Activating one reflex often facilitates another, antagonistic one. Since Charles Sherrington first identified successive induction more than 100 years ago, it has been demonstrated in a wide range of species, from aphids to grasshoppers to dogs and humans. We show a particularly orderly example in zebrafish (Danio rerio) larvae and identify the simple dynamic process that seems to underlie it

John Staddon

Robert Macphail

Stephanie Padilla

English

Nature Precedings

Successive Induction in Larval Zebrafish  
J. E. R. Staddon1, R.C. MacPhail2, and S. Padilla3
 
ABSTRACT 
Activating one reflex often facilitates another, antagonistic one.  Since Charles 
Sherrington first identified successive induction more than 100 years ago, it has 
been demonstrated in a wide range of species, from aphids to grasshoppers to 
dogs and humans.  We show a particularly orderly example in zebrafish (Danio 
rerio) larvae and identify the simple dynamic process that seems to underlie it. 
 
Charles Sherrington, more than one hundred years ago, studied the reflexive behavior of a 
variety of decerebrate mammals.  From his own work and the work of others he identified a set 
of reflex properties such as latency, habituation, and refractory period, that can be observed in all 
animal species.  Sherrington also identified the properties of interaction between reflexes.  One 
of the most interesting is successive induction, which is the facilitation of one reflex by the 
preceding excitation of an antagonistic one.  For example, “…the extension-reflex predisposes to 
and may actually induce a flexion-reflex, and conversely the flexion-reflex predisposes to and 
may actually induce an extension-reflex”i,ii. 
 Successive induction (also known as contrast) has been identified in a variety of species 
with a range of responses.  In response to changes in illumination, for example, aphids (Aphis 
fabae) show ‘antagonistic induction’ and ‘antagonistic inhibition’: under appropriate conditions, 
flight induced by light enhances the subsequent settling response, and settling reciprocally 
enhances the photokinetic responseiii.  A similar pattern of activity change in response to change 
in illumination has been shown in locusts (Locusta migratory migratorioides,iv and most recently 
in zebrafish larvae (Danio rerio)v, and related research cited therein.   
 Sherrington’s analysis of the properties of single reflexes led him to postulate the 
existence of the synapse, a junction between nerves with well-defined properties.  The synapse 
was subsequently observed directly, but the process underlying successive induction has not 
been identified, and its physical basis has not been established.  In this note we describe some 
new data on successive induction and a simple theory for its operation.  
 MacPhail et al. (2009) measured the movement of individual zebrafish larvae (6 days 
post-fertilization [dpf]) separately housed in 96-well microtiter plates. The movement (cm/unit 
time) of each larva as a function of changes in the level of visible vs. infrared light (perceptual 
dark) was recorded with a video-tracking system.  The average data are extremely orderly and 
highly repeatable.  The basic results are: 
1. In the dark (infrared illumination only) not preceded by light, activity level is low and 
constant.  
2. In the light, activity level slowly increases to an intermediate asymptote.  
                                                 
1Department of Psychology and Neuroscience, Duke University, Durham NC and Department of Psychology, 
University of York, York U.K. 
2 Toxicity Assessment Division and 4Integrated Systems Toxicology Division, National Health and Environmental 
Effects Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park NC and Department 
of Psychology and Curriculum in Toxicology, University of North Carolina at Chapel Hill, Chapel Hill NC USA 
3Integrated Systems Toxicology Division, National Health and Environmental Effects Research Laboratory, U.S. 
Environmental Protection Agency, Research Triangle Park NC and Curriculum in Toxicology, University of North 
Carolina at Chapel Hill, Chapel Hill NC USA. 
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3. In dark, preceded by a period of light, activity reaches a high level and then slowly 
declines.  This is an example of successive induction: suppression of activity in the light 
facilitates activity in subsequent dark.     
These properties are summarized in Figure 1, which shows the effect of continuous dark (red 
triangles), continuous light (open circles) and alternating light and dark (white/red squares) on 
the activity level of groups of zebrafish larvae.   
The Process 
The process can be modeled by a system of two leaky reservoirs.  First consider reservoir B in 
Fig. 2 and let the water level in B, x2, represent activity level.  In the light, activity slowly 
increases to an intermediate asymptotic value.  This behavior can be modeled by B filling at a 
steady rate with an outflow determined by its level: the higher the level, the faster the outflow, 
yielding an equilibrium level where inflow is equal to outflow (k2x2 in Fig. 2) where x2 is the 
level and k2 is, in effect, the size of the leak.  If inflow occurs only during light, we have then a 
simple model for behavior in the light (open circles in Figure 1).  
 To capture successive induction, however, the inflow to B must be the outflow from a 
second (upstream) reservoir, A, which fills up only during the light, and mainly empties into B in 
the dark.    The large activity (x2) increase observed in the dark after a period of light implies that 
inflow to B, in fact, comes from A, which fills at a steady rate (V, say) only during the light 
period.    
If A empties only slowly in the light (k1L is small), it will fill up during the light.  The 
increase in activity in dark after a light period then corresponds to an increase in the A → B 
discharge rate in the dark (k1D >> k1L).  In other words, A fills up in the light, but also leaks 
(slowly) into B, yielding the slow increase in B level (i.e., activity) in light.  But in dark, the 
discharge rate from A → B increases, thus producing an increase in the level of B (i.e., an 
increase in activity).  The increase in the level of B is transient, however, because V (inflow to 
A) is assumed to equal zero in the dark – so that A eventually empties, the flow into B ceases, 
and then B also empties (activity declines to zero).  
These events are combined in Figure 2, which is a physical analog to the process.  It has 
the following ingredients:    
1. x2 corresponds to observed activity level.   
2. The inflow into reservoir A is at a constant rate V that is positive when the light is on and 
zero when it is off. 
3. A leaks into reservoir B at a rate proportional to its level, x1, and the setting of the valve 
(size of the leak) k1D/L, whose value depends on light level, large in dark, small in light:  
k1D >> k1L  
4. B leaks at a rate proportional to its level, x2, and the size of the leak k2.   k2 is constant. 
We hope this physical description will adequately explain the relatively simple process 
that is described more formally by the following two difference equations:  
),()()()1(
),()()1(
2221/12
1/111
txktxtxktx
txktxVtx
LD
LD
−+=+
−+=+
  (1, 2) 
where t is discrete time, V is in effect a scale parameter and k1 takes on different values in the 
dark and light: k1D >>  k1L, and V = 0 in dark and V > 0 in light. 
2 
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Equation 1 describes the flow into and out of reservoir B;  x1 will obviously have a 
maximum (asymptote) at V/k1L.  The outflow from A, k1D/Lx1, is the inflow to B.  The level in B, 
similarly, has an asymptote at x2/(1-k1D/L+k2).   In the light, because k1 is then small, the effective 
asymptote is x2/(1+k2).   
Thus, after a period in the light, x1 will be large and x2 will be small.  When the light goes 
out, k1 increases allowing a large increase in k1x1 and thus an increase in x2.  But, because V is 
zero in the dark, k1x1 soon diminishes, and, after a lag, so does activity, x2.   
Tests 
 We look first at the qualitative fits between model and data and then look at more 
quantitative fits.   
Qualitative fits. Preceding dark time has no effect: Figure 3 (left panel) shows data from 
two experiments in which the larvae were exposed to 20 min of bright light (51.9 lux) preceded 
by either 10 minutes or 20 minutes of dark, and followed by 10 minutes of dark.  The curves are 
identical, showing (a) the high replicability of the data with this preparation; (b) successive 
induction: activity in the dark is elevated by prior light, and (c) that duration of the initial dark 
period has no effect, which is as the model predicts because inflow, V, is zero in the dark.  
More light yields more activity in subsequent dark:  Figure 3 (right panel) shows activity 
in 20 minutes of dark preceded by either 5 or 15 minutes of light (i.e., x1 is larger).  There is 
more activity in the dark when preceded by a longer light period, as the model predicts.  Figure 4 
shows a simulation of this experiment.  The pattern is the same, more light yields more 
subsequent activity, but the peak of the 15-min-light line is roughly 3 times higher than the 5-
min peak, rather than about 1.5 times higher, as in the data in Figure 3.   
Quantitative fits: Figure 5 shows successive induction in 10 minutes of dark following 20 
minutes of light (triangles); the magenta line shows a simulation, for which the parameter values 
were fitted by inspection.   The model readily captures the approximately linear increase in 
activity in the first few minutes of light as well as the rise-and-fall in subsequent dark.  
Figure 6, top panel, shows a quantitative fit to a complicated light-dark series, shown by 
the on-off graph at the top.  Note particularly the sharp response to a single, brief (60-s) light 
period (at 30 min). Figure 6, bottom panel, shows the reverse effect – of a brief dark period (at 
20 min).  The parameters for both fits are the same, only the initial conditions are different. Both 
graphs show that the fit is good for the first 30-40 min, although the model tends to over-predict 
activity in the latter portions of the experiments.   
DISCUSSION AND CONCLUSION 
The average activity-level changes caused by light-dark changes in this procedure are highly 
replicable.  Moreover, the process represented by Equations 1 and 2 captures the essentials of the 
effect of light and dark on activity in zebrafish larvae, at least for the first 30-40 min or so of the 
experiment.   Once the procedure was completely standardized, as it was for the two separate 
experiments shown in Figure 6, the same simulation parameter values seem to apply for any on-
off input sequence.   
 The model fails, however, in two respects.  First, the difference between the relative 
peaks in Figures 3 (right panel) and 4 shows that the assumption that x2 is directly related to 
measured activity level is too simple,  Simulated activity level (x2) increases too much with 
additional time in light.  This discrepancy is independent of particular parameter values; it is a 
consequence of the linearity of the model.  For a comprehensive model it is both plausible 
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(activity surely does have an upper limit) and necessary to include a non-linear limiter for rate, 
i.e., some negatively accelerated function relating x2 to actual activity. 
 Second, the model over-predicts dark activity in the latter part (> 35 min) of the two 
experiments shown in Figure 6.  This discrepancy also cannot be eliminated by changing 
parameter values without impairing the fit earlier in the experiments.  Because predicted and 
actual activity levels are high at the end of these experiments, a rate-limiting assumption for x2 
would improve the model fit here also, but at the cost of increased complexity. 
Our aim at this stage, however, is not so much to provide a necessarily complex model 
that fits every detail as to expose the essential process that seems to underlie successive 
induction in these experiments.  That process clearly involves a hidden variable (x1) that 
increases during time in the light and then facilitates activity in subsequent dark in a fashion 
consistent with a depleting store.   The relative simplicity of the process, like the simplicity of 
the synapse identified by Sherrington, suggests a comparably simple underlying physiology.  We 
look forward to new research at the neural and molecular levels that might elucidate further these 
striking effects.   
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ACKNOWLEDGEMENTS 
 
JERS thanks Duke University for research support and the University of York (UK) for 
hospitality during the preparation of this report.  The authors thank Beth Padnos, Brenda Proctor 
and Dr. David Kurtz for maintenance and upkeep of the zebrafish colony and Deborah Hunter 
for the video-tracking analysis of the zebrafish locomotion.   
This manuscript has been reviewed by the National Health and Environmental Effects 
Research Laboratory of the U.S. Environmental Protection Agency and approved for publication.   
Approval does not signify that the contents reflect the views of the Agency, nor does mention of 
trade names or commercial products constitute endorsement or recommendation for use.       
 
 
FIGURE LEGENDS 
1. Successive induction in response to light changes in 6-dpf zebrafish larvae.  Average 
activity level (measured as distance moved in 2-min periods) increases to an intermediate 
asymptote in continuous light, rises to a high level then declines in the dark following a 
light period, or stays at a low level in continuous dark not preceded by light 
(experimental details in MacPhail et al., 2009). Reproduced with permission of the 
journal publisher. 
 
2. A physical analog to successive induction.  Level in reservoir B, x2, corresponds to 
activity level.  Reservoir A fills up at a steady rate V which is directly related to light 
level.  A drains into reservoir B at a rate k1x1, which is determined by light level: k1 is 
small in the light and large in the dark.  Reservoir B drains at a constant rate k2.  Thus, in 
the light, A fills up.  In subsequent dark, B rapidly fills (activity level rises) and then 
declines. 
3. Left panel:  Lack of effect of two different prior dark periods on subsequent light and 
dark.  Right panel:  Effect of light-period duration (longer light yields more activity in 
subsequent dark).  Horizontal bars indicate periods of light (unfilled) and dark (filled). 
From MacPhail et al. (2009). Reproduced with permission of the journal publisher. 
 
4. Effect of light-period duration (simulation of results in right panel of Figure 3).  
Parameters: V = 5, k1D = 0.2, k1L = 0.04, k2 = 0.9; initial conditions:  x1(0), x2(0), both set 
equal to 0. Peak ratio is proportional to prior light-duration ratio.  Horizontal bars indicate 
periods of light (unfilled) and dark (filled). 
5. Data (triangles): Effect of 20-min light on activity in subsequent dark.  Activity increases 
approximately linearly in light then increases rapidly and declines in the dark.  
Simulation (line) used the following parameter values: V = 5, k1D = 0.2, k1L = 0.04, k2 = 
0.9, initial conditions:  x1(0), x2(0), both set equal to 0.  Horizontal bar indicates periods 
of light (unfilled) and dark (filled). 
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6. Top panel: Effect of repeated light and dark periods on activity level (blue triangles) and 
simulation (line) – note the effect of a brief light period at 30 min and a longer light 
period beginning after 60 min.  Bottom panel: Effect of repeated light and dark – note the 
effect of a brief dark period at 20 min.  Horizontal bars in both panels indicate periods of 
light (unfilled) and dark (filled). Parameters for both simulations (blue line) were: V = 5, 
k1D = .07, k1L = .01, k2 = .8.  Initial conditions were x1(0) = 15 for the top graph and 20 for 
the bottom (to account for the initial burst due to unmeasured effects); x2(0) = 0 for both. 
 
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Figure 1 
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Figure 2 
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Figure 3 
 
 
 
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Figure 4
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Figure 5 
 
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Figure 6 
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FOOTNOTES 
 
ii Sherrington, C. S. The Integrative Action of the Nervous System. New Haven: Yale University 
Press, 1906. (Reprinted, 1947.) 
ii Staddon, J.E.R. (1983/2003). Adaptive Behavior and Learning. Cambridge University Press.  
http://psychweb.psych.duke.edu/department/jers/abl/TableC.htm
iii Kennedy, J. S. Coordination of successive activities in an aphid: reciprocal effects of settling 
on flight. (1965) Journal of Experimental Biology, 43, 489-509. 
iv Moorhouse, J. F., Fosbrooke, I. H. M., & Kennedy, J. S. “Paradoxical driving” of walking 
activity in locusts. (1978) Journal of Experimental Biology, 72, 1-16. 
v MacPhail, R. C., Brooks, J., Hunter, D.L., Padnos, B, Irons, T.D.  and Padilla, S.  (2009)  
Locomotion in larval zebrafish: influence of time of day, lighting and ethanol.  NeuroToxicology 
30 (2009) 52–58. 
 
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Successive Induction in Larval Zebrafish

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Successive Induction in Larval Zebrafish

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