Failure to detect abnormal levels of impulsivity in SHR may be related to the sensitivity of DRL performance to incentive motivation 30: A subject that is not motivated to complete the DRL task may engage in other activities, producing longer IRTs that would be wrongly attributed to self control. With very long target times, such as those used by Bull et al. 22 and van den Bergh et al. 23, it is possible that successful performance is a result of periodic desertion of the task due to flagging motivation, rather than controlled waiting associated with self-control. Failure to detect abnormal impulsivity in SHR using DRL may be due to SHR's reduced motivation for the incentive relative to control strains – more frequent desertion of the waiting task may have been wrongly interpreted as more controlled waiting.

To isolate impulsivity from motivation, we propose to complement measures obtained from DRL with those obtained from a lever-holding task (LHT). In LHT, releasing a lever or button is reinforced only if it had been pressed longer than a specified interval; early releases restart the clock but are not reinforced. Variations of LHT have been used as a timing task in animals 3132.

In LHT and DRL, reinforcement is contingent on emitting a response (lever or button press in DRL; lever or button release in LHT) after withholding it for a minimum time. Both tasks differ in what subjects are required to do between responses: Waiting activities in LHT are restricted to those that keep the switch depressed, whereas in DRL they are anything other than pressing the switch. Like short IRTs in DRL, short response durations in LHT are deemed impulsive. Supporting this characterization of LHT inefficiency, Baldwin and colleagues 33 demonstrated that methylphenidate reduces the variability of response durations and the frequency of very short durations in children with ADHD.

As the case for DRL, the interpretation of LHT performance is not without confounds. A subject exposed to LHT contingencies may produce shorter "impulsive" response durations because of reduced motivation or poor motor control, not because of an impulsive tendency to release the lever early. Conversely, reduced motivation and poor motor control are unlikely to contribute to shorter IRTs in DRL: Smaller rewards yield longer IRTs in rats and pigeons 30. Longer "self-controlled" IRTs in DRL may result from low motivation to complete the task. Conversely, reduced motivation is unlikely to result in longer response durations in LHT. Thus, demonstration of impulsivity in both LHT and DRL cannot be attributed to motor impairment or enhanced motivation. Some studies have taken advantage of the complementary nature of LHT and DRL to interpret the behavioral effects of drugs in rats 34353637 and to evaluate timing in children 37, as is our strategy here.

A second hypothesis concerning the failure to detect impulsivity in SHR using DRL derives from the use of DRL "efficiency" as an (inverse) measure of impulsivity. Efficiency is typically inferred from the proportion of responses that exceed the target interval. Efficiency measures are intuitive and descriptive, but do not take full advantage of the data for drawing inferences, as would a truly efficient model of the behavior. A change in efficiency indicates that the distribution of IRTs changed, but it does not tell us precisely how it changed 38. Four responses spaced just under the target interval followed by a reinforced response are given the same efficiency score (20%) as a burst of 4 closely spaced responses followed by a reinforced response; yet the former performance is more inefficient in most senses of that term. Moreover, despite having the same efficiency score, responses that are spaced almost right would score better in most measures of timing than a burst of responses would. DRL efficiency ignores much of the information contained in performance, some of which may be critical to distinguish levels of impulsivity across strains of rats.

Richards and colleagues 38 suggested an analytic technique that might characterize DRL performance using more information than is provided by efficiency measures. Their peak deviation analysis identifies deviations in the IRT distribution from a random process, defined as one in which interval terminations occur randomly with constant probability. A constant-rate random process entails a negative exponential distribution of IRTs. In DRL, very short IRTs ("bursts") and IRTs around the target interval ("peak") are typically much more frequent than expected from a constant-rate random process. Using this analysis, van den Bergh 23 showed that bursts tended to be more frequent and peak IRTs tended to be shorter in SHR than in Wistar (WST); these tendencies, however, did not reach statistical significance.

Peak deviation analysis may reveal differences in DRL performance between SHR and control strains, but it is unclear how these differences should be linked to impulsivity. In the following analysis we develop a plausible behavioral mechanism for both DRL and LHT performance, and test it against data collected from SHR and two other strains. Some of the model parameters are directly related to the ability of rats to inhibit responses, and thus provide a measure of impulsivity. We then evaluate differences in these parameters across strains and reconcile our conclusions with prior data reported on SHR impulsivity.

Rats took between 43 and 55 days to complete Experiment 1 [Additional file 1]. The median rat took 1 session to acquire T < 1.5 s and 2 sessions to acquire T ≥ 1.5 s. Only 3 rats failed to acquire a target time in less than 10 sessions (S4 at T = 1.5 s; S6 and W4 at T = 5 s). To compensate for their exclusion, data from W2 and L7 were excluded from T = 1.5 s and above, and data from L2 were excluded from T = 5 s. Rat L3 was accidentally not trained on T = 1.5 s, so data for this rat in this condition is missing – no compensation for "slow learning" was conducted. Response durations were stable for all strains in all target times, except for LE rats in T = 5 s and WKY rats in T = 0.25 s, where the median response duration increased by 12% and decreased by 10%, respectively, over the last 2 sessions.

Figure 2 shows the proportion of response durations greater than target time T; because this metric indicates the proportion of responses that were reinforced, it has traditionally served as a measure of response efficiency. At T = 0.25 s, LE and WKY rats were more likely to produce long durations than SHRs. At T = 0.5 s and T = 0.75 s, the proportion of long durations in LE and WKY decreased to SHR levels. At longer target times, LE rats produced longer durations than either SHRs or WKY rats. Thus, by traditional inference from differences in efficiency, SHR were more impulsive than WKY for T = 1 s, but SHR were more self-controlled than WKY for T > 1. Neither of these strains showed anything like the self-control of LE for T > 1 s. Whether performance at target times less than one second speaks more to self control or to motor control is moot.

Very long response durations can be even more inefficient than very short ones; a short response just under T can at most halve the rate of reinforcement; a long response can reduce it as 1/t. A more direct measure of efficiency is rate of reinforcement – the average number of reinforcers obtained on a minute of experimental session while the lever was extended. Applying this metric to LHT 5 s, LE was more efficient than SHR, collecting 5.6 reinforcers per minute, and SHR at 2.2 was more efficient than WKY at 1.6 reinforcers per minute.

Efficiency is only one index of LHT performance; distributions of response durations provide a more complete picture. To illustrate this, Figure 3 shows the cumulative probability distribution of response durations for 3 target times T, pooled within each strain. Whereas probability density functions are more intuitively compelling, they require that data be binned, and they are sensitive to the amount of data in each bin; cumulative distributions are less sensitive to data aggregation procedures. To ground these cumulative distributions to intuitions, the insets in each give the corresponding densities. Each curve in Figure 3 shows the probability y that a response duration was shorter than x. Efficiency (proportion of reinforced responses) may be directly recovered from these plots as 1 - B(T) where B(T) is the ordinate corresponding to an abscissa of x = T, designated by the vertical dotted lines. Simply extend a horizontal line from the intersection of the dotted line with the curve, over to the y-axis; efficiency is the complement of that intercept.

The midpoints and slopes of cumulative distributions in Figure 3 were correlated with T, but for longer values of T distributions showed an extra inflection on the left side (see the bottom panel of Figure 3). This inflection represents a distinct population of short duration responses. What controls the parameters of this population of response durations? One possibility is that these were carried over from prior target times, but this is unlikely, for three reasons: 1. At short T, before the inflection in the distribution appeared, the probability density function of response durations was inverted-U shaped (e.g., Figure 3, inset of top panel), whereas the function of the inflection decreases monotonically as response duration increases. 2. When the inflection appeared, it increased the relative frequency of very short durations. 3. Such bimodal distributions have been reported before under widely different pre-training conditions, both in LHT (e.g., 34) and for IRTs in DRL (e.g., 38).

We suggest here that the bimodal distribution of response durations may be the output of two mechanisms operating in temporally regulated responses: A timing mechanism that produces a distribution of durations around the target times, and a random response process that produces shorter durations. The operation of these mechanisms is described more precisely by the Temporal Regulation (TR) model.

LHT performance by SHR, WKY, and LE rats was well described by the mixture of exponentially and normally distributed response durations of the TR model. For all strains, the sensitivity of the normally distributed portion of the response durations to the target time supports its characterization as the output of a timing process. For SHR and LE it is a simple scalar process, whereas for WKY, the dispersion of the normally distributed durations did not accord with Weber's Law 474849, increasing faster up to about 2 s and slower thereafter.

Mean timed responses were generally shorter for SHR and WKY than for LE rats, suggesting that SHR and WKY rats have a bias to release the lever earlier than LE rats. This result is consistent with SHR as an animal model of the response inhibition deficit that characterizes ADHD 50, but it is inconsistent with the use of WKY as a control strain: If SHRs are just as impulsive as WKY rats, the source of impulsivity may lie in their common genetic background, thus rendering SHR-WKY comparisons uninformative. The performance of SHR and WKY was similarly suboptimal, resulting in lower efficiency in producing intervals longer than the target time.

The dispersion of timed responses of SHR and LE, but not WKY, was well described by the linear function known as the Generalized Weber's Law. The parameters of SHR suggest that timing precision was not compromised in SHR: if anything, they are more precise than LE. Timing precision in SHR appears to be inconsistent with recent reports of poor time reproduction – the closest analog to LHT – in ADHD 51. These investigations, however, also indicate that ADHD patients, like SHRs, systematically underestimate long target intervals 525354555657. Only one of these reports describes a measure of precision that allows an estimation of Weber fraction w 57. This research indicates that children with ADHD are not only more impulsive than controls, but that their timing is also less precise. SHRs showed analogous impulsivity relative to LE, as shown by θ_SHR, but no comparable timing imprecision.

In synthesis, the idiosyncratic performance of WKY in LHT suggests that it may not be the appropriate control strain to evaluate impulsivity in SHR. A comparison between SHR and LE performance suggests that SHRs are less capable of inhibiting reinforced responses – the critical feature of ADHD-related impulsivity. This result may stem from an inhibitory deficit intrinsic to the SHR strain which would support its use as an animal model of ADHD-related impulsivity. This result could also be interpreted as a difficulty in holding down the lever for SHR, relative to LE, due to a motor limitation or its lower body weight; it could also be interpreted as diminished motivation due to lower rates of reinforcement (in turn derived from inefficient responding). Experiment 2 was intended to disambiguate these alternate interpretations of LHT data.

The same 18 rats of Experiment 1 served, after approximately 60 days of resting, under the same housing, feeding, and handling conditions as in Experiment 1. The experiment was conducted in the same chambers used in Experiment 1, but the clicker was replaced with a Sonalert 2.9 kHz tone generator (ENV 223AM).

Analysis was conducted on IRTs from the last 3 sessions of DRL 5 s and DRL-LH 5 s. Because response rates were substantially lower in DRL 60 s, analysis was conducted on the last 5 sessions of this schedule. IRTs were binned so that each bin contained 1% of a rat's data. Cumulative distributions similar to those of Figure 3 were constructed for each strain. A model-comparison analysis was conducted to determine whether TR's timing parameters were reliably different across strains. Once again, we asked whether θ and w varied across strains. Four models were compared using AICc. One model allowed none of the timing parameters to vary across strains; a second model allowed θ but not w to vary; a third one allowed w but not θ to vary; a fourth one allowed both parameters to vary. When fitting each model, estimates of q and λ were fitted to each individual animal. Model selection rules and confidence computation were the same as in Experiment 1. For comparison, this analysis was also conducted on the LHT 5 s data analyzed in Experiment 1.

Two features of DRL were varied: the presence or absence of an upper limit (the limited hold) and the target time, 5 or 60 s. In all these variations, the performance of SHR, WKY, and LE rats was well described by the TR model (Figure 7).

One variation in particular, DRL-LH 5 s, is most readily comparable to LHT 5 s, because both schedules have the same target time and an adjusting upper limit. The critical difference between these schedules is what rats were required to do while "waiting": in LHT they had to wait holding down the lever, whereas in DRL they had to wait by staying away from the lever. The complementary nature of LHT and DRL permits establishing whether shorter timed responses are influenced by factors other than impulsivity. Estimates of TR timing parameters from DRL-LH 5 s were close to those obtained from LHT 5 s, suggesting that these parameters are relatively robust over the nature of the waiting responses. Without the limited hold, performance was generally both less accurate (deviations of response threshold θ from 1 were greater in all strains) and less precise (Weber fractions w were greater in all strains).

The invariance of parameter values across specific tasks indicates that TR has some generalizability. The relativized timing parameters it provides (θ and w) are also invariant across moderately short (1–5 s) target times. However, when the target time of DRL was 60 s, response thresholds declined and Weber fractions increased in all strains. We believe this was due to a mixture of timing responses that usually fell short, and an occasional return from delinquency that was usually reinforced. Lapses of attention may have garnered an occasional reinforcement for flagging performance and resuscitated behavior under DRL 60 s. In LHT, this safety net was not available. These differences are reflected in the fact that it would be virtually impossible for a LHT 60 s schedule to sustain any responding. Our results indicate that different processes may be engaged when target times are very different, which confounds the interpretation of changes in TR parameters across widely different target times.

SHRs had lower thresholds for responding (θ) than WKY and LE in DRL schedules, and lower thresholds than LE in LHT schedules. Whereas a reduced ability to press a lever and infrequent engagement in the waiting task would result in shorter LHT timed responses, the same deficits in DRL would result in longer timed responses. The complementary contingencies of LHT and DRL schedules provide converging evidence that impetuous responding reflected in lower values of θ for SHR cannot be attributed to motor deficits or differences in body weight. It is also very unlikely that impulsivity in SHR was confounded with reduced motivation due to low rate of reinforcement; such hypothesis may explain shorter response durations in LHT but not shorter IRTs in DRL. This evidence that response inhibition in SHR is impaired supports the use of SHR as an animal model of ADHD-related impulsivity.

Estimates of θ for WKY were substantially greater on DRL 5 s than on LHT 5 s (but was reined in somewhat by the limited-hold contingency). If WKY were less motivated or less able to work for food than other strains, we would expect increased desertion, which would help DRL performance but not LHT performance. This was just the difference we found. The hypothesis of reduced motivation in WKY is supported by evidence of reduced instrumental responding for sucrose pellets in this strain 59. Consistent with prior observations 2260, WKY's different thresholds in the complementary tasks suggests that this strain may not provide consistent baseline levels of response inhibition required for the assessment for impulsivity in SHR.

There were no systematic between-strain differences in the Weber fractions in DRL comparable to those seen in LHT (Figure 5), where LE were less precise than the other two strains. These results confirm that the precision of temporal estimates of SHRs is not compromised, unlike that of children with ADHD 57.

Bull and colleagues 22 compared the distribution of IRTs from SHR, WKY, and Sprague-Dawley (CD) rats under DRL 60 s. Estimates of TR timing parameters from Bull et al.'s data indicate that θ_SHR = 0.4 and θ_WKY = 0.69, which are comparable to our estimates (0.52 and 0.61 respectively; see Figure 8). It is surprising, however, that θ_CD = 0.33, which is even lower than the response threshold of SHR. Compared to our data, CD rats in Bull et al.'s experiment appear to be extraordinarily impulsive. Estimates of w in Bull et al.'s rats were substantially larger than in our Experiment 2: Whereas our estimates of w in DRL 60 s ranged between 0.4 and 0.5 (Figure 9), estimates for Bull et al's data ranged between 1.2 and 1.6. This is indicative of poorer control of lever pressing by the target time in Bull et al.'s rats. Furthemore, Bull et al's rats were substantially more efficient (10–35%) than ours (1–6%). Several factors in their investigation may have contributed to these effects. Mainly, we suspect that their large target-duration step size used for shaping DRL performance (DRL 30 s immediately preceded DRL 60 s) may have strained waiting times beyond schedule control. In contrast, we introduced DRL 60 s progressively over the course of many sessions, respecting each animal's pace of acquisition. Relative to our data, poorly timed responding in Bull et al's study resulted in flatter IRT distributions and, consequently, enhanced "efficiency". These differences in results underline the importance of shaping procedures in DRL and question the use of efficiency as a measure of impulsivity.