Pascal Pernot

Scaling factors for ab initio vibrational frequencies: comparison of uncertainty models for quantified prediction

Keywords: Bayesian data analysis, Model calibration, Scaling factor, Vibrational frequency

Bayesian Model Calibration is used to revisit the problem of scaling factor calibration for semi-empirical correction of ab initio calculations. A particular attention is devoted to uncertainty evaluation for scaling factors, and to their effect on prediction of observables involving scaled properties. We argue that linear models used for calibration of scaling factors are generally not statistically valid, in the sense that they are not able to fit calibration data within their uncertainty limits. Uncertainty evaluation and uncertainty propagation by statistical methods from such invalid models are doomed to failure. To relieve this problem, a stochastic function is included in the model to account for model inadequacy, according to the Bayesian Model Calibration approach. In this framework, we demonstrate that standard calibration summary statistics, as optimal scaling factor and root mean square, can be safely used for uncertainty propagation only when large calibration sets of precise data are used. For small datasets containing a few dozens of data, a more accurate formula is provided which involves scaling factor calibration uncertainty.

For measurement uncertainties larger than model inadequacy, the problem can be reduced to a weighted least squares analysis. For intermediate cases, no analytical estimators were found, and numerical Bayesian estimation of parameters has to be used.

Introduction

The final stage in the development of a model, after calibration on an experimental dataset and proper validation, consists in its use for prediction: "If the experimental dataset is sufficiently broad, there is a reasonable expectation that the results will be accurate to something like the target accuracy". [START_REF] Pople | Nobel lecture: Quantum chemical models[END_REF] The estimation of uncertainty for the results of computational chemistry is indeed of paramount importance, notably to their use in multiscale modeling. [START_REF] Pancerella | Metadata in the Collaboratory for Multi-Scale Chemical Science[END_REF][START_REF] Frenklach | Transforming data into knowledge. Process Informatics for combustion chemistry[END_REF] The concept of Virtual Measurement has been introduced by Irikura 4 to take advantage of the standardized procedures defined by the Guide to the Expression of Uncertainty in Measurement (also known as "the GUM"), [START_REF] Bipm | IUPAC, IUPAP, and OIML. Guide to the expression of uncertainty in measurement (GUM)[END_REF] and to apply them in the case of quantum chemistry modeling. Random uncertainties have been shown to be very small, and the major uncertainty factor are biases due to basis-set and/or theory limitations. For quantum chemistry to be predictive, i.e. to be able to predict observables with confidence intervals, one has to correct for these biases, which commonly requires semi-empirical corrections. Uncertainty attached to these corrections have to be considered in the final uncertainty budget, to which they constitute often a major contribution.

Scaling of harmonic vibrational frequencies is an important example of calibration method in computational chemistry, where estimation of a vibrational frequency ν is obtained by multiplying the corresponding harmonic vibrational frequency ω, routinely calculated by standard computational chemistry codes, by an empirical scaling factor s (Fig. 1)

ν = ω s (1)
Optimal scaling factors have been computed for extensive sets of theory/basis-set combinations. [START_REF] Scott | Harmonic Vibrational Frequencies: An Evaluation of Hartree-Fock, Möller-Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors[END_REF][START_REF] Wong | Vibrational frequency prediction using density functional theory[END_REF][START_REF] Merrick | An evaluation of harmonic vibrational frequency scale factors[END_REF][START_REF] Johnson | NIST Computational Chemistry Comparison and Benchmark Database, Release 14[END_REF] In the majority of publications about scaling factors, two summary statistics are provided for each theory/basis-set combination: the optimal scaling factor and the root mean squares. From a reference dataset of experimental {ν i } N 1 and calculated vibrational frequencies {ω i } N 1 the optimal scaling factor obtained by the least-squares procedure is

ŝ = ω i ν i / ω 2 i (2)
and the quality of the correction is estimated by the root mean squares (rms) value

γ = 1 N (ν i -ŝω i ) 2 1/2 (3)
To our knowledge, these values are not explicitly used for uncertainty propagation, but the rms provides an estimate of the residual uncertainty resulting from the scaling correction ("something like the target accuracy", 1 or "a surrogate for uncertainty" according to [START_REF] Irikura | Uncertainties in scaling factors for ab initio vibrational frequencies[END_REF] ).

In a recent article (hereafter referred to as Paper I), Irikura et al. [START_REF] Irikura | Uncertainties in scaling factors for ab initio vibrational frequencies[END_REF] treated the problem of uncertainty propagation from scaled frequencies, and, using procedures advocated by the GUM, 5 insisted that the scaling factor itself is subject to uncertainty, and proposed that this uncertainty is the major contribution to prediction uncertainty. On the practical side, prediction uncertainty would be proportional to the calculated harmonic frequency; on the factual side, these authors declare that scaling factors for vibrational frequencies are accurate to only two significant figures, whereas all other studies overstate their precision by reporting them with four figures. This approach has been adopted by the National Institute of Standards and Technology (NIST) and put into practice in the Computational Chemistry Comparison and Benchmark DataBase (CCCBDB), [START_REF] Johnson | NIST Computational Chemistry Comparison and Benchmark Database, Release 14[END_REF] section XIII.C.2, where all scaling factors are provided with uncertainties derived according to the procedure of Paper I.

In the present paper, we revisit the problem of scaling factor calibration and we recast it in the Bayesian Model Calibration framework, reputed for providing consistent uncertainty evaluation and propagation. [START_REF] Kennedy | Bayesian calibration of computer models[END_REF][START_REF] Gregory | Bayesian Logical Data Analysis for the Physical Sciences[END_REF][START_REF] Bipm | GUM: propagation of distributions using a Monte Carlo method[END_REF] Section 2 presents the methodological elements used for calibration and validation procedures, which are applied to representative vibrational frequency and zero point vibrational energy datasets in Section 3. Bayesian calculations used in this study are fairly standard, but for the sake of completeness and for readers unfamiliar with statistical modeling, details are provided in the Appendix .

Figure 1: Correlation plot between calculated harmonic frequencies ω i and measured frequencies ν i for a set of vibrations extracted from the CCCBDB for the HF/6-31G* combination of theory/basis-set (dots). The full line is the regression line ν = sω; the dashed line is a visual aid to appreciate the bias.

Methods

Statistical model for scaling factor calibration

Considering a measured frequency ν obs , one can assume that it is related to the true value ν true by

ν obs = ν true + ǫ (4)
where ǫ ∼ N(0, ρ 2 ) is a normal random variable centered at zero, with variance ρ 2 , representing the measurement uncertainty in the hypothesis of additive white noise. In the following, we assume that ρ is known beforehand.

Calculated harmonic vibrational frequencies ω are affected by random errors, related to numerical convergence defined by non-zero thresholds and the choice of starting point in geometry optimization, and to non-zero thresholds in wave-function optimization. [START_REF] Irikura | Uncertainty associated with virtual measurements from computational quantum chemistry models[END_REF] It has been shown

that the associated uncertainties are negligible when compared to the measurement uncertainties. [START_REF] Irikura | Uncertainty associated with virtual measurements from computational quantum chemistry models[END_REF] In the following, one can thus assume that the harmonic vibrational frequencies, being deterministically calculated, have fixed values.

If one makes the hypothesis of a linear relationship between ν true and ω, the calibration model resulting from this analysis is

ν obs = sω + ǫ (5)
For a single frequency, there is an optimal scaling parameter ŝ = ν obs /ω. As ν obs is uncertain, with standard uncertainty ρ, the value of s cannot be known exactly and has a standard uncertainty u s = ρ/ω. For a calibration dataset with uniform measurement uncertainty ρ, it can be shown that the optimal value for s is still given by Eq. 2, and its standard uncertainty by u s = ρ/ N i=1 ω 2 i (c.f. Appendix A.3). Applicability of this formula is subject to one condition: the model (Eq. 5) should be statistically valid. This means that the residuals ν obs i ŝω i should have a normal distribution with variance ρ 2 . Normality is not always verified, but most important, the variance condition is typically violated when precise data are used for calibration. The linear model (Eq. 5) is typically unable to reproduce a given set of measured frequencies within their uncertainty range. In such a case, the width of the distribution of residuals is dominated by model misfit, not by measurement uncertainty, and the model is invalid.

An option would be to seach for a better model than the linear scaling, which is beyond the purpose of this study. Instead, we consider here that the misfit is not deterministically predictable. The solution to preserve the linear scaling model in a statistically valid model, is thus to introduce a stochastic variable ξ to represent the discrepancy between model and observations

ν obs = sω + ξ + ǫ ( 6
)
This equation is similar to the basic statistical model introduced by Kennedy and O'Hagan for Bayesian calibration of model outputs. [START_REF] Kennedy | Bayesian calibration of computer models[END_REF] The discrepancy variable could formally depend on ω, but we observed that the residuals between model and observations are not notably frequency dependent (Fig. 2), and the same is assumed for ξ which is considered null in average with

variance σ 2 ξ ∼ N(0, σ 2 ) (7)
The calibration equation depends thus on two unknown parameters s and σ.

Uncertainty propagation

The calibration model (Eq. 6) being linear with regard to uncertain variables s, ξ and ǫ, and in the hypothesis of normally distributed uncertainties, we can use the standard uncertainty propagation rules 5 to estimate the value and uncertainty on predicted vibrational frequencies:

ν = s ω (8)
V ar(ν) = ∂ν ∂s

2 s=s V ar(s) + ∂ν ∂ξ 2 ξ=0 V ar(ξ) + ∂ν ∂ǫ 2 ǫ=0 V ar(ǫ) (9) = ω 2 V ar(s) + σ 2 + ρ 2 (10)
The terms due to covariances have been omitted from this equation as the three variables are independent by hypothesis. In order to provide evaluated predictions of vibrational frequencies, we need therefore to estimate s, u 2 s = V ar(s) and σ 2 from the calibration dataset. This is done in the next section, using Bayesian model calibration.

(A) (B)
Figure 2: Residuals between calculated harmonic frequencies ω i and measured frequencies ν i for a set of vibrations extracted from the CCCBDB for the HF/6-31G* combination of theory/basisset (dots). (A) bottom: residuals as a function of ω. In order to suppress the grouping effect linked with frequencies, the residuals were also plotted as a function of their order in the reference set (A)-top. (B): plot of the cumulative density function (CDF) for the residuals against a normal CDF shows that globally there is very little deviation from normality.

Bayesian Model Calibration (BMC) 2.3.1 General case

Starting from the statistical calibration model (Eq. 6), one derives the following expression for the posterior probability density function of the parameters, given a set of N measured and calculated frequencies (details are reported in Appendix A.1)

p(s, σ| ν obs i , ρ i , ω i N i=1 ) ∝ 1 σ N i=1 (σ 2 + ρ 2 i ) 1/2 exp - 1 2 N i=1 ν obs i -sω i 2 σ 2 + ρ 2 i ( 11
)
Inferences from this pdf have to be done generally by numerical methods, [START_REF] Gregory | Bayesian Logical Data Analysis for the Physical Sciences[END_REF] as will be applied later to zero point vibrational energies. For vibrational frequencies, we first derive an adapted, simplified, model.

The case of negligible measurement uncertainties

In the commonly met situation where the amplitude of ξ is much larger than the other sources of uncertainty (σ ≫ ρ), we can consider the approximate measurement model

ν obs i = sω i + ξ (12)
for which the posterior pdf can be simplified to

p(s, σ| ν obs i , ω i N i=1 ) ∝ 1 σ N +1 exp - Nγ 2 2σ 2 exp - (s -s) 2 N i=1 ω 2 i 2σ 2 (13)
This expression is amenable to analytical derivation of the estimates for the parameters (see Appendix A.2):

• the average value for s is identical to the optimal value provided by least-squares analysis s = ŝ;

• the standard uncertainty on s, u s is related to the rms γ by the formula

u s = γ N/ ((N -3) ω 2 i );
• the estimate of σ 2 is related to γ according to σ 2 = γ 2 N/(N -3).

Using these estimates, we can establish an explicit expression for the standard uncertainty of ν:

u ν = γ N N -3 ω 2 i ω 2 i + 1 (14)
Confidence intervals can be defined for prediction purpose, e.g. the 95% confidence interval for ν, assuming the normality of uncertainty is given by

CI 95 (ν) = [ŝω -1.96 u ν , ŝω + 1.96 u ν ] (15)
It can be seen that for large calibration sets of few hundreds of frequencies N/(N -3) ≃ 1 and ω 2 / i ω 2 i ≪ 1, and thus

u ν ≃ γ (16)
In such conditions, it is thus possible to derive directly confidence intervals from the the summary calibration statistics ŝ and γ provided by the reference literature. 6, 7, 8

The Multiplicative Uncertainty (MU) method

Irikura et al., [START_REF] Irikura | Uncertainties in scaling factors for ab initio vibrational frequencies[END_REF] after a thorough analysis of the uncertainty sources, established that the major contribution to uncertainty propagation would be the uncertainty on the scaling factor ŝ. They estimate u s from the weighted variance of s with weights a i = ω 2 i . This weighting scheme is derived in two steps: (1) they propose that the probability density function (pdf) for the scaling factor is a linear combination of pdf's for individual scaling factors in the reference set; and (2) from the comparison of the expression of the average value derived from this proposition with the least-squares solution Eq.2. This way, they obtain a standard uncertainty

u * s ≃ 1 ω 2 i ω 2 i (s i -ŝ) 2 1/2 (17)
which can be related to γ by u * s ≃ γ N/ ω 2 i . This uncertainty is different, and generally smaller, than the dispersion of s values within the calibration set

σ s = 1 N (s i -ŝ) 2 1/2 (18)
The uncertainty on a scaled frequency is then reduced to

u ν ≃ ωu * s (19)
hence the name of "Multiplicative Uncertainty" (MU) used hereafter.

The salient feature of Eq. 19 is that uncertainty should be proportional to the calculated harmonic frequency. But, if one observes correlation plots for reference datasets (e.g. Fig. 1, ω > 2000 cm -1 ), this is not the case. When contrasted with the BMC approach, one understands that the multiplicative approach "absorbs", at least partially, model inadequacy in u * s . It is thus implicitly assumed in this approach that the model (Eq. 5) is in a statistical regime, although it is not. These points will be illustrated and discussed in the next section.

3 Applications and discussion

Vibrational frequencies

We illustrate the BMC and MU approaches on the HF/6-31G* combination of theory/basis-set.

The reference dataset, plotted in Fig. 1, has been downloaded from the NIST/CCCBDB in July 2008. 9

Calibration

Using the BMC model and estimators on the reference set, we obtain ŝ = 0.8984 ± 0.0005, and σ = 45.3 ± 0.6 cm -1 (Table 1), which is consistent with the value of the rms obtained by Merrick et al. [START_REF] Merrick | An evaluation of harmonic vibrational frequency scale factors[END_REF] for the same theory/basis-set combination. For this dataset, the CCCBDB proposes ŝ = 0.899 ± 0.025. We cross-checked this value using Eq. 17 (Table 1). The standard uncertainty on ŝ evaluated by both methods differ thus by a factor 50, which is expected to have noticeable effect on prediction uncertainty. In order to visualize this effect, we plotted the 95 percent confidence intervals in both cases (Fig. 3). It is immediately visible that the the MU approach has a tendency to underestimate uncertainty at low frequencies and to overestimate it at high frequencies. In comparison, the BMC approach is more balanced.

Validation

In order to comfort the observations of the previous section (3.1.1), we split the calibration dataset in two subsets by using the odd indexes for calibration, and the even ones for validation (the frequencies being ordered per molecule, this provides a quasi-random selection with regard to frequency value). In this case, one gets slightly different values of the parameters, as reported in Table 1. Using these values, we generate 95% confidence intervals and calculate the frequency of inclusion of the experimental values of the validation subset within these intervals (Fig. 3).

For a consistent estimator, one should find a frequency close to 95%. BMC succeeds for 94.7%, whereas the MU model succeeds for only 83% of the frequencies in the validation set (Table 1).

Considering the size of tha samples, the difference is significative, and the consistency of the multiplicative uncertainty approach in this context can be questioned.

Test on a restricted frequency scale

As stated in Paper I, "to apply the fractional bias correction, it is important to select a class of frequencies similar to the ones to be estimated". For instance, if one selects in the reference set only those frequencies between 3180 and 3500 cm -1 , one gets a much more uniform picture than with the full reference set. The calibration procedure was done with this limited set of 479 frequencies, providing ŝ = 0.9050 ± 0.0087 (Table 1). In this case, we note that the uncertainty factor for s is practically identical to the standard deviation calculated from the sample (0.00869 vs. 0.00871): u * s ≃ σ s . Due to the restricted frequency range, one has indeed ω 2 i / i ω 2 i ≃ 1/N (cf. Eqs 17 and 18).

The restricted set has been split in two using index parity, as before. The scaling factor obtained by MU from the calibration subset is now ŝ = 0.9052 ± 0.0071, and 95.0% of the validation frequencies fall within the 95% confidence interval. This result is now identical to the one obtained with BMC (Table 1), the confidence intervals obtained by both methods being indistinguishable.

It appears thus that in restrictive conditions, the MU method can be valid for reference sets where the individual scaling factors are uniformly distributed with regard to the harmonic frequencies. In such case however, the uncertainty is reduced to a conventional unweighted standard deviation.

Uncertainty propagation

The relative importance of both factors u 2 s and σ 2 (ρ = 0 in this example) in Eq. 10 can be evaluated on the example of a calculated harmonic frequency in the higher range ω = 3000 cm -1 (Table 2). In this case, the uncertainty on the scaling factor contributes only to one thousandth of the total prediction variance.

For any practical purpose, the uncertainty on the scaling factor of vibrational frequencies can therefore be neglected. The uncertainty on σ is also much too small to be relevant for confidence intervals calculation. One can thus safely apply the uncertainty propagation formula (Eq. 16), using the rms provided by most reference articles dealing with scaling factors calibration. 6, 7, 8

Zero Point Vibrational Energies

We consider ZPVE as a an additional test because the reference datasets are considerably smaller than for the vibrational frequencies (e.g. 39 molecules in the Z1 set of Merrick et al. [START_REF] Merrick | An evaluation of harmonic vibrational frequency scale factors[END_REF] ), which is expected to enhance the role of the uncertainty on the scaling factor. In the absence of a systematic review of measurement errors for ZPVE of polyatomic molecules, we consider in the following that they can be neglected. The uncertainties reported by Irikura 14 for diatomic molecules are indeed very small (on the order of 0.01 cm -1 ), but transposition to larger molecules is not straightforward.

Using our measurement model and estimators on the reference set, one gets ŝ = 0.9135 ± 0.0027 and σ = 0.73 ± 0.09 kJ mol -1 (Table 3), which is consistent with the rms obtained by Merrick et al. [START_REF] Merrick | An evaluation of harmonic vibrational frequency scale factors[END_REF] for the HF/6-31G* theory/basis-set combination. Relative uncertainties on these parameters have been increased by one order of magnitude, compared with the vibrational frequencies case. The validation exercise shows once more that the Multiplicative Uncertainty model fails to provide correct confidence intervals, with a score of only 0.63 for CI 95 .

In such a case of small reference dataset, it is interesting to check if the approximate formula (Eq. 16) for uncertainty propagation which was validated for large sets of vibrational frequencies begins to break down, i.e. the contribution of the multiplicative term involving u s stays negligible or not, for the larger ZPVE values. For instance, if one considers a calculated ZPVE of 100 kJ mol -1 , one has u ν = (100 * 0.0027) 2 + 0.73 2 = 0.78 kJ mol -1 , to be compared to γ = 0.71 kJ mol -1 . It is to be noted also that the uncertainty on σ might contribute at the same level, u σ = 0.09 kJ mol -1 . Taking all uncertainty sources into account trough Eq. 51 by Monte

Carlo Uncertainty Propagation, one gets u ν = 0.77 kJ mol -1 . Apparently, the fluctuations of σ do not have an effect and only the uncertainty on the scaling factor has a noticeable effect, albeit quite small.

In the same conditions, for the combination B3LYP/6-31G*, one gets γ = 0.423 kJ mol -1

and u ν = 0.472 kJ mol -1 , to be compared with an exact value of u ν = 0.466 kJ mol -1

(Table 3). There is globally only a 10% increase compared to the rms γ. In this range of ZPVEs, γ still provides a good approximation of the uncertainty factor (Table 2). However, the amplitude of the discrepancy between γ and u ν will probably increase with the size of the molecule. In consequence, for uncertainty propagation with ZPVEs, notably for large molecules, it would be safer to use the full UP formula (Eq. 14), involving the multiplicative uncertainty factor. Compilations of scaling factors should thus report the easily calculated value of u s = γ N/ ((N -3) ω 2 i ), in addition to the rms γ.

Non-negligible experimental uncertainties

When the measurement uncertainty becomes comparable to the rms, model discrepancy should be vanishing, and confidence intervals for prediction should include the measurement uncertainty, i.e. u 2 ν = ω 2 u 2 s + σ 2 + ρ 2 . In the absence of an exhaustive compilation of experimental uncertainties on measured ZPVE, we performed simulations assuming a uniform uncertainty distribution over the full dataset. In order to test the sensitivity of the model parameters to this uncertainty, we repeated the estimations of previous section, using Eq. 27, for different values of ρ between 0.1 and 1.0 kJ mol -1 . The results are reported in Fig. 4.

As expected from the properties of the posterior pdf, the average/optimal value of the scaling factor is insensitive to the amplitude of ρ. Moreover, we observe only a slight increase of u s from 0.002 to 0.004. A transition from a constant u s , defined by the ρ = 0 limit, to a linear increase consistent with the weighted least squares limit (Eq. 50) is observed around ρ = γ, where both limits intersect. A closer look shows that the transition occurs indeed at values of ρ slightly smaller than γ, in a region (ρ ≃ 0.35) where u s displays a minimum.

The evolution of σ is more dramatic: it displays a sharp decrease and falls down to zero as soon as the measurement uncertainty reaches and overpasses the value of the rms γ. For values of ρ below 0.25, σ obeys to the σ 2 + ρ 2 = γ 2 law (represented as a dashed line in Fig. 4), but the calculated decrease becomes much faster in the transition zone. The uncertainty on σ increases notably in the transition region observed for s.

In the limit of large experimental uncertainties, the uncertainty propagation formula can be written as

u 2 ν = ω 2 u 2 s + ρ 2 (20) = ρ 2 1 + ω 2 / ω 2 i (21)
In this region of large measurement uncertainty, the inadequacy variable ξ becomes useless, as the calibration with the scaling factor alone enters a statistical regime.

Conclusion

A reanalysis of scaling factors calibration in the aim of providing quantified predictions shows that for large validation sets of accurate data, as used for vibrational frequencies, faithful prediction uncertainties can be derived from the standardly reported optimal scaling factor and rms. For much smaller datasets of a few dozens of data, as in the case of ZPVEs, uncertainty on the scaling factor should also be reported. The following limit formulas have been validated

and are proposed for uncertainty propagation from a given calculated harmonic frequency ω:

• large calibration sets of precise data (ρ ≪ γ): u ν (ω) = γ;

• small calibration sets of precise data (ρ ≪ γ):

u ν (ω) = γ N N -3 (1 + ω 2 / i ω 2 i );
• sets of data with large uniform uncertainty (ρ ≥ γ): u ν (ω) = ρ 1 + ω 2 / i ω 2 i .

A general estimation framework, based on Bayesian Model Calibration, has been defined for those cases where the limit conditions defined above are not met.

The Multiplicative Uncertainty method proposed by Irikura et al. [START_REF] Irikura | Uncertainties in scaling factors for ab initio vibrational frequencies[END_REF] (u ν ≃ ωγ N/ ω where ǫ i ∼ N(0, ρ 2 i ) is the measurement uncertainty of ν obs i , and ξ ∼ N(0, σ 2 ) is a discrepancy function between the linear model and the observations. This model has two unknown parameters, s and σ, to be estimated on a calibration dataset consisting of N calculated harmonic frequencies {ω i } N i=1 , and their corresponding observed frequencies ν obs i N i=1 . In the Bayesian data analysis framework, [START_REF] Sivia | Data Analysis: A Bayesian Tutorial[END_REF][START_REF] Gregory | Bayesian Logical Data Analysis for the Physical Sciences[END_REF] all information about parameters can be obtained from the joint posterior pdf p s, σ| ν obs i , ρ i , ω i N i=1 . In order to simplify the notations, we will omit in the following the list indices when they are not necessary.This pdf is obtained through Bayes theorem p(s, σ| ν obs , ρ, ω ) ∝ p({ν} |s, σ, {ρ, ω}) p(s, σ)

where p( ν obs |s, σ, {ρ, ω}) is the likelihood function and p(s, σ) is the prior pdf.

As the difference between observation and corrected frequency has a normal distribution

ν obs i -sω i ∼ N(0, σ 2 + ρ 2 i ) (24)
the likelihood function for a single observed frequency is

p(ν obs i |s, σ, ρ i , ω i ) = 2π σ 2 + ρ 2 i -1/2 exp - 1 2
ν obs i -sω i 2 σ 2 + ρ 2 i ( 25
)
Considering that all frequencies are measured independently (with uncorrelated uncertainty) the joint likelihood is the product of the individual ones, i.e.

p ν obs |s, σ, {ρ, ω} = N i=1 2π σ 2 + ρ 2 i -1/2 exp - 1 2 N i=1 ν obs i -sω i 2 σ 2 + ρ 2 i ( 26
)
As there is a priori no correlation between s and σ, we use a factorized prior pdf p(s, σ) = p(s)p(σ). In the absence of a priori quantified information on s, a uniform pdf p(s) = cte is used. For σ,we have to consider a positivity constraint, and we use a Jeffrey's prior, p(σ) ∝ σ -1 .

The posterior pdf is finally defined up to a proportionality factor which is irrelevant for the following developments p(s, σ| ν obs , ω, ρ ) ∝ σ -1

N i=1 σ 2 + ρ 2 i -1/2 exp - 1 2 N i=1 ν obs i -sω i 2 σ 2 + ρ 2 i (27)
A.2 Case of negligible measurement uncertainties

For the analysis of vibrational frequencies, it is generally considered that experimental uncertainties are negligible (ρ i = 0). The general expression for the posterior pdf (Eq. 27) can be simplified accordingly to p(s, σ| ν obs , ω ) ∝ σ -N -1 exp -1 2σ

from which we can derive analytical estimates for the parameters and their uncertainties.

A.2.1 Estimation of s

The marginal density for s is obtained by integration over σ p(s| ν obs , ω ) =

A.4 Uncertainty propagation

In the Bayesian framework, the posterior pdf p(s, σ| ν obs , ρ, ω ) can be used to estimate the uncertainty of predicted frequencies p(ν ′ |ρ ′ , ω ′ , ν obs , ρ, ω ) = dsdσ p(ν ′ |s, σ, ρ ′ , ω ′ )p(s, σ| ν obs , ρ, ω )

where

p(ν ′ |s, σ, ρ ′ , ω ′ ) ∝ (σ 2 + ρ ′2 ) -1/2 exp - (ν ′ -sω ′ ) 2 2(σ 2 + ρ ′2 ) (52)
results from the stochastic model (Eq. 12). This integral has generally to be evaluated numerically.

Figure 3 :

 3 Figure 3: Confidence intervals at 95% level calculated with Bayesian Model Calibration (left column) and Multiplicative Uncertainty (right column) methods, in two representative frequency regions from the calibration dataset for the HF/6-31G* combination of theory/basis-set (dots).

Figure 4 :

 4 Figure 4: Evolution of measurement model parameters with the amplitude of an hypothetical uniform experimental measurement uncertainty ρ on ZPVE; B3LYP/6-31G* combination of theory/basis-set (green squares with error bars). The brown vertical dashed line indicates the value of the rms γ. Top panel: the red dashed lines represent the 1σ confidence interval in the limit of null experimental uncertainty; the blue dashed line represent the 1σ confidence interval in the weighted least squares limit. Bottom panel: the red dashed line represents the σ 2 + ρ 2 = γ 2 law, truncated to positive values of σ.

2 i 2 -N/ 2 ( 2 i

 2222 ν obs , ω ) ∝ 1 + (sŝ) 2 ω Nγ 34)which has the shape of a Student's distribution 16Stt(x) ∝ 1 + x 2 n -(n+1)/2(35)Bayesian analog to weighted least squares. The posterior pdf for s is then p(s| ν obs , ω, ρ ) ∝ uncertainty over the dataset, the scaling factor uncertainty varies linearly with ρ u s = ρ/ ω

Table 1 :

 1 Statistical estimates and validation for MU and BMC models for vibrational frequencies extracted from the CCCBDB for the HF/6-31G* combination of theory/basis-set.

		Summary stat.	MU		BMC
		ŝ	σ s	γ(cm -1 )	u s	%CI 95	u s	σ(cm -1 ) %CI 95
	All frequencies (2738)
	Full set	0.8984 0.069	45.3	0.024	-	0.0005	45.3	-
	Calibration set 0.8986		45.3	0.024	-	0.0007	45.3	-
	Validation set	-	-	-	-	83.0	-	-	94.6
	Frequencies between 3180 and 3500 cm -1 (479)
	Full set	0.9050 0.0087	28.7	0.0087	-	0.0004	28.8	-
	Calibration set 0.9052		23.3	0.0071	-	0.0005	23.4	-
	Validation set	-	-	-	-	95.0	-	-	95.4

Table 2 :

 2 Uncertainty propagation with calibrated model for a set of 2738 vibrational frequencies extracted from the CCCBDB for the HF/6-31G* combination of theory/basis-set and for a set of 39 ZPVE of the Z1 set for the B3LYP/6-31G* combination.

be recovered by the Bayesian approach, except when the dataset spans a restricted frequency range, in which case it is reduced to a trivial, unweighted, standard deviation. The use of the scaling factor uncertainties as reported presently (November 2008) in the CCCBDB 9 cannot therefore be recommended. I would like to stress out that the validity of the formulas for uncertainty propagation depends to some extent on the normality of the residuals ν iŝω i of the linear regression.

Inspection of histograms of residuals (see e.g. Fig. 1 in Ref. 7 ) shows that this is not always the case. The customary approach to choose an optimal theory/basis-set combination is to assess their performance by the rms alone, maybe weighted by computational cost considerations. 6,7,8 One could also consider a "normality criterion" in order to reject theory/basis-set combinations providing non-normal residuals and from which the summary statistics cannot be used faithfully for uncertainty propagation. Analysis of restricted ranges of data as presently done by some authors for vibrations 8 is one way to improve the normality of residuals.

Semi-empirical correction of ab-initio results by scaling is presently very common and efficient for many observables. It certainly would be a large step towards the general applicability of uncertainty propagation, if statistically pertinent estimators were systematically reported in the literature devoted to the calibration of these correction models.

Acknowledgments

I would like to thank Prof. Leo Radom for providing me with the Z1 ZPVE dataset. B. Lévy is warmly acknowledged for helpful discussions.

A Appendix A.1 Bayesian analysis of scaling factor calibration model

We consider the measurement model

Posing n = N -1 and x 2 = (N -1)/N (sŝ) 2 ω 2 i /γ 2 , we can directly use the properties of the Student's distribution

to derive s = ŝ (37)

Estimation of σ

The marginal density for the standard uncertainty of the stochastic variable ξ is

Using the formula

one obtains readily the following estimates σ = γ (43)

A.3 Case of very large measurement uncertainties

When model discrepancy is negligible compared to measurement uncertainties, i.e. when the standard linear model is in a statistical regime, one recovers standard statistical analysis, the


Camille Faure

Rym Djerbi-Bouillié

Anaïs Domingot

Haniaa Bouzinba-Segard

Saïd Taouji

Yanis Saidi

Sandra Bernard

Floriane Carallis

Romy Rothe-Walther

Jean-Luc Lenormand

Romy Walther

Eric Chevet

Sandrine Bourdoulous
email: sandrine.bourdoulous@inserm.frcamille.faure@inserm.fr

Allosteric inhibition of HER2 by Moesin-mimicking compounds targets HER2-positive cancers and brain metastases

Keywords: HER2-positive breast cancer, Moesin, ERM family, Brain metastases, Allosteric inhibition

come

INTRODUCTION

Human Epidermal Growth Factor Receptor 2-positive breast cancer (HER2+ breast cancer) is defined by amplification of the HER2/neu oncogene and/or overexpression of its associated HER2 transmembrane receptor protein [START_REF] Du | Mechanisms of receptor tyrosine kinase activation in cancer[END_REF]. HER2+ breast tumours represent approximately 20-25% of breast cancers and are associated with a higher grade, more aggressive phenotype, and worse prognosis. With the advent of antibody-based (Trastuzumab, Pertuzumab) or small molecule tyrosine kinase inhibitors (Lapatinib) targeting HER2, the prognostic landscape for HER2+ breast cancer patients has considerably improved [START_REF] Montor | Receptor tyrosine kinases and downstream pathways as druggable targets for cancer treatment: the current arsenal of inhibitors[END_REF]. However, both de novo and acquired resistance to trastuzumab and cardiotoxic side effects of these inhibitors remain a significant obstacle for extensive use of these treatments [START_REF] Kreutzfeldt | The trastuzumab era: current and upcoming targeted HER2+ breast cancer therapies[END_REF]. About 30% of HER2+ breast tumours express a truncated form of HER2 (p95HER2), which confers resistance to trastuzumab and is associated with worse outcome in trastuzumab-treated patients [START_REF] Saez | p95HER-2 predicts worse outcome in patients with HER-2-positive breast cancer[END_REF][START_REF] Chumsri | High p95HER2/HER2 Ratio Associated With Poor Outcome in Trastuzumab-Treated HER2-Positive Metastatic Breast Cancer NCCTG N0337 and NCCTG 98-32-52 (Alliance)[END_REF]. More recently, somatic HER2 gene mutations were detected in a range of human cancer types that functionally activate HER2, drive and maintain cancers, and that can also confer resistance to HER2-directed drugs [START_REF] Connell | Activating HER2 mutations as emerging targets in multiple solid cancers[END_REF]. Finally, these targeted therapies have limited ability to cross the bloodbrain barrier (BBB) and show low efficacy against brain lesions. Brain metastasis, occurring in up to 50% of the trastuzumab-treated patients, is an end in breast cancer progression [START_REF] Kodack | Emerging strategies for treating brain metastases from breast cancer[END_REF], requiring novel therapies for successful treatment.

HER2 is a member of the HER family (EGFR/HER1, HER2, HER3, HER4) of transmembrane receptor tyrosine kinases (RTK) involved in various cellular processes including cell proliferation, motility, resistance to apoptosis, invasiveness, and angiogenesis. This RTK displays unique properties.

Structurally, HER2 contains an extracellular domain (amino-acids locked in an open conformation, a hydrophobic transmembrane domain (aa 640-672), a cytosolic juxtamembrane region (673-701), a tyrosine kinase domain (aa 720-977), and a C-terminal tail with regulatory tyrosine residues (978-1255) [START_REF] Ullrich | Signal transduction by receptors with tyrosine kinase activity[END_REF][START_REF] Olayioye | The ErbB signaling network: receptor heterodimerization in development and cancer[END_REF][START_REF] Garrett | The crystal structure of a truncated ErbB2 ectodomain reveals an active conformation, poised to interact with other ErbB receptors[END_REF]. A critical distinction defining its unique cell-signalling mode is its ability to promote its ligand-independent auto-dimerization and phosphorylation [START_REF] Fiore | erbB-2 is a potent oncogene when overexpressed in NIH/3T3 cells[END_REF], as well as liganddependent heterodimerisation and phosphorylation with the other HER family members [START_REF] Garrett | The crystal structure of a truncated ErbB2 ectodomain reveals an active conformation, poised to interact with other ErbB receptors[END_REF][START_REF] Graus-Porta | ErbB-2, the preferred heterodimerization partner of all ErbB receptors, is a mediator of lateral signaling[END_REF]. In HER2+ breast cancers, HER2/HER3 heterodimerisation promotes HER2 phosphorylation and phosphorylation of the kinase defective HER3, leading to stimulation of the downstream oncogenic PI3K/AKT pathway, while HER2 homodimerisation leads to downstream oncogenic RAS/MAPK and indirect PI3K/AKT pathway activation [START_REF] Fiore | erbB-2 is a potent oncogene when overexpressed in NIH/3T3 cells[END_REF][START_REF] She | Breast tumor cells with PI3K mutation or HER2 amplification are selectively addicted to Akt signaling[END_REF][START_REF] Junttila | Ligandindependent HER2/HER3/PI3K complex is disrupted by trastuzumab and is effectively inhibited by the PI3K inhibitor GDC-0941[END_REF]. ERM (Ezrin, Radixin, Moesin) proteins are involved in many cellular processes [START_REF] Hughes | Understanding ERM proteins--the awesome power of genetics finally brought to bear[END_REF]. These cytosolic proteins localise at cell surface-associated structures, such as microvilli and cell-adhesion sites [START_REF] Bretscher | ERM proteins and merlin: integrators at the cell cortex[END_REF].

They link transmembrane proteins and the cortical cytoskeleton by interacting with a RxxTYxVxxA motif located in the juxtamembrane region of several adhesion molecules, such as the hyaluronic receptor CD44, through their N-terminal FERM domain and by interacting through their C-terminal domain with F-actin [START_REF] Yonemura | Ezrin/radixin/moesin (ERM) proteins bind to a positively charged amino acid cluster in the juxta-membrane cytoplasmic domain of CD44, CD43, and ICAM-2[END_REF][START_REF] Hamada | Structural basis of adhesionmolecule recognition by ERM proteins revealed by the crystal structure of the radixin-ICAM-2 complex[END_REF][START_REF] Mori | Structural basis for CD44 recognition by ERM proteins[END_REF]. They are critical players in cell migration, growth and adhesion, but also cell invasion and metastasis formation [START_REF] Hughes | Understanding ERM proteins--the awesome power of genetics finally brought to bear[END_REF][START_REF] Bretscher | ERM proteins and merlin: integrators at the cell cortex[END_REF].

Here, we found that HER2 possesses a binding motif in its intracellular juxtamembrane region allowing allosteric inhibition by members of the ERM family. In HER2+ breast cancers, low Moesin expression correlates with increased HER2 expression. Through a high content screen designed to identify Moesinmimicking compounds, we discovered Zuclopenthixol. This compound efficiently inhibited activation of oncogenic forms of HER2, specifically blocked HER2+ breast cancer progression both in vitro and in vivo. Finally, known to cross the blood-brain barrier, it attenuated the growth of HER2+ breast tumours following brain implantation. These findings reveal a novel class of allosteric HER2 inhibitors with activity on both breast-and brain-localised tumours, which could markedly improve the treatment of HER2+ breast cancer and metastases.

MATERIALS AND METHODS

Reagents

A list of the antibodies used in this work is provided in Supplementary Table 1.

Zuclopenthixol hydrochloride, Flupenthixol, and derived analogs were synthetized and purified by Roowin (Riom, France).

Plasmids and mutagenesis

The list of primers and siRNA used in this work is provided in Supplementary Table 2.

The vectors used in this work are detailed in the Supplementary Materials and Methods

Cell culture and transfection

HBMECs (human bone marrow endothelial cells) kindly provided by Dr. B. Weksler (Weill Medical College of Cornell University, NY) and Caco-2/TC7 cells kindly provided by Dr M. Rousset (Université Pierre et Marie Curie, Paris) were cultured as described previously [START_REF] Schweitzer | Characterization of a newly established human bone marrow endothelial cell line: distinct adhesive properties for hematopoietic progenitors compared with human umbilical vein endothelial cells[END_REF], [START_REF] Chantret | Differential expression of sucrase-isomaltase in clones isolated from early and late passages of the cell line Caco-2: evidence for glucose-dependent negative regulation[END_REF]. The porcine kidney epithelial cell line LLC-PK1, the human breast cancer cell lines (SKBR3, BT474, MDAMB-231 and HCC1954) were obtained from the American Type Culture Collection (Manassas, VA) and were maintained in DMEM or RPMI-1640 (HCC1954) containing 10% FBS. All cell lines were cultured under 5% CO2 at 37°C. HBMECs and LLC-PK1 were transfected using Amaxa Inc nucleofector system (Kit V and U015 program) or Biorad electroporation system, respectively as previously described [START_REF] Gautreau | Morphogenic effects of ezrin require a phosphorylationinduced transition from oligomers to monomers at the plasma membrane[END_REF][START_REF] Lambotin | Invasion of endothelial cells by Neisseria meningitidis requires cortactin recruitment by a phosphoinositide-3-kinase/Rac1 signalling pathway triggered by the lipo-oligosaccharide[END_REF]. SKBR3, BT474 and HCC1954 were transfected with Amaxa using Kit C and E009 program. Proliferation and soft agar colony formation assays are described in supplementary methods. Periodic tests for Mycoplasma and authentication were performed using commercially available kits.

Transcriptomic analyses

HER2 and Moesin mRNA expression levels in patients with breast invasive carcinoma (n=526), stomach adenocarcinoma (n=478), bladder urothelial carcinoma (n=408), pancreatic adenocarcinoma (n=178), colorectal adenocarcinoma (n=379), ovarian serous cystadenocarcinoma (n=304), kidney renal clear cell carcinoma (n=533) and kidney renal papillary cell carcinoma (n=290) were from TCGA, Firehose Legacy. HER2 and Moesin mRNA levels in patients with cervical squamous cell carcinoma (n=278) were from TCGA, PanCancer Atlas. mRNA data were z-scores relative to diploid samples (RNA Seq V2 RSEM) downloaded through cbioportal (http://www.cbioportal.org). Cancer cell lines mRNA expression data were obtained from E-MTAB-2706 study (https://www.ebi.ac.uk/arrayexpress/).

Breast cancer tissue array

Sections from breast cancer tissue array (FFPE) including IHC results of HER2\ER\PR\Ki67 for 3 normal breast tissue and breast fibroadenoma, 2 breast cystosarcoma phyllodes, 7 breast intraductal carcinoma and 60 breast invasive ductal carcinoma, with duplicate cores per case were purchased from US Biomax, Inc (https://www.biomax.us/tissue-arrays/Breast/BR1503f). They were processed for immunohistochemistry using HER2, Ezrin or Moesin antibodies using a fully automated Leica (Hesse, Germany) BondIII stainer, according to the manufacturer's recommendations. Sections were then lightly counterstained with hematoxylin, dehydrated and cleared in graded alcohol and Ottix plus (MM-France), and finally covered with glass slips. Samples were scanned using a Lamina multilabel slide scanner (PerkinElmer) and were classified based on visual scoring of Moesin-positive tumour cells as Moesin low (0 to 10%), intermediate (11-50%) or high (>50%) expressing samples.

Tumour progression in orthotopic xenograft model

Experiments were performed on the TrGET platform of centre de Recherche de Cancérologie de Marseille (Institut Paoli Calmettes, Marseille, France) in accordance with the guidelines of the Institut National de la Santé et de la Recherche Médicale. The experimental protocol was approved by the Animal Experimentation Ethics Committee of Marseille (APAFIS#2079-2015092811101360 v3). Briefly, 5.10 6 BT474 cells resuspended in 100 µl (50% matrigel and 50% PBS) were implanted orthotopically in the mammary fat pad of NOD.Cg-Prkdc scid/J mice anesthetized with ketamine and xylazine and administered with metacam (SC, 1 mg/kg). Estradiol pellets were implanted subcutaneously. Metacam was administered 24h and 48h post implantation. Nineteen days after implantation, mice were randomized into 3 groups to be administered intraperitoneally during three weeks with vehicle (10% DMSO in PBS, 5 days a week, n=9), 4 mg/kg Zuclopenthixol (5 days a week, n=8) or 5 m/kg Zuclopenthixol (3 days a week, n=9). Mice weight and tumour volume were assessed 2 to 3 times a week using a calliper. At the end of the experiment, the collected tumours were photographed, weighed, cut into halves to be either frozen in liquid nitrogen or embedded in OCT and frozen at -80°C.

A tissue Lyzer™ was used to solubilize tumour proteins in a buffer containing 50 mM Tris pH=8.8, 25 mM NaCl, 1 mM EDTA, 1% Triton, 10% glycerol and 1 mM phosphatase (AEBSF and 1 mM orthovanadate) and 10 µg/mL protease inhibitors (aprotinin, leupeptin, pepstatin). 5 µm thick sections were immobilised on superfrost™ plus microscope slides and proceeded for immunofluorescence or immunochemistry analysis. Samples were scanned using a Lamina multilabel slide scanner (PerkinElmer) and were further analysed using confocal microscopy (spinning disk Leica, 40x). For quantitative analysis, fluorescence intensity of KI67 and DAPI labelling were measured using ImageJ software (NIH) and the proliferation index is displayed as a ratio between KI67-stained area over DAPIstained area.

Tumour progression in intracranial xenograft model

Experiments were performed by Oncodesign contract research organization (Dijon, France). The experimental protocol was approved by the Animal Experimentation Ethics Committee OnCoMet (n° study: 180078ET100). Briefly, 1.10 5 BT474 cells resuspended in 2 μL RPMI 1640 medium were stereotactically implanted into the caudate nucleus of the right cerebral hemisphere of 25 female BALB/c Nude mice, 4-5 weeks old, under gas anaesthesia with isoflurane. Drinking water was supplemented with estradiol (2.5 µg/mL). In the first set of experiments, magnetic resonance imaging (MRI) was performed at day 10, mice were then randomized and intraperitoneally received Zuclopenthixol (n=10, 7 mg/kg on Monday and Tuesday and 10 mg/kg on Wednesday, Thursday and Friday) or vehicle (n=10, 20% w/v hydroxypropyl-β-cyclodextrin per day for 5 consecutive days a week) and a second MRI was performed at day 20. In the second set of experiments, implanted mice were randomized at day 3 and intraperitoneally received Zuclopenthixol, vehicle at doses identical to the first set or received lapatinib (100 mg/kg, PO, N=10). MRI were performed at days 15 and 26 postimplantation. During MRI, mice were continuously anesthetized using isoflurane. Gadopentetate dimeglumine (Gd-DTPA, Magnevist, Bayer Healthcare Pharmaceuticals, Germany) was injected intravenously at 0.4 mmol/kg. MRI were acquired on a 4. 7T horizontal magnet (PharmaScan, Bruker Biospin GmbH, Germany) equipped with an actively shielded gradient system with the following parameters: time of repetition=700 ms, echo time=12 ms, field of view=40 mm × 40 mm, acquisition matrix=384 × 384, slice thickness=0.8 mm, slice gap=0.8 mm, slice number=10 and number of averages=4. The positions of the slices were determined using sagittal, coronal and axial imaging. MRI images were acquired under Para Vision (PV5.1, Bruker Biospin) and analysed under ImageJ. Regions of interest were drawn manually on anatomical images. Tumour volume was computed from these regions by multiplying the number of voxels by the voxel volume (in mm 3 ).

Statistical analysis

Statistical analyses were performed by GraphPad Prism 5 software. Unpaired/paired Student t test was used to analyze the statistical difference of two groups. One-or two-way ANOVA test followed by multiple comparison test, as indicated, was used to analyze the statistical difference between multiple groups. The correlation between HER2 and ERM expression was analyzed by Spearman r correlation coefficient. Data are presented as the mean ± SD or sem as indicated. P value <0.05 was considered statistically significant.

Additional Materials and Methods are provided in the Supplementary Information.

RESULTS

ERM proteins Ezrin and Moesin interact with HER2 and address HER2 to ERM-enriched regions

A direct interaction between the FERM domain of the ERM proteins and a R/KxxxYxL/V/IxxA motif located in the cytosolic juxtamembrane regions of InterCellular Adhesion Molecules (ICAM-1,-2, -3) CD43 and CD44 was previously reported [START_REF] Yonemura | Ezrin/radixin/moesin (ERM) proteins bind to a positively charged amino acid cluster in the juxta-membrane cytoplasmic domain of CD44, CD43, and ICAM-2[END_REF][START_REF] Mori | Structural basis for CD44 recognition by ERM proteins[END_REF]. We identified in the cytosolic juxtamembrane region of HER2 a similar ERM binding motif between Lys-676 and Leu-691, that was absent in other EGFR family members (Fig. 1A). To address whether this motif also allows interaction of HER2 with the ERM proteins, we generated a glycoprotein D-tagged HER2 form harbouring mutations in the critical amino acid residues involved in this ERM binding motif (gD-HER2-EBM*) (Fig. 1A). When ectopically expressed in human endothelial cells (HBMEC), the wild type gD-tagged form of the receptor (gD-HER2-WT) coimmunoprecipitated with Ezrin and Moesin (Fig. 1B). Although gD-HER2-EBM* construct was immunoprecipitated to a lower extent, interaction was drastically reduced with this construct (Fig. 1B).

In addition, both endogenous HER2 (Sup Fig. 1A) and gD-HER2-WT (Fig. 1C) were efficiently pulled down by the FERM domain of Ezrin fused to GST (GST-FERME) but not with GST alone, while gD-HER2-EBM* was poorly pulled down with GST-FERME (Fig. 1C), demonstrating weak binding of this mutated form to the FERM domain of Ezrin.

To investigate whether this interaction was direct, we first used a protein-protein interaction assay based on oxygen singlet transfer (AlphaScreen®). We detected an association between the biotinylated peptide encoding the cytosolic juxtamembrane region of HER2 (biot-JMHER2) and GST-FERME, whereas a low signal was generated using GST alone or in the absence of any peptide (Fig. 1D). This interaction was dose-dependent (Sup Fig. 1B and1C). Addition of non-biotinylated peptide coding for the juxtamembrane region of HER2 competed with biot-JMHER2/FERME interaction in a dose-dependent manner [maximum competition effect of 80%, apparent Kd (Kda) =13 nM], whereas competition was poorly efficient upon addition of non-biotinylated HER2 peptide harbouring mutations of the key residues in the EBM motif (45% inhibition, Kda = 67 nM) (Sup Fig. 1D). The biot-JMHER2/FERME interaction was in the same range of affinity as the interaction measured between GST-FERME and a biotinylated peptide coding for the cytosolic juxtamembrane region of CD44 (biot-JMCD44) containing a known ERM binding motif (Kda = 8 nM) (Sup Fig. 1E-G). Second, using surface plasmon resonance (SPR), we measured a high affinity interaction between GST-FERME and immobilized biot-JMHER2 peptide (Kd = 4.49 ± 1.52 nM) (Fig. 1E), which was similar to the one observed with immobilized biot-JMCD44 peptide (Kd = 5.79 ± 0.12 nM) (Sup Fig. 1H). No interaction was observed with GST alone or on immobilized peptide coding for the cytosolic region of CD147 (cytoCD147), a receptor which does not interact with ERM, as negative control (Fig. 1E). These results demonstrate that HER2 contains an ERM binding motif in its cytosolic juxtamembrane region allowing direct interaction with the FERM domain of ERM proteins.

In polarized epithelial cells, such as Caco2/TC7 intestinal epithelial cells, HER2 mostly localised at the basolateral membrane (Fig. 1F, top panels), a localisation resulting from the interaction of its Cterminal motif with PDZ domain-containing proteins [START_REF] Borg | ERBIN: a basolateral PDZ protein that interacts with the mammalian ERBB2/HER2 receptor[END_REF][START_REF] Shelly | Polar expression of ErbB-2/HER2 in epithelia. Bimodal regulation by Lin-7[END_REF]. A bipartite sorting signal (aa 692-701) next to the ERM binding motif is also necessary to ensure its proper targeting to the basolateral membrane [START_REF] Dillon | Basolateral targeting of ERBB2 is dependent on a novel bipartite juxtamembrane sorting signal but independent of the C-terminal ERBIN-binding domain[END_REF]. Less documented is the apical membrane localisation of HER2. We observed here that HER2 localises at the apical surface of Caco2/TC7 cells within ERM-enriched microvilli (Fig. 1F, top panels). When expressed in LLC-PK1 epithelial cells, which are deficient in the μ1B subunit of the AP1B adaptor complex, leading to significant amounts of HER2 that are missorted to the apical membrane [START_REF] Dillon | Basolateral targeting of ERBB2 is dependent on a novel bipartite juxtamembrane sorting signal but independent of the C-terminal ERBIN-binding domain[END_REF], both gD-HER2 WT and gD-HER2-EBM* were found at the lateral junctions, however only the WT form of HER2 co-localised with Ezrin within apical microvilli (Fig. 1F, bottom panels), indicating that HER2 interaction with ERM proteins controls the subcellular localisation of HER2 within ERM-enriched structures.

ERM proteins control the ligand-independent activation of HER2

We next observed that, when overexpressed in HBMEC, gD-HER2-EBM* exhibited higher levels of tyrosine phosphorylation compared to gD-HER2-WT (Sup Fig. 2A), suggesting that loss of HER2/ERM interaction might potentiate receptor activation. To test this hypothesis, we overexpressed gD-HER2-WT in HBMEC with GFP-tagged Ezrin or Moesin. The phosphorylation level of HER2 was reduced by more than 75% when co-expressed with Ezrin or Moesin (Fig. 1G). Expression of Ezrin (FERME) or Moesin (FERMM) FERM domains alone was sufficient to reduce the phosphorylation level of overexpressed HER2 (Fig. 1H and Sup Fig. 2B). To confirm this result, we overexpressed HER2 with VSVg-tagged Ezrin or with two previously described VSVg-tagged mutants of Ezrin: the T567D mutant mimicking the phosphorylation of a conserved threonine in the C-terminal actin binding site, which stabilises Ezrin in an active open conformation, and the non-phosphorylable mutant T567A [START_REF] Gautreau | Morphogenic effects of ezrin require a phosphorylationinduced transition from oligomers to monomers at the plasma membrane[END_REF][START_REF] Fievet | Phosphoinositide binding and phosphorylation act sequentially in the activation mechanism of ezrin[END_REF], or GFP as a negative control. The phosphorylation level of HER2 was reduced by 20 and 30% when coexpressed with Ezrin or with the T567A Ezrin mutant, and reduced by 55% when co-expressed with the T567D Ezrin mutant (Sup Fig. 2C). HER2 inhibition promoted by these forms of Ezrin was accompanied by a proportional reduction in the downstream activation of ERK and AKT protein kinases (Fig. 1G and Sup Fig. 2C). Accordingly, expression of gD-HER2-WT induced a 2 to 3-fold increase in the rate of endothelial cell proliferation, which was reduced by 70 to 85% when co-expressed with FERME, whereas FERME did not affect the basal cell proliferation (Fig. 1I). As expected, expression of FERME had no effect on HER2-EBM* activation (Fig. 1H), nor on HER2-EBM*-induced cell proliferation (Fig. 1I). In contrast, expression of the FERM domains of FAK or PYK2 (FERMF and FERMP) had no effect despite their related structure but lesser sequence similarity (Sup Fig. 2B), indicating that this inhibitory effect was specific to the ERM proteins.

Conversely, depletion of Ezrin, Moesin, or both in HBMEC induced respectively a 2, 3 and 4-fold increase in activation of endogenous HER2, together with a 3-fold increase in AKT activation, whereas depletion of the actin binding protein cortactin, as a control, did not affect HER2 activation (Fig. 1J).

Accordingly, depletion of Ezrin and Moesin further increased HER2 activation and the proliferation rate of endothelial cells expressing gD-HER2-WT, while it had no further effect on HER2-EBM* activation, nor on HER2-EBM*-induced cell proliferation (Sup Fig. 2D and2E). These experiments showed that Ezrin and Moesin exert a constitutive inhibitory effect that prevents the ligand-independent activation of HER2. However, although HER2 is the preferential heterodimerisation partner of the other HER family members [START_REF] Garrett | The crystal structure of a truncated ErbB2 ectodomain reveals an active conformation, poised to interact with other ErbB receptors[END_REF][START_REF] Graus-Porta | ErbB-2, the preferred heterodimerization partner of all ErbB receptors, is a mediator of lateral signaling[END_REF], expression of the Ezrin-VSV-g or of FERME did not alter the ligand-dependent activation of HER2 in heterodimers with EGFR/HER1 or with HER3 upon EGF or HRG stimulation, nor downstream activation of AKT and ERK MAPK (Sup Fig. 2F and2G). These results demonstrate that ERM proteins are allosteric inhibitors of HER2 by interacting with the ERM binding motif present in its juxtamembrane region. This interaction specifically prevents the ligand-independent activation of HER2.

The unbalance in ERM/HER2 expression contributes to HER2 activation in HER2+ breast cancers

Interestingly, we observed a significant inverse correlation between HER2 and Moesin transcripts (r=-0.2866, P=0.0161) in 70 commonly used human breast cancer cell lines, whereas a positive or no correlation between HER2 and Ezrin or Radixin mRNA expression was observed (Ezrin: r=0.3386, P= 0.0041; Radixin: r= -0.1509, P= 0.2123) (Fig. 2A). At the protein level, we also detected an inverse correlation between HER2 and Moesin expression in breast cancer cell lines with different HER2 status, while they expressed similar levels of Ezrin and Radixin (Fig 2B and Sup Fig. 3A-B). A significant inverse correlation between Moesin and HER2 mRNA expression levels (Spearman correlation coefficient=-0.3010; P<0.0001) was also observed in 526 patients-derived breast invasive carcinoma (Fig. 2C).

Among ERM protein members, a negative correlation with HER2 expression was also seen with Radixin, whereas a positive correlation was found with Ezrin (Ezrin: r=0.1538, P=0.0004; Radixin: r=-0.1783, P<0.0001) (Fig. 2C). Likewise, immunohistochemistry analysis performed on tissue microarray containing 67 ductal carcinomas with different HER2 status revealed a significant inverse correlation between Moesin and HER2 protein expression levels, while Ezrin remains expressed in HER2+ breast cancers (Fig. 2D and Sup Fig. 4A-C). Finally, similar observation was found in most cancer types known to have abnormalities in ERBB2 gene (cervix, stomach, bladder, pancreas, colon, ovary and kidney) (Sup Fig. 5). Altogether, these results indicated that low Moesin expression was significantly associated with HER2+ cancers and, based on our previous results, we hypothesized that this might contribute to aberrant activation of HER2.

To test this hypothesis, we overexpressed Moesin, Ezrin or their respective FERM domains in SKBR3 or BT474, two breast cancer cell lines overexpressing HER2 and devoid of Moesin expression (Fig. 2B).

Their overexpression reduced the aberrant activation of HER2 by 60% in BT474 (Fig. 2E) and by 40% and 100% respectively in SKBR3 cells (Sup Fig. 6A). This effect was accompanied by decreased AKT activation (Sup Fig. 6A) and inhibition of cell proliferation (Fig. 2F and Sup Fig. 6B-C). Interestingly, in HCC1954 breast cancer cell line expressing Moesin, although HER2 expression level was similar to SKBR3 and BT474 cells, HER2 activation was lower in these cells (Fig. 2B). The overexpression of Ezrin, FERME or Moesin in HCC1954 totally inhibited cell proliferation (Sup Fig. 6D-E). To strengthen this result, we fused FERME, or GFP as a control, to a cell-penetrating peptide derived from the Epstein-Barr virus ZEBRA transcription factor (28) (Sup Fig. 6F). As expected, incubation of SKBR3 cells with 0.3 to 0.9 µM FERME-Zebra induced a dose-dependent inhibition of HER2 activation up to 85%, whereas Zebra-GFP did not modify HER2 activation (Sup Fig. 6G). Altogether, these results demonstrate that ERM proteins are key allosteric regulators of HER2 activation. The unbalance in ERM/HER2 protein levels contributes to HER2 activation in HER2+ breast cancers.

Identification of ERM-mimicking compounds to inhibit HER2 activation

As overexpression of ERM proteins efficiently reverted HER2 activation in HER2+ breast cancers, we designed a strategy aimed at identifying ERM mimicking compounds that would actively block HER2 (Fig. 3A). Compounds were first selected on their ability to interfere with the HER2/FERME interaction measured using the above-described AlphaScreen® assay (Fig. 1D). After removal of the false positives (True hit screen), to eliminate compounds interfering with the HER2/FERME interaction through binding to GST-FERME, we performed a counter-screening AlphaScreen® assay to identify hits showing competition with the CD44/FERME interaction. The remaining hits were then characterized for their ability to directly bind to the ERM binding motif of HER2 using SPR, to inhibit HER2 activation and HER2dependent cell proliferation and for their absence of toxicity on cells that do not overexpress HER2.

Finally, the best hits were tested in vivo in an orthotopic xenograft model to evaluate their ability to inhibit HER2-dependent tumour growth. 1463 molecules were screened from 2 Prestwick chemical libraries consisting of small molecules composed mostly of approved drugs selected for their high chemical and pharmacological diversity, as well as for their known bioavailability and safety in humans, and a collection of natural products, mostly derived from plants, rich in diverse chemotypes. Results of the first screen at 24h are shown in Fig. 3B. Among the 77 compounds showing inhibition of HER2/FERME interaction, 31 were true hits confirmed in dose-response experiments (Data summarized in Table 1). Interestingly, some compounds, such as tolfenamic acid and 4,4'-(2,3-Dimethyltetramethylene) dipyrocatechol, were already known to block the growth of HER2+ cancer cells [START_REF] Liu | The nonsteroidal anti-inflammatory drug tolfenamic acid inhibits BT474 and SKBR3 breast cancer cell and tumor growth by repressing erbB2 expression[END_REF][START_REF] Zavodovskaya | Nordihydroguaiaretic acid (NDGA), an inhibitor of the HER2 and IGF-1 receptor tyrosine kinases, blocks the growth of HER2-overexpressing human breast cancer cells[END_REF]. Eleven hits were found to selectively interfere with HER2/FERME interaction and not with CD44/FERME interaction, and 4 molecules were validated to selectively bind to the ERM binding motif of HER2 using SPR. Among them, phenylbutazone and ebselen induced a poor inhibition of HER2 activation, isoliquiritigenin inhibited HER2 activation but, as it possessed genotoxic structural alerts, it was unsuitable for drug discovery. Finally, Zuclopenthixol hydrochloride was found to achieve potent HER2 inhibition both in vitro and in vivo (results detailed below).

Zuclopenthixol is an ERM-mimicking compound conferring efficient allosteric inhibition of HER2

In vitro, Zuclopenthixol induced a dose-dependent inhibition of the HER2/FERME interaction reaching 87% (IC50=9.8 µM) at 24h with no or low disruption of CD44/FERME interaction (Table 1).

Zuclopenthixol selectively bound to the ERM binding motif of HER2 as assessed using SPR (Sup Fig. 7A) and induced a dose-dependent inhibition of gD-HER2-WT overexpressed in HBMEC, accompanied by a proportional reduction in the activation of AKT and ERK protein kinases, whereas, as expected, it had no effect on gD-HER2-EBM* activation, nor on gD-HER2-EBM*-induced activation of AKT and ERK protein kinases (Sup Fig 7B). Zuclopenthixol also promoted a dose-dependent inhibition of HER2 activation in SKBR3 cells (Sup Fig 7C). Treatment with 3-5 µM Zuclopenthixol reduced by 45% and 55% the cell proliferation of SKBR3 or BT474, respectively, whereas no effect was observed on the proliferation of breast cancer cells that do no overexpress HER2 (MDAMB-231) (Fig. 3C and Sup Fig. 7D), demonstrating that this compound selectively inhibits HER2-dependent cell proliferation. Finally, as expected HCC1954 were also sensitive to the inhibitory effect of Zuclopenthixol, although they express Moesin (Sup Fig. 7E).

We then tested the effect of Zuclopenthixol on the anchorage-independent proliferation of breast cancer cell lines, as it correlates closely with tumorigenicity in animal model [START_REF] Schwartz | Integrins, oncogenes, and anchorage independence[END_REF]. Treatment with 5 µM Zuclopenthixol induced a 50% decrease in the size of SKBR3 micro-colonies (Fig. 3D) and completely blocked the development of micro-colonies formed by BT474 cells (Fig. 3E), whereas it had no effect on the development of MDAMB-231 micro-colonies (Fig. 3F). As a positive control, AG1478, a non-specific HER2 kinase inhibitor, induced a 75% decrease in the size of SKBR3 micro-colonies, whereas it had no effect on the formation of MDAMB-231 micro-colonies (Sup Fig. 7F). These results demonstrate that Zuclopenthixol selectively inhibits the anchorage-independent proliferation of breast cancer cell lines overexpressing HER2.

Zuclopenthixol is a typical antipsychotic from the thioxanthene family (commercialized as Clopixol, Cisordinol, or Acuphase) that acts by blockade of dopamine receptors. Similar results were observed with the related thioxanthene molecule Flupenthixol (Sup Table 3). However, poor or no effects were observed with other closely related dopamine antagonists, such as antipsychotics of the thioxanthene family (Chlorprothixene) or phenothiazine family (Thioproperazine) (Sup Table 3). Finally, close analogs of Zuclopenthixol were synthetized. Analog 1 inhibited the HER2/FERME interaction in vitro, HER2 activation and the anchorage-independent growth of SKBR3, although less efficiently than Zuclopenthixol and Flupenthixol, whereas no significant effects were observed with Analogs 2 and 3 (Sup Table 3). These data indicate that Zuclopenthixol and Flupenthixol were the most effective compounds in vitro, and that they promote blockade of HER2 by a mechanism independent of their neuroleptic activity.

As expected, Zuclopenthixol also efficiently inhibited HER2 activation, as well as both the anchoragedependent and -independent proliferation of gastric (NCI-87) and ovary (SKOV3) cell lines overexpressing HER2, demonstrating its potent action on HER2+ cancers (Sup Fig. 8A-C). Finally, Zuclopenthixol induced a dose-dependent inhibition of the truncated form of HER2 (p95HER2), which is resistant to antibody-based therapy, accompanied by a reduction in activation of AKT and ERK protein kinases (Sup Fig. 8D), and inhibited cell proliferation induced by the expression of mutated forms of HER2, V777L and V842I, two activating mutations in the kinase domain found in cancer patients and conferring resistance to tyrosine kinase inhibitors (Sup Fig. 8E). These results demonstrate that, by targeting the ERM binding motif in the juxtamembrane region of HER2, Zuclopenthixol may confer advantages over existing HER2-targeted therapies.

Zuclopenthixol inhibits the HER2-dependent tumour growth in vivo

To explore the potential of Zuclopenthixol to reduce the growth of HER2-overexpressing tumours in vivo, we used BT474 cells orthotopically implanted in the mammary fat pad of immunodeficient NOG mice (Fig. 4A). Treatment with Zuclopenthixol (4mg/kg, 5 days a week), or vehicle as a control, was initiated 19 days after cell engraftment. While control tumours followed an exponential growth curve, Zuclopenthixol treatment rapidly slowed down the tumour growth, to reach a meaningful tumour growth inhibition index of 40% 10 days post-treatment (Day 29), with a sustained effect until the Day 40 (Fig. 4B and4C). Accordingly, tumours from Zuclopenthixol-treated mice were macroscopically smaller (Fig. 4D) and exhibited a 40% reduction in tumour weight compared to the control (P=0.0196) (Fig. 4E). Zuclopenthixol treatment was overall well tolerated as indicated with the monitoring of mice body weight (Fig. 4F). Similar results were obtained with another scheme of Zuclopenthixol administration (5 mg/kg, 3 days a week), with a tumour growth inhibition index of 30% at Day 29 (Fig. 4B and4C) and a 35% reduction in tumour weight compared to the control (P=0.0354) (Fig. 4C and4D).

Biochemical analyses revealed a 45% decrease in HER2 activation in tumour lysates from Zuclopenthixol-treated animals compared to vehicle-treated animals, accompanied by a reduction in the activation of ERK protein kinases (Fig. 4G and4H). In agreement with a tumour growth inhibitory effect, Zuclopenthixol decreased by 85% the fraction of Ki-67-positive tumour cells (Fig. 4I and4J).

Altogether, these results provide strong evidence of the potent HER2 inhibitory effect of Zuclopenthixol on human breast cancer cells overexpressing HER2 in vivo.

Zuclopenthixol reduces the growth of HER2-dependent brain tumours

A major issue in the management of HER2+ breast cancers remains the disease progression in the central nervous system, since 30 to 50% of patients will develop brain metastases. This high incidence mainly results from the limited ability of actual therapies to cross the BBB [START_REF] Witzel | Breast cancer brain metastases: biology and new clinical perspectives[END_REF] and the blood-tumour barrier remains largely intact [START_REF] Tanaka | Distribution analysis of epertinib in brain metastasis of HER2-positive breast cancer by imaging mass spectrometry and prospect for antitumor activity[END_REF]. Because Zuclopenthixol is an antipsychotic with a known ability to cross the BBB, we addressed its capacity to reduce the growth of BT474 cells implanted in the caudate nucleus of the right hemisphere of immunodeficient Nude mice. Day 10 after intracranial implantation, mice were treated with Zuclopenthixol (M, Tu: 7 mg/kg; W, Th, F: 10 mg/kg; IP; n=10) or with vehicle (IP, n=10) (Fig. 5A). At Day 20, brain tumours from the vehicle-treated group were of 75 mm 3 average size, representing a 24.3-fold increase in their growth compared to Day 10. Zuclopenthixol administration was associated with smaller tumours (50 mm 3 ) exhibiting significantly slower progression with a 14-fold increase in their growth compared to day 10, therefore demonstrating a real benefit of Zuclopenthixol administration on HER2+ brain tumour progression (Fig. 5B-D). We next compared the efficiency of Zuclopenthixol (M, Tu: 7 mg/kg; W, Th, F: 10 mg/kg; IP; n=10) over Lapatinib (100 mg/kg 5d/w; PO; n=10) (Sup Fig. 9A). Treatments were initiated day 3 post-implantation. At Day 16 and Day 26, while Lapatinib had no effect as compared to control mice that received vehicle, Zuclopenthixol had reduced tumour size by 35 to 50% as compared to Lapatinib-treated tumours (Sup Fig. 9B-E). Combined, these data indicate that Zuclopenthixol would be promising as a therapeutic agent for HER2+ breast cancer with brain metastasis.

DISCUSSION

Much research has been conducted in recent years to improve the treatments for HER2+ breast cancer, especially in light of incomplete action, adverse effects and de novo or acquired resistance to HER2 targeted therapies. This implies the development of pharmaceuticals that act on mutated and truncated forms of the receptor and on brain metastatic disease, the incidence of which is increasing due to the improved management of systemic disease and increased survival rates. This study revealed an inhibitory mechanism of HER2 by the ERM proteins and the translation of this discovery into the identification of a novel class of anti-HER2 inhibitors targeting the cytosolic juxtamembrane region of HER2. Among the molecules identified, the antipsychotic drug Zuclopenthixol demonstrated a potent action on the progression of human breast cancers overexpressing HER2, on cancer cells expressing mutated or truncated forms of HER2 and, due its ability to penetrate through the BBB, on HER2+ breast cancer-derived brain tumours. Overall, this inhibitor, via its mode of action, presents several advantages over existing anti-HER2 therapies and could thereby represent an important additional option in future HER2-targeted cancer therapy, in particular for brain tumour progression.

Among the large family of RTKs, HER2 displays unusual structural features conferring unique properties. Here, we have highlighted a novel structural particularity of this receptor, which, unlike other RTK family members, possesses a functional R/KxxxYxL/V/IxxA motif allowing interaction with ERM proteins [START_REF] Yonemura | Ezrin/radixin/moesin (ERM) proteins bind to a positively charged amino acid cluster in the juxta-membrane cytoplasmic domain of CD44, CD43, and ICAM-2[END_REF][START_REF] Hamada | Structural basis of adhesionmolecule recognition by ERM proteins revealed by the crystal structure of the radixin-ICAM-2 complex[END_REF][START_REF] Mori | Structural basis for CD44 recognition by ERM proteins[END_REF]. We further demonstrated that this interaction tightly controls HER2 localisation and activation. ERM proteins link membrane proteins to the cortical actin cytoskeleton, and therefore are known as key regulators of receptor localisation, trafficking and/or recycling at the cell plasma membrane thus controlling their surface availability and signalling [START_REF] Mcclatchey | Merlin and the ERM proteins--regulators of receptor distribution and signaling at the cell cortex[END_REF]. To date, direct interaction of ERM proteins with transmembrane proteins has only been described for adhesion molecules [START_REF] Hamada | Structural basis of adhesionmolecule recognition by ERM proteins revealed by the crystal structure of the radixin-ICAM-2 complex[END_REF]. The associations described between ERM proteins and several signalling receptors, including EGFR, occur indirectly through interaction with the adapter NHERF-1 (or ERM-binding phosphoprotein 50), that binds to the C-terminal sequence of these receptors [START_REF] Mcclatchey | Merlin and the ERM proteins--regulators of receptor distribution and signaling at the cell cortex[END_REF][START_REF] Weinman | The association of NHERF adaptor proteins with g protein-coupled receptors and receptor tyrosine kinases[END_REF]. The subcellular localisation of HER2 is tightly regulated by different mechanisms, such as interaction with specific protein partners. For instance, the co-localization of HER2 with PMCA2 (plasma membrane ATPase2) in actin-rich membrane domains seems required for its stabilisation at the plasma membrane [START_REF] Jeong | PMCA2 regulates HER2 protein kinase localization and signaling and promotes HER2-mediated breast cancer[END_REF]. By interacting with NHERF-1, Ezrin may also help membrane retention of the HER2-PMCA2-NHERF-1 complex [START_REF] Jeong | Inhibition of ezrin causes PKCalphamediated internalization of erbb2/HER2 tyrosine kinase in breast cancer cells[END_REF][START_REF] Jeong | The scaffolding protein NHERF1 regulates the stability and activity of the tyrosine kinase HER2[END_REF]. The interaction of the PDZ domain ERBIN to the C-terminal part of HER2 has a critical role in restricting this receptor to the basolateral membrane of epithelial cells [START_REF] Borg | ERBIN: a basolateral PDZ protein that interacts with the mammalian ERBB2/HER2 receptor[END_REF]. Here, we demonstrated that, by interacting directly with HER2, ERM proteins redirect HER2 receptor within ERM-rich regions.

Interestingly, a basolateral targeting signal able to redirect the apically localised receptor to the basolateral membrane domain of polarized epithelial cells has also been described in the amino acid sequence following ERM binding motif [START_REF] Dillon | Basolateral targeting of ERBB2 is dependent on a novel bipartite juxtamembrane sorting signal but independent of the C-terminal ERBIN-binding domain[END_REF]. Hence, our work, together with other studies, demonstrates that the cytosolic juxtamembrane region of HER2 plays a key role in the regulation of its subcellular distribution.

Previous investigations have also shown that the juxtamembrane region plays a crucial role in the activation of HER receptors upon ligand binding, by stabilizing the formation of asymmetric kinase domain dimers allowing the transphosphorylation process [START_REF] Zhang | An allosteric mechanism for activation of the kinase domain of epidermal growth factor receptor[END_REF][START_REF] Jura | Mechanism for activation of the EGF receptor catalytic domain by the juxtamembrane segment[END_REF][START_REF] Brewer | The juxtamembrane region of the EGF receptor functions as an activation domain[END_REF]. Despite the unique structural conformation of the extracellular domain of HER2 locked in an open and active conformation [START_REF] Garrett | The crystal structure of a truncated ErbB2 ectodomain reveals an active conformation, poised to interact with other ErbB receptors[END_REF], HER2 remains in inactive homodimers unless overexpressed [START_REF] Nagy | Distribution of resting and ligand-bound ErbB1 and ErbB2 receptor tyrosine kinases in living cells using number and brightness analysis[END_REF] suggesting an endogenous mechanism able to restrain its ligand-independent activation [START_REF] Jura | Mechanism for activation of the EGF receptor catalytic domain by the juxtamembrane segment[END_REF][START_REF] Brewer | The juxtamembrane region of the EGF receptor functions as an activation domain[END_REF]. Here, we provide evidence that interaction of ERM proteins with the juxtamembrane region of HER2 prevents this ligand-independent activation. Accordingly, loss of ERM protein expression or mutations in the ERM binding motif of HER2 both enhanced HER2 activity. Furthermore, recurrent somatic mutations in the HER2 juxtamembrane domain were found in different patient tumours (https://cancer.sanger.ac.uk/cosmic), among which, the most frequent (R678Q) was shown to enhance HER2 activity [START_REF] Pahuja | Actionable Activating Oncogenic ERBB2/HER2 Transmembrane and Juxtamembrane Domain Mutations[END_REF]. It is tempting to speculate that mutations lying in this sequence would result in HER2 activation through interference with ERM binding. Taken together, these results demonstrate that ERM proteins are key allosteric regulators of HER2 activation, most likely by exerting a constraint on the juxtamembrane region of HER2 that hampers stabilisation in activated dimers. This mechanism prevents spontaneous HER2 activation in physiological condition suggesting that ERM binding precludes HER2-dependent oncogenic transformation, whereas loss of Moesin expression concomitant to HER2 overexpression in HER2+ breast cancers further contributes to the oncogenic activation of HER2.

Interestingly, we found a highly significant inverse correlation between Moesin expression and HER2 status in both cell lines and primary tumors of different cancers, including breast, cervix, stomach, bladder, pancreas, colon, ovary and kidney, indicating a potent role of Moesin in the development of HER2-positive cancers. As no mutation in Moesin gene can account for its downregulation in HER2positive cancers, this observation strongly suggests that epigenetic mechanisms, which perturbations represent hallmarks of human cancer cells, may directly or indirectly promote silencing of Moesin expression in HER2-positive cancer cells. Among epigenetic deregulation described in human cancers are changes in patterns of DNA methylation [START_REF] You | Cancer genetics and epigenetics: two sides of the same coin?[END_REF], the transcription of long non-coding RNAs, or microRNA (miRNA) that regulate gene expression by repressing translation and/or by promoting degradation of their target mRNA [START_REF] He | MicroRNAs: small RNAs with a big role in gene regulation[END_REF]. Future studies will aim at characterizing the mechanisms by which Moesin expression is repressed in HER2-positive cancer cells.

The restriction of HER2 activation through ERM binding prompted us to translate our findings into pharmacological intervention on HER2+ breast tumours. The design of a high throughput screening method based on this interaction to find Moesin-mimicking compounds allowed us to identify Zuclopenthixol, a neuroleptic belonging to the group of thioxanthene commonly used to treat acute episodes of mental disorders by blockade of dopamine receptors. As expected, this compound could bind the juxtamembrane region of HER2 and block HER2 activation. As a consequence, it specifically reduces HER2-dependent proliferation and HER2-positive breast tumour progression in vivo. Due to this original mode of action, Zuclopenthixol is active on several intrinsically altered forms of HER2 such as the p95 truncated form of HER2 expressed in up to 30% of patients that confers resistance to antibodies-based therapies, or oncogenic forms of HER2 with activating mutations in the kinase domain (V777L and V842I) conferring resistance to tyrosine kinase inhibitors. Finally, this compound, able to rapidly penetrate the brain, shows significant activity on the progression of aggressive HER2+ breast cancer-derived brain tumours. Interestingly, the closely related dopamine antagonist Flupenthixol had similar effects, while others such as Chlorprothixene did not interact with the juxtamembrane region of HER2, demonstrating a mechanism independent of their neuroleptic activity. These effects were observed at well tolerated doses of Zuclopenthixol hydrochloride (4 to 10 mg/kg in mice), higher than recommended for chronic administration in humans (150-300 mg every 2 weeks).

However, concentration may be further increased by steps of 50-100 mg once or twice weekly in patients requiring higher doses, or shorter intervals between doses. In addition, the time course of the antipsychotic action revealed a progressively enhanced response to antipsychotic drugs that follows an exponential curve with repeated drug administration [START_REF] Li | Antipsychotic-induced sensitization and tolerance: Behavioral characteristics, developmental impacts, and neurobiological mechanisms[END_REF]. Given these advantages over existing therapies, Zuclopenthixol or Flupenthixol, would therefore provide a valuable treatment of HER2+ breast cancers and of a wide range of other HER2 overexpressing tumours, to efficiently combat primary tumours and derived-brain metastases in combination with the current HER2-targeted drugs.

Taken together, through the discovery of an unexpected allosteric regulation of HER2 activation by the ERM proteins, we identified Zuclopenthixol as an ERM mimicking compound. Our work reveals a new approach to target oncogenic forms of HER2. It provides the proof of concept that Zuclopenthixol possesses efficient anti-tumour activity in HER2+ primary cancers and brain metastases and could be used in addition to HER2 targeted therapies to prevent and treat HER2+ cancers. In blue are compounds that also interfere with CD44/FERM E interaction. In green are compounds that failed to interact with HER2 in SPR. In yellow are compounds that did not significantly inhibited HER2 activation. In red are compounds that selectively interfered with HER2/ FERM E interaction, interacted with HER2 in SPR, and inhibited HER2 activation in HER2-positive breast cancer cells. ND, non determined.

Figure 1 :

 1 Figure 1: HER2 interaction with the ERM proteins Ezrin and Moesin addresses HER2 in ERM-enriched regions and control its ligand-independent activation (A) Top, consensus sequence of the ERM binding motif and sequence alignment of the cytoplasmic juxtamembrane regions of adhesion molecules binding ERM proteins and of the HER family members. Basic and acidic residues are shown in blue and red, respectively. The basic clusters located in the ERM binding motif are underlined. Glutamines are shown in green. Key residues of the ICAM-2 binding motif to Radixin FERM domain are boxed in brown. Bottom, schematic depiction of gD-tagged HER2 vectors showing the transmembrane domain (TM) and the juxtamembrane region (JM) of gD-tagged wild type HER2 (gD-HER2-WT), and the mutant generated with alanine and glycine substitutions within the ERM binding motif (gD-HER2-EBM*). (B) Human endothelial cells (HBMECs) were transfected with vectors encoding gD-HER2-WT or gD-HER2-EBM*. Lysates were immunoprecipitated with an anti-gD antibody and analysed by western blot using anti-Moesin, anti-Ezrin and anti-gD antibodies. (C) HBMECs were transfected with gD-HER2-WT or gD-HER2-EBM* constructs and cell lysates were analysed by western blot with anti-gD antibody (left panel). Decreasing concentrations of respective cell lysates were pulled down with GST-FERME and analysed by western blot with anti-gD and anti-GST antibodies (right panels). (D) On the left, AlphaScreen® assay with 125 nM GST-FERME (red), or GST (blue) incubated with 10 nM biotinylated JM HER2 peptide (biot-JMHER2). A representative experiment is shown (n=3) where data are mean ± sem (n=2). On the right, AlphaScreen® assay with 83 nM GST-FERME incubated in the presence (red) or in the absence (blue) of 9.25 nM biot-JMHER2 peptide. Data are mean ± sem (n=2). (E) Peptides encoding the cytosolic JM region of HER2 (biot-JMHER2, red) or the short cytosolic tail of CD147 (cytoCD147, blue) were captured on a streptavidin-coated sensor chip (surface immobilization level of 60 and 115 resonance units (RU), depending on their respective molecular weight). GST (dotted lines) or GST-FERME (solid lines) were used as analytes and injected sequentially at 40 nM, 200 nM and 1000 nM to perform single-cycle kinetics. (F) Top panels, confluent monolayers of Caco-2/TC7 enterocytes were labelled with anti-Z01 (red) and anti-HER2 (green) antibodies (top panels) or with anti-Ezrin (red) and anti-HER2 (green) antibodies (lower panels). Images of xy/xz plans and xz sections (z-cut) are shown. Merged images of the same fields are presented in the right panel (overlay) and higher magnifications of the inset are presented in the bottom panels. Horizontal black arrows indicate the lines on the xy plan where the z-cut presented underneath were selected. Bars represent 10 μm. Bottom panels, LLC-PK1 epithelial cells transfected with vectors encoding gD-HER2-WT or gD-HER2-EBM* were labelled with anti-Ezrin (red)

Figure 2 :

 2 Figure 2: The unbalance in ERM/HER2 expression contributes to HER2 activation in HER2+ breast cancers (A) Color-coded representation of HER2, Moesin (MSN), Ezrin (EZR) or Radixin (RDX) mRNA expression levels in 70 commonly used breast cancer cell lines from E-MTAB-2706 study (https://www.ebi.ac.uk/arrayexpress/). Spearman correlation coefficients r=-0.4771 (MSN), r=0.3354 (EZR), r=-0.2542 (RDX); P value (two-tailed), P<0.0001 (MSN), P=0.0045 (EZR), P=0.337 (RDX). Cell lines used in this study are highlighted in grey. (B) Lysates from breast cancer cell lines (MDAMB-231, SKBR3, BT474 and HCC1954) were analysed by western blots using anti-phospho HER2 (pY1248-HER2), anti-HER2, anti-Moesin or anti-Ezrin antibodies. (C) Color-coded representation of the mRNA expression level of HER2, Moesin (MSN), Ezrin (EZR) and Radixin (RDX) in samples from 526 patients with breast invasive carcinoma from TCGA cohort (http://www.cbioportal.org). Spearman correlation coefficients r=-0.3010 (MSN), r=0.1538 (Ezrin), r=-0.1783 (Radixin); P value (two-tailed) P<0.0001, P=0.0004 (Ezrin), P<0.0001 (Radixin). (D) Representative images of human breast carcinoma sections from each molecular subtype labelled by immunohistochemistry with anti-HER2 (brown) and anti-Moesin or anti-Ezrin (red) antibodies. TNBC = triple negative breast cancers. Bars represent 50 μm. The immunohistochemistry analysis

Figure 3 :

 3 Figure 3: Zuclopenthixol is an ERM-mimicking compound conferring allosteric inhibition of HER2 (A) Screening strategy used to identify Moesin mimicking compounds. 1463 drugs from commercially available libraries were screened for their ability to compete with HER2/FERME interaction leading to the identification of 77 first hits. After removal of the false positive, 31 remaining compounds were submitted to a counter-screen to select hits showing no competition with CD44/FERME interaction. 11 hits were characterized for their ability to bind peptide encoding the JM domain of HER2 in SPR, to selectively inhibit HER2 activation and HER2-dependent cell proliferation and for their absence of toxicity on cells that do not overexpress HER2. The best hit (Zuclopenthixol) was tested in vivo in an orthotopic xenograft model. (B) Signal of HER2/FERME interaction 24h after the addition of compounds (Zuclopenthixol is shown in red). (C) Proliferation curve of HER2+ (SKBR3 or BT474) or HER2-negative (MDAMB-231) breast cancer cell lines treated with vehicle or with 3 µM Zuclopenthixol assessed by real time impedance-based cell proliferation assay. Arrows indicate beginning of the treatment. A representative experiment is shown (n=2-4) where data are mean ± SD (n=2-4); statistical analysis are paired t test, **** P<0.0001. (D-F) Anchorage-independent growth of SKBR3 (D), BT474 (E) or MDAMB-231 (F) cells treated with vehicle or 5 µM Zuclopenthixol. Representative images and quantification of the colony mean area are shown where data are mean ± sem (n=2), unpaired t test, ** P<0.01 (n=5-25) (D); (n=1), unpaired t test, * P<0.05 (n=2-5 replicates) (F); (n=1), unpaired t test, ns P=0.59.8 (n=2-4 replicates) (F).

Figure 4 :

 4 Figure 4: Zuclopenthixol inhibits the HER2-dependent tumour growth in orthotopic xenograft model (A-J) 5.10 6 BT474 cells were implanted orthotopically in the mammary fat pad of NOD.Cg-Prkdc scid/J mice, in the presence of estradiol supplement. After 19 days, mice were randomized in 3 groups (n=8 or 9 mice/group) and administered intraperitoneally with Zuclopenthixol (4 mg/kg per day for 5 days a week n=8, or 5 mg/kg per day for 3 days a week; n=9) or vehicle (10% DMSO in PBS; n=9,) during 3 weeks. (A) Scheme of the protocol used in vivo. (B) Individual tumour volume of vehicle-treated or Zuclopenthixol-treated mice. Arrow indicate beginning of the treatment at Day 19. (C) Mean tumour volume of vehicle-treated or Zuclopenthixol-treated mice, normalized to the tumour volume at Day 19. Data are mean ± sem; two-way RM ANOVA followed by Bonferroni's multiple comparison test, ** P<0.01, *** P<0.001, **** P<0.0001. (D) Tumours collected at the end of the experiment. (E) Scatter plot showing tumour weight at the end of the experiment and mean ± sem; one-way ANOVA followed by Bonferroni's multiple comparison test, * P<0.05. (F) Mean weight of mice monitored 3 times a week during the treatment. (G) Western blot analysis of the tumour lysates from vehicle-or Zuclopenthixol-treated mice (4 mg/kg) using antibodies directed against activated HER2 (pY HER2), activated ERK (pERK), activated Akt (pAkt) or Clathrin as a loading control. (H) Quantification of the results presented in G where data are mean ± sem (n=4), multiple paired t test * P<0.05.(I) Representative images of immunohistochemistry analysis of tumour sections from vehicle-or Zuclopenthixol-treated mice using antibodies directed against HER2 (brown) and Ki67 (red). Bars represent 100 μm.(J) For quantitative analysis, sections were also labelled in immunofluorescence and the proliferation index (KI67/DAPI) is displayed on the right where data are mean ± sem (n=2-4); unpaired t test **** P < 0.0001.

Figure 5 : 3 V

 53 Figure 5: Zuclopenthixol reduces the growth of HER2-dependent brain tumours (A-D) 1.10 5 human breast cancer BT474 cells were intracranially implanted in immunodeficient BALB/c Nude mice supplemented in estradiol. 10 days after (D10), tumour volume was evaluated by MRI and mice were randomized to be treated with Zuclopenthixol (M, Tu: 7 mg/kg; W-F: 10 mg/kg IP; n=10) or with vehicle (20% w/v hydroxypropyl-β-cyclodextrin (HP-β-CD) IP; n=10). 10 days after (D20) another MRI was performed to monitor brain tumour growth. (A) Scheme of the protocol used in vivo.

Table 1 :

 1 Compounds showing inhibition of HER2/FERME interaction in AlphaScreen®.

			CONFIRMATION			COUNTER SCREEN		HER2 interaction (SPR)	HER2 inhibition
		Inhibition 1h	IC50	Inhibition 24h	IC50	Inhibition 1h	IC50	Inhibition 20h	IC50
		(%)	(µM)	(%)	(µM)	(%)	(µM)	(%)	(µM)
	Merbromin	98.5	0.246	86	0.46	100	0.016	ND	ND
	Chicago sky blue 6B	99	0.003	98.6	0.024	100	0.077	ND	ND
	4,4'-(2,3-Dimethyltetramethylene) dipyrocatechol	78	2.2	84	1.1	97	0.070	ND	ND
	R(-) Apomorphine hydrochloride hemihydrate	18	ND	66	3.9	35	0.16	86	9.4
	Cynarin	69	0	36	1459	96	0.055	74	0.35
	Myricetin	94	2	95	7	100	0.084	99	0.9
	Lansoprazole	49	80.9	28	22.12	83	0.007	78	22.55
	Oxybenzone	12	ND	52	1.27	0	ND	54	1.06
	Abietic Acid	64	0	0	ND	94	0.76	64	1.15
	Acitretin	82	20.1	33	23.55	87	8.95	74	11.06
	Cefsulodin sodium salt	75	1.9	29	1.559	95	4.37	69	10.3
	Ethoxyquin	85	30.5	23	21.76	82	3	68	4.92
	Tiratricol, 3,3',5-triiodothyroacetic acid	88	6.1	89	5.4	94	0.016	ND	ND
	Alexidine dihydrochloride	65	6.2	41	157	67	4.86	29	9.50
	Carbidopa	38	0.000001	93	2.3	96	0.00005	95	36.37
	Paroxetine Hydrochloride	56	59	71	2.294	91	1.1	80	5.38
	Tenatoprazole	65	115.3	82	14.6	95	0.098	93	1.62
	Entacapone	52	0.04	42.8	0.136	68	1.18	ND	ND
	Thimerosal	53.9	0.5	20	42	94	0.0003	ND	ND
	Tolfenamic acid	62	134.5	43	26.71	65	33.68	52	26.84
	Chloroxine	64	11.7	0	ND	49	ND	0	ND	-
	Rotenone	21	0.04	61	23.8	0	N/A	0	N/A	-
	alpha-Ergocryptine	30	0.16	45	2.3	0	N/A	0	N/A	-
	Syrosingopine	37	4.6	59	7.8	0	N/A	0	N/A	-
	Bromocryptine mesylate	38	2.4	49	13.3	0	N/A	7	N/A	-
	Misoprostol	24	0.023	65	156.7	23	0.22	47	981.7	-
	Norgestimate	53	0.43	70	8.9	77	51.1	69	24.53	-
	Ebselen	77.9	0.045	39.6	43.9	52	1585	ND	ND	+	-
	Phenylbutazone	60.4	0.68	16.8	667	0	ND	ND	ND	+	-
	Isoliquiritigenin	33	20.3	44	4	0	N/A	15	56.7	+	+
	Zuclopenthixol hydrochloride	73	50	87	9.8	0	ND	53	10.3	+	+
	TOTAL		31				11			4	2

ACKNOWLEDGEMENTS

We thank B.B. Weksler, M. Rousset, M. Arpin, J. Delon, J. Baselga, M. Sliwkowski, H. Enslen and E Charafe-Jauffret for kindly providing reagents. We thank Remy Castellano and Yves Collette of the TrGET platform (Institut Paoli Calmettes) and Oncodesign for the animal experiments. We thank the Biophysical and Structural Chemistry platform of the Institut Européen de Chimie et Biologie (Pessac/Bordeaux, France) and the platforms of the Institut Cochin (Imag'IC, Cybio, HistIM) for their expert technical assistance. This work was supported by the Centre National de la Recherche Scientifique, the Institut National de la Santé et de la Recherche Médicale, the Université de Paris, the Association pour la Recherche contre le Cancer (SFI20101201780 and PJA 20131200363), The Fondation de France (00016391), the GEFLUC Association (GEFLUC2016) and the Société de Transfert de Technologies (SATT) Ile de France Innov (ANR-10-SATT-05-01). C Faure was supported by Fondation de France and SATT. R Djerbi-Bouillié was supported by a doctoral fellowship from the Ministère de la Recherche and by ARC. A Domingot was supported by a doctoral fellowship from the Ligue Contre le Cancer and ARC. S Bernard was supported by a doctoral fellowship from the Université Paris Diderot and ARC.