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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 2018 Feb 14;115(9):2246–2251. doi: 10.1073/pnas.1714220115

Humans quickly learn to blink strategically in response to environmental task demands

David Hoppe a,b, Stefan Helfmann b, Constantin A Rothkopf a,b,c,1
PMCID: PMC5834680  PMID: 29444860

Significance

Eye blinks serve the purpose of maintaining healthy vision but during a blink visual information processing is interrupted. While a multitude of medical, cognitive, and psychological factors have been shown to influence blinking, the present study establishes quantitatively how human blinking behavior is dynamically adapted to environmental task demands. In our experiment participants quickly learned to blink strategically. A minimal computational model captures the observed behavior as a trade-off between internal, physiological benefits and external, task-related costs given perceptual uncertainties. Crucially, the model allows predicting an individual subject’s temporal dynamics of blinking and provides an explanation of the long-known distribution of interblink intervals. Taken together, this provides a basis for future research using blinking as a behavioral marker.

Keywords: eye blinks, interblink intervals, computational modeling, internal costs, individual differences

Abstract

Eye blinking is one of the most frequent human actions. The control of blinking is thought to reflect complex interactions between maintaining clear and healthy vision and influences tied to central dopaminergic functions including cognitive states, psychological factors, and medical conditions. The most imminent consequence of blinking is a temporary loss of vision. Minimizing this loss of information is a prominent explanation for changes in blink rates and temporarily suppressed blinks, but quantifying this loss is difficult, as environmental regularities are usually complex and unknown. Here we used a controlled detection experiment with parametrically generated event statistics to investigate human blinking control. Subjects were able to learn environmental regularities and adapted their blinking behavior strategically to better detect future events. Crucially, our design enabled us to develop a computational model that allows quantifying the consequence of blinking in terms of task performance. The model formalizes ideas from active perception by describing blinking in terms of optimal control in trading off intrinsic costs for blink suppression with task-related costs for missing an event under perceptual uncertainty. Remarkably, this model not only is sufficient to reproduce key characteristics of the observed blinking behavior such as blink suppression and blink compensation but also predicts without further assumptions the well-known and diverse distributions of time intervals between blinks, for which an explanation has long been elusive.


Blinking is an omnipresent involuntary process, which humans carry out 15–17 times per minute (1), on average. It primarily serves the physiological purpose of cleaning the surface of the eye and providing a stable tear film (2), of preventing optical aberrations (36), and thus maintaining good quality of vision (7). Besides these positive consequences, blinking has an immediate negative consequence on perception as during blinking the stream of visual information is interrupted (Fig. 1A). Moreover, in addition to the break of optic signals due to the occlusion of the pupil by the upper lid, neural processing is inhibited (8, 9). This leads to perceptual gaps every 2–3 s. If not timed correctly, these gaps can lead to negative outcomes in numerous situations. In social interaction, for example, microexpressions have a duration between 160 ms and 500 ms and can therefore easily be missed due to a blink (10). Indeed, humans have been shown to reduce these gaps by combining blinks with saccades (11, 12), during which neuronal processing is also inhibited. The same has been shown for animals (13, 14). Overall, the positive effects of blinking on the maintenance of proper vision and the negative effects of the interruption of vision constitute a fundamental trade-off. Hence, controlling actively when to blink provides a behavioral advantage compared with blinking at random points in time.

Fig. 1.

Fig. 1.

Experimental design and stimulus generation. (A) Schematic time course for a single blink (from ref. 9; reprinted with permission from AAAS). (B) Four different IBI distributions found by ref. 33 (reprinted from ref. 33). The shapes are not equally frequent. Most subjects showed J-shaped (62%), symmetric was the least often (4%), and bimodal and irregular comprised 12% and 22% of the cases, respectively. (C) Task design. In each block a gray dot (0.3°) moved on a circular trajectory for 100 consecutive laps. The trajectory was not visible to the subject. In each lap three to five events occurred. An event comprised the circle being replaced with a comic face for 50 ms. Subjects attempted to detect as many of the events as possible by pressing a button. (D) Event generation for a single block. Three to five events per lap were drawn from a mixture of a uniform and a Gaussian distribution. (D, Lower) Sample laps and events are shown. Overall, four different conditions were presented to the participants. The conditions differed with respect to the mean of the Gaussian distribution.

Investigations of the control of blinking have revealed an intriguing multitude of additional factors influencing human blink rates so that blinking is often used as a behavioral marker for a variety of internal processes. Blinking is closely intertwined with cognitive functions connected to dopamine (see ref. 15 for a recent review). In particular, blink rates reflect the progress of learning (16) and the perception of time (17). Blinking is also affected by our current goals and actions. It depends on what task we are solving (see refs. 1820 for reviews), how long we are on the task (21), and how difficult the task is (22), and it is an indicator of what we remember afterward (23). Even the coordination of blinks and saccades is influenced by cognitive factors (24). Finally, blinks have been shown to be synchronized across people during conversation and thus might play a role during human social communication (25). While blinking is clearly related to these cognitive processes, it is still debated whether the appropriate measure is the blinking rate during a task, the spontaneous blinking rate, or possibly the distribution of times between two consecutive blinks, the so-called interblink interval (IBI) distribution, or whether these quantities are potentially inherently related (see ref. 26 for a recent discussion). Thus, a better understanding of the process underlying blinking behavior is beneficial to understanding a wide range of perceptual and cognitive processes.

Although numerous empirical studies have established the importance of blinking, quantitative explanations have been scarce. Current models assume a linear increase in urge when blinking is suppressed (27) or an oscillating blink generator (28), but both models considered voluntary blink suppression and do not incorporate any task-related influences. One reason might be that environmental regularities and task-related costs are usually complex and unknown. The lack of quantitative models is surprising, considering the strong contingencies between environmental statistics and gaze behavior, which have been explained successfully through modeling (2932). As with blink rates, few computational approaches exist that describe the temporal course of blinking. In particular, the IBI distribution is an active research area. In their seminal paper, Ponder and Kennedy (33) found four different types of IBI distributions (Fig. 1B). Since then, many studies have presented similar results showing that subjects’ IBI distributions show great variability (e.g., ref. 34). However, the origin of these different IBI distributions and their variability is unclear.

Here we address the question of how blinking behavior is related and adapted to the current task. We conducted a controlled blinking experiment with parametrically generated environmental statistics. Using an event detection paradigm, we created a direct connection between temporary loss of visual information due to blinking and task performance. Crucially, knowing the probabilistic structure of the task, we are able to investigate how blinks are linked to internal beliefs about task parameters and how participants adapted their blinking to the task. The computational model treats blinking dynamics as the result of a trade-off between the physiological need to blink and the task-related cost of blinking given subjects’ beliefs. The model captures our subjects’ strategic blinking behavior in the experiment and provides a quantitative explanation for changes in blinking behavior. Importantly, based on the computational model we derive the temporal structure of blinking behavior including the IBI distribution on the basis of an individual subject. This provides an explanation of the classic IBI distributions observed in numerous experiments and lays the groundwork for quantitative studies investigating blinking behavior, task structure, and subjects’ perceptual uncertainties.

Results

Subjects directed their gaze to a gray dot moving on a circular trajectory (counterclockwise) displayed on a computer monitor to detect events (Fig. 1C). A circular trajectory was chosen to avoid blinks being triggered by saccades (11, 12). Velocity of the dot was chosen to lead to smooth pursuit without catch-up saccades. Events were defined by replacing the dot with a stylized face for 50 ms. Hence, a normal blink (9, 35, 36) could lead to missing an event. Events were generated probabilistically and were drawn from a mixture of a Gaussian distribution (Fig. 1D) using a mixing weight of P=0.8 and a uniform distribution with mixing weight of 0.2. On each lap the number of events was randomly chosen between three and five. Over the course of 100 consecutive laps subjects could learn the relationship between the angle at which the dot was on its circular trajectory and the probability of an event occurring. Overall, subjects completed four blocks differing with respect to the location of the Gaussian. Blocks were presented in a random order. After each block subjects were given the percentage of detected events as feedback.

Overall, 25 subjects (8 male) participated in the experiment in exchange for course credit. Their age ranged from 19 y to 56 y (M = 26.52, SD = 10.97). Seven subjects wore glasses; however, sufficient accuracy of the eye tracker and the detection of blinks was ensured for all participants (see Materials and Methods for details on the detection of blinks).

Behavioral Results.

Data from nine consecutive laps are shown for a single participant in Fig. 2A. Visual inspection yields the first indications for a connection between event probability and blinking behavior. Overall, the distribution of blink locations for all participants showed a similar time course across all conditions (Fig. 2B, Top). As conditions differed only with respect to the mean of the Gaussian while sharing the same variance, data were aggregated by normalizing the event distribution to peak at 180° (Fig. 2B, Bottom). The data show that blinking behavior was clearly affected by the distribution of event probabilities. Instead of being distributed uniformly over the circle, two characteristics of the distribution of blinks can be observed: First, blinking is suppressed in the area of high event probability (HEP) (±2 SDs from the center of the mixture distribution). Fewer blinks occurred in the HEP area (blink rate rHEP = 11.28) compared with the remaining part (rnot HEP = 20.46; Fig. 2C). The 95% credibility interval for the difference in blinking rates was [8.67,9.67]. This indicates that blinking behavior is adapted to the event distribution to avoid missing events. Second, visual inspection indicates an asymmetry of blinking counts before and after the HEP region. Indeed, we found a higher number of blinks after (blink rate rafter HEP = 25.16; Fig. 2D) than before the HEP region (blink rate rbefore HEP = 15.76; 95% credibility interval for the difference was [8.71,10.01]).

Fig. 2.

Fig. 2.

Behavioral results. (A) Raw data (blinks and events) for a single participant in nine consecutive laps. Top row depicts the temporal dynamics of blinks and events. Bottom rows show histograms for the blinks and events aggregated over the angular locations of the laps. (B) Blinking frequencies over locations within the circular trajectory. (Top) Histograms are shown for all four conditions. Center of the event-generating mixture distribution is indicated by a green bar for each condition. (Bottom) Data from all conditions were normalized by rotation. The normalized event-generating distribution was centered to 180°. (C) Comparison of the mean number of blinks aggregated for all conditions between the area ±2 SDs (HEP) from the center and the remaining part of the circle. Error bars correspond to the SEM. (D) Differences in number of blinks between the 60° area before and after the HEP area. Again, error bars correspond to the SEM. (E) Percentage of blinks occurring in the HEP area over the course of 100 laps. Chance level assumes that blinks are uniformly distributed over the circle (red dashed line). For the percentage of blinks occurring in the areas before and after the HEP area see Fig. S1C. For the course of absolute blink rates see Fig. S1 A and B.

To investigate how learning of the event distribution affected blinking, we computed the proportion of blinks in the HEP area over the course of the 100 laps (Fig. 2E). The proportion of blinks occurring in the HEP region declined over the course of the first laps and was constant afterward. This indicates that in the beginning subjects learned the hidden event distribution by observing the event locations. Bayesian change-point analysis (37) revealed that the steady state was reached on average after about 13 laps (95% credibility interval of the change point was [9.15, 17.47]).

A Computational Model for Blinks.

The design of our experiment gives access to the statistical structure of the task in terms of a probabilistic generative model. Crucially, we are able to determine the loss of information due to a blink by quantifying the influence on task performance at each point in time during the experiment. This is a distinct advantage compared with investigations studying human blinking behavior during reading or free viewing, where it is difficult to capture the consequences of blinking quantitatively.

The computational model is motivated by capturing the fundamental trade-off between costs and benefits of blinking and comprises two distinct components that control blinking behavior: (i) internal costs for blink suppression and (ii) external task-related costs for blink execution. Internal costs for blink suppression arise due to the subjects’ physiological need to blink from time to time to maintain healthy vision. Formally, we denote the costs for blink suppression as cs. It is important to note that cs does not depend on the current location within the lap, since it is independent of the task. Further, our data suggest that cs does not depend on the time since the last blink (Supporting Information and Fig. S5). The second factor is the cost associated with blink execution ce(θ). It points in the direction opposite to cs, as more blinks lead to higher costs. This component denotes the amount of task performance that is lost in the case of a blink. In our experimental procedure this is the probability of detecting events. In contrast to the costs for blink suppression cs, the task-related costs ce(θ) depend on the current angle and therefore are not constant over the course of a lap (higher blink-related costs in the HEP region). Whether to blink or not to blink at any point in time therefore can be described as a trade-off between cs and ce(θ).

Here we assume that the probability of a blink occurring at an angle θ can be modeled as being inversely proportional to the sum of the costs of blink suppression cs and blink execution ce,

P(blinkatθα,ψ)1(1α)cs+αce(θ,𝝍), [1]

where cs is the cost for blink suppression, ce(θ,ψ) is the cost for blink execution in terms of reduced task performance, α is between 0 and 1 and regulates how much weight is put on the task, and ψ=[mixing proportion, perceptual uncertainty] are parameters describing the subject’s belief about the experiment given previous observations. Intuitively, a weight of α=1 corresponds to blinking only because of the external task and therefore suppressing blinks for maintaining vision while a weight of α=0 corresponds to putting complete priority on maintaining healthy vision and thereby blinking only to lubricate the cornea (Fig. 3A).

Fig. 3.

Fig. 3.

Computational model results. (A) Schematic overview of the generative model. Our model forms a belief about the probabilistic nature of the task environment. This belief structure is used for action selection while balancing multiple costs. For a more detailed visualization of the computational steps involved in building our subjects’ belief see Fig. S2. (B) Model results for blinking behavior. Shown are number of blinks per degree (black line; also Fig. 2B) and the fitted model (orange line). (C) Model prediction of the temporal statistics of the blinking behavior. (Left) The distribution of the IBIs. The histogram depicts all our subjects’ data. (Right) The distribution of number of blinks per lap. Data are shown in black, and model predictions are shown in orange. (D) Probability of blinking depending on the location on the circle (x axis, from 0° to 360°) and the time since the last blink (y axis, from 0 s to 5 s). (Right) Model predictions. (Left) Subject data. We weighted very short IBIs using a cumulative Gaussian (32). This accounts for motor delays, making two blinks occurring with close to zero IBI very unlikely. (E) Single-participant results. From Top to Bottom: Blinking proportion over the circle, IBI distributions, blinks per lap, and blinking probability in the angle and time domain are shown for three participants. The fitted model is depicted in orange, and data are shown in black. Bottom row contains the theoretical distribution (Left), samples from the theoretical distribution matched to the number of blinks of the individual subject (Center), and our subjects’ data (Right). Results for all participants can be found in Figs. S3 and S4 and Table S1.

The cost for blinking ce(θ) is derived as the probability of missing an event and therefore depends on the current angle θ,

P(miss|θ,μ,σ2,p)=n(θ)P(event atθμ,σ2,p), [2]

where μ,σ2 and p are the parameters of the mixture distribution generating the events, θ is a location during the lap, and n(θ) is the average number of events left at each location during a particular lap (see Supporting Information for details).

The subjects’ belief about the costs for blinking is furthermore influenced by their uncertainty about the true underlying event distribution during the experiment. We accounted for the imperfect knowledge by assuming that subjects do not have access to the exact parameters of the mixture distribution. In particular, we allowed the mixing proportion to be different from the true value that was used for event generation. In addition, we hypothesized that subjects have perceptual uncertainty given previous observations about the exact parameters describing the Gaussian distribution from which the events are drawn. Overall, four parameters (mixing proportion p, cost trade-off α, average blinking rate r, and the spread of the temporal uncertainty) were estimated from data across subjects. For parameter estimation only data from the subjects’ steady-state behavior were used, as the changes in blinking behavior at the beginning of a block are related to learning the new event distributions. Thus, changes in the subjects’ belief, which occur during learning the experimental statistics at the beginning of a new block, would affect these estimates. Change-point analysis revealed that steady-state behavior was reached after 20 laps.

Model Results.

We fitted our model to the aggregated blinking data. The result is shown in Fig. 3B. Our model is capable of reflecting the characteristic course of blinking behavior. Moreover, we are now able to link both main effects, blink suppression as well as blink compensation, to computational quantities in our model: (i) Blink suppression follows from putting a higher value on the ongoing task. This leads to a higher proportion of blinks related to the ongoing external task. In the current experiment, this means that few blinks are carried out in those regions around the circular trajectory of the target where the probability of an event is high and thus the loss of task-related information is high. (ii) The asymmetric shape of the curve is due to uncertainties in the subjects’ belief where exactly the probability of an event is highest and the dynamic changes in this belief structure due to observing events over the course of a lap. Specifically, similar to a survival process, the fewer events have been observed during a lap, the higher the probability that an event is imminent. Finally, closer inspection of the probability of blinking in Fig. 3B reveals a less steep decrease in blinking probability at around 90°. In this region the belief that all events from the previous lap have already occurred is small given the perceptual uncertainty and past event observations.

The results further suggest that the mixing rate of the mixture distribution is underestimated by our subjects (p^=0.58 compared with p=0.8). This is not surprising since learning a complex mixture distribution from noisy observations is a hard task (e.g., ref. 38). Hence, our subjects know less about the task statistics compared with an ideal observer. Perceptual uncertainty due to observations of events as well as uncertainty from storing events in memory was estimated to be σperc=29.6.

A crucial property of the proposed model of the probability of blinking is that it allows deriving the temporal statistics of subjects’ blinking data. The probability of a specific IBI d (time between two consecutive blinks) can be computed as follows: Assume a blink occurring at a random location θ with probability P(blink atθ). Since the next blink is executed at θ+d for the next d time steps, no blink occurs. Finally, d time steps after the first blink the next blink occurs. This yields

P(blink atθd)=P(blink atθd)[k=θd+1θ1(1P(blink atθk))]P(blink atθ). [3]

IBI distributions can be obtained by repeating this process for all values of θ and d and averaging over θ. Thus, our approach yields an analytic description of the distribution of IBIs as a product of geometric distributions, which has an intuitive link to blinking as sequential Bernoulli trials with varying probabilities. Note that previous empirical studies have proposed a power-law distribution to describe the IBI distributions (39). However, our approach explicitly incorporates the nonstationary nature of the blinking rate in our task. By using this procedure we are able to recover main characteristics of the temporal dynamics (Fig. 3 C and D) of subjects’ blinks. Crucially, no further parameters need to be estimated.

As prior research on blinking has shown large individual differences, we fitted our model to each subject independently. We estimated the parameters for the cost trade-off as well as for the mean blinking rate on a subject-by-subject basis. The uncertainties about the temporal structure and the event-generating distribution were assumed to be the same across participants. We therefore used the respective values estimated from the aggregated data. Results for three subjects are shown in Fig. 3E. Individual blinking strategies were highly variable and IBIs were qualitatively different across subjects. Remarkably, our model captures and explains this variability. As a consequence, we are able to link qualitative differences in behavior between individuals to quantitative differences in model components. The model suggests that the variability in blinking behavior can be ascribed to differences among subjects in motivational as well as physiological parameters. Specifically, three of the four IBI histogram shapes (J-shaped, bimodal, irregular) consistently found by previous studies can be explained through motivational differences across subjects combined with the temporal structure of the task. The analysis further reveals that the least frequently found shape (symmetric) does not result from differences in the trade-off between task demands and physiological needs or from differences in the general blinking rate.

Overall, participants detected 87% of all events. Two participants showed very low performance scores (smaller than 70%, >2σ) and were excluded from the analysis. We tested whether subjects who put greater weight on the external task, i.e., a higher estimated α parameter, showed better performance (Fig. S6). Linear regression revealed a significant relationship between the individually estimated values for α and the percentage of detected events, r(23)=0.51,p=0.01. Importantly, this means that subjects blinked more strategically instead of less often, as we found no significant connection between smaller blinking rates and higher performance, r(23)=0.38,p=0.07.

Discussion

In our study, we investigated how blinking behavior is related to internal costs and environmental visual demands. In particular, while prior research has provided various accounts of the link between blinks and task demands, there exists little work quantifying this connection. We created an event detection task tailored to studying blinking behavior quantitatively. Subjects detected events while fixating on a moving dot. The event probability was linked to the spatial location of the dot, a regularity subjects could learn over the course of the experiment. Our design provides full control and knowledge regarding the temporal statistics of the visual input as well as the reward structure of the task. In particular, the consequences of blinking on the loss of information can be quantified.

The probabilistic design of the experiment allowed developing a computational model of blinking behavior. The basic assumption is that blinking is the consequence of a trade-off between an internal urge to blink to maintain healthy vision and external task requirements of not blinking when crucial information needs to be acquired from the environment. Given subjects’ perceptual and memory uncertainties about the event-generating process in the experiment, it is possible to quantify the cost of blinking in terms of task performance, i.e., the probability of detecting an event.

The behavioral data show two main effects: First, blinking was significantly suppressed in the HEP region, i.e., where most events occurred. Our computational model results suggest that this effect can be explained in terms of minimal loss of task-relevant information. This result is in accordance with prior research that reported a connection between blink suppression and task performance (40). Also, in classical psychophysical experiments blinks have been shown to occur around the time of response (41) and toddlers watching movies showed suppressed blinking at scenes containing affective and physical events (42). Thus, subjects who weighted costs associated with the external task more tended to blink more strategically and therefore avoided blinking in the HEP region.

Second, more blinks occurred after the HEP region compared with before. Although the probability of missing an event is symmetrical around the peak of the event-generating distribution, the observed blinking pattern is not. This asymmetry is predicted by our model if we account for observations made over the course of a lap. The event probability and therefore the probability of missing an event during a blink are proportional to the number of events left. Hence, blinking earlier in a lap leads to greater loss of detection performance. With every observed event the number of events left in a lap decreases. Finding this asymmetry of blinking strategies in our data reveals two properties of our subjects’ information processing: Subjects learned the number of events per lap and they were able to dynamically incorporate recent information about observed events for deciding when to blink. Compensation between episodes of suppression has been reported in the past (40). While other studies argue that blinks take on a role of breakpoints to facilitate mental processing (43), in our study, blinking was well described in terms of collecting maximal task-relevant information.

The distribution of IBIs is highly variable across humans (33). Four different shapes have been identified repeatedly: J-shaped, irregular plateau, bimodal, and symmetric (33, 44, 45). Here, we showed that three of these shapes arise as an immediate consequence of the trade-off between internal and external task costs. Our model is capable of capturing the characteristics of the first three types (see also individual model fits for all data in Figs. S3 and S4). One participant (subject 19 in Fig. S4), however, showed a symmetric distribution which was not well fitted by our model. One explanation could be that the symmetric shape (the least often according to ref. 33) does not arise from interacting with the task but from physiological properties that were not captured by our model.

Few models have been developed to describe blinking behavior. In their urge model, the authors of ref. 27 assumed a linear increase in urge when blinking is suppressed. However, the model does not account for any external task-related influences. In another study (28) it was proposed that blinks are generated by an oscillating blink generator. However, both studies used voluntary blink suppression. Here we presented a computational model that explicitly included task-related goals as well as intrinsic costs, thereby building a natural connection to the reward-related learning literature involving dopamine. Hence, the model can be applied to a broader area of investigations as long as some properties about the environmental statistics are known. While we presented results for a psychophysical detection task, our approach is not limited to simple stimuli. Recent developments in machine learning and deep neural networks (e.g., ref. 46) have paved the way for retrieving statistical regularities even in complex and dynamic visual scenarios. In combination with these methods, our blinking model can readily be applied to many real-world problems. Better understanding of and, in particular, quantitative insights into human blinking behavior are also relevant for building technical aid systems (ref. 47, for example) and detecting mental states during critical tasks to prevent accidents (48).

Materials and Methods

Blink Detection.

Blinks were detected using an infrared eye-tracking device (Tobii EyeX eye tracker; 60 Hz). This technique has been used in past research (e.g., refs. 17 and 39). During blinking and thus closed eyes, the eye-tracking device loses track of the pupils and cannot determine the gaze location. These artifacts were identified and used to detect blinks by analyzing their temporal structure. We tested different thresholds on three subjects while manually recording blinks and chose the threshold with the best agreement. For the analysis, blinks were treated as point processes. Using this procedure we found similar statistics regarding blink rates and IBIs compared with studies using magnetic search coils (e.g., ref. 18), manual video analysis (45), and EEGs (23).

Experiment Setup.

The test subjects were seated in front of a computer screen (Flatron W2242TE monitor; 1,680 × 1,050-pixel resolution, 60-Hz refresh rate) at a distance of about 55 cm. All experimental procedures were carried out in accordance with the guidelines of the German Psychological Society and approved by the ethics committee of the Darmstadt University of Technology. Subjects gave informed consent and were aware that their eye movements were recorded; however, they were told about the purpose of the task after the experiment to prevent conscious control of the blinking behavior.

Supplementary Material

Supplementary File
pnas.201714220SI.pdf (1.7MB, pdf)

Footnotes

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1714220115/-/DCSupplemental.

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