Nikolaj Bittner

Denis Golež

Michele Casula

Philipp Werner

Photo-induced Dirac cone flattening in BaNiS 2

Keywords: numbers: 71, 10, Fd, 05, 70, Ln

Using a real-time implementation of the self-consistent GW method, we theoretically investigate the photoinduced changes in the electronic structure of the quasi two-dimensional semi-metal BaNiS2. This material features four Dirac cones in the unit cell and our simulation of the time-and momentum-resolved nonequilibrium spectral function reveals a flattening of the Dirac bands after a photo-doping pulse with a 1.5 eV laser. The simulation results are consistent with the recently reported experimental data on photo-doped BaNiS2 and ZrSiSe, another Dirac semi-metal. A detailed analysis of the numerical data allows us to attribute the nonequilibrium modifications of the Dirac bands to (i) an increased effective temperature after the photo-excitation, which affects the screening properties of the system, and (ii) to nontrivial band shifts in the photo-doped state, which are mainly induced by the Fock term.

I. INTRODUCTION

Photo-induced changes in band dispersions and quasiparticle life-times have been reported in different classes of solids. In charge-transfer insulators such as cuprates, for example, the photo-doping across the charge transfer gap results in substantial band shifts and band broadenings, [START_REF] Novelli | [END_REF][2][3][4][5][6] which can be explained by the induced changes in the electrostatic energy (Hartree shifts) 6,7 and enhanced nonlocal charge fluctuations. [8][9][10] In correlated semiconductors, photoexcitation typically leads to a narrowing of the gap, which is referred to as band gap renormalization. 11,12 However, recent experiments on excitonic systems revealed a richer behavior with a transient enhancement 13 or suppression [14][15][16] of the band gap, which was attributed to the underlying excitonic order. [17][18][19][20] In weakly or moderately correlated metals, electronelectron interactions typically result in a narrowing of the bands near the Fermi level, so that photo-excitation and its associated heating effects are naively expected to lead to a band widening. However, in the Dirac semi-metal BaNiS 2 , a recent photo-doping study 21 has observed a flattening of the Dirac cone in the photo-doped state (Fig. 1). Remarkably, this flattening of the Dirac cone persists up to 1 ps, indicating a bottleneck in the electronic dynamics. Similar measurements have also been reported in photo-doping experiments on ZrSiSe, a different material with Dirac dispersions. 22 These experimental results suggest a nontrivial effect of the photo-induced changes on the screening environment in these materials. Indeed, temperature-dependent equilibrium calculations 21,22 point to an important role of the nonlocal interactions in this unusual response of the electronic structure to photo-carriers. As an extreme case of photo-manipulation of relativistic materials, recent photo-emission studies have demonstrated an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal T d -MoTe 2 . 23 To get deeper insights, a proper modeling and simulation of the nonequilibrium states in Dirac semi-metals is needed. Be-cause these materials are moderately correlated, and the timedependent screening of long-ranged interactions apparently plays an important role, a promising approach is the nonequilibrium implementation of the GW method. 24 This formalism has been successfully used to study transport in mesoscopic systems, 25 relaxation dynamics in various electron-boson coupled systems, 26,27 as well as the nonthermal destruction of ordered states. 28 In combination with dynamical mean field theory, 29 it allowed to reveal the effects of nonlocal charge fluctuations in photo-doped charge transfer insulators. 8 However, nonequilibrium GW studies of bulk materials have to the best of our knowledge been performed so far mainly in simple model contexts. Here, we bridge the gap to realistic nonequilibrium materials simulations by treating an ab initio model 21,30 for BaNiS 2 within the framework of nonequilibrium GW , to study the effect of photo-excitation with a 1.5 eV pump pulse on the electronic structure and in particular the Dirac cone dispersion.

Our simulations reproduce the nontrivial band flattening, in qualitative agreement with the experimental findings based on time-resolved angle-resolved photoemission spectroscopy (tr-ARPES) (see Fig. 1). These encouraging results, in combination with the controlled many-body framework, allow us to address the central question of the paper: which many-body processes are mainly responsible for these photo-induced modifications in the electronic structure and which aspects are specific to Dirac systems? The direct access to the timedependent self-energy and the screened interaction (or polarization) enables an analysis of the physical processes driving the photo-induced band renormalization of the Dirac states. In particular, we will clarify the effect of the photo-induced heating on the screening properties, and reveal the importance of the photo-induced Fock exchange modifications, which result from the nonthermally populated bands. The paper is organized as follows. Sections II and III introduce the realistic two-band model for BaNiS 2 and the realtime GW method used in the numerical simulations, respectively. Section IV discusses equilibrium properties of this correlated material, while Section V analyzes the time-dependent changes in the Dirac dispersion of BaNiS 2 after a photoexcitation. Section VI summarizes our findings.

II. MODEL

We consider a two-dimensional (2d) two-orbital system representing the low-energy electronic structure of BaNiS 2 at half-filling, as determined in Refs. 21,30. Within this ab-initio derived description, we will focus on the charge dynamics, which is relevant to study the renormalization of the Dirac states seen in tr-ARPES. Thus, we restrict the model to spinless fermions, and treat BaNiS 2 by the Hamiltonian

H(t) = H kin + H int + H dip (t), (1)
with a kinetic term of the tight-binding form

H kin = α,k E α -µ -t α (cos(k x ) + cos(k y )) + t ′ α cos(k x ) cos(k y ) n kα + α =β,k [t α,β sin(k x ) sin(k y )d † kα d kβ + H.c.] . (2)
Here, we have introduced the creation operators d † kα for spinless fermions in the orbitals α = z 2 , x 2 -y 2 with momentum k, and n kα = d † ka d ka . The momentum is defined in a rotated Brillouin zone with basis vectors k 1 = (1, 1)/ √ 2 and k 2 = (1, -1)/ √ 2. We will neglect the z dependence of the dispersion. The hopping parameters and local energies in eV units are taken from Ref. 30:

E z 2 = -0.64, E x 2 -y 2 = 0.24, t z 2 = -0.68, t x 2 -y 2 = 0.28, t ′ z 2 = 0.66, t ′ x 2 -y 2 = -0.96, t z 2 ,x 2 -y 2 = 0.28, t x 2 -y 2 ,z 2 = 0.28. (3)
The interaction term is restricted to density-density interactions of the form

H int = 1 2 ij αβ V |i-j| n iα n jβ - 1 2 i α V loc n iα n iα , which may be split into the non-local intraorbital interaction 1 2 ij αβ δ α,β V |i-j| n iα n jβ - 1 2 i
α V loc n iα n iα and the interorbital interaction

1 2 ij αβ (1 -δ α,β )V |i-j| n iα n jβ .
Hence, in momentum space, the interaction becomes

H int = 1 2N k,k ′ ,q αβ δ α,β V (q)d † k+qα d kα d † k ′ -qβ d k ′ β - 1 2N k1,k2,k3 α V loc d † k1+k3-k2α d k 1 α d † k2α d k 3 α + 1 2N k,k ′ ,q αβ (1 -δ α,β )V (q)d † k+qα d kα d † k ′ -qβ d k ′ β , (4)
where N is the number of k points in the 2d Brillouin zone.

To obtain an interaction V which takes into account the 3d nature of the material, we will consider a system of stacked layers with interlayer distance I c . In this setup, the interaction vertex of the layered 3d system is given by 31

V (q, k z ) = 1 4πǫ 0 2πe 2 κ 0 |q| sinh(|q|I c ) cosh(|q|I c ) -cos(k z I c )
, ∀α, β.

(5) where q = (q x , q y ) denotes the momentum in the 2d layers, and k z the momentum perpendicular to the planes. For BaNiS 2 , we take the in-plane lattice constant a = 3.140 Å and I c = 8.91 Å. The dimensionless momenta q x a, q y a and k z I c are in the range [-π, π]. κ 0 is the dielectric constant, which takes into account the screening from other bands, which have been discarded in the downfolding to the low-energy model. The constrained Random Phase Approximation (cRPA) 32 interaction of the closely related compound BaCoS 2 suggests a screening of the bare interaction by κ 0 ≈ 10. 33 Indeed, the interaction with κ 0 = 10 results in a flattening of the Dirac cones after the photo-excitation by ≈ 5% (see Appendix A), which is in reasonable agreement with the experimental results (Fig. 1). 21 However, for a better visualisation of the photo-induced effects, we choose in the following simulations κ 0 = 6, which results in stronger correlations and larger band shifts, without qualitatively changing the results.

From Eq. ( 5), the effective interaction within a single 2d layer is obtained by averaging over k z :

V (q) = I c π π/Ic kz,cut dk z V (q, k z ). (6)
Because the Coulomb-like interaction V (q, k z ) has a singularity at q = (0, 0) and k z = 0, we introduce a small-momentum cutoff for the integration along the k z direction. This cuts off the long-ranged part of the interaction, V (q → 0), as illustrated in Fig. 2. In the actual calculations, we use k z,cut I c = 0.23. We have checked that this k z,cut is small enough that the results are not qualitatively affected. Due to the strong hybridization between the d and p orbitals in BaNiS 2 , we describe the photo-excitation of the system by /8 /8

Figure 2: Effective 2d interaction from Eq. ( 6) with kz,cutIc = 0.31 (blue), 0.27 (light blue), and 0.23 (dark red). Here, the momentum q is scaled with the lattice constant a.

a laser-induced (dipole allowed) population transfer between the orbitals,

H dip (t) = k A(t)d † kz 2 d kx 2 -y 2 + H.c. . (7)
Here, the pump pulse

A(t) = A 0 e -(t-t0) 2 /τ 2 sin(ω(t -t 0 ))
with frequency ω has a Gaussian envelope with a maximum A 0 at time t 0 and a full width at half maximum τ .

Energy and temperature will be measured in units of eV and time will be measured in units of fs.

III. METHOD A. Green functions

We will treat the equilibrium and nonequilibrium properties of model (1) within the GW approximation. 28 The time evolution of the correlated system is simulated using the NESSi software library, 34 which is based on the L-shaped Kadanoff-Baym contour formalism. 29 It is convenient to introduce a spinor representation for the two orbitals:

Ψ k ≡ d k,1 d k,2 . (8)
The corresponding 2×2 Green's function is given by the contour C ordered expectation value:

Ĝk (t, t ′ ) = -i T C Ψ k (t)Ψ † k (t ′ ) (9)
and is determined from the solution of a Dyson equation with appropriate self-energy. For later use, we also introduce the single-particle density matrix

ρ k,αβ = Ψ † k,β Ψ k,α and its lo- cal component ρ loc,αβ = 1 N k ρ k,αβ
, where N denotes the number of k points in the 2d Brillouin zone. All the results shown will be calculated for 20 × 20 k points.

B. Hartree-Fock approximation

To calculate the Hartree and Fock self-energies, we employ the usual mean-field decoupling of the interaction term (4). The 2×2 Hartree self-energy in orbital space is then given by

Σ H q,αβ (t) =δ αβ V (|q| = 0)ρ loc, ᾱ ᾱ(t) + [V (|q| = 0) -V loc ]ρ loc,αα (t) , (10)
where the first term corresponds to the inter-orbital interaction and the second term to the non-local intra-orbital interaction.

An overline marks the opposite orbital.

As is seen in Fig. 2, for small cutoff k z,cut the potential V (|q| = 0) becomes very large. To avoid numerical problems resulting from this, we impose charge neutrality, so that the attractive potential of a neutralizing homogeneous background shifts the total Hartree term to zero. In other words, Σ H q ∝ ρ tot , and ρ tot = 0, if the homogeneous background is taken into account. In practice, we set the Hartree self-energy in the initial equilibrium state to zero, while the orbitally-resolved components take nonzero values in the photo-excited nonequilibrium state.

The 2×2 Fock self-energy term in orbital space is given by

Σ F k,α ᾱ(t) = - 1 N q V (q)ρ k-q,α ᾱ(t), Σ F k,αα (t) = - 1 N q V (q)ρ k-q,αα (t) + V loc ρ loc,αα (t). (11)

C. GW approximation

In the GW method 24 the effect of screening is taken into account at the Random Phase Approximation level. This formalism can be derived from a Luttinger-Ward functional and hence yields a conserving approximation. In addition to the Hartree and Fock contributions, we consider the electronic self-energy

Σ GW k,αβ (t, t ′ ) = i 1 N q G k-q,αβ (t, t ′ )W q,αβ (t, t ′ ), (12)
where W q,αβ is the screened interaction, whose self-energy is given by the polarization

Π q,αβ (t, t ′ ) = -i 1 N k G k+q,αβ (t, t ′ )G k,βα (t ′ , t). ( 13
)
We obtain a closed set of equations by considering the Dyson equation relating the bare and screened interactions,

Ŵq = Vq + Vq * Πq * Ŵq , (14)
where * marks the convolution on the Kadanoff-Baym contour and the hat symbol indicates 2 × 2 matrices in orbital space. Equation ( 14) is valid in the density-density approximation. General interactions would require a two-particle basis. 35 The interaction vertex Vq , with V q,αβ = V q , is instantaneous in time, i.e. Vq (t, t ′ ) = Vq δ C (t, t ′ ) with δ C denoting the contour δ-function. Thus, in the actual implementation, we treat it separately. In practice, we define the charge susceptibility as χq = Πq + Πq * Vq * Πq + . . . (15) and numerically compute it by solving the integral equation 34 χq -Πq * Vq * χq = Πq .

(

) 16
The effective interaction is then determined as Ŵq = Vq + Vq * χq * Vq .

In order to calculate the spectral functions, we use traces over the orbital indices, i.e.

G loc = 1 N k G k with G k = Tr Ĝk . ( 17
)
The local spectral functions at time t p are calculated from the forward-Fourier transformation with respect to t ′ over a time interval of length t max ,

A loc (t p , ω) = - 1 π Im tp+tmax tp dt ′ G R loc (t p , t ′ )e -iω(t ′ -tp) . ( 18
)
For the k-dependent spectral functions, we apply instead a backward-Fourier transformation with respect to t:

A k (t p , ω) = 1 π Im tp+tmax tp dtG R k (t, t p + t max )e iω(tp+tmax-t) . (19)
IV. EQUILIBRIUM PROPERTIES A. Bandstructure the form of four spots with strong intensity, in agreement with Refs. 21,30. A consequence of the Dirac dispersions is an approximately linear increase in the density of states away from the Fermi energy, as indicated by the (strongly broadened) local spectral functions plotted in Fig. 4.

In order to illustrate renormalization effects on the band dispersion due to different self-energy contributions, we plot in Fig. 3(a) the band structure obtained by keeping only the Hartree-Fock (HF) terms of the full GW self-energy (red dashed lines) and the "quasi-particle GW" (QPGW) peak position (red solid lines). The HF contribution leads to a widening of the band structure compared to its non-interacting counterpart (green dashed line). On the other hand, including additionally the Σ GW k self-energy contribution results in a flattening of the band dispersion. The QPGW bands in Fig. 3(a) corresponds to the poles of the quasi-particle GW spectral function 36 A

k (ω) ∝ 1 ω -ǫ k + µ -Σ H -Σ F k -ReΣ GW k (E k ) , (20)
where E k is the self-consistent solution of the equation

E k = ǫ k -µ + Σ H + Σ F k + ReΣ GW k (E k ). (21)

B. Temperature dependence

An interesting question concerns the temperature dependence of the screening in this Dirac semi-metal, since this has an important effect on the correlated electronic structure. We analyze here the fully screened interaction Ŵq (Eq. ( 14)) computed for different temperatures T , using the cutoff k z,cut I c = 0.23. This function is related to the frequency-dependent dielectric constant by Ŵq = Vq * ǫ-1 q (with ǫq = 1 -Vq * Πq ). In Fig. 5(a), we plot the real part of the screened interaction q Vq ] is shown by the dashed line. As one can see, the local component of the static screened interaction increases with decreasing temperature, i.e. the screening becomes less effective. The q ≡ |q| = 0 component (inset of Fig. 5(a)) suggests that this comes primarily from the temperature dependence of the strongly screened long-range interaction, since the static value of the long-range interaction increases significantly as temperature is reduced. This is a characteristic feature of Dirac semi-metals such as BaNiS 2 , whereas in "conventional" metals with a large density of states at the Fermi level, one finds the opposite temperature-dependent screening behavior (see Appendix E).

Second, in Fig. 5(b), we plot the imaginary part in the unusual temperature evolution of the screened interaction seen in panel (a).

Another characteristic property of 2d Dirac systems is the appearence of a long wavelength plasmon, which has a smaller plasma frequency in the q → 0 limit than a conventional 2d metal. 37 This plasmon can be identified in the momentum-resolved spectra [START_REF] Novelli | [END_REF] 2 Tr[Im Ŵq (ω)] as the small peak at low frequencies (see Fig. 6). For illustration, we additionally indicate by the red dashed line the energy dispersion of the plasmon obtained from the analytical formula in Ref. 37, valid for the conical model with Coulomb interactions, and the parameters for BaNiS 2 . The Dirac prediction nicely matches our numerical results in the q → 0 limit.

In addition to the plasmon, we notice the broad feature centered around ω ≈ 6 eV, which is associated with the peak shown in the inset of Fig. 5(b).

V. NON-EQUILIBRIUM RESULTS

A. Pulse excitation

In this section, we investigate the time-dependent modifications in the electronic structure and screening properties of BaNiS 2 after a photoexcitation. We simulate the photoexcitation of the system with a short light pulse by direct dipole allowed transitions between the orbitals contributing to the Dirac cone (see Eq. ( 7)). For the pump pulse we choose the parameters ω = 1.5 eV, A 0 = 0.15, τ ≈ 2.3 fs, and t 0 = 3.6π/ω , unless otherwise specified. While this pulse frequency is consistent with the experiments in Ref. 21, the pulse duration is shorter (it contains only about five cycles), due to computational limitations in the accessible time range. Before the pump, the system is in equilibrium at T = 0.07 eV, where its low-energy properties are dominated by the Dirac physics. The following results are obtained using a 20 × 20 grid in momentum space. A finer k grid does not significantly change the results.

B. Nonequilibrium screening

First, we analyze the screening effects after the photoexcitation. In Fig. 7, we plot the real and imaginary parts of the time-dependent screened interaction. As one can see, the static screened interaction is slightly reduced after the photoexcitation (Fig. 7(a)), while the peak in the imaginary part is slightly shifted from ω ≈ 1.8 eV to higher energies. This is qualitatively similar to the effect of heating in equilibrium (c.f. Fig. 5). For comparison, we plot in the same figure also the equilibrium result for T = 0.12 eV, which is the temperature T eff of the thermalized system (black solid line). The lowfrequency effective interaction [START_REF] Novelli | [END_REF] 2 Tr[Re Ŵ R loc (t, ω = 0)] after the pulse resembles the equilibrium result at T = 0.12 eV. On the other hand, the peak in [START_REF] Novelli | [END_REF] 2 Tr[Im Ŵ R loc ] is shifted to slightly higher frequencies than in equilibrium. This indicates some differences in the broadening or energy position of the bands, but these differences are rather small. The inset shows that the thermalization of the q = 0 component is slower than in the case of the local component.

An analysis of the q dependent nonequilibrium results shows that the q → 0 plasmon and the broad peak near ω ≈ 6 eV are enhanced, while for larger q the pulse induces mainly a broadening of the features, again in qualitative agree-Figure 8: Difference ∆A k between the spectral function of the photo-excitated system (t ≈ 10.9 fs) and the initial equilibrium spectral function (T = 0.07 eV). The dashed lines indicate the QPGW peak positions from Eq. ( 20) for the initial equilibrium state (blue dashed line) and after the photo-excitation (red dashed line). Both spectral functions are calculated with tmax = 6.8 fs. ). The blue line corresponds to the equilibrium spectrum at T = 0.07 eV and the red line to the nonequilibrium spectrum after the pulse at t ≈ 10.9 fs. Solid (dashed) vertical lines indicate the positions of the QPGW bands (bands which take into account the Hartree-Fock contribution to the full GW self-energy). (b) Difference between the QPGW energies of the upper ("+") and lower ("-") band at ka = (π/5, π/5) in equilibrium (dark red dashed line with dots) and after a photo-excitation (dark red solid line with dots) as a function of T or Teff. In addition, we plot the analogous results taking into account only the Fock (blue lines with triangles) and Hartree-Fock (light blue lines with squares) contributions to the full GW self-energy. The effective temperature after the photo-excitation is estimated from the total energy. ment the effect of increasing temperature equilibrium. Hence, from the nonequilibrium behavior of W it appears that the photo-induced changes in the screening environment are essentially equivalent to the changes induced by heating. If significant differences in the band renormalization between photo-doped and heated systems are found, it is hence unlikely that the dominant effect is the nonthermal screening environment.

C. Nonequilibrium spectral function

To study the time-and momentum-resolved spectral function, we calculate A k (t, ω) in analogy to Eq. (18). In Fig. 8, we plot the difference between the photo-excited (t ≈ 10.9 fs) and the equilibrium spectrum (T = 0.07 eV). Even though the spectral resolution is limited because of the short Fourier window (t max = 6.8 fs), it is obvious that the spectral weight in the momentum region associated with the Dirac cone is shifted towards ω = 0, which implies a flattening of the Dirac dispersion. In addition, the figure shows a significant broadening of the bands in the photo-excited state, consistent with the results from a recent GW +DMFT study. 8 To clearly illustrate the flattening of the Dirac cones, we plot in Fig. 9 the spectra of the equilibrium and photo-excited system for ka = (π/5, π/5). While the photo-excitation induces both shifts and broadenings of the spectra, the peak positions are slightly shifted towards ω = 0. This result, which is not sensitive to the cut-off value k z,cut , [START_REF]The only effect of kz,cut is a rescaling of the dispersions[END_REF] is consistent with a flattening of the Dirac cone.

For a better visualisation of the energy shifts, we indicate in the same figure the QPGW peak positions E k from Eq. ( 20) by vertical solid lines. We furthermore show by vertical dashed lines the peak positions obtained by keeping only the Hartree-Fock contribution to the full GW self-energy. The photoinduced change of the interorbital Hartree-Fock contribution along the Γ → M direction can be calculated as (see Appendix C):

∆Σ F k,αα + ∆Σ H αα = - 1 N q V (q)∆ρ k-q,αα (t), (22)
where ∆ρ represents the photo-induced change in the charge density distribution. Since the photo-excitation reshuffles charge from orbital α = 1 to orbital α = 2, corresponding to ∆ρ αα < 0 (> 0) for the states below (above) FL, it results in the flattening of the effective bandstructure obtained by keeping the Hartree-Fock terms of the GW selfenergy. This is clearly visible by looking at the dashed lines in Fig. 9(a). Moreover, we can see that the bandstructure which accounts only for the Hartree-Fock contributions responds more strongly to the photo-doping than the full QPGW bandstructure, which indicates that the non-retarded (Hartree-Fock) and retarded self-energy diagrams have opposite effects on the correlated electronic structure, and that the former dominate the band shifts. Similar effects as in the photo-doped system can be found by increasing the temperature in equilibrium, as is shown in Appendix B. However, the nonthermal population created by the photo-doping leads to a stronger flattening than a simple heating. For a quantitative analysis of the corresponding band renormalizations, we plot in Fig. 9(b) the energy difference between the upper and lower band at ka = (π/5, π/5) at different temperatures and after the photo-excitation. For a proper comparison between equilibrium and nonequilibrium results, we estimate the effective temperature T eff after pumping from the change in the total energy, i.e. we search for the equilibrium system with T = T eff and the same total energy as the photo-excited system. In Fig. 9(b), we show that the flattening of the cone is qualitatively similar in the photodoped and heated system, but the effect of photo-doping is significantly stronger. Comparing separately the effects of the Fock, Hartree-Fock, and the full GW self-energy on the band shifts, we see that the nonthermal contribution to the Dirac cone flattening is primarily due to the Fock term. The enhanced band-flattening in the photo-doped state and the importance of the Fock contribution represent the main results of this study. Together with the analysis in Sec. V B we may conclude that rather than an effect of nonthermal screening, the pronounced changes measured by tr-ARPES in photo-excited BaNiS 2 originate from the Fock exchange.

VI. SUMMARY

We presented a theoretical study of the effect of photoexcitation on the electronic structure of BaNiS 2 and the possibility of a photo-induced Dirac cone flattening in this quasi two-dimensional Dirac material. Our study combined an abinitio inspired model for BaNiS 2 with a nonequilibrium GW treatment of the photo-induced dynamics. This advanced methodology allowed us to study both the screening properties and interactions in the nonequilibrium state and their effect on the nonequilibrium electronic structure.

Calculating the effective screened interaction at different temperatures in equilibrium, we demonstrated a non-trivial screening enhancement with increasing temperature, which is a hallmark of Dirac systems. In particular, we showed that this effect comes primarily from a strong screening of the long-range part of the interaction, since the q = 0 component of the screened interaction decreases strongly with increasing temperature. This can be traced back to the properties of the polarization function, which exhibits a positive temperature slope within the Dirac region, in contrast to a conventional metal.

Our nonequilibrium simulations of BaNiS 2 revealed both an effective heating of the solid after a photo-excitation, and photo-induced nonthermal effects. By computing the effective of the photo-doped systems, and from comparisons with data, we concluded that the changes in the screening environment can to a large extent be explained by the heating effect. On the other hand, the band renormalization effects are much stronger in the photo-doped state than in thermalized systems at the corresponding effective temperature.

A separate analysis of the Hartree and Fock contributions to the QPGW bandstructure showed that this nonthermal effect is mainly driven by the Fock exchange and the out-ofequilibrium charge distribution. Our study demonstrates that a nontrivial combination of heating, modifications in the screening environment, as well as band shifts due to the Fock term are all relevant to describe photo-doped Dirac semi-metals. This exemplifies the usefulness of unbiased nonequilibrium many-body simulations for the interpretation of ultrafast timeresolved experiments on correlated solids. momentum-resolved spectral functions. However, the peak position of the upper band does not change with temperature, whereas the lower band shifts toward ω = 0.

Figure 1 :

 1 Figure 1: Dirac cone flattening for the left (a) and the right (b) branch after photo-excitation with a 1.5 eV laser, measured with tr-ARPES. The black lines show the equilibrium dispersion, and the red lines the dispersion measured after the photo-doping pulse. The k-points are aligned along the Γ-M direction, Γ (M) being located at k = 0 (k = ±1.00 Å-1 ) (Experimental data adapted from Ref. 21.)

Figure 3 :

 3 Figure 3: (a) k-dependent band dispersion Ak(ω) for BaNiS2 calculated for T = 0.07 eV on a 20×20 k grid. For the Fourier transformation we use a time window tmax = 6.8 fs. The intensity is measured in units 1/eV. The red dashed line represents the Hartree-Fock contributions to the band structure, while the solid red line shows the QPGW band structure defined by Eq. (20). For comparison, we also show the noninteracting band dispersion by the green dashed line. The horizontal dashed line corresponds to the Fermi level FL. (b) Ak(ω = 0) plotted in the first Brillouin zone, showing the four Dirac points (surrounded by high intensity regions) on the diagonals. The intensity is measured in units 1/eV.

Figure 3 (Figure 4 :

 34 Figure 3(a) shows the correlated electronic structure of BaNiS 2 (Eqs. (1)-(3)) along the momentum path Γ =(0, 0) → M=(π, π) → X=(π, 0) → Γ =(0, 0), while the spectral function at the Fermi energy, A k (ω = 0), is shown as a function of k = (k x , k y ) in Fig. 3(b). The band dispersion is calculated from A k (ω) with t max = 6.8 fs. This relatively short Fourier window leads to a broadening of the bands. However, we choose here the same value as in the later nonequilibrium simulations with pump pulse, where the time window is restricted by the limited maximum simulation time. As one can see, a Dirac cone appears along the k-path from (0, 0) to (π, π). The Fermi surface consists of four very small Fermi pockets encircling the Dirac points, which are clearly visible in Fig. 3(b) in

1 2

 1 Tr[Re Ŵloc ] as a function of T . For comparison, the local component of the 'bare' interaction V loc = 1 2 Tr[ 1 N

1 2Figure 5 :Figure 6 :

 156 Figure 5: Screened interaction W calculated for different temperatures. Panels (a) and (b) show the real and imaginary part of the local component Wloc(ω), respectively. The inset shows the corresponding q = 0 components.

Figure 7 :

 7 Figure 7: Time-dependent (a) real and (b) imaginary part of the local screened interaction W (ω) after a photo-excitation. The equilibrium results at the initial T = 0.07 and the temperature of the thermalized system (T = Teff = 0.12) are shown by dashed and solid black lines, respectively. In the main panels, the blue lines are on top of the solid black lines.

Figure 9 :

 9 photo-excitation, QPGW photo-excitation, HF photo-excitation, Fock equilibrium, QPGW equilibrium, HF equilibrium, Fock

Figure 11 :

 11 Figure 11: (a) Temperature dependence of the QPGW band structure calculated from Eq. (20). (b) k-resolved spectral function calculated at ka = (π/5, π/5) for T = 0.07 eV (blue line) and T = 0.12 eV (red line).

Acknowledgments

This work was supported by ERC Consolidator Grant No. 724103 (NB, PW), and Swiss National Science Foundation Grant No. 200021 196966 (PW). The calculations have been performed on the Beo04 cluster at the University of Fribourg. DG is supported by Slovenian Research Agency (ARRS) under Program J1-2455 and P1-0044.

Appendix A: Flattening of the Dirac cone for κ0 = 10

To illustrate the flattening of the Dirac cone in BaNiS 2 after a photo-excitation in a model with a more realistic screening parameter, we performed a nonequilibrium GW simulation with κ 0 = 10 (see Eq. ( 5)). The initial temperature is set to T = 0.07 eV and the system is excited by a pump pulse with parameters ω = 1.5 eV, A 0 = 0.1, τ = 1.3 fs. In Fig. 10 we show the results of the simulations, where the black line illustrates the left branch of the Dirac cone in equilibrium and the red line shows the dispersion after a photo-excitation (measured at t = 8.9 fs). Even though the limited k-point resolution makes a direct comparison difficult, one can see by comparison to Fig. 1 that the photo-induced Dirac cone flattening in our simulation is comparable to the flattening observed in the tr-ARPES experiments.

Appendix B: Temperature dependence of the band structure In Fig. 11(a) we show the QPGW peak positions at different temperatures (see Eq. ( 20)). As one can see, the band structure of BaNiS 2 does not significantly change as temperature is increased. However, at certain k points, one finds a small broadening of the upper band at higher temperatures, whereas the lower band shows a simultaneous shift towards ω = 0. To illustrate this, we plot in Fig. 11(b) A k (ω) for ka = (π/5, π/5) at T = 0.07 eV and 0.12 eV (T eff from Sec. V). As one can see, increasing the temperature leads to a broadening of the The photo-doping of the system leads to the time-dependent changes in the local (loc) charge density distribution with respect to the equilibrium (eq) situation. For simplicity, we focus only on the diagonal contributions:

The changes of the charge density distribution during the pulse are

From this, we can obtain the changes in the Hartree selfenergy due to the photo-excitation. Using the definition of the Hartree self-energy:

with ρ tot = ρ loc,00 + ρ loc,11 , we get

In other words, the Hartree component leads to a narrowing of the band width after the photo-excitation. Additionally, we note that for a fixed value of the long-range Coulomb interaction V (q = 0) the local interaction V loc = 1/N q V (q) is larger for smaller κ 0 . Hence, the effect of a narrowing band width due to the photo-induced Hartree shift should be larger for smaller κ 0 . Now, let us focus on the photo-induced changes in the interband Fock term. Using Eq. ( 11) we get

q)∆ρ k-q,αα (t) + V loc ∆ρ loc,αα (t).

(C5)

Thus, from Eq. (C1) and Eq. (C5) we obtain

where ∆ρ k,αα < 0 (> 0) for the states below (above) the FL. It follows that along the relevant direction Γ → M in momentum space, the photo-induced changes in the Hartree-Fock contributions to the GW self-energy lead to a flattening of the bands directly after the pulse. This effect should be larger for interactions with smaller κ 0 . in Fig. 12. As one can see, Π q=0 (ω = 0, β) computed from the compressibility sum rule

shows a linear increase below T ≈ 0.1, which can be described by the analytical expression for Dirac cone dispersions derived in Ref. 21 (gray dashed line). In the above equation, f denotes the Fermi function and D(ǫ) the density of states.

We note that for the comparison with our results we choose a definition of the polarization function without a negative sign. At higher temperatures one observes deviations from this linear behavior, which originate from thermal excitations beyond the Dirac region. Within our GW approximation, the Dirac behavior of the polarization (Π q=0 (ω = 0) = Tr[Re Πq=0 (ω = 0)]) is not entirely reproduced (see blue line in Fig. 12). The reason is that GW breaks the compressibility sum rule, which can be restored by including vertex corrections beyond the GW approximation. 38 However, at T 0.1 we still see a qualitatively similar temperature dependence with a positive temperature slope, which is qualitatively different from the temperature dependence for conventional metals.

Appendix E: Equilibrium screening in a conventional metal

To illustrate the different screening behavior in a conventional metal, compared to the Dirac semi-metal BaNiS 2 , we analyze the temperature dependence of the screened interaction in a highly doped system (≈ 50%). We consider the model described by Eq. ( 1) and shift the chemical potential away from the Dirac points to approximately the energy of the upper peak in A loc (see Fig. 13(a)). This results in a large, ring-shaped Fermi-surface, as shown in Fig. 13(b).

The calculation of the real part of the screened interaction 1 2 Tr[Re Ŵloc ] at different temperatures in this conventional metallic case yields a reduced screening with increasing T (see Fig. 13(c)), and a long-ranged static component which is almost completely suppressed at T = 0.2 eV. In the imaginary part of W loc one finds a pronounced peak around ω ≈ 2.0 eV (see Fig. 13(d)), which approximately corresponds to the band splitting, as shown in panel (a). This peak is slightly shifted to lower energies by decreasing T . In the long-range part of the interaction (inset) one observes a similar shift of the peak at ω ≈ 6 eV. Interestingly, for ω ≤ 1 eV, we see a clear enhancement of 1 2 Tr[Im Ŵloc ] with decreasing temperature. These results illustrate that the screened interaction (and polarization) in a conventional metal show the opposite temperature behavior from a Dirac semi-metal, such as BaNiS 2 (c.f. Fig. 5).


Yohan Reynaud
email: yohan.reynaud@improve-innov.com

Caroline Buffière
email: caroline.buffiere@inrae.fr

Benoît Cohade
email: benoit.cohade@inrae.fr

Mélissa Vauris
email: melissa.vauris@inrae.fr

Kevin Liebermann
email: kevin.lieberman.pro@gmail.com

Noureddine Hafnaoui
email: noureddine.hafnaoui@inrae.fr

Michel Lopez
email: michel.lopez@improve-innov.com

Isabelle Souchon
email: isabelle.souchon@inrae.fr

Didier Dupont
email: didier.dupont@inrae.fr

Didier Rémond
email: didier.remond@inrae.fr

True ileal amino acid digestibility and digestible indispensable amino acid scores (DIAASs) of plant-based protein foods

Keywords: plant protein, pea, soya, wheat, food matrix, digestibility, DIAAS

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Gross domestic product (GDP) per capita is positively correlated with dietary energy intake. Since it does not influence the contribution of protein to dietary energy (i.e., protein provides 5-15% of total energy) (Gerbens-Leenes, Nonhebel, and Krol 2010), demand for protein may increase worldwide as global per-capita GDP climbs. Indeed, research has found that, as standards of living improve, so does the percentage of energy provided by animal-based products. However, in general, the production of animal protein has a greater environmental impact than does the production of plant protein, as measured via the quantity of greenhouse gases emitted per gram of protein [START_REF] González | Protein efficiency per unit energy and per unit greenhouse gas emissions : Potential contribution of diet choices to climate change mitigation[END_REF]. Since 2004, the availability of commercial plant-protein-based foods has increased dramatically in France; the source of protein in these foods is most often soya, wheat, and pea (GEPV, 2019).

However, there are two major concerns regarding protein quality in these products: 1) the products may contain antinutritional factors, such as trypsin inhibitors or tannins that limit protein digestion [START_REF] Gilani | Impact of Antinutritional Factors in Food Proteins on the Digestibility of Protein and the Bioavailability of Amino Acids and on Protein Quality[END_REF], and 2) the products may lack certain indispensable amino acids (IAA). Assessing the nutritional quality of the protein in plant-based products remains a significant challenge, complicating efforts to design innovative foods that will respond to the growing demand for protein.

The Food and Agriculture Organisation (FAO) has defined an index for assessing nutritional protein quality that integrates the notion of amino acid bioavailability, namely the digestible indispensable amino acid score (DIAAS) (FAO, 2013). The DIAAS compares the digestibility of individual amino acids at the end of the small intestine (i.e., true ileal digestibility, which is a better proxy for bioavailability than whole-tract digestibility) to a standard of reference. Protein digestibility has largely been studied using protein isolates: the true ileal digestibility of soya, wheat, and pea proteins has been reported to be 91.5% [START_REF] Gaudichon | Ileal Losses of Nitrogen and Amino Acids in Humans and Their Improtance to the Assessment of Amino Acid Requirements[END_REF][START_REF] Bos | Human Nutrition and Metabolism Postprandial Kinetics of Dietary Amino Acids Are the Main Determinant of Their Metabolism after Soy or Milk Protein Ingestion in Humans[END_REF], 93.4% [START_REF] De Vrese | Protein-Bound D -Amino Acids , and to a Lesser Extent Lysinoalanine, Decrease True Ileal Protein Digestibility in Minipigs as Determined with 15Nlabeling[END_REF], and 89.4-91.5% [START_REF] Gausserès | The gastro-ileal digestion of 15N-labelled pea nitrogen in adult humans[END_REF](Gausserès et al., , 1997;;[START_REF] Mariotti | The Influence of the Albumin Fraction on the Bioavailability and Postprandial Utilization of Pea Protein Given Selectively to Humans[END_REF], respectively. However, little is known about the digestibility of these proteins when they are in foods that are traditionally consumed by humans, such as tofu and seitan. However, it is now well known that the food matrix and its transformation during processing affects the digestibility and use of the nutrients [START_REF] Thorning | Whole dairy matrix or single nutrients in assessment of health effects: current evidence and knowledge gaps[END_REF]. Heat treatments, for instance, may inactivate antitrypsin factors in foods, thus increasing protein digestibility, as illustrated by autoclaved and non-autoclaved soybean flour [START_REF] Li | Response of Nutrient Digestibilities to Feeding Diets with Low and High Levels of Soybean Trypsin Inhibitors in Growing Pigs[END_REF]. But these treatments may also impact protein structure [START_REF] German | Thermal Dissociation and Association Behavior of Soy Proteins[END_REF] and food structure [START_REF] Le Feunteun | Impact of the Dairy Matrix Structure on Milk Protein Digestion Kinetics: Mechanistic Modelling Based on Mini-pig In Vivo Data[END_REF], which influence such factors as enzyme diffusion, substrate accessibility and, subsequently, protein digestibility.

It is thus crucial to estimate the digestibility of proteins in foods as they are actually consumed.

We hypothesized that protein digestibility in commonly consumed plant-based food could be different that observed in protein isolates, because of the manufacturing processes involved (heat treatment, coagulation), as previously observed for animal products [START_REF] Bax | Cooking temperature is a key determinant of in vitro meat protein digestion rate: Investigation of underlying mechanisms[END_REF] [START_REF] Barbé | The heat treatment and the gelation are strong determinants of the kinetics of milk proteins digestion and of the peripheral availability of amino acids[END_REF].

The aim of this study was to determine the nutritional quality of protein in four plant-based foods (seitan, tofu, soya milk, and a pea emulsion) that differed in their structure (gel vs. liquid) and protein source (wheat, soya and pea). Seitan and tofu were chosen because of the growing interest of French consumers towards these plant-based protein foods. Protein digestibility of the tested foods was evaluated in minipigs, and the DIAAS was calculated.

Materials and methods

Animal handling and surgery

All the procedures were carried out in accordance with European guidelines (Directive 2010/63/EU) and approved by the Auvergne Animal Experimentation Ethics Committee (CEMEAA) and the French government (APAFIS#11001-2017082312525562v2). For the experiment, we used six adult Yucatan miniature pigs (mean mass at 8 months = 20.2 ± 1.5 kg).

Three weeks before the experiment began, the pigs were surgically fitted with two permanent catheters, which were placed in the hepatic portal vein and the upper hepatic vein. They were also fitted with a T-cannula (made of silicone rubber; ID: 12 mm, OD: 17 mm) placed 10 cm upstream from the ileocaecal valve.

To differentiate endogenous and dietary proteins, the pigs were given a continuous perfusion of 13 C-leucine solution through the upper hepatic vein catheter [START_REF] Hess | Comparison of the isotope dilution method for determination of the ileal endogenous amino acid losses with labelled diet and labelled pigs[END_REF] for five days before the experiment. They received a loading dose of 1 mg.kg -1 and then a continuous dose of 1 mg.kg -1 .j -1 at a rate of 1.5 ml.h -1 . Prior to initiating the perfusion, a blood sample was taken to determine the basal level of 13 C-leucine enrichment.

The pigs were housed in individual pens in a ventilated room kept at a constant temperature (21°C). Between the experimental trials, the pigs were given 500 g/d of a concentrate containing 16% protein, 1% fat, 4% cellulose, and 5% ash (Porcyprima; Sanders Centre Auvergne, France) distributed in equal portions at 8.00 and 16.00. The pigs had ad libitum access to water.

Test meals

We tested two solid and two liquid foods: seitan (wheat-based protein), tofu (soya-based protein), soya milk (soya-based protein), and a pea emulsion (pea-based protein; a soybean oilin-water emulsion containing a pea isolate). The seitan, tofu, and soya milk were of commercial origin. The seitan and tofu were ground (the final median particle sizes were 5.1 ± 0.1 mm for the tofu and 3.5 ± 0.1 mm for the seitan (n = 4 trials)) and then freeze dried. The soya milk had undergone ultra-high temperature (UHT) processing. We created the emulsion using a commercial pea isolate (Pisane M9, Lot: N16231O04, Cosucra, Belgium) and commercial soybean oil (Emile Noël, France). A pre-emulsion was generated using a homogeniser (T-50 Ultra-Turrax, IKA, Germany) equipped with a 15 G dispersing tool (IKA, Germany) run at 10,000 rpm for 1 min. This pre-emulsion was then homogenised twice using a bench-top homogeniser (PandaPLUS 2000, GEA, USA) run at 1,000 bar. We added maltodextrine, sugar, and soybean oil to all the foods to ensure they had equal levels of protein (30.0 g), fat (23.1 g), and calories (980 kcal), in each test-meal (Table S1, supplementary information 1). The testmeals containing seitan, tofu, soya milk, and pea emulsion weighed 290 g, 435 g, 1,162 g, and 1,175 g, respectively. To estimate the basal flows of endogenous amino acids in the ileum, pigs were also given a protein-free test-meal, in which the protein source was replaced by 30 g of a mixture of free amino acids (in proportions resembling those found in meat), assumed to be completely absorbed from the small intestine. An indigestible transit marker, chromium oxide (Cr2O3), was added (0.3% of the food's dry matter content). The characteristics of the different foods tested are described in Erreur ! Source du renvoi introuvable..

Sampling and chemical analysis

Each pig was given each of the food types in a randomly determined order. Experimental trials were separated by at least two days. During each trial, the pigs had ad libitum access to water. All food types were ingested in less than 15 min.

Portal-vein blood samples

Blood samples (3 ml) were taken from the portal vein before food ingestion and 60, 210, and 360 min after ingestion. The samples were immediately centrifuged (1,500 G, 10 min, 4°C).

The plasma was removed, frozen in liquid nitrogen, and stored at -80°C. Deproteinisation was carried out using trichloroacetic acid precipitation. The supernatant was purified using cation exchange chromatography and free amino acids were then converted into their N-acetyl-propyl derivatives. It was then possible to measure the 13 C-enrichment of free leucine in the plasma ( 13 C-Leuplasma pv) using gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS; IsoPrime, GV Instruments).

Ileal effluent samples

Between 60 min and 540 min post meal ingestion, ileal effluent was collected continuously in plastic bags (Sachet Whirl-Pak bags; volume: 120 ml, size: 7.5 x 18.5 cm) attached to the ileal cannula. The bags were regularly renewed based on bursts of digestion. The effluent samples were immediately transferred to pre-weighed aluminium dishes kept at -20°C. We created pools corresponding to 1 h of sampling, and stored them at -20°C.

The resulting samples were freeze dried (Cryotec AQ 1460). Dry matter (DM) content was determined after the samples were dried for an additional 24 h in a 60°C oven. The digesta were finely ground.

To estimate levels of chromium oxide (the indigestible transit marker), the samples were first subjected to a step of mineralisation (550°C, 6 h), followed by nitric acid dissolution (3 min of boiling in 5% HN03 -[w/w]) and filtration (Whatman filter paper: 4-7 µm). They were then analysed using microwave plasma-atomic emission spectrometry (4210 MP-AES, Agilent).

Next, we created a sample representative of the entire postprandial period for each animal for each food type. These samples contained a fixed percentage (based on DM) of each of the hourly effluent pools, starting from the first-time chromium oxide appeared.

Total nitrogen content (Ncontent) was determined using an elemental analyser (vario ISOTOPE cube, Elementar). To estimate the amino acid content of food and digesta, we first performed four separate standardised hydrolysis procedures [START_REF] Aoac | Official Methods of Analysis[END_REF]: sample placement in 6N HCl for 24 h at 110°C, sample placement in 6N HCl for 48 h at 110°C (for branchedchain amino acids), sample placement in 6N HCl for 24 h at 110°C after peroxidation with H2O2 (for sulphur-containing amino acids); and sample placement in 4N Ba(OH)2 for 16 h at 110°C (for tryptophan). A fraction of each hydrolysate was dried and then resuspended in a dilution buffer to which D-glucosaminic acid had been added as the injection standard. The levels of the various amino acids (AAcontent) were determined using ion exchange chromatography and ninhydrin post-column detection (L-8900 high-speed amino acid analyser, Hitachi).

The level of 13 C-leucine enrichment was measured for the hydrolysed samples using gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS; IsoPrime, GV Instruments), as described for the plasma samples.

Calculations

Flows are expressed as g of AA or N over the 9-h postprandial period. The digestibility of crude protein (CP = N x 6.25) is of no great relevance. Whereas the factor 6.25 used to convert N to CP in food is not perfect but close to reality [START_REF] Mariotti | Converting nitrogen into protein -Beyond 6.25 and Jones' factors[END_REF], it does not apply to ileal contents in which about 30% of N is in non-protein form (urea, ammonia, creatinine, etc.) [START_REF] Miner-Williams | Endogenous Components of Digesta Protein from the Terminal Ileum of Pigs Fed a Casein-Based Diet[END_REF]. The CP flows in the present study were indeed about twice as high as the total AA flows, illustrating the inconsistency of using the factor of 6.25 for evaluating protein content in ileal samples. Such discrepancies between CP ant total AA have been observed previously in pigs and minipigs [START_REF] Hennig | Relative ileal amino acid flows and microbial counts in intestinal effluents of Goettingen Minipigs and Saddleback pigs are not different[END_REF]. Thus, the digestibility calculations in this study were performed only for AAs, and the digestibility of proteins in the text refers to digestibility of total AAs.

Total flows of N and amino acids in the ileum

The flows of N and amino acids (AA) were determined using the chromium oxide data and the following equation: Xi = Xcontent × DM × Crintake/Crcontent, where X is N or an AA, DM is the total dry matter in the ileal sample, Xcontent is the amount of nitrogen or a specific amino acid in the ileal sample, and Crintake and Crcontent are the quantity of chromium oxide in the food type and ileal sample, respectively.

Flows of endogenous crude protein and amino acids in the ileum

The flow of endogenous leucine in the ileum (Leuendo) was calculated using the following equation: Leuendo = Leui x ( 13 C-Leucontent -13 C-Leufood)/( 13 C-Leuplasma pv -13 C-Leufood), where Leui is the quantity of leucine in the ileal sample and 13 C-Leucontent, 13 C-Leufood, and 13 C-Leuplasma pv are the levels of 13 C-leucine enrichment in the ileal sample, food type, and portal vein plasma, respectively.

The flows of other endogenous amino acids in the ileum (AAendo) were determined using the following equation: AAendo = Leuendo x ([AA]/[Leu])PFcontent, where ([AA]/[Leu])PFcontent is the ratio between the levels of a given AA and leucine in the ileal samples from the trial in which the pigs were fed the protein-free meal.

Ileal digestibilities of crude protein and amino acids

Apparent ileal digestibility of crude protein and amino acids

The apparent ileal digestibilities (AIDs) of nitrogen and the amino acids were expressed as percentages and determined with the equation AID(X) = 100 x ([Xmeal -Xi]/ Xmeal), where X is N or an AA.

Standardised ileal digestibility of crude protein and amino acids

Basal flows of endogenous nitrogen and amino acids (Xbasal endo) were defined as the flows of N and AAs in the ileum following the ingestion of the protein-free meal (PF).

The standardised ileal digestibilities (SID) of nitrogen and amino acids were expressed as percentages and determined with the equation: SID(AA) = 100 x (Xmeal -[Xi -Xbasal endo]/Xmeal), where X is N or an AA.

True ileal digestibility of amino acids

The true ileal digestibilities (TID) of amino acids were expressed as percentages and determined with the equation TID(AA) = 100 x (AAintake -[AAi -AAendo]/AAintake).

Data and statistical analysis

Data were analysed using an analysis of variance (ANOVA) using protein source and animal as fixed effects (GLM procedure of SAS®). Comparisons of the means were performed using Duncan's multiple range test at a 95% confidence level. The paired t-test was used for certain specific comparisons between tofu and soya milk. Data are presented as means ± SEM.

Results

Amino acid profiles of the foods

The amino acid profiles of the different foods tested are presented in Erreur ! Source du renvoi introuvable.. As expected, the legume-based foods-the tofu, pea emulsion, and soya milk-were relatively rich in lysine. Their lysine content accounted for 5.6 to 7.0 % of CP content. In contrast, for seitan, the cereal-based food, Lysine accounted for only 1.4 % of CP content. Conversely, seitan contained higher levels of sulphur-containing amino acids (SAAs) than did the other foods (3.8 vs 1.4 to 2.9 % of CP content, for the other foods). Compared with the reference amino acid profile for adults (FAO, 2013), seitan had lower than recommended levels of lysine and threonine, and pea emulsion had lower than recommended levels of SAAs. The soya-based foods (tofu and soya milk) had similar, well-balanced amino acid profiles; individual IAA content met or exceeded the reference amino acid profile.

Apparent ileal digestibility

Although we observed significant differences between the foods tested regarding the AIDs of some of the amino acids (Lys, Met, Asp/Asn, Cys, Glu/Gln) (Table 2), the AIDs for the total AAs were very similar (77-84%). The AID of lysine was lower for seitan (54%) than for the other food types (range: 83-87%). The AID of methionine (49%) was lower for the pea emulsion than for soya milk and seitan (90%), while tofu had an intermediate value (69%). The AID of cysteine was lower for tofu and pea emulsion (36 and 44%, respectively) than for seitan and soya milk (74 and 79%, respectively).

Standard ileal digestibility

The protein free test meal showed that the contribution of the basal endogenous flow to the total amino acid flow at the ileum averaged 3.7 ± 1.0 g over the postprandial period studied.

The amino acid pattern of this endogenous flow is given in Table S2 (supplementary information 2). Standard ileal digestibility (SID; Table 3) takes into account this basal endogenous flow. It is the value of ileal digestibility most often reported in the literature. The SIDs of the total AAs were 91, 92, 89, and 87% for the seitan, pea emulsion, soya milk, and tofu, respectively.

True ileal digestibility

Based on leucine enrichments, the contribution of endogenous protein secretions to total protein flow at the ileum was about 2/3 for seitan, pea emulsion and tofu, but it was only 1/2 for soya milk (Table 4). Although numerically greater for the solids than for the liquids, endogenous leucine flow was not significantly different between the 4 foods tested. The use of 13 C-leucine enrichments allowed taking into account not only basal endogenous flow, but also endogenous losses specific to the food tested. Thus, whereas basal endogenous leucine flow was estimated to be 0.23 ± 0.06 g, total endogenous leucine flows were 0.37 ± 0.11, 0.48 ± 0.09, 0.31 ± 0.03, and 0.26 ± 0.06 for seitan, tofu, soya milk and pea emulsion respectively.

The difference of specific endogenous leucine flow between tofu and soya milk was particularly noteworthy (0.25 ± 0.09 vs 0.08 ± 0.03, respectively, P = 0.05). In our calculations the basal and total endogenous flows of the other AA relied on the same profile of endogenous AA (that observed with the PF meal), as the same differences were observed for them.

True ileal digestibility (TID; Table 4) takes into account total endogenous flows (basal + specific). The TID of the total AAs were very high, and did not differ significantly between the foods tested (92-97%). The TIDs for all the individual amino acids were also very high.

Although the soya milk and the tofu had the same protein source, they displayed small differences in the TIDs of their amino acids: the TID of methionine was lower for tofu, and, conversely, the TID of leucine and isoleucine was lower for soya milk.

Nutritional protein quality of the foods

The digestible indispensable amino acid content of the food is presented in Table 5. DIAAS (FAO and WHO, 1991;FAO, 2013) of the four foods tested was calculated for the three age groups (< 6 months; 6 months to 36 months; older child, adolescent, and adult) (Table 6). The digestible amino acids that were limiting did not differ between score types or age groups, except for the soya milk, for which leucine was the limiting amino acid for newborns, whereas it was lysine for children below 3 years old, and valine above 3 years old.

Discussion

TID is considered as the best predictor of the bioavailability of dietary protein amino acids.

However, it is difficult to measure. In this study, we used a miniature pig model as an animal model for humans, pig being considered as the animal model best adapted for the study of digestion in the upper part of the gut (stomach + small intestine) [START_REF] Rowan | Comparison of the ileal and faecal digestibility of dietary amino acids in adult humans and evaluation of the pig as a model animal for digestion studies in man[END_REF]. We used the approach of a single test meal in animals otherwise receiving a standard diet. This means that the animals were not subjected to a period of continuous adaptation to the meal being tested.

They were exposed to the meals just once before the TID measurement (at least one week before), to check the palatability of the meals. The TID obtained with this standardized approach reflects more what happens in humans, who are characterized by the diversity of their diet. Indeed, it does not exacerbate the potential negative effect of chronic exposure to the potential presence of antinutritional factors, such as lectins that may significantly affect endogenous secretions and gut health [START_REF] Vasconcelos | Antinutritional properties of plant lectins[END_REF].

For the TID measurement, it is necessary to distinguish between residual dietary proteins and endogenous proteins within the chyme collected at the end of the small intestine. Since targeted foods with isotopic intrinsic labelling of proteins were not at our disposal, we opted for the 13 C-leucine labelling of endogenous proteins. This method is less subject to the biases associated with rapid amino acid recycling than is the labelled dietary protein method. However, it does not allow the direct measurement of the endogenous flow of each amino acid, in contrast with the use of labelled proteins [START_REF] Hess | Comparison of the isotope dilution method for determination of the ileal endogenous amino acid losses with labelled diet and labelled pigs[END_REF]. In the present study, the endogenous flow of leucine was extrapolated to the other amino acids, using the amino acid pattern of the ileal chyme collected after a protein free meal (thus containing only endogenous secretion). Endogenous secretions can be separated into basal secretions (those observed with the protein free meal) and the specific endogenous losses in response to the food tested. For the TID calculation in the present study, we postulated a similar pattern of amino acids between basal and specific endogenous secretions. This is an approximation; in fact, the amino acid composition of the specific losses can slightly differ from that of the basal secretions. For instance, some foods containing polyphenols can specifically increase salivary proline-rich proteins (PRP) secretion [START_REF] Jansman | Production of proline-rich proteins by the parotid glands of rats is enhanced by feeding diets containing tannins from faba beans (Vicia faba L.)[END_REF], which are low in indispensable amino acids and hardly digested by digestive enzymes. In addition, some peptides released during digestion can specifically increase mucin secretions (threonine-rich proteins) [START_REF] Plaisancié | A novel bioactive peptide from yoghurts modulates expression of the gel-forming MUC2 mucin as well as population of goblet cells and Paneth cells along the small intestine ☆[END_REF].

There were no data in the literature on the digestibility of plant-based protein foods.

Common understanding is that proteins in plant food feature lower digestibility than that in animal products, but evidence is lacking to support this for protein-rich plant foods that are commercially available. Indeed, most digestibility measurements have been performed on plant protein isolates, or raw materials. This study is the first to characterise the true ileal digestibility (TID) of proteins in seitan, tofu, and soya milk; foods commonly consumed by humans. We found that their TIDs were high: 98, 95, and 92%, respectively. Although slightly higher, these values are consistent with those seen for wheat protein isolates (93%) [START_REF] De Vrese | Protein-Bound D -Amino Acids , and to a Lesser Extent Lysinoalanine, Decrease True Ileal Protein Digestibility in Minipigs as Determined with 15Nlabeling[END_REF] and soybean protein isolates (91.5-96%) [START_REF] Bos | Human Nutrition and Metabolism Postprandial Kinetics of Dietary Amino Acids Are the Main Determinant of Their Metabolism after Soy or Milk Protein Ingestion in Humans[END_REF][START_REF] Rutherfurd | Protein Digestibility-Corrected Amino Acid Scores and Digestible Indispensable Amino Acid Scores Differentially Describe Protein Quality in Growing Male Rats[END_REF]. The TID of the protein in pea emulsion (94%) resembled the TIDs previously observed for pea isolates (90-98%) [START_REF] Mariotti | The Influence of the Albumin Fraction on the Bioavailability and Postprandial Utilization of Pea Protein Given Selectively to Humans[END_REF][START_REF] Rutherfurd | Protein Digestibility-Corrected Amino Acid Scores and Digestible Indispensable Amino Acid Scores Differentially Describe Protein Quality in Growing Male Rats[END_REF]. Furthermore, the TIDs of the protein of the plant food we tested are comparable to those of animal proteins: 91-98% for meat [START_REF] Oberli | High true ileal digestibility but not postprandial utilization of nitrogen from bovine meat protein in humans is moderately decreased by high-temperature, long-duration cooking[END_REF][START_REF] Hodgkinson | Cooking Conditions Affect the True Ileal Digestible Amino Acid Content and Digestible Indispensable Amino Acid Score (DIAAS) of Bovine Meat as Determined in Pigs[END_REF][START_REF] Kashyap | Ileal digestibility of intrinsically labeled hen's egg and meat protein determined with the dual stable isotope tracer method in Indian adults[END_REF] and 94-95% for milk [START_REF] Bos | Assessment of net postprandial protein utilization of 15N-labelled milk nitrogen in human subjects[END_REF][START_REF] Rutherfurd | Protein Digestibility-Corrected Amino Acid Scores and Digestible Indispensable Amino Acid Scores Differentially Describe Protein Quality in Growing Male Rats[END_REF].

Whatever the structure of the food, solid or liquid, the endogenous secretions were only slightly affected and the protein digestibility remained high. The differences between soy milk and tofu were however especially noteworthy, because they clearly illustrated the so-called matrix effect [START_REF] Thorning | Whole dairy matrix or single nutrients in assessment of health effects: current evidence and knowledge gaps[END_REF]: different digestion of food products deriving from the same raw material. Indeed, based on leucine flows, it can be estimated that the coagulation process of soya milk in tofu production leads to an increase in specific endogenous losses. In a previous study with the same soya milk and tofu [START_REF] Reynaud | Temporal changes in postprandial intragastric pH: comparing measurement methods, food structure effects, and kinetic modelling[END_REF], we observed a very different evolution of gastric pH over the postprandial period. Apart from the potential difference in gastric emptying due to difference in nutrient solubility of the two protein sources [START_REF] Schop | Increasing intake of dietary soluble nutrients affects digesta passage rate in the stomach of growing pigs[END_REF] or to the difference in test-meal volume, this difference may have an impact on the gastric pre-digestion of soya proteins and modify the nature of the peptides released during intestinal digestion, which in turn could affect endogenous ileal losses [START_REF] Hodgkinson | The effect of dietary peptide concentration on endogenous ileal amino acid loss in the growing pig[END_REF]. On the other hand, tofu making slightly increased branched chain amino acids and nearly all amino acids, whereas it decreased the digestibility of sulphur-containing amino acids.

Whereas the heat treatment applied during tofu making (70-85°C) may have decreased antiprotease activity and increased protein digestibility, the coagulation process could explain the negative effect on sulphur-containing amino acids. Indeed, it seems that sulphur-containing amino acids mainly occur inside the molecular aggregates of the gels and are surrounded by hydrophilic subunits [START_REF] Peng | Particle formation and gelation of soymilk: Effect of heat[END_REF], which could make them less accessible to digestive enzymes, and explain their lower digestibility.

Seitan had the lowest nutritional protein quality (DIAAS range: 20-31%) due to its low lysine content. This result concurs with what has been seen for wheat protein in bread (DIAAS: 20%) [START_REF] Han | Digestible indispensable amino acid scores of nine cooked cereal grains[END_REF]. Lysine has also been found to be a limiting amino acid in whole-grain wheat, but the DIAASs calculated for whole-grain wheat are generally higher (30-60%) [START_REF] Cervantes-Pahm | Digestible indispensable amino acid score and digestible amino acids in eight cereal grains[END_REF][START_REF] Mathai | Values for digestible indispensable amino acid scores (DIAAS) for some dairy and plant proteins may better describe protein quality than values calculated using the concept for protein digestibility-corrected amino acid scores (PDCAAS)[END_REF]. This difference may be attributable to seitan's lower lysine levels-they were only half the lysine levels of whole-grain wheat. The DIAASs of the pea emulsion were intermediate (42-64%), and SAAs were limiting across all age groups. These values are consistent with those observed for a pea isolate (45-84%) [START_REF] Mathai | Values for digestible indispensable amino acid scores (DIAAS) for some dairy and plant proteins may better describe protein quality than values calculated using the concept for protein digestibility-corrected amino acid scores (PDCAAS)[END_REF].

Because the seitan and the pea emulsion were almost completely digested, the nutritional protein quality of these two food types is essentially defined by their amino acid profiles, which were unbalanced. In contrast, the tofu and soya milk had similar, well-balanced profiles. Thus, the differences in the nutritional quality of their proteins is essentially determined by the digestibility of their amino acids. Indeed, because soya milk has a well-balanced amino acid composition, with high digestibility, its DIAAS is high (78% to 116%), and the limiting amino acid evolves according to the age-related reference profile, whereas for tofu, the reduced digestibility of the sulphur-containing amino acids makes them limiting, whatever the reference profile, and leads to a 15% decrease in DIAAS values in comparison to soya milk. Whatever the case, in agreement with the results previously reported for soya isolates [START_REF] Mathai | Values for digestible indispensable amino acid scores (DIAAS) for some dairy and plant proteins may better describe protein quality than values calculated using the concept for protein digestibility-corrected amino acid scores (PDCAAS)[END_REF] [START_REF] Rutherfurd | Protein Digestibility-Corrected Amino Acid Scores and Digestible Indispensable Amino Acid Scores Differentially Describe Protein Quality in Growing Male Rats[END_REF], the DIAAS of soya milk and tofu proteins, for the adult population, are close to those reported for milk and meat [START_REF] Mathai | Values for digestible indispensable amino acid scores (DIAAS) for some dairy and plant proteins may better describe protein quality than values calculated using the concept for protein digestibility-corrected amino acid scores (PDCAAS)[END_REF] [START_REF] Hodgkinson | Cooking Conditions Affect the True Ileal Digestible Amino Acid Content and Digestible Indispensable Amino Acid Score (DIAAS) of Bovine Meat as Determined in Pigs[END_REF], indicating the good nutritional quality of the proteins of these products.

Conclusions

The four plant-based protein food studied here-seitan, pea emulsion, soya milk, and tofu-displayed similar, high values of true ileal digestibility of amino acids. For the tofu and soya milk (both soya-based foods), the difference in nutritional protein quality was primarily driven by differences in AA digestibility, because the foods' AA profiles were well balanced.

For the seitan and the pea emulsion, the lower nutritional protein quality was essentially explained by the degree of amino acid imbalance and the amounts of limiting amino acids relative to standard profiles.

b

  Percent of leucine of endogenous origin in leucine flowing at the ileum c Endogenous leucine flowing at the ileum relative to ingested leucine

Table 1

 1 Dry matter (DM), crude protein (CP), and amino acid (AA) contents in seitan, tofu, soya milk and pea emulsion.

	Seitan	Tofu	Soya milk	Pea emulsion

Table 2

 2 Apparent ileal digestibility (AID) of amino acids in seitan, tofu, soya milk and pea emulsion in minipigs. Values are means ± SEM, n = 6. a

		Seitan	Tofu	Soya milk	Pea emulsion	P
	N, %	74.1 ± 4.6	56.5 ± 6.4	71.3 ± 2.5	68.0 ± 3.5	NS
	Indispensable amino acids, %
	Histidine	82.1 ± 4.7	81.3 ± 2.9	82.7 ± 3.7	81.8 ± 2.5	NS
	Isoleucine	83.6 ± 3.4	81.0 ± 2.4	81.0 ± 3.4	84.7 ± 2.0	NS
	Leucine	84.7 ± 3.2	80.4 ± 3.0	79.3 ± 3.1	84.8 ± 2.0	NS
	Lysine	54.3 b ± 8.9	83.0 a ± 3.1	84.8 a ± 2.9	86.6 a ± 2.0 0.001
	Methionine	90.1 a ± 1.9	69.4 c ± 5.6	89.7 a ± 2.8	49.3 b ± 10.2 0.001
	Phenylalanine	85.2 ± 3.0	81.1 ± 3.0	82.3 ± 2.9	84.7 ± 1.7	NS
	Threonine	49.8 ± 10.6	58.5 ± 6.4	67.9 ± 4.8	66.0 ± 3.7	NS
	Tryptophan	75.3 ± 8.5	77.4 ± 2.4	84.3 ± 2.4	83.6 ± 2.6	NS
	Valine	78.9 ± 4.3	75.4 ± 3.3	78.1 ± 3.5	80.3 ± 3.2	NS
	Dispensable amino acids, %
	Arginine	55.7 ± 9.4	61.9 ± 6.0	67.1 ± 8.2	75.4 ± 3.0	NS
	Alanine	69.6 ± 6.9	72.4 ± 4.6	74.6 ± 3.8	79.1 ± 2.6	NS
	Aspartic acid/Asparagine	55.1 b ± 9.9	78.0 a ± 3.8	80.1 a ± 3.9	75.7 a ± 3.2 0.024
	Cysteine	74.1 a ± 3.9	35.8 b ± 10.2	78.5 a ± 3.8	44.4 b ± 11.3 0.004
	Glutamic acid/Glutamine	94.9 a ± 1.0	86.6 b ± 2.0	85.8 b ± 3.6	84.3 b ± 2.5 0.019
	Glycine	45.0 ± 9.7	52.6 ± 5.5	68.5 ± 5.2	56.9 ± 6.5	NS
	Proline	89.6 ± 3.2	79.7 ± 4.4	81.9 ± 4.0	82.7 ± 2.8	NS
	Serine	80.4 ± 3.9	74.1 ± 4.4	77.6 ± 3.6	78.8 ± 2.4	NS
	Tyrosine	79.4 ± 4.9	76.1 ± 3.8	79.0 ± 3.6	86.0 ± 3.1	NS
	Total Amino Acids	83.7 ± 3.4	77.1 ± 3.3	80.2 ± 3.6	79.9 ± 2.5	NS
	a Different uppercase letter in the same line show significant differences (P < 0.05) among the different
	food types for nireogen (N) and amino acids.

Table 3

 3 Standard ileal digestibility (SID) of amino acids in seitan, tofu, soya milk and pea emulsion in minipigs. Values are means ± SEM, n = 6. a

		Seitan	Tofu	Soya milk	Pea emulsion	P
	N x 6.25, %	94.0 ± 4.6	76.0 ± 6.4	92.2 ± 2.5	97.4 ± 3.5	NS
	Indispensable amino acids, %
	Histidine	90.1 ± 4.7	87.9 ± 2.9	89.5 ± 3.7	90.2 ± 2.5	NS
	Isoleucine	91.2 ± 3.4	86.6 ± 2.4	86.9 ± 3.4	93.1 ± 2.0	NS
	Leucine	91.9 ± 3.2	86.6 ± 3.0	86.0 ± 3.1	93.2 ± 2.0	NS
	Lysine	76.4 ± 8.9	88.2 ± 3.1	90.5 ± 2.9	93.0 ± 2.0	NS
	Methionine	94.0 a ± 1.9	75.7 b ± 5.5	95.5 ± 2.8 a	71.3 b ± 10.2 0.013
	Phenylalanine	93.8 ± 3.0	89.0 ± 3.0	91.0 ± 2.9	95.8 ± 1.7	NS
	Threonine	74.7 ± 10.6	73.5 ± 6.4	83.1 ± 4.8	86.9 ± 3.7	NS
	Tryptophan	87.3 ± 8.5	91.3 ± 2.4	97.5 ± 2.4	99.7 ± 2.6	NS
	Valine	89.7 ± 4.3	83.8 ± 3.3	87.0 ± 3.5	92.5 ± 3.2	NS
	Dispensable amino acids, %
	Arginine	80.9 ± 9.4	76.1 ± 6.0	80.2 ± 8.2	92.5 ± 3.0	NS
	Alanine	85.7 ± 6.9	82.7 ± 4.6	86.0 ± 3.8	93.5 ± 2.6	NS
	Aspartic acid/Asparagine	78.3 ± 9.9	84.3 ± 3.8	86.7 ± 3.9	84.5 ± 3.2	NS
	Cysteine	92.1 a ± 3.9	62.8 b ± 10.2 101.2 a ± 3.8 101.9 a ± 11.3 0.011
	Glutamic acid/Glutamine	97.8 ± 1.0	92.0 ± 2.0	91.6 ± 3.6	93.5 ± 2.5	0.019
	Glycine	74.8 ± 9.7	75.0 ± 5.5	92.6 ± 5.2	90.5 ± 6.5	NS
	Proline	94.2 ± 3.2	89.5 ± 4.4	91.7 ± 4.0	97.8 ± 2.8	NS
	Serine	91.4 ± 3.9	83.7 ± 4.4	88.0 ± 3.6	92.5 ± 2.4	NS
	Tyrosine	88.5 ± 4.9	83.6 ± 3.8	87.0 ± 3.6	95.9 ± 3.1	NS
	Total Amino Acids	92.3 ± 3.4	86.0 ± 3.3	89.3 ± 3.6	92.6 ± 2.5	NS
	a Different uppercase letter in the same line show significant differences (P < 0.05) among the different
	food types for protein (N x 6.25) and amino acids.

Table 4

 4 True ileal digestibility (TID) of amino acids in seitan, tofu, soya milk and pea emulsion in minipigs. Values are means ± SEM, n = 6. a Different uppercase letter in the same line show significant differences (P < 0.05) among the different food types for amino acids.

		Seitan	Tofu	Soya milk	Pea emulsion	P
	Leuendo/Leutotal ileum (%) b	71.6 a ± 7.7	67.0 a ± 7.0	46.1 c ± 4.8	62.4 a,b ± 5.3 0.025
	Leuendo/Leuintake (%) c	11.7 ± 3.4	12.8 ± 2.0	9.0 ± 0.8	9.7 ± 1.8	NS
	TID, %
	Indispensable amino acids, %
	Histidine	95.6 ± 1.1	95.7 ± 2.1	92.2 ± 3.2	91.8 ± 1.2	NS
	Isoleucine	96.1 a ± 1.3	92.9 a,b ± 1.7	89.1 b ± 2.9	94.6 a ± 1.0	0.035
	Leucine	96.4 a ± 1.0	93.3 a ± 1.9	88.3 b ± 2.6	94.5 a ± 0.9	0.009
	Lysine	90.1 ± 5.3	93.9 ± 2.1	92.5 ± 2.4	93.9 ± 1.2	NS
	Methionine	97.8 a ± 1.1	85.6 b ± 6.0	99.3 a ± 2.5	80.3 b ± 7.7	0.034
	Phenylalanine	99.9 ± 2.0	98.6 ± 2.2	94.7 ± 2.3	98.3 ± 1.3	NS
	Threonine	94.1 ± 5.3	93.0 ± 4.5	90.6 ± 3.9	92.4 ± 2.7	NS
	Tryptophan	92.2 ± 4.6	102.6 ± 2.4	99.8 ± 2.1	99.6 ± 3.5	NS
	Valine	96.8 ± 1.9	93.3 ± 2.2	90.4 ± 2.9	94.8 ± 1.4	NS
	Dispensable amino acids, %
	Arginine	94.7 ± 4.8	90.4 ± 4.3	84.0 ± 7.1	94.2 ± 1.5	NS
	Alanine	96.7 ± 3.1	94.7 ± 3.2	90.6 ± 3.1	96.3 ± 1.3	NS
	Aspartic acid/Asparagine	92.3 ± 3.4	91.0 ± 2.9	88.9 ± 3.5	85.7 ± 2.0	NS
	Cysteine	99.0 ± 5.6	83.8 ± 11.7	104.6 ± 4.2	100.8 ± 9.9 NS
	Glutamic acid/Glutamine	99.6 ± 0.6	97.7 ± 1.5	93.4 ± 3.2	94.8 ± 1.0	NS
	Glycine	87.9 ± 10.2	94.3 ± 4.6	97.4 ± 4.3	91.3 ± 7.1	NS
	Proline	98.2 ± 1.1	103.2 ± 3.4	97.1 ± 3.2	102.7 ± 3.0 NS
	Serine	99.8 ± 2.5	95.9 ± 3.4	92.8 ± 3.0	96.0 ± 1.6	NS
	Tyrosine	94.4 ± 1.5	92.0 ± 2.8	90.1 ± 3.0	97.7 ± 2.5	NS
	Total Amino Acids	97.5 ± 1.5	95.0 ± 2.3	92.3 ± 3.0	94.2 ± 1.3	NS

a

Table 5

 5 Digestible indispensable amino acids (g/ 100 AA) in seitan, tofu, soya milk and pea emulsion in minipigs. Values are means ± SEM, n = 6. a

		Seitan	Tofu	Soya milk	Pea emulsion	P
	Histidine	1.34 c ± 0.03	5.91 b ± 0.06 5.65 b ± 0.10 7.10 a ± 0.04 0.001
	Isoleucine	3.79 b ± 0.05	4.94 a ± 0.09 4.74 a ± 0.16 4.85 a ± 0.05 0.001
	Leucine	7.15 c ± 0.07	8.13 b ± 0.17 7.46 c ± 0.22 8.74 a ± 0.08 0.001
	Lysine	1.34 c ± 0.08	5.91 b ± 0.13 5.65 b ± 0.15 7.10 a ± 0.09 0.001
	Methionine	2.00 a ± 0.02	1.07 c ± 0.07 1.42 b ± 0.04 0.42 d ± 0.04 0.001
	Cysteine	2.08 a ± 0.12	1.17 b ± 0.16 1.82 a ± 0.07 0.96 b ± 0.09 0.001
	Phenylalanine	5.37 b ± 0.11	5.76 a ± 0.13 5.30 b ± 0.13 5.95 a ± 0.08 0.001
	Tyrosine	2.40 c ± 0.04	2.84 b ± 0.09 2.70 b ± 0.09 3.30 a ± 0.08 0.001
	Threonine	2.27 b ± 0.13	3.71 a ± 0.18 3.73 a ± 0.16 3.86 a ± 0.11 0.001
	Tryptophan	2.73 b ± 0.13	2.63 b ± 0.06 2.82 b ± 0.06 3.23 a ± 0.11 0.002
	Valine	3.95 b ± 0.08	4.90 a ± 0.12 4.70 a ± 0.15 4.95 a ± 0.07 0.001

a Different uppercase letter in the same line show significant differences (P < 0.05) among the different food types for amino acids.

Table 6

 6 Digestible indispensable amino acid scores (DIAAS, %), and limiting amino acid for seitan, tofu, soya milk and pea emulsion.Scores were calculated using the recommended amino acid scoring patterns for three age groups(FAO, 2013).

	Seitan	Tofu	Soya milk	Pea emulsion

Table S2 N

 S2 and amino acids ileal flows observed in minipigs (n = 6) receiving a protein-free diet. Values are means ± SEM.

		Ileal flow, g
	N (Dumas method)	1.82 ± 0.51
	Indispensable amino acids
	Histidine	0.09 ± 0.02
	Isoleucine	0.13 ± 0.04
	Leucine	0.24 ± 0.06
	Lysine	0.14 ± 0.04
	Methionine	0.04 ± 0.01
	Phenylalanine	0.22 ± 0.06
	Threonine	0.29 ± 0.09
	Tryptophan	0.14 ±0.04
	Valine	0.20 ± 0.05
	Dispensable amino acids
	Arginine	0.14 ± 0.04
	Alanine	0.38 ± 0.10
	Aspartic acid/Asparagine	0.31 ± 0.09
	Cysteine	0.14 ± 0.04
	Glutamic acid/Glutamine	0.45 ± 0.12
	Glycine	0.38 ± 0.10
	Proline	0.30 ± 0.08
	Serine	0.23 ± 0.06
	Tyrosine	0.10 ± 0.03
	Total amino acids	3.72 ± 1.01

Acknowledgements

We would like to thank Julien Hermet, the head of the animal care department, and Philippe Lhoste and Yohan Delorme, both animal care workers. We are also grateful to Jessica Pearce for correcting the English of the manuscript and to Denys Durand for the help he provided in performing the surgery with Didier Rémond.

The project was funded by IMPROVE SAS and INRAE. A PhD grant was funded by IMPROVE SAS through a CIFRE procedure (CIFRE n°2016/0719) Role of the funding source: IMPROVE SAS provided foods and INRAE performed the experimental work.

Author Contributions

DR designed the study. CB, BC, MV, YR, and DR performed the experiments, and NH conducted the amino acid dosages. DR, CB, and YR analysed the data. DR and YR drafted the manuscript, and all the authors helped revise it.