Jiaxin Xu

Jrme Bobin

Anne De De Vismes Ott

Christophe Bobin

Spectral unmixing for activity estimation in Gamma-Ray Spectrometry

A challenging problem in the domain of gamma-ray spectrum analysis is the rapid detection of artificial radionuclides, which are present at low activity levels. We introduce in this paper new algorithms for activity estimation based on spectral unmixing techniques, which aim to decompose a measured spectrum into individual spectra of radionuclides. We propose to tackle the activity estimation problem as an inverse problem, where individual activities appear as mixing weights related to individual spectra. In contrast to standard approaches, this allows us to account for the full spectrum of each radionuclide (i.e. peaks and Compton continuum). In this article, we investigate different approaches to solve the underlying spectral unmixing problem: standard regularized least squares regression (LS) and a novel regularized maximum likelihood estimation that allows to precisely account for the true Poisson statistics of the physical process underlying the detection. Both methods implement the non-negativity constraint to enforce the fact that the activity of radionuclides cannot be negative. Experimental results on simulated and measured spectra are presented and compared to standard methods, it is shown that the proposed approach leads to more accurate estimations, especially when the counting rate is low, which gives a significant advantage for the rapid detection.

Index Terms-gamma-ray spectrometry, spectral unmixing, inverse problem.

I. INTRODUCTION

G AMMA-RAY spectrometry is one of the main technics used for measuring the activity concentrations of radionuclides in environmental samples because it is direct, nondestructive, rapid and multi-elementary. It particularly plays a central role to monitor the radiological environment or perform radioecology studies, which are some of the goals of The French Institute for Radiation Protection and Nuclear Safety (IRSN) 1 . More precisely, radioactivity in environmental samples is measured in the laboratory of environmental radioactivity metrology (LMRE), which is in charge of emergency preparedness. This task mandates the rapid measurements in case of an incident or an accident with releases so as to give rapid and reliable information to the population, as described in [START_REF] De Vismes | Fission product activity ratios measured at trace level over france during the fukushima accident[END_REF]. In this context, a gamma-ray spectrum is the histogram of the number of detected events as a function of the energy deposited by the gamma-ray or X-ray in the detector. Due to the possible interactions between photons and the material 1 https://www.irsn.fr/EN/Pages/home.aspx of the detector (see for instance [START_REF] Knoll | Radiation Detection and Measurement[END_REF] for more details). The spectrum obtained for one photon has two main components: a peak at the photon energy, called total absorption peak, and a continuum at lower energy, called Compton continuum. Depending on its decay scheme, a radionuclide can emit several photons and its individual spectrum thus comprises several peaks and associated continua. Finally the spectrum obtained with the measurement of an environmental sample (by HPGe detector) as shown in Figure 1 is the sum of the individual spectra of each radionuclide and the background spectrum. Radionuclides are classically identified thanks to their characteristic peak energy and quantified from the peak surface related to the activity via the detection efficiency. We introduce a novel spectral unmixing algorithm that precisely take into account the exact Poisson statistics of the measured spectra. More precisely, spectral unmixing can be regarded as an inverse problem where a given gamma spectrum is composed of M channels:

x = [x 1 , ...x M ] (1)
For ∀i ∈ M , the Poisson process of radioactive decay leads us to model the problem as:

x i ∼ P([Φa] i + b i ) (2)
We note the spectral signatures of each radionuclide with Φ = [φ 1 , ...φ N ] and a = [a 1 , ...a N ] for their mixing weights, where N is the number of radionuclides. In (2), [Φa] i is the sum of the counting rates for each radionuclide on the ith channel. Similarly, b i stands for the counting rate of background spectrum on the ith channel. The aim is to decompose the measurement x into individual spectra of radionuclides and the background spectrum b (see Figure 1). The spectral signatures Φ and a background spectrum b being known in advance, the activity estimation problem is therefore equivalent to finding the mixing weights a.

A well-known challenge of the gamma-ray spectral analysis is the low statistics of the counting rate, which has attracted more attention in the field of rapid detection and rapid characterization of sources under emergency conditions. For example, the 137 Cs is an artificial radionuclide present in environmental samples in France. In practice, the detection of 137 Cs takes more than a week after the sampling. The objective of this study is to improve the gamma-ray spectral analysis and focus particularly on the artificial radionuclides at low statistics. A common strategy used to analyze gamma-ray spectrum is the peak area calculation. For example, Genie2000 from Canberra is a commercial software based on a step of peak research followed by a Gaussian fit to get the peak surface. This process is usually based on Region of interest (ROI) as described in [START_REF] Gilmore | Practical Gamma-ray Spectrometry[END_REF]. As shown in Figure 2, the net area n N is calculated by correcting from the background with:

n b = p 2b (n b1 + n b2 ) (3)
The performance of this approach is limited. Firstly, the calculation of net areas considers the counting distribution is approximately Gaussian, which is not valid at low statistics since an radioactive source emits photons randomly according to Poisson process. Secondly, a gamma-ray spectrum consists of photon-peaks and Compton continua, the problem of interference between individual spectra is difficult to handle with this peak-based analysis.

Peak-based analysis is a popular approach that has been implemented [START_REF] Kirkpatrick | Poisson statistical methods for the analysis of low-count gamma spectra[END_REF] to further account for the exact Poisson statistics of the measurements. However, this technique only relies on region of interest at the vicinity of related peaks and does not take into account the entire spectrum. [START_REF] Kirkpatrick | Poisson statistical methods for the analysis of low-count gamma spectra[END_REF] however shows the benefit of taking care of the Poisson statistics. The application of full-spectrum analysis of gamma-ray spectrum [START_REF] Hendriks | Full-spectrum analysis of natural γ-ray spectra[END_REF] uses re-weighted least squares for spectral unmixing of gamma-ray spectra. In this article, the authors demonstrated that compared to the standard peak-based analysis, using the full spectrum improves the sensitivity and reduces the time of measurement.

Activity estimation problem in gamma-ray spectrometry has been also studied in [START_REF] Sepulcre | Sparse regression algorithm for activity estimation in γ spectrometry[END_REF], which considers activity estimation as a sparse regression problem. In this article, the authors propose to estimate the number of individual electrical pulses and their arrival times. Other contributions of the activity estimation in the field of machine learning algorithms were also applied to gamma-ray spectral analysis as presented in [START_REF] Yoshida | Application of neural networks for the analysis of gamma-ray spectra measured with a ge spectrometer[END_REF], where peak energy data are applied to neural networks. In [START_REF] Sharma | Anomaly detection in gamma ray spectra: A machine learning perspective[END_REF], the measured spectra are used to anomaly detection in gamma-ray spectra. However, approaches based on neural networks do not allow to precisely account the physical model underlying the detection.

B. Contribution

In this paper, we investigate a new approach for the estimation of the activity of radionuclides from gamma-ray spectra. The proposed approach relies on spectral unmixing techniques, which have been introduced independently in the field of remote sensing and hyperspectral imaging [START_REF] Keshava | Spectral unmixing[END_REF], [START_REF] Iordache | Sparse unmixing of hyperspectral data[END_REF]. In contrast to peak-based algorithms, spectral unmixing allows to make profit of the full spectrum of each radionuclide (i.e. peaks and Compton continuum). Accounting for all the information carried out by the spectrum should allow to improve activity estimation by lowering interferences between radionuclides'spectra. The paper is organized as follows: Section II explores the use of unmixing algorithms for radioactivity estimation. To this end, two approaches are evaluated: i) a standard regularized least-squares estimator and ii) a novel regularized maximum Poisson likelihood estimator. In Section III, spectral unmixing is applied to simulated spectra, where we evaluate the estimation performance of the proposed algorithms. Comparisons are carried out with standard methods. Next, experimental results on real spectra are presented in Section IV. Section V provides conclusions and perspectives of this work.

II. ACTIVITY ESTIMATION ALGORITHMS

In this section, we study algorithms for activity estimation in gamma-ray spectrometry. Recall the model described in (2), we formulate the linear combination of each individual spectrum in the following matrix form:

y = Φa + b (4)
The mixing weights a is an array with non-negative entries, which is a property that will be enforced in the unmixing process. The estimation of a from a measured spectrum x can be addressed by minimizing a distance between x and the model y. For that purpose, we investigate two different approaches: a standard least squares approach and a new Poisson statistics-based method.

A. Least squares unmixing algorithm

Spectral unmixing can be tackled as a standard regression problem. In this context, a classical approach consists in finding the solution a that minimizes the least squares error:

âLS ∈ argmin a≥0 1 2 Φa + b -x 2 2 (5)
Because of the non-negativity constraint, there is no closedform expression for this problem. However, it can be recast as a generic inverse problem of the form:

â ∈ argmin a f (a) + g(a) (6)
In the present unmixing problem, this can be recast as:

âLS ∈ argmin a i. a≥0 + 1 2 Φa + b -x 2 2
where the regularization term i. A≥0 is the characteristic function of the convex set (i.e. non-negative orthant) {a ≥ 0}. It is precisely defined as follows:

i. a≥0 = 0, if a ≥ 0 ∞, otherwise (7)
Since this function is non-differentiable, solving the problem in ( 5) cannot be performed with standard gradient descent algorithms but requires the use of recently introduced proximal algorithms [START_REF] Parikh | Proximal algorithms[END_REF]. In brief, one can tackle this optimization problem with the Forward-Backward splitting (FBS) algorithm [START_REF] Combettes | Signal recovery by proximal forwardbackward splitting[END_REF] since it verifies the following properties:

• The fidelity term is differentiable, and its gradient is defined as:

∇f (a) = Φ T (Φa + b -x)
Furthermore, the above gradient is Lipschitz with constant L = Φ T Φ 2 , where . 2 stands for the spectral norm of a matrix (i.e. its largest eigenvalue). • The regularization term is convex and admits a proximal operator [START_REF] Parikh | Proximal algorithms[END_REF], which is generically defined as:

prox g (x) = argmin y g(y) + 1 2 y -x 2 2 (8)
The proximal operator of the non-negativity constraint ( 7) is simply defined as the orthogonal projection onto the non-negative orthant:

proxi. a≥0 = 0, if a < 0 a, otherwise (9)
In the sequel, we make use of an accelerated version of the FBS algorithm coined FISTA [START_REF] Beck | A fast iterative shrinkage-thresholding algorithm for linear inverse problems[END_REF]. The algorithm is summarized in Algorithm 1. This algorithm is guaranteed to converge to the unique minimum of (5) when the gradient step γ ≤ 1/L. In practice, the algorithms stops when the relative variation of a between two consecutive iterations is lower than 10 -12 .

Algorithm 1 Pseudocode of FISTA with constant stepsize

Input: Fix the step size 0 < γ < 1/ Φ T Φ 2
Fix the number of iterations: k max Initialization:

a 0 = 0, t 1 = 1, a 1 y = a 0 while k < k max do a k = prox i. a≥0 a k y -γΦ T (Φa k y + b -x) t k+1 = 1+ √ 1+4t 2 k 2 a k+1 y = a k + t k -1 t k+1 (a k -a k-1 ) end while

B. Poisson unmixing algorithm

From a statistical perspective, the least squares approach is equivalent to a maximum likelihood estimate assuming that the underlying noise is additive, white and Gaussian. To further account for the precise Poisson statistics of the spectroscopic measurement, we introduce a novel estimator that combines the maximization of the likelihood related to the Poisson statistics along with the non-negativity of the activities to be estimated. Therefore the probability of a given energy channel i to measure x i counts is given by:

P X i = x i [Φa] i + b i = λ xi i e -λi x i ! (10)
where λ i = [Φa] i + b i . Thanks to the statistical independence of each channel, the joint probability or likelihood for the different channels is then given by:

P X = x Φa + b = i λ xi i e -λi x i ! (11)
Maximizing the likelihood is equivalent to minimizing the neglog-likehood, which leads to the following Poisson statisticsbased activity estimator:

âP oisson ∈ argmin a≥0 i [Φa] i + b i -x i log ([Φa] i + b i ) (12)
which can be recast in the following vector formulation:

âP oisson ∈ argmin a≥0 Φa + b -x log (Φa + b)
where is the Hadamard product.

In contrast to the optimization problem that defines the least squares estimator, the above minimization problem cannot be solved with the FBS algorithm since none of the two terms is differentiable. Fortunately, both terms admit a proximal operator, which makes the application of first-order primaldual algorithms such as the Chambolle-Pock (CP -see [START_REF] Chambolle | A first-order primal-dual algorithm for convex problems withapplications to imaging[END_REF]) algorithm possible. The description of the CP algorithm to compute âP oisson is given in Algorithm 2. In this pseudocode, as defined in [START_REF] Sharma | Anomaly detection in gamma ray spectra: A machine learning perspective[END_REF], the proximal operator of the neg-loglikelihood f of the joint Poisson distribution of the measurements is:

prox λf (y) = y + b -λ + (λ -y -b) 2 + 4λx 2 -b (13)
Algorithm 2 Pseudocode of chambolle-pock algorithm

Input:

Fix the parameters: σ, τ > 0 and στ < 1/ Φ T Φ 2 . Fix the number of iterations: k max Initialization:

a 0 = 0, ā0 = a 0 , u 0 = Φa 0 while k < k max do v = u (k) + σΦā (k) u (k+1) = v -σ prox (1/σ)f v σ a (k+1) = prox i. a≥0 a (k) -τ Φ T u (k+1) ā(k+1) = a (k+1) + θ(a (k+1) -a (k) ) end while
where x and b stand for the measured spectrum and the background spectrum. Similarly to the FBS algorithm, the convergence of the CP algorithm is ensured to convergence στ < 1/ Φ T Φ 2 and θ = 1. The step parameters σ and τ are chosen with σ = 10 -4 → 10 -3 and τ = 0.9/(σ * L) for a better convergence rate. The choice of σ is related to the total number of counts in the mesured spectrum. σ = 10 -4 → 10 -3 is suitable for simulated spectra and real spectra that we used in this work. The stop criterion of the algorithm is as the FBS algorithm with relative variations of a lower than 10 -12 .

III. NUMERICAL EVALUATION ON SYNTHETIC DATA

In this section, we evaluate the estimation performance of the proposed algorithms with simulated gamma-ray spectra. In contrast to standard unmixing problems that involve additive Gaussian noise, the Poisson nature of the measurements' statistics makes it highly dependent on the actual mixing. In the context of gamma-ray spectrometry, the ability to estimate precisely the mixing weight of a given radionuclide will therefore strongly depend on the contribution of the others. To further highlight the performances of the unmixing methods, the following mixing scenarios are investigated:

• Case 1: we consider the mixture of 2 radioactive sources with different energies: 200 keV and 500 keV, 1000 keV and 500 keV. In this case, it will be possible to assess the impact of the Compton contribution of a given radionuclide on the determination of another radionuclide.

• Case 2: we investigate a typical routine aerosol filter sample with 5 radionuclides: 7 Be , 22 Na , 40 K , 137 Cs , 210 Pb.

The mixing weights are fixed to customarily observed values. In this test, we further evaluate the ability to estimate the level of a low-activity artificial radionuclide such as 137 Cs for different total count numbers.

A. Description of the simulations

Each individual spectral signature of radioactive sources is defined by its radioactive decay process and the detection efficiency of the measurement, depending on the detector and the counting geometry. In this work, the simulations are performed with the Monte Carlo N-particle (MCNP) Transport Code, a software package for simulating radiation transport developed by Los Alamos National Laboratory [START_REF] Briesmeister | MCNP: A General Monte Carlo N-Particle Transport Code[END_REF]. The sampledetector configurations are simulated for a HPGe detector (60 percent of relative efficiency) and a 60 mL cylindrical counting geometry. For case 1, the spectral signatures of sources with specific energies are simulated with MCNPX (MCNP eXtended). For case 2, the simulations are composed of mixtures of realistic spectral signatures of radionuclides. We make use of MCNP-CP (A Correlated Particle Radiation Source Extension of a General Purpose Monte Carlo N-Particle Transport Code) [START_REF] Berlizov | MCNP-CP: A Correlated Particle Radiation Source Extension of a General Purpose Monte Carlo N-Particle Transport Code[END_REF] to compute their individual spectral signatures. It simulates physics of nuclear decay and the subsequent emissions.

B. Experiments on the combination of two radioactive sources

We consider the mixture of two radioactive sources at 500 keV, noted φ 1 , and 200 keV/1000 keV, noted φ 2 . The measured spectra are defined as follows:

x ∼ P(φ 1 a 1 + φ 2 a 2 + b) (14)
where a 1 and a 2 stand for the individual activities (mixing weights) of the sources. b is the spectrum of the background radiation. As shown in Figure 3-a and Figure 3-b, we generate simulations as follows: a 1 for source 500 keV kept fixed and we change a 2 for 200 keV/1000 keV. Next, we simulate 30 gamma-ray spectra for each linear combination level by random Poisson process as described in [START_REF] Chambolle | A first-order primal-dual algorithm for convex problems withapplications to imaging[END_REF].

In order to compare the performance of the algorithms to those of spectral analysis based on the calculation of peak areas, we perform a peak area determination process according to algorithms discussed in [START_REF] Gilmore | Practical Gamma-ray Spectrometry[END_REF]. For comparison purposes, it should be noted that the mixing weight is not a good measure for quantifying the activity levels of different sources due to the different Compton continuum levels of source 200 keV and 1000 keV. One way to overcome this problem is to use the net area (defined in [START_REF] Gilmore | Practical Gamma-ray Spectrometry[END_REF]) of the peaks associated to radioactive sources, this is done by converting the estimated mixing weights into net areas of peaks respectively. The performances of these three estimators are compared in Figure 3, the first column for mixtures of 500keV and 200 keV, the second column for mixtures of 500keV and 1000 keV. Error bars are computed based on Monte Carlo simulations with relative error defined by a-â a . The median values and confidence intervals between percentile 25 and percentile 75 are displayed.

Results

• The estimated values obtained with the three estimators are compared to the real simulated values in Figure 3-c the Poisson unmixing provides more accurate estimations with lower uncertainty.

• The results show that the estimation performance of each algorithm improves when the radioactivity level increases (see the evolution of estimation relative error for source 200 keV and 1000 keV in Figure 3-i,j). Compared to the source 500 keV, we get larger relative errors for 200 keV/1000 keV with low couting rate. This confirms again the limitation in low activity measurements.

• The peak-based analysis cannot detect the source of 200 keV (see Figure 3-g), however, it can be detected in the case of 1000 keV (Figure 3-f). We can conclude that, comparing to the estimator considering only the peak, the proposed spectral unmixing estimators using the full spectrum improves the estimation performance, which provides significant benefits when the peak of a source is located under the continuum of other sources.

C. Realistic simulations of routine aerosol samples

The comparisons are carried out on simulated spectra that are composed of 5 radionuclides: 7 Be, 22 Na, 40 K, 137 Cs, 210 Pb. These 5 radionuclides are the most commonly found in standard aerosol samples. The level of counting rate of each radionuclide is fixed to values that are customarily in real data.Hence, these data simulate a realistic setting to test the proposed unmixing methods. As described in [START_REF] Briesmeister | MCNP: A General Monte Carlo N-Particle Transport Code[END_REF], we simulate the measured spectra with the simulated spectral signatures Φ and a background radiation spectrum b. After fixing the mixing weights of each radionuclide a, the counting time is changed in the simulation process with a factor β.

x ∼ P([Φa + b] × β) ( 15
)
We generate also 30 simulations for each mixture using random Poisson processes. Next, we apply the least squares unmixing and Poisson unmixing algorithms to the simulated spectra. The estimation performances have been therefore assessed for the 5 radionuclides in Figure 4 with relative error

Results

• Compared to least squares unmixing, we get lower relative errors with the Poisson unmixing for 7 Be, 22 Na, 40 K and 137 Cs, which are composed of peaks and significant continuum contributions. The results obtained for 210 Pb indicate that both estimators have similar performances for estimating a spectrum which consists of dominant peak.

• With respect to the number of counts carried out by the factor β, the realistic levels in experimental measurements are illustrated in gray regions of Figure 4. The analysis shows the advantage of Poisson unmixing in the task of activity estimation in the environmental samples.

As mentioned previously, the activity estimation at low statistics is a difficult problem to handle in the spectral analysis. We evaluate more precisely the estimation of the lowactivity radionuclide 137 Cs. For this purpose, we perform a scenario of simulations with 5 radionuclides described at the beginning of this section, the counting rate of 137 Cs ranges from 0 to a realistic level in practice. Figure 5 plots the estimation performance of 137 Cs while the mixing weights of other radionuclides are fixed. The results demonstrate that the Poisson unmixing improves the estimation performance for low-activity source.

The results shown in this section with simulated data confirm the good performance of using spectral unmixing approach. Further experiments on real spectra will be performed in the next section.

IV. EXPERIMENTAL RESULTS WITH REAL SPECTRA FROM AEROSOL SAMPLES' MEASUREMENTS

In this section, we aim to validate the proposed approaches for real data. We focus on the measurement of aerosol samples which is a part of the surveillance network in the laboratory. In the framework of the radiological environmental monitoring program in France or for research purpose in radioecology, we are concerned with measuring levels of radioactivity in environmental samples. In France, 137 Cs is an artificial radionuclide present in the environment due to the global fallout (atmospheric nuclear weapon tests and Chernobyl accident) and in the air due to resuspension phenomenon. The aerosol filters are collected weekly by the 10 high flow (800 m 3 .h -1 ) air samplers of the OPERA-Air network. Their volume higher than 120 000 m 3 enables to determine the 137 Cs activity concentration in the air at trace level around 0.1 µBq.m -3 . It is well known that rapid detection of artificial radionuclides is mandatory for emergency preparedness. In practice, we detect the presence of 137 Cs from the measurement of an aerosol sample more than one week after the sampling. It is of interest to evaluate the different approaches with short-time counting statistics. For this purpose, a scenario of measurements is performed in the laboratory with an aerosol sample. These measurements are performed half an hour after the sampling in a continuous manner with defined counting times for 8 days. The progressive measurements are described in Table .  I. These measured spectra are subsequently analyzed with proposed spectral unmixing algorithms and Genie2000 used in the laboratory. Since spectral signatures are required for the spectral unmixing algorithms, a spectral library is simulated for the detector and geometry used in this experiment. The contribution of this section is as follows: firstly, we discuss the choice of spectral signatures since the subset of active radionuclides is unknown in practice. Next, the results are compared with those performed with Genie2000.

A. Dimension of spectral library

As discussed in the previous section, the spectral unmixing process aims to estimate the mixing weights of spectral signatures. However, finding the optimal subset of spectral signatures is important to estimate mixing weights more accurately. In the context of this experiment, it is well known that we can detect several short-lived radionuclides after the sampling, which decay very fast as time goes on. Accordingly, the first measurement (Figure 6-a) contains more contributions comparing to the last measurement (Figure 6-b). The last measurement Figure 6-b corresponds to a routine aerosol measurement: the predominant peak at 477 keV is characteristic of 7 Be, a cosmic-ray induced radionuclide. It gives also rise to the Compton continuum from 165 to 313 keV. Other peaks enable to identify and quantify other natural radionuclides: 40 K at 1460 keV or 210 Pb at 46 keV. 137 Cs and 22 Na can also be determined at trace level thanks to their respective peak at 662 keV and 1274 keV.

Consequently, the real subset of active spectral signatures for each measurement is different. In order to study the impact of the dimension of the spectral library when we use spectral unmixing estimators, we apply the two algorithms with spectral signatures according to:

• 7 Be, 22 Na, 40 K, 137 Cs, 210 Pb, so that the measured spectra are supposed to be separated to these 5 radionuclides: Φ 5 = [φ 1 , ...φ 5 ]. More specifically, as discussed in other spectral unmixing applications, badly chosen spectral signatures can introduce a bias on the estimation. To confirm this assumption, quantitative analysis with simulations have been carried out as described in [START_REF] Briesmeister | MCNP: A General Monte Carlo N-Particle Transport Code[END_REF]. Spectra s1 → s11 have been simulated with similar activity levels than the measurements. Considering the mixing weights of 7 Be, 22 Na, 40 K, 137 Cs, 210 Pb as constants, we simulate other natural radionuclides with realistic decreasing levels. Figure 8 compares the estimation performance of these 5 natural radionuclides using Φ 5 = [φ 1 , ...φ 5 ] and Φ 10 = [φ 1 , ...φ 10 ] for simulated spectra.

Results

• As shown in the first column of Figure 8, by using Φ 5 = [φ 1 , ...φ 5 ] to unmix spectra in which other radionuclides decay quickly, the spectral unmixing provides bias in the first measurements.

-For 7 Be, 22 Na and 40 K (respectively Figure 8a,c,e), Poisson unmixing tends to over-estimate the activities with respect to the least squares unmixing.

Statistically the Poisson unmixing is more sensitive to the choice of spectral library. The reason is, firstly, the logarithmic scaling in the likelihood term introduces more significant residual errors ( 7 Be at high activity levels), secondly, Poisson unmixing aims to precisely fit the measured spectrum with the full spectrum ( 22 Na and 40 K with significant continuum contributions). -The 137 Cs(Figure 8-g)impacted by continua of other radionuclides and present at low activity level is more overestimated by least squares unmixing. -The estimation of 210 Pb (Figure 8-i]) which is dominated by the peak, is less impacted by the spectral library.

• The results obtained with a more complex spectral library Φ 10 = [φ 1 , ...φ 10 ] are shown in the second column of Figure 8. The estimation is more accurate with this second strategy. In summary, we obtained similar results than those for real spectra. It highlights that the accurate identification of spectral signatures is the precondition for the spectral unmixing.

B. Comparisons with peak calculation analysis

We compare the results of the proposed spectral unmixing estimators with those of Genie2000 used in the laboratory. As discussed previously, we use the results obtained with spectral signatures in dimension of 10, which is more suitable for spectral unmixing of the measured spectra. We focus on the results of the 5 concerning radionuclides and two natural radionuclides 212 Bi and 214 Bi. The estimated values are compared in Figure 9 and Figure 10. • As shown in Figure 9-e,f, the activity of short-lived radionuclides decreases in the first two days after the sampling. This is confirmed by the similar results obtained with three estimators.

• Figure 10 indicates that, the 137 Cs has not been detected in the end of the measurements with least squares unmixing. Contrarily, we obtain similar estimated values with Poisson unmixing and Genie2000. This may be motivated by a bias introduced by the background spectrum, since at low statistics, the least squares unmixing introduces a peak as a false peak in the background spectrum. The analysis shows that, 137 Cs , present at the lowest activity level, is identified and quantified with Poisson unmixing algorithm four days before the usual method Genie2000.

In this section, we can conclude from the experiments on real measurements that, firstly, for spectral unmixing estimators, the lack of knowledge of active radionuclides leads to underfitting or over-fitting the model which introduce a bias to the results. Secondly, Poisson unmixing yields significant improvement for estimating radioactivity, especially when the counting rate is low, which is a key advantage for the rapid detection of anomaly in the air.

V. CONCLUSION

We present in this paper activity estimation algorithms based on spectral unmixing, which exploit the full spectrum of radionuclides and introduce the measured spectrum with pure spectral signatures known in advance. We formulate the spectral unmixing problem by inverse problem to estimate mixing weights of each radionuclide in the measured spectrum. We propose two estimators: least squares regression approach using FISTA algorithm and Poisson unmixing based on Poisson statistics using Primal-dual algorithm. Results on simulated and real spectra provide good performance with the least squares unmixing and the Poisson unmixing. The latter which precisely takes into account the Poisson statistics of the physical process underlying the detection, presents significant advantages when the counting rate is low. In the context of rapid detection which leads to measuring low level activity in environmental samples, an important advantage is that the time for detection and identification has been reduced for artificial radionuclides. The discussion in section IV concerning the problem of spectral library dimension emphasizes the importance of using an optimal spectral library with spectral unmixing estimators. This opens perspectives on estimating jointly the set of active radionuclides: the aim is to select in the complex spectral library, the smallest number of radionuclides that best fit the measured spectrum.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Gamma-ray spectrum model

  Figure 3-e,f for source 500 keV and Figure 3-i,j for source 200 keV/1000 keV. It has to be pointed out that,

(a) Estimation of 7 Fig. 4 :

 74 Fig. 4: Estimation relative error obtained by Poisson unmixing and LS unmixing, the gray region represents the range of counts numbers in real spectra that we measured for aerosol samples.

Fig. 5 :

 5 Fig. 5: Estimation of 137 Cs in the case that activity levels of other radionuclides and background radiation are fixed. Estimation results for Monte-Carlo simulations are compared to the real values of the mixing weight of 137 Cs.

• 7

 7 Be, 22 Na, 40 K, 137 Cs, 210 Pb, 208 Tl, 212 Bi, 212 Pb, 214 Bi, 214 Pb, with respect to Φ 10 = [φ 1 , ...φ 10 ]. As results, Figure.7 illustrates the estimated mixing weights for the 11 measured spectra with both strategies for spectral signatures choice. Comparing both experiments, we get more stable estimated values with Φ 10 = [φ 1 , ...φ 10 ]. However, in the case of Φ 5 = [φ 1 , ...φ 5 ], the estimated values we obtained with the two estimators converge in the last measurement.

Results • Figure 9

 9 -a,b,c,d show the results for7 Be, 22 Na, 40 K, 210 Pb. At the end of the measurements, the mixing weights estimated by Poisson unmixing and LS unmxing are closed to those obtained with Genie2000. This is motivated by the sufficient counting rate obtained with the last measurement during 4 days (as shown in the inset of each figure).

Fig. 6 :Fig. 7 :

 67 Fig. 6: Measured spectra for s1 and s11

(a) Estimation of 7

 7 Be with Φ 5 (b) Estimation of 7 Be with Φ 10 (c) Estimation of 22 Na with Φ 5 (d) Estimation of 22 Na with Φ 10 (e) Estimation of 40 K with Φ 5 (f) Estimation of 40 K with Φ 10

( g )

 g Estimation of 137 Cs with Φ 5 (h) Estimation of 137 Cs with Φ 10 (i) Estimation of 210 Pb with Φ 5 (j) Estimation of 210 Pb with Φ 10

Fig. 8 :

 8 Fig. 8: Results on simulations with similar activity levels of the real spectra for s1 → s11. The first column according to spectral signatures Φ 5 = [φ 1 , ...φ 5 ], the second column according to Φ 10 = [φ 1 , ...φ 10 ]. The estimated mixing weights are compared to real values for the 11 spectra and the results of s11 on the right of each figure.

Fig. 9 :

 9 Fig. 9: The results obtained by net peak area analysis of Genie2000 are converted to mixing weights by a i = Snet i Snet φ i (S net i :the measured net area of ith radionuclide, S net φi : the net area of ith spectral signature). The results are plotted as a function of the ending time of each measurement.

Fig. 10 :

 10 Fig. 10: Estimation of 137 Cs. The least squares unmixing provides zero as mixing weight for 137 Cs at the end of the measurements. The estimated value obtained by Poisson unmixing is presented with error bar that we obtained in the simulations.

TABLE I :

 I Successive measurements with increasing counting times carried out on an aerosol filter sampled on 19/04/2019 8:46:00

		Start time	Counting time(s)
	s1	19/04/2018 09:10:53	1800
	s2	19/04/2018 09:41:42	1800
	s3	19/04/2018 10:12:30	1800
	s4	19/04/2018 10:44:11	3600
	s5	19/04/2018 11:45:03	3600
	s6	19/04/2018 12:46:59	5400
	s7	19/04/2018 14:20:23	10800
	s8	19/04/2018 17:22:17	54000
	s9	20/04/2018 08:41:41	28000
	s10 20/04/2018 16:29:59	240000
	s11 23/04/2018 11:44:44	320000


Éva Sivadó

Meddy El Alaoui
email: elalaoui@covalab.com

Frédéric Delolme

Robert Kiraly

László Fesüs

Saïd El

Saïd El Alaoui

Keywords: Transglutaminases Deamidation Transamidation Fluorescent-detection SDS-PAGE Tissue transglutaminase, Sandwich ELISA, Monoclonal antibody, Polyclonal antibody

Transglutaminases (TGs) are a family of structurally and functionally related enzymes, which catalyse calcium dependent posttranslational modifications of proteins by generating protein-protein crosslink, amine incorporation or deamidation. For many years TGs mediated deamidation was considered to be a side-reaction, but recently substrate specific deamidations have been reported. Here we describe an optimised SDS-PAGE assay for the easy and rapid monitoring of the TG reaction with small peptides. The relative proportion of deamidation to transamidation was evaluated by densitometric analysis and confirmed by nanoLC-nano-ESI/MS. We addressed to further investigate the effect of reaction conditions on transamidation and deamidation reactions of TG1, TG2 and FXIII-A enzymes using a panel of glutamine containing peptides substrates. The ratio of transamidation to deamidation was enhanced at high excess of the acyl-acceptor substrate and increasing pH. In addition, it was influenced by peptides substrates as well. Whereas deamidation was favoured at low cadaverine concentrations and acidic pH, no significant effect of calcium was observed on the ratio of transamidation/deamidation. Under our experimental conditions particular deamidation always occurred in vitro even at high excess of the acyl-acceptor substrate, and the reaction outcome was shifted to deamidation at neutral pH. Our results provide clear evidence of the deamidation in transglutaminase reaction and may serve as an important approach for in vivo analysis of the deamidation to understand better the role of TGs in biological events.

• • • • • • • • • • • • • • • • .

Introduction

Transglutaminases (TGs; EC 2.3.2.13) are widely distributed enzymes with pleiotropic functions. Nine members have been described in mammals: keratinocyte (TG1), tissue (TG2), epidermal (TG3), prostate (TG4), type 5 (TG5), neuronal (TG6), type 7 (TG7), blood coagulation factor XIII-A subunit (FXIII-A), and the catalytically inactive erythrocyte band 4.2 protein (Griffin et al. 2002).

The distribution and physiological roles of TGs have been investigated in various cell types and tissues. TG2 is the most studied member of the TGs family. This multifunctional protein has diverse cellular localisation and is implicated in several physiological (regulation of cell survival/death processes, cell adhesion, migration, signal transduction, proliferation) and pathological processes (coeliac disease, neurodegenerative disorders, fibrosis, inflammatory diseases, metabolic diseases and cancer) (Fesus and Piacentini 2002). TG1 mainly exists in the upper spinous and granular layers of the skin, it is involved in the terminal differentiation of keratinocytes by the formation of the cross-linked cell envelope [START_REF] Kim | Expression of transglutaminase 1 in human epidermis[END_REF]. Thrombin-activated factor FXIII-A (FXIII-A) plays essential role in the stabilisation of fibrin clots and in wound healing through the formation of isopeptide bounds [START_REF] Ariëns R A S | Role of factor XIII in fibrin clot formation and effects of genetic polymorphisms Review article Role of factor XIII in fibrin clot formation and effects of genetic polymorphisms[END_REF].

TGs catalyse Ca 2+ -dependent posttranslational modifications of proteins by generating protein-protein crosslink (between specific γ-carboxamide group of a glutamine and ε-amino group of a lysine side chains), amine incorporation or deamidation. In the first step active site cysteine reacts with the γ-glutaminyl group of the proteins or peptides leading to the formation of a thioester intermediate. In the second step the acyl group is transferred to an amine substrate resulting in the formation of isopeptide bond or the water can act as an alternative nucleophile leading to site-specific deamidation of the glutamine residue [START_REF] Folk | Mechanism and basis for specificity of transglutaminase-catalyzed ε-(γ-glutamyl) lysine bond formation[END_REF]Lorand and Graham 2003). Many of these crosslinking reactions occur within 5 to 10 min, for example in case of FXIII-A between glutamine (Gln 398; 399) and lysine (Lys 406) residues of the fibrin γ-chains [START_REF] Chen | Gamma-gamma cross-Linking Sites in Human and Bovine Fibrin[END_REF]. Whereas cross-linking of fibrin αchains involving Gln 221; 237; 328; 366 and Lys 208; 606 takes place more slower [START_REF] Matsuka | Factor XIIIA-catalyzed cross-linking of recombinant alpha C fragments of human fibrinogen[END_REF][START_REF] Ariëns R A S | Role of factor XIII in fibrin clot formation and effects of genetic polymorphisms Review article Role of factor XIII in fibrin clot formation and effects of genetic polymorphisms[END_REF].

Deamidation of glutamine and asparagine residues is one of the most prevalent posttranslational modifications, which converts an uncharged amino acid to a negatively charged residue introducing alternations in the protein's conformation. The protein function can be changed as it is determined by its global structure and electrostatic protein-protein interaction can be modulated as well (Berg et al. 2002). Deamidation can occur in different ways (non-enzymatically, by glutamines or phosphate activated glutaminases) regulating several biological processes (Robinson and Robinson 2001;[START_REF] Hensley | Glutamine and cancer: cell biology, physiology, and clinical opportunities[END_REF]Schousboe et al. 2014). Moreover cytotoxic necrotizing factors in Escherichia coli and necrotoxin in Bordetella, which are considered to be functional relatives of TGs, can induce the formation of stress fibers by the deamidation of Rho proteins (Schmidt et al. 1998).

Deamidation by TGs was believed to be a side-reaction and taking place only in the absence of primary amines or at low pH when their availability is limited (Fleckenstein et al. 2002). But, recently it has been reported that selective deamidation in small heat shock protein [START_REF] Boros | Site-specific transamidation and deamidation of the small heat-shock protein Hsp20 by tissue transglutaminase[END_REF]) and βB2, βB3-crystallins [START_REF] Boros | Tissue transglutaminase catalyzes the deamidation of glutamines in lens βB2and βB3-crystallins[END_REF]) can occur in a substrate specific manner. Respectively, the substrate affinity and reaction conditions can influence the propensity for deamidation and transamidation (Stamnaes et al. 2008). Many research works are focusing on the examination of transglutaminase cross-linking activity, which is linked to some diseases like fibrosis and neurodegeneration. So far TGs mediated deamidation activity has been related to coeliac disease [START_REF] Folk | Mechanism and basis for specificity of transglutaminase-catalyzed ε-(γ-glutamyl) lysine bond formation[END_REF]Lorand and Graham 2003), and only few reports have been published on its role in other physiopathological processes (Nemes et al. 2000;[START_REF] Boros | Tissue transglutaminase catalyzes the deamidation of glutamines in lens βB2and βB3-crystallins[END_REF]Schmid et al. 2011;[START_REF] Iwai | Transglutaminase 2-dependent deamidation of glyceraldehyde-3-phosphate dehydrogenase promotes trophoblastic cell fusion[END_REF]. These studies support the potential role of TGs dependent deamidation in the regulation of biological processes.

In this study we report an optimised sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE) assay for the rapid and easy detection of both transamidated and deamidated peptides. TG1, TG2, FXIII-A enzymes and a panel of glutamine containing peptides were examined to determine how the ratio of deamidation to transamidation can be influenced by some reaction parameters, such as substrates affinity, amine donor concentration, Ca 2+ concentration and pH. The identity and the relative quantity of the reaction products were confirmed by liquid chromatography-mass spectrometry (LC-MS) analysis. Our results are well correlated with the

F o r R e v i e w O n l y
published data, cited above. Unexpectedly, under our reaction conditions, we found that particular deamidation is always occurring in vitro, even at high excess of the acyl-acceptor substrates.

Materials and methods

Materials

All materials were obtained from Sigma-Aldrich (France), otherwise it is indicated. Recombinant human TG2 (rhu-TG2), recombinant human keratinocyte transglutaminase (TG1), and recombinant human blood coagulation factor XIII-A (FXIII-A) were purchased from Zedira (Darmstadt, Germany). Peptides were obtained from Covalab (Villeurbanne, France). MilliQ Water for mass spectrometry analysis was accessed from Elga system.

Synthetic peptides substrates

FAM labeled peptides substrates were synthetized according to the standard method of Covalab. Isoenzyme specific glutamine containing peptides have been reported by Sugimura et al (2006Sugimura et al ( , 2008) ) and used to develop specific TGs activity assays (Thomas et al. 2006;[START_REF] Perez Alea | Development of an isoenzyme-specific colorimetric assay for tissue transglutaminase 2 cross-linking activity[END_REF]. K9 is a natural TG2 sequence based on βcasein [START_REF] Cleary | Characterizing the specificity of activated Factor XIII for glutamine-containing substrate peptides[END_REF]. Among the natural reactive glutamine sides in fibrinogen α-chains a short peptide sequence containing Q238 [START_REF] Matsuka | Factor XIIIA-catalyzed cross-linking of recombinant alpha C fragments of human fibrinogen[END_REF] was chosen for our experiments. The corresponding deamidated control peptides were synthetized by Covalab (Table 1).

Transglutaminase reaction

5 μM of specific glutamine donor substrates labeled with FAM fluorescent and cadaverine (5-1000 µM) as an acyl acceptor were incubated with their corresponding isoenzymes at 37 °C. 18 mU/ml of TG1, TG2, or thrombin (1U/ml) activated FXIII-A were applied in the assay buffer (20 mM Tris pH 7.2, 8.0 or MES pH 5.0, 6.0, 150 mM NaCl, 10 mM DTT) in the presence or absence of 10 mM EDTA. pH was 7.2, unless the effect of pH (5-8) was examined. The enzymatic reaction was initiated by the addition of 5 mM CaCl 2, except in the experiments in which the effect of Ca 2+ was investigated (0.1-5 mM).

SDS PAGE assay

The assay was previously reported by Kenniston et al. (2013) and modified as briefly described below. After the incubation time the enzymatic reaction was stopped by boiling the sample in 6X SDS-loading buffer (9.3 w/w DTT, 12 wt.% SDS, 47 v/v% glycerol, 0.06 wt.% bromophenol blue in 0.5 M Tris-HCl, pH 6.8). The reaction products were run on SDS-PAGE (15% T, 2.6% C; T represents the total concentration of polyacrylamide monomer expressed in a g per 100 ml and C is the percentage of bis-polyacrylamide) and visualized by fluorescence detection (Luminescent Image Analyzer LAS-1000 plus, Fujifilm).

Liquid chromatography-mass spectrometry analysis (LC-MS)

The samples were diluted 10 times in a solution of 0.1% formic acid before analysis. Mass spectrometry analysis were performed on a linear ion trap LTQ Velos (Thermo Scientific, San Jose California) with nano-Electrospray ionization source coupled in-line to a nanoRSLC system Ultimate 3000 (Thermo Scientific, Germering, Germany). 1µL of sample was injected via the autosampler. Samples were first desalted and concentrated on a reverse phase precolumn C18 PepMap100, 300 µm i.d x 5 mm, 5 µm, 100 Å (Thermo Scientific) for 3 min at 20 µL/min with H 2 O/Acetonitrile -98/2-0.1% Formic acid. Samples were then separated on a nanocolumn Acclaim C18, 15 cm x 75 µm i.d, 2 µm (Thermo Scientific). The HPLC gradient was 5-55% solvent B (A = 5% acetonitrile,

F o r R e v i e w O n l y
0.1% formic acid; B = 80% acetonitrile, 0.1% formic acid) in 30 min follow to 5 min 99% B. The total duration was set to 50 minutes at a flow rate of 300 nL/min. The oven temperature was kept constant at 40°C.

MS spectra were recorded in the mass range m/z 500-1100 in positive ionisation mode, the enhanced scan rate was used for the full MS spectrum.

Data analysis

Relative intensity of fluorescent bands were analysed with ImageJ and plotted with GraphPad Prism 5 (GraphPad Software Inc., San Diego, CA, USA) software.

Results and discussion

Determination of transamidation and deamidation rates by transglutaminases

Post-translational modifications (PTMs) behave as powerful regulatory elements that often define protein function through covalent modification. Because PTMs profoundly affect protein behavior, they are typically tightly controlled, and dysregulation is strongly associated with numerous diseases [START_REF] Huang | Human proteins with target sites of multiple post-translational modification types are more prone to be involved in disease[END_REF]. Deamidation is an exception among PTMs due to its enzymatic and nonenzymatic and spontaneous nature.

Deamidation is the transformation of eligible glutamine and also asparagine residues into glutamate and aspartate/isoaspartate. Susceptibility for nonenzymatic deamidation is conditioned by the primary sequence, by the lack of three-dimensional structure, and is facilitated by high temperatures, extreme pH or high ionic strength. Deamidation affects a great number of proteins (calmodulin, , tubulin, synapsin, Alzheimer's β-amyloid, histone H2B, cytochrome-C, …), and has therefore wide biological repercussions because it can lead to structural changes and/or modify their life-span [START_REF] Beaumatin | N52 monodeamidated Bcl x L properties in vivo and in vitro shows impaired oncogenic[END_REF]. Although there are select examples of deamidation serving functional roles, it is generally considered to represent degradation and is associated with a growing list of agerelated, neurological, aggregation-prone, and autoimmune diseases [START_REF] Lindner | Age-dependent deamidation of asparagine residues in proteins[END_REF].

While in vivo deamidation of Asn to Asp was clearly established, transglutaminase mediated-deamidation of Gln is not fully understood and rather it was believed to be only a side-reaction, occurring when the second substrate is not available or at acidic pH. However, during about a decade many reports were focused on the study of the mechanism of hydrolysis of the specific Gln residues in order to elucidate the role of transglutaminases in the physiopathology of some diseases and coeliac disease in particular.

In order to evaluate the deamidation reaction of transglutaminase to convert Gln to Glu, several methods were used depending on whether the Gln substrates were natural (e.g. proteins) or synthetic (e.g. peptides). In case of proteins, deamidations were analysed through molecular modelling and biological activity (Sjöström et al. 1998;Fleckenstein et al. 2002b) whereas synthetic peptides were analysed by various technics such as mass spectrometry (MS & LC/MS), size exclusion chromatography (SEC), capillary electrophoresis (EC), HPLC, 2D gels, WB (Boros S, Quarsten H, Stamnaes J, Heil A).

In this work we optimised an electrophoresis assay based on sodium dodecyl sulphate polyacrylamide gel (SDS-PAGE) for the rapid and easy detection of both transamidated and deamidated peptides. All reaction products of FAM fluorescein-labelled peptides could be simultaneously detected with high resolution and specificity. The relative ratio of deamidation and transamidation was evaluated by densitometric analysis (Fig. 1b,e). The identity and the proportion of the reaction products were confirmed by nanoLC-nano-ESI/MS analysis. The relative quantities were calculated from Extraction Ions Chromatogram Areas of the doubly charged ions of each species (Fig. 1c,f), assuming that all the species have the same response factors. The data obtained by LC-MS are in good

F o r R e v i e w O n l y
correlation with the results of densitometric analysis, indicating that the optimised SDS-PAGE assay is a reliable method for the semi-quantitative examination of both transamidated and deamidated reaction products.

There is always deamidated substrate production during transglutaminase reaction

In this study TG1, TG2, FXIII-A enzymes and five glutamine containing peptides (K5, T26, F11, K9 and αC(Q328)) (Table 1) were examined to determine how the ratio of deamidation to transamidation can be influenced by some reaction parameters such as: the substrates affinity, amine donor concentration, Ca 2+ concentration and pH. K5 (Sugimura et al. 2008), T26, F11 (Sugimura et al. 2006) were described as an isoenzyme preferred glutamine substrates having high affinity to TG1, TG2 and FXIII-A respectively, whereas K9 [START_REF] Cleary | Characterizing the specificity of activated Factor XIII for glutamine-containing substrate peptides[END_REF] and fibrinogen αC(Q328) peptides [START_REF] Matsuka | Factor XIIIA-catalyzed cross-linking of recombinant alpha C fragments of human fibrinogen[END_REF] are known as natural glutamine donor substrate for TG2 and FXIII-A.

Applying high excess of the amine donor substrate (cadaverine), the ratio of transamidation to deamidation was increased, whereas deamidation was favored at low cadaverine concentrations. In the absence of the second substrate no crosslinked product was detected (Fig. 2). In addition this effect appeared to be substrate dependent and confirm the results obtained by the group of Sollid L (Stamnaes J et al, 2008). TG2 transamidase activity was rather higher with K9 (Fig. 2b) than with T26 peptide (Fig. 2c) indicating better recognition of natural glutamine substrate. This difference was not observed with FXIII-A as the reactivity is higher with F11 than fibrinogen αC(Q328) peptides. Indeed upon the same reaction conditions the relative ratio of deamidated/transamidated fibrinogen αC(Q328) peptide was increased (Fig. 2e) whereas F11 peptide was preferred for transamidation (Fig. 2d). This slight difference in the deamidation/transamidation rate may be explained by the influence of the neighbouring amino acids relative to the targeted Gln and may effect the affinity of the enzymes. Indeed Boros et al (2005[START_REF] Boros | Tissue transglutaminase catalyzes the deamidation of glutamines in lens βB2and βB3-crystallins[END_REF] reported that TG2 can process site-specific deamidation, and a proline at position +2 to the specific glutamine residue may positively influence deamidation (Fleckenstein et al. 2002b).

Moreover the results reveal that TG2 and FXIII-A catalysed substrate deamidation could always occur as an excess of primary amine did not completely inhibit deamidation (Fig. 1 b-e). However deamidation by TG1 is less obvious in all conditions studied and this could be explained that K5 may not be good substrate of this enzyme for deamidation (Fig. 1a). Using natural and good substrate for TG1 will be of interest to complete this work.

Effect of pH on the transglutaminase catalysed deamidation

Fleckenstein et al described that TG2 catalyzed reaction of gliadin substrate is strongly influenced by pH.

Here we extended the investigation for two other isoenzymes and five peptide substrates as detailed in the materials & methods (Fig. 3). In all cases the transamidation and deamidation reactions were analysed in buffers with pH values ranging from 5 to 8. TG1 (Fig. 3a) and FXIII-A (Fig. 3 d,e) seem to not be active at acidic pH, however at pH 6.0 fibrinogen αC(Q328) peptide was deamidated in the majority (Fig. 3e). At pH 8.0 all the peptides were converted to transamidate forms by all the corresponding enzymes. In the condition of neutral pH, TG1 was not active due probably to the low kinetic reaction, whereas TG2 and FXIII-A were able to convert the peptides to transamidated and deamidated products. The proportion of each product depends on the type of the enzyme and also the glutamine substrate. T26 was highly deamidated by TG2 whereas the natural substrate K9 was in the majority transamidated (Fig. 3b,c) and with FXIII-A the deamidation was more important to the transamidation for both substrates (Fig. 3d,e). These results further demonstrate that the rate of the transamidation reactions is significantly increased at alkaline pH indicating the importance of the nucleophily of the amine which must be unprotonated. As the pKa of the cadaverine amine is around 10 it's expected that the transamidation reaction can be favoured over deamidation. Indeed in the report of Fleckenstein (2002) using 5-BP as an amine donor with pKa around 10.5 they proposed a general base-catalyzed-deacylation mechanism for the transamidation reaction through the nucleophilic attack on the thiol ester intermediate. Increasing of the pH narrow the pKa of the base would decrease its protonation and consequently the competition by water molecules is blocked explaining the increase of transamidation rate.

F o r R e v i e w O n l y
Effect of Ca 2+ on the transglutaminase catalysed deamidation It is well known that Ca 2+ is required for the activation of transglutaminases through inducing a large conformational change in the enzyme structure [START_REF] Venere | Opposite effects of Ca(2+) and GTP binding on tissue transglutaminase tertiary structure[END_REF]Pinkas et al. 2007). Because of the large difference in the open and closed conformations, we hypothesised that depending on Ca 2+ binding, more transient conformers with different hydrodynamic radius can be exhibited. Probably at lower Ca 2+ concentrations the substrate-binding channel could be particularly covered and the entrance of the second substrate can be inhibited resulting on the deamidation of the glutamine donor substrate via hydrolysis. Transamidation and deamidation were analysed with different Ca 2+ concentrations ranging from 0.1 to 5 mM as described in material & method (Fig. 4). At lower Ca 2+ concentration (0.1-0.2 mM) TG2 seems to not be active (Fig. 4 b,c) whereas TG1 converted the majority of K5 to transamidated product (Fig. 4a). With FXIII-A we observed high activity with F11 substrate (Fig. 4d) and low activity with natural substrate (Fig. 4e) that can be explained by the high affinity of the enzyme to the synthetic substrate. By increasing Ca 2+ concentration the enzymes were more active and both transamidation and deamidation occurred at different rate depending on the Gln substrate: transamidation was more observed with TG1 and TG2 using K5 and T26 substrates respectively and more deamidation was obtained with TG2 and FXIII-A using K9 and fibrinogen αC(Q328). Based on these results no significant effect of calcium was obtained on the ratio of transamidation/deamidation.

In conclusion, our assay based on SDS-PAGE provides an easy and rapid method for monitoring the transglutaminase reaction with synthetic small peptides. The fractions of native, deamidated and transamidated peptides can be successfully separated and their rates were confirmed by nanoLC-nano-ESI/MS. Under our experimental conditions we noticed that particular deamidation always occurs, even at high molar concentration (148-200 fold molar excess) of amine donor substrate and it is preferred at low to neutral pH. These data provide further evidence for the simultaneous reactions of transamidation and deamidation, however further work should be confirmed in vitro and in vivo at the endogenous proteins level. Knowledge about the in vivo regulation of the transamidation versus deamidation is therefore crucial for the elucidation of the transglutaminase enigma. Most of the transglutaminase activity assays are based on detection of the transamidated products. Since the deamidation is no longer believed as a side reaction, TG activity cannot be accurately evaluated only by detecting the cross-linked products. calcium-dependent post-translational modifications of proteins. This transamidase activity consists of protein crosslinking via isopeptide bonds (between a specific glutamine and a lysine residue) and also of the incorporation of lowmolecular weight amines [START_REF] Folk | The epsilon-(gamma-glutamyl)lysine crosslink and the catalytic role of transglutaminases[END_REF]. In the absence of amine donors, the enzyme is able to catalyze site-specific deamidation (Lorand and Graham 2003).

In mammals, nine distinct TG members have been identified: TG1, TG2, TG3, TG4, TG5, TG6, TG7, factor XIIIa, and the enzymatically inactive erythrocyte band 4.2 protein (Griffin et al. 2002). TG2, also known as tissue transglutaminase (tTG), is the most studied and widely distributed member of the TGs family in various cellular locations. It is mainly localized in the cytosol, but it can be represented in the extracellular matrix, in the nucleus, and associated with the mitochondria and plasma membrane as well [START_REF] Gundemir | Transglutaminase 2: a molecular Swiss army knife[END_REF]. Besides the transamidation activity that stabilizes tissues, it can bind and hydrolyze GTP and ATP that regulate signal transduction as a G protein [START_REF] Lai | Regulation of human tissue transglutaminase function by magnesium-nucleotide complexes. Identification of distinct binding sites for Mg-GTP and Mg-ATP[END_REF], it has intrinsic kinase activity [START_REF] Mishra | Tissue transglutaminase has intrinsic kinase activity: identification of transglutaminase 2 as an insulin-like growth factor-binding protein-3 kinase[END_REF], and it exhibits protein disulphide isomerase activity [START_REF] Hasegawa | A novel function of tissue-type transglutaminase: protein disulphide isomerase[END_REF].

tTG is constitutively expressed in several tissues, while its expression is induced by external stimuli or as part of their differentiation in some other types of cells (Zemskov et al. 2006). The control of tTG primarily occurs at the transcription level (Griffin et al. 2002). Retinoids are wellknown regulators of the enzyme [START_REF] Nagy | Identification and characterization of a versatile retinoid response element (retinoic acid receptor response element-retinoid X receptor response element) in the mouse tissue transglutaminase gene promoter[END_REF]. Moreover, response elements for transforming growth factor-β1 (Ritter and Davies1998) and stress-induced transcription factors (NF-κB, hypoxia inducible factor) are located in the tTG promoter [START_REF] Mirza | A role for tissue transglutaminase in hepatic injury and fibrogenesis, and its regulation by NF-kappaB[END_REF][START_REF] Jang | Transglutaminase 2 suppresses apoptosis by modulating caspase 3 and NF-kappaB activity in hypoxic tumor cells[END_REF]. This multifunctional protein has diverse cellular localization and displays diverse functions in several physiological (e.g., signal transduction, proliferation, cell adhesion, migration, Abstract Tissue transglutaminase (tTG) belongs to the multigene transglutaminase family of Ca 2+ -dependent protein cross-linking enzymes. There is a strong evidence that tTG is involved in pathology, such as neurodegenerative diseases, cancer, and celiac disease. To study physiopathological implication of tTG, a sandwich immunoassay has been developed with a new monoclonal antibody for the capture and polyclonal antibody both generated in house. Using this ready to use assay, the tTG protein level can be measured in human tissue homogenates and cells extracts easily in about 4 h. The limit of detection is 1.7 ng/ml; the coefficients of intra-and inter-assay variations range from

Introduction

Transglutaminases (TGs; EC 2.3.2.13) are a family of structurally and functionally related enzymes that catalyze regulation of cell survival/death processes), and pathological processes (fibrosis, inflammatory diseases, neurodegenerative disorders, metabolic diseases, coeliac disease, and cancer) (Fesus and Piacentini 2002).

In previous studies, we developed different assays for measuring tTG and other TG isoenzymes activities. These assays (now commercially available) can be used to quantify transglutaminase specific activities in different biological samples (Thomas et al. 2006;[START_REF] Perez Alea | Development of an isoenzyme-specific colorimetric assay for tissue transglutaminase 2 cross-linking activity[END_REF]). However, to address a better correlation between the presence of the enzymes and their functions, the quantification of both enzyme activity and enzyme level is needed. Moreover, the measurement of enzyme activity alone will not reflect the presence of possible inactive form of TG proteins in tissues, as it was published by Siegel et al. (2008). Since it is evident, a test measuring active and nonactive tTG should be a tool of interest to study the enzyme involvement in different biological processes.

Attempts were made by few groups to measure tTG protein level in various sources of samples. The analytical sensitivity of these assays was 0.1 ng/ml [START_REF] Brevé | Validated sandwich ELISA for the quantification of tissue transglutaminase in tissue homogenates and cell lysates of multiple species[END_REF]) and 40 pg/ml (Wolf et al. 2011). However, in the first case, the authors used polyclonal antibodies that cannot be used for routine assay development due to the limited availability of the antibody and the variability from batch to batch production. In the second publication, the main problem of the use of fluorimetric assay is the interference of the relative fluorescence with the biological material, such as blood. In the present study, we developed and validated a sandwich enzyme-linked immunosorbent assay (ELISA) for the quantitative detection of tTG protein level using our newly developed monoclonal and polyclonal antibodies. However, the analytical sensitivity of this assay is around 2 ng/ml, which is less sensitive but more accurate and robust test. Our new and ready to use assay represents an easy tool for the detection and quantification of tTG in various human and guinea pig samples, including serums, tissue homogenates, and cell extracts. This ELISA assay can be used to study the expression and function of tTG and complement the data obtained by tTG activity assay, respectively.

Materials and methods

Chemicals

Recombinant human tTG (rhu-tTG), recombinant human keratinocyte transglutaminase (TG1), recombinant human epidermal transglutaminase (TG3), recombinant human neuronal transglutaminase (TG6), recombinant human transglutaminase 7 (TG7), and recombinant human factor XIII (FXIII) were obtained from Zedira (Darmstadt, Germany). Horseradish peroxidase (HRP) conjugated goat anti-rabbit IgG (H + L) was purchased from Jackson ImmunoResearch Europe Ltd. (Suffolk, UK). Corning immuno 96-stripwell flat-bottom plates and cell culture dishes, protease inhibitor cocktail, phenylmethanesulfonyl fluoride (PMSF), bovine serum albumin (BSA), hypoxanthine-aminopterin-thymidine medium (HAT), DMEM medium, culture media and supplements, protease inhibitor cocktail, Freund's complete adjuvant and Freund's incomplete adjuvants were obtained from Sigma-Aldrich (France). Tetramethylbenzidine (TMB) staining solution, Covalight chemiluminescent reagent, and blocking buffer were obtained from Covalab (Villeurbanne, France).

Generation of monoclonal antibodies

Mouse monoclonal IgG antibodies (Mabs) against tTG were prepared by immunizing 6-8-week-old female Balb/c mice with rhu-tTG. The immunization, the fusion of murine myeloma cell line (Sp2/O-Ag-14) and spleen cells from the best responding animal, respectively, HAT (hypoxanthine-aminopterin-thymidine medium) selection of hybridomas were performed according to the standard method of Covalab (Villeurbanne, France) described by El Alaoui et al. (1991).

Generation of polyclonal antibodies

Rabbit polyclonal IgG antibodies against tTG were prepared by immunizing 3-month-old white female new Zealand rabbits with rhu-tTG according to the standard method of Covalab (Villeurbanne, France).

Selection of tTG antibody couple

To achieve the best signal-to-noise ratio for the sensitivity level desired in sandwich ELISA, a panel of monoclonal and polyclonal antibodies was examined by check board titration, using rhu-tTG as antigen (data not shown). After selection of 3F3 monoclonal and Cov2005 polyclonal antibodies, ELISA assay condition was optimized.

Cell culture

HEK293AD cell line stable transfected with rhu-tTG was kindly provided by Dr. Laszló Fesüs and Dr. Kajal Kanchan (Department of Biochemistry and Molecular Biology, University of Debrecen, Hungary) [START_REF] Kanchan | Identification of a specific one amino acid change in recombinant human transglutaminase 2 that regulates its activity and calcium sensitivity[END_REF]. HEK293AD-tTG cells were grown in DMEM supplemented with 10 % fetal bovine serum (FBS), L-glutamine (300 mg/ml), and penicillin/streptomycin 1 3 (100 U/ml) at 37 °C in an atmosphere of 5 % CO 2 . SHEP neuroblastoma cell extracts were kindly provided by Dr. Sandrine Wittmann (Centre Léon Bérard, France). To initiate retinoic acid-mediated differentiation, cells were grown in the low-serum medium containing 10 μM retinoic acid.

Sample preparation

Both cell types were collected and washed twice with phosphate-buffered saline (PBS), resuspended in RIPA buffer [50 mM Tris/HCl (pH 7.5), 150 mM NaCl, 1 mM EDTA, 1 mM DTT, 0.5 % Nonidet P40, 10 % glycerol, and protease inhibitor cocktail] and incubated for 30 min with gentle agitation at 4 °C. The cells were sonicated twice on ice and finally centrifuged at 10000 g for 10 min at 4 °C.

Livers were surgically removed from guinea pigs and washed with 140 mM NaCl. Liver homogenates were prepared in ice-cold buffer containing 140 mM NaCl, 40 mM Tris/HCl (pH 7.5), 3 mM EDTA, 2 mM DTT, 1 mM PMSF, and protease inhibitor cocktail. Supernatant was collected after centrifugation at 25000 g for 30 min at 4 °C.

Erythrocytes were separated by centrifugation at 2000 rpm for 5 min at 4 °C. The red blood cell (RBC) containing pellet was washed three times with ice-cold PBS. Followed by lysis of isolated RBC in lysis buffer [5 mM NaHPO 4 (pH 8.5), 0.3 mM PMSF, 1 mM EDTA, and protease inhibitor cocktail] and centrifuged at 3500 rpm for 20 min at 4 °C. Protein content was determined by the Bradford method using BSA as standard. Samples were stored at -80 °C.

Western blotting

Tissue transglutaminase expression levels in different samples were evaluated also by western blot (WB). Cell lysates, tissue homogenates (20 or 50 μg of total protein), human red blood cell lysates (200 μg), and rhu-tTG were electrophoresed on a 10 % polyacrylamide gel (SDS-PAGE) and transferred to nitrocellulose membranes (Amersham) according to the manual of wet-transfer (Bio-Rad). The membranes were blocked with 5 % non-fat dried milk in PBS for 1 h at 37 °C and then incubated with mouse monoclonal 3F3, 7D2, 6F1, 6B5, or rabbit polyclonal Cov2005 antibodies (5 μg/ml dilution in 1 % non-fat milk/ TBST) overnight at 4 °C. After washing with TBST, HRPconjugated secondary anti-mouse or anti-rabbit antibodies were added and incubated for 1 h at 37 °C. After the final washing, immunoblots were visualized by the incubation of the membranes with chemiluminescence solution.

Luminescence was measured using ImageMaster VDS-CL (GE Healthcare).

Assay procedure

The microplate wells were coated overnight at 4 °C with 100 μl of 15 μg/ml 3F3 mouse anti-transglutaminase Mab diluted in 50 mM bicarbonate buffer (pH 9.5) and were blocked for 3 h at room temperature (RT) with 300 μl blocking buffer. Plates were stored and desiccated at 4 °C until examination.

To prepare an ELISA standard curve, serial dilution of rhu-tTG was prepared in the range of 15.6-1000 ng/ml. 100 μl of rhu-tTG or protein samples (ranging from 13.2 to 250 ng/ml of total protein), diluted in wash/dilution buffer (TBS with 0.05 % Tween 20, pH 7.4), were added to the wells and incubated for 2 h at 37 °C with gentle shaking. After washing with wash/dilution buffer, 100 μl of 2 μg/ml Cov2005 rabbit anti-transglutaminase polyclonal antibody diluted in wash/dilution buffer was added for 1 h at 37 °C with gentle shaking. Subsequently, the wells were incubated with 100 μl of HRP-conjugated goat anti-rabbit IgG (H + L) diluted 1/10000 in wash/dilution buffer. After the final washing step, 100 μl of TMB staining solution was added to the wells and incubated for 5 min at RT. Color development was stopped by the addition of 100 μl 0.5 N H 2 SO 4 , and the absorbance was determined at 450 nm using a microplate reader (Multiskan, Labsystem, Helsinki, Finland).

Specificity

For the determination of the antigen specificity of the assay, a serial dilution of recombinant human tTG, TG1, TG3, TG6, TG7, and FXIIIa was prepared in a concentration range of 15.6-1000 ng/ml; then, the same ELISA protocol was applied as described above.

Evaluation of accuracy

For the estimation of intra-assay variation, three dilutions of guinea pig liver homogenates were prepared and measured tenfold within one ELISA cycle. The inter-assay variation was assessed by measuring each of the three diluted liver samples fourfold on five different days.

Data analysis

Values are reported as mean ± SD. Data were analyzed with GraphPad Prism 5 (GraphPad Software Inc., San Diego, CA, USA).

3

Results

Selection and differential screening of Mabs to tTG

To select the best Mabs specific to tTG which will react with the enzyme in various samples from different species, two types of tests (ELISA and WB) were made using rhu-TG, cell extracts, and tissue homogenates. Therefore we undertook a differential screening with these samples of clones preselected for their secretion of antibodies reacting positively with tTG. Of seven clones tested for further screening on the tTG from different samples, only four (clones: 3F3, 7D2, 6B5, and 6F1) secreted Mabs with restricted specificity to human, mouse, and guinea pig tTG. They were typed as an IgG1 (6F1, 6B5), IgG2a (3F3), and IgG3 (7D2) with kappa light chain.

In Fig. 1, the selected four Mabs and the polyclonal antibody Cov2005 were analyzed by western blot against rhu-tTG. 3F3 and 7D2 showed clear reactivity with rhu-tTG whereas 6F1 and 6B5 had low immuno-reactivity (Fig. 1a). To investigate the cross reactivity of the antibodies with the tTG from other species, liver homogenates from mouse, rat, and guinea pig were used to test the antibodies. It is apparent from Fig. 1b that 3F3 was specific to rhu-tTG and guinea pig tTG, whereas 7D2 and Cov2005 showed good reactivity with rhu-tTG, mouse, rat, and guinea pig tTG.

For further investigation of the specificity to human, mouse, and guinea pig, we tested the Mabs for their use as captured antibodies in sandwich ELISA assay. Indeed, a comparison of the immuno-reactivity of the antibodies was tested for their (1) affinity and specificity to tTG from human, mouse, and guinea pig; (2) stability during their adsorption in the microtiter plates; and (3) sensitivity. Under our experimental procedures, mouse and rat tTGs could not be detected efficiently in liver and blood samples, and hence, the specificity of our assay was limited to human and guinea pig samples (data not shown). Development of the sandwich ELISA assay, sensitivity, and accuracy of the test Among the four Mabs studied, the combination of 3F3 as capture antibody with rabbit polyclonal Cov2005 detection antibody led to the best signal-to-noise ratio and was chosen for all further experiments. The absorbance of the blank, containing all reagents expect rhu-tTG, was 0.132 ± 0.017.

There is a linear relationship between absorbance and concentration of rhu-tTG up to 0.5 μg/ml (Fig. 2). The limit of detection (LOD), defined as mean plus three times, the SD of the background optical density was 1.77 ng/ml.

Specificity

Having good immuno-reactivity of 3F3 antibody to rhu-tTG, we sought to define the specificity of this antibody using the available recombinant TG isoforms (TG1, TG3, TG6, TG7, and FXIIIa). Serial dilutions of each TG were prepared and used as described in "Materials and methods".

The antigen specificity of the assay was determined using purified human recombinant tTG, TG1, TG3, TG6, TG7, and FXIIIa. No cross reactivity was observed up to 1 μg/ml (Fig. 3), indicating the specificity of the two antibodies (3F3 and Cov2005) for tTG. The use of high-specific antibodies to tTG is crucial as in cell lysates or tissue homogenates other isoenzymes of TG family are expressed (e.g., erythrocytes, neuronal cells or tissues, and lung tissues), particularly during the investigation of the role of tTG in the pathogenesis of neurodegeneration or fibrosis, in which other isoenzymes can be involved as well. These results were confirmed by WB (results not shown).

Reproducibility

To determine the reproducibility of sandwich ELISA, intraand inter-assay coefficients of variation (%CV) were calculated in the range from 1 to 2 and 7 to 10 % (Table 1) depending on tTG concentrations in the dilutions of HEK293AD-tTG cell lysates.

The recovery of tTG in crude samples was estimated by spiking HEK293AD-tTG and human red blood cell lysates with 0.05 or 0.1 μg/ml of rhu-tTG. The mean recoveries were between 80 and 97 % (Table 2).

Stability

For the stability, study plates were stored for 3 and 12 month at 4 °C to analyze the variation of the sandwich ELISA system and all the reagents. No significant loss in signal intensity was detected, and the storage of 3F3 Mabcoated plates over prolonged periods does not affect the quality of tTG detection (data not shown).

Measurement of tTG levels in samples

The immunoassay assay was evaluated on tissues and cell homogenates (guinea pig liver homogenate, SHEP and HEK293AD-tTG cell lysates, and human red blood cell lysates) for the determination of tTG level. The results were confirmed by Western blot using both the capture and detection antibodies (Fig. 4). The tTG protein level visualized by immunoblotting related well correlated with the enzyme concentration obtained by the immunoassay (Fig. 4b,c). Recombinant tTG was detected at the same position than the sample bands, confirming that full length was detected. The detectable concentration of tTG in human red blood cell lysate was low (Fig. 4a), but the obtained curve was linear up to 2 mg/ml dilution, indicating that there was no interference with matrix components.

In guinea pig liver homogenate, the highest level of tTG was obtained. The stable-transfected HEK293AD-tTG cell line expresses around 710 ng tTG per mg of protein, which is in similar range than what it was determined in SHEP cells. Whereas, upon retinoic acid treatment, we observed approximately three times increase in the enzyme level in SHEP cell lysates.

Discussion

To investigate the role of tTG in health and disease, an accurate, reliable and quantitative test measuring the enzyme level is needed. This is of importance to address expression and functional questions with regard to members of the TG family. Despite some effort to develop such assay [START_REF] Brevé | Validated sandwich ELISA for the quantification of tissue transglutaminase in tissue homogenates and cell lysates of multiple species[END_REF]Wolf et al. 2011), no test was reported to be used as a gold standard. In this respect, new assay was developed and evaluated for measuring tTG level in different samples thanks to the new antibodies (monoclonals and polyclonal).

To develop the sandwich ELISA, the monoclonal and polyclonal antibodies were tested by check board titration to reach the best signal-to-noise ratio and specificity for tTG. The combination of mouse monoclonal 3F3 as a capture antibody and rabbit polyclonal Cov2005 as detecting antibody was proved to be the best. Our assay is highly specific for tTG isoform without any cross-reactivity with TG1, TG3, TG6, TG7, and FXIIIa. This result is important for the investigation of the specific role of tTG. Indeed, it is well established that several TG isoforms are expressed in the same tissue, such as liver, brain, and skin, in which tTG, TG1, TG3, TG5, and TG6 are found, and in blood, tTG and FXIII are well present.

The assay was validated by measuring the intra-and inter-assay variations. The coefficients of intra-and interassay variations spanned from 1 to 2 % and from 7 to 10 %, respectively, which were proved to be within the appropriate range (Taverniers et al. 2004). The analytical sensitivity of our assay was up to 1.77 ng/ml. This value of LOD is not so low as that described by [START_REF] Brevé | Validated sandwich ELISA for the quantification of tissue transglutaminase in tissue homogenates and cell lysates of multiple species[END_REF]. However, the optimized conditions are the result of a tradeoff between incubation time of different steps and assay sensitivity. Therefore, using the ready to use assay, the ELISA protocol can be performed in a reasonable time (4 h) and the sensitivity should be enough to measure tTG in biological samples. However, to increase the sensitivity of our sandwich ELISA, the development of a second generation of this assay using fluorescence or chemiluminescence is planned in the future.

In this study, we demonstrated that using our sandwich ELISA assay, tTG could be measured in cell lysates, tissue homogenates, and red blood cell lysates. We chose cell lines which naturally express tTG (Human neuroblastoma SHEP) and a transfected one (HEK293AD-tTG) to measure the change of the enzyme level during the experimental treatments. Moreover, these cell lines express high amount of tTG. In the case of the neuroblastoma cell line, the high expression level can be correlated with the pathological processes [START_REF] Liu | Activation of tissue transglutaminase transcription by histone deacetylase inhibition as a therapeutic approach for Myc oncogenesis[END_REF]). In addition, retinoids are wellknown regulators of tTG [START_REF] Nagy | Identification and characterization of a versatile retinoid response element (retinoic acid receptor response element-retinoid X receptor response element) in the mouse tissue transglutaminase gene promoter[END_REF], which modulate the transcription level of the enzyme through binding to the retinoic acid receptors. Indeed, we observed a significant increase in tTG protein level in neuroblastoma cells after retinoic acid treatment. Guinea pig liver is known to express quite high level of tTG [START_REF] Folk | Mechanism of action of guinea pig liver transglutaminase. I. Purification and properties of the enzyme: identification of a functional cysteine essential for activity[END_REF], and thus, it is widely used and accepted as a standard reference of the endogenous tTG. Moreover, guinea pig models can be used for the investigation of diseases correlated with tTG, such as cartilage hypertrophy in the spontaneous guinea pig model of osteoarthritis [START_REF] Huebner | Transglutaminase 2 is a marker of chondrocyte hypertrophy and osteoarthritis severity in the Hartley guinea pig model of knee OA[END_REF]). Using our test, we quantified the highest level of tTG in guinea pig liver homogenate confirming the existing data. In addition to liver, tTG is well expressed in red blood cells [START_REF] Bergamini | Conformational stability of human erythrocyte transglutaminase. Patterns of thermal unfolding at acid and alkaline pH[END_REF]; however, our test was not as sensitive (as described by others), as we found the lowest tTG content in human erythrocytes lysates. This can be explained by the loss of the enzyme protein during the sample preparation as confirmed by WB (Fig. 4) when using the monoclonal 3F3 (a) and the polyclonal Cov2005 (b). These results were confirmed several times with different blood samples using a mixture of protease inhibitors. The other limitations of our Mab 3F3 was the lack of the cross reactivity with the mouse and rat tTG. Indeed, recognizing the importance of rodent models, the development of a specific immunoassay to measure mouse and rat tTG will be proposed.

In conclusion, our validated sandwich ELISA assay presents a reliable, sensitive, and highly specific tool for the detection and quantification of human and guinea pig tTG in several sources of samples, such as cell lysates, tissue homogenates, and erythrocytes lysates to investigate the contribution of tTG in the physiological and pathological processes.

  Figure captionsFig. 1 Relative quantification of transglutaminase reaction products using SDS-PAGE analysis and fluorescent detection. TG2 was incubated with FAM-K9 peptide (a, b, c), thrombin activated FXIIIa with FAM-fibrinogen αC (325-336) peptide (d, e, f) and with cadaverine in the presence of Ca 2+ for 20 min (TG2) or 5 h (FXIII-A) at 37 °C. Q: reactive glutamine containing control peptide, E: deamidated control peptide. (b, e) Densitometry analysis of the SDS-PAGE. (c, f) Relative quantification of the reaction products by nanoLC-nano-ESI/MS

  Fig. 1

  Fig. 2 Fig. 3

F

  Covalab S.A.S, 11 Avenue Albert Einstein, 69100 Villeurbanne, France 1 3

Fig. 1 Fig. 2 Fig. 3

 123 Fig. 1 Characterization of the generated antibodies by western blot. a Verification of the immuno-reactivity of the selected mouse monoclonal 3F3, 7D2, 6F1, and 6B5 antibodies against rhu-tTG. b Determination of the genus specificity of the monoclonal 3F3, 7D2, and polyclonal Cov2005 antibodies. PC rhu-tTG positive control, lane 1 mouse liver homogenate, lane 2 rat liver homogenate, lane 3 guinea pig liver homogenate. 0.1 μg of rhu-tTG and 50 μg of protein per slot were applied

Fig. 4

 4 Fig. 4 Detection of tTG in cultured mammalian cells, isolated human erythrocytes lysates, and guinea pig liver homogenates. a Sandwich ELISA assay. Values are mean ± standard deviation of three experiments performed as duplicates. b Western blot with mouse monoclonal 3F3 antibody. c Western blot with rabbit polyclonal Cov2005 antibody. 20 μg (lane 1-4) and 200 μg (lane 5) of protein per slot were applied. PC rhu-tTG positive control

  Fig 1

Table 1

 1 Sequence of the glutamine containing amine acceptor-and deamidated control peptides

of a sandwich ELISA assay for quantification of human tissue transglutaminase in cell lysates and tissue homogenates Éva Sivadó 1 • Sabrina Lareure 1 • Valérie Attuil-Audenis 1 • Saïd El Alaoui 1 • Vincent Thomas 1

  Condemi E, Tuchscherer G, et al (2011) Tissue transglutaminase-mediated glutamine deamidation of β-amyloid peptide increases peptide solubility, whereas enzymatic cross-linking and peptide fragmentation may serve as molecular triggers for rapid peptide aggregation. J Biol Chem 286:12172-12188. doi: 10.1074/jbc.M110.176149 Schmidt G, Selzer J, Lerm M, Aktories K (1998) The Rho-deamidating cytotoxic necrotizing factor 1 from Escherichia coli possesses transglutaminase activity: Cysteine 866 and histidine 881 are essential for enzyme activity. J Biol Chem 273:13669-13674. doi: 10.1074/jbc.273.22.13669

	Nemes Z, Demény M, Marekov LN, et al (2000) Cholesterol 3-sulfate interferes with cornified envelope assembly Amino Acids (2017) 49:597-604
	by diverting transglutaminase I activity from the formation of cross-links and esters to the hydrolysis of DOI 10.1007/s00726-016-2347-4
	glutamine. J Biol Chem 275:2636-2646. doi: 10.1074/jbc.275.4.2636
	Perez Alea M, Kitamura M, Martin G, et al (2009) Development of an isoenzyme-specific colorimetric assay for ORIGINAL ARTICLE
	tissue transglutaminase 2 cross-linking activity. Anal Biochem 389:150-156. doi: 10.1016/j.ab.2009.03.029
	o r R e v i e w O n l y F o r R e v i e w O n l y Pinkas DM, Strop P, Brunger AT, Khosla C (2007) Transglutaminase 2 Undergoes a Large Conformational Change upon Activation. 5:2788-2796. doi: 10.1371/journal.pbio.0050327 Robinson NE, Robinson a B (2001) Molecular clocks. Proc Natl Acad Sci U S A 98:944-949. doi: 10.1073/pnas.98.3.944 Development Received: 11 September 2016 / Accepted: 4 October 2016 / Published online: 19 October 2016 Schmid AW, Biotechnol Appl Biochem 43:171-179. doi: 10.1042/BA20050161 © Springer-Verlag Wien 2016
	1 3

Schousboe A, Scafidi S, Bak LK, Waagepetersen HS MM (2014) Glutamate Metabolism in the Brain Focusing on Astrocytes. Adv Neurobiol 11:11-30. doi: 10.1007/978-3-319-08894-5 Sjöström H, Lundin KEA, Molberg, et al (1998) Identification of a gliadin T-cell epitope in coeliac disease: General importance of gliadin deamidation for intestinal T-cell recognition. Scand J Immunol 48:111-115. doi: 10.1046/j.1365-3083.1998.00397.x Stamnaes J, Fleckenstein B, Sollid LM (2008) The propensity for deamidation and transamidation of peptides by transglutaminase 2 is dependent on substrate affinity and reaction conditions. Biochim Biophys Acta -Proteins Proteomics 1784:1804-1811. doi: 10.1016/j.bbapap.2008.08.011 Sugimura Y, Hosono M, Kitamura M, et al (2008) Identification of preferred substrate sequences for transglutaminase 1 -Development of a novel peptide that can efficiently detect cross-linking enzyme activity in the skin. FEBS J 275:5667-5677. doi: 10.1111/j.1742-4658.2008.06692.x Sugimura Y, Hosono M, Wada F, et al (2006) Screening for the Preferred Substrate Sequence of Transglutaminase Using a Phage-displayed Peptide Library IDENTIFICATION OF PEPTIDE SUBSTRATES FOR TGASE 2 AND FACTOR XIIIA *. 281:17699-17706. doi: 10.1074/jbc.M513538200 Thomas V, El Alaoui S, Massignon D, et al (2006) Development and evaluation of a modified colorimetric solidphase microassay for measuring the activity of cellular and plasma (Factor XIII) transglutaminases.

Table 1

 1 Intra-and inter-assay variations of tTG sandwich ELISA assay

	Sample/well (μg)	n	tTG (μg/ml)		% CV
			Mean	SD
	Intra-assay variation
	5	10	0.231	0.01	2
	10	10	0.536	0.01	1
	20	10	0.802	0.02	2
	Inter-assay variation
	5	5	0.219	0.02	7
	10	5	0.538	0.04	8
	20	5	0.820	0.08	10

Acknowledgments

We would like to thank Agnès Degiuli (University Lyon 1, CNRS, INSA, CPE-Lyon, Institute for Molecular and Supramolecular Chemistry and Biochemistry) to provide free access for Luminescent Image Analyzer (LAS-1000 plus, Fujifilm). E.S. was supported by a Marie Curie research grant (''TRANSPATH'', FP7 No 289964) and R.K. was supported by Janos Bolyai Research Fellowship of the Hungarian Academy of Science.

Acknowledgments We would like to thank Prof László Fésüs (Department of Biochemistry and Molecular Biology, Hungary) and Sandrine Wittmann (Centre Léon Bérard, France) for cell samples. E.S. was supported by a Marie Curie research grant (''TRANS-PATH'', FP7 No 289964).

Compliance with ethics requirements

Conflict of interest Éva Sivadó declares that she has no conflict of interest, Sabrina Lareure declares that she has no conflict of interest, and Valérie Attuil-Audenis declares that she has no conflict of interest. Saïd El Alaoui declares that he has no conflict of interest, and Vincent Thomas declares that he has no conflict of interest.

Study with human subjects All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Informed consent was obtained from all patients for being included in the study.

Study with animals

All institutional and national guidelines for the care and use of laboratory animals were followed.