Discovery of a series of 1H-pyrrolo[2,3-b]pyridine compounds as potent TNIK inhibitors

Article abstract of DOI:10.1016/j.bmcl.2020.127749

In an in-house screening, 1H-pyrrolo[2,3-b]pyridine scaffold was found to have high inhibition on TNIK. Several series of compounds were designed and synthesized, among which some compounds had potent TNIK inhibition with IC₅₀ values lower than 1 nM. Some compounds showed concentration-dependent characteristics of IL-2 inhibition. These results provided new applications of TNIK inhibitors and new prospects of TNIK as a drug target.

Full text of DOI:10.1016/j.bmcl.2020.127749

Vision Research 138 (2017) 1–11
Contents lists available at ScienceDirect
Vision Research
journal homepage: www.elsevier.com/locate/visres
Pre- and post-saccadic stimulus timing in saccadic suppression of
displacement – A computational model
Arnold Ziesche a, Julia Bergelt a, Heiner Deubel b, Fred H. Hamker a,
⇑
a Technische Universität Chemnitz, Straße der Nationen 62, 09107 Chemnitz, Germany
b Ludwig-Maximilians-Universität, Leopoldstraße 13, 80802 München, Germany
a r t i c l e i n f o
a b s t r a c t
Article history:
When the target of a saccadic eye movement is displaced while the eyes move this displacement is often
not noticed (saccadic suppression of displacement, SSD). We present a neurobiologically motivated, com-
putational model of SSD and compare its simulation results to experimental data. The model offers a sim-
ple explanation of the effects of pre- and post-saccadic stimulus blanking on SSD in terms of peri-saccadic
network dynamics. Under normal peri-saccadic conditions pre-and post-saccadic stimulus traces are
recurrently integrated with reference to present and future eye position, whereas blanking diminishes
the pre-saccadic stimulus trace and thus leads to an uninfluenced integration of the post-saccadic stim-
ulus trace. We show that part of the intersubject variability in SSD can be explained by differences in
decision thresholds of this integration process.
Received 15 November 2016
Received in revised form 1 June 2017
Accepted 2 June 2017
Available online 18 July 2017
Number of Reviews = 2
Keywords:
Saccadic suppression of displacement
Computational model
Proprioception
Ó 2017 Elsevier Ltd. All rights reserved.
Corollary discharge
Reference frames
Coordinate transformation
1. Introduction
detection performance also occurs when the target stimulus is
not blanked after but before the saccade (pre-gap effect).
With each shift of our gaze, the image on the retina abruptly
changes. However, we do not perceive these jumps during eye
movements. Rather, the world appears stable to us. This phe-
nomenon has been termed ‘visual stability across eye movements’.
While multiple experiments explored different aspects of visual
stability, we here focus on the experimental paradigm known as
saccadic suppression of displacement (SSD, e.g., Bridgeman,
Hendry, & Stark, 1975). It revealed that subjects are unable to per-
ceive small peri-saccadic displacements of stimuli which they can
well detect when they occur during fixation. In other words, sub-
jects perceive the world as visually more stable than it actually is.
Meanwhile, several studies addressed different aspects of SSD.
Deubel, Bridgeman, and Schneider (1996) found that the
detectability of stimulus displacements can be considerably
improved when the stimulus at the saccade target is not displaced
during the saccade but first removed and then shown after a blank-
ing period of about 250 ms at its displaced position, known as the
blanking or (post-)gap effect. Less attention has been given to the
observation by Deubel et al. (1996) that an improvement of the
Zimmermann, Morrone, and Burr (2013) found that a prolonged
viewing time prior to saccade onset also improves the detection of
stimulus displacements. Zimmermann et al. (2013) and
Zimmermann, Born, Fink, and Cavanagh (2014) further revealed
that a displacement detection reduction does not require a sac-
cade: similar decrements in performance occur during fixation if,
instead of the execution of a saccade, a mask is presented.
An early theory proposed to explain the SSD effect – the object
reference or visual search theory (Bridgeman, 2007; Deubel et al.,
1996) states that the visual system uses visual objects, usually
the stimulus at the saccade target, to recalibrate spatial perception
after the saccade. According to this theory, small displacements of
the saccade target are not noticed because the visual system
assumes that the saccade target stays stable during the saccade
and ascribes any deviances of the target which should be in the
center of the fovea after the saccade to an imprecise eye move-
ment. Only if the target displacements are too large the visual sys-
tem uses other information such as proprioception to recalibrate
spatial perception, which leads to the detection of the stimulus dis-
placements. In this framework the blanking effect is explained by a
spatiotemporal ‘constancy’ window: Only if the saccade target
stimulus is found within this spatiotemporal window the world
is perceived as stable. If the object reappears after this window
⇑
Corresponding author.
E-mail address: fred.hamker@informatik.tu-chemnitz.de (F.H. Hamker).
URL: https://www.tu-chemnitz.de/informatik/KI/index.php.en (F.H. Hamker).
http://dx.doi.org/10.1016/j.visres.2017.06.007
0042-6989/Ó 2017 Elsevier Ltd. All rights reserved.

2
A. Ziesche et al. / Vision Research 138 (2017) 1–11
has closed, the stability assumption is dropped and target displace-
ments are detected (Bridgeman, 2007).
2.1. Anatomy
Based on a similar assumption but spelled out in a computa-
tional framework, Niemeier, Crawford, and Tweed (2003) proposed
a Bayesian transsaccadic integration model. They attempted to
predict the perceived displacement of a stimulus by combining
the stimulus position, an internal estimate of the eye positions
(e.g. efference copy) and an expectation about the probability of
peri-saccadic target displacements (the prior). The model rests on
the assumption that the brain computes this prior for each exper-
imental condition, while the underlying mechanisms however, are
not part of the model. They fitted the model to their own recorded
data by using a sharply tuned prior in the non-blanking condition
and a broadly tuned one in the blanking condition.
Atsma, Maij, Koppen, Irwin, and Medendorp (2016) criticised
this model as it necessarily relies on the integration of a displace-
ment vector (the combined visual and motor signals) and a prior
around zero displacement. Thus, independent of the size of the true
displacement it always predicts a reduction of the perceived dis-
placement. They proposed a different model which in parallel
applies not only an integration but also a separation of the pre-
and post-saccadic stimuli and weighting both using the factors dis-
placement size and viewing time to compute the final percept.
They found that the degree of integration and separation depends
on displacement size, where small displacements show a stronger
weight for integration. However, Atsma et al. (2016) do not address
the blanking condition with their model. Further, viewing time is
not explicitly modeled but only implicitly in the probability den-
sity function coding the precision of the stimulus.
Our proposed model rests on the assumption that parietal areas,
such as the lateral intraparietal area (LIP), receive two different
kinds of eye position information (Fig. 1). First, a proprioceptive
information about eye position (Andersen, Bracewell, Barash,
Gnadt, & Fogassi, 1990; Bremmer, Distler, & Hoffmann, 1997), pre-
sumably from the somatosensory cortex (Wang, Zhang, Cohen, &
Goldberg, 2007; Xu, Wang, Peck, & Goldberg, 2011; Xu, Karachi,
& Goldberg, 2012), and second, a preparatory corollary discharge
about the intended saccade displacement (Colby, Duhamel, &
Goldberg, 1996; Melcher & Colby, 2008; Wurtz, 2008) which pre-
sumably originates in the superior colliculus (SC) and is routed
via the mediodorsal nucleus (MD) and the frontal eye field (FEF,
Sommer & Wurtz, 2004, 2008). However, the exact origins of these
eye position signals are not critical assumptions but rather provide
a source of inspiration for the model design. Importantly, both eye
position signals are used to transform a visual stimulus position
signal, which is encoded in a retinocentric reference frame coming
from early extrastriate areas, into an intermediate reference frame.
The representation of stimulus position in the intermediate refer-
ence frames is then used to compute the stimulus position in a
head-centered reference frame (Galletti, Battaglini,
& Fattori,
1995; Mullette-Gillman, Cohen, & Groh, 2005). The computation
of an explicit head-centered reference frame is not a critical
requirement of the model but slightly improves the simulation
results (Ziesche & Hamker, 2011, 2014).
2.2. Model
Understanding SSD by computing a unitary percept from pre-and
post-saccadic stimulus contributions as suggested by Atsma et al.
(2016) is not novel and has been already proposed in a neuro-
computational model of SSD (Ziesche & Hamker, 2014), which has
the further advantage that time is explicitly part of the model
description. This model explains the blanking effect as an uninflu-
enced integration of the post-saccadic stimulus as the neural trace
of the pre-saccadic stimulus has declined during the blanking per-
iod. Further, the eye dependent parameters have been fully updated
at the time of post-saccadic stimulus presentation. In the non-
blanking condition, both the pre- and post-saccadic stimulus, are
integrated into a single percept. However, as the model has to link
the pre-saccadic with the post-saccadic view it uses an egocentric
reference frame based on internal eye position signals. In the non-
blanking condition, the eye position signals have not been fully
updated as the displacement occurs during saccade. Ziesche and
Hamker (2014) further explained how predictive remapping, first
reported by Duhamel, Colby, and Goldberg (1992), and corollary dis-
charge are linked to saccadic suppression of displacement. However,
the model does not require a saccade to show a reduction of dis-
placement detection. Bergelt and Hamker (2016) applied the model
to a masking experiment without a saccade and could well account
for the observation of Zimmermann et al. (2014).
We use the concept of basis function networks (Pouget, Denève,
& Duhamel, 2002) to combine a retinotopic retinal signal (modeled
in a one-dimensional neuron layer Xr) with proprioceptive (mod-
eled in a 1D layer XePC) and corollary discharge (modeled in a 1D
layer XeCD) signals. The basis functions are realized in two two-
dimensional layers XbPC and XbCD in which the retinal signal is
modulated by proprioception and corollary discharge respectively.
From these basis function representations we read out a head-
centered stimulus representation in an output layer Xh (Fig. 2).
To further investigate the properties of the neuro-
computational model, in particular with respect to variations of
the stimulus timings, we applied it to the most relevant experi-
mental variations of Deubel et al. (1996).
Fig. 1. Putative anatomical relationship of the model to the human brain. After the
initial processing of stimulus properties in early visual areas, spatial information is
represented in the parietal cortex in various reference frames. The core of the model
may be localized in the human homologue of the lateral intraparietal area (LIP). It
receives stimulus position information in retinotopic coordinates from early
extrastriate areas, proprioceptive eye position information from primary
2. Material and methods
The neuro-computational model has been originally introduced
to explain the peri-saccadic mislocalization of briefly flashed stim-
uli in complete darkness (Ziesche & Hamker, 2011). It has then
been slightly adapted to the paradigm of saccadic suppression of
displacement (Bergelt & Hamker, 2016; Ziesche & Hamker, 2014).
As the model has been described in detail before, we will here
describe its properties on a coarse level.
somatosensory cortex (S1), and
a phasic corollary discharge signal encoding
planned saccade displacement originating from the superior colliculus (SC) and
routed via mediodorsal nucleus (MD) and frontal eye field (FEF) to LIP. All this
spatial information is integrated in LIP and then decoded to yield a spatial percept
of the stimulus position.

A. Ziesche et al. / Vision Research 138 (2017) 1–11
3
Since we use a fully dynamic neural network based on rate-coded
neurons (Hamker, 2005; Zirnsak, Beuth, & Hamker, 2011) we
model the time courses of the input signals realistically to obtain
explanations of phenomena of peri-saccadic spatial perception
which occur on fine time scales (see below). For details on the
implementation of the network layers and connection patterns
we refer the reader to our previous publications (Bergelt &
Hamker, 2016; Ziesche & Hamker, 2011, 2014). For a simplified
version of the equations describing the interactions of the model
layers, see the grey boxes in Fig. 2.
The continuous firing rates of the neurons at the output layer
Xh are fed into a decision process based on competing, accumulat-
ing decision neurons (Hamker, 2007; Usher & McClelland, 2001) to
reach a decision about the stimulus displacement (justified by
Kiani, Hanks, & Shadlen, 2008; Stanford, Shankar, Massoglia,
Costello, & Salinas, 2010). Since we aim at replicating the findings
from Deubel et al. (1996) we use a decision process with two deci-
sion neurons, one voting for a forward target displacement, the
other voting for a backward target displacement. The procedure
is similar to our previous application of the model (Ziesche &
Hamker, 2011), however there we used a decision process which
came up with spatial location percept. The details of the modified
two-choice decision process are presented below.
The principle functionality of the model on the SSD task has
been described previously (Bergelt & Hamker, 2016; Ziesche &
Hamker, 2014), which we briefly summarize here. Our model pos-
tulates that the pre-saccadic stimulus trace is integrated with the
post-saccadic stimulus trace to compute the location of a stimulus.
As our model also contains feedback connections (Fig. 2) any pre-
sent evidence affects the processing of new evidence. Thus, the
pre-saccadic stimulus trace affects the post-saccadic processing
and stabilises the percept in favour of the pre-saccadic evidence.
This explains that small displacements during saccade become
unnoticed. Thus, in its core SSD has similarities to visual masking.
In order to align pre- and post-saccadic views egocentric reference
frames in form of the two eye position signals are used. One eye
position signal, the proprioceptive signal, computes the stimulus
in reference of the pre-saccadic position and the other, the corol-
lary discharge, in reference of the future eye position. The interac-
tion of the stimulus encoded in the pre-saccadic reference frame
with the corollary discharge leads to predictive remapping, i.e.
the response of a neuron to a stimulus presented in its future
receptive field (Ziesche & Hamker, 2014). When we selectively dis-
rupted either predictive remapping or corollary discharge the
model predicts a bias in reporting displacements opposite to the
saccade direction, as the predictive component is in part or fully
suppressed.
2.2.1. Timing of the physiological signals
In our previous presentation of the model (Ziesche & Hamker,
2011) where it had been applied to explain the mislocalization of
brief flashes around saccades in total darkness, we presented var-
ious parameter variations of the timing of the physiological signals.
Here, we choose specific values for these timings to achieve a good
data fit. However, we were careful to choose parameter values
which are in the range of suitable values derived from the param-
eter variations in Ziesche and Hamker (2011). Specifically, the
parameters we use here produce comparable outcomes as in the
previous study. We used the following timing parameters for the
physiological eye position signals:
The proprioceptive (PC) eye position signal encodes the eye
position during fixation but does not move with the eye during
the saccade. Rather, it represents the pre-saccadic eye position
during the saccade until it starts updating to the new eye position
some time after saccade offset as suggested by experimental data
(Wang et al., 2007; Xu et al., 2011, 2012). In our simulations, the
neural activity representing the post-saccadic eye position is
turned on tPC; on ¼ 32 ms relative to saccade offset. At the same time
ðtPC; off ¼ 32 msÞ, the activity representing the pre-saccadic eye
position starts to decay. In the present study, we use a faster decay
factor rPC; off ¼ 15 (as compared to rPC; off ¼ 35 in Ziesche &
Hamker, 2011). As the eye-position is mathematically computed
by a differential equation, the change needs some time to become
effective, which takes additional 30–40 ms to become fully estab-
lished. Thus, the model is well consistent with the observation that
proprioceptive eye position lags behind the true eye position (Xu
et al., 2011; Wang et al., 2007), but the model LIP gain fields update
50–100 ms earlier than those recently reported for monkeys (Xu
et al., 2012). As macaque monkeys did not show any difference
between blank and step trials, different than in humans (Joiner,
Cavanaugh, FitzGibbon, & Wurtz, 2013), a full replication of mon-
key data may not be a requirement to explain data of SSD experi-
ments run with humans and we kept the parameters of the original
model (Ziesche & Hamker, 2011).
Fig. 2. Our model of peri-saccadic stimulus localization is composed of three cell
types, XbPC and XbCD (in LIP), which receive retinal input from early extrastriate
areas as well as eye position information presumably from S1 and FEF, and Xh
which encodes stimulus positions in a head-centered reference frame. The input
layer Xr represents stimulus position retinotopically in a single dimension, modeled
by Gaussian receptive fields. The stimulus signal is gain-modulated in XbPC by the
proprioceptive eye position signal ðXePCÞ and in XbCD by the corollary discharge
(XeCD). Both maps, XbPC and XbCD feed into the head-centered layer Xh. In order to
allow interactions of these two forward connections, the maps XbPC and XbCD both
encode space in the same coordinate system. Thus, the corollary discharge
implicitly encodes eye position information, as motivated by an observation of
Cassanello and Ferrera (2007). For simplicity, we use the same eye position signal
ðXePCÞ to modulate corollary discharge from MD (and SC) with eye position. The
grey boxes in each layer show a simplified version of the neurons equations. In layer
Xr, Stim is the input from earlier areas and in Xr as well as in Xh, S is the synaptic
depression. In all layers, Gain is the gain modulation factor. PC is the proprioceptive
eye position signal and CD is the corollary discharge signal.
The corollary discharge (CD) signal is a transient representation
of the planned saccade displacement in retinotopic coordinates
whose temporal dynamics are well motivated from single cell
recordings in the superior colliculus, the frontal eye field and the

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A. Ziesche et al. / Vision Research 138 (2017) 1–11
mediodorsal nucleus (MD) of the thalamus (Sommer & Wurtz,
2004, 2008). In the present study, we use a faster decay factor
bCD ¼ 65 (as compared to bCD ¼ 150 in Ziesche & Hamker, 2011).
A faster decay factor in the CD signal leads to a more pronounced
mislocalization opposite to the saccade direction when stimuli are
flashed in total darkness after saccade onset, which has been
observed in experimental data as well (Ziesche & Hamker, 2011).
Thus, the present choice of parameters is still consistent with
observations in previous studies. Further, it is also likely that decay
and rise times of the CD and PC signals vary in individual subjects.
spikes if and only if mc > Rsmax where R is a random number
between 0 and 1. The spiking activity of the neuron is smax ¼ 1
while the non-spiking activity is 0. Thus the activity at the spik-
ing time step t is
ꢀ
smax
;
if mc > Rsmax
t
~
mc ¼
:
ð2Þ
0;
else
Then, the activity of the spiking neuron is averaged to obtain a
rate.
nꢀ1
X
1
n
t
~
mc ¼
mc
ð3Þ
2.2.2. Details of the decision process
The computation of the input to the decision process consists of
several steps (see Fig. 3):
t¼0
4. In the previous step we introduced rate-coded neurons
encoding evidence for the presence of a stimulus at each
spatial position with a resolution of 0.5 degrees. In this step,
we collect all these evidences into two evidences mf and mb,
one for forward jumps and one for backward jumps. For this
we use the pre-saccadic stimulus position cpre as a decision
1. The input IDP to the decision process consists of the firing rates
of Xh, i.e. IDi P ¼ rXi h when they are above a threshold of 0.04. The
start time of the accumulation process is set to 28 ms after sac-
cade offset for conditions where the displaced stimulus reap-
pears during the saccade and 60 ms after stimulus onset
when the displaced stimulus reappears after saccade offset.
We chose not to couple the accumulation onset to stimulus
onset for peri-saccadic stimuli since peri-saccadic detectability
of stimuli is suppressed (Volkmann, Riggs, White, & Moore,
1978). The timing of 28 ms after saccade offset is set to a similar
timing as the updating of the proprioceptive eye position signal
(see above), assuming that this signal might be used to trigger
the accumulation process. The interval between stimulus onset
and accumulation onset for stimuli appearing after saccade off-
set is roughly set to the time where the stimulus activity
reaches Xh.
border:
X
mf ¼
mb ¼
mc
mc
ð4Þ
ð5Þ
cPcpre
X
c6cpre
5. We implement a competition between the decision neurons
by subtracting each input from the other:
mf :¼mf ꢀ mb
mb :¼mb ꢀ mf
ð6Þ
ð7Þ
6. Accumulating decision neurons are implemented as in
Hamker (2007). The ODE of each of the two decision neurons
df and db is:
2. The position information encoded in the input IDP is decoded
using template matching with precalculated templates of much
t
dt
sDN df=bðtÞ ¼ mf=b
ð8Þ
higher spatial resolution than the number of entries in IDP. Each
entry codes 4 degrees. Hence the templates represent stimulus
position with a step size of 0.5 degrees. Template matching is
done using correlation. The match mc of the template tci repre-
with time step hDN ¼ 1, time constant sDN ¼ 50. Each decision
neuron dc is initialized with a baseline firing rate of 0.1 before
the decision process begins. A decision is made when one of
the neurons reaches the threshold dthresh ¼ 0:3 to 0:9 (the
senting a stimulus at position c with neurons i is
X
mc ¼
rXj htcj :
ð1Þ
threshold is systematically varied). If none of the neurons
j
DN
reaches this threshold after t
highest activity at that time wins (see Kiani et al., 2008).
¼ 70 ms, the neuron with the
max
The spatial resolution of the decision neurons equals the one of
the templates.
DN
trials
7. This whole process is repeated c
¼ 100 times and then aver-
3. We introduce noise by first transforming the rate coded input to
a spiking neuron model using a Poisson spike train and then
transforming it back to rate coded input by averaging. To be
more specific, one time step of the input mc (the template
match from the previous step) is equivalent to n time steps of
aged to compute the average number of ‘forward jump’
responses over all trials.
2.2.3. Simulation of experimental paradigms
We simulate the experimental paradigm from Deubel et al.
(1996) for four different experiments (Fig. 4). For easy reference,
we use the same numbering of experiments as in Deubel et al.
~
the spiking neuron mc (n ¼ 20 is the bin size). Spiking is simu-
lated in the simplest way: In each of the n time steps the neuron
Fig. 3. The decision process used in the model. It decodes the stimulus position from the activity in the head-centered map Xh. First we apply a template matching for each
time step. This has the advantage of increasing the spatial resolution by using appropriate pre-calculated templates. After noise is added the noisy template matches are split
into those encoding spatial positions representing a forward stimulus jump and a backward stimulus jump. The evidences for forward and backward jumps are summed up
for both directions and subtracted from each other, thereby implementing a competition between both. These two values serve as input to accumulating decision neurons
which compete until a threshold is reached. We repeat the entire process 100 times to yield an average percept mimicking 100 experimental trials.

A. Ziesche et al. / Vision Research 138 (2017) 1–11
5
(1996). In all experiments, we simulate saccadic eye movements
from 0° towards a stimulus at the saccade target which is pre-
sented at 8° (saccades are simulated by the saccade generator from
Van Wetter & Van Opstal (2008)). In experiments I and II the target
stimulus jumps once the saccade is detected by the experimental
equipment. In experiment I, the stimulus jumps either þ1ꢁ (i.e.
in saccade direction) or ꢀ1ꢁ (opposite to saccade direction). Before
it reappears at its displaced position, it is blanked for a variable
time from 0 ms to 270 ms. In experiment II, this time is set fixed
to either 0 ms or 250 ms and the target jump is varied between
ꢀ2ꢁ and þ2ꢁ. In experiment III, the stimulus is displaced immedi-
ately when the saccade is detected by þ1ꢁ or ꢀ1ꢁ and is blanked
for 250 ms after a variable time of 0 ms to 150 ms. In experiment
IV, the stimulus also jumps immediately when the saccade is
detected by þ1ꢁ or ꢀ1ꢁ. However, here the jump is preceded by a
variable blanking of the stimulus from 20 ms to 200 ms. In other
words, the stimulus disappears before saccade onset (for most
conditions).
small displacements are often unnoticed. The experimental data
shows a large in between-subject variability. In comparison, panel
C shows the performance in the blanking (post-gap) condition
(250 ms gap). Here, the psychometric curves are steep which indi-
cates good detection performance. In the 0 ms gap condition small
displacements are not detected well and the model replicates a
response bias towards positive displacements. In the model, this
effect is due to various causes which can be seen in detail in the
activity traces of the input and output layers of the model in
Fig. 6. Long time (for example 200 ms) before saccade onset the
stimulus which is presented at the saccade target evokes activity
in the retinal input layer Xr at a retinotopic position representing
the saccade target (indicated by the horizontal green line). At the
same time, proprioceptive eye position in XePC encodes the pre-
saccadic eye position which is 0° (indicated by the horizontal black
line). The model combines these activities into a head-centered
stimulus position which correctly encodes the saccade target in
the output layer Xh. Closer to saccade onset (50 ms before) the
corollary discharge signal in XeCD rises which leads to a distortion
in positive spatial direction of the activity in Xh. Shortly after sac-
cade onset (10–20 ms) suppression in XbPC (Ziesche & Hamker,
2011) leads to reduced activity in Xh which retains for the whole
saccade time. Later (around 50 ms after saccade onset) the retinal
input signal in Xr starts to reflect the stimulus movement on the
retina in the opposite direction of the saccade (towards the nega-
tive saccade amplitude). This leads to further distortions of the
head-centered output signal in Xh. Finally, shortly before the eye
reaches its post-saccadic position, the decision process starts accu-
mulating evidence from Xh (indicated by the vertical blue lines in
Fig. 6). Around the same time the proprioceptive eye position sig-
nal in XePC starts updating to the new eye position. This leads to
3. Results
3.1. The SSD effect
To demonstrate that our model replicates the experimental data
from Deubel et al. (1996), in particular the pre-gap and post-gap
effects, we replot the experimental data along with our model sim-
ulations in Fig. 5. Fig. 5A shows that the detection performance
increases with gap duration. The main SSD effect is shown in
Fig. 5B. The psychometric curves for displacement detection with-
out target blanking (0 ms gap) are shallow which indicates that
Fig. 4. The experimental paradigms for saccadic suppression of displacement which we simulate. Paradigms are adopted from Deubel et al. (1996), but simplified for
simulation in the model. For easy reference, we kept the original numbering of the experiments. In all experiments, we simulate saccadic eye movements from fixation at 0°
towards a saccade target stimulus which is presented at a position of 8°. Spatial positions are shown on the vertical axes, time is shown on the horizontal axes. Thick lines are
stimuli, thin lines are eye trajectories. In all experiments we change the scene 30 ms after saccade onset. A, In experiments I and II the stimulus is hidden 30 ms after saccade
onset. After a gap of variable length it reappears at a slightly different position. In experiment I the stimulus gap is varied (0 ms, 50 ms, 100 ms, 180 ms, or 270 ms) and
stimulus jumps are either þ1ꢁ or ꢀ1ꢁ. In experiment II the stimulus gap is either 0 ms or 250 ms and stimulus jump is varied (ꢀ2ꢁ; ꢀ1ꢁ; 0ꢁ; þ1ꢁ, or þ2ꢁ). B, In experiment III the
stimulus jumps immediately by either þ1ꢁ or ꢀ1ꢁ when the saccade is detected, but it is blanked again after a variable time (0 ms, 25 ms, 50 ms, 75 ms, 100 ms, 125 ms, or
150 ms) for 250 ms. We also refer to the jumped stimulus before the gap as a pre-gap stimulus pulse. C, Experiment IV is similar to experiment I with the difference that the
stimulus jumps when the saccade is detected (by either þ1ꢁ or ꢀ1ꢁ) but there is a stimulus gap of variable length (200 ms, 180 ms, 160 ms, 140 ms, 120 ms, 100 ms, 80 ms,
60 ms, 40 ms, or 20 ms) right before the stimulus jump. Thus, for most gap durations the stimulus disappears before saccade onset (‘‘pre-gap” condition).

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A. Ziesche et al. / Vision Research 138 (2017) 1–11
Fig. 5. Comparison of subject performance and model performance. Gray lines are subjects (replotted from Deubel et al., 1996), solid lines are model performances for a
decision threshold of 0.7. A, Experiment I, the main finding of the blanking effect. B, Experiment II with no gap. C, Experiment II with a 250 ms gap. D, Experiment III. E,
Experiment IV, the main finding of the pre-gap effect.
increased activity and further distortions in Xh and also affects the
still ongoing accumulation process in the decision neurons. In the
end (about 200 ms after saccade onset) the peri-saccadic distor-
tions end and a correct representation of stimulus position in Xh
is restored.
(indicated by the vertical blue line). Hence, stimulus position is
immediately represented correctly in Xh.
3.3. The pre-gap effect
In sum, distortions of the stimulus representation around the
decision time are due to changes in all of the input signals, the
corollary discharge, the stimulus movement on the retina, and
the proprioceptive eye position signal. The feedback connections
from Xh to XbCD stabilize the activity pattern in Xh such that the
disturbances of the input signals do not affect the activity pattern
in Xh immediately but only slowly. Thus, also peri-saccadic stimu-
lus displacements do not influence Xh immediately but only later
in the accumulation process where they have a weaker effect.
Together, the peri-saccadic distortions of Xh due to updates in
the input signals and the stabilization of Xh due to feedback loops
explain the SSD effect.
The second main finding of Deubel et al. (1996) is the so called
pre-gap effect. Here they show that the detection performance is
not only restored for post-saccadic stimulus blanking but also for
pre-saccadic stimulus blanking. Our model is able to replicate this
effect (Fig. 5E). It offers an explanation in terms of its feedback
loops. With a long pre-saccadic gap there is no previous activity
in the head-centred output layer Xh when the displaced stimulus
enters the system. Thus, any response of Xh to the new stimulus
– although potentially distorted – immediately reflects the dis-
placed stimulus position. In other words, when the pre-gap is a
long enough, the detection performance might still be biased but
displacements are detected well (i.e. the psychometric curve is
steep).
3.2. The blanking effect
3.4. The effect of the decision threshold
One main finding of Deubel et al. (1996) is the so called blank-
ing effect, i.e. that detection performances for stimulus displace-
ments are completely restored when the displacement does not
occur immediately during the saccade, but after a blanking period
of the stimulus. Fig. 7 shows the activity traces for a blanking per-
iod of 250 ms. Although the peri-saccadic distortions in Xh are the
same as in the no-gap condition (Fig. 6), they have ceased at the
time where the activity of the post-gap stimulus enters the system
The behavioral data from Deubel et al. (1996) shows intersub-
ject variability in most experiments. Remarkably, the variability
in the model for different decision thresholds is very similar to
the one of the subjects (Fig. 8). We will now describe how the deci-
sion threshold influences the SSD effect using the no-gap condition
(Fig. 8B). Fig. 9 shows the activities of the decision neurons for
three different thresholds in the 0 ms gap, 0° target displacement

A. Ziesche et al. / Vision Research 138 (2017) 1–11
7
Fig. 6. Activity traces of model layers for SSD simulations with 0 ms gap and 0° displacement. Time relative to saccade onset is plotted on the horizontal axes, spatial position
on the vertical axes. The horizontal black and green lines indicate the spatial positions of pre-saccadic fixation and planned saccade target, respectively. The vertical blue lines
indicate the time where the decision process starts to accumulate evidence from Xh neurons. A, Time course of events. The top graph shows the simulated eye trajectory, the
middle graph shows the stimulus which is switched off 30 ms after saccade onset and turned on at its displaced position the same time. B, Activities of Xh neurons. They
represent stimulus position in head-centered coordinates and are read out by the decision process. C, Activities of Xr neurons. They represent stimulus position in retinotopic
coordinates and serve as visual input to the model. D, Activities of XePC neurons. They represent proprioceptive eye position in the orbit (i.e. in head-centered coordinates). E,
Activities of XeCD neurons. They represent the planned saccade displacement (i.e. the planned saccade target in retinotopic coordinates). (For interpretation of the references
to colour in this figure caption, the reader is referred to the web version of this article.)
condition. As the main effect of the decision threshold the decision
times increase (indicated by the circles at the end of the lines). Fur-
thermore, for longer decision times the accumulated evidence
changes. While the evidence for a forward displacement is stronger
in the first period of about 10–20 ms, later (20–40 ms) the evi-
dence for a backward displacement is stronger. Thus, longer deci-
sion times are predicted to lead to tendency to decide for
backward displacements.
Since the model performance varies in the same range as the
subjects’ performance (Fig. 8), we were interested whether it is

8
A. Ziesche et al. / Vision Research 138 (2017) 1–11
Fig. 7. Activity traces of model layers for SSD simulations with 250 ms gap and 0° displacement. The format is the same as in Fig. 6. A, The time courses of the saccade and
stimulus presentation. B, C, The activity traces of the head-centered output neurons in Xh and the retinal input neurons in Xr decay during the stimulus gap. When the
stimulus reappears, around the time of accumulation onset (vertical blue line), all peri-saccadic perturbations in the activities are gone. D, E, Activities of XePC and XeCD
neurons are identical to those in the 0 ms gap condition (Fig. 6). (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of
this article.)
possible to assign each subject a model threshold which explains
the subjects’ data well across all experiments. To this end, we com-
pared each subject’s performance with each threshold’s perfor-
mance separately for all experiments using the mean square
error (Fig. 10). Indeed we found that subjects could be assigned
with at least a range of likely thresholds. For example, subject OS
shows a performance similar to the model with a threshold of
0.6–0.7. Subject AM is close to thresholds of 0.7–0.8 except for
experiment II with 250 ms gap. However, in that experiment all
subjects’ and all thresholds’ performances are almost identical any-
way. Subjects TM and CE are both close to smaller thresholds and
subject CK is similar to a threshold of 0.8. In sum, at least part of
the variability among the subjects can be well explained by a dif-
ferent integration threshold.

A. Ziesche et al. / Vision Research 138 (2017) 1–11
9
Fig. 8. Comparison of subject performance and model performance. Dotted lines are subjects (replotted from Deubel et al., 1996), solid lines are model performances for
different thresholds in the decision process. A, Experiment I. B, Experiment II with no gap. The data points marked by circles indicate the decisions which are detailed in Fig. 9.
C, Experiment II with a 250 ms gap. D, Experiment III. E, Experiment IV.
Fig. 9. Activity traces of the decision neurons for SSD simulations with 0 ms gap and 0° jump and different decision thresholds (0.3, 0.6, and 0.9 in panels A, B, and C
respectively). The colored circles at the top indicate to which data point in Fig. 8B the decisions lead. Each panel shows activity traces of all 100 trials. Blue lines are the
activities of the neuron representing a forward jump decision, red lines are neurons representing a ‘backward jump’ decision. The horizontal grey line is the decision
threshold. Once either neuron’s activity exceeds the threshold, it wins the trial, indicated by a circle in the color of the winning neuron. After that, the trial ends. (For
interpretation of the references to colour in this figure caption, the reader is referred to the web version of this article.)
However, a parameter that directly counteracts with the deci-
sion threshold is the speed of the accumulation process. Thus, a
variation of the strength of the CD signal (cCD in Eq. 14 of
Ziesche & Hamker, 2011) leads to a similar effect. Lowering a
threshold is similar to speeding up the accumulation process by
a stronger CD signal. Thus, behavioral data can not dissociate a
variation of the decision threshold from a variation of the speed
of the accumulation process.
4. Discussion
Saccadic suppression of displacement (SSD) has been explained
at different levels of abstraction. The object reference theory
(Bridgeman, 2007; Deubel et al., 1996) assumes a built in assump-
tion of visual stability. It proposes a post-saccadic spatiotemporal
window around the saccade target in which displacements of the
target are tolerated without noticing any instability. This theory

10
A. Ziesche et al. / Vision Research 138 (2017) 1–11
Fig. 10. Comparison of subjects with model thresholds for each panel of Fig. 8. Each panel shows a matrix in which each entry indicates the mean squared error (MSE)
between the subject’s psychometric and the particular model’s psychometric curve. Black indicates a low MSE. The typical range of best-fitting thresholds for each subject is
the same across all experiments. Panels correspond to the same experiments as in Fig. 8. White rows indicate experiments in which the subject did not participate.
explains the target blanking effect as follows: because the target
could not be found after the saccade, the assumption of stability
is broken, and displacements become visible. How such proposed
mechanisms may be implemented in the brain has not been dis-
cussed further.
The model can also explain the target blanking effect in which dis-
placements become apparent when the target is blanked after the
saccade: In this case, no stabilization occurs because the peri-
saccadic network dynamics have been ceased. In addition, the pro-
pioceptive signal and thus the gain fields have fully updated to the
present fixation position. In the case of target blanking before the
saccade the activity of the target stimulus only slowly decreases
in the network due to feedback connections. Thus, depending on
the length of the blanking, it influences the peri-saccadic network
activity to a varying amount. Our model is fully self-consistent and
it does not require to make particular distinctions between the
blanking and non-blanking cases. Moreover, it provides a simple
explanation of the pre-gap effect in terms of network perturbations
which need about 100 ms to decay. Its explanation of SSD is dis-
tinct from the object reference theory since it rather relies on
transsaccadic integration than on an explicit object reference. In
contrast to the theory of optimal trans-saccadic integration our
model does not need to make any assumptions about a priori prob-
ability distributions. Rather the observed effects in SSD emerge
naturally from the time courses of the involved signals, which
are grounded on physiological data.
Optimal trans-saccadic integration (Niemeier et al., 2003) for-
malized some of the above ideas in a Bayesian framework and sug-
gested that peri-saccadic perception represents the optimal
solution to the integration of noisy visual and extraretinal signals.
One drawback, however, is the need for explaining the post-
saccadic blanking effect by a change in the prior probability den-
sity distribution, which is a free parameter. Atsma et al. (2016) pro-
posed a slightly different Bayesian model which not only integrates
but also separates the pre-and post-saccadic stimulus representa-
tions. This model has not been directly tested on the blanking
effect, but generally tuned to combine the pre-and post-saccadic
representations of stimuli. However, the model has no internal
spatio-temporal representation of the stimuli as this is beyond
the mathematical formalism used.
Our model is the first that explains the SSD effect on a neural
basis by simple dynamic properties of the visual system: the
displacement is not perceived since the network activity of the dis-
placed stimulus interacts with the network dynamics of peri-
saccadic updating which stem from the pre-saccadic stimulus,
the corollary discharge, and proprioceptive eye position informa-
tion. The head-centered representation of pre-saccadic stimulus
feeds back to the incoming displaced stimulus response and stabi-
lizes the representation in the presence of small displacements.
Our comparison of model simulation results to the experimen-
tal results lead to an experimentally testable prediction. As the
subjects’ performance co-varies with the decision thresholds, fas-
ter decisions (i.e. induced by lower thresholds) should lead to a for-
ward bias in the psychometric curves. Other parameters in
isolation do not account for such a variation. However, we cannot
rule out that the combined effects of multiple parameters may lead

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Acknowledgements
This research has been supported by the Federal Ministry of
Education and Research within the grant ‘‘Visuospatial Cognition”
(BMBF 01GW0653) and partly within the program ‘‘US-German
collaboration on computational neuroscience” (BMBF 01GQ1409).
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