Anthony Strock

Nicolas P Rougier

Xavier Hinaut

Latent space exploration and functionalization of a gated working memory model using conceptors

Introduction. Working memory is the ability to maintain and manipulate information. We introduce a method based on conceptors that allows us to manipulate information stored in the dynamics (latent space) of a gated working memory model. Methods. is la er model is based on a reservoir: a random recurrent network with trainable readouts. It is trained to hold a value in memory given an input stream when a gate signal is on and to maintain this information when the gate is o . e memorized information results in complex dynamics inside the reservoir that can be faithfully captured by a conceptor. Results. Such conceptors allow us to explicitly manipulate this information in order to perform various, but not arbitrary, operations. In this work, we show (1) how working memory can be stabilized or discretized using such conceptors, (2) how such conceptors can be linearly combined to form new memories, and (3) how these conceptors can be extended to a functional role. Conclusion. ese preliminary results suggest that conceptors can be used to manipulate the latent space of the working memory even though several results we introduce are not as intuitive as one would expect.

Introduction

A recent and major enhancement of the Reservoir Computing (RC) paradigm has been proposed by Jaeger (2014) and Jaeger (2017) under the form of conceptors which are able to capture the subspace of internal states of a Recurrent Neural Network (RNN). In the case of Echo State Networks (ESN), conceptors can be used to capture the trajectory of reservoir states when the reservoir is fed with a particular input pa ern (see gure 1).

ese conceptors allow to extend the capacity of the original ESNs by taking advantage of these new representations. For example, (Jaeger, 2014;[START_REF] Bao | Action recognition based on conceptors of skeleton joint trajectories[END_REF][START_REF] Bartle | Recognizing Human Internal States: A Conceptor-Based Approach[END_REF]Gast et al., 2017) showed how to use them for the recognition of temporal sequences while using them for the storage and retrieval of multiple temporal sequences. More recently, Mossakowski, Diaconescu, and Glauer (2019) proposed an implementation of fuzzy logic based on conceptors, while Liu, Ungar, and Sedoc (2019) used conceptors for online learning of sentence representations, and He and Jaeger (2018) proposed a general way to use conceptors during the learning of multiple tasks.

Conceptors yield several advantages when compared to classical reservoirs since Jaeger (2014) demonstrated that conceptors can be used for performing symbolic operations in the latent space of the di erent input pa erns. Such symbolic operations have been already exploited in the framework of deep learning community and they provide impressive results. For instance, in natural language processing (NLP), Mikolov et al. (2013) showed that arithmetic operations such as "king -men + woman" give a vector similar to "queen". More recently, [START_REF] Brock | Neural photo editing with introspective adversarial networks[END_REF] proposed a method to edit global image features based on operations performed on the latent space of generative adversarial networks (GANs). Conceptors provide similar logical operations in the framework of the reservoir computing paradigm. For instance, Jaeger (2014) proposes an operator that quanti es if a stimulus is similar to an already known conceptor. By associating one conceptor per class, it is possible to measure if a stimulus belongs to a class (positive evidence) or none (negative evidence). Beyond logical operations, linear combinations of conceptors allow to implement continuous morphing between set of states: they were used to create morphing between two time series corresponding to the extended interpolation of the time series (e.g. a morphing between two sine-waves with di erent frequencies is a sine-wave with an intermediate frequency). is capacity of performing operations in the latent space resonates strongly with the notion of working memory (WM) as found in neuroscience. It is generally de ned as the capacity to hold information for a short period of time as well as the capacity to manipulate this information in order to achieve some task or to reach a speci c goal. In this context, we have introduced in (Strock, Hinaut, and Rougier, 2020) a reservoir with feedback connections that implements a gated working memory, i.e. a generic mechanism to maintain information at a given time (corresponding to when the gate is on, see gure 3). In this model, the memory is encoded in the dynamics of the reservoir and information can be maintained without any sustained activity.

is absence of sustained activity is precisely what makes it di cult to manipulate the underlying information and this is also the reason why some authors (Mongillo, Barak, and Tsodyks, 2008;Stokes, 2015;Masse et al., 2019;Manohar et al., 2019) have suggested the existence of a mechanism to temporarily store information in synaptic weights. In this context, conceptors provide a plausible explanation for such a transfer as well as an explicit method for manipulating information; even if the conceptor mechanisms are for the moment not as biologically plausible as the reservoirs themselves.

In this article, we explore the nature of operations carried on by such conceptors and explore the different ways to combine them such as to explicitly manipulate memories. Even though the results we introduce in this article are preliminary and to some extents, counter-intuitive, this leads us to consider the notion of functional conceptors that would allow to arbitrarily manipulate working memory in the latent space.

Methods

Conceptors overview

Considering an ESN R that has been trained1 to produce the sequence O 1 when presented with input sequence I 1 , Jaeger (2014) demonstrated that it is possible to build an ESN R * that will spontaneously produce the sequence O 1 , in the absence of any input (see Figure 1). e activity of this new R * can be decoded using the read-out weights of R. is is actually similar to the principle of the full-FORCE method introduced in (DePasquale et al., 2018) where internal weights are trained to match the internal activity of a teacher network receiving the desired output as input. However, Jaeger (2014) principle is applicable to multiple input pa erns with the assumption that each input pa ern makes the reservoir evolve in a separable region of the internal high dimensional space. In order to build R * , he proposed to approximate the activity of R when it receives any of these input pa erns. en he equips R * with a set of recurrent connections (i.e. the conceptors) that are speci c to each couple of input/output and that will project the internal state into the relevant sub-space. Jaeger (2017) shows in particular how these conceptors can be considered as long-term memories for temporal pa erns. Conceptors can store temporal pa erns and reactivate them later with negligible loss of recall/precision. More generally, conceptors can be considered as long-term memories of internal states subspaces.

Models

Echo State Networks (ESN)

In this work we consider Echo State Networks (ESN) with feedback from readout units to the reservoir (Jaeger, 2001). e system is described by the following update equations:

x[n] = tanh (W in u[n] + W x[n -1] + W f b y[n -1]) + ξ y[n] = W out x[n]
where u[n], x[n] and y[n] are respectively the input, the reservoir and the output at time n. W , W in , W f b and W out are respectively the recurrent, the input, the feedback, the output weight matrices and ξ is a uniform white noise term added to reservoir units.

Controlling ESN dynamics using a conceptor

Following (Jaeger, 2014) notations, the equation for a conceptor C enforcing some particular dynamics can be wri en as:

x[n] = C tanh (W x[n -1] + b)
where C is the conceptor (possibly changing over time), x[n] is the state of the model at time n, W is the recurrent matrix and b is a constant bias. is can be extended to the general case where we also have an input u[n] (with input matrix W in ) (or similarly a feedback), and writes: Using a conceptor C is similar to a change of W in W = W C (and W out in W out C if there is feedback).

x[n] = C tanh (W x[n -1] + W in u[n] + W f b y[n -1]) y[n] = W out x[n] I 1 Input R R* I 1 Input I 2 Input O 2 Output O 1 Output O 1 Output O 1 Output A ? Output B I 1 Input I 2 Input O 2 Output O 1 Output C O 2 Output O 1 Output C 1 C 2 W R W R W R W R W R W R W R W R W R Figure 1.
In our implementation, we thus consider:

x[n] = tanh ((W + W f b W out ) C x[n -1] + W in u[n]) y[n] = W out x[n]

Computing conceptors

In order to compute a conceptor for some given dynamics, it is necessary to collect all the states of the reservoir and to concatenate them in a matrix X. e conceptor C is then de ned as:

C = XX T XX T + α -2 I -1 = R R + α -2 I -1
where R = XX T is similar to a covariance matrix, and α (a.k.a the aperture) controls how close from the identity matrix C is.

Aperture adaptation

Intuitively, the aperture of a conceptor controls the precision of the internal states representation. However, no information on internal states is lost, because it is possible to change the aperture of a conceptor C without the need to recompute the conceptor from scratch. To change the aperture, one only need to adapt the conceptor C as follows:

φ(C, γ) = C C + γ -2 (I -C) -1
where φ(C, γ) represents the same states than C with a di erent aperture, and γ is controlling how the aperture is modi ed. Intuitively, φ(C, γ) modi es the aperture of C by a factor of γ.

Linear combination

Given two conceptors C and B and λ ∈ R, the linear combination of conceptor C and B is de ned as:

C = λC + (1 -λ)B
In the following when λ ∈ [0, 1] we will talk about interpolation, when λ > 1 about right-extrapolation, and when λ < 0 about le -extrapolation.

Boolean operations

Boolean operations can be wri en as:

C ∨ B = I + C(I -C) -1 + B(I -B) -1 -1 -1 C ∧ B = C -1 + B -1 -I -1 ¬C = I -C
However, as highlighted in (Mossakowski, Diaconescu, and Glauer, 2019), ∨ and ∧ are not idempotent (i.e. C ∨ C = C and C ∧ C = C). More precisely if C (resp. B) is a conceptor built with the covariance matrix R (resp. Q), Jaeger proposes to build C ∨ B using the covariance matrix R + Q that is by design not idempotent. What we propose here is to consider instead the matrix βR

+ (1 -β)Q with β ∈ [0, 1] instead of R + Q, or if we want it to be symmetric (R + Q)/2. Similar calculation gives the following new ∨ β and ∧ β . C ∨ β B = I + βC(I -C) -1 + (1 -β)B(I -B) -1 -1 -1 C ∧ β B = βC -1 + (1 -β)B -1 -1
is way of building the OR operation also has a data driven intuition. If we note β = n n+p where n (resp. p) is the number of data points used to build R (resp. Q) then bR + (1 -b)Q is the "correlation matrix" obtained by taking the union of all the data points. Moreover, if we choose β = 0.5 then there is a direct link between the two ways of de ning the OR operator: C ∨ B = φ(C ∨ 0.5 B, 2). In this study, the aperture was mostly not in uencing the results, thus we show only the results for ∨.

Gating task

We consider the gating task described in (Strock, Hinaut, and Rougier, 2020). In this task the model receives an input V that is continuously varying over time and another input being either 0 or 1 (trigger or gate T ). To complete the task, the output has to be updated to the value of the input when the trigger is active and to remain constant otherwise (similarly to a line a ractor). In other words, the trigger acts as a gate that controls the entry of the value in the memory (the output). Figure 2 describes this task.

Value (V) Trigger (T) Output (M)

Gated Working Memory Reservoir

We consider a reservoir with feedback from readout units to the reservoir (see Figure 3). In (Strock, Hinaut, and Rougier, 2020) we showed that this gated working memory reservoir is able to learn to robustly gate information in presence of noise and of a distracting input.

e model behaves as a line a ractor even if few values are used for training (about 10 values is enough). We also provided a minimal model version and showed an equivalence with GRU (Gated Recurrent Unit) cells [START_REF] Cho | Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation[END_REF], which are a simpli ed version of Long-Short Term Memory (LSTM) cells.

Implementation details

We consider a reservoir of 1000 neurons that has been trained to solve a gating task described in Figure 2 A. e overall dynamics of the network we consider are described by the following equations:

x[n] = tanh ((W + W f b W out ) C x[n -1] + W in u[n]) + ξ y[n] = W out x[n]
where u[n], x[n] and y[n] are respectively the input, the reservoir and the output at time n. W , W in , W f b , W out and C are respectively the recurrent, the input, the feedback, the output and the conceptor weight matrices and ξ is a uniform white noise term added to reservoir units. W , W in , W f b are uniformly sampled between -1 and 1, and le untrained. Only W is scaled to have sparsity level equal to 0.5 and a spectral radius of 0.1. If not stated otherwise, the noise is selected uniformly between -10 -4 and 10 -4 . e major di erence with Jaeger's proposal in the way the pa erns are stored is that in our case patterns are stored implicitly when solving the gating task. In other words, the pa erns are stored by training W out and not by explicitly recomputing an internal weight matrix. However as mentioned in (DePasquale et al., 2018), training W out when there is a feedback is equivalent to recomputing the internal weight matrix W as

W * = W + W f b W out .
When W out is computed to solve the gating task, the conceptor C is considered to be xed and equal to the identity matrix (C = I). W out is trained for 25,000 time steps. At each time step there is a 0.01 probability of having a trigger and the input value (V) is uniformly randomly sampled between -1 and 1. During training, the average holding time of the value in memory is therefore about 100 time steps.

A er training, in normal mode, the conceptor C is equal to a conceptor C m that is generated and associated to a constant value m. In order to compute this conceptor C m , we impose a trigger (T = 1) as well as an input value (V = m) at the rst time step, such that the reservoir has to maintain this value for 100 time steps. During these 100 time steps, we use the identity matrix in place of the conceptor.

e conceptor C m is then computed according to

C m = XX T XX T + I a -1
, where X corresponds to the concatenation of all the 100 reservoir states following the trigger, each row corresponding to a time step, I the identity matrix and a the aperture. In all the experiments the aperture has been xed to a = 10. For the conceptors pre-computed in Figure 4 and 6, the reservoir have been initialised with its last training state.

Results

Constant-memory conceptors

e idea behind what we named constant-memory conceptors is to capture explicitly the dynamics of a reservoir maintaining a value and to use this conceptor to later constrain the dynamics of any reservoir, inducing an alternative memory in the output as represented on gure 4. In order to build a constantmemory conceptor C m , we consider the gated reservoir working memory model that receives a trigger and an input value m at time t = 0. We collect the states of the reservoir for 100 iterations from which we build the conceptor C m and apply it immediately to the model. Results of this procedure is shown on gure 4B where ve conceptors are built (gray bands) and applied immediately (white bands) without noticeable modi cation on the output of the reservoir since the actual dynamics and the dynamics stored in the conceptor are congruent. On gure 4A, we used the same procedure to build a set of 11 conceptors whose captured dynamics correspond to 11 values uniformly spread between -1 and +1. On gure 4C, a er 100 iterations following the presentation of a new value, we apply the closest conceptor (Frobenius norm, inducing a distance between conceptors) from the previous set of 11 constant-memory conceptors. One can see that on gure 4C that the input value is rst maintained (grey band) and jumps rapidly to the closest discretized value when the conceptor is actually applied and constrained the dynamics. ese constant-memory conceptors also exhibit a nice property regarding the long term maintenance of a memory. e initial gated working memory model is already quite robust regarding the long term maintenance of memory in the absence of internal noise (i.e. inside the reservoir). When it is trained for a few hundreds of time steps, it is able to maintain a memory for several thousands of time steps (see gure 5A) before the memory starts to slowly degrade. When conceptors are applied, this slow degradation vanishes ( gure 5B): the RMSE without conceptor is of 4.21e-02 ± 1.84e-02 (mean ± std) whereas with conceptors it is 1.02e-03 ± 6.95e-04. In the presence of internal noise (inside the reservoir), the initial gated working memory model is much less robust and memory starts to degrade a er only a few thousand time steps (see gure 5C). More precisely, a 10 -4 noise (std(ξ) = 10 -4 ) prevents the model to maintain a value for a much longer time than the time that has been used to train it ( gure 5C). However, when conceptors are applied, their bene t is even more obvious: a er one hundred thousand time steps, without conceptor the memory converge towards a few values, whereas with conceptors the memory remains( gure 5D). e RMSE without conceptor becomes 1.39e-01 ± 7.66e-02 (3.3 times greater than without noise), whereas the RMSE with conceptors becomes 2.85e-03 ± 1.98e-03 (2.8 times greater than without noise).

Linear interpolation of constant-memory conceptors

In Figure 6, we show two main ideas: (1) how a linear interpolation between two conceptors can allow to generalize the gating of other values, and (2) a representation of the space in which lies the conceptors and their link to the memory they encode.

(1) Interpolation and extrapolation C of conceptor C 0.1 and conceptor C 1.0 has been computed as C = λC 1.0 + (1 -λ)C 0.1 with 31 λ values uniformly spread between -1 and 2. Even though the interpolated (λ ∈ [0, 1]) conceptors obtained are not exactly equivalent to C m conceptors obtained in Figure 4, they seem to also correspond to a retrieved memory value that is maintained. e mapping between λ and the value is non-linearly encoded. For rightextrapolation (λ ∈ [1, 2]) the conceptor seems to be linked to a noisy version of a C m conceptor: the output activity is not constant, but its moving average is constant. For le -extrapolation (λ ∈ [-1, 0]), the conceptor obtained does not seem to encode any information anymore: all the output activities collapse to zero. (2) Principal Component Analysis (PCA) have been performed using 201 pre-computed conceptors associated to values uniformly spread between -1 and 1. e rst three components already explain approximately 85% of the variance.

e rst component seems to non-linearly encode the absolute value of the memory (Figure 6B) whereas the second component seems to non-linearly encode the memory itself (Figure 6C). e curved line composed of conceptors C m (Figure 6E-G) shows visually why the extrapolation does not work as we expected.

Functional conceptors

In this section, we show three examples where conceptors have a functional role: (1) constantmemory conceptors when triggers are received, (2) a conceptor enforcing triggers, and (3) the con-junction/disjunction of constant-memory conceptors. By functional we mean that conceptors do not only store and reactivate a dynamical pa ern. Conceptors can do much more than constrain the dynamics in an a ractor. Conceptors can also constrain the dynamics in a space where the behavior is input-dependent, i.e. the outputs are some function of the inputs.

Constant-memory conceptors when triggers are received. When a constant-memory conceptor C m is applied to the gated working memory model, it seems to quickly force the output y to match the value m, making it insensitive to the input value. However, the actual behavior is a bit di erent as illustrated on gure 7. On this gure, we can observe that the readout value of the resevoir under the in uence of a conceptor C 0.5 is destabilized when a trigger occurs. More precisely, the trigger induce an instanteneous readout equal to the input until quickly relaxing to the constant value of the conceptor (0.5).

is con rms that the combination of a reservoir and a constant-memory conceptor remains sensitive to the input. Said di erently, a constant-memory conceptor C m is not the mere storage of the value m but rather a function that constrains the dynamics of the reservoir such that when applied, the readout will eventually read m a er some time. Conceptor enforcing triggers. is functional aspect of conceptor can be further illustrated by building the following conceptor C T : during 100 time steps, the reservoir receives constant triggers (T = 1) and has therefore to follow the value (V) it receives as input. Conceptor C T is constructed from the states taken by the reservoir during these 100 time steps. Figure 8 shows what happens when this conceptor is subsequently applied: independently of the trigger signal, the output of the reservoir follows the input. Everything happens as if the reservoir was receiving a continuous trigger signal and the conceptor acts as a pass-through lter that modi es the behavior of the gated working memory as a whole (instead of modifying each individual value). is result suggests that conceptors may probably be extended to store arbitrary functions that act in the latent space of the reservoir. We do not know yet how to specify such arbitrary functions inside a conceptor, but the preliminary results we introduced are encouraging even though more theoretical work is needed.

Conjunction/disjunction of constant-memory conceptors.

e last example where we show this functional aspect of conceptors is the disjunction of conceptors. a trigger occurs the output jumps towards the value v to be maintained and then relaxes to another value that depends on v.

In Figure 9, we show the values towards which the output relaxes (i.e. relaxation values) when the disjunction of two constant-memory conceptors is applied. First, as the disjunction of twice the same conceptor C m ∨ C m is either equivalent to the same conceptor or to an aperture adaptation of it (i.e.

C m ∨ C m = φ(C m , 2) and C m ∨ β C m = C m )
, the value towards which the disjunction C m ∨ C m relaxes is the value of the conceptor itself (i.e. m). en, we realized that we could predict what would be the relaxation values in di erent cases: in general the relaxation value was mostly either almost zero or the maximum of the absolute values of the two conceptors multiplied by the sign of the new value to be maintained. We propose the following formula to predict the value towards which C m 1 ∨ C m 2 relaxes:

v relax (m 1 , m 2 , v) =            m 1 if m 1 = m 2 sign(v) × max(|m 1 |, |m 2 |) if min(|m 1 |, |m 2 |) < |v| or m 1 = -m 2 0 otherwise (1)
where v is the initial value (V ) proposed along with the trigger, m 1 (resp. m 2 ) is the constant associated to conceptor m 1 (resp. m 2 ), v relax (m 1 , m 2 , v) is the ultimate value reached while applying conceptor C m 1 ∨C m 2 . Said di erently, the conceptor C m 1 ∨C m 2 implements a conditional assignment (modulo the sign): if the input value at time of trigger is bigger than the minimum between m 1 and m 2 then it will converge towards the maximum of m 1 and m 2 , otherwise it will converge towards 0. e predictions made by the formula are less accurate for extreme values such as for v = 1.00 (see Figure 9).

We hypothesize a similar formula for relaxation values of n constant-memory conceptors:

v relax (m 1 , ..., m n , v) =                m 1 if m 1 = ... = m n sign(v) × max(|m 1 |, ..., |m n |) if min(|m 1 |, ..., |m n |) < |v| or (∀i, j |m i | = |m j | and ∃i, j such that i > j and m i = -m j ) 0 otherwise
where v is the initial value (V ) given along with the trigger, m i is the constant associated to conceptor

C m i , v relax (m 1 , m 2 , ..., m n , v) is the ultimate value reached while applying conceptor n i=1 C m i .
to another constant-memory conceptor. Nevertheless, we have shown empirically that in all scenarios a linear combination of two constant-memory conceptors lead to a value that is maintained. However, this new memory is slightly oscillating around the combination of the constant values (see Figure 6). is oscillation being a direct consequence of the perturbation of the system (i.e. the input).

Moreover, the disjunction of constant-memory conceptors gives an example of functional conceptor. However, it does not implement what we expected. In the case of two conceptors with two constant values v 1 and v 2 such that 0 ≤ v 1 ≤ v 2 , we would expect that the disjunction encodes the two values simultaneously. More speci cally, we expected such disjunction to implement a choice function (i.e. a conditional assignment) between the two values stored in each conceptor. Instead, the disjunction implements another conditional assignment, that does not converge towards v 1 but only towards 0 or v 2 depending on the given input value. To some extent, v 1 and v 2 in uence the disjunction with di erent qualitative roles. Moreover, in the low rank case (i.e. when the recurrent weights are the sum of a low rank matrix and a random perturbation) only the largest xed points can be stable (Schuessler et al., 2020). erefore, we can hypothesize that in the general case of a disjunction of n > 2 constantmemory conceptors, only the extreme value ma er in the composite conceptor.

Even though our results are preliminary and will require more work to fully characterize how operations can be composed intuitively, this work opens the door to another form of working memory: a procedural (or functional) working memory. Instead of temporarily memorizing declarative information, this kind of working memory would be able to memorize procedural information (e.g. how a task should be performed, which processes should be applied, etc.). For instance, imagine you are given some instructions which are to sum up a series of numbers. In order to complete this task, it is necessary to keep track of the current sum (e.g. in a classical short-term declarative working memory) that needs to be updated each time a new number is given. However, it is also necessary to remember the preliminary instruction (i.e summing up) in another form of working memory that needs to span the whole experiment and which is procedural in nature. is procedural nature makes this working memory quite peculiar because instead of memorizing a given information, it needs to memorize a procedure -here, a sequence of operations depending on the context -that needs to be applied each time an input is given. It is not yet clear how such memory could be encoded in the brain (e.g. sustained activity, dynamic activity, transient weights) and we think conceptors might be key in answering such a question, but more experimental and theoretical work will be needed. Similar conceptors than the ones we computed with our gated working memory reservoir model are likely to be computed with other working memory models (Lim and Goldman, 2013;Nachstedt and Tetzla , 2017;[START_REF] Bartle | Recognizing Human Internal States: A Conceptor-Based Approach[END_REF]: it would be interesting to see whether the functional conceptors obtained are similar (i.e. our results would be generally applicable), or on the contrary, if di erences occur.

Compliance with Ethical Standards

Authors declare they have no con ict of interest. Ethical approval: is article does not contain any studies with human participants or animals performed by any of the authors.

Figure 2 .

 2 Figure 2. Gating task. Each column represents a time step (time increases from le to right), colored discs represent inputs (V and T ) and the output (M ).

ξ

  Figure 3. e Gated Working Memory Reservoir model The reservoir receives a random signal V in [-1, +1] and a trigger signal T in {0, 1}. The output M is fed back to the reservoir.

Figure 4 .

 4 Figure 4. Approximation with conceptors and discrete conceptors. In A, B and C the model receives the same inputs across time. Black lines: Evolution of the reservoir readout y. Each black line in A. represents a di erent trial where a di erent conceptor is applied. Gray lines: the discrete value considered for each conceptor. Light gray areas: time period when conceptors are computed for the current value. A. Di erent trials showing various discrete conceptors applied. B-C. Conceptors C m are computed using the 100 time steps following a trigger while C = I (light gray areas). B. The conceptor C m is directly applied during the 400 following time steps. C. The closest conceptor among the discretized conceptor is applied during the 400 following time steps. Dashed lines represents the memory that should have been kept if not discretized.

Figure 5 .

 5 Figure 5. Stability comparison with or without conceptor, with or without noise. Black: Evolution of the readout y. lines: the discrete value considered. Light areas: time when conceptors are computed for the current value. A-B No noise. C-D 0.0001 noise. A and C No conceptor used. B and D Discrete conceptor are applied.

Figure 6 .

 6 Figure 6. Generalisation of constant-memory conceptors m . Red: two constant-memory conceptors: C 0.1 and C 1.0 . Black: Inferred conceptors, i.e. linear interpolation and extrapolation between C 0.1 and C 1.0 . A Temporal evolution of the readout for di erent conceptors. B-G : constant-memory conceptors C m for 201 values of m uniformly spread between -1 and 1. B-D Link between principal components of the conceptors and the memory they are encoding. For the interpolated conceptors, the memory is considered as the mean in the last 1000 time steps. E-G Representation of the conceptors in the three principal components of the C m conceptors.

Figure 7 .

 7 Figure7. Influence of trigger with constant-memory conceptors. A constant-memory conceptor C 0.5 is applied while receiving several triggers. Gray: the input value (V). Black: Evolution of the readout y. When a trigger occurs (indicated by dots on the Ticks line) the readout transitorily goes to the current input value before going back to the value memorized by the conceptor.

Figure 8 .

 8 Figure8. Pass-through conceptors. This conceptor is able to modify the behavior of the gated working model by le ing all the values to pass through the reservoir up to the output, independently of the gating signal (time steps 1000 to 1500). Black: Evolution of the readout y. Gray: the input value (V). Light gray areas: no conceptor is applied (i.e. C = I). White areas: the conceptor simulating a constant trigger is applied (i.e. C = C T ), thus the input is redirected to the output.

  Conceptors general idea A Considering an ESN R that outputs the sequence O 1 when an input I 1 is presented, it is possible to build an ESN R * that spontaneously outputs the sequence O 1 in the absence of any input. B Considering an ESN R that respectively outputs the sequences O 1 and O 2 when input I 1 and I 2 are presented, it is not possible to define R * as in A since we cannot define the expected output in the absence of input. C Considering an ESN R that respectively outputs the sequences O 1 and O 2 when input I 1 and I 2 are presented -with the supplementary conditions that the inner representation corresponding to inputs I 1 and I 2 are separable -it is possible to build an ESN R * equipped with a set of feedback weights C 1 or C 2 such that

o ine with ridge regression

We also studied how the conjunction constant-memory conceptors were in uencing the dynamics.

If the disjunction of conceptors is similar to a union (or sum), then the conjunction of conceptors is similar to an intersection. Moreover, as the memory is represented as the output, the memory cannot be simultaneously the value m and the value m present. It is thus harder to predict what would be the behavior of such conceptor. In practice, as for the disjunction, when a trigger occurs the output jumps towards the value v to be maintained and then relaxes to another value. However, in that case the value towards which it relaxes is easy to describe, it is always almost zero. e conjunction of constant-memory conceptors acts therefore as C 0 .

Discussion

Conceptors are powerful tools for performing explicit operations in the latent space of a reservoir even though the composition of such operations remains a di cult task. Using a reservoir model of gated working memory, we have shown another way to enforce a particular memory through the use of adhoc conceptors. ese constant-memory conceptors therefore provide a synaptic form to the memory, and we have shown how they can be used to stabilize or discretize the memory. However, the e ect of conceptors composition is counter-intuitive and largely di ers from what we would naturally expect.

For instance, we have seen that the linear interpolation of constant-memory conceptors does not create another constant-memory conceptor, or at least it does not correspond to one we would have computed.

e reason being that the space of constant-memory conceptors is not a straight line. Hence, they cannot be linearly interpolated: a mere linear combination of constant-memory conceptors could not lead


Audrey Stoessel

Nadja Groysbeck

Lucile Guyot

Lina Barret

Yves Nominé

Leonel Nguekeu-Zebaze

Ambre Bender

Laetitia Voilquin

Thomas Lutz

Nikita Pallaoro

Marie Blocat

Celia Deville

Murielle Masson

Guy Zuber

Bruno Chatton

Mariel Donzeau
email: mariel.donzeau@unistra.fr

Modular conjugation of a potent Anti-HER2 immunotoxin using co-associating peptides

Keywords: immunotoxin, co-assembly, peptide, HER2, cytotoxicity

Immunotoxins are emerging candidates for cancer therapeutics. These biomolecules consist of a cell targeting protein combined to a polypeptide toxin.

Associations of both entities can be achieved either chemically by covalent bonds or genetically creating fusion proteins. However, chemical agents can affect activity and/or stability of the conjugate proteins and additional purification steps are often required to isolate the final conjugate from unwanted by-products. As for fusion proteins, they often suffer from low solubility and yield.

In this report, we describe a straightforward conjugation process to generate an immunotoxin using co-associating peptides (named K3 and E3), originating from the tetramerization domain of p53. To that end, a nanobody targeting the human epidermal growth factor receptor 2 (nano-HER2) and a protein toxin fragment from Pseudomonas aeruginosa Exotoxin A (TOX) were genetically fused to the E3 and K3 peptides. Entities were produced separately in E. coli in soluble forms and at high yields. The nano-HER2 fused to the E3 or K3 helixes (nano-HER2-E3 and nano-HER2-K3) and the co-assembled immunotoxins (nano-HER2-K3E3-TOX and nano-HER2-E3K3-TOX) presented binding specificity on HER2 overexpressing cells with relative binding constants in the low nanomolar to picomolar range. Both toxin modules (E3-TOX and K3-TOX) and the combined immunotoxins exhibited similar cytotoxicity levels compared to the toxin alone (TOX). Finally, nano-HER2-K3E3-TOX and nano-HER2-E3K3-TOX evaluated on various breast cancer cells were highly potent and specific to kill HER2-overexpressing breast cancer cells with IC 50 values in the picomolar range. Altogether, we demonstrate that this non-covalent conjugation method using two co-assembling peptides can be easily implemented for modular engineering of immunotoxins targeting different types of cancers.

INTRODUCTION

The human epidermal growth factor receptor 2 (HER2) is a cell surface receptor overexpressed in about 15-20% of breast cancers. Amplification of HER2 is associated with tumor invasion and metastasis. Introduction of an anti-HER2 therapy using the humanized monoclonal antibody trastuzumab targeting specifically the extracellular domain of HER2 has largely improved patient care. [START_REF] Romond | Trastuzumab plus adjuvant chemotherapy for operable HER2-positive breast cancer[END_REF] However, intrinsically or acquired resistance has restricted the success of the trastuzumab. [START_REF] Heyde | mRNA Profiling Reveals Determinants of Trastuzumab Efficiency in HER2-Positive Breast Cancer[END_REF][START_REF] Chakrabarty | Trastuzumab-Resistant Cells Rely on a HER2-PI3K-FoxO-Survivin Axis and Are Sensitive to PI3K Inhibitors[END_REF] Since two decades, new anti-HER2 therapies have been under investigation. One emerging therapeutic is immunotoxins, which combine the specific targeting of antibodies with the high cytotoxic properties of bacterial or plant protein toxins. [START_REF] Simon | Immunotoxin Therapies for the Treatment of Epidermal Growth Factor Receptor-Dependent Cancers[END_REF][START_REF] Kreitman | Immunotoxins for targeted cancer therapy[END_REF][START_REF] Wayne | Immunotoxins for leukemia[END_REF] Upon specific binding to extracellular receptors and receptor-mediated endocytosis, immunotoxins get internalization into target cells, where the toxin domain unfolds its effect. These therapeutic biomolecules have demonstrated excellent anti-cancer properties at very low concentrations due to the enzymatic activity of the toxin fragment, which lowers the amount of molecules needed to kill cancer cells. [START_REF] Tsuchikama | Antibody-drug conjugates: recent advances in conjugation and linker chemistries 1-14[END_REF][START_REF] Wolf | Pseudomonas exotoxin A: From virulence factor to anti-cancer agent[END_REF] One of the most widely used toxin fragments originates from Pseudomonas aeruginosa exotoxin A. It contains separate activities: a domain II for intracellular trafficking and a catalytic domain (domain III) inactivating the eukaryotic translation elongation factor 2 (eEF-2) by ADP-ribosylation. [START_REF] Michalska | Pseudomonas Exotoxin A: optimized by evolution for effective killing[END_REF] Immunotoxins can be produced as chimeric proteins. For instance, an affibody, an antibody mimetic molecule, directed against HER2 genetically fused to a modified exotoxin A fragment PE38 showed elevated cytotoxicity towards HER2 overexpressing cells. [START_REF] Amiri Tehranizadeh | The immunotoxin activity of exotoxin A is sensitive to domain modifications[END_REF][START_REF] Guo | HER2-targeted immunotoxins with low nonspecific toxicity and immunogenicity[END_REF] However, the weakness of such an approach is the expression level and the solubility issue of the recombinant immunotoxins. To overcome these problems, both the targeting and toxin moieties can be produced separately and are then chemically conjugated. [START_REF] Pirzer | Generation of Potent Anti-HER1/2 Immunotoxins by Protein Ligation Using Split Inteins[END_REF][START_REF] Lee | A chemical conjugate between HER2-targeting antibody fragment and Pseudomonas exotoxin A fragment demonstrates cytotoxic effects on HER2-expressing breast cancer cells[END_REF] For example, the scFv (single chain variable fragment) of trastuzumab and a minimal exotoxin A fragment (PE24) that were expressed independently and conjugated via a disulfide bond-containing linker, had strong cytotoxic effects on HER2 breast cancer cells. [START_REF] Lee | A chemical conjugate between HER2-targeting antibody fragment and Pseudomonas exotoxin A fragment demonstrates cytotoxic effects on HER2-expressing breast cancer cells[END_REF] But the drawback of such an approach is the use of reducing agents, leading to improper protein folding, and therefore lowering solubility and/or activities of the conjugate proteins.

Moreover, additional purification steps are required to isolate the desired conjugate from by-products present in the conjugation mixture. These additional purification steps often result in low yields and make the chemical conjugation a time-consuming and cost ineffective process.

In this study, we report a novel straightforward conjugation procedure based on co-assembly of a single chain antibody (nanobody or VHH) targeting HER2 receptor and a truncated variant of the exotoxin A from Pseudomonas aeruginosa via two peptides (named E3 and K3), originating from the tetramerization domain of p53 (residues 325-355). [START_REF] Brokx | A stable human p53 heterotetramer based on constructive charge interactions within the tetramerization domain[END_REF] These peptidic domains consist of a β-strand followed by a αhelix. The α-helical charged interface involving lysine and acid glutamic residues (E343, E346 and K351) modulates tetramer stability through salt bridges. Thus charge-reversal mutations at positions 343, 346 and 351 was previously shown to favor heterotetramerization. [START_REF] Brokx | A Stable Human p53 Heterotetramer Based on Constructive Charge Interactions within the Tetramerization Domain[END_REF] While E3 (variant E343, E346 and E351) associates solely into dimers through β-strand interactions, K3 (variant K343, K346 and K351) forms tetramers with low stability. However, when mixed together in equimolar amounts, these peptides associate exclusively into dimer of primary dimers. This non-covalent interaction between E3 and K3 peptides was demonstrated to be strong and specific enough to allow heterotetramerization of macromolecules inside living cells for the engineering of bifunctional bio-molecules. [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] Using this technology to coassemble a nanobody anti-HER2 with a truncated optimized fragment of the exotoxin A from Pseudomonas aeruginosa, we generate extremely stable heterotetrameric immunotoxins having a specific cytotoxic activity on HER2 positive breast cancer cells.

RESULTS

Design of the immunotoxin

We designed novel immunotoxins able to co-assemble via E3 and K3 peptides (Figure 1A andB). [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] We choose a nanobody targeting the extracellular domain of HER2 (henceforth referred to as nano-HER2). [START_REF] Kijanka | Rapid optical imaging of human breast tumour xenografts using anti-HER2 VHHs site-directly conjugated to IRDye 800CW for image-guided surgery[END_REF][START_REF] Hartmann | VHH characterization. Comparison of recombinant with chemically synthesized anti-HER2 VHH[END_REF] The nano-HER2 sequence was genetically fused to the N-terminal part of K3 sequence (Figure 1A). [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] The selected toxin module derives the Pseudomonas exotoxin A variant PE24, [START_REF] Hollevoet | In Vitro and In Vivo Activity of the Low-Immunogenic Antimesothelin Immunotoxin RG7787 in Pancreatic Cancer[END_REF][START_REF] Bauss | Characterization of a re-engineered, mesothelin-targeted Pseudomonasexotoxin fusion protein for lung cancer therapy[END_REF] where the intracellular trafficking domain has been replaced by a furin cleavage site (FCS) described elsewhere [START_REF] Kaplan | Protection of the Furin Cleavage Site in Low-Toxicity Immunotoxins Based on Pseudomonas Exotoxin A[END_REF] , and the B-cell epitopes and the protease-sensitive regions have been removed. [START_REF] Bauss | Characterization of a re-engineered, mesothelin-targeted Pseudomonasexotoxin fusion protein for lung cancer therapy[END_REF] This toxin part (hereinafter referred to as TOX) was then genetically fused to the C-terminal part of the E3 peptide (Figure 1A). The design of the immunotoxin was also carried out to obtain the opposite configuration, namely nano-HER2-E3 combined with K3-TOX, given rise to nano-HER2-E3K3-TOX (Figure 1B).

Production, yield and oligomeric states of the recombinant proteins

Recombinant VHH and TOX moieties were produced at high levels in E. coli (Figure S1A and S2A), and purified by immobilized metal affinity chromatography (IMAC) followed by a preparative size exclusion chromatography (SEC) (Figures S1B andC, and Figure S2B andC). Typical elution profiles revealed that the unfused nano-HER2 displayed a single peak with an apparent molecular weight of 21 kDa corresponding to a theoretical molecular weight of a monomer, while nano-HER2-E3

and nano-HER2-K3 behaved like a 63 kDa dimer and a 105 kDa tetramer, respectively (Figure 2A and Table S1). TOX constructs gave the same results in terms of oligomeric states, namely a homodimer of 68 kDa for E3-TOX and a homotetramer of 152 kDa for K3-TOX, respectively (Figure 2A). In all cases, single peaks were observed indicating an oligomerization state of nearly 100%. The final yields of the recombinant proteins after the two purification steps (Figures S1C andS2C) were around 100 mg/L for the nano-HER2-E3 and nano-HER2-K3, and in the range of 7 to 10 mg/L for the E3-TOX and K3-TOX (Table S2).

The secondary structure content of the recombinant proteins was next explored using far-UV circular dichroism (CD) spectroscopy, and the content of secondary structure elements was estimated using CDPro suite software. [START_REF] Sreerama | Estimation of Protein Secondary Structure from Circular Dichroism Spectra: Comparison of CONTIN, SELCON, and CDSSTR Methods with an Expanded Reference Set[END_REF] The far-UV CD spectra of the tagged E3 and K3 constructs are highly similar (Figure 2B).

The nano-HER2-E3 and the nano-HER2-K3 folded in 18% ± 1 and 16%± 1 of α-helix, compared to 5% ± 2% for the parental nano-HER2, indicating a rough increase of 27 to 32 amino acids in α-helix conformation per monomer (Figure 2B, and Table 1).

These predictions are in agreement with previous results where adding E3 or K3 peptide to a con1 construct leads to an increased of almost 30 amino acid residues in α-helix. [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] Regarding the TOX proteins, the α-helix portions increased in the similar way than for the nanobody constructs when compared to the parental TOX (Figure 2B and Table 1). Thus, secondary structures following addition of the E3 or K3 peptides stayed almost constant regardless of the constructs.

Finally, the thermal stability evaluation of the nano-HER2 recombinant proteins was performed using a fluorescence-based thermal shift assay (Figure S3). The melting profiles of the recombinant proteins were highly similar, indicating that fusion of the tagged constructs did not compromise the intrinsic stability of the VHH domain.

In vitro formation of the heterotetramer complexes

Following the two purification steps, we studied the efficiencies of coassociation between the nanobody and toxin modules in various conditions.

Evaluation of modularity and efficiency of heteromerization were first analyzed in phosphate saline buffer at pH 7.4 using size exclusion chromatography (SEC). When equimolar amounts of either nano-HER2-E3 and K3-TOX, or nano-HER2-K3 and E3-TOX proteins were mixed together and analyzed by SEC, an apparent 125 kDa complex was produced, which was compatible with the theoretical molecular weight of the heterotetramer (Figure 3A and B, and Table S1). Thus, both elution profiles confirmed that the homotetramer dissociates to the benefit of a more stable heterotetrameric complex. As the extracellular micro-environment of a solid tumor is acidic, [START_REF] Wike-Hooley | The relevance of tumour pH to the treatment of malignant disease[END_REF] the stability of the co-assembled immunotoxin nano-HER2-K3E3-TOX was assessed at low pH. Equimolar amount of nano-HER2-K3 and E3-TOX were mixed together and run on size exclusion chromatography in PBS pH 6. As shown in figure 3C, the nano-HER2-K3E3-TOX complex runs exactly at the same apparent molecular weight than the complex form at pH 7.4. Thus the nano-HER2-K3E3-TOX is stable at pH 6.

The quality of the protein assemblies in regard to colloidal stability was monitored by Dynamic Light Scattering analysis (DLS)(Figure S4). All complexes, including the heterotetramers display apparent hydrodynamic diameters of size below 14 nm with a low polydispersity index (PDI) in a range of 0.20, with the complete absence of unwanted protein-aggregates.

The nanobodies and the co-associated immunotoxins retain cell-binding properties.

To assess whether the formation of heterodimers via E3 and K3 helixes does not affect the binding of the nano-HER2, binding efficiencies of nanobodies and coassembled immunotoxins were then measured on HER2-positive HCC1954 cells to determine relative binding constants. Thus, the recombinant proteins were randomly conjugated to NHS-Alexa488 dye via lysine residues and compared to the labeled parental nano-HER2 (Figure 4A and S5A). Following incubation with HCC1954 cells, fluorescence signals were measured using fluorescence-activated cell sorting (FACS). As shown in Figure 4B, monovalent nano-HER2 displayed an apparent binding constant (EC 50 ) of 21.8 nM (± 4.8), somewhat lower than the value previously described elsewhere on HER2-positive SKBR3 cells. [START_REF] Kijanka | Rapid optical imaging of human breast tumour xenografts using anti-HER2 VHHs site-directly conjugated to IRDye 800CW for image-guided surgery[END_REF] The same experiment performed with the homodimer nano-HER2-E3 and the homotetramer nano-HER2-K3 exhibited relative binding efficiency values 1.0 nM (± 0.1) and 0.2 nM (± 0.1)

indicating an increased binding efficiency of around 20-and 100-fold, respectively.

These results pointed to an avidity effect of the dimer and tetramer nanobodies for improved binding to HER2 receptor. However, labeling either E3-or K3-TOX module prior assembly with the respective nanobody counterpart resulted in a significant drop in binding constants (Figure S5B). This result was likely due to a steric hindrance of the fluorophore preventing association between the toxin and the VHH modules as shown by analytical gel filtration (Figure S5C). Thus, labeling purified immunotoxin complexes resolved this issue (Figure S5). Indeed, Alexa488-labeled immunotoxin complexes displayed only a slight lower binding efficiency than their respective nanobody counterparts (Figure 4A Overall, these results demonstrate the binding efficiency and specificity of the co-associated immunotoxins on HER2 cell surface receptor. Following incubation, the fluorescence was measured by fluorescence-activated cell sorting (FACS).

The relative mean of fluorescence (RFM) was plotted against nanobody concentration (at monovalent concentration), and Kd values were determined using sigmoidal fitting with R software. (n≥6) and SD.

Co-assembly of the toxin with the nanobody via E3 or K3 peptides does not impair its cytotoxicity

Because oligomerization may harm the structural and functional integrity of the toxin, we evaluated the enzymatic activities of the toxins and the immunotoxins using an in vitro coupled transcription/translation assay using rabbit reticulocyte lysate and a luciferase reporter gene (Figure 5A). Increasing concentrations of either TOX, E3- TOX, K3-TOX, or the co-assembled were added to the lysate in the presence of NAD+, the essential cofactor for the ADP-ribosylation of the eEF-2 elongation factor. [START_REF] Pastrana | A nonradioactive, cell-free method for measuring protein synthesis inhibition by Pseudomonas exotoxin[END_REF] Translation efficiencies were monitored by measuring luciferase activities (Figure 5A). Determination of the inhibition dose-response curve yielded a half-inhibition (IC 50 ) at 235 pM (± 45) for the TOX comparable to the E3-TOX at 164 pM (± 30), and both co-assembled immunotoxins, HER2-E3K3-TOX and HER2-K3E3-TOX with IC50 of 160 pM (± 15) and 260 pM (± 20), respectively. The homotetramer K3-TOX showed a slightly reduce inhibition activity with an IC50 of 610 pM (± 50). Thus, addition of the helix and co-assembly of the nanobody with the toxin via E3 or K3 peptides did not compromise the enzymatic activity of the toxin.

The cytotoxic activity of all constructs were then also assessed by electrotransferring the recombinant proteins and complexes into various cell lines. [START_REF] Freund | Targeting endogenous nuclear antigens by electrotransfer of monoclonal antibodies in living cells[END_REF] Both TOX and E3-TOX moieties yielded more than 90% of cell death after 72 h (Figure 5B). As a control, the transduced nano-HER2-E3 did not have any cytotoxic effects.

Specific cytotoxicity of the immunotoxins on HER2-positive breast cancer cells

Given the high binding affinity of the nano-HER2 for HER2 positive cancer cells and the high cytotoxicity of the TOX modules, we sought to determine the cytotoxicity of the co-assembled immunotoxins.

Thus, the cytotoxic effect and the specificity of the co-assembled immunotoxin, nano-HER2-K3E3-TOX, were evaluated on different breast cancer cell lines being either HER2-positive or HER2-negative. Three HER2-positive (HCC1954, BT474 and SBKR3), two HER2-negative (MCF7 and MDA-MB-231), and a non-human myoblastic cell line (H9C2(2-1) rat) were tested. [START_REF] Dai | Breast Cancer Cell Line Classification and Its Relevance with Breast Tumor Subtyping[END_REF] The cells were incubated for 72 h with increasing concentrations of either the immunotoxin nano-HER2-K3E3-TOX or the nano-HER2-K3 or the E3-TOX complexes (Figure 6A and6B). The nano-HER2-K3E3-TOX revealed high cytotoxicity at picomolar levels on the HER2 overexpressing cell lines, compared to the toxin and to the VHH alone. The IC 50 values for BT474, HCC1954 and SKBR3 cells were 30 pM (± 4), 39 pM (± 15), and 160 pM (± 25), respectively (n ≥ 10) (Figures 6A, and Table 2). The toxin alone, E3-TOX, had lower cytotoxic effects, in the range of 5 to 10 nM for HER2-positive cells and for MCF7 cells (Table 2). Thus the nano-HER2-K3E3-TOX immunotoxin was 185, 595 and 65 fold more potent on HCC1954, BT474 and SKBR3 cells, respectively, compared to the free toxin (E3-TOX) (Figure 6A and Table 2). No significant differences between the free toxin and the immunotoxin were noted in HER2-negative cells, supporting the notion that HER2 overexpression increases the uptake of the immunotoxin (Figure 6B and Table 2). In fact, MCF7, HER2-negative cell line, were affected to the same extent by the free toxin and by the immunotoxin with an IC 50 from 8.02 to 6.20 nM (± 0.15). Of note, the viability of MDA-MB-231 as well as H9C2(2-1) cell lines, was not affected by the immunotoxin (IC 50 ≥ 300 nM) (Figure 6B, and Table 2). Similarly, the opposite configuration, namely the nano-HER2-E3K3-TOX displayed the same cytotoxicity as the nano-HER2-K3E3-TOX on HER2-positive cell lines and no effects on MDA-MB-231 (Figure S7 and data not shown).

The proteolytic stability of the constructs was also assessed by incubating both immunotoxins in 80% of serum (FBS) at 37 °C during 1, 5, 12 and 24 h.

Immunotoxin cytotoxicity was then tested on HER2-positive HCC1954 cells. Nano-HER2-K3E3-TOX retained its full cytotoxic activity even after 24 h incubation in serum at 37 °C with IC50 of 27.0 pM (± 6.3)(Figure 6C).

Altogether, these results indicate that the cytotoxicity of both immunotoxins is dependent on the specific association between the nano-HER2 and the toxin via the E3 and K3 helixes, and correlates with the presence of the HER2 receptor on the cell's surface. In addition, they show that the immunotoxin complexes are very stable at pH 6.00 as well as in serum.

DISCUSION

In this study, we developed a straightforward co-assembly technique to produce an immunotoxin combining a nanobody directed against HER2 and a toxin via two peptides E3 and K3. [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] The non-covalent and highly specific pairing of the E3 and K3 peptides yielded to the generation of heterotetrameric immunotoxins, composed of two VHH and two toxin molecules. We clearly demonstrate that the engineered immunotoxins retain their specific binding and toxic properties, hence being specifically toxic for HER2-overexpressing breast cancer cells.

Because production of immunotoxins is impeded in eukaryotic cells due to their high toxicity, most engineering applications for their production relies on the design of chimeras produced in E. coli. [START_REF] Amiri Tehranizadeh | The immunotoxin activity of exotoxin A is sensitive to domain modifications[END_REF][START_REF] Guo | HER2-targeted immunotoxins with low nonspecific toxicity and immunogenicity[END_REF][START_REF] Bauss | Characterization of a re-engineered, mesothelin-targeted Pseudomonasexotoxin fusion protein for lung cancer therapy[END_REF] However, fusion proteins often suffer from low solubility and low yield. [START_REF] Amiri Tehranizadeh | The immunotoxin activity of exotoxin A is sensitive to domain modifications[END_REF][START_REF] Behdani | Development of VEGFR2-specific Nanobody Pseudomonas exotoxin A conjugated to provide efficient inhibition of tumor cell growth[END_REF] For example, an affibody anti-HER2 fused to a PE38 fragment from the exotoxin A of Pseudomonas aeruginosa was not soluble and was purified from the inclusion bodies 10 while a chimeric recombinant immunotoxin composed of a VHH directed against the vascular endothelial growth factor receptor 2 and the PE38 fragment was produced at a final yield of 9.2 mg / L. [START_REF] Behdani | Development of VEGFR2-specific Nanobody Pseudomonas exotoxin A conjugated to provide efficient inhibition of tumor cell growth[END_REF] Another strategy is to generate both moieties independently, which in addition to improved yield and solubility, makes it possible to produce the antibody domain in eukaryotic cells. Different protein conjugation strategies have been explored. For instance, a HER2-scFv fragment has been chemically conjugated to PE24 via N-succinimidyl-3-(2-pyridyldithio)propionate (SPDP). [START_REF] Lee | A chemical conjugate between HER2-targeting antibody fragment and Pseudomonas exotoxin A fragment demonstrates cytotoxic effects on HER2-expressing breast cancer cells[END_REF] The HER2-(scFv)-PE24 end product was then purified by size exclusion chromatography. However, the highest yield of the obtained conjugation was only 58% and required additional purification steps. An elegant protein trans-splicing (TPS) technology was also reported for the conjugation of either the Trastuzumab-targeted HER2 or two VHHs targeting different epitopes of HER1 (EGFR) to the PE24 fragment of the Exotoxin A from Pseudomonas. [START_REF] Pirzer | Generation of Potent Anti-HER1/2 Immunotoxins by Protein Ligation Using Split Inteins[END_REF] Coupling efficiencies in the range of 50-70% were achieved and it was not possible to distinguish molecules with a toxin/antibody ratio of 2 from those with partial coupling. Finally, an additional step was also required to remove the unconjugated mAb.

The use of co-assembling peptides offers several significant advantages. Both moieties can be produced separately, overcoming solubility and yield issues reported for chimeric immunotoxins. Indeed, the VHH was produced at a yield of 100 mg/L and the toxin module showed a high solubility yield. In addition, neither reduction nor chemical conjugation is required, thereby avoiding subsequent purification steps, making it a very simple and convenient technology. Following assembly of the nano-HER2 and the toxin via E3 and K3, the heterotetramer immunotoxin complexes were able to efficiently and specifically kill HER2-expressing breast cancer cells. In addition, the bivalence format of the nanobody can probably trigger an efficient cellular uptake through receptor clustering. [START_REF] Moody | Trigger Internalization and Lysosomal Targeting of Therapeutic Receptor:Ligand Complexes[END_REF][START_REF] Wang | Control of epidermal growth factor receptor endocytosis by receptor dimerization, rather than receptor kinase activation[END_REF] Upon endocytosis, the toxin part can be cleaved from the immunotoxin by the furin protease at the FCS in the early endosome and the enzymatic domain can reach the cytosol, where it finally inhibits translation. [START_REF] Wolf | Pseudomonas exotoxin A: From virulence factor to anti-cancer agent[END_REF] The cytotoxicity of the immunotoxins was highly specific to HER2 overexpressing cells with an efficacy of more than 65-fold compared to the toxin alone, or to HER2 low expressing or HER2 negative cells.

The present study describes a very straightforward process for generating an immunotoxin without chemical conjugation and additional purification steps to remove unreacted compounds and side products from the desired conjugation product. The association between E3 and K3 helices ensures a highly homogenous end product.

In addition, this fully modular technology enables the replacement of the nano-HER2 moiety with any other target-specific binding domain to target other types of cancer cells. Finally, the possibility to produce both entities separately overcomes the solubility and yield issues of a full recombinant immunotoxin and offers the possibility to express the target moiety in an eukaryotic organism, to achieve post-translational modifications if needed, for proper folding or activity.

Experimental procedures

Cell Lines HCC1954, MDA-MB-231, BT474 and H9C2 (2-1) cell lines were maintained as monolayers in RPMI without Hepes, supplemented with 10 % fetal calf serum (FCS)

and Gentamycin. MCF7, Caski, HeLa, MRC5 and SBKR cell lines were maintained as monolayers in Dulbecco's modified Eagle's medium (DMEM) (1 g/L Glucose) supplemented with 10 % fetal calf serum (FCS) and Gentamycin. For BT474 and MCF7, the medium was supplemented with 10 µg / ml Insulin.

Recombinant plasmid constructions

Nano-HER2 DNA sequences described elsewhere [START_REF] Hartmann | VHH characterization. Comparison of recombinant with chemically synthesized anti-HER2 VHH[END_REF] were amplified by PCR using HER2-For GATATACCATGGAAGTTCAACTGG and HER2-Rev ATGTGCACTAGTTGCGGCCGCAGAGCTAACCGTCACTTGGGTACC primers.

HER2 PCR fragment was digested with NcoI-SpeI and ligated into the pETOM-P40M1-E3 or -K3 digested with NcoI-SpeI to replace the P40M1 sequences. [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] An optimized sequence encoding for the TOX used in this study was synthetized by Integrated DNA Technologies (IDT) and amplified by PCR using specific primers:

For-TOX TCTACTAGTGCAATGGGGTCTGGTGGCTGT and Rev-TOX:

GAGCTTAAGAATAATGTTAAGTAGAAAG. The resulting PCR fragment digested with SpeI-EcoRI with has been then cloned into SpeI-EcoRI of the pETOM-E3 and pETOM-K3. [START_REF] Vigneron | Self-Associating Peptides for Modular Bifunctional Conjugation of Tetramer Macromolecules in Living Cells[END_REF] The E3 and K3 sequences were amplified by PCR using NheI-K3-For GCTCGCTAGCGGTAACAACACCAGCTCCTCTC and HindIII-K3-Rev GCTCAAGCTTTTAACCCCCTGGCTCCTTCCCAGCC oligonucleotides and cloned into a pET6His-eGFP vector.

Expression and purification of the recombinant fusion proteins

Briefly, E3 and K3 fusion proteins were overexpressed in E. coli BL21 (DE3) pLysS with 0. In vitro protein transcription/translation inhibition assay.

Inhibition of protein translation was performed using rabbit reticulocyte lysate (RRL) (Promega) and by measurement of luciferase activity. The assay was performed as suggested by the manufacturer (Promega) in a total volume of 15 µl.

Briefly, RRL was mixed with T7 expression plasmid encoding for the firefly luciferase and incubated for 90 min at 30 °C with or without increasing concentration of recombinant TOX. Then 5 µl of each reaction were transferred to a black 96-well plate and assayed for luciferase activity, as previously described. [START_REF] Diring | A cytoplasmic negative regulator isoform of ATF7 impairs ATF7 and ATF2 phosphorylation and transcriptional activity[END_REF] A control without any protein added served as positive control and was set as relative protein translation of 100 %. At least three independent experiments were carried out.

Circular Dichroism

CD experiments were performed at 20.0 ± 0.1 °C on a Jasco J-815 spectropolarimeter with 0.1 mm path-length quartz-Suprasil cells (JASCO Inc., Easton, MD USA). Acquisition parameters as continuous scan rate, response time, and bandwidth were 50 nm/min, 1.0 s, and 1 nm, respectively. The absorbance of the buffer and the sample was kept as low as possible to ensure good signal-to-noise ratio. All spectra are systematically corrected by subtracting the solvent spectrum obtained under identical conditions.

Thermal Shift Assay

TSA experiments were carried out on real-time PCR systems (StepOnePlus;

Applied Biosystems, Darmstadt, Germany). Purified nano-HER2, nano-HER2-E3 and nano-HER2-K3 were mixed with diluted Sypro Orange dye (final 2500-fold dilution from stock solution; Invitrogen, Carlsbad, CA, USA) in Phosphate Buffered Saline,

Dynamic Light Scattering analysis (DLS)

DLS was performed at 25°C using different protein concentration on a Malvern Zetasizer devise (Malvernpanalytical). Results analysis was performed using Zetasizer software.

Transient siRNA transfections

Transient siRNA transfections were performed using Lipofectamine RNAiMAX

Cytotoxicity Assay

5 000 cells were seeded per well in a 96-well plate and incubated for 24 h.

Cells were then treated with increased concentrations of toxin, VHH, or immunotoxins. After 72 h, a crystal violet assay was conducted. [START_REF] Feoktistova | Crystal Violet Assay for Determining Viability of Cultured Cells[END_REF] The absorbance was measured in a Tecan reader (595 nm). IC 50 values were calculated by fitting a sigmoidal model with R software. Wells with cells treated with PBS were set at 100% of cell viability.

Supporting Information Available

DNA and proteins sequences, figures showing additional representations of the immunotoxin, purification steps and SEC analysis of recombinants proteins, thermal stability profiles, and cells viability assays with recombinant immunotoxin.

Figure 1 :

 1 Figure 1: Representations of heterotetrameric immunotoxins. Schematic representation of either nano-HER2-K3E3-TOX (A) or nano-HER2-E3K3-TOX (B) co-assembled immunotoxins with coding sequences of each module, as indicated. Theoretical oligomerization states of the corresponding proteins, and the resulting co-assembled immunotoxins are depicted.

Figure 2 .

 2 Figure 2. Physicochemical analysis of the K3 and E3 constructs. (A) Preparative gel filtration of purified nano-HER2 derivatives (above) and TOX constructs (below). The column was pre-calibrated with standard proteins as indicated (IgG, BSA, ovalbumin, and cytochrome C). A sample of each peak was analyzed by SDS-PAGE and by Coomassie blue staining. (B) Far-UV circular dichroism spectra of the indicated assemblies were recorded for samples at a monomeric concentration of 69 µM in phosphate saline buffer and are presented as an average of ten successive scans. CD signal is expressed in mean residue ellipticity (deg•cm 2 •dmol -1 ). Data were collected in the 185-270 nm range at 20 °C.

Figure 3 .

 3 Figure 3. Co-association of the immunotoxins. Gel filtration of (A) purified nano-HER2-K3 (blue), E3-TOX (red), and a mixture of equimolar amounts of nano-HER2-K3 and E3-TOX (green), (B) purified nano-HER2-E3 (red), K3-TOX (blue), and a mixture of equimolar amounts of nano-HER2-E3 and K3-TOX (green), and analysis by SDS-PAGE and Coomassie blue staining of the peak fractions. (C) Gel filtration of co-assembled nano-HER2-K3/E3-TOX immunotoxin run at pH 6 (dotted green line) and SDS-PAGE and Coomassie staining analysis of the peak fraction.

  and 4B). Nano-HER2-K3E3-TOX immunotoxin exhibited an EC 50 of 2.5 nM ± 0.3 and the nano-HER2-E3K3-TOX immunotoxin an EC 50 of 3.7 nM ± 0.4. No detectable binding was observed on HER2 low-expressing cells MDA-DB-231 or on HER2-silenced HCC1954 cells using smallinterfering oligonucleotides (Figure S6A and S6B).

Figure 4 .

 4 Figure 4. Apparent binding constants of the constructs on antigen-overexpressing cells. (A) Cartoon representing the binding of the labeled constructs [*] on HER2 cell surface receptor. (B) HCC1954 cells were titrated by increasing amounts of Alexa488-labeled recombinant proteins, as indicated [*].

Figure 5 :

 5 Figure 5: Cytotoxicity of the TOX modules. (A) Toxins and Immunotoxins inhibit protein translation.Recombinant proteins were tested in an in vitro transcription/translation assay using rabbit reticulocyte lysate and the luciferase activity as reporter. This assay was performed in triplicate.Sigmoidal curve fitting was performed using R software. (B) TOX and E3-TOX purified proteins were electro-transferred into various cell lines. After 72 h, cell viability was estimated as a percentage relative to cells transduced with PBS buffer. Analysis corresponds to at least an average of three independent experiments. Error bars represent standard deviations. Student's t-test was performed: *P<0.05, **P<0.01, ***P<0.001.

Figure 6 .Table 2 .

 62 Figure 6. The immunotoxin nano-HER2-K3E3-TOX shows high cytotoxicity and specificity for HER2 overexpressing cells. (A) HER2-positive and (B) HER2-negative cells were treated for 72 h with the nano-HER2-K3E3-TOX, nano-HER2-K3, and E3-TOX alone (n≥10). (C) HER2-positive HCC1954 cells were treated for 72 h with the nano-HER2-K3E3-TOX previously incubated in 80 % serum at 37°C for

pH 7 .

 7 4 to a final volume of 20 µl and a final protein concentration of 5 µM. The samples were submitted to a denaturation kinetic from 25 to 95 °C at a rate of 1°C/min. The fluorescence of Sypro Orange dye was recorded in real time (excitation with a blue LED source and emission filtered through a ROX emission filter). The fluorescence profiles were fitted to a Boltzmann sigmoid equation to determine the melting temperature. Each experiment was repeated four times.

(

  Invitrogen, P/N 56532) according to the manufacturer's instructions. STARD3targeting siRNAs and HER2-targeting siRNAs were SMARTpool ON-TARGETplus obtained from Dharmacon. For controls, siRNAs ON-TARGETplus non-targeting pool from Dharmacon were used. siRNAs were used at 10 nM final concentration and cells were transfected 24 h -72 h prior to experiments.Fluorescence-Activated Cell Sorting (FACS)Trypsinized cells were incubated with a mixture of equimolar ratio of recombinant proteins as indicated, for 30 min at 4 °C in PBS, 0.5% BSA, 2 mM EDTA. Cells were washed twice in PBS, 0.5% BSA, 2 mM EDTA and analyzed with BD Accuri™ C6 Plus flow cytometer (BD Bioscience). The relative mean fluorescence intensities were normalized and plotted against the concentration of the nano-HER2 at monomer concentration. The data shown here are single point measurements.

Table 1 :

 1 Secondary structure contents of the constructs: aa refers to the numbers of amino acids determined considering the percentage of each secondary structure content and assuming a single element.

		ALPHA		BETA		OTHERS
		%	aa	%	aa	%	aa
	Nano-HER2	5 ± 2	7	41 ± 8	61	54 ± 9	79
	Nano-HER2-E3	19 ± 1	39	30 ± 3	64	52 ± 2	110
	Nano-HER2-K3	16 ± 1	34	33 ± 3	70	51 ± 3	109
	TOX	7 ± 2	20	39 ± 3	114	54 ± 4	156
	E3-TOX	20 ± 2	61	28 ± 2	88	53 ± 3	166
	K3-TOX	17± 1	53	31 ± 2	98	52 ± 2	164

  5 mM isopropyl thiogalactoside (IPTG). After 24 h at 20°C, the cells were harvested, re-suspended 20 mM Phosphate buffer pH 8, 250 mM NaCl and 10 mM imidazole. Following lysis in a cell disruptor (Constant Systems Ltd), cell debris were removed by ultra-centrifugation, and the supernatant was applied to IMAC chromatography charged with cobalt (GE Healthcare Saclay, France). IMAC purified proteins were subsequently loaded on HiLoad 16/60 Superdex 200 prep grade column or on Superdex 200 Increased 10/300 (GE Healthcare, Bio-sciences AB, Sweden) operating at a flow rate of 0.5 ml/ min. Fractions were separated on SDS-

	PAGE gels and analyzed by Coomassie blue. The heterotetramers were prepared by
	incubating together E3 and K3 targeted recombinant proteins at 1:1 molar ratio 5 min
	at RT followed in some experiments by a second purification on Superdex 200
	Increased 10/300 GL size exclusion chromatography. Complex formation between
	labeled recombinant proteins was control by analytical chromatography on Superdex
	200 Increased 5/150 GL.
	Protein labeling
	Recombinant proteins were labeled with either NHS-Ester Alexa488 dye using
	DyLight TM Microscale Antibody Labeling Kit following the protocol as described by

the manufacturer (Thermo-Scientific, USA). Labeled proteins are indicated as [*] in text and figures.

Acknowledgements

This work was supported by funds and/or fellowships from the Centre National de la Recherche Scientifique, the University of Strasbourg, the French Ministry of Research and the Ligue Régionale contre le Cancer (CCIR-GE). The CD device was funded with the help of the Association pour la Recherche sur le Cancer (ARC n.8008). Lucile GUYOT is supported by a grant from the French ANRT agency (CIFRE N°2018/1643). We thank C.L. Tomasetto and J.C. Amé for very helpful advises, and R. Wagner for the anti-HER2 nanobody clone.