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Reaction time changes with the hazard rate for a behaviorally relevant event when monkeys perform a delayed wrist movement task
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Neuroscience Letters 433 (2008) 152–157
Reaction time changes with the hazard rate for a behaviorally relevant event when monkeys perform a delayed wrist movement task Yoshiaki Tsunoda ∗ , Shinji Kakei Department of Behavioral Physiology, Tokyo Metropolitan Institute for Neuroscience, 2-6 Musashi-dai, Fuchu, Tokyo 183-8526, Japan Received 1 November 2007; received in revised form 14 December 2007; accepted 31 December 2007
Abstract Anticipating the timing of behaviorally relevant events is crucial for organizing movement. The time to initiate actions based on events (i.e., reaction time (RT)) is a useful measure to quantify states of anticipation. Few studies have examined how anticipation affects the timing of limb movements. We addressed this question behaviorally with two macaque monkeys performing delayed wrist movement tasks. The interval between target onset and go signal (i.e., foreperiod) varied randomly from 1 to 2 s. The probability that the go signal was about to occur (i.e., hazard rate) increased as the foreperiod increased. The kinematics of wrist movements was not influenced by foreperiod duration. Analyzing RT data with the LATER model indicated that RT distributions swiveled on reciprobit plots as foreperiods increased, suggesting that changes in RT distributions were due to changes in anticipation. RT was inversely related to hazard rate. To better understand the general implications of anticipatory states, we introduced an additional rectangular foreperiod distribution that ranged from 0.9 to 1.5 s. For that distribution, the hazard rate peaks were higher than those of the 1–2 s distribution. Changes in RT were clearly explained by quantitative differences in hazard rate. The decrease in RT in the 0.9–1.5 s foreperiod distribution was greater than that in the 1–2 s foreperiod. Thus, monkeys learned the temporal structure of foreperiod distributions and anticipated the onset of the go signal, based on hazard rates. © 2008 Elsevier Ireland Ltd. All rights reserved. Keywords: Anticipation; Timing; Hazard rate; Foreperiod; Reaction time; Wrist movement
Timing is essential for organizing action, and experience enables humans and animals to anticipate the onset of an event. Such anticipation benefits task performance. For example, cues that provide information about when a stimulus will appear decrease subsequent reaction time (RT) to the stimulus [14,20,21]. To anticipate the onset of behaviorally relevant events, a representation of the passage of time must exist in the brain that is used to estimate the probability that an event is likely to occur [5,16,20,21]. For example, suppose an event will occur at one of two times (t1 , t2 ), and it is equally likely that the event will occur at one of those two times (p1 = p2 = 0.5). The probability that the event will occur at t1 is 0.5 just prior to t1 . However, if the event fails to occur at t1 , the probability that the event will occur at t2 becomes 1.0. This is known as the hazard rate [10,15], which should govern anticipation [5]. Recent studies clearly demonstrate that humans and animals learn the probabilistic distribution of a go signal to anticipate its
∗
Corresponding author. Tel.: +81 42 325 3881; fax: +81 42 321 8678. E-mail address: [email protected] (Y. Tsunoda).
0304-3940/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2007.12.063
onset in delayed saccade tasks [5,16]. In those studies, the delay between a cue stimulus and the go signal (i.e., the foreperiod) was a random variable with a continuous probability distribution (unimodal, bimodal, or rectangular). To examine states of anticipation, the authors analyzed RTs across different foreperiods and found that they were inversely related to hazard rates (see [5] for details). Recently, Leon and Shadlen [9] demonstrated that neurons in the macaque lateral intraparietal area (LIP) encode signals related to the perception of time. Moreover, during saccade tasks, LIP neurons display activity that corresponds to internal representation of elapsed time and hazard rate [5]. Neurons in the macaque LIP participate in planning and making decisions about eye movements [17]. However, other cortical areas, such as the parietal reach region (PRR) and the premotor cortex, participate in planning [8,24] and making decisions [3] about limb movements. Indeed, we found that neuron activity in the premotor cortex gradually increased during preparatory periods in which hazard rates for go signal onset increased [7]. Furthermore, recent studies demonstrated that neurons in the pre-supplementary motor area [1] and the primary motor cortex
Y. Tsunoda, S. Kakei / Neuroscience Letters 433 (2008) 152–157
[20,23] encode signals related to the perception of time. This physiological evidence implies that limb movements are subject to hazard rates for behaviorally relevant events independent of the saccade system. However, few studies have examined the relationship between hazard rates and performance in limb movement tasks [21]. Riehle et al. [21] examined RT in a manual response task that had discrete foreperiods (600, 900, 1200, 1500 ms) with equal probabilities of 0.25. The authors demonstrated that RT decreased as foreperiod increased. However, unlike recent saccade studies [5,16] they did not quantify the impact of hazard rate on RT. Therefore, in the present study, we quantified the relationship between limb movement RT and hazard rate, as was recently done in saccade studies [5,16]. We examined RTs of two macaque monkeys as they performed a delayed wrist movement task. To facilitate the comparison of limb RT to saccade RT, we distributed the go signal onset in the same way it was distributed in the eye movement task of Oswal et al. [16]. To evaluate the effects of hazard rate on RT, we conducted an additional experiment with a different foreperiod distribution. All experimental protocols were approved by the Animal Care and Use Committee of Tokyo Metropolitan Institute for Neuroscience and were in accordance with the Japan Neuroscience Society Guidelines for Care and Use of Laboratory Animals in Neuroscience. Two monkeys (Macaca fuscata; monkey W, 7.2 kg; monkey E, 5.9 kg) were trained to perform a delayed wrist movement task, which has been described in detail [7]. Briefly, each monkey sat in a primate chair with its forearm supported in a pronated position, facing a screen (RDS173X; MITSUBISHI, Tokyo, Japan) that displayed a cursor and targets. A PC-based real-time experimental control system (TEMPO; Reflective Computing, St. Louis, MO) was used for stimulus presentation and data collection. With its right hand, the monkey grasped a two-axis manipulandum that controlled the cursor. The cursor moved in proportion to the monkey’s wrist movement. To initiate a trial, the monkey placed the cursor inside a central target (Fig. 1A). After a variable hold period (0.8–1 s), a target appeared at one of eight peripheral locations evenly distributed at 45◦ angles around the central target. After a variable foreperiod (1–2 s in 5-ms steps), the central target was extinguished. This served as the go signal, instructing the monkey to move the cursor from the central target to the peripheral target as quickly as possible. Acquiring a target required a 20◦ change in wrist angle. Monkeys were required to begin the wrist movement within 500 ms of the onset of the go signal. Wrist position data were analyzed offline using MATLAB (The MathWorks Inc., Natick, MA). To determine velocity, horizontal (x) and vertical (y) position signals were digitally filtered and differentiated (velocity = (dx/dt)2 + (dy/dt)2 ). For each trial, the start of a movement was defined as the time that the velocity exceeded a threshold of 15 deg/s (<10% mean peak velocity). RT was the interval between the go signal and movement onset. Trials for which the RT was <50 ms were excluded. RT data were collapsed across target direction, which increased the amount of data analyzed.
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Fig. 1. (A) Delayed wrist movement task. A trial began when the monkey positioned the cursor (black dot) inside a central target (square). After a trial began, a peripheral target appeared, signaling the start of the foreperiod. The 1–2 s foreperiod varied randomly across trials. At the end of the foreperiod, the central target was extinguished, signaling the monkey to make the required movement. (B) The top panel shows the probability density distribution of go signal onset as a function of the foreperiod (Eq. (1)). The probability remained constant for the 1–2 s interval. The middle panel shows the hazard rate for the 1–2 s foreperiod (Eq. (2)). The hazard rate increased hyperbolically across 1–2 s foreperiods. The bottom panel shows the subjective hazard rate (i.e., anticipation function), which was normalized to the peak of Ar (t) (Eq. (3)).
The probabilistic distribution of the foreperiod was rectangular (i.e., ‘aging’ foreperiod [16]) (Fig. 1B), the function of which was: f (t) =
1 (for 1.0 ≤ t ≤ 2.0 s), 200
otherwise f (t) = 0.
(1)
Ideally, anticipation should be governed by the hazard rate (Fig. 1B). That is, the probability that the go signal will occur at time t divided by the probability that it has not yet occurred: h(t) =
f (t) (1 − F (t))
(2)
t where F(t) is the cumulative distribution, 0 f (s)ds (Fig. 1B). We calculated subjective hazard rates [5] based on the assumption that elapsed time is known with uncertainty that scales with time (Weber’s law [4]). The probability distribution f(t) was first blurred by a normal distribution, of which the
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Y. Tsunoda, S. Kakei / Neuroscience Letters 433 (2008) 152–157
standard deviation was proportional to elapsed time. f˜ (t) =
1 √
φt 2π
∞
f (τ)e−(τ−t)
2 /(2φ2 t 2 )
dτ
(3)
−∞
The coefficient of variation φ was a Weber fraction for time estimation (φ = 0.26; based on previous studies in monkeys [5,9]). Eq. (3) is based on the notion that the monkey’s estimation of elapsed time carried uncertainty. Thus, an event at objective time t0 was perceived as occurring at t0 ± σ. Subjective hazard rates were obtained by substituting f˜ (t) and its definite integral, F˜ (t) in Eq. (2). We referred to subjective hazard rates as anticipation function, Ar (t). For ease of interpretation, anticipation function was normalized to the peak of Ar (t) (Fig. 1B). Because RT distributions have a long tail toward longer RT, the reciprocal of RT follows a Gaussian distribution. Plotting cumulative RT distributions on a probit scale as a function of reciprocal RT (a reciprobit plot) yields a straight line. RT dis-
Fig. 2. (A) The LATER model. When an appropriate stimulus appears, a decision signal S begins to rise linearly at rate r from an initial level S0 representing prior probability [2]. When S reaches threshold ST , the response is triggered. The rate of rise r varies randomly across trials with a Gaussian distribution (μ, σ). As a result, distribution of reciprocal reaction time over a number of trials is Gaussian. (B) Plotting the cumulative distribution on a probit scale as a function of the reciprocal of reaction time (a reciprobit plot) yields a straight line. Changes in S0 without changing r alter the slopes of plots, such that the lines pivot about the infinite-time intercept I (left panel). Changes in r, without changing S0 , result in a parallel shift of the plots (right panel).
tributions can be explained by a simple decision-making model – the LATER model (see Fig. 2 for details) [2,18,19]. Manipulating prior probability, anticipation [2], or urgency [19] alters the median RT in a manner comparable to swiveling the reciprobit plot about the fixed point I where the distribution intercepts the t = ∞-axis (Fig. 2B, left panel). In contrast, changing μ by modifying the information supply generates a parallel shift of the plot, without changing the slope (Fig. 2B, right panel) [18]. To determine whether reciprobit distributions could be modeled more accurately by a swiveling or parallel shift, we calculated maximum likelihood for a set of RT data using methods that have been described previously [16,19]. To quantify the relationship between hazard rate and RT, we fitted mean RT of successive 50-ms intervals in the 1–2 s foreperiods using a weighted sum of subjective hazard rates: RT(t) = we + wr Ar (t − τ) + ε
(4)
where RT was reaction time, we was a constant term, and wr was the weight for the anticipation function, delayed by time shift τ. We obtained the coefficients and their standard errors to minimize the sum of the squared regression errors (ε2 ; leastsquares method). We set τ as 60 ms based on a previous report [5]. Each monkey learned to execute the required wrist movements quickly and accurately (success rate >92%). Monkey W made 3935 successful responses, and Monkey E made 2457. To examine whether foreperiods affected the kinematics of wrist movements, we separated responses into four groups, based on four successive 250 ms foreperiod intervals from 1 to 2 s. Position traces of wrist movements overlapped between
Fig. 3. Kinematics of wrist movements. The foreperiod was divided into four equally sized time intervals (1000–1250, 1250–1500, 1500–1750, 1750–2000 ms). Responses were divided into four groups, according to the duration of the foreperiod. Wrist deviations (A) and velocity profiles (B) of wrist movements overlapped to a great degree from initiation to the end of movement for monkey W (left panels) and monkey E (right panels).
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foreperiod intervals (Fig. 3A). Velocity profiles were also consistent throughout foreperiod intervals (Fig. 3B). These kinematics features suggested that monkeys made highly stereotyped wrist movements that were not affected by foreperiod duration. Fig. 4A shows RT distributions for the four intervals, plotted on reciprobit plots. All distributions were well-fit with straight lines and agreed with those predicted by the LATER model (Kolmogorov–Smirnov one-sample tests, P > 0.1). There were significant differences in RT distributions, which were foreperiod dependent (Kolmogorov–Smirnov two-sample tests, P < 0.05). Median RTs for the four intervals decreased progressively for longer foreperiods. For both monkeys, a log-likelihood analysis indicated that the plots swiveled rather than shifted as foreperiods increased (Fig. 4A). Log-likelihood differences were 19.0 for monkey W and 36.2 for monkey E. Fig. 4B shows mean RTs for successive 50-ms intervals of the 1–2 s foreperiods. The RT clearly decreased between 1.0 and 2.0 s (regression analysis, P < 0.001; RT decreases were 80 ms for monkey W and 50 ms for monkey E). Mean RTs across foreperiods were inversely related to the anticipation function (Eq. (4), wr for Monkeys W and E was −103.9 ± 6.6 and −66.0 ± 4.9; R2 = 0.93 and 0.91, respectively) (Fig. 4B). Because the anticipation function was normalized to 1 with its peak, the fits (wu ) estimated RT reduction (ms) per unit change in anticipation.
155
To better understand the general implications of anticipatory states, we applied a rectangular distribution of 0.9–1.5 s foreperiods to the task for monkey E. The anticipation function for the 0.9–1.5 s distribution differed from that of the 1–2 s distribution. For instance, the peak was obtained more quickly (short duration of 0.6 s) (Fig. 5A). We recorded 1038 responses using the 0.9–1.5 s foreperiod distribution. Mean RT decreased by ∼100 ms as the foreperiod increased (Fig. 5B). The decrease was greater than that observed for the 1–2 s distribution. RT was well-fit by the weighted sum of the anticipation function (wr was −139.8 ± 8.0, R2 = 0.97). The absolute value of wr was significantly larger in the 0.9–1.5 s distribution than in the 1–2 s distribution (t-test, P < 0.001). Analyzing RT with the LATER model revealed that the slopes of the distributions on reciprobit plots favored swivel rather than shift. The results were consistent with those reported for a saccade task [16] and indicate that changes in RT reflect changes in anticipation. The 1750–2000 ms intervals had a small distribution of short (<150 ms) RTs (Fig. 4A). In our task, animals know in advance what movement is required in response to the go signal. As the hazard rate increases toward the end of the foreperiod, animals are likely making anticipatory responses. We suspect that the relatively short RTs we observed were due to those anticipatory responses. In order to generalize the effects of hazard rate on RT, we examined RT for two rectangular foreperiod distributions. Dif-
Fig. 4. (A) Cumulative distributions of reaction times in four successive foreperiod intervals for two monkeys, plotted on reciprobit plots. Solid lines represent best LATER fits to the main distribution, which swiveled around an intercept with the infinity axis of reaction time (not shown). There were small populations of anticipatory responses falling on a straight line (dashed) that differed from that of the main population. (B) Reaction time decreased as foreperiods increased. Black dashed curves were fit to the data using the weighted sum of the anticipation function (Eq. (4), weights in text). Error bars represent the standard error of the mean.
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A trial-by-trial correlation between preparatory neural activity and limb movement RT has been reported in premotor cortex [22] and PRR [24]. Furthermore, anticipatory activity for the onset of a predictable event has been observed in neurons in the prefrontal [13] and premotor cortex [11]. Thus, a fronto-parietal motor network [6] may have a role in anticipating the onset of events related to limb movement. A clearer understanding of the neural correlates of anticipation related to limb movements is subject to future study. Acknowledgments
Fig. 5. Anticipation function of rectangular foreperiods of 0.9–1.5 s. (A) The solid curve represents the anticipation function of the 0.9–1.5 s distribution. The dashed curve represents anticipation function of 1.0–2.0 s distribution (shown in Fig. 1). The value was normalized to the peak value of the 1.0–2.0 s distribution. (B) Reaction times of successive 50-ms intervals for monkey E. The dashed curve was fit to the data using the weighted sum of the anticipation function (Eq. (4), weights in text).
ferences in the anticipation function for the two distributions were reflected in RT. The decrease in RT for the 0.9–1.5 s distribution (∼100 ms) was larger than that for 1–2 s distribution (∼50 ms) in monkey E. That is, RT decreased more rapidly in a shorter interval. On average, the duration of the foreperiod was shorter for the 0.9–1.5 s distribution than for the 1–2 s distribution. Therefore, the animal might have better estimated elapsed time for the 0.9–1.5 s distribution. In addition, the variability (i.e., range) of the 0.9–1.5 s distribution (0.6 s) was smaller than that of the 1–2 s distribution (1 s), which might have facilitated prediction of the foreperiod duration. These factors would likely result in larger, more rapid decreases in RTs for the 0.9–1.5 s distribution. Fitting analysis demonstrated that, although the coefficient wr slightly overestimate the size of the decreases, the relationship between decreases for the two distributions could be estimated. Indeed, the absolute value of wr was larger for 0.9–1.5 s distribution than for the 1–2 s distribution, reflecting the size of RT decreases. To better understand anticipatory states, it is also necessary to examine RT in non-aging foreperiods, during which anticipation or hazard rate remains constant [12]. We calculated the anticipation function of Riehle et al.’s [21] distribution and found that its shape was comparable to that of our 0.9–1.5 s distribution. The Riehle et al. [21] results show that RT decreased by ∼100 ms for two monkeys. Visual inspection suggests that their RT data could be clearly fit by the weighted sum of anticipation function, and the coefficients wr were similar to those in our 0.9–1.5 s distribution (wr for Monkeys 1 and 2 were −111.8 and −131.9, R2 = 0.89 and 0.83, respectively). Thus, by fitting anticipation function to RT data, wr quantified anticipatory processes.
We are grateful to Drs. H. Takuwa and W. Matsui for their help during the early stages of this research. We thank Drs. K. Yamamoto, S. Tomatsu, and J. Lee for valuable discussions and comments. This work was supported by the Tokyo Metropolitan Organization for Medical Research and grants-in-aid from PRESTO, Japan Science and Technology Agency, and the Ministry of Education, Culture, Sports, Science and Technology to SK. References [1] D. Akkal, L. Escola, B. Bioulac, P. Burbaud, Time predictability modulates pre-supplementary motor area neuronal activity, NeuroReport 15 (2004) 1283–1286. [2] R.H.S. Carpenter, M.L.L. Williams, Neural computation of log likelihood in the control of saccadic eye movements, Nature 377 (1995) 59– 62. [3] P. Cisek, J.F. Kalaska, Neural correlates of reaching decisions in dorsal premotor cortex: specification of multiple direction choices and final selection of action, Neuron 45 (2005) 801–814. [4] J. Gibbon, Scalar expectancy theory and Weber’s law in animal timing, Psychol. Rev. 84 (1977) 279–325. [5] P. Janssen, M.N. Shadlen, A representation of the hazard rate of elapsed time in macaque area LIP, Nat. Neurosci. 8 (2005) 234–241. [6] P.B. Johnson, S. Ferraina, L. Bianchi, R. Caminiti, Cortical networks for visual reaching: physiological and anatomical organization of frontal and parietal lobe arm regions, Cereb. Cortex 6 (1996) 102–119. [7] S. Kakei, D.S. Hoffman, P.L. Strick, Direction of action is represented in the ventral premotor cortex, Nat. Neurosci. 4 (2001) 1020–1025. [8] K. Kurata, S.P. Wise, Premotor cortex of rhesus monkeys: set related activity during two conditional motor tasks, Exp. Brain Res. 69 (1988) 327– 343. [9] M.I. Leon, M.N. Shadlen, Representation of time by neurons in the posterior parietal cortex of the macaque, Neuron 38 (2003) 317–327. [10] R.D. Luce, Response times: Their role in inferring Elementary Mental Organization, Oxford University Press, New York, 1986. [11] K.H. Mauritz, S.P. Wise, Premotor cortex of the rhesus monkey: neuronal activity in anticipation of predictable environmental events, Exp. Brain Res. 61 (1986) 229–244. [12] R.S. Nickerson, D.W. Burnham, Response times with nonaging foreperiods, J. Exp. Psychol. 79 (1969) 452–457. [13] H. Niki, M. Watanabe, Prefrontal and cingulate unit activity during timing behavior in the monkey, Brain Res. 171 (1979) 213–224. [14] A.C. Nobre, Orienting attention to instants in time, Neuropsychologia 39 (2001) 1317–1328. [15] A.C. Nobre, A. Correa, J.T. Coull, The hazards of time, Curr. Opin. Neurobiol. 17 (2007) 465–470. [16] A. Oswal, M. Ogden, R.H.S. Carpenter, The time course of stimulus expectation in a saccadic decision task, J. Neurophysiol. 97 (2007) 2722– 2730. [17] M.L. Platt, P.W. Glimcher, Neural correlates of decision variables in parietal cortex, Nature 400 (1999) 233–238.
Y. Tsunoda, S. Kakei / Neuroscience Letters 433 (2008) 152–157 [18] B.A.J. Reddi, K.N. Asrress, R.H.S. Carpenter, Accuracy, information, and response time in a saccadic decision task, J. Neurophysiol. 90 (2003) 3538–3546. [19] B.A.J. Reddi, R.H.S. Carpenter, The influence of urgency on decision time, Nat. Neurosci. 3 (2000) 827–830. [20] L. Renoult, S. Roux, A. Riehle, Time is a rubberband: neuronal activity in monkey motor cortex in relation to time estimation, Eur. J. Neurosci. 23 (2006) 3098–3108. [21] A. Riehle, S. Grun, M. Diesmann, A. Aertsen, Spike synchronization and rate modulation differentially involved in motor cortical function, Science 278 (1997) 1950–1953.
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[22] A. Riehle, J. Requin, The predictive value for performance speed of preparatory changes in neuronal activity of the monkey motor and premotor cortex, Behav. Brain Res. 53 (1993) 35–49. [23] S. Roux, M. Coulmance, A. Riehle, Context-related representation of timing processes in monkey motor cortex, Eur. J. Neurosci. 18 (2003) 1011–1016. [24] L.H. Snyder, A.R. Dickinson, J.L. Calton, Preparatory delay activity in the monkey parietal reach region predicts reach reaction times, J. Neurosci. 26 (2006) 10091–10099.
Neuroscience Letters 433 (2008) 152–157
Reaction time changes with the hazard rate for a behaviorally relevant event when monkeys perform a delayed wrist movement task Yoshiaki Tsunoda ∗ , Shinji Kakei Department of Behavioral Physiology, Tokyo Metropolitan Institute for Neuroscience, 2-6 Musashi-dai, Fuchu, Tokyo 183-8526, Japan Received 1 November 2007; received in revised form 14 December 2007; accepted 31 December 2007
Abstract Anticipating the timing of behaviorally relevant events is crucial for organizing movement. The time to initiate actions based on events (i.e., reaction time (RT)) is a useful measure to quantify states of anticipation. Few studies have examined how anticipation affects the timing of limb movements. We addressed this question behaviorally with two macaque monkeys performing delayed wrist movement tasks. The interval between target onset and go signal (i.e., foreperiod) varied randomly from 1 to 2 s. The probability that the go signal was about to occur (i.e., hazard rate) increased as the foreperiod increased. The kinematics of wrist movements was not influenced by foreperiod duration. Analyzing RT data with the LATER model indicated that RT distributions swiveled on reciprobit plots as foreperiods increased, suggesting that changes in RT distributions were due to changes in anticipation. RT was inversely related to hazard rate. To better understand the general implications of anticipatory states, we introduced an additional rectangular foreperiod distribution that ranged from 0.9 to 1.5 s. For that distribution, the hazard rate peaks were higher than those of the 1–2 s distribution. Changes in RT were clearly explained by quantitative differences in hazard rate. The decrease in RT in the 0.9–1.5 s foreperiod distribution was greater than that in the 1–2 s foreperiod. Thus, monkeys learned the temporal structure of foreperiod distributions and anticipated the onset of the go signal, based on hazard rates. © 2008 Elsevier Ireland Ltd. All rights reserved. Keywords: Anticipation; Timing; Hazard rate; Foreperiod; Reaction time; Wrist movement
Timing is essential for organizing action, and experience enables humans and animals to anticipate the onset of an event. Such anticipation benefits task performance. For example, cues that provide information about when a stimulus will appear decrease subsequent reaction time (RT) to the stimulus [14,20,21]. To anticipate the onset of behaviorally relevant events, a representation of the passage of time must exist in the brain that is used to estimate the probability that an event is likely to occur [5,16,20,21]. For example, suppose an event will occur at one of two times (t1 , t2 ), and it is equally likely that the event will occur at one of those two times (p1 = p2 = 0.5). The probability that the event will occur at t1 is 0.5 just prior to t1 . However, if the event fails to occur at t1 , the probability that the event will occur at t2 becomes 1.0. This is known as the hazard rate [10,15], which should govern anticipation [5]. Recent studies clearly demonstrate that humans and animals learn the probabilistic distribution of a go signal to anticipate its
∗
Corresponding author. Tel.: +81 42 325 3881; fax: +81 42 321 8678. E-mail address: [email protected] (Y. Tsunoda).
0304-3940/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2007.12.063
onset in delayed saccade tasks [5,16]. In those studies, the delay between a cue stimulus and the go signal (i.e., the foreperiod) was a random variable with a continuous probability distribution (unimodal, bimodal, or rectangular). To examine states of anticipation, the authors analyzed RTs across different foreperiods and found that they were inversely related to hazard rates (see [5] for details). Recently, Leon and Shadlen [9] demonstrated that neurons in the macaque lateral intraparietal area (LIP) encode signals related to the perception of time. Moreover, during saccade tasks, LIP neurons display activity that corresponds to internal representation of elapsed time and hazard rate [5]. Neurons in the macaque LIP participate in planning and making decisions about eye movements [17]. However, other cortical areas, such as the parietal reach region (PRR) and the premotor cortex, participate in planning [8,24] and making decisions [3] about limb movements. Indeed, we found that neuron activity in the premotor cortex gradually increased during preparatory periods in which hazard rates for go signal onset increased [7]. Furthermore, recent studies demonstrated that neurons in the pre-supplementary motor area [1] and the primary motor cortex
Y. Tsunoda, S. Kakei / Neuroscience Letters 433 (2008) 152–157
[20,23] encode signals related to the perception of time. This physiological evidence implies that limb movements are subject to hazard rates for behaviorally relevant events independent of the saccade system. However, few studies have examined the relationship between hazard rates and performance in limb movement tasks [21]. Riehle et al. [21] examined RT in a manual response task that had discrete foreperiods (600, 900, 1200, 1500 ms) with equal probabilities of 0.25. The authors demonstrated that RT decreased as foreperiod increased. However, unlike recent saccade studies [5,16] they did not quantify the impact of hazard rate on RT. Therefore, in the present study, we quantified the relationship between limb movement RT and hazard rate, as was recently done in saccade studies [5,16]. We examined RTs of two macaque monkeys as they performed a delayed wrist movement task. To facilitate the comparison of limb RT to saccade RT, we distributed the go signal onset in the same way it was distributed in the eye movement task of Oswal et al. [16]. To evaluate the effects of hazard rate on RT, we conducted an additional experiment with a different foreperiod distribution. All experimental protocols were approved by the Animal Care and Use Committee of Tokyo Metropolitan Institute for Neuroscience and were in accordance with the Japan Neuroscience Society Guidelines for Care and Use of Laboratory Animals in Neuroscience. Two monkeys (Macaca fuscata; monkey W, 7.2 kg; monkey E, 5.9 kg) were trained to perform a delayed wrist movement task, which has been described in detail [7]. Briefly, each monkey sat in a primate chair with its forearm supported in a pronated position, facing a screen (RDS173X; MITSUBISHI, Tokyo, Japan) that displayed a cursor and targets. A PC-based real-time experimental control system (TEMPO; Reflective Computing, St. Louis, MO) was used for stimulus presentation and data collection. With its right hand, the monkey grasped a two-axis manipulandum that controlled the cursor. The cursor moved in proportion to the monkey’s wrist movement. To initiate a trial, the monkey placed the cursor inside a central target (Fig. 1A). After a variable hold period (0.8–1 s), a target appeared at one of eight peripheral locations evenly distributed at 45◦ angles around the central target. After a variable foreperiod (1–2 s in 5-ms steps), the central target was extinguished. This served as the go signal, instructing the monkey to move the cursor from the central target to the peripheral target as quickly as possible. Acquiring a target required a 20◦ change in wrist angle. Monkeys were required to begin the wrist movement within 500 ms of the onset of the go signal. Wrist position data were analyzed offline using MATLAB (The MathWorks Inc., Natick, MA). To determine velocity, horizontal (x) and vertical (y) position signals were digitally filtered and differentiated (velocity = (dx/dt)2 + (dy/dt)2 ). For each trial, the start of a movement was defined as the time that the velocity exceeded a threshold of 15 deg/s (<10% mean peak velocity). RT was the interval between the go signal and movement onset. Trials for which the RT was <50 ms were excluded. RT data were collapsed across target direction, which increased the amount of data analyzed.
153
Fig. 1. (A) Delayed wrist movement task. A trial began when the monkey positioned the cursor (black dot) inside a central target (square). After a trial began, a peripheral target appeared, signaling the start of the foreperiod. The 1–2 s foreperiod varied randomly across trials. At the end of the foreperiod, the central target was extinguished, signaling the monkey to make the required movement. (B) The top panel shows the probability density distribution of go signal onset as a function of the foreperiod (Eq. (1)). The probability remained constant for the 1–2 s interval. The middle panel shows the hazard rate for the 1–2 s foreperiod (Eq. (2)). The hazard rate increased hyperbolically across 1–2 s foreperiods. The bottom panel shows the subjective hazard rate (i.e., anticipation function), which was normalized to the peak of Ar (t) (Eq. (3)).
The probabilistic distribution of the foreperiod was rectangular (i.e., ‘aging’ foreperiod [16]) (Fig. 1B), the function of which was: f (t) =
1 (for 1.0 ≤ t ≤ 2.0 s), 200
otherwise f (t) = 0.
(1)
Ideally, anticipation should be governed by the hazard rate (Fig. 1B). That is, the probability that the go signal will occur at time t divided by the probability that it has not yet occurred: h(t) =
f (t) (1 − F (t))
(2)
t where F(t) is the cumulative distribution, 0 f (s)ds (Fig. 1B). We calculated subjective hazard rates [5] based on the assumption that elapsed time is known with uncertainty that scales with time (Weber’s law [4]). The probability distribution f(t) was first blurred by a normal distribution, of which the
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standard deviation was proportional to elapsed time. f˜ (t) =
1 √
φt 2π
∞
f (τ)e−(τ−t)
2 /(2φ2 t 2 )
dτ
(3)
−∞
The coefficient of variation φ was a Weber fraction for time estimation (φ = 0.26; based on previous studies in monkeys [5,9]). Eq. (3) is based on the notion that the monkey’s estimation of elapsed time carried uncertainty. Thus, an event at objective time t0 was perceived as occurring at t0 ± σ. Subjective hazard rates were obtained by substituting f˜ (t) and its definite integral, F˜ (t) in Eq. (2). We referred to subjective hazard rates as anticipation function, Ar (t). For ease of interpretation, anticipation function was normalized to the peak of Ar (t) (Fig. 1B). Because RT distributions have a long tail toward longer RT, the reciprocal of RT follows a Gaussian distribution. Plotting cumulative RT distributions on a probit scale as a function of reciprocal RT (a reciprobit plot) yields a straight line. RT dis-
Fig. 2. (A) The LATER model. When an appropriate stimulus appears, a decision signal S begins to rise linearly at rate r from an initial level S0 representing prior probability [2]. When S reaches threshold ST , the response is triggered. The rate of rise r varies randomly across trials with a Gaussian distribution (μ, σ). As a result, distribution of reciprocal reaction time over a number of trials is Gaussian. (B) Plotting the cumulative distribution on a probit scale as a function of the reciprocal of reaction time (a reciprobit plot) yields a straight line. Changes in S0 without changing r alter the slopes of plots, such that the lines pivot about the infinite-time intercept I (left panel). Changes in r, without changing S0 , result in a parallel shift of the plots (right panel).
tributions can be explained by a simple decision-making model – the LATER model (see Fig. 2 for details) [2,18,19]. Manipulating prior probability, anticipation [2], or urgency [19] alters the median RT in a manner comparable to swiveling the reciprobit plot about the fixed point I where the distribution intercepts the t = ∞-axis (Fig. 2B, left panel). In contrast, changing μ by modifying the information supply generates a parallel shift of the plot, without changing the slope (Fig. 2B, right panel) [18]. To determine whether reciprobit distributions could be modeled more accurately by a swiveling or parallel shift, we calculated maximum likelihood for a set of RT data using methods that have been described previously [16,19]. To quantify the relationship between hazard rate and RT, we fitted mean RT of successive 50-ms intervals in the 1–2 s foreperiods using a weighted sum of subjective hazard rates: RT(t) = we + wr Ar (t − τ) + ε
(4)
where RT was reaction time, we was a constant term, and wr was the weight for the anticipation function, delayed by time shift τ. We obtained the coefficients and their standard errors to minimize the sum of the squared regression errors (ε2 ; leastsquares method). We set τ as 60 ms based on a previous report [5]. Each monkey learned to execute the required wrist movements quickly and accurately (success rate >92%). Monkey W made 3935 successful responses, and Monkey E made 2457. To examine whether foreperiods affected the kinematics of wrist movements, we separated responses into four groups, based on four successive 250 ms foreperiod intervals from 1 to 2 s. Position traces of wrist movements overlapped between
Fig. 3. Kinematics of wrist movements. The foreperiod was divided into four equally sized time intervals (1000–1250, 1250–1500, 1500–1750, 1750–2000 ms). Responses were divided into four groups, according to the duration of the foreperiod. Wrist deviations (A) and velocity profiles (B) of wrist movements overlapped to a great degree from initiation to the end of movement for monkey W (left panels) and monkey E (right panels).
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foreperiod intervals (Fig. 3A). Velocity profiles were also consistent throughout foreperiod intervals (Fig. 3B). These kinematics features suggested that monkeys made highly stereotyped wrist movements that were not affected by foreperiod duration. Fig. 4A shows RT distributions for the four intervals, plotted on reciprobit plots. All distributions were well-fit with straight lines and agreed with those predicted by the LATER model (Kolmogorov–Smirnov one-sample tests, P > 0.1). There were significant differences in RT distributions, which were foreperiod dependent (Kolmogorov–Smirnov two-sample tests, P < 0.05). Median RTs for the four intervals decreased progressively for longer foreperiods. For both monkeys, a log-likelihood analysis indicated that the plots swiveled rather than shifted as foreperiods increased (Fig. 4A). Log-likelihood differences were 19.0 for monkey W and 36.2 for monkey E. Fig. 4B shows mean RTs for successive 50-ms intervals of the 1–2 s foreperiods. The RT clearly decreased between 1.0 and 2.0 s (regression analysis, P < 0.001; RT decreases were 80 ms for monkey W and 50 ms for monkey E). Mean RTs across foreperiods were inversely related to the anticipation function (Eq. (4), wr for Monkeys W and E was −103.9 ± 6.6 and −66.0 ± 4.9; R2 = 0.93 and 0.91, respectively) (Fig. 4B). Because the anticipation function was normalized to 1 with its peak, the fits (wu ) estimated RT reduction (ms) per unit change in anticipation.
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To better understand the general implications of anticipatory states, we applied a rectangular distribution of 0.9–1.5 s foreperiods to the task for monkey E. The anticipation function for the 0.9–1.5 s distribution differed from that of the 1–2 s distribution. For instance, the peak was obtained more quickly (short duration of 0.6 s) (Fig. 5A). We recorded 1038 responses using the 0.9–1.5 s foreperiod distribution. Mean RT decreased by ∼100 ms as the foreperiod increased (Fig. 5B). The decrease was greater than that observed for the 1–2 s distribution. RT was well-fit by the weighted sum of the anticipation function (wr was −139.8 ± 8.0, R2 = 0.97). The absolute value of wr was significantly larger in the 0.9–1.5 s distribution than in the 1–2 s distribution (t-test, P < 0.001). Analyzing RT with the LATER model revealed that the slopes of the distributions on reciprobit plots favored swivel rather than shift. The results were consistent with those reported for a saccade task [16] and indicate that changes in RT reflect changes in anticipation. The 1750–2000 ms intervals had a small distribution of short (<150 ms) RTs (Fig. 4A). In our task, animals know in advance what movement is required in response to the go signal. As the hazard rate increases toward the end of the foreperiod, animals are likely making anticipatory responses. We suspect that the relatively short RTs we observed were due to those anticipatory responses. In order to generalize the effects of hazard rate on RT, we examined RT for two rectangular foreperiod distributions. Dif-
Fig. 4. (A) Cumulative distributions of reaction times in four successive foreperiod intervals for two monkeys, plotted on reciprobit plots. Solid lines represent best LATER fits to the main distribution, which swiveled around an intercept with the infinity axis of reaction time (not shown). There were small populations of anticipatory responses falling on a straight line (dashed) that differed from that of the main population. (B) Reaction time decreased as foreperiods increased. Black dashed curves were fit to the data using the weighted sum of the anticipation function (Eq. (4), weights in text). Error bars represent the standard error of the mean.
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A trial-by-trial correlation between preparatory neural activity and limb movement RT has been reported in premotor cortex [22] and PRR [24]. Furthermore, anticipatory activity for the onset of a predictable event has been observed in neurons in the prefrontal [13] and premotor cortex [11]. Thus, a fronto-parietal motor network [6] may have a role in anticipating the onset of events related to limb movement. A clearer understanding of the neural correlates of anticipation related to limb movements is subject to future study. Acknowledgments
Fig. 5. Anticipation function of rectangular foreperiods of 0.9–1.5 s. (A) The solid curve represents the anticipation function of the 0.9–1.5 s distribution. The dashed curve represents anticipation function of 1.0–2.0 s distribution (shown in Fig. 1). The value was normalized to the peak value of the 1.0–2.0 s distribution. (B) Reaction times of successive 50-ms intervals for monkey E. The dashed curve was fit to the data using the weighted sum of the anticipation function (Eq. (4), weights in text).
ferences in the anticipation function for the two distributions were reflected in RT. The decrease in RT for the 0.9–1.5 s distribution (∼100 ms) was larger than that for 1–2 s distribution (∼50 ms) in monkey E. That is, RT decreased more rapidly in a shorter interval. On average, the duration of the foreperiod was shorter for the 0.9–1.5 s distribution than for the 1–2 s distribution. Therefore, the animal might have better estimated elapsed time for the 0.9–1.5 s distribution. In addition, the variability (i.e., range) of the 0.9–1.5 s distribution (0.6 s) was smaller than that of the 1–2 s distribution (1 s), which might have facilitated prediction of the foreperiod duration. These factors would likely result in larger, more rapid decreases in RTs for the 0.9–1.5 s distribution. Fitting analysis demonstrated that, although the coefficient wr slightly overestimate the size of the decreases, the relationship between decreases for the two distributions could be estimated. Indeed, the absolute value of wr was larger for 0.9–1.5 s distribution than for the 1–2 s distribution, reflecting the size of RT decreases. To better understand anticipatory states, it is also necessary to examine RT in non-aging foreperiods, during which anticipation or hazard rate remains constant [12]. We calculated the anticipation function of Riehle et al.’s [21] distribution and found that its shape was comparable to that of our 0.9–1.5 s distribution. The Riehle et al. [21] results show that RT decreased by ∼100 ms for two monkeys. Visual inspection suggests that their RT data could be clearly fit by the weighted sum of anticipation function, and the coefficients wr were similar to those in our 0.9–1.5 s distribution (wr for Monkeys 1 and 2 were −111.8 and −131.9, R2 = 0.89 and 0.83, respectively). Thus, by fitting anticipation function to RT data, wr quantified anticipatory processes.
We are grateful to Drs. H. Takuwa and W. Matsui for their help during the early stages of this research. We thank Drs. K. Yamamoto, S. Tomatsu, and J. Lee for valuable discussions and comments. This work was supported by the Tokyo Metropolitan Organization for Medical Research and grants-in-aid from PRESTO, Japan Science and Technology Agency, and the Ministry of Education, Culture, Sports, Science and Technology to SK. References [1] D. Akkal, L. Escola, B. Bioulac, P. Burbaud, Time predictability modulates pre-supplementary motor area neuronal activity, NeuroReport 15 (2004) 1283–1286. [2] R.H.S. Carpenter, M.L.L. Williams, Neural computation of log likelihood in the control of saccadic eye movements, Nature 377 (1995) 59– 62. [3] P. Cisek, J.F. Kalaska, Neural correlates of reaching decisions in dorsal premotor cortex: specification of multiple direction choices and final selection of action, Neuron 45 (2005) 801–814. [4] J. Gibbon, Scalar expectancy theory and Weber’s law in animal timing, Psychol. Rev. 84 (1977) 279–325. [5] P. Janssen, M.N. Shadlen, A representation of the hazard rate of elapsed time in macaque area LIP, Nat. Neurosci. 8 (2005) 234–241. [6] P.B. Johnson, S. Ferraina, L. Bianchi, R. Caminiti, Cortical networks for visual reaching: physiological and anatomical organization of frontal and parietal lobe arm regions, Cereb. Cortex 6 (1996) 102–119. [7] S. Kakei, D.S. Hoffman, P.L. Strick, Direction of action is represented in the ventral premotor cortex, Nat. Neurosci. 4 (2001) 1020–1025. [8] K. Kurata, S.P. Wise, Premotor cortex of rhesus monkeys: set related activity during two conditional motor tasks, Exp. Brain Res. 69 (1988) 327– 343. [9] M.I. Leon, M.N. Shadlen, Representation of time by neurons in the posterior parietal cortex of the macaque, Neuron 38 (2003) 317–327. [10] R.D. Luce, Response times: Their role in inferring Elementary Mental Organization, Oxford University Press, New York, 1986. [11] K.H. Mauritz, S.P. Wise, Premotor cortex of the rhesus monkey: neuronal activity in anticipation of predictable environmental events, Exp. Brain Res. 61 (1986) 229–244. [12] R.S. Nickerson, D.W. Burnham, Response times with nonaging foreperiods, J. Exp. Psychol. 79 (1969) 452–457. [13] H. Niki, M. Watanabe, Prefrontal and cingulate unit activity during timing behavior in the monkey, Brain Res. 171 (1979) 213–224. [14] A.C. Nobre, Orienting attention to instants in time, Neuropsychologia 39 (2001) 1317–1328. [15] A.C. Nobre, A. Correa, J.T. Coull, The hazards of time, Curr. Opin. Neurobiol. 17 (2007) 465–470. [16] A. Oswal, M. Ogden, R.H.S. Carpenter, The time course of stimulus expectation in a saccadic decision task, J. Neurophysiol. 97 (2007) 2722– 2730. [17] M.L. Platt, P.W. Glimcher, Neural correlates of decision variables in parietal cortex, Nature 400 (1999) 233–238.
Y. Tsunoda, S. Kakei / Neuroscience Letters 433 (2008) 152–157 [18] B.A.J. Reddi, K.N. Asrress, R.H.S. Carpenter, Accuracy, information, and response time in a saccadic decision task, J. Neurophysiol. 90 (2003) 3538–3546. [19] B.A.J. Reddi, R.H.S. Carpenter, The influence of urgency on decision time, Nat. Neurosci. 3 (2000) 827–830. [20] L. Renoult, S. Roux, A. Riehle, Time is a rubberband: neuronal activity in monkey motor cortex in relation to time estimation, Eur. J. Neurosci. 23 (2006) 3098–3108. [21] A. Riehle, S. Grun, M. Diesmann, A. Aertsen, Spike synchronization and rate modulation differentially involved in motor cortical function, Science 278 (1997) 1950–1953.
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[22] A. Riehle, J. Requin, The predictive value for performance speed of preparatory changes in neuronal activity of the monkey motor and premotor cortex, Behav. Brain Res. 53 (1993) 35–49. [23] S. Roux, M. Coulmance, A. Riehle, Context-related representation of timing processes in monkey motor cortex, Eur. J. Neurosci. 18 (2003) 1011–1016. [24] L.H. Snyder, A.R. Dickinson, J.L. Calton, Preparatory delay activity in the monkey parietal reach region predicts reach reaction times, J. Neurosci. 26 (2006) 10091–10099.