no external stimulation. The idea is that if the amplitude distribution and autocorrelation functions of the residual match those of the Purkinje cell firing during the no stimulus condition⁴ (no stimulus in dark for steps 1 and 3, in light for steps 2 and 4; see Experimental paradigms for details), the information encoded in the Purkinje cell firing by the applied external stimuli has been successfully extracted or predicted. The Ansari-Bradley test was applied to test any statistical difference in the amplitude distributions of residual and Purkinje cell firing during no external stimulus. The autocorrelation function of the residual was considered to be the same as that of Purkinje cell firing during no external stimulus if the former resides in a ±0.1 range of the latter. Cells that passed this residual check following each of the four steps of regression and the prediction check were subjects for further analysis.

Experimental setup and surgical procedure

Two adult male squirrel monkeys weighing between 800 and 900 g were utilized for these experiments. Animals were placed in a primate chair daily for several weeks before any surgery was performed to acclimatize them to the experimental setup. All surgery was performed in a sterile operating suite using induction by Ketamine and inhalation anesthesia using Isofluorane. For head fixation, a stainless steel bolt was secured to the occiput using small, stainless steel screws and dental cement. This bolt fit into a receptacle on the monkey chair to fix the head in the center of a magnetic field generated by two sets of field coils driven in quadrature. For eye movement recording, a prefabricated eye coil constructed of Teflon-insulated stainless steel wire (Cooner) was implanted under the conjunctiva at the limbus of either eye, sutured to the sclera, and the twisted ends of the coil wire led to an occipital plug. A stainless steel recording chamber aimed at the flocculus was implanted and secured with dental cement over a fenestra in the skull. All wounds were treated daily with antibiotics. The Animal Welfare and Use Committee of Washington University approved all procedures and experiments.

Animals were seated in a primate chair with their heads fixed. The chair was placed in the center of a white cylindrical screen 1 m diam (extending 36 cm above and 50 cm below the animal's head) on which black random dots were projected. This is the optokinetic stimulus (OKS). The right or left side of the animal was placed down so that rotation of the OKS about an earth vertical axis produced upward or downward nystagmus. The eye coil output was led to a phase-locked detector whose output gave signals proportional to horizontal and vertical eye position. Vertical and horizontal eye velocities were calibrated. Horizontal and vertical eye position, OKS velocity, and chair velocity were continuously digitized at a sampling frequency of 200, 100, and 100 Hz, respectively, with the use of a CED 1401 interface (Cambridge Electronic Design) for display and storage using the Spike-2 program. The output of a threshold detector, signaling the occurrence of action potentials, was sampled with a resolution of 0.01 ms and stored in the same way. Raw data were also stored on VCR tape (Neurodata PCM).

Experimental paradigms

Stimuli used for all paradigms in the present experiment were 0.5-Hz sinusoids. Although the system identification technique mentioned above is valid for inputs with a wider frequency range, we used this stimulus to directly compare present results with previous related works using the same type of stimulus (Miles and Braitman 1980; Miles et al. 1980; Partsalis et al. 1995a,b; Watanabe 1984, 1985; Zhang et al. 1993, 1995). Therefore only gains and phases at 0.5 Hz were evaluated in the transfer functions estimated in steps 1, 2, 3, and 4 above. To change the animals' VOR gain, suppression of the VOR (VOR_s) or reversal of the VOR (VOR_r) and enhancement of the VOR (VOR_e) paradigms were utilized for low gain and high gain training, respectively.⁵ In the VOR_s paradigm, the chair moves in phase with and at the same speed as the OKS (peak speed: ±40 or ±80 deg/s). In VOR_r, the chair moves in phase with the OKS but with a velocity amplitude twofold that of the chair (chair peak speed: ±40 deg/s). In VOR_e, the chair moves out of phase with the OKS at twice the speed (chair peak speed: ±40 deg/s). Animals were trained toward low or high VVOR gains for 4-7 h a day. During the training, Purkinje cells were isolated at various stages of VVOR gain. After the isolation VF, VOR_d, VOR_r, VOR_s, VOR_e, nostimL, and nostimD were performed for about 60 s each. VOR_r, VOR_s, and VOR_e were recorded to check the performance of the model that was identified by using VF and VOR_d paradigms, while no stimulus paradigms were used as references to evaluate the residual following the model fit (see System identification technique). If the cell was still isolated after this recording set, the training was continued and the same recording set was repeated every hour until we lost the cell.

Unit recording, identification of Purkinje cells

Floccular and ventral parafloccular V zone Purkinje cells were identified by the occurrence of complex spikes (CS) and by their characteristic discharge patterns during vertical VOR_r, VOR_s, or VOR_e. CS could not always be recorded simultaneously during SS recording but were usually seen in close physical proximity to the sites of SS recording.

Data handling

Data analysis and model simulation were performed in Matlab (Mathworks) running on a Pentium III based PC. Vertical eye velocity, eye acceleration, head acceleration, and OKS acceleration were calculated by using a three-point low-pass differential digital filter (Usui and Amidror 1982) from vertical eye position, eye velocity, head velocity, and OKS velocity, respectively. Low-pass filters (combination of 5, 7, and 9 point moving average FIR filters: cutoff frequency 10 Hz) were applied to reduce high-frequency noise in the eye acceleration exaggerated by the differential filtering. Retinal slip velocity was calculated as eye velocity-OKS velocity-head velocity after interpolating (cubic spline) OKS and head velocity traces so that their sampling frequency and time stamp match those of eye velocity. Retinal slip acceleration was then calculated from slip velocity by using the same digital filters used to obtain eye acceleration. Purkinje cell instantaneous firing rate (FR) was calculated as the reciprocal of each inter-spike interval (Partsalis et al. 1995a,b; Zhang et al. 1993, 1995).

Saccades and postsaccadic drifts, if any, were eliminated from eye movement traces by using an automated desaccading algorithm that was visually checked on the computer screen. Data periods corresponding to saccades and the postsaccadic slide were eliminated from both head and OKS movements as well as from Purkinje cell FR.

Gain of the VOR was measured as vertical eye velocity divided by head velocity. More precisely, the following regression was executed and the coefficient c was referred to as the gain of the VOR
where vel_x(t) and vel_h(t) are desaccaded, vertical eye velocity and head velocity traces during VOR_d, respectively, d denotes the dc term that was close to 0 in most cases, and (t) is the error term.  [s] is a delay between eye velocity and head velocity from which the phase of the VOR at 0.5 Hz was calculated as 180°. The coefficients c and d were determined by solving the normal equation derived from the above equation to minimize the square sum of (t) with a given . The value of  that gives the minimum square sum of (t) was globally searched.

After this preprocessing, all signal traces were resampled at the sampling points of desaccaded Purkinje cell FR data to allow signal processing in the analysis mentioned in the System identification technique section.

We also analyzed the cells with a conventional method (Watanabe 1984, 1985) that averages Purkinje cell firing over cycles and fits sinusoidal wave to it to compare results with the new method. BFGS algorithm (Polak 1971) was used for this nonlinear parameter estimation of the amplitude and phase parameters of the sinusoid.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Fifty-three floccular V zone Purkinje cells that showed downward eye movement sensitivity were well isolated and recorded for extended periods at 78 VVOR gains between 0.4 and 1.5 from 2 monkeys. Cells with clear upward eye movement sensitivity were very rare and were not evaluated in this report. The 53 cells were isolated while animals were being adapted by visual-vestibular interaction paradigms, thus those that did not show firing modulation during these paradigms were not recorded in the current experiment. The quantitative analysis of these 53 cells is the subject of the remainder of this report. Thirteen cells of the 53 could be continuously recorded for up to 7 h and thus provided data at multiple VOR gains.

Figure 2 illustrates the behavioral paradigms presently employed and the accompanying Purkinje cell responses in a recording ensemble of a typical cell at a normal VVOR gain of 0.98. Only 10 s of over 60 s of recorded traces are shown. In each eye velocity trace, the sharp deflections are fast phases of nystagmus or saccadic eye movements and will not be considered further.

View larger version (57K): [in this window] [in a new window]   Fig. 2. Eye movements and corresponding Purkinje cell SS activities during experimental paradigms employed. VF, VORd, VORs, VORe and VORr are visual following, VOR in dark, suppression of VOR, enhancement of VOR, and reversal of VOR paradigms, and NostimL and NostimD are no stimulus in light and dark condition, respectively. E is vertical eye velocity in deg/s, IFR is instantaneous Purkinje cell SS FR in spk/s, and D and H are optokinetic stimulus (OKS) and vestibular chair velocity in deg/s. The OKS and chair traces are shown in the same panels in gray and black lines, respectively. Ten seconds of about 60 s of data for each paradigm are shown.

During VOR_d modulation amplitude calculated by averaging over 30 stimulus cycles in this Purkinje cell is very small (±4.8 spk/s). Other Purkinje cells also showed small modulation during VOR_d no matter what the VOR gain (mean modulation amplitude of entire sample to 40 deg/s head velocity is 12.3 ± 8.0 spk/s). However, this small modulation amplitude clearly correlates with VVOR gain state (Fig. 3). During VF this Purkinje cell FR increased during downward eye movement. Modulation in each stimulus cycle varied substantially. In VOR_e Purkinje cell FR increases during downward eye velocity or upward head velocity. During VOR_s the eye is relatively stable within the orbit, and Purkinje cell FR increases during downward head movement or small upward eye movement (eye velocity not completely suppressed). During VOR_r, Purkinje cell FR increases during downward eye movement or downward head movement. Among these visual-vestibular mismatch paradigms, the largest modulation was usually observed during VOR_r, suggesting that all inputs to Purkinje cells evoked by this stimulus are additive (Lisberger and Fuchs 1978) (see Fig. 11). The bottom two panels in Fig. 2, nostimL and nostimD, illustrate the baseline firing herein defined as the intrinsic noise underlying Purkinje cell FR modulation. The extinction of the light (nostimD) results in a decrease of the spontaneous background discharge (75 of 78 samples, 96.2%).

View larger version (52K): [in this window] [in a new window]   Fig. 3. Three-dimensional polar diagram of Purkinje cell firing pattern during VORd recorded at different VOR gains. Each black dot represents a single Purkinje cell. The x-y plane represents amplitude (radius) and phase (angle) of the Purkinje cell firing modulation in a polar coordination. The z-axes represents VOR gain at which the cells were recorded. Note that a clear correlation between VOR gain and the amplitude of Purkinje cell modulation exists.

Of these paradigms, the VF was used to identify the preFL and FL visual and efference copy subsystems G(s), G(s), nonFL visual subsystem G(s), and postFL subsystem G_postFL(s). VOR_d is used to identify preFL and FL vestibular subsystem G(s) and nonFL vestibular subsystem G(s). VOR_e, VOR_s, VOR_r are used to check the adequacy of the model. If the model can predict Purkinje cell firing during the paradigms that were not used to identify the subsystems, the model is probably useful in interpreting the VVOR/VOKR system. NostimL and nostimD are used to evaluate the residual after identification of the subsystems and predictions of Purkinje cell firing.

Figure 3 illustrates a three-dimensional (3D) polar diagram of Purkinje cell modulation recorded at different VOR gains, representing VOR gain versus modulation amplitude and phase calculated by averaging over more than 28 cycles during VOR_d paradigm. Note that the modulation amplitude to 40 deg/s of head velocity is very small ranging from 0.4 to 37 spk/s (mean 12.8 ± 8.5 spk/s). However, this small modulation amplitude changes in parallel with VOR gain along the phase angle of around 20 deg. The modulation amplitude of the cell population increases in phase with head velocity as VOR gain increases, and it decreases in phase with head velocity or increases in an out-of-phase manner with head velocity. This result is comparable with Watanabe's result (Watanabe 1984, 1985). The observed increase in Purkinje cell modulation in-phase with head velocity after high gain adaptation may be causal in the increase in FTN and Y group modulation out-of-phase with head velocity. The FTN and Y group modulation causes larger eye velocity (Partsalis et al. 1995a; Zhang et al. 1995). That is, the observed change in the Purkinje cell modulation is in the correct direction to induce the adaptation. However, we cannot simply conclude from this result that the adaptation occurred in flocculus. To pinpoint the site or sites responsible for the observed change in Purkinje cell firing pattern and VVOR gain change, we utilized the system identification technique as follows.

Figure 4 illustrates a summary of the signal processing of a typical cell executed in step 1 to determine the characteristics of the preFL and FL subsystems G(s) and G(s) using the VF paradigm. In the retinal slip velocity and acceleration panels, black dots are the desaccaded, resampled and nonlinearly transformed signals, and the faint trace is the original slip signal. It has been shown in similar multiple linear regression analyses that coefficients for retinal slip signals are very small (Hirata et al. 1998; Suh et al. 1999), even though flocculus receives retinal slip information via DLPN as illustrated in Fig. 1A. A possible reason for the small coefficients in the linear regression analysis is a nonlinear relationship between retinal slip and Purkinje cell firing as seen in firing properties of lateral terminal nucleus cells in relation to slip velocity (Mustari and Fuchs 1989). If such a nonlinear signal transformation also exists in the preFL and FL visual pathway, linear regression analyses cannot properly evaluate the contribution of slip signals.

View larger version (61K): [in this window] [in a new window]   Fig. 4. Reconstruction of Purkinje cell SS FR during VF paradigm (bottom) by a multiple regression model consisting of retinal slip velocity (top), retinal slip acceleration (2nd), efference copy (3rd), and a dc term (not shown) for a typical cell. In the top 3 panels, gray lines are original traces including saccadic periods and black lines are after desaccade. In the bottom panel, the gray trace is the original Purkinje cell SS FR, and the black dots are the reconstruction by the model. Ten seconds of about 60 s of data are shown.

Figure 5 plots retinal slip versus Purkinje cell FR during VF paradigm of the same cell as in Fig. 4. In the top panel of Fig. 5, desaccaded Purkinje cell FR during VF paradigm is plotted against desaccaded retinal slip velocity as dots. There is a clear nonlinear relationship between the slip velocity and Purkinje cell FR that shows saturation at slip velocities beyond a ±10 deg/s range. A sigmoidal function a/{1  e^{b(rslp_vel+c)}} that is commonly used to express this kind of saturation property was fit to the plots and superimposed on them as a black line. For curve fitting, parameters a, b, and c were estimated by using a nonlinear optimization method, BFGS algorithm (Polak 1971), which is categorized in quasi-Newton methods. Due to such nonlinearity, a linear regression analysis may result in a small coefficient for retinal slip velocity. In other words, a multiple linear regression model that just includes a linear term of retinal slip velocity is not adequate to evaluate the contribution of slip velocity to Purkinje cell firing, because it can only evaluate its "linear contribution." Therefore a nonlinear transformation using the fitted sigmoidal function was included in the model as shown in Fig. 1B to evaluate the slip contribution more properly (see APPENDIX for more details of this nonlinear transformation). The middle panel in Fig. 5 shows the same figure for slip acceleration. In contrast to slip velocity, slip acceleration is almost linearly related to Purkinje cell firing. Different sigmoids were used for different cells. Estimated sigmoids for all the cells examined are superimposed in the bottom panel of Fig. 5. Thick traces are their averages.

View larger version (64K): [in this window] [in a new window]   Fig. 5. Linearization of retinal slip velocity and acceleration to Purkinje cell FR. The top panel illustrates retinal slip velocity vs. Purkinje cell FR during VF (dots) and a fitted sigmoidal function. Coefficients of the sigmoidal function were estimated by using a nonlinear optimization method under the least-squares criteria. Only desaccaded parts of the data were used. Note the saturation in Purkinje cell FR outside a ±10 deg/s range of retinal slip velocity. The 2nd panel shows the same for retinal slip acceleration. Note that the relatively linear relation between the retinal slip acceleration and Purkinje cell FR. The bottom 2 panels are superposition of the fitted sigmoidal functions of all cells examined (dashed lines). The left panel is for retinal slip velocity, and the right panel is for retinal slip acceleration. Thick solid traces are averages.

The efference copy trace in Fig. 4 is shown in a similar format to retinal slip. Eye velocity was used for the efference copy of eye movement. Dots are the desaccaded and resampled traces, and the faint trace is the original eye velocity. The P cell firing panel shows Purkinje cell FR (faint) and the reconstructed firing rate (dots) by a multiple linear regression model with the above three explanatory variables and the dc term (Eq. 3). The regression was performed by using the entire 60 s of data. As can be seen, the dots roughly overlie the original Purkinje cell FR trace; however, there is still considerable variability in the firing evident both above and below the dots. This variability can be accounted for by an evaluation of the residual noise in the firing pattern following the extraction of the signal components by the regression and comparison of this noise to that of the spontaneous Purkinje cell discharge in the nostimL (Fig. 6). The estimated coefficients are evaluated in Fig. 12. The delay terms _x, _r estimated for the entire 78 samples are 0.0176 ± 0.0078 and 0.054 ± 0.011 s, respectively.

View larger version (55K): [in this window] [in a new window]   Fig. 6. Residual check following the regression executed in Fig. 4. Top left: the residual FR for a typical cell shown in Figs. 4 and 5. Top right: the histogram of the residual (black bars) and that of Purkinje cell FR during the nostimL condition (spontaneous firing rate; gray line). Note that there is a slight deviation of the 2 histograms from a Gaussian distribution and that the 2 histograms are almost identical. Bottom: autocorrelation functions of the residual (black), the original FR before the regression (light gray), and the spontaneous firing rate (dark gray). Note that shape of the autocorrelation function of the residual is almost a delta function, and identical to that of the spontaneous firing rate.

Figure 6 illustrates the evaluation of the residual component of Purkinje cell FR following the regression illustrated in Fig. 4. The top right panel compares the amplitude distribution of the residual (black bars) that deviates slightly from a Gaussian distribution, and the spontaneous firing rate during nostimL (gray line). The difference between these two non-Gausian distributions was not statistically significant (P > 0.397, Z = 0.2635, Ansari-Bradley test). The bottom panel compares the autocorrelation functions of the spontaneous firing rate during nostimL (dark gray) and the residual after the regression (black). The autocorrelation functions were calculated from each data set with the same data length so that the variance in the estimation for the functions are comparable. The oscillation seen in the autocorrelation function of the original firing (light gray) is not seen in that of the residual, and its delta function like shape is almost identical to that of the spontaneous firing rate. The similarity in autocorrelation functions assures that the frequency content of the two signals are identical and that of the amplitude distribution assures that the two signals have the same probability density function. These similarities in frequency content and probability density function indicate that the two signals are statistically identical if we focus only on the linear aspect of the signals as in the current study (Usui and Toda 1991).⁶ Thus these results confirm that the modulation in the original Purkinje cell FR in response to VF stimulation was successfully extracted by the model and only the noise with characteristics that are statistically identical to those of Purkinje cell FR during nostimL remained as the residual.

Figure 7 illustrates a summary of the signal processing executed in step 2 (Eq. 4) on the same cell in Fig. 4 to determine the transfer function G(s) of the preFL and FL system using VOR_d. The format is the same as Fig. 4. The reconstructed FR indicates that there is only a small modulation in Purkinje cell firing during VOR_d. The residual was evaluated as shown in Fig. 8 in the same way as in Fig. 6. The estimated coefficients are evaluated in Fig. 12. The delay term _h estimated for the entire 78 samples is 0.0104 ± 0.0070 s.

View larger version (49K): [in this window] [in a new window]   Fig. 7. Reconstruction of Purkinje cell SS FR during VORd paradigm (bottom) by a multiple regression model consisting of head velocity (top), head acceleration (2nd), efference copy (3rd), and a dc term (not shown) for the same cell as in Fig. 4. Format is the same as in Fig. 4.

View larger version (50K): [in this window] [in a new window]   Fig. 8. Residual check following the regression executed in Fig. 7. Top 2 panels are in the same format as Fig. 6. Note that the 2 histograms are almost identical and that the larger deviation of the 2 histogram from a Gaussian distribution than those of Fig. 6. Bottom panels: autocorrelation functions as in the one shown in Fig. 6 and magnified traces of the original firing rate (gray) and the residual (black). Note that the shape of the residual is almost a delta function and identical to that of the spontaneous firing rate.

In Fig. 8, the amplitude distribution of the residual (black bars in histogram) again compares favorably to that of the spontaneous Purkinje cell discharge during nostimD (gray line). Note that the histogram deviates more from a Gaussian distribution than that shown in Fig. 6. In this case, the Ansari-Bradley test revealed that there was no statistically significant difference between the two distributions (P > 0.109, Z = 1.2325). Comparison of the autocorrelation of the residual (black) and the spontaneous firing rate (dark gray) calculated from the same length of data show that their delta function like shapes are almost identical.

Figure 9 illustrates a summary of the signal processing employed in step 3 (Eq. 7) on the same cell as in Figs. 4 and 7, to determine the transfer functions G_postFL(s) and G(s) by using the VF paradigm.

View larger version (74K): [in this window] [in a new window]   Fig. 9. Reconstruction of Purkinje cell SS FR during VF paradigm (bottom) by a multiple regression model consisting of retinal slip velocity (top), retinal slip acceleration (2nd), eye position (3rd), eye velocity (4th), eye acceleration (5th), and a dc term (not shown) for the same cell as in Fig. 4 and 7. Format is the same as in Fig. 4.

Results of the residual check for this regression were almost identical to those shown in Fig. 6 and thus are not illustrated here.

Figure 10 illustrates a summary of the signal processing in step 4 (Eq. 8) from the same cell as in previous figures to determine the transfer function G(s) by using the VOR_d paradigm.

View larger version (58K): [in this window] [in a new window]   Fig. 10. Reconstruction of Purkinje cell SS FR during VORd paradigm (bottom) by a multiple regression model consisting of eye position (top), eye velocity (2nd), eye acceleration (3rd), head velocity (4th), head acceleration (5th), and a dc term (not shown) for the same cell as in previous figures. Format is the same as in Fig. 4.

Results of the residual check for this regression were almost identical to those shown in Fig. 8 and thus are not illustrated here.

The above system identification procedure was applied to all 53 cells recorded at 78 different VVOR gains. Criterion used for the residual check were 1) the amplitude distribution of residual is not statistically different from that of the spontaneous Purkinje cell FR during nostimL or nostimD conditions (Ansari-Bradley test, P > 0.01), 2) the autocorrelation function of the residual is within a ±0.1 range of that of the spontaneous FR. Forty-nine cells of 53 (92.5%) at 73 VOR gains of 78 (93.6%) passed the residual checks after all 4 steps in the system identification procedure. For four cells that did not pass the residual checks, the model was not appropriate to describe their firing properties. Changing the model structure such as adding an eye jerk term and/or a retinal slip position term might let more cells pass the residual check, but we did not pursue this possibility in this report. To further check the model adequacy, cells that passed the residual checks were tested in the prediction check as follows.

Figure 11 illustrates the predictions and reconstruction of FR for three representative Purkinje cells (A-C) during visual-vestibular mismatch, VF, and VOR_d paradigms. These predictions or reconstruction of FR were made employing the preFL and FL part of the model identified in steps 1 and 2 [G(s), G(s), G(s)]. Only two stimulus cycles (4 s) in A and B, and 5 s in C are illustrated out of more than 60 s of the predicted or reconstructed periods. In each panel, light blue sharp trace is the original FR; dark blue dots illustrate the model prediction or reconstruction. Regions indicated by orange arrows are desaccaded periods. The predicted and reconstructed FR were decomposed into the head, retinal slip, and eye motion components that correspond to the first, second, and third term in Eq. 1, and are indicated by green, red, and yellow, respectively. During VOR_r all the components interact additively. During VOR_s, the major contribution to the FR is from head movement as there was little eye movement or retinal slip. The eye movement components contribute negatively to the modulation while the retinal slip contribution is positive. During VOR_e, the eye movement and retinal slip components contribute positively to the FR while the head movement component results in a negative contribution. During VF, the eye movement and retinal slip components are additive while during VOR_d the head and eye movement components subtract from each other resulting in minimal modulation.

View larger version (65K): [in this window] [in a new window]   Fig. 11. Prediction and reconstruction of Purkinje cell FR and decomposition of the predicted and reconstructed Purkinje cell FR during VORr, VORs, VORe, VF, and VORd of 3 typical cells (A, B, C). In each panel, the spiky cyan trace is the original Purkinje cell FR, and dark blue dots are predicted Purkinje cell FR (for VORr, VORs, VORe) or reconstructed Purkinje cell FR (for VF, VORd). The green, yellow, and red areas indicate contribution of head, eye, and retinal slip movement to the predicted or reconstructed Purkinje cell FR, respectively. Each component is the output of each prefloccular and floccular subsystem, G, G or G.

In all cases (VOR_r, VOR_s, VOR_e), the predicted Purkinje cell FR overlies the original firing traces and approximates the signal content embedded in the noisy original Purkinje cell firing. Forty-six cells of 49 (93.9%) recorded at 69 VOR gains of 73 (94.5%) that passed the residual check, passed this prediction check. Those cells that did not pass the prediction check after passing the residual check may have nonlinear firing properties, and visual and vestibular signals might interact nonlinearly on these cells. Of the 13 cells continuously recorded at multiple VOR gains, 11 passed all of the checks. By using the 46 cells recorded at 69 VOR gains, changes in characteristics of the model subsystems during VVOR adaptation were evaluated.

Figure 12 illustrates the sensitivities of Purkinje cell FR represented as coefficients of the model to its input and output signals at different VVOR gains. Sensitivities to sensory input signals, i.e., retinal slip velocity, acceleration, head velocity, acceleration, and efference copy are illustrated on the left, and those to motor output signals, i.e., eye position, velocity, and acceleration are on the right. Each dot represents an estimate from a single cell. Dots connected by lines are from cells recorded for several hours during high or low gain training and recorded at several VOR gains.

View larger version (40K): [in this window] [in a new window]   Fig. 12. Sensitivities of Purkinje cell FR to sensory input (left column) and motor output signals (right column) vs. VOR gain. Each dot represents an estimate from each Purkinje cell. Error bar shows ±1 SD of parameter estimation error evaluated by a Monte Carlo simulation (see APPENDIX for more details). Data from the same cell recorded at multiple VOR gains are connected by dashed lines. The black lines are regression lines. Regression lines whose slope is statistically different from 0 (P < 0.05) are marked by an asterisk.

Sensitivities to retinal slip velocity showed both positive and negative values in the entire range of the VOR gain examined. Sensitivities to retinal slip acceleration also showed positive and negative values but more negative values at lower VOR gains and more positive values at higher VOR gains. Except for one cell, head velocity sensitivities showed negative values in the entire VOR gain range examined. Head acceleration sensitivities in most cells (54/69 samples, 78.3%) were also negative values. Sensitivities to the efference copy signal showed negative values over the entire VOR gain range except for one cell showing a small positive value. For the sensitivities to motor output signals, eye position sensitivity showed negative values in most cases (55/69 samples, 79.7%). The same results can be seen in eye velocity (68/69, 98.6%) and eye acceleration (67/69, 97.1%) sensitivities. These results for negative sensitivities to eye velocity and acceleration coincide with previous studies (Gomi et al. 1998; Shidara et al. 1993), but the same negative sensitivities to eye position as to eye velocity and acceleration do not. This is probably because nonFL pathways were taken into consideration in our model in contrast to previous studies.

The thick black line in each panel represents a regression line. To evaluate the contribution from each cell equally, only one data point at the largest or smallest VOR gain from a cell recorded at multiple VOR gains was used to calculate the regression line and to perform statistical tests. It was found that slopes of the regression lines of retinal slip acceleration and head velocity are significantly different from 0 [P < 0.0046 (F₀ = 8.9328) for slip acceleration, P < 0.0073 (F₀ = 7.9279) for head velocity], indicating that the Purkinje cell FR sensitivities to these signals changed in parallel with VOR gain change. The retinal slip acceleration sensitivity increased from a negative value at low VOR gain to a positive value at high VOR gain, while the head velocity sensitivity decreased its negative value (increased downward sensitivity) with increasing VOR gain. No statistically significant change was found for retinal slip velocity (P > 0.259, F₀ = 1.3031), head acceleration (P > 0.214, F₀ = 1.5877), efference copy (P > 0.483, F₀ = 0.4991), eye position (P > 0.194, F₀ = 2.9160), eye velocity (P > 0.405, F₀ = 0.7058), and eye acceleration (P > 0.707, F₀ = 0.1424).

Directions of the changes in head velocity _h and retinal slip acceleration _r sensitivities of the cells recorded at multiple VOR gains do not necessarily coincide with those of the population. Seven cells (63.6%) for _r and 6 cells (54.6%) for _h of 11 continuously recorded cells changed their retinal slip acceleration or head velocity sensitivities in the same direction as the population when the first and the last recording points of each cell were compared. Out of six cells that were recorded at more than three VOR gains, five for _r and six for _h showed inconsistent directional changes; i.e., in some periods they increased their sensitivity but in other periods they decreased it. It appears that individual Purkinje cells change their sensitivities almost randomly during VOR adaptation, but as a population their sensitivities to retinal slip acceleration and head velocity change toward a certain direction, and contribute to the ongoing VOR adaptation (cf. DISCUSSION).

In each panel, there is scatter in the data points around the regression line. Since these coefficients were estimated from a finite length of data (more than 60 s), the estimates are stochastic variables. In other words, there is always a certain amount of variance in the parameter estimation. Also, if there is any multicolinearity in the multiple linear regression models, estimated coefficients show large variance (Hines and Montgomery 1990). To evaluate the variance in the parameter estimation, we performed a Monte Carlo simulation (Press et al. 1988) (see APPENDIX for details) to give an estimate of reliability of the estimated parameters in terms of their variances.

The results of the Monte Carlo simulation for each cell are indicated in each panel in Fig. 12 as error bars on each plot indicating ±1 SD. Those that do not show the error bar are ones whose estimation error is less than the size of the symbol employed. As can be seen, the estimation error (SD) is fairly small in comparison with the variability seen in each panel of Fig. 12, indicating that most of the variability does not arise from the parameter estimation error but from the variability among the properties of individual Purkinje cells. The small variances in estimated parameters also assure that there is no multi-colinearity among the explanatory variables of the multiple linear regression models that may make the parameter estimations unreliable.

In Fig. 2, Purkinje cells' mean FR during nostimD is smaller than that during nostimL. Figure 13 illustrates VOR gain versus mean FR of Purkinje cells during nostimL (open circles) and nostimD (filled circles). Gray and black plots aligned on the same VOR gain are from the same cell. As seen in Fig. 2, most cells (63/69 samples, 91.3%) decreased their mean FR when the light was off. Only six samples showed the opposite characteristic. Five samples of these six were recorded at VOR gains <1 (0.84, 0.74, 0.71, 0.62, 0.40), and differences between light and dark condition of these six cells are very small (0.71, 1.57, 2.65, 0.80, 5.07, 1.94 spk/s). Dashed and solid lines are regression lines of open (in light) and filled (in dark) circles, respectively. Slope of the regression line for the light condition is not significantly different from 0 (P > 0.419, F₀ = 0.6615), indicating that Purkinje cell's FR in light did not change in parallel with VOR gain. On the other hand, the slope of the regression line for the dark condition showed a slight difference from 0 (P < 0.062, F₀ = 3.5923). This result indicates that dc FR during nostimD depends on the VOR gain.

View larger version (17K): [in this window] [in a new window]   Fig. 13. VOR gain vs. mean FR of Purkinje cells during nostimL (open circle) and nostimD (filled circle) conditions. Open and filled circles aligned on the same VOR gain are from the same cell. Dashed and solid lines are regression lines of open (in light) and filled (in dark) circles, respectively. The result indicates that dc firing rate during nostimD depends on the VOR gain.

Figure 14 plots VOR gain versus system characteristics (gains and phases) at 0.5 Hz of preFL and FL (G, G, G), postFL (G_postFL), and nonFL (G, G) subsystems in a 3D polar representation. Each black circle represents an estimate from each Purkinje cell. The projection of the black circle atop each thin vertical line onto the ordinate represents the VOR gain at which each Purkinje cell was recorded. The intersection of the base of each thin vertical line with the polar plane indicates the estimated gain (radius) and phase (angle) characteristics of the system. In each figure, the slanted heavy black line is a regression line (the 1st principal component) indicating the average characteristics of the system in relation to VOR gain. The line is in the plane (dotted line) perpendicular to the polar plane.

View larger version (63K): [in this window] [in a new window]   Fig. 14. Three-dimensional polar representation of VOR gain vs. system characteristics at 0.5 Hz of prefloccular/floccular subsystems (G, G, G), postfloccular system (GpostFL), and nonfloccular subsystems (G, G). Each dot represents an estimate from each Purkinje cell. Length of the thin black line under each dot represents gain of the VOR at which the cell was recorded. The intersection of the base of each thin vertical line with the polar plane indicates the estimated gain (radius) and phase (angle) of the system. The heavy black line is a regression line (1st principle component) that is in the plane (dotted line) perpendicular to the polar plane. Asterisks indicate that the slope of the regression line is statistically different from 0 (P < 0.0075). Note that average characteristics of G and G change in parallel with VOR gain.

It was found that system characteristics of the preFL and FL vestibular pathway G and non-FL vestibular pathway G changed in parallel with VOR gain [slopes of the regression lines are significantly different from 0; P < 0.0075 (F₀ = 7.8635), P < 0.000011 (F₀ = 24.5431), respectively] while the postFL pathway G_postFL, preFL and FL efference copy pathway G, and nonFL visual pathway G showed minimal changes [P > 0.804 (F₀ = 0.0621), P > 0.4380 (F₀ = 0.6125), P > 0.273 (F₀ = 1.2290), respectively]. Slope of the preFL and FL retinal slip pathway G also showed no significant difference from 0 [P > 0.2026 (F₀ = 1.6723)], although sensitivities of Purkinje cells to retinal slip acceleration changed in parallel with VOR gain. A reason for this result may be that the change in retinal slip acceleration sensitivity _r in the transfer function of G(s) does not have much of an affect on the value of the transfer function at 0.5 Hz, rather, its effects are more profound at higher frequencies (see Fig. A1 in APPENDIX). These results suggest that there are multiple sites of adaptation for VVOR motor learning.

There are several types of floccular Purkinje cells classified in terms of their firing sensitivities to eye and head motions (ex. Fukushima et al. 1999). Figure 15A plots head velocity sensitivity versus eye velocity sensitivity of each cell recorded at various VOR gains. The eye velocity sensitivities were estimated in the system identification procedure step 1 as the parameter _e while the head velocity sensitivities were in step 2 as _h. Diameter of circles surrounding the plots is proportional to the VOR gain at which the cell was recorded. Plots connected by a line are from a same cell recorded at multiple VOR gains. The diagonal line indicates the same sensitivity to head and eye velocity. Cells above the diagonal line are dominated by the eye velocity sensitivity while those below the line are dominated by the head sensitivity. There is no clear segregation of the cells that are dominated by eye velocity sensitivity and those that show almost equal sensitivity to eye and head velocity.

View larger version (24K): [in this window] [in a new window]   Fig. 15. Head velocity sensitivity vs. eye velocity sensitivity of each cell recorded at various VOR gains (A), and head motion contribution vs. eye motion contribution to Purkinje cell FR during VORd (amplitude of head velocity stimulus is 40 deg/s; B). In both panels, diameter of circles surrounding each plot is proportional to the VOR gain at which the cell was recorded. Plots connected by a line are from a same cell recorded at multiple VOR gains. The diagonal line indicates the same sensitivities to head and eye velocity (A) or same contribution from head and eye movement signals to Purkinje cell modulation (B). Cells on the diagonal line in B indicate no modulation during VORd, while those above or below the line indicate in-phase modulation with down eye movement or that with down head movement, respectively. Note that distributions are a continuum, and there is no clear segregation of the cells that are dominated by eye velocity sensitivity (so called eye velocity cell) and those that show almost equal sensitivity to eye and head velocity (gaze cell).

Sensitivities alone do not adequately describe the modulation of the cell when the eye and head velocity are no longer equal after VOR adaptation. Figure 15B illustrates head motion contribution versus eye motion contribution to Purkinje cell firing during VOR_d (head velocity 40 deg/s) calculated by using preFL and FL part of the model based on their eye and head velocity sensitivities. The diagonal line indicates the same contribution from head and eye movement. Cells on this line indicate no modulation during VOR_d, while those above or below the line indicate in-phase modulation with down eye movement or that with down head movement, respectively. Distance from each dot to the diagonal line is the modulation amplitude of each Purkinje cell during VOR_d. It is seen that more cells are distributed above the diagonal line than below. Most of cells distributed below the diagonal line were recorded at low VOR gains. Again, there is no clear dichotomy of eye movement dominant and gaze cells.

Figure 16 plots the prediction of VOR gain by the model versus measured behavioral VOR gain. If the data sample analyzed in the current work represents the entire property of the VOR system, the predicted VOR gain should match the experimentally measured VOR gain. If the data sample is too small or biased, it is most likely that the model cannot predict the behavior of the entire system, namely, eye movement in response to head movement measured as VOR gain. In the model, the gain of the VOR can be defined as an absolute value of the Laplace transform of eye movement divided by that of head movement during VOR in dark, that is

where s = j2f (f = 0.5 Hz). In Fig. 16, each dot represents the VOR gain calculated from gain and phase characteristics estimated by using each Purkinje cell FR data. The dashed line whose slope is unity shows the expected values of VOR gain if the model prediction perfectly matches to the experimentally measured VOR gains. The solid line is a regression line of the model estimation whose slope is 0.94. Thus we conclude that the model accurately predicts the behavioral gain change at 0.5 Hz.

View larger version (27K): [in this window] [in a new window]   Fig. 16. Model prediction of the VOR gain vs. behavioral gain. The black line indicates the ideal prediction whose slope is 1. When the model prediction is equal to behavioral VOR gain, each plot should lie on the line. Note that each plot is an estimate by a model whose characteristics were identified based on each Purkinje cell FR. The gray line is a regression of model estimates whose slope is 0.94. Note that as a population, the model prediction closely matches to the actual behavior.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

System identification approach

The flocculus receives multi-modal inputs from upstream neuronal systems. Its output, Purkinje cell activity is transferred to downstream neuronal systems and is eventually fed back to flocculus as one input. Therefore observed changes in flocculus Purkinje cell firing pattern after VOR motor learning (Lisberger et al. 1994b; Watanabe 1984; Fig. 3) do not necessarily mean that a site of the learning is in flocculus. To pinpoint which neuronal system or systems in the entire VVOR/VOKR system caused the change in Purkinje cell firing pattern and the resultant VOR gain change, we undertook the system identification approach based on a new VVOR/VOKR model. We showed that this method is valid within the stimulus range currently employed (see Model below) and found multiple adaptive sites for VVOR learning.

There have been similar models for VOR adaptation (Gomi and Kawato 1992; Lisberger 1994; Lisberger and Sejnowski 1992; Quinn et al. 1998) evaluating adaptable elements in the VOR system. Of these, the present model is novel in that the characteristics of the subsystems were identified using only experimental data while those in the previous models were determined heuristically. Also, the previous models allowed adaptive changes in a confined subsystem or subsystems such as in preFL and FL vestibular subsystem or/and nonFL vestibular subsystems. In the present model, no presumption for adaptability of subsystems was made, thus all subsystems were free to change their characteristics. If flocculus is the only site responsible for VVOR gain adaptation, we should see changes in characteristics in the preFL and FL subsystem and no change in the other subsystems. If both flocculus and FTNs are the adaptive sites, we should see changes in both the preFL and FL and nonFL subsystems, and no change in the others. The current result showed that the latter is the case supporting the multiple sites hypothesis.

An advantage of the system identification approach is that it is not necessary to record the input and output signals in each and every possible adaptive site. If there are several possible sites, simultaneous single-unit recordings from each site might be required in a conventional neuro-physiological method. Also, by using the system identification technique, we can separately evaluate the contribution of each input modality to the output. Another advantage is that we can understand and interpret the system in terms of the control and information theoretical point of view by analyzing behaviors of the identified model, such as evaluation of stability, prediction of the system output in response to unknown input. A disadvantage in using this approach is that all conclusions are based on an assumption that the model is correct. If the model is not adequate within the stimulus range and dynamic range of interest, the conclusions are not reliable. Thus it is important to evaluate model adequacy as discussed below.

Model

Results obtained from the system identification approach depend on the model structure, the structure of the transfer function of each subsystem, and the estimated parameters of the transfer functions. The structure of the present model was very general in that it consists of floccular and nonfloccular components to which any neuronal groups participating in VVOR/VOKR control can be assigned. The anatomical correspondence of model components will be discussed below. The basic structure is similar to previous models (Gomi and Kawato 1992; Lisberger and Sejnowski 1992; Miles et al. 1980; Quinn et al. 1998) but more anatomically plausible in that visual pathways that do not go through flocculus are included (N. Gerrits, personal communication). There are cells in the vestibular nuclei that convey eye movement-related signals, but the current model (Fig. 1A) does not explicitly illustrate this pathway. However, axon collaterals of these ascending vestibular nuclear cells terminate in PMT subgroups, and thus the oculomotor-related ascending activity is reflected in the efference copy signal. Therefore the vestibular neurons conveying eye signals are included in the prefloccular efference copy pathway in the current model.

The structure of the transfer function of each subsystem and estimated parameters of the transfer functions determine the performance of the model. Two ways to check the model performance are the evaluation of the residual signals following model fitting to the experimental data, and the prediction of system outputs in response to unknown inputs that were not used to estimate the parameters. It was shown that the statistical properties of the residual signals following the fitting for parameter estimation and the predictions were identical to those of spontaneous Purkinje cell firing. If the model is not adequate to describe the data, variance of the residual may be either larger (model is too simple) or smaller (model is too complex or the structure is inadequate) than that of the spontaneous firing rate. Therefore the model is valid at least within the stimulus range currently employed. In general, if the input signal used for system identification contains frequency components and an amplitude range that covers the dynamic range of a system, the system can be fully identified. If the input covers only a limited amplitude and frequency range, then the characteristics of the system within that amplitude and frequency range can be identified. Presently a single frequency of sinusoidal stimulation, 0.5 Hz was utilized and thus the analysis was confined to the evaluation of system characteristics at this frequency. The 0.5-Hz stimulus was used to directly compare the present results with results of many previous experiments in which the same type of stimulus was utilized. Stimuli with a wider frequency band will be used in the future to address issues such as the frequency dependence of VOR adaptation (Hirata et al. 2000; Raymond and Lisberger 1998).

One might argue that multicollinearity among regressors in the multiple linear regression models currently used may have an effect on the validity of the estimated parameters (R. A. McCrea, personal communication). There is apparent multicollinearity between eye velocity and head velocity during head motion, thus we avoided using these two signals together in parameter estimations (see METHODS). Another possible collinear relation may be between eye velocity and retinal slip velocity, because retinal slip velocity is calculated as optokinetic stimulus velocity minus eye velocity minus head velocity. If the eye velocity trace evoked by sinusoidal optokinetic and vestibular stimulus movements are purely sinusoidal, the calculated retinal slip is also sinusoidal, then there is a collinear relation between the two signals unless they have a 90 deg phase shift. However, actual eye velocity traces are not a pure sinusoid, rather they usually show significant deviation from a sine wave especially when they are evaluated without averaging over many cycles. After the sinusoidal component (optokinetic and vestibular stimulus) is subtracted from eye velocity, the deviation left is the retinal slip velocity thus preventing a collinear relation between eye velocity and slip velocity. One way to confirm this is to perform a Monte Carlo simulation in which the same regression is executed many times by changing only its error term, and the variance of the estimated coefficients for terms that might have a collinear relation (i.e., retinal slip velocity and eye velocity) is evaluated. If these two signals are collinear, the estimated coefficients for them should show large variance (Montgomery and Peck 1992). As demonstrated in Fig. 12 (_r and _e), this was not the case. Moreover, if the parameters were estimated improperly due to any collinearity, the prediction of the Purkinje cell firing pattern in response to unknown inputs that were not used to estimate the parameters most likely would fail. As mentioned in RESULTS (Fig. 11) and in the above discussion, for 46 cells recorded at 69 different VOR gains of 49 cells at 73 VOR gains, predictions of Purkinje cell firing patterns during visual-vestibular mismatch paradigms were successful. These results form strong evidence against collinearity between retinal slip and eye velocity in the paradigms currently employed.

Noisy Purkinje cell firing

One distinctive feature of the Purkinje cell is the large variability in its instantaneous firing rate. Brain stem neurons participating in the VVOR/VOKR show much smaller variability and exhibit almost sinusoidal modulation to sinusoidal velocity stimuli (Blazquez et al. 2000; Partsalis et al. 1995a,b; Zhang et al. 1993, 1995), thus simpler analysis methods based on averaging-over-cycles could be used in these studies. It was shown in this and in previous studies (Gomi et al. 1998; Shidara et al. 1993; Yamamoto et al. 1997) that floccular V zone Purkinje cells have an eye position component (Fig. 12, c_x), and eye position is not always the same in each cycle during sinusoidal VOR, OKR, and other visual-vestibular interaction paradigms. Therefore in the present system identification problem, firing data were evaluated without averaging.

It was shown that the variability evaluated in spontaneous activity of Purkinje cell both in light and dark is almost white noise whose distribution is non-Gaussian (Figs. 6 and 8). This whiteness assures that the variability can be averaged out when outputs from many Purkinje cells converge to one FTN. Typical standard deviation of the spontaneous activity in a Purkinje cell is about 40 spk/s, which is reduced to 4 spk/s if the noise components from 100 Purkinje cells are independent and are simply averaged at the FTN. One possible functional meaning of such variability is to increase the ability to detect signal components encoded by the Purkinje cell. According to the theory of stochastic resonance (Stacey and Durand 2000; Wiesenfeld and Moss 1995), noise imposed on a weak sub-threshold signal aids detection of the weak signal at target neurons receiving the signal, when the signal itself cannot cross threshold to fire the target neurons. This may make it possible for FTNs to detect very small modulation in Purkinje cell firing such as that observed during the VOR_d paradigm.

The estimated sensitivities of individual Purkinje cells to sensory input and motor output, and the gain and phase characteristics of the subsystems calculated from these sensitivities indicated a large variability. This may have been an estimation error due to the estimation from a finite length of data with the large variability in Purkinje cell firing. However, variability observed in Fig. 12 was larger than the estimation error determined by the Monte Carlo simulation. This indicates that the sensitivities of individual cells to sensory input and motor output signals actually vary from cell to cell. Some of the cells recorded at several VOR gains exhibited changes in their sensitivities in opposite directions, even though as a population, Purkinje cell activity showed a certain directional change or trend in parallel with the VOR gain adaptation. This paradoxical phenomena can be understood by its analogy to the magnetic dipoles in a magnetic substance stated by Weber as the molecular magnet theory. When a magnetic substance is exposed to an alternated magnetic field, it shows the same alteration in its magnetization level, but each dipole demonstrates a different degree of alignment in each cycle. The magnetic field can be thought as error signal that drives VOR motor learning, and the dipole is each Purkinje cell.

Anatomical correspondence of model subsystems

Present results showed that prefloccular/floccular vestibular subsystem G, and nonfloccular vestibular subsystem G contain elements that are modifiable in the process of VVOR gain adaptation. Other subsystems, i.e., the prefloccular/floccular efference copy subsystem G, prefloccular/floccular visual subsystem G, postfloccular subsystem G_postFL, and nonfloccular visual subsystem G did not show significant changes in their gain and phase characteristics during VVOR motor learning. G represents the neuronal pathway from the vestibular organ to flocculus Purkinje cells consisting of the semicircular canals, FPNs, flocculus cortical neurons, and finally the floccular Purkinje cell, while G includes all neuronal circuits activated during vestibular stimulation other than the one passing through flocculus. PVP neurons in MVN, Y group neurons, other FTNs in SVN, and the interneurons in SVN projecting to Y group have been identified as a part of this neuronal substrate. Note that individual FTN and Y group neurons receive both floccular and nonfloccular vestibular inputs. The former is included in G_postFL and the latter in G. Extra-ocular motor neurons and the oculomotor muscle plant are included in G_postFL. The motoneurons and muscle plant as well as the retina and vestibular organ are commonly assumed not to change their characteristics during VOR motor learning.

Within G, it has been suggested that FPNs do not change their characteristics with VOR adaptation (Miles et al. 1980). Therefore the only possible modifiable site in G is in the floccular cortex. Within G, PVP neurons did not show adaptive changes in their activity (Lisberger et al. 1994a; S. M. Highstein and A. M. Partsalis, unpublished observations). Therefore the possible adaptive sites in G are confined to Y group neurons and FTNs. It has been demonstrated experimentally that Y group (Partsalis et al. 1995b) and FTN (Lisberger et al. 1994b) contain modifiable elements for vertical and horizontal VOR adaptation, respectively.

Neuronal substrates involved in G, G, G_postFL or G that did not show changes with VVOR adaptation are the PMT nuclei and premotor vestibular neurons that send collateral to the PMT in G, and the synaptic efficacy of Purkinje cell input to Y group and other FTNs in G_postFL. G includes the retina and subsequent cerebral cortical areas, DLPN and NRTP, floccular cortical neurons, and the Purkinje cell. In the nonfloccular visual pathway G, a part of the optokinetic direct pathway that is activated at 0.5 Hz and does not go through the flocculus is involved. Flocculectomy abolished about 30% of smooth pursuit eye movement gain and 50% of the initial slow phase velocity of OKN in response to a constant velocity stimulus (Zee et al. 1981) while total cerebellectomy abolished smooth pursuit (Westheimer and Blair 1974). Therefore G includes those components involved in smooth pursuit or equivalently in the optokinetic direct pathway in the cerebellum other than the flocculus, e.g., the uvula, nodulus, and paraflocculus.

Role of flocculus in VOR motor learning

How do the changes in the G, and G subsystems achieve VOR adaptation? More specifically, how are the flocculus, Y group, and/or FTNs functioning during the process of VOR adaptation? Figure 17 illustrates a modified version of the model shown in Fig. 1B. Circuits functioning during VOR_d are indicated in solid lines, whereas ones for visual signals functioning only in light condition are in dotted lines. Schematic velocity waveforms based on the results shown in Fig. 14 are illustrated in each pathway when the head is moved sinusoidally at 0.5 Hz (thin: normal gain; thick: high gain). Arrows on G and G indicate the direction of the change in the system gain after VOR high gain adaptation. Change in the gain of G following high gain adaptation is in the correct direction to cause an adaptive VOR gain change. On the other hand, the output of G is in the incorrect direction to cause the VOR gain change observed.

View larger version (28K): [in this window] [in a new window]   Fig. 17. The model and schematic representation of the input-output relationship for each subsystem during normal (thin waveforms) and high gain condition (thick waveforms). Thick arrows indicate the direction of changes in the gain characteristic during the high gain adaptation. The dotted line indicates the circuit that do not function during VORd. The waveforms are schematically drawn based on the gain and phase characteristics at 0.5 Hz of each subsystem shown in Fig. 14. Note that the waveforms are in a velocity format. Dashed waveforms are putative outputs of GpostFL(s) when the output of G(s) is separately transferred by GpostFL(s) without interacting with the efference copy signal at the Purkinje cell.

Thus the flocculus changes its gain in a direction opposite to the behavioral gain change while the nonfloccular vestibular pathway changes in a direction to support the behavior. However, the flocculus also receives the efference copy signal during head rotation. Although the system characteristics of the efference copy pathway (G) does not change, the magnitude of the efference copy signal changes depending on the amplitude of the eye movement. Thus when eye velocity increases as the result of high gain adaptation, Purkinje cell firing modulation caused by the efference copy input increases, and in turn causes further increase in eye velocity. Thus the efference copy pathway forms a positive feedback loop that may potentially make the VOR system unstable. To prevent this instability the increment of change in this positive feedback as a consequence of VOR gain adaptation must be compensated. Apparently the prefloccular/floccular system accomplishes this as a population by increasing the system gain to head motion to cancel the change in the efference copy signal. Therefore individual Purkinje cells may exhibit only a small modulation during VOR_d.

In Fig. 3 the amplitude of this small modulation is actually correlated with VOR gain, and this small change is in the correct direction to cause observed VOR adaptation (in agreement with Watanabe 1984). The larger modulation at higher VOR gains in Fig. 3 means that the amount of increase in the system gain of G at higher VOR gains is not enough to compensate the increment in the efference copy signal fed back to flocculus. If the increase in the modulation amplitude is too big, the VOR system may become unstable due to the positive feedback loop. Qian (1995) demonstrated by using the generalized Lisberger-Sejnowski model, which has a similar structure to our current model, that small violations of the stability condition will not completely break down the VOR system over the time scale of the normal VOR.

Purkinje cell firing pattern in relation to Y neurons

Y-group neurons receive the terminals of floccular Purkinje cells and have been shown to reflect the signals carried on Purkinje cells (Partsalis et al. 1995b). During rapid modification of the VVOR, the Purkinje cell modulation is the inverse of that of the Y-group and could account for the visually driven modifications of Y-group firing rate modulation. Namely, during the VOR_e Purkinje cells increase their firing during downward eye movement while Y-group neurons increase their firing during upward eye movement. The same pattern is true for VOR_r. During VOR_s Purkinje cells fire during downward head movement and Y neurons during upward head movement. Because Purkinje cells inhibit their target neurons, the reciprocal relationship between Purkinje and Y neurons makes it plausible that Purkinje modulation is causal in generating Y-group responses during rapid modifications of the VVOR (also cf. Partsalis et al. 1995a,b). However Y-group neurons that modulate little during VOR_d in the naïve condition learn to modulate during VOR_d in phase with head movement in the low gain condition and out of phase with head movement in the high gain state. As V zone Purkinje cells show only small modulation during VOR_d no matter what the VVOR gain, all the responses of Y cells cannot be caused by Purkinje cell modulation alone during VOR_d after VOR adaptation. This is another piece of evidence suggesting that the Y-group is one site of learning and memory when the VVOR gain is changed.

Y-group neurons also exhibited decrease in their dc firing rate after VOR low gain adaptation and increase in that after high gain adaptation (Partsalis et al. 1995a). As shown in Fig. 13, floccular Purkinje cells increase their dc firing rate in darkness as a population after low gain adaptation. Since Purkinje cells inhibit Y-group neurons, these changes in Purkinje cell dc firing rate might be causal to the observed changes in Y-group dc firing rate after VVOR adaptation.

Site(s) of VOR motor learning

Both the brain stem and the flocculus have been suggested to be the sites responsible for VOR motor learning in the primate by the multiple site hypothesis (Miles and Lisberger 1981). The multiple site hypothesis is supported by a series of physiological experiments and model simulations. Direct evidence has been provided by Lisberger et al. (1994a,b), who showed that both floccular and ventral parafloccular Purkinje cells and FTNs changed their firing patterns in response to rapid head motion after low and high gain VOR adaptation. They showed that the change in FTN firing occurred 12.9 ms after the onset of the stimulus while that in Purkinje cells was 27.3 ms on average. These results suggested that the FTNs are the main locus of VOR adaptation but that there is also adaptation in the flocculus, the same conclusion reached in the present report.

On the other hand, there is physiological evidence in primate that changes in flocculus Purkinje cell firing during VOR in darkness alone can induce VOR gain adaptation (Watanabe 1984, 1985). In this experiment, it was shown that the majority of floccular H zone Purkinje cells continuously recorded before and after low or high gain VOR adaptation changed their firing modulation during sinusoidal horizontal head rotation (0.3 Hz), which was suggested to be inducing the observed VOR gain adaptation. The current result on VVOR adaptation (Fig. 3) is also comparable to Watanabe's result. On the contrary, Miles et al. (1980) showed that Purkinje cells exhibited little or no modulation in response to sinusoidal horizontal head rotation (0.2 Hz) during VOR in darkness in both normal and high VOR gain situations, but they did modulate after low gain adaptation induced by reversing prisms. A possible reason for the discrepancy in these similar experiments is how the learning was induced; namely Miles et al. (1980) used goggles for about 1 wk, and Watanabe and we used visual-vestibular mismatch stimulus for only several hours. There might be different neuronal mechanisms for relatively short-term and long-term VOR motor learning.

Miles et al. (1980; Miles and Braitman 1980) also examined the head velocity sensitivity of Purkinje cells before and after the adaptation by using the VOR suppression paradigm and found a change in sensitivity. However, this change was in the "wrong" direction to induce the observed behavioral change, i.e., the head velocity sensitivity increased after high gain adaptation, which actually would decreases eye velocity. This result coincides with the current result in that the downward head velocity sensitivity _h increased after high gain adaptation (Fig. 12).

A role for the flocculus resulting from this wrong directional change during VOR adaptation was suggested by Miles and Lisberger (1981) to maintain the combined eye-head tracking (Miles et al. 1980) after the VOR is adapted to new gain. Lisberger and Sejnowski (1992) and Lisberger (1994) showed in their model simulations that this change in head velocity sensitivity in Purkinje cells might be required to avoid "run-away" eye movements in response to step head velocity stimuli. This is a similar conclusion to the one made in the current report, in which the change in the prefloccular/floccular vestibular subsystem compensates for the change in the efference copy signal after the change in VOR gain and maintains stability of the VOR system during a prolonged 0.5-Hz sinusoidal head rotation.