Respiratory control requires feedback signals from the viscera, including mechanoreceptors and chemoreceptors. We previously showed that typical pulmonary stretch receptor (PSR) spike trains provide the central nervous system with ∼31% of the theoretical maximum information regarding the amplitude of lung distension. However, it is unknown whether the spatiotemporal convergence of many PSR inputs onto second-order neurons (e.g., pump cells) results in more, or less, information about the stimulus carried by second-order cell spike trains. We recorded pump cell activity in adult, anesthetized, paralyzed, artificially ventilated rabbits during continuous manipulation of ventilator rate and volume to test the hypothesis that less information is carried by spike trains of individual pump cells than PSRs. Using previously developed analytic methods, we quantified the information carried by the pump cell spike trains and compared it with the same values derived from PSR data. Our results provide evidence that rejects our hypothesis: pump cells as a group did not carry significantly less information about the lung distension stimulus than PSRs, although that trend was implied by the data. By comparing the response variances with the theoretical minimum, we discovered that the trend toward information loss depends on response strength, with higher mean responses associated with larger response variances in pump cells than in PSRs. Thus spatiotemporal integration may result in information loss within certain analytic/stimulus parameters, but this is counterbalanced by the consistency of pump cell responses during brief integration times and/or low stimulus amplitudes, resulting in retention of total information.
- respiratory control
- sensory processing
- noise analysis
- Shannon information
depending on the system, second-order neurons may or may not reflect the activity patterns demonstrated by primary afferents. In the respiratory control system, a typical lung inflation is more than adequate to evoke activity in pulmonary stretch receptors (PSRs), slowly adapting mechanoreceptors that transduce each lung inflation into a burst of action potentials (1; see 28, 29 for reviews), as well as in second-order neurons (5, 6, 10). The reflex cessation of phrenic motor output that results from lung inflation (i.e., activation of sufficient numbers of PSRs at sufficient firing rates) (see Ref. 11 for review), originally described by Hering and Breuer (18), presumably requires the activation of either or both types of nucleus tractus solitarius (NTS) neurons: pump cells and inspiratory beta cells. Both cell types receive monosynaptic excitatory drive from PSRs in cats (3, 4, 6). In contrast to beta cells, which have been implicated in phrenic facilitation during inspiration (19) and receive additional excitatory drive from central inspiratory neurons, pump cell excitation is derived primarily from PSR inputs (5, 10), and recent studies in the rat have demonstrated a disfacilitation/inhibition of pump cells during central inspiration (21, 22). In the rat, pump cell axons project within the NTS and to respiratory-related regions in the ventrolateral medulla (14, 16); in the cat, they project to similar medullary sites, as well as to pontine respiratory centers (15). Thus pump cells are situated to potentially influence local autonomic reflexes (i.e., NTS processing) and respiratory rhythmogenesis. Because of the strategic network location of the pump cells, we are interested in the precision with which pump cell activity reflects lung distension, which will necessarily limit the feedback-control performance of central respiratory regulatory circuitry.
In a previous study (27), we used a method designed for continuous, dynamic, naturalistic stimuli to quantify the information content and encoding/decoding efficiencies in PSR spike trains. Several questions were raised, including “How much information about lung distention is carried by individual spike trains at the next hierarchical level of the system?” Although there are theoretical arguments for increases or decreases in information in individual pump cell spike trains compared with PSRs, it is unclear how accurate a representation of lung distension is required to effectively control phrenic output, which ends relatively abruptly during normal eupneic breathing [except for postinspiratory activity (31)]. Using the analytic method developed in our previous PSR study (27), we quantified the information content in the spike trains of pump cells. By comparing the information content regarding lung inflation in individual spike trains of the presynaptic (PSR) cell population with that of the postsynaptic (pump) cell population, we tested the hypothesis that less information is carried by individual pump cells in their spike trains than by their primary afferent counterparts.
Experiments were conducted on five adult male Dutch-Belted and seven adult male New Zealand White rabbits. All procedures were approved by the University of Delaware Institutional Animal Care and Use Committee.
Saffan (10–18 and 3–14 mg·kg−1·h−1 during surgery and recordings, respectively, with variability in dose necessitated by adipose accumulation/release) was administered continuously via the marginal ear vein, such that somatic, cardiac, and respiratory responses to noxious paw pinch were eliminated. Cannulas were inserted into a femoral artery and vein for subsequent measurement of blood pressure and administration of drugs, respectively. All incisions were preceded by liberal application of lidocaine topical anesthetic to the area. The neck was opened via a ventral midline incision, and the trachea was intubated below the larynx. During artificial ventilation (see below), tracheal pressure (TP) was monitored via a sidearm of the tracheal tube. Activation of laryngeal mechanoreceptors was prevented by dissociation of the larynx from the lower airways. The animals breathed spontaneously until they were placed on a stereotaxic apparatus (see below). Rectal temperature was maintained at 36.5–38.0°C for the entire experiment via a servo-controlled blanket and/or an infrared lamp. A slow (15–20 ml/h iv) drip of 5% dextrose in physiological saline was provided throughout the surgical and recording procedures.
A lateral incision was made in the right side of the neck extending from the base of the jaw to the apex of the scapula. The musculature overlying the right vagus nerve (VN) and phrenic nerve (PhN) was separated and then either retracted or removed by cautery. The nerves were carefully dissected free, and the PhN was looped with a small piece of suture for later identification. The entire area was covered with warm mineral oil-soaked cotton, and the skin was temporarily closed with wound clips.
The animal was placed in a stereotaxic frame (David Kopf Instruments, Tujunga, CA), mounted in a head holder, and suspended by a thoracic vertebral clamp (T1-T3). Then the head was ventroflexed, and the animal was paralyzed with vecuronium bromide (55- to 70-μg boli iv at ∼45-min intervals) and artificially ventilated (Harvard Apparatus, Holliston, MA) with expiratory CO2 maintained at 4.5–5.3% by adjustment of minute volume. Bilateral pneumothoraces were performed using plastic tubes placed in small holes created between the ribs dorsolaterally. This, combined with taut suspension of the vertebral column, eliminated ventilation-related movement of the brain stem. An end-expiratory load of 1–2 cmH2O was applied to prevent complete collapse of the lungs after each inflation.
The brain stem was approached dorsally via a midline incision extending from the first cervical vertebra to the occipital ridge. The nuchal muscles were retracted, the overlying dura was cleared of connective tissue and freed from the occipital bone, and the area was covered with physiological saline-soaked cotton, with the dura intact. The PhN was then transected and placed on a bipolar silver wire electrode for subsequent recording of inspiratory activity. The VN was placed intact on the same type of electrode, and the activity of both nerves was amplified and filtered (100–500 times, 300–5,000 Hz; Neurolog, Digitimer, Hertfordshire, UK). Both nerves were covered with a mineral oil-petroleum jelly mixture to prevent dehydration. In some animals, ECG was also recorded via subcutaneous pin electrodes placed on either side of the chest.
Once the animal was suspended and the nerves were hung and their activity was monitored, the Hering-Breuer reflex was tested by a sustained inflation of the lungs (3–6 mmHg TP) for two to three central respiratory cycles. All animals that were used for subsequent NTS recordings showed cessation of phrenic output during hyperinflation.
With iridectomy scissors and fine forceps, the brain stem was exposed by removal of the dura overlying the fourth ventricle and surrounding region. Head ventroflexion obviated the need for removal or retraction of the cerebellar vermis. A micromanipulator mounted to the stereotaxic device was used to place pulled glass microelectrodes (∼4–10 MΩ impedance at 1 kHz) filled with 2 M NaCl on the surface of the brain stem perpendicular to the horizontal plane. After rapid penetration of the medulla to depths corresponding to the dorsal NTS, a piezoelectric drive (EXFO, Burleigh, ND) was used to advance the electrodes in 1- to 2-μm steps. If necessary, fine forceps were used to make small (∼1-mm-diameter) openings in the pia to prevent breakage of electrode tips during initial penetration; care was taken not to disturb superficial blood vessels. Extracellular recordings were amplified and filtered (500–5,000 times, 200–5,000 Hz; Neurolog) and were obtained ipsilateral (i.e., on the animal's right side) to the recorded PhN and VN.
Pump Cell Classification and Stimulation
Once a respiratory-related unit was isolated, it was categorized as a pump, a beta, or an alpha cell via several classical criteria. “No-inflation” tests in which lung inflation was withheld for three to four consecutive breaths were performed to ensure that a cell was a pump cell, as opposed to a beta cell (which also fires in bursts during inspiration). Only cells that showed no alteration in firing rate (most were silent) during the no-inflation test were considered to be pump cells (Fig. 1B). Neurons that fired only during PhN discharges, and not during lung inflation in the absence of PhN activity, were considered alpha cells. In addition, lung hyperinflations (see above) were used to ascertain the presence of significant PSR inputs. Finally, ipsilateral VN recordings were backaveraged, triggered from spike events, to ensure that recordings were from pump cells, and not from PSR axons, which demonstrate a distinct unitary waveform, whereas VN backaverages triggered from pump cell spike times were featureless (Fig. 1C) (12). Arterial pressure and TP signals were transduced and amplified using conventional equipment (Gould-Statham, Los Angeles, CA). Arterial pressure, expiratory CO2
After confirmation of a pump cell recording, ventilation depth and rate were changed manually during the recording (Fig. 1A). Although this naturalistic stimulus consists of inflation-deflation sequences, it is less predictable than a fixed-ventilation paradigm (see Fig. 11B in Ref. 27). Often, alterations in ventilation resulted in reflex alteration in blood pressure, which in some cases caused loss of the recording (Fig. 1A). In this study, we considered only pump cells in which a recording of >4 consecutive min was maintained during TP manipulations. This ensured >48,000 observations of stimulus-response pairs (see below). Because of this large number of observations relative to the number of stimulus “categories” and because theoretical and actual joint probability distributions are of the same dimension, the additive sampling bias associated with information estimates is negligible (7, 27). After the experiment, the three-dimensional locations of the recording sites were determined by stereotaxic coordinates relative to calamus scriptorius and the dorsal surface and mapped onto standardized sections (Fig. 1D) (20).
Information theoretical analyses.
To quantify the information in the pump cell spike trains about the TP stimulus, we used the analysis methods described by Rogers et al. (27). The spike times were corrected for PSR conduction delay and distance to the NTS from the lungs. This correction (7–9 ms) varied slightly from pump cell to pump cell only on the basis of conduction distance, with the assumption of an average PSR conduction velocity of 19 m/s in this species (27). A window of fixed width was placed over the (time-corrected) spike train and stimulus waveform. At that window position, the spikes within the window were counted, and the average TP amplitude was also calculated. These two values defined which bin was incremented in a cooccurrence matrix. The window was then slid down the TP stimulus and spike train by 5 ms, the spike count and mean TP amplitude were recomputed at this new position, and the appropriate bin in the cooccurrence matrix was updated by one count. This process was repeated until the entire continuous record was characterized. The values in all bins were divided by the total number of observations to create a discreet joint probability distribution from the cooccurrence matrix. In addition to the stimulus-response joint probability (Pstim,resp) distribution, the cooccurrence matrix provides the stimulus and response probability (Pstim and Presp) distributions in its marginal distributions (Fig. 2) (27). The vector product of Pstim and Presp defines a joint probability distribution with maximum entropy (Pstim,resp), given the constraints of the Pstim and Presp distributions. That is, Pstim,resp describes the expected distribution if no lawful stimulus-response relationship exists. The degree to which this is untrue defines information. That is, information quantity is determined by the amount by which the entropy of this special joint distribution is reduced by a lawful relationship between the stimulus and response (i.e., the entrophy of the actual joint probability derived from the cooccurrence matrix). Thus a normalized version of information is given by I = (H*stim,resp − Hstim,resp)/Hstim,resp, where Hstim,resp and Hstim,resp are the entropies associated with Pstim,resp and Pstim,resp, respectively (Fig. 2) (27). This normalized measure of information is especially useful in comparing information quantities between neurons with different Pstim distributions.
The three free parameters in this analytic method are the number of categories into which the dynamic range of the stimulus and response are divided and the sliding window width. These parameters were systematically changed to new values for each analysis run. Sliding window widths of 5, 10, 20, 30…220, 230, 240, and 250 ms were used. In the previous study (27), we measured the central delay time in the rabbit Hering-Breuer reflex at ∼152 ms, which defines an upper limit for the integration time of the PSR signal by the nervous system, and our range of sliding window widths covers intervals just larger than individual excitatory postsynaptic potentials through those >1.5 times systemic (reflex) delay times. The dynamic range of the stimulus was divided into between 2 and N categories, where N is the greater of either 20 or the number of categories required to divide the dynamic range of the stimulus into 1-mmHg categories. The response was divided into between 2 and M categories, where M is equal to 1 + the maximum number of spikes observed at a given window width at any position along the data. The maximum information (I) conveyed at a given window width was determined by systematically changing M and N, such that information and encoding/decoding efficiencies were calculated at every possible combination of M and N (27). In addition, the amount of information (I∼1) conveyed when the stimulus is divided into 1-mmHg categories and the response is divided into M categories (hereafter referred to as the X∼1 discretization level) was determined. Because it is a physically based metric, I∼1 allows for direct comparison between the quantity of information carried by spike trains of different cells by standardizing M and N to each cell (27). That is, we require the system to discriminate between 1-mmHg-wide categories at full spike response resolution. In all cases, I and I∼1 are calculated as fractions of the theoretical maxima (see above) given the stimulus and response discretization. We are particularly interested in how I and I∼1 change as a function of observation/integration time (i.e., sliding window width). This relationship has theoretical and biophysical importance (27) and serves as an additional means to compare cell performance.
In addition to information estimates, we estimated the encoding (E) and decoding (D) efficiencies, as previously described (27). Briefly, E quantifies how much of the spike train (response) entropy is utilized to transmit information about the stimulus [(Hstim,resp − Hstim,resp)/Hresp], whereas D describes how much of the TP stimulus entropy is used to convey information [(Hstim,resp − Hstim,resp)/Hstim]. Using conditional probability distributions (i.e., Pstim resp and Presp stim), we examined encoding and decoding processes (27). All information theoretical analysis was performed using custom-written software in C++ and Matlab (Mathworks, Natick, MA), both running on a personal computer.
PSR vs. pump cell.
The characteristics of the population of pump cells were compared with those of the population of PSRs (i.e., their major excitatory presynaptic input) described by Rogers et al. (27). In addition, we examined whether E and D in pump cells were significantly different from E and D in PSRs. We used an unpaired two-tailed t-test, performed at each window width size, to evaluate whether I, I∼1, E, E∼1, D, or D∼1 was significantly different between the two cell types, with P < 0.05 used as our significance criterion. We also compared the average global maximum values (i.e., maxima over all window widths for each cell) of I, E, and D for the pump cells and compared these with those of the PSRs. To investigate the variability of the response within a given category, we analyzed variance and Fano factor (response variance ÷ mean) and compared the former with the theoretical minimum. To compare cell types (PSR vs. pump), we used the X∼1 stimulus/response discretization level at window widths ≤50 ms. The differences in the deviations from the theoretical minimum response variances were used to assess PSR vs. pump cell performance.
Of the 67 pump cells identified, 18 were chosen for analysis on the basis of clear, uninterrupted recording epochs during TP manipulation. Among these, no additional physiological criteria were imposed. No differences in the calculated metrics were observed between the neurons recorded in Dutch-Belted and New Zealand White rabbits. All recordings were made in ventral/ventrolateral regions of the NTS at rostrocaudal levels corresponding to the area postrema (Fig. 1D).
Figure 2 depicts results typical of the information theoretical analysis in which high levels (X∼1) of discretization are demanded. The Pstim and Presp distributions are calculated directly from the data. The Pstim,resp distribution, produced by the vector product of Pstim and Presp, contains the maximum entropy (i.e., randomness) possible given those distributions. The Pstim,resp distribution, calculated directly from the data, is shown as well and clearly demonstrates less entropy than the Pstim,resp distribution. This implies that specific responses are associated more closely with specific stimulus levels, and vice versa.
Figure 3, top, provides measures of information as a function of window width for one pump cell. This relationship, a saturating function, was typical of the pump cells analyzed and means that increasing the response observation time beyond 50–100 ms provides only minimal (if any) gains in information about the TP stimulus. Also, the increase in the (normalized) information values does not result from a decrease in the normalizing entropies (Hs,r and Hs,r∼1 in Fig. 3) but, rather, from an increased certainty in the stimulus-response relationship. Taken over all pump cells and all combinations of stimulus and response discretization levels and window widths, the average global maxima (range) for I and I∼1 were 0.287 (0.192–0.388) and 0.204 (0.128–0.268), respectively. The combinations of stimulus and response that resulted in the maximum information being conveyed at each window width were similar to those of the PSRs, in that usually fewer than six stimulus and response categories produced I (data not shown).
Encoding and Decoding Efficiency
An example of encoding (E and E∼1) and decoding (D and D∼1) efficiency values as a function of window width is also shown in Fig. 3. Similar to the information metrics, these were typically saturating functions of window width. The saturating values indicate that at window widths >50 ms, little more of the stimulus (Fig. 3, Hs) or response (Hr) entropy was used to convey information. Average global maxima (range) for E, E∼1, D, and D∼1 were 0.709 (0.491–0.887), 0.446 (0.266–0.593), 0.701 (0.431–0.881), and 0.462 (0.238–0.740), respectively.
The two processes, encoding and decoding, are mathematically determined by the conditional probability distributions Presp|stim and Pstim|resp, respectively. Examples of these functions for one pump cell are provided in Fig. 4. As illustrated by the surface plots (original data plus interpolated points), decoding and encoding are not only physiologically distinct processes, they are also mathematically independent functions. Whereas encoding describes the process of estimating the pump cell response on the basis of a given stimulus, decoding is the process by which one may estimate the stimulus given a particular pump cell response. The accuracy of the estimate depends on the character of the function in the conditional dimension (i.e., within each category), and this differs between the two processes. In the example shown in Fig. 4, encoding provides a more certain estimate, because the functions are typically described by a single distinct maximum within a given category, even at high stimulus levels. On the other hand, decoding is characterized by decreased certainty of the stimulus estimate when response level is greater than five spikes, indicated by the broad, shallow functions within a given category at those values (Fig. 4). E and D are global measures of estimate certainty over all categories in a given plot, such that high certainty of estimate in one category may offset low certainty in others. Nonetheless, examination of the subregional nature of these conditional probability functions provides insight into how particular stimulus or response patterns impact information. Although the means and ranges of E, D, E∼1, and D∼1 were very similar, this analysis directed us to implicate the higher variability associated with larger responses as the source of differences between PSR and pump cell information transmission (see below).
Pump Cells vs. PSRs
We compared the I, E, and D estimates in the pump cells with the same metrics from the PSRs (Table 1) (27). The data demonstrate that the (mean) maximum I, E, and D values are not significantly different between PSRs and pump cells. Importantly, although the average maximum information (I or I∼1) is diminished in pump cells compared with PSRs, the reduction is not statistically significant. In addition to the global measures (Table 1), we analyzed the group data as a function of window width. Data for the six measures of PSR vs. pump cell performance across all cells within a given window width are shown in Fig. 5. Not 1 of the 156 possible intra-window-width comparisons revealed a statistically significant (P < 0.05) difference between PSR and pump cell performance, although a consistent trend toward decreased performance was evident.
Response Mean and Variance
To investigate the variability of the response within a given stimulus category, we analyzed variance and Fano factor. A typical result, showing that variance tends to deviate from the theoretical minimum (scalloped function) (13) as window width increases is shown in Fig. 6 (top). However, the variance of the response within a given stimulus category does not increase proportionally with the mean response but, instead, grows at a more modest rate as a function of window width (Fig. 6, bottom). All cases where response variance approached that of the mean occurred at very small response means (i.e., near or at zero spikes), and except for this domain, they never approached the relationship characterized by a Poisson process (variance = mean) at any window width examined (see methods).
The primary difference between the variability of the pump cell response and the response of the PSRs is that the former is greater at higher response levels (cf. Fig. 6 with Fig. 10 in Ref. 27). Since the overwhelming majority of variances for mean responses <0.5 spikes lie on the theoretical minimum, we compared the pump cell variances for mean responses ≥0.5 spikes with those of PSRs. If we consider mean responses ≥0.5 spikes at all window widths ≤50 ms at X∼1 discretization levels, the average pump cell Fano factor is 0.4094 ± 0.4364, while the same PSR metric is 0.186 ± 0.149, even though the fraction of pump cell mean responses (57.9%) included in this category was similar to that of PSR responses (62.6%). This higher degree of variability in the higher mean responses can be demonstrated by measuring the difference between these variances and the theoretical minimum variance (scalloped function in Fig. 6, top). Figure 7 shows the differences between the actual and theoretical minimum response variances (σ2 − σ2min) for all PSRs and pump cells: 66.7% of the PSR response variances are within 0.1 spikes2 of the theoretical minimum, while only 25.9% of the pump cell response variances are that small. Moreover, the average differences between the actual and theoretical minimum variances are significantly smaller (P < 0.001) for PSRs (0.112 spikes2) than for pump cells (0.657 spikes2). Therefore, PSR response variances lie closer to the theoretical minimum than pump cell responses. These measures, which are consistent with Fig. 4 (top), are distinct from I∼1, because the information metrics also reflect low (<0.5 spikes) response data, which make up a significant fraction of the responses because of the nature of the TP stimulus waveform. Thus the major difference between PSR and pump cell information lies in the consistency with which higher mean responses covary with stimulus values. No significant difference between PSRs and pump cells was observed for variances associated with mean responses <0.5 spikes.
In this study, we used the respiratory control system as a model system for neural information processing, with particular interest in the impact of spatiotemporal integration on information quantity carried by spike trains of second-order neurons (pump cells) compared with their first-order sensory afferent counterparts (PSRs). A variety of theoretical arguments in support of the loss or gain of information at the single-cell level as a result of such integration can be proposed. For example, when the information carried by spike trains of individual PSRs is compared with that of pump cells, an increase in the latter compared with the former may be expected by virtue of the convergence of PSRs with a variety of TP thresholds and dynamic ranges. In this case, a pump cell's activity may be expected to possess increased information (or, at least, to be capable of finer discriminations among stimulus categories) compared with any one of its PSR inputs. On the other hand, because of the RC nature of the postsynaptic cell membrane and the inability for individual synaptic inputs to cause postsynaptic spikes because of their small amplitude and short duration (6), the fidelity of the spike-generating process in pump cells caused by synaptic drive may be inferior to that of the generator-potential mechanism involved in formation of single PSR spikes. In addition, the integration of excitatory or inhibitory synaptic inputs from sources other than PSRs (e.g., inhibition during central inspiration) (21, 22) may contribute to a reduction in the consistency of pump cell responses. Unless these are perfectly correlated with PSR drive, other inputs will add “noise” to a system where TP signal representation is the presumed cybernetic goal of the spike code and thereby reduce information at the single-cell level. Although it was not obvious a priori which effects would be stronger and result in loss or gain of information, we assumed that information loss (at the single-neuron level) would occur as hierarchical levels are ascended because of the additive noise associated with integration/convergence. Given our sampling of the populations of PSRs (27) and pump cells (present study), we conclude that our hypothesis is not supported by the present data; i.e., information about the TP stimulus is well retained at the level of second-order neurons. Interestingly, this is in contrast to a closely related system, that mediating the cardiovascular reflexes (e.g., baroreflexes). The Hering-Breuer reflex and baroreflex require processing of pulsatile inputs (PSRs and arterial baroreceptors), but only the respiratory control system contains second-order neurons that mimic afferent spike patterns. Although our results show that pump cells retain a great deal of the same information contained in PSR inputs, arterial baroreceptor-driven second-order neurons in the NTS appear to encode the rate of change of (mean) blood pressure in their spike activity (25, 26, 35), rather than its absolute value, which is clearly represented by the activity of individual baroreceptors (2, 8, 30).
The approach of quantifying mutual information in spike trains of individual neurons has a rich history (17, 24, 32–34) and has clearly advanced the field. However, the primary drawback to this approach is that it cannot address the fundamental parallel nature of the nervous system, in which information is presumably encoded in the simultaneous spike trains of a population of many neurons. In the respiratory control system, pump cell activity should reflect the averaged information in (a subset of) the PSR population, and our results support this supposition. However, because of our “serial-recording” approach, we cannot make any definitive claims regarding the total information in the activity of the entire population of pump cells because of the potential for redundancy of information among individual spike trains (27). Only in extremely rare instances (or incredibly simple neural systems) is it possible to simultaneously record a reasonable fraction (i.e., a representative diversity) of the spike trains of a single class of neurons, such as the output cells of a single hierarchical level of a system. In one study that measured retinal ganglion cell activity ex vivo (32), total information as a function of cells included in the population analysis demonstrated that information about visual stimuli rapidly increases as a function of cell (i.e., spike train) numbers considered but saturated soon after at least one neuron of each class was included. Considerable technical barriers prevent such measurements in the respiratory control system, and no similar subclassification has been proposed for pump cells.
All the advantages and disadvantages of the analytic method (e.g., using spike count as the code) described by Rogers et al. (27) apply here, including the relationship between the degree of discretization and information quantity. Similar to the PSRs, the number of stimulus categories at which the maximum pump cell information (I) was transmitted was typically low (<6), and forcing higher resolution (e.g., to I∼1 levels) results in less information (cf. Fig. 3, top left, with Fig. 3, top right). In addition, maximum encoding (E) and decoding (D) levels occurred with patterns of categorization, such as in those for PSRs (27).
The findings that information saturates as a function of window width (Fig. 3, top) and is a relatively well retained in pump cell spike trains (Fig. 5) are by no means foregone conclusions. These depend on the biophysical integration time of individual PSR inputs, their relative synchrony, and the network architecture. The constancy of the pump cell activity at low stimulus levels is guaranteed by the (subthreshold) integration required to depolarize the cell to threshold. During this same period, individual PSR activity may vary slightly compared with the absolutely consistent pump cell response (i.e., silence). However, at suprathreshold stimulus values, the response of the pump cell is more variable than that of the PSR (Figs. 6 and 7). Our preliminary analysis of computer simulations (9) confirms the notion that the degree of PSR input synchrony (i.e., within 1 ms) increases as PSR-to-pump convergence ratios increase, yielding maximum pump cell information by the time the ratio reaches 50:1 and 100:1. This is consistent with physiological data, which suggest that excitatory postsynaptic potentials with amplitudes of 120–239 μV and half-width durations of 0.65–1.25 ms (6) require convergence ratios ≥50:1 to produce a pump cell membrane potential that covaries with the TP amplitude and to produce a spike train with a characteristic rate associated with a given stimulus amplitude (9). Thus the fundamental network architecture is ultimately constrained by the biophysical properties of the first-to-second order connection. This architecture enables a signal-processing scheme that preserves information about the amplitude of lung distension in its individual second-layer elements.
Impact of Naturalistic Stimulation and Biophysical Constraints
Perhaps the most intriguing result is that although there appears to be a consistent trend of diminished information within each integration time in pump cells compared with PSRs, it is not statistically significant (Fig. 5, top). The source of this trend is revealed when one considers the variability in the responses of pump cells vs. PSRs (Fig. 4, top, and Fig. 7). The increased variability of pump cell activity associated with larger responses implies that there is loss of information compared with PSR responses (Fig. 7). The fact that the lungs spend a considerable fraction of their time in a relatively “deflated” state allows for the retention of information by the pump cells, because response variances reach the theoretically low limits during this state, regardless of window width.
Although the overall trend is a (statistically insignificant) decrease in information in pump cells (Fig. 5, top), this trend is reversed at narrow window widths of 5 or 10 ms. That is, the same mechanisms that contribute to relative loss of information at longer integration times (mass averaging associated with PSR convergence, lung inflation-unrelated inputs to pump cells, the biophysical properties of the pump cell membrane, or a combination of these mechanisms) may actually increase information transmission at short integration times. This has important physiological implications, e.g., that synaptic integration and spike-generating mechanisms are extremely reliable over short time scales, but this also reflects the nature of responses at narrow window widths (i.e., 0 or 1 spike). As observation time increases, decreased consistency of the responses ensues, particularly at suprathreshold stimulus levels. The certainty of neuronal silence at low stimulus levels (even at wide window widths) or the use of narrow window widths at higher stimulus levels counterbalances this effect and results in statistically insignificant information loss. A Pstim distribution skewed toward low TP values, either natural or experimental (Fig. 2), enables good overall information transmission, despite the pump cell response noise. Sources of this noise may include PSR inputs, which are relatively consistent (Fig. 7) (27), but their minute inconsistencies may combine to cause larger variability in pump cell firing. The overarching finding is the relative equivalence (in information terms) of two different biophysical processes that produce spike trains: 1) single PSR sensory transduction mechanisms involving integration of many mechanosensitive ion channel conductances and 2) synaptic integration of PSR inputs at the pump cell membranes.
Finally, our result that Fano factors first decrease from window widths of 5 to 50 or 100 ms and then increase as window widths increase (not all data shown) is a feature shared by PSRs (27) as well by neurons in a completely unrelated system, the motion-sensitive H1 neuron in the fly visual system (13, 33). The initial decrease is due to the fact that small window widths typically have means spike counts <0.5, and their variances are very close to the theoretical minimum (i.e., most responses are 0 spikes, some are 1 spike, and no other responses are ever observed). Because this is near the origin of the curve, Fano factors are near 1. However, the fact that any growth in variance lags far behind that of the mean suggests that there is a fundamental underlying principle in the tuning of the passive and/or active membrane properties in pump cells and H1 neurons. This feature (i.e., very reliable encoding) seems to be favored by systems with relatively few neurons. Conversely, in systems with far greater numbers of neurons, such as lateral geniculate nucleus and V1 neurons in the primate visual system, (spike count) variance-to-mean ratios may easily exceed that of a Poisson process (23).
In conclusion, our results suggest that information carried by individual neuronal spike trains is comparable at two consecutive hierarchical levels, and any information that is lost is due to reduction in consistency of larger-amplitude responses. Thus the mechanism of spatial integration, particularly over integration times on the order of typical membrane time constants, enables transmission of lung distension information in a relatively lossless fashion between PSRs and pump cells. The natural question arises as to the cybernetic usefulness of duplicating lung distension information in a central population. The likely answer is that second-order NTS neurons provide a convenient site for modulation of information transfer required by a variety of respiratory-related behaviors (e.g., vocalizations and coughing) and under various conditions (e.g., hypoxia).
This work was supported by National Heart, Lung, and Blood Institute Grant R01 HL-68143 (R. F. Rogers).
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- Copyright © 2007 the American Physiological Society